integrated hydrological modeling of surface - groundwater ... · integrated hydrological modeling...

INTEGRATED HYDROLOGICAL

MODELING OF SURFACE -

GROUNDWATER INTERACTIONS

The case of Denpasar-Tabanan Basin in the

Southern Bali Island

Abenet Tadesse Teketel

March, 2017

SUPERVISORS:

Dr. Maciek W. Lubczynski

Dr. Zoltan Vekerdy

INTEGRATED HYDROLOGICAL

MODELING OF SURFACE -

GROUNDWATER INTERACTIONS

The case of Denpasar-Tabanan Basin in the

Southern Bali Island

Abenet Tadesse Teketel

Enschede, The Netherlands, March, 2017

Thesis submitted to the Faculty of Geo-Information Science and Earth Observation

of the University of Twente in partial fulfilment of the requirements for the degree of

Master of Science in Geo-Information Science and Earth Observation.

Specialization: Water Resource and Environment Management

SUPERVISORS:

Dr. Maciek W. Lubczynski

Dr. Zoltan Vekerdy

THESIS ASSESSMENT BOARD:

Dr. Ir. Christiaan van der Tol

Dr. W. van Verseveld (External Examiner, Deltares, The Netherlands)

DISCLAIMER

This document describes work undertaken as part of a programme of study at the Faculty of Geo-Information Science and

Earth Observation of the University of Twente. All views and opinions expressed therein remain the sole responsibility of the

author, and do not necessarily represent those of the Faculty.

INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION

i

ABSTRACT

The Denpasar-Tabanan (D-T) Basin (2270 km2) located in the southern part of Bali Island, Indonesia, is a

densely populated area, also typical destination of international tourism. The basin is composed of

unconsolidated volcanic materials storing groundwater in an unconfined aquifer. That aquifer provides the

main water supply of the Bali Island although it often undergoes crises of water shortage. Therefore, it is

crucial to understand its complex dynamic of surface-groundwater (SW-GW) interactions and to evaluate

its groundwater resources to improve water management.

The dynamics of SW-GW- interaction was numerically simulated using three-dimensional steady-state and

transient models. For that purpose, MODFLOW-NWT with stream flow routing (SFR2) and unsaturated

zone flow (UZF1) packages were used. All data, including time series of rainfall, stream discharge, and

potential evapotranspiration for the four-year period from 1st January 2009 to 31st December 2012, were

simulated on a daily basis.

The steady-state model groundwater inflow consisted of: RUZF (95%) and qsg (5%). The groundwater outflow

consisted of: qgs (47.8%), ETss (23.4%), Exfgw (22.6%), and qg (6.1%) of total groundwater outflow. In the

transient model simulation, groundwater inflow consisted of Rg (75.4%), qsg and ∆Sgi were 3.3% and 21.3%

of total groundwater inflow respectively. Regarding transient model groundwater outflow, qgs (30.4%), Exfgw

(29.4%), ETg (14.1%) followed by ∆Sgout (18.9%) and qg (7.2%) of total groundwater outflow respectively. It

was observed that in the years analysed the net recharge was largely positive and that streams largely gain

groundwater, which reflects good groundwater potential of the D-T basin.

The calibrated transient model showed large spatiotemporal variability of groundwater fluxes. The Rg ranged

from 7.64 (January) to 2.30 mmday-1 (August) with the mean 3.36 mmday-1, Rn from 5.84 (January) to 0.26

mmday-1 (August) with the mean 1.34 mmday-1, ETg from 1.05 (February) to 0.65 mmday-1 (July), Exfgw from

1.48 (March) to 1.37 mmday-1 (December) and qgs from 1.48 (January) to 1.37 mmday-1 (August). The

temporal variability of fluxes was mainly due to seasonal variability of driving forces changing from dry to

wet season. The large spatial variability of groundwater fluxes was primarily due to large variety of land

covers and large spatial variability of rainfall.

Key Words: Surface-groundwater interactions, Bali, Volcanic aquifer, Water balance, MODFLOW-NWT

ii

ACKNOWLEDGEMENTS

The preparation and completion of this thesis work would not have been possible without the involvement

and contribution of kind persons around me. First, I thank the almighty God for the gift of life, good health

and for His guidance to this far. Many thanks to the Netherlands Fellowship Program (NFP) for the

generous financial support throughout my study period.

I would like to express my deep gratitude to my first supervisor, Dr. Maciek W. Lubczynski, for his

supervision, patience, words of encouragement, constructive ideas and invaluable remarks throughout this

research work. My deep gratitude also goes to my second supervisor Dr. Zoltan Vekerdy, for his supervision,

useful comments, remarks, and words of encouragement, throughout the thesis study. It would be so

difficult without their help. Sincere thanks to Dr. Tom H.M. Rientjes, Dr. ir. Suhyb Salama, and ir. Arno M.

van Lieshout for their valuable comments during the process of this research starting from thesis proposal.

You all patiently directed my wild imaginations to a worthwhile research item and ensured that I stayed

within the scope of the study by frequently correcting my work. Sincere thanks to Miss Novi Rahmawati

(Ph.D. candidate), who selflessly ensured I had all the necessary data, and for guiding me through the data

that are written in Balinese language. My thanks are extended to government of Indonesia especially to

Indonesian Agency for Meteorology, Climatology, and Geophysics Locally called DPPU; Biro of Geospatial

Information, “BIG”; and Ministry of Energy and Mineral Resources of Indonesia, “KLPU” for sharing the

meteorological and hydrological data for all station that are available in Bali Island.

Many thanks to the administrative and teaching staff of the ITC-WRM Program. It is here where I learned

most of my theoretical foundations in water resources management. To my fellow classmates, thank you

for the quality time spent together as one big ‘family’; in a way, you helped me in the completion of this

thesis. Last but not the least, my heartfelt gratitude to my family for their unconditional love, patience and

support to the seemingly endless journey. Special thanks to my dad and mom for this encouragement and

trust that forever keeps me strong. I am because you were. To my elder brother, my greatest source of

inspiration.


iii

TABLE OF CONTENTS

1. INTRODUCTION .............................................................................................................................................. 1

1.1. Background ...................................................................................................................................................................1 1.2. Problem statement ......................................................................................................................................................2 1.3. Research setting ...........................................................................................................................................................3

1.3.1. Research objectives ................................................................................................................................... 3

1.3.2. Research question ..................................................................................................................................... 3

1.3.3. Novelty of the study ................................................................................................................................. 3

1.3.4. Research hypothesis.................................................................................................................................. 3

1.3.5. Assumptions .............................................................................................................................................. 3

2. RESEARCH METHOD AND MATERIALS ............................................................................................... 4 2.1. Study area ......................................................................................................................................................................4

2.1.1. Location ...................................................................................................................................................... 4

2.1.2. Monitoring network .................................................................................................................................. 5

2.1.3. Climate ........................................................................................................................................................ 5

2.1.4. Topography and land cover .................................................................................................................... 6

2.1.5. Hydrology ................................................................................................................................................... 7

2.1.6. Hydrogeology ............................................................................................................................................ 8

2.1.7. Previous studies in the area ..................................................................................................................... 8

2.2. Data processing............................................................................................................................................................9

2.2.1. Watershed boundary .............................................................................................................................. 10

2.2.2. Precipitation ............................................................................................................................................ 10

2.2.3. Potential evapotranspiration ................................................................................................................ 12

2.2.4. Interception and infiltration rate ......................................................................................................... 13

2.2.5. Stream discharge .................................................................................................................................... 14

2.2.6. Hydraulic properties .............................................................................................................................. 15

2.2.7. Head observation ................................................................................................................................... 15

2.2.8. Groundwater abstraction ...................................................................................................................... 15

2.3. Modeling flow chart ................................................................................................................................................. 16 2.4. Conceptual model..................................................................................................................................................... 16

2.4.1. Defining Hydrostratigraphic units ...................................................................................................... 17

2.4.2. Defining the flow system ...................................................................................................................... 17

2.4.3. Defining preliminary water balance .................................................................................................... 18

2.4.4. Defining the boundaries of the model ............................................................................................... 18

2.5. Numerical model ...................................................................................................................................................... 18

2.5.1. Software selection .................................................................................................................................. 18

2.5.2. Aquifer geometry and grid design ....................................................................................................... 20

2.5.3. Driving forces ......................................................................................................................................... 20

2.5.4. State variables ......................................................................................................................................... 21

2.5.5. Parametric data ....................................................................................................................................... 21

2.5.6. Boundary conditions ............................................................................................................................. 22

2.6. Model calibration ...................................................................................................................................................... 24

2.6.1. Steady-state model calibration ............................................................................................................. 24

2.6.2. Warming-up period for transient model calibration ........................................................................ 24

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2.6.3. Transient model calibration .................................................................................................................. 25

2.7. Error assessment and sensitivity analysis ............................................................................................................. 25 2.8. D-T basin water balance ......................................................................................................................................... 26

3. RESULTS AND DISCUSSION ..................................................................................................................... 28 3.1. Data processing calculation results........................................................................................................................ 28

3.1.1. Filling missed data for precipitation .................................................................................................... 28

3.1.2. Consistency of the precipitation records ............................................................................................ 28

3.1.3. Spatial data interpolation of rainfall ..................................................................................................... 29

3.1.4. Interception and infiltration rate .......................................................................................................... 31

3.1.5. Potential Evapotranspiration [PET] .................................................................................................... 32

3.1.6. Consistency of stream discharge .......................................................................................................... 34

3.2. Steady-state model calibration ................................................................................................................................ 36

3.2.1. Calibrated head and error assessment ................................................................................................. 36

3.2.2. Calibrated stream discharges ................................................................................................................. 38

3.2.3. Hydraulic conductivities ........................................................................................................................ 39

3.2.4. Water budget of the steady-state simulation using GHB conditions at the sea coast ................. 39

3.2.5. Spatial variability of groundwater fluxes ............................................................................................. 42

3.2.6. Effects of changing GHB conductance upon lateral groundwater outflow to the ocean .......... 43

3.2.7. Water budget of the steady-state simulation using CHD boundaries at the sea coast ................ 43

3.2.8. Sensitivity analysis ................................................................................................................................... 45

3.3. Transient model calibration .................................................................................................................................... 46

3.3.1. Calibration heads and error assessment .............................................................................................. 47

3.3.2. Calibrated stream discharges ................................................................................................................. 50

3.3.3. Hydraulic conductivities and specific yield ......................................................................................... 55

3.3.4. Water budget of the transient-state simulation .................................................................................. 56

3.3.5. Temporal variability of groundwater fluxes ....................................................................................... 57

3.3.6. Spatial variability of groundwater fluxes ............................................................................................. 58

3.3.7. Yearly steady-state and transient variability of water fluxes ............................................................ 59

3.3.8. Sensitivity analysis ................................................................................................................................... 61

4. CONCLUSIONS AND RECOMMENDATIONS .................................................................................... 63 4.1. Conclusions ............................................................................................................................................................... 63 4.2. Recommendations .................................................................................................................................................... 64

Appendix I ................................................................................................................................................................. 69

Appendix II .................................................................................................................................................................. 69

Appendix III ................................................................................................................................................................ 70

Appendix IV ................................................................................................................................................................. 71

Appendix V .................................................................................................................................................................. 71

Appendix VI ................................................................................................................................................................. 74

Appendix VII ............................................................................................................................................................... 75


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LIST OF FIGURES

Figure 1: Geological map and cross section across the study area (Modified after Purnomo & Pichler, 2015).

.......................................................................................................................................................................................... 2

Figure 2: Location and elevation map of the D-T basin. ........................................................................................ 4

Figure 3: Monitoring stations of D-T basin .............................................................................................................. 5

Figure 4: Mean monthly rainfall; maximum, minimum, and mean temperature at station Kuta of D-T basin.

For the location of the station see Appendix V. ...................................................................................................... 6

Figure 5: Land use map and percent area coverage of D-T basin. ........................................................................ 7

Figure 6: Watershed boundaries, stream segments and gauging location of D-T basin. For the name of each

station see Appendix V (B). ......................................................................................................................................... 7

Figure 7: Geology of the study area. ........................................................................................................................... 8

Figure 8: Potentiometric surface of Bali Island (Modified after Nielsen & Widjaya, 1989). ............................. 9

Figure 9: Double mass curve for a precipitation data (after Gómez, 2007). ..................................................... 11

Figure 10: Methodology of flow chart. ................................................................................................................... 16

Figure 11: Geological cross section across the study area (After Ministry of Energy and Mineral Resources

of Indonesia)................................................................................................................................................................ 17

Figure 12: Proposed boundary conditions and locations in the D-T basin. ..................................................... 23

Figure 13: Schematic diagram of MODFLOW-NWT setup of D-T basin model. ......................................... 26

Figure 14: Daily rainfall after filling missed data at station Kuta for the years from 2009 to 2013. For the

location of station see Appendix V (A)................................................................................................................... 28

Figure 15: Double mass curves of the precipitation gauges [units in mm]. The double mass curve in A & C

shows consistency in the data but B & D shows inconsistency in the data. For the location of stations see

Appendix V (A). .......................................................................................................................................................... 29

Figure 16: Sample significance test results of rainfall record on January 10, 2009. ......................................... 30

Figure 17: Standard model variogram; distance in a unit of [m] and semi-variance in a unit of [m2]. .......... 30

Figure 18: Kriged prediction and Kriging variance of D-T basin for long-term average rainfall from

01/01/2009 to 01/01/2012 [unit – mday-1]. .......................................................................................................... 31

Figure 19: Spatially variable interception (A) and infiltration rate (B) of D-T basin. ...................................... 32

Figure 20: Temperature coefficient of determination for Sanglah and Kuta stations. .................................... 32

Figure 21: Spatially variable crop coefficient (A) and extinction depth (B) for D-T basin. ........................... 33

Figure 22: Average Rainfall (P), Infiltration rate (Pr), Interception rate (I) and Potential evapotranspiration

(PET) for four hydrological years from 2009 to 2012. ......................................................................................... 33

Figure 23: Sample double mass curve and frequency distribution for the stream gauge discharge data [Q-

stream discharge in m3sec-1]. For the location of station and log transform see Appendix V. ...................... 35

Figure 24: Relation between rainfall and stream discharge. The oval shape indicates uncertainty on the

relation between measured stream flow and rainfall pattern. [RF – rainfall and Q – stream discharge]. For

the location of stream gauging stations see Appendix V. .................................................................................... 35

Figure 25: Relationship between simulated and observed heads in the D-T basin during steady-state IHM

for the year from 2009 to 2012. ............................................................................................................................... 36

Figure 26: Potentiometric surface with location of heads, stream segments of the D-T basin during steady-

state IHM. The stream segments with black lines indicates those that were not included during model

calibration. Heads in m a.s.l. ..................................................................................................................................... 37

Figure 27: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after steady-state

IHM [unit - mday-1]. ................................................................................................................................................... 39

Figure 28: Schematic representation volumetric water budget in case of steady-state IHM for the entire

model of D-T Basin [ All units - mmyear-1]. .......................................................................................................... 41

Figure 29: Spatially variable ETss of D-T Basin for calibrated steady-state IHM [Unit – mday-1]. ................ 42

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Figure 30: Spatially variable Rg map for calibrated steady-state IHM in D-T Basin [Unit – mday-1]. ............ 43

Figure 31: The relationship between GHB conductance and head dependent boundary flow rate. The GHB

conductance that masked by orange circle indicate the final value that was selected. In MODFLOW-NWT

the GHB conductance is calculated based on polyline objects as in Section 2.4.6. ......................................... 43

Figure 32: Sensitivity of model for horizontal hydraulic conductivity (A) & Vertical unsaturated zone

hydraulic conductivity (B). ......................................................................................................................................... 45

Figure 33: Sensitivity of model for UZF1 package parameter and driving forces: (C) extinction depth, (D)

infiltration rate, (E) extinction water content, (F) potential evapotranspiration. .............................................. 46

Figure 34: Sensitivity of model for (G) Brooks-Corey-Epsilon & (H) saturated water content. .................. 46

Figure 35: Relationship between simulated and observed heads for the transient IHM of 11 observation

points. ............................................................................................................................................................................ 47

Figure 36: The potentiometric surface and stream segments of the D-T basin during transient model

calibration at the last stress period, December 31, 2012. ...................................................................................... 48

Figure 37: Time series for the comparison of yearly observed and daily simulated heads for D-T basin. P –

rainfall, Hobs – observed heads, and Hsim – simulated heads. ............................................................................... 49

Figure 38: Relationship between observed and simulated discharge in the D-T basin for the transient-state

model calibration of 13 stream gauge (2009 - 2012). For the location of gauges see Appendix V (A & B).

The oval shape in Figure 37 (J, K, and L) show that uncertainty in the measured rainfall and stream

discharges. Because it is expected that at high rainfall records, stream discharge is higher and the opposite

is true. Q – stream discharge and RF – rainfall. ..................................................................................................... 54

Figure 39: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after Transient-

state IHM [unit - mday-1]............................................................................................................................................ 56

Figure 40: Temporal variability of groundwater fluxes in transient model calibration for gross recharge (Rg),

net recharge (Rn), surface leakage (Exfgw), and groundwater evapotranspiration (ETg). ................................... 57

Figure 41: Temporal variability of rainfall, actual infiltration and PET ............................................................ 58

Figure 42: Spatially variable ETg map for calibrated transient IHM during dry (A) and wet (B) period in D-

T Basin [Unit – mday-1]. ............................................................................................................................................. 59

Figure 43: Spatially variable Rg map for calibrated transient IHM during dry (A) and wet (B) period in D-T

Basin. ............................................................................................................................................................................. 59

Figure 44: Sensitivity of model for horizontal hydraulic conductivity [Kh], maximum unsaturated zone

vertical hydraulic conductivity [Kvun], extinction depth [EXTDP], extinction water content [EXTWC],

Saturated water content [WCsat], and Brooks-Corey-Epsilon [BC]. .................................................................... 61

Figure 45: Effects of changing unsaturated zone vertical hydraulic conductivity [Kvun] upon infiltration (A)

and Exfgw (B), effects of changing extinction depth [EXTDP] and GHB conductance upon ETg (C) and qg

(D) respectively. ........................................................................................................................................................... 62


vii

LIST OF TABLES

Table 1: Available data from the year 2009 to 2012 (Tmax - maximum temperature, Tmin - minimum

temperature, RH – relative humidity, WS – wind speed, SS - sunshine duration, n.a - indicates that the data

are not available within the study periods, EXTDP – Extinction depth, Kh – saturated hydraulic

conductivity, and Sy - specific yield). ........................................................................................................................ 10

Table 2: Interception loss rate that used in D-T Basin......................................................................................... 14

Table 3: Aquifer characteristics value of the basin (T - transmissivity, Sy – specific yield, Kh - horizontal

hydraulic conductivity, SWL - surface water level). The location of bores can be seen in Appendix I. ...... 15

Table 4: D-T extinction depth based on land cover. ............................................................................................ 21

Table 5: Observed and simulated head with calculated error assessment for 11 piezometers, Hobs – Observed

head, Hsim – Simulated head [units – m]. ................................................................................................................. 36

Table 6: Observed and simulated stream discharge with calculated error assessment for 16 gauges: Qobs –

observed stream discharge; and Qsim – simulated stream discharge [unit - m3day-1]. Stations that are

highlighted by red colour indicate those station that are not used for model calibration and show the model

response for those stations........................................................................................................................................ 38

Table 7: Total water balance of D-T basin at steady-state IHM [mmday-1]. ..................................................... 40

Table 8: water balance of land surface and unsaturated zone [mmday-1]. ......................................................... 40

Table 9: Water balance of groundwater in steady-state IHM [mmday-1]. .......................................................... 41

Table 10: Water balance of groundwater in steady-state condition [mmday-1]................................................. 44

Table 11: Observed, Hobs and simulated head, Hsim with calculated error assessment for 11 piezometers.

[Units – m]. .................................................................................................................................................................. 48

Table 12: Observed and simulated stream discharge with GHB conductance of 0.1 m2day-1 per unit length

calculated error assessment for 16 gauges in m3day-1. Stations that are highlighted by red colour indicate

those station that are not used for model calibration and shows the model performance for those stations.

....................................................................................................................................................................................... 55

Table 13: Final calibration output for model parameters and model variables in the D-T basin: EXTDP –

extinction water content; EXTWC – extinction water content; THTS – saturated volumetric water content;

THTI – initial volumetric water content; STRTOP – streambed top; STRTHICK – streambed thickness;

SLOPE – stream slope; STRHC1 – streambed hydraulic conductivity; WIDTH1 – stream width; Kvun –

maximum unsaturated zone vertical hydraulic conductivity; Kh – horizontal hydraulic conductivity; Sy –

specific yield; and C – conductance. ........................................................................................................................ 56

Table 14: Long term average groundwater budget for entire model in transient-state IHM [mmday-1] for the

2009-2012. IN – inflow to the aquifer system, OUT – outflow from the aquifer system, GW – groundwater.

....................................................................................................................................................................................... 57

Table 15: The yearly variability of driving forces and different groundwater balance components over the

three hydrological periods 1st January 2009 till 31st December 2012 MODFLOW-NWT simulation period

[All units in mm year-1]. ............................................................................................................................................. 60

viii

LIST OF ABBREBATIONS

∆S Change in storage

BGI Biro of Geospatial Information

BMKG Indonesian Agency for Meteorology, Climatology, and Geophysics

CHD Time-Variant Specified-Head

DEM Digital Elevation Model

DPPU Ministry of Public Works

D-T Denpassar - Tabanan

ETg Groundwater Evapotranspiration

ETo Reference Evapotranspiration

ETun Unsaturated zone evapotranspiration

Exfgw Groundwater exfiltration

EXTDP Extinction depth

EXTWC Extinction water content

FAO Food and Agriculture Organization

GHB General Head Boundary

GUI Graphical User Interface

ho Head in the aquifer

hs Head in streams

I Interception

IHM Integrated hydrological modelling

Kc Crop coefficient

KESDM Ministry of Energy and Mineral Resources of Indonesia

Kh Horizontal hydraulic conductivity

Kvun Maximum unsaturated zone vertical hydraulic conductivity [UHC]

m a.s.l Meters above sea level

MAE Mean Absolute Error

ME Mean Error

MODFLOW Modular three dimensional finite-difference flow model

NS Nash-Sutcliffe efficiency

NWT Newtonian

P Precipitation

Pe Actual infiltration

PET Potential evapotranspiration

Pr Infiltration rate

q Stream discharge at the outlet of the catchment

Q Discharge

qd Dunnian saturated excess runoff

qg Lateral groundwater outflow

qgs Groundwater loss to the stream

qh Hortonian runoff

qsg Groundwater gain from the stream

Rg Gross recharge

RH Relative humidity

RMSE Root Mean Square Error


ix

Rn Net recharge

RUZF Unsaturated zone recharge

Ro Total runoff

RVE Relative Volumetric Error

SFR2 Surface flow routing package

SS Sunshine duration

SW-GW Surface water and groundwater

Sy Specific yield

Tmax Maximum temperature

Tmin Minimum temperature

UPW Upstream Weighting Package

UZF1 Unsaturated zone flow package

WCsat Saturated water content

WS Wind speed

Y Overall model performance


1

1. INTRODUCTION

1.1. Background

Surface water and groundwater and (SW-GW) are very crucial for the well-being of humans and for the

nature in general (Sophocleous, 2002). The significance of these resources is increasing through time, as the

number of population is rapidly increasing (Fitts, 2002 & Anderson et al., 2015). Recently, research effort

has been extended to understand the interaction between SW-GW and to quantify the flow between these

resources, since, understanding of the link between them is needed for effective management of the resource

(Lubczynski & Gurwin, 2005; Sophocleous, 2005; Hassan et al., 2014 & Ala-aho et al., 2015). The

hydrological interactions between SW-GW occur through the unsaturated zone and by infiltration into or

exfiltration from the saturated zone (Anibas et al., 2009).

The groundwater basin of D-T is located in the most developed area of Bali Island, Indonesia. The Island

is located at 80 south of the equator and has an area of 5,380 km2, while the area for D-T basin is 2270 km2.

The island of Bali has a variety of volcanic topographic units such as eroded early Quaternary volcanoes,

active stratovolcanoes, thick tephra deposits, pyroclastic flow slopes and closed caldera lakes (Nielsen &

Widjaya, 1989; Kayane et al., 1993 & Purnomo & Pichler, 2015). These topography types can be classified

into two categories. The Quaternary upper volcanic sequence and the Pliocene lower calcareous sequence

(Figure 1). The latter is composed of a sequence of limestone, the "prepatagung formation", and calcareous

sandstone. The thickness of this aquifer material is unknown, whereas the thickness of the Quaternary upper

formation is considered to be up to 150 m. This Quaternary upper formation is composed of different

materials of volcanic origin. It includes mainly unconsolidated sand & gravel, volcanic ash, lava flow, breccia,

lahar, "pumic", clay and tuff (Rai et al., 2015 & Purnomo & Pichler, 2015).

Cole (2012) stated that groundwater is the most widely used resource in Bali Island as aquifers are

characterized by high permeability. Mainly the Quaternary volcanic aquifer is the most productive and it can

produce up to 7862 m3day-1. Nielsen & Widjaya (1989), strongly recommended for the expansion of well

systems for irrigation and municipal demands, due to their finding that 75% of the recharge reaches to the

Quaternary upper formation called production aquifer. However, no research has been done regarding

integrated hydrological model [IHM].

This research focuses on assessing the interaction between SW-GW resources and estimate the groundwater

budget of the D-T basin. The interaction of SW-GW is best quantified through IHM (Lubczynski & Gurwin,

2005 & Kumar, 2015). MODFLOW-NWT is one of the models developed that link surface, unsaturated

and saturated zone in a reliable manner. The model is working under ModelMuse Graphical User Interface

(GUI) and merge with unsaturated zone flow package [UZF1] and stream flow routing package [SFR2]

(Niswonger et al., 2011 & Hassan et al., 2014). Therefore, in this study MODFLOW-NWT was conducted

to quantify the exchange flux between surface, unsaturated and saturated zones for the simulation period of

four years from 2009 to 2012. Groundwater study in D-T basin was selected because: (i) the basin is located

in the most developed area on the Bali Island and having high potential of groundwater resources but

sometimes suffers from water scarcity; (ii) it is representative of unconsolidated aquifer around the world,

i.e. it consists of volcanic aquifer with intergranular porosity and medium to high permeability; (iii) there is

2

a four years of hydrological data available; (iv) groundwater recharge has been studied by Nielsen & Widjaya

(1989) using analytical methods and Artabudi (2012), that can be used for comparing the final findings.

Geological and cross section map of Bali Island

Figure 1: Geological map and cross section across the study area (Modified after Purnomo & Pichler, 2015).

1.2. Problem statement

Groundwater is the most popular water resources in Bali Island. However, Bali is affected by frequent crises

of water shortage (Purnomo & Pichler, 2015 & Straub, 2011). There is also a lack of knowledge and

mismanagement of SW-GW resources which causes decline of the water table, saltwater intrusion and

deterioration of water quality. Cole (2012) stated that the Island lacks official government statistics and

documentation regarding the available amounts of water resources. Furthermore, he mentioned the need

for reliable studies on SW-GW resources for successful water utilization and management. Besides, the

author of this study found that Bali groundwater has only been studied by Nielsen & Widjaya (1989) who


3

did recharge assessment but only by analytical methods and Artabudi (2012) who estimated groundwater

recharge using remote sensing application. The interaction of SW-GW and groundwater recharge using

IHM has not been studied in Bali Island.

1.3. Research setting

1.3.1. Research objectives

The overall objective of the study is to develop an IHM of D-T basin for management purpose.

Specific objectives:

1. To set up the numerical model in D-T based on the data from 2009 till 2012.

2. To calibrate steady-state and transient IHM of the D-T basin.

3. To estimate the water balance of the D-T basin.

4. To characterize the dynamics of SW-GW interactions in the D-T basin.

1.3.2. Research question

1. How to integrate various sources of data in the IHM?

2. What are the key components of spatiotemporal variability of the water balances in the D-T basin?

3. How does the water balance of the D-T basin vary on daily and/or yearly basis?

4. How do the SW and GW resources interact?

1.3.3. Novelty of the study

The findings of this study will increase the understanding of an unconsolidated aquifer of the D-T basin

and can be used as an asset for management purpose by including the following novelties:

1. First-time use of IHM in the D-T basin. No research has been done in the area related to SW-GW

interactions.

2. Use of daily streamflow measurement for IHM calibration.

1.3.4. Research hypothesis

It is hypothesized that the calibration of the integrated transient numerical model of the D-T basin gives a

reliable estimate of the SW-GW exchange flux and groundwater budget.

1.3.5. Assumptions

- Eventual leakages across the bottom boundary of the volcanic aquifer have a negligible impact on the flow

system of the modeled aquifer.

- Eventual lateral fluxes across watershed boundaries are negligible.

- Variable density groundwater flow, advection and dispersive salt transport have a negligible impact on the

flow system of the modeled aquifer.

- Due to lack of groundwater abstraction data both the steady-state and transient-state IHM were calibrated

without groundwater abstraction data. Therefore, the impact of groundwater abstraction in the water budget

of D-T basin have a negligible impact.

4

2. RESEARCH METHOD AND MATERIALS

2.1. Study area

2.1.1. Location

The D-T basin is located in the south-west of Bali Island, Indonesia with geographical coordinates of 8º39'S

latitude and 115º13'E longitudes. It is part of the Bali Island with estimated area coverage of 2270 km2;

whereas the whole Bali Island has an estimated area of 5,380 km2. The D-T basin has elevation variation

from 0 to 2850 m a.s.l with the highest elevation located in the north and north-east of the basin and with

the lowest elevation located in the south (Figure 2). The study mainly focused on the southern part of the

area; where most population part of Bali lives in D-T basin, the study excluded Nusa Dua and Nusa Penida

peninsula.

Location of D-T Basin

Figure 2: Location and elevation map of the D-T basin.


5

2.1.2. Monitoring network

The D-T basin, the southern Bali Island hydro-climatologically data such as rainfall, temperature, stream

level, groundwater level, and pumping test data were monitored and available. These hydro-climatological

data are available in the daily basis from 1st January 2009 to 31st December 2012 except for groundwater

level. In D-T basin there are 21 meteorological stations, of all this 18 of them have sparsely located rain

gauge stations and the remaining 3 are temperature, relative humidity, radiation and wind speed monitoring

stations. Stream level at the southern basin outlet was monitored on a daily basis using 16 discharge gauge

stations. The groundwater level was monitored by using 11 boreholes and dug wells (Figure 3).

Monitoring Stations

Figure 3: Monitoring stations of D-T basin

2.1.3. Climate

Based on average monthly rainfall, Bali has a pattern of monsoon type climate. Monsoon pattern occurs due

to the air circulation changing direction every six months across the Indonesian region. In the area, month

from April till the end of September is dry season and from October till the end of March is the wet season.

The air mass that brings the rain from the northwest equatorial wind in the wet season and the southeast

wind from Australia in the dry season (Figure 2) cause the seasonal pattern in the area (Kayane et al., 1993).

Bali has an average annual rainfall of 2150 mm. Generally, during the rainy season, part of rainfall will

evaporate, other part will be taken up by the plant, some will run as overland flow and the remaining infiltrate

to the subsurface. About 30 to 50% of total rainfall has been estimated to infiltrate into the Quaternary

terrains. In fact, the percentage which infiltrate depends upon geological conditions, vegetation cover, land

use, and slope (Nielsen & Widjaya 1989). On average, the temperature ranges from 27-30 0C (Figure 4) and

humidity 85-90 %. Moreover, in Bali soil and air temperature decreases at a lapse rate of 0.62 0C/100 m

with elevation (Kayane et al., 1993).

6

Figure 4: Mean monthly rainfall; maximum, minimum, and mean temperature at station Kuta of D-T basin. For the

location of the station see Appendix V.

2.1.4. Topography and land cover

The Island of Bali is a mountain chain that extends from the West to the East with volcanoes in Mount

Batur (1717m) and Gunung Agung (3142 m) still active (Figure 1). The mountain chain that runs along the

island of Bali causes morphological regions of Bali to be divided into several topographic and physiographic

units (Purnomo & Pichler, 2015). Since the Northern part is high elevated, major drainage network is located

in the south as well as the central part the D-T basin. In other respect, the most common land covers of D-

T basin are Forest, 6%; bare soil, 9%; Agriculture, 68.3%; buildings, 13%; grassland and others, 3.4% (Figure

5).

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Min. Temp Mean. Temp

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7

Land use map

Percent area ratio

Figure 5: Land use map and percent area coverage of D-T basin.

2.1.5. Hydrology

The D-T watershed boundaries are defined by topographic divides and delineate areas where surface water

runoff drains into a common surface water body. The defined watershed boundaries are determined by

science-based hydrologic principles, not favoring any administrative boundaries (Figure 6). Streams flow

from the north side to the south direction following the valleys. Most of the streams are perennial (Rai et

al., 2015), while their discharges originated from groundwater and surface runoff formed by precipitation.

The data from 16 stream gauges were available in a daily basis from 01/01/2009 to 31/12/2012.

Watershed boundaries of D-T basin

Figure 6: Watershed boundaries, stream segments and gauging location of D-T basin. For the name of each station see Appendix V (B).

0.48%

3.43%

5.99%

8.96%

12.82%

68.32%

100.00%

Water

Grass

Forest

Bare Soil

Buildings

Aggriculture

Total

8

2.1.6. Hydrogeology

Geologically, the study area is part of the “Sunda-Banda" volcanic islands arc. The arc is caused by the Indo-

Australian and Eurasia plates. Since the late Tertiary, this process drives volcanism and produces a vast

distribution of volcanic rocks (Figure 7). The Quaternary upper volcanic sequence which is also called

unconsolidated layer and the Pliocene lower calcareous sequence also called consolidated layer, are the two

dominant geologic formations of the area (Figure 1 & Figure 11). These volcanic rocks are rich in mafic

minerals and exhibits considerable relief at the north (Purnomo & Pichler, 2015). Hills that surrounds

Northern area forms surface water divides that coincide with the groundwater divides. Consequently, there

is no flow contribution from outside of the basin and the outflow is the only through the streams discharge

and lateral groundwater outflow towards the Indian ocean.

Pumping tests were conducted by Ministry of energy and mineral resources of Indonesia, locally "KESDM"

to evaluate the characteristics of the aquifer systems and groundwater potential of the basin. All the pumping

tests were carried out in Quaternary layer and the Tertiary layer is considered to be an impervious layer.

Because of that, it was assumed that there is no hydraulic contact between the upper Quaternary and lower

Tertiary layer.

D-T basin Geological map

Figure 7: Geology of the study area.

2.1.7. Previous studies in the area

Nielsen & Widjaya (1989), estimated groundwater recharge in southern Bali through five different

techniques for the year from 1980 to 1983. Based on analysis of well hydrographs they found that the

recharge value of 468 mm per annum, annual infiltration (≈25% of rainfall) gave 437 mm year-1, base flow

separation gave 272 mm per annum, flow net analysis gave 492 mm per annum. Finally, they built an

analytical model based on land use and soil type and found recharge value of 645 mm per annum in light

soil, 538 mm per annum in medium soil and 376 mm per annuam in heavy clay soil. Based on the above

findings, they recommended the expansion of well systems for tourism, irrigation, and municipal demands.


9

They also showed the piezometric/potentiometric map of the area, in which groundwater flows from

northern to the southern side of the basin (Figure 8). Additionally, Artabudi (2012) estimated the net

recharge of Denpasar in two ways: (1) using “the Global Satellite mapping for precipitation” for the data

from 2005 to 2009, the groundwater recharge value of 218 – 220 mmyear-1 was estimated; and (2) using in-

situ rainfall data the groundwater recharge value of 650 – 660 mmyear-1 was obtained.

In the study area, the Quaternary volcanic aquifer which is also called the unconsolidated layer is the most

productive and it can produce up to 7862 m3day-1. This unconfined aquifer is characterized by high

permeability and its volcanic rocks are characterized by intermediate hydraulic conductivity (Kh). Sand and

gravel of volcanic origin are highly permeable with transmissivity value of over 700 m2day-1 (Rai et al., 2015

& Purnomo & Pichler, 2015). Southern Bali piezometric map

Figure 8: Potentiometric surface of Bali Island (Modified after Nielsen & Widjaya, 1989).

2.2. Data processing

Data collection is a prerequisite in groundwater modeling. Meteorological and hydro-geological data need

to be collected as well as processed for effective model simulation of a given area (Kumar, 2015). In this

study, the meteorological and hydrogeological data are available as shown in Table 1. Data such as

groundwater depth, pumping test, hydrogeological and geological maps were collected from Ministry of

Energy and Mineral Resources of Indonesia (locally "KESDM"). Most of the meteorological data such as

daily rainfall, air temperature, relative humidity, streams level, and rating curves were collected from Ministry

of Public Works (Locally called "DPPU"). Additionally, the land use map and 2012 daily rainfall data were

collected from Biro of Geospatial Information (BIG) and Indonesian Agency for Meteorology, Climatology,

and Geophysics (Locally called "BMKG") respectively.

Initially, in the data processing step, the missing rainfall data was filled using the coefficient of correlation

method (Teegavarapu & Chandramouli, 2005). Then, a double mass curve was used to check the consistency

of rainfall and stream discharge data (Searcy & Hardison, 1960). Afterward, all the available data (Table 1)

10

was converted in a way that MODFLOW-NWT can accept it. For instance, the available point observation

of rainfall data was interpolated into rainfall map using kriging method. Kriged prediction was selected

because it is a best linear unbiased predictor (Sterk & Stein, 1997; Hengl et al., 2007; Webster & Oliver,

2007; & Zhang et al., 2012). Spatially variable crop coefficient (Kc), interception rate and infiltration rate

were estimated using the 2009 land use map of the D-T basin. Using FAO Penman-Monteith method the

available Tmax, Tmin, RH, WS, & SS together with spatially variable Kc data were used to calculate potential

evapotranspiration (PET). The hydraulic head was calculated from elevation and groundwater depths data.

Finally, the IHM was built and simulated in daily time steps for a four hydrological years from 1st January

2009 to 31st December 2012.

Table 1: Available data from the year 2009 to 2012 (Tmax - maximum temperature, Tmin - minimum temperature, RH –

relative humidity, WS – wind speed, SS - sunshine duration, n.a - indicates that the data are not available within the

study periods, EXTDP – Extinction depth, Kh – saturated hydraulic conductivity, and Sy - specific yield).

Required data Available data No. of stations

Required Units

Frequency of available data

Watershed boundary DEM - - -

Infiltration rate Rainfall 18 mday-1 daily

Potential evapotranspiration

Tmax, Tmin, RH, WS, SS

3 mday-1 daily

Stream discharge Stream level & rating curve

16 m³day-1 daily

Hydraulic head Groundwater depth

11 m yearly

Groundwater abstraction

n.a. n.a. m³day-1 n.a.

Tidal head Tidal head 1 m daily

Model top elevation DEM - m a.s.l. -

Crop coefficient Land use map - - -

Interception Land use map - - -

EXTDP Land use map - - -

Kh , Sy Kh, Sy 14, 2 mday-1, - n.a.

2.2.1. Watershed boundary

The D-T watershed boundaries were defined by topographic divides and delineating areas where surface

water runoff drains into a common surface water body. The defined watershed boundaries were determined

upon science-based hydrologic principles, not favoring any administrative boundaries. The SRTM (Shuttle

Radar Topographic Mission) 90 m DEM (digital elevation model) was used to delineate these watershed

boundaries. The SRTM 90 m DEM provided by NASA, has significant importance in determining the flow

direction and in delineating catchment areas according to their stream flow. This data is available on the

internet with free of charge by USGS, (http://srtm.csi.cgiar.org/). Initially, the available DEM data was

filled into remove small imperfections in the data using hydrology spatial analyst tool in ArcGIS, then using

the filled DEM map, a raster map of flow direction from each cell to its steepest downslope neighbor was

generated. Then, a raster map of accumulated flow into each cell was generated. Afterward, the steam gauges

were used as a snap pour points to the cell of highest flow accumulation within a 1000 m distance. Finally,

the contributing area above a set of cells or watershed boundaries was obtained (Figure 6).

2.2.2. Precipitation

Precipitation is one of the first essential input data in IHM. Precipitation is used in UZF1 package to be

partitioned into runoff, infiltration, evapotranspiration, unsaturated-zone storage and recharge. Precipitation

http://srtm.csi.cgiar.org/


11

together with potential evapotranspiration is the input driving forces of UZF1 packages of MODFLOW-

NWT (Niswonger et al., 2006). The D-T basin rainfall was measured using tipping bucket at 18 sparsely

distributed rain gauge stations (Figure 3 and Appendix V). From the total number of stations, only the

station called Kuta has missed rainfall data.

Estimation of the Missing Precipitation Records

Rainfall records can be missed due to instrument malfunction, tree growth or other reason. Filling the missed

data is one of the most important tasks to be carried out in many hydrological studies. The most commonly

applied methods that are recently used for filling missed data are inverse distance, inverse exponential, the

coefficient of correlation weighted method, and others (ASCE, 1996). In this study, the “coefficient of

correlation weighted method” (CCWM) was used to fill missing data as proposed by Teegavarapu &

Chandramouli (2005) & Gómez (2007). Reliable estimation of missed data using CCWM is strongly

dependent on spatial autocorrelation in which the data nearby are more similar than that of far apart. Once

the correlation coefficient is determined, the missed data at a given station is calculated using equation 2.1.

n

1imir

mirn

1iiP

mP (2.1)

where Pm - precipitation at the base station m; Pi - precipitation at station i, n – number of nearby stations,

and rmi - correlation coefficient of station i with nearest n stations. The correlation coefficient, rmi, is obtained

from SPSS by using the method known as “Pearson - Moment Correlation Coefficient” between closest

stations (Appendix III).

Consistency of the precipitation records

Hydrological data consist of time series data that are collected at a particular location. The use of raw data

without checking for consistency in IHM can bring lots of error and uncertainty. Therefore, before

hydrological data are used in such study, they should be tested by the double-mass curve technique to ensure

their reliability (Searcy & Hardison, 1960). The Double-Mass curve is plotted as cumulative of one station

(y-axis) against the average cumulative of nearby stations (x-axis) as in Figure 9.

Figure 9: Double mass curve for a precipitation data (after Gómez, 2007).

12

Deviation from or break in the slope of the double mass curve means that there is a change in the

consistency of proportionality between the variables or simply it shows the degree of change in the relation.

Such deviation might be due to gauge location, observation method or exposure. The precipitation records

can usually be adjusted by coefficients determined from the double-mass curve (Equation 2.2).

bP

bδ

aδaP (2.2)

where Pa - adjusted precipitation, Pb - observed precipitation, δa - the slope of the graph at the time was

observed and δb - the slope of the graph to which records are adjusted.

2.2.3. Potential evapotranspiration

McMahon et al., (2013) define potential evapotranspiration [PET] as "the rate at which evapotranspiration

would occur from a large area completely and uniformly covered with growing vegetation which has access

to an unlimited supply of soil water, and without advection and heating effects." PET is one of the driving

forces in the UZF1 package. In the UZF1 package, the PET is applied at the land surface and decreases

linearly with depth down to the assigned extinction depth where evapotranspiration no longer occurs (Allen

et al., 1998). In most case PET calculated using FAO Penman-Monteith method (Equation 2.3). The

method is recommended by the scientific community as the best estimate of evapotranspiration with

minimum error compared to other methods (Wang et al., 2012). FAO Penman-Monteith method is

applicable if data such as daily air temperature, wind speed, relative humidity, atmospheric pressure and

relative sunshine duration are available. Consequently, the method was adapted for reference

evapotranspiration computation, since, the required data such as daily air temperature, wind speed, relative

humidity, atmospheric pressure and relative sunshine duration was available from the two stations namely

called station Sanglah and Kuta.

Before ETo computation using the equation 2.3, the correlation between Tmax, Tmin, and Tmean for the available

stations were constructed. A good coefficient of correlation between the station means that temperature is

uniform spatially. Then, the computed ETo would be spatially uniform but temporally variable. In the case

of low coefficient of correlation between Tmax, Tmin, and Tmean of the different stations kriging interpolation

method would be applied to generate the spatially variable ETo values.

Note that, the computation equations to estimate evapotranspiration as shown in Equation 2.3 and

Appendix II are the one that were applied in this study based on the available data. There are many possible

ways of determining one parameter based on the availability of data in a given area. For detail study

interested readers are referred to Allen et al.,(1998) & Raes & Munoz (2009).

)2U*0.34γ(1Δ

)aes(e2U273T

900*γG)n(R*Δ*0.408

oET

(2.3)

where ETo - reference evapotranspiration [mmday-1], ∆ - slope vapour pressure curve [kPa°C-1], Rn - net

radiation at the crop surface [MJm-2day-1], G - soil heat flux density [MJm-2day-1], 𝛾 - psychrometric constant

[kPaoC-1], T - mean daily air temperature at 2 m height [°C], U2 - wind speed at 2 m height [ms-1], es - vapour

pressure [kPa], ea - actual vapour pressure [kPa], es-ea, - saturation vapour pressure deficit [kPa], Rn again can

be calculated using the equations as in Appendix II.


13

The computed ETo needs to be converted into PET since MODFLOW-NWT requires PET rather than

ETo. The single and dual crop coefficient (Kc) are the two approaches to converting ETo into PET (Allen

et al., 1998). The former approach calculates as in equation 2.4; in which the Kc depends on crop type and

growing stage, whereas, in the latter case the Kc splits it to two other factors. The first factor for evaporation

and second factor for transpiration difference between crop reference surface (Zehairy, 2014 &

Weldemichael, 2016). Dual crop coefficient requires sufficient data about crop/vegetation and soil and

hence for this study spatially variable but temporally invariable single crop coefficient approach was applied.

cK*oETPET (2.4)

where PET - potential evapotranspiration [mmday-1], and Kc- crop coefficient [-].

The spatially variable Kc in this study area was estimated based on the land use and vegetation cover. The

D-T basin mainly covered by agricultural land, forest, bare soil, and grass. The Kc value for bare soil which

is about 9 % of the study area was assigned as 0.61. About 6 % of the area covered with forest and the Kc

of trees was assigned as 1.0 (Allen et al., 1998). Agriculture land that covers 68% of the total area and the

majority of the agricultural land was covered by rice field. The Kc values of rice during initial, crop

development, mid-season, and late season stages were 0.62, 0.75, 1.16 and 0.67 respectively (Choudhury et

al., 2013). It was assumed that the Kc value for rice field to be during crop development stage. The Kc value

of 0.75 was used for agriculture land. After defining the crop coefficient for each land cover and vegetation

type, the spatially variable Kc was obtained for 500 * 500 grid cells. Then, the spatiotemporal variability of

PET was calculated using Equation 2.4.

2.2.4. Interception and infiltration rate

Interception rate is the amount of rainfall that is retained by vegetation above the surfaces. The rate depends

mainly on the rainfall duration, density, and morphology of vegetation cover. The interception loss from a

given land cover can be calculated by using Equation 2.5 (Zehairy 2014 & Weldemichael 2016).

)other

A*other

If

A*f

(I*PI (2.5)

where I - canopy interception per grid cell [mday-1], P - precipitation [mday-1], If, and Iother - interception loss

rate by forest, and agriculture respectively in [%] of precipitation, and Af other Aother - area ratios coverage

per grid for forest and agriculture respectively.

The D-T basin interception loss was calculated as in Equation 2.5. The spatial variability of interception rate

was calculated per grid cells and subtracted from spatially variable precipitation rate to get spatially variable

infiltration rate. Several kinds of the literature suggested interception ratio, i.e. If and Iother based on land

cover. For instance, Ghimire et al., (2012) determined rainfall interception by natural and planted forests in

the middle mountains of central Nepal. According to their finding, interception loss for the evergreen

natural forest was 22.4% of precipitation. Since similar forest type is present in the D-T basin (Heim, 2015),

this study adapted the value of interception ratio 22.4% of precipitation as a value for forest cover. Van Dijk

& Bruijnzeel (2001) also studied rainfall interception in upland West Java, Indonesia for mixed agricultural

cropping system involving cassava, maize, and rice. According to their finding interception loss for the

agricultural land was 14.4% of precipitation. The final finding of Van Dijk & Bruijnzeel (2001) for mixed

crops was conducted in this study as interception loss rate for agriculture farmland. Finally, Corbett et al.,

(1968) determined rainfall interception by annual grass and chaparral and found that grass has an

14

interception loss rate of 6.5% of the total rainfall. This finding for grass was used in this study as interception

loss from grassland. The values are summarized in Table 2.

Table 2: Interception loss rate that used in D-T Basin

D-T Land cover Interception loss Adapted literature

Forest cover 22.4% Ghimire et al., (2012)

Agriculture [mainly rice] 14.4% Van Dijk & Bruijnzeel (2001)

Grassland 6.5% Corbett et al., (1968)

As stated earlier the infiltration rate was calculated as the difference between rainfall and interception rate

(Equation 2.6). Infiltration is the amount of water that percolate to the unsaturated zone. The infiltration

rate highly depends on the vertical hydraulic conductivity and degree of saturation of the unsaturated zone.

The higher the vertical hydraulic conductivity, the easy through which water can pass through the soil, then

the higher the infiltration rate would be and vice versa. When the infiltration rate is higher than the vertical

hydraulic conductivity, the water hardly passes through the soil pores, then the excess rainfall will be

redirected to the streams.

IPPr (2.6)

where Pr - infiltration rate per grid cell [mday-1], P - precipitation [mday-1]. This infiltration rate is one of the

driving forces that was used in the UZF1 package to estimate the unsaturated zone storage and unsaturated

zone evapotranspiration, and groundwater recharge (Niswonger et al., 2006).

2.2.5. Stream discharge

According to Braca (2008), the stage-discharge relation or rating curve in an open channel flow is used to

convert the series of stage records into discharge records. Similarly, it is used to convert forecasted flow

hydrographs into stage hydrographs. The relationship is highly affected by section and channel controls.

The latter is due to hydraulic properties and roughness of the surface downstream. Such hydraulic properties

can be channel size, shape, slope, and curvature. On the other hand, the former can be caused by natural or

man-made processes. Rock ledge, sand bar, and debris are grouped under natural processes. Dam, Weir,

Flume, and Spillway are grouped under man-made processes. Because of the underlining reasons, the

knowledge of channel features and a time series of stage and discharge together with low and high flow

measurements are required to construct efficient rating curves. The stage-discharge relation can be calculated

using the simplified forms of Manning equation (ISO, 2010) as shown in Equation 2.7.

)( ahCQ (2.7)

where Q - discharge [m3day-1], h - stage [m], a - gauge height of zero flow [m], ah - effective depth of

water on the control, C - calibration coefficient [m2day-1], α - slope of rating curve [-].

The D-T basin has 16 sparsely located discharge stations (Figure 6 and Appendix V). The data that was

collected from "DPPU" was daily stream level for the year 2009 to 2012 together with rating curve for each

station but it lacks stream discharges data. The availability of rating curve that was constructed using

HYMOS (Sankhua & Srivastava, 2011) saves the time to convert the stages into stream discharges.

Therefore, the four-year daily stream level data were converted into stream discharge for each station and


15

then missing discharge data and its consistency was adjusted in the same manner as precipitation – section

2.1.1. Afterward, the final result was used as a state variable in SFR2 package (Niswonger & Prudic 2005).

2.2.6. Hydraulic properties

The pumping tests were used to obtain the aquifer characteristics such as transmissivity and storativity. Such

data together with other data was used to build a numerical modeling and evaluate the resources in the given

area. Table 3 shows the aquifer characteristics of D-T basin, this test value was used as an initial value in the

model and then adjusted during the model calibration.

Table 3: Aquifer characteristics value of the basin (T - transmissivity, Sy – specific yield, Kh - horizontal hydraulic

conductivity, SWL - surface water level). The location of bores can be seen in Appendix I.

ID

Latitude

Longitude

T

[m2day-1]

Sy

Kh

[mday-1]

SWL

[m]

Thickness

[m]

Bottom

elevation [m]

PZ1 8°25'29.21" 115°12'50.48" 1821.6 67.5 100.1 27.5 126.5

PZ2 8°30'56.37" 115°27'02.07" 2340.1 36.2 50.4 64.6 11.6

PZ3 8°20'9.69" 115°21'13.83" 134.8 2.7 89.8 50.2 140.1

PZ4 8°12'42.08" 115°17'17.63" 57.6 1.2 148.2 47.6 195.5

DP2 8°37'14.17" 115°14'0.91" 390.2 0.25 2.9 18.8 131.2 149.5

DP3 8°23'19.05" 115°13'20.55" 690.5 5.4 22.3 128.9 150.1

DP4 8°30'21.10" 115°12'33.51" 550.2 4.3 21.6 128.4 150.0

DP5 8°39'19.45" 115°11'46.89" 760.1 0.24 5.9 22.1 127.9 150.5

DP6 8°38'36.55" 115°13'56.06" 385.8 2.8 14.1 135.9 148.5

DP7 8°33'55.05" 115°10'50.25" 280.5 2.1 19.1 130.9 147.7

DP13 8°37'26.58" 115°14'09.05" 298.6 2.1 10.8 139.2 151.2

sbo1 8°31'44.41" 115°12'5.08" 7.1 0.1 62.0 62.2 130.2

sbo2 8°27'48.60" 115°11'15.25" 8.9 0.2 62.0 70.5 129.9

sbo3 8°32'18.33" 115°09'56.42" 5.4 0.1 4.2 111.0 115.2

sbo4 8°19'30.60" 115°22'00.83" 8.5 0.7 31.6 118.3 151.1

sbo9 8°22'33.38" 115°17'06.45" 110.1 0.8 9.9 140.1 151.0

sbe10 8°32'20.20" 115°06'54.27" 43.1 0.4 38.9 111.1 151.4

2.2.7. Head observation

In the study area, all groundwater level measurements are undertaken in Quaternary deposits and show

strong spatial variation to topographic altitude differences. However, such data were available neither daily

nor monthly rather monitoring records show one record per year besides, the monitoring stations have low

spatial coverage over the study area (Figure 3).

2.2.8. Groundwater abstraction

The D-T basin groundwater abstraction data could not be found in public services as well as from Ministry

of Energy and Mineral Resources of Indonesia, locally "KESDM". It was found out that the data is

confidential and the ministry is not willing to share the data even for study purposes. Because of the

underlining reason, the author builds the model without groundwater abstraction. Therefore, the result of

this model should be used with caution in case future model implemented using groundwater abstraction

data.

16

2.3. Modeling flow chart

The overall activities going to be applied to answer the research questions and to come up with the

targeted objectives is summarized in the flow chart (Figure 10).

Figure 10: Methodology of flow chart.

2.4. Conceptual model

According to Anderson & Woessner, (1992), there are three essential steps in modeling protocol. These are

(1) “to establish the purpose of the model”, (2) “formulation of the conceptual model of the system”, and

(3) “formulation of the numerical model of the system”. The purpose of the model is for better

representation of the flow between surface, unsaturated zone and saturated zone. It is useful in

understanding the interaction and estimating the water balance in the D-T basin. A conceptual model is a


17

“pictorial representation” of the flow system. It is used to configure the field problem into a simple and

meaningful schema and then, field problem can be easily analysed. Most of the errors in modelling arise

during formulation of a conceptual model and the generated error in the conceptual model can propagate

into the numerical model. Then, the final output of the model rarely represents real world scenarios.

Therefore, modelers should give attention in understanding field data and formulation of the conceptual

model. There are four steps to formulating conceptual model: defining hydrostratigraphic units, defining

the flow system, defining preliminary water balance, and defining the boundaries of the model.

2.4.1. Defining Hydrostratigraphic units

The hydrostratigraphic unit is used to define the aquifer type (Anderson & William, 1992). Stratigraphic

units can be merged into one hydrostratigraphic unit or treated as independent hydrostratigraphic units, this

depends on the hydrogeological formation of the layers. As stated earlier, the D-T basin consists of the

Quaternary and Tertiary geological strata. The upper Quaternary volcanic sequence consists of

unconsolidated sand & gravel, volcanic ash, lava flow, breccia, lahar, "pumic", clay and tuff (Figure 11),

whereas, Tertiary or Pliocene lower calcareous consists of a sequence of limestone, “prepatagung”

formation, calcareous sandstone, sand, and Graywacke, this layer also called the consolidated layer (Nielsen

& Widjaya, 1989 & Purnomo & Pichler, 2015). In this study, the individual geological

formation/stratigraphic unit was considered to be an independent hydrostratigraphic unit. This was due to

the fact that the stratigraphic units have different physical properties and have a different hydrogeologic

formation. The upper Quaternary volcanic sequence or the unconsolidated layer is a pervious layer where

most of the borehole are presented, whereas, the lower Tertiary layer consists of limestone and such

geological formation is impervious, so that groundwater is rarely present in this layer. Concluding, the upper

layer is considered as an unconfined aquifer. This aquifer type is bounded with the water table at the top

and with the impervious layer, an aquiclude at the bottom.

Geological cross section Bali Island, Indonesia

Figure 11: Geological cross section across the study area (After Ministry of Energy and Mineral Resources of Indonesia)

2.4.2. Defining the flow system

The mountain chain that runs along the island of Bali causes morphological regions of Bali to be divided

into several topographic and physiographic units (Purnomo & Pichler, 2015). Since the Northern part of

18

the D-T basin is high elevated, major drainage network of rivers/streams is located in the south as well as

in the central part of the basin (Figure 6). The groundwater flow system of D-T basin is directed from the

higher hydraulic head, in the North to the lower head, in the South as in Figure 8. However, close to the sea

coast the aquifer flow system is dependent on the tidal movement (Pauw et al., 2014). The influence of the

tidal movement on the groundwater head and flow, is taken into account using fresh/seawater boundaries

(Mulligan et al., 2011; Durden et al., 2013 & Pauw et al., 2014).

2.4.3. Defining preliminary water balance

In the D-T basin rainfall is the only source of water to the system. At first, part of the incoming rainfall is

intercepted and evaporated back to the atmosphere due to vegetation and others bodies; and then, part of

it becomes recharge and finally some will either evaporate or drain to the streams as overland flow. For

groundwater basin, recharge from unsaturated zone and stream discharge to the groundwater was

considered as the inflow to the aquifer system. Groundwater evapotranspiration, surface leakage, lateral

groundwater outflow and stream discharge from groundwater was considered as an outflow from the

system, the schematic representation of D-T basin is presented in section 2.7.

2.4.4. Defining the boundaries of the model

Model boundaries need to be defined critically since the defined boundaries can have a tremendous effect

on the final output of the model. In the study area there are physical and hydrological conceptual model

boundaries. The southern, south-eastern and south-western sides of the basin were surrounded by the

physical boundary, i.e. the Indian Ocean. The groundwater flow system near to the sea coast is highly

influenced by the tidal effect or forcing of the sea (Mulligan et al., 2011 & Pauw et al., 2014). Thus, the

impact of tidal forcing on the groundwater flow of D-T unconfined aquifer was take into account by

defining a reliable numerical boundary condition as in section 2.4.6. Apart from these, the lower Pliocene

calcareous sequence underneath the unconfined aquifer considered as the bedrock of the basin/impervious

layer and hence there is no flow out from basin bottom. The northern, north-eastern, and north-western

sides of basin is surrounded by hydrological boundaries. The defined hydrological boundaries are mountain

ranges/watershed divide at the north; streamlines at the north-east as well as north-west side (Figure 1). The

watershed boundaries are defined by topographic divides and they identify the surface water runoff divides.

Besides, they usually do represent groundwater flow dividers in the case of an unconfined aquifer (Heswijk,

2013). Therefore, flux along the watershed divide or streamlines was considered as zero or no in/outflow

from these boundaries.

2.5. Numerical model

According to Anderson & William (1992), the third step in modeling protocol is the formulation of the

numerical model of the system. Numerical modeling is actually the numerical representation of hydrological

system regime and considers the aquifer properties are divided in space and time. Numerical modeling

includes software selection, general model assumptions, grid design, aquifer geometry design, aquifer

parameterization and boundary conditions.

2.5.1. Software selection

Software selection is dependent on the environment being modeled and objectives. In this study,

MODFLOW-NWT software was used to develop the model. According to Niswonger et al., (2011)


19

MODFLOW-NWT is working under ModelMuse Graphical user Interface (GUI) and merged with UZF1;

SFR2 and other packages. It is a Newton formulation of MODFLOW-2005, is one of the models that

developed to link saturated and unsaturated zone. MODFLOW-2005 is block centered with finite difference

concept, that computes head with an average head for the cell that surrounds the node (McDonald &

Harbaugh, 1988). Therefore, this model was used to quantify the exchange flux between surface, unsaturated

and saturated zones. MODFLOW-NWT is selected for D-T basin because: (i) it will integrate surface,

unsaturated and saturated zone; (ii) it is a standalone and public domain with excellent documentation, and

(iii) it is MODFLOW base model, hence it can possibly be compared with other models.

UZF1 Package

Integrating and modeling the unsaturated zone and saturated zone/groundwater in three dimensions is quite

troublesome. Since modeling unsaturated zone based on Richards’s equation is highly nonlinear and it is

difficult to solve it (Niswonger et al., 2011). However, recently UZF1 package is developed to simulate the

flow in the unsaturated zone into one-dimension form of Richard’s equation. "The one-dimension form of

Richards’s equation is approximated by a kinematic wave equation to simulate the flow of water and storage

in vertical components in response to gravity potential gradients only and ignores negative potential

gradients", equation 2.8. This package is a substitution for the Recharge and Evapotranspiration Packages

of MODFLOW-2005, which integrate the flow with the three-dimensional groundwater flow system

(Niswonger et al., 2006). UZF1 Package in MODFLOW-NWT uses input data such as saturated water

contents, maximum unsaturated zone vertical hydraulic conductivity and Brooks-Corey exponents,

infiltration rate, evapotranspiration demand, extinction depth and extinction water content at specific stress

period. The Brooks-Corey exponents are used to define the relation between unsaturated zone vertical

hydraulic conductivity and water content. The extinction depth and extinction water content at specific

stress period are essential components to simulate evapotranspiration. Extinction depth is “defined based

on the dominant vegetation of the area in which the depth extends beneath the soil zone” and

evapotranspiration ceases underneath this depth (Hassan et al., 2014). Extinction water content is the water

content in unsaturated zone below which evaporation will be neglected. Using the above input data, the

package partition flows into evapotranspiration, recharge, and runoff into the stream. Nonetheless, the

package does not allow for parameter estimation, the parametric values are shown in section 2.4.5.

0)(

i

Z

K

t

(2.8)

where θ - volumetric water content [m3m-3], K(θ) - unsaturated hydraulic conductivity as a function of

water content [mday-1], i - ET rate per unit depth [m-1], t - time [day].

SFR2 Packages

SFR2 package is used to simulate the exchange flux between stream and groundwater as well as the flow

and storage in the unsaturated zone beneath the stream. In this package, the flow computation method

between stream and aquifer is the same as River Package in MODFLOW-2005 (Niswonger & Prudic 2005).

The “flow computation between the two resources is based on Darcy’s law and assuming uniform flow

between them” (Equation 2.9). Additionally, simulation of flow and storage in the unsaturated zone beneath

the stream is based on the kinematic wave approximation to Richards’s equation. In the approximation

techniques, it is assumed that the flow is in the vertically downward direction, horizontal flow component

is ignored. The zone assumed to be homogeneous and isotropic, and diffusion is neglected. Because the

20

flow is assumed to be vertical downward direction, SFR2 packages fill the unsaturated zone pores from the

top down sequence. Seepage across the streambed can exhibit either horizontal or vertical component of

flow.

SFR2 package in MODFLOW-NWT uses input data such as stream flow network, streambed top, stream

slope, streambed thickness, streambed hydraulic conductivity, stream width, channel roughness, bank

roughness, saturated and initial water contents, maximum unsaturated zone vertical hydraulic conductivity,

Brooks-Corey exponents, flow into upstream end, SFR2 packages parametric values were shown in section

2.3.5. The package can simulate volumetric water discharge, it allows the user to add or subtract water from

stream due to precipitation, runoff, and evapotranspiration (Niswonger & Prudic 2005).

)()( hohschohsM

KWLQl (2.9)

where Ql; - volumetric flow between a given section of streams and volume of aquifer [m3day-1]; K - hydraulic

conductivity of streambed sediment [mday-1]; W - width of the stream [m]; L - length of the stream [m]; M

- thickness of the streambed deposits extending from top to the bottom of streambed [m]; hs - the head in

stream [m]; ho - head in the aquifer [m]; and C – riverbed conductance [m2day-1].

2.5.2. Aquifer geometry and grid design

Block-centred steady/transient with a grid size of 500 * 500 m, one-layer unconfined IHM was developed

because of the single hydrostratigraphic unit. Small grid cell size was proposed in order to compromise the

model accuracy and computation time. Mehl & Hill, (2010) mentioned that “highly refined grids have a

better representation of the system and address more detailed resources management issues”. Aquifer

geometry design is in forms that defining top and bottom of the model layer and defining water table

distributions. This single layer is represented by layer type 1, which is utilized the uppermost layer of a

model, and only where unconfined conditions are expected to persist in the layer throughout the entire

period of simulation.

2.5.3. Driving forces

Driving forces can vary in space and time. The number of driving forces in a given model depends on the

intended purpose of the modeling. By fixing the model parameter value, the output of the model will be

affected due to change of driving forces through time. The proposed driving forces in this study area were

precipitation, infiltration rate, and PET. Initially, the driving forces are available on a daily basis for four

years (01/01/2009 – 31/12/2012). These time series data are point observation (Figure 3 and Appendix V;

A & B) but the MODFLOW-NWT required as interpolated map. Because of this, raster map was generated

for each driving force. For instance, from the available eighteen-point observation rainfall data, the

spatiotemporal rainfall map was generated using kriging interpolation method; this method was chosen

because it is a best linear unbiased predictor [BLUP] that gives a minimum error of variance (Sterk & Stein,

1997; Hengl et al., 2007; & Webster & Oliver, 2007). In order to generate spatiotemporal infiltration rate,

first spatially variable but temporally uniform interception rate was generated using the land use map of the

D-T basin. Then, spatiotemporal infiltration rate was generated by subtracting the interpolated interception

rate from spatiotemporal rainfall map- section 2.1.1 & 2.1.2. In addition to this, the spatiotemporal PET

was generated by simple multiplication of the spatiotemporal ETo and spatially variable but temporally

uniform Kc interpolated map – Section 2.23. Finally, the spatiotemporal infiltration rate and PET were

imported as ASCII raster file into UZF1 packages (Niswonger et al., 2011).


21

2.5.4. State variables

In this study, the defined state variables are hydraulic heads and stream discharges. As the driving forces can

have a different value at the different time and space, the state variables can also have a different value in

different time and space. In the D-T basin, there are 11 groundwater levels and 16 stream gauge records.

The daily basis of stream discharge record was available from locally called "DPPU". The four-year time

series stream discharge data show temporal variability for each station. Groundwater level records from 11

stations were not on a daily basis rather the records are once in a year. Since groundwater assessment

required groundwater monitoring stations, the available initial heads from 11 stations was used as starting

heads in the steady-state IHM. Then, these head again was used as an initial head value for transient IHM.

Since there is a shortage of time series groundwater fluctuation, the transient model is calibrated mainly

based on daily stream discharge data.

2.5.5. Parametric data

The UZF1 package is used to calculate vadose zone evapotranspiration, saturated zone evapotranspiration,

gross recharge, groundwater exfiltration, and change in storage in the vadose zone as a function of the inputs

assigned to the package including infiltration rate, PET, extinction water content [EXTWC], and extinction

depth [EXTDP]. First the package satisfying the evapotranspiration demand, then, the remaining water

moves to underlying aquifer as UZF recharge. In the steady-state model, the average infiltration rate over

the four years was calculated per grid cells after subtracting the spatially variable but temporally uniform

interception rate from kriging prediction rainfall map - section 3.1. In the transient model, the infiltration

input was calculated as a daily variable for each time step in order to account for the spatiotemporal

variability of subsurface fluxes. In the same manner, the spatially variable PET value assigned in the model

using spatiotemporal ETo and spatially variable but temporally uniform Kc. On top of that, spatially uniform

Brooks-Corey exponent as 3.5; maximum unsaturated vertical hydraulic conductivity as 0.35 m day-1 and

adjusted during model calibration; saturated water content as 0.5 m3 m-3; and the extinction water content

as 0.06 m3m-3 was used to all cells. The model top was taken as the land surface where the infiltration was

applied. In addition to these, the extinction depth was adapted from literature. The extinction depth was

assigned to each land cover (Table 4) and spatially variable extinction depth was generated for 500 * 500 m

grids. Furthermore, “the recharge and discharge location option” [NUZTOP] was selected as “Top active

cell (3)”; “vertical hydraulic conductivity source” [IUZFOPT] was assigned as “Specify vertical hydraulic

conductivity (1); “number of trailing waves” [NTRAIL2] was set to 16 (notice, it ranges between 10 to 20);

“number of wave sets” [NSETS2] was set to 20 since the infiltration rate varies through time, and finally

“route discharge to streams, lakes, or SWR reaches” [IRUNFLG]; “Simulate evapotranspiration”

[IETFLG]; “Print summary of UZF budget terms” [IFTUNIT]; and “calculate surface leakage” inverse of

[NOSURFLEAK] were selected. For Newton Solver the “Head tolerance” [HEADTOL] was set as 0.0001

m and adjusted during model calibration; “Flux tolerance” [FLUXTOL] set as 500 m3day-1 and adjusted

during model calibration; “Maximum number of outer iterations” [MAXITEROUT] 1000; and “Model

complexity” [OPTIONS] set as Complex (Hassan et al., 2014 & Niswonger et al., 2006).

Table 4: D-T extinction depth based on land cover.

D-T Land cover EXTDP [m b.g.s] Adapted literature

Forest 2.5 Shah et al., (2007)

Agriculture and Grass 1.45 Mishra et al., (1997) & Francis et al., (2014)

Bare soil 0.5 Shah et al., (2007) &Francis et al., (2014)

22

The D-T basin streams that flow from the north to the south were simulated by the SFR2 packages. Most

of the D-T streams are perennial and the stream segments are hydraulically connected with groundwater

(Rai et al., 2015). Prior to setting up the model, the map of each stream segments and reaches were prepared

in ArcGIS. Each stream segments were assigned a unique number and the numerical value that was assigned

in each stream segments was arranged from smallest to largest, in order to define the flow direction of the

streams. Then, the generated stream segments were imported into the model and required input data (section

2.4.1) were defined in each stream segments through the SFR2 package. In this package, spatially uniform

values such as “maximum unsaturated zone vertical hydraulic conductivity” [UHC]; “Brooks-Corey

exponents” [EPS]. “Saturated volumetric water content” [THTS]; “Initial volumetric water content” [THTI]

were used the same as in UZF1 package. “Streambed vertical hydraulic conductivity” [STRHC1] was set as

one-tenth of the horizontal hydraulic conductivity and adjusted during model calibration (Niswonger &

Prudic 2005). “Streambed top” [STRTOP] was set to be between 1m to 3.5 m and adjusted during model

calibration; “Streambed thickness” (STRTHICK) set between 0.35 to 0.5 and adjusted during model

calibration; and “stream slope” (SLOPE) set as 0.025 and adjusted during model calibration. “The stage

calculation” [ICALC] set as 1, this value represents the rectangular channel; the stream reaches were set a

width of 2 to 12 m and adjusted during model calibration. The length ranged from 1 km to 20 km in the

cells depending on the generated stream segments in ArcGIS. “Manning’s roughness coefficient for the

channel reaches” (ROUGHCH) and “Bank roughness” (ROUGHCBK) were set as 0.035 and 0.06

respectively. “Tolerance” [DLEAK] was set as 0.0001 m3day-1; “Number of trailing wave increments”

[NSTRAIL] was set to 20, “Maximum number of trailing waves” [NSFRSETS] set as 30, and “Maximum

number of cells to define unsaturated zone” [ISUZN] set to 10. Additionally, “Unsaturated flow

(ISFROPT); “Print streams (ISTCB2) as print flows in listing file”; “Streambed properties” (ISFROPT) as

“Specify some streambed properties by reach (can’t inactivate streams)” were selected.

Aquifers have different properties, which describe the capacities to transfer water through the soil medium.

The properties can vary by several orders of magnitude and show strong spatial variation. In the case of

unconfined aquifer these properties are explained by horizontal hydraulic conductivity (Kh) and specific

yield (Sy). For instance: (1) Sy, the difference of total porosity (n) and specific retention (Sr), is an important

parameter during model calibration. It is defined as “the volume of water that unconfined aquifer releases

by gravity forces from storage per unit surface area of the aquifer per unit decline in the water table”

(Kruseman & Ridder, 1994); (2) Kh is another core calibration parameter. It is defined by Fitts (2002) as the

easy with which water can pass through the soil. The higher Kh the easy water transmits through the medium

and vice versa. During steady-state IHM, thirty-four internally homogenous, uniform Kh zones were defined

based on hydraulic properties (section 2.1.7) and streambed hydraulic conductivity. The value as indicated

in Table 3 were used as a guideline for model calibration. During transient IHM, both Kh and Sy were defined

in the model. The Kh zonas and their value from steady-state IHM was used as an initial value and adjusted

during model calibration. Additionally, spatially uniform Sy was set as 0.24 in the modelled area and adjusted

during model calibration. Spatially invariant Sy was assigned, because the unconsolidated layer of the basin

shows nearly similar sorted aquifer materials (Figure 7).

2.5.6. Boundary conditions

Figure 12 shows the proposed boundary conditions of D-T basin. Two boundary condition type were

defined in the D-T basin. At the north, northeast, and northwest of the study area were no-flow boundaries

due to the presence of hydrological boundaries, i.e. watershed divide at the north and streamlines at the

northeast and northwest of the basin. A no-flow boundary condition was also defined at the bottom of

unconfined aquifer since the Quaternary deposit was considered as an impermeable geological formation.


23

The area defined by no-flow boundaries were assumed to prevent water from entering or leaving the system

(Anderson & William 1992).

In the D-T basin the south, southeast, and southwest areas were bounded by Ocean. The numerical

boundary conditions at the sea coast and the effect of assigning different boundary condition on the

groundwater flow and head distribution were studied by Mulligan et al., (2011) & Pauw et al., (2014) using

SEWAT. According to them, the fresh/seawater boundary is represented in three ways: using time-variable

specified head (CHD); the general-head boundary (GHB) or periodic boundary condition (PBC) packages.

The CHD and GHB packages were supported by MODFLOW-NWT, however, the PBC package was not

supported by MODFLOW-NWT rather in SEWAT. In this study the PBC package was not covered,

interested readers are recommended the above articles. Mulligan et al., (2011) studied “Tidal boundary

conditions in SEWAT” and they found that the GHB have an advantages over CHD or PBC; (1) the CHD

or PBC boundaries reduce the amplitude of heads or create difficulty in matching the simulated and

observed heads; (2) incorrect simulation of fluxes and salt advection into the aquifer (salt advection is not

covered in this study); (3) reduce the high contrast in hydraulic conductivity and “eliminating potential

numerical problems”. Pauw et al., (2014) studied “regional scale impacts of tidal forcing on groundwater

flow in unconfined coastal aquifer”. Emphasizing the need to consider tidal forcing in the coastal aquifer

and that the assigned boundary condition at the fresh/seawater interface governs the amount of

groundwater flow from the groundwater divides to the intertidal area. The groundwater flow and head

distribution are best quantified through GHB conditions. Moreover, the USGS coastal aquifer studies such

as Bakker et al., (2013); Durden et al., (2013); & Masterson et al., (2016) strongly recommended the need

to use GHB to represent the ocean. They also refer that GHB condition is the most widely used numerical

boundary conditions at sea coast. Therefore, in this study, the numerical boundary condition at the sea coast

was assigned as GHB conditions (Figure 12).

Proposed boundary conditions in D-T basin.

Figure 12: Proposed boundary conditions and locations in the D-T basin.

The GHB conditions defined in the model as a polyline objects and the head at that boundaries was

represented as equivalent fresh-water head of sea level. In MODFLOW-NWT, the GHB conductance is

calculated as an average value between the GHB conductance per unit length* “object section intersected

24

length” and GHB condition parameter * “object section intersected length”. These GHB condition

parameter value of 10-4 was used as a recommended value and this was multiplied by user-specified

multipliers to determine the GHB conductance (Niswonger et al., 2011). Furthermore, a separate model was

built using the CHD boundaries and head along the coast was assumed to vary through position and time,

h = f(x,y,t) (Franke et al., 1987). Then, the water balance results of this model was compared with the GHB

model output results.

2.6. Model calibration

Calibration refers to the adjustment of model parameter values to find the best fit with the observations. It

is also called "model fitting" or "history matching" (Barnett et al., 2012). Model calibration is not an easy

task rather complex step because it needs the understanding of advanced mathematics, statistics and

software packages as well as proper characterization of the study area. Calibration of MODFLOW-NWT

model has been done by adjusting model parameters, i.e. hydraulic conductivity (Kh) and specific yield (Sy)

together with UZF1, SFR2 and GHB conductance input variables. In the case of steady-state IHM

calibration was carried out with objectives to minimize differences between observation and model

prediction heads and stream discharges, whereas, in the case of transient IHM, calibration was carried out

with the objective to reproduce pattern of stream discharges and minimize differences between observation

and model prediction stream discharges as well as heads. Barnett et al., (2012) suggested that manual

calibration has an advantage over automatic calibration; in which physically meaningful judgment could be

applied. Consequently, manual/trial and error calibration techniques were carried out in this study for a

better understanding of the real world behavior. A steady-state and transient model were simulated based

on the hydrological conditions for the period of 2009 till 2012.

2.6.1. Steady-state model calibration

Steady-state IHM was built based on the assumption that stream discharges and heads do not change with

time. Steady-state IHM was calibrated based on the average of the hydrological conditions in the study

period from 1st January 2009 to 31st December 2012. Thirty-four internally homogenous, uniform Kh zones

were defined based on pumping test result and streambed hydraulic conductivity. The value as indicated in

Table 3 were used as a guideline for model calibration. These values were assigned in “Upstream Weighting

Packages” [UPW] and adjusted during model calibration till model error assessment criterion was fulfilled -

section 2.6. The steady-state model calibration also adjust input parameters such as the maximum

unsaturated zone hydraulic conductivity (Kvun) in UZF1 package; GHB conductance in GHB package and

also the “Streambed vertical hydraulic conductivity” [STRHC1]; “Streambed top” [STRTOP]; “Stream

width”; “Streambed thickness” (STRTHICK); and “stream slope” (SLOPE) in SFR2 packages (Niswonger

& Prudic 2005). Moreover, all initial models calculations were set into meter and day.

2.6.2. Warming-up period for transient model calibration

One hydrologic year data from 1st January 2009 to 31st December 2009 or 365-time steps data were applied

as warming-up period, in such a way the model possible minimizing the influence of initial state conditions

on the transient simulation (Navarro & Playan, 2007). The model with one-year data was calibrated to assess

the model response to the daily variation of stream flows. Once, the model has response to the warming up

period, the transient model can be built. In this study, contrary to Hassan et al., (2014), the data that was

used in the warming up period was not discarded rather three-years data from 1st January 2010 to 31st

December 2012 were added into it and in total four-year from 1st January 2009 to 31st December 2012 was

considered as a transient model simulation period.


25

2.6.3. Transient model calibration

Transients IHM is applied when pumping wells start up and shut down and/or in response to transient state

variables. In this study, the transient model is required due to the response to transient state variables. The

transient IHM simulation period from 1st January 2009 to 31st December 2012 which is equal to 1461 days

is considered as stress periods and by considering the variation of stream discharges daily time steps were

generated. As quoted by Anderson (1992); Schlumberger (2011); & Fitts (2002), the time step is important

because the size of time steps affects the error in the water balance as well as the stability of the solution. In

a nutshell, the initial conditions in the transient model were adapted from a steady-state model and the

stream discharges value for each stress period was given to MODFLOW-NWT through SFR2 packages.

Then, the Kh and Sy as a calibrated parameter together with other input variables as indicated in steady-state

model calibration were adjusted during model calibration till model error assessment criterion - section 2.6

riches.

2.7. Error assessment and sensitivity analysis

The model should be evaluated after calibration by statistical analysis to test how well the calibrated model

result fits with observed data. Model performance was carried out for both hydraulic heads and stream

discharges. To assess the difference between measured and observed heads three different measure errors

were used. These are the mean error (ME), mean absolute error (MAE) and root mean squared error

(RMSE) calculated by using equation 2.10 to 2.12. In most cases RMSE is used to check the performance

and when RMSE is close to zero then the model has good performance and when RMSE highly deviate

from zero the model has poor performance Anderson and Woessner (1992) and Mason & Hipke (2013).

ni iso hh

nME 1 )(

1 (2.10)

ni iso hh

nMAE 1 )(

1 (2.11)

ni iso hh

nRMSE 1

2)(1

(2.12)

where ho - observed head [m], hs - simulated head [m], n - umber of observation.

The model performance for stream discharges were evaluated using different objective functions, the

selection of objective functions depends on the calibration purpose. Equation 2.13 to 2.15 show the main

objective function as recommended by Nash and Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007);

Moriasi et al., (2007); & Akhtar et al., (2009). These are the relative volumetric error (RVE), Nash-Sutcliffe

efficiency (NS) and overall model performance (Y). RVE is used to evaluate the fitness in terms of volume

under hydrograph. According to them, when the RVE approximate to 0 the model has the best

performance; when the RVE ranges from ± 5 % the model has well performance; when the RVE is between

± 5 % ± 10 %, the model has reasonable performance. NS is used to evaluate the fitness of the shape of

hydrograph, NS between 0.9 and 1 mean that the model performs extremely well. NS between 0.8 and 0.9

means that the model performs very well. NS between 0.6 and 0.8 mean that the model performs reasonably

well. NS below 0.6 means the model has low performance.

100*)(1

1 1

ni obs

ni sim

niobs

Q

QQRVE (2.13)

26

2

1

12

)(

)(1

ni meanobs

ni simobs

QQ

QQNS (2.14)

||1 RVE

NSY

(2.15)

where Qobs - observed stream discharge [m3day-1], Qsim - simulated stream discharge [m3day-1], Qmean - mean

stream discharge [m3day-1], ho - observed head [m], hs - simulated head [m], n - the number of observation.

A sensitivity analysis is the process of varying model input parameters over a reasonable range, i.e. range of

uncertainty in the value of the model parameter and observing the relative change in model response. The

sensitivity analysis in the D-T basin were performed in order to assess the effects of model parameters and

adjusted variables (Section 2.4.5) on the calibrated model. The sensitivity of each model parameters were

established with a percent factor of -30 to 30%. When one parameter analysed, other model calibration

parameters will remain the same. Then, their effects of uncertainty on the calibrated model would be

interpreted.

2.8. D-T basin water balance

As stated earlier, MODFLOW-NWT integrate surface, unsaturated/vadose and saturated zone. It is

working under ModelMuse GUI and coupled with UZF1, and SFR2 (Niswonger et al., 2011; Hassan et al.,

2014; Tian et al., 2015; & Tian et al., 2016). The interaction of the three zone under MODFLOW-NWT

model in the D-T basin can be shown as in Figure 13. The schematic diagram and summary of the water

balance below follows (Hassan et al., 2014).

Water balance components of D-T basin

Figure 13: Schematic diagram of MODFLOW-NWT setup of D-T basin model.

where P - precipitation, I - canopy interception, ETuz - vadose zone evapotranspiration, ETg - groundwater

evapotranspiration, Exfgw - groundwater exfiltration, Rg - gross recharge, qH - hortonian runoff, qD - dunnian


27

saturated excess runoff, qgs - groundwater leakage into the stream, qsg - stream leakage to the groundwater, qg

- lateral groundwater outflow, all units are in [mday-1].

The water balance of D-T basin and the daily flux for surface, unsaturated and saturated zone can be

calculated as below. For the entire basin, the water balance can be calculated as in Equation (2.16).

SqqETP g (2.16)

where ET - total evapotranspiration, q - stream discharge at the basin outlet, and ∆S - change in basin

storage. Total evapotranspiration and change in basin storage can be estimated as in Equation (2.17) and

(2.18) respectively.

guz ETIETET (2.17)

guz SSS (2.18)

where, ∆Suz - the change in storage in the vadose zone and ∆Sg - the change in storage in the saturated zone.

Moreover, the general surface and unsaturated zone water balance of the area can be written as in Equation

(2.19).

uzuzge

eogw

SETRP

PRIExfP

OR uzuzgogw SETRRIExfP (2.19)

where Ro - the total runoff to streams, Pe - actual infiltration rate. Finally, the groundwater zone water balance

is expressed as in equation 2.20 below.

ggwgn

gggssgn

ETExfRR

SqqqR

OR ggwgggssgg ETExfSqqqR (2.20)

where Rn - net recharge to the groundwater. Sophocleous (2005) & Hassan et al.,(2014) stipulated that,

estimating net recharge give an advantage of understanding the dynamics and sustainability of groundwater

resources then estimating gross recharge.

28

3. RESULTS AND DISCUSSION

This chapter describes results and discussion of the three parts, namely data processing, steady-state model

calibration, and transient model calibration.

3.1. Data processing calculation results

The hydro-meteorological calculations were made for the model inputs which including precipitation,

interception rate, infiltration rate, and evapotranspiration. The consistency of the data was checked through

the double mass curve; that the commutative of a given station versus commutative of nearby stations

expected to be linearly correlated as in section 3.1.2. Spatial variability of rainfall data was generated using

the kriging interpolation method.

3.1.1. Filling missed data for precipitation

The correlation coefficient between station Kuta and the nearby stations such as Ubung and Sanglah was

0.72 and 0.75 respectively (Appendix III). Because the relation coefficient is good enough Equation 2.1 was

applied to fill the missed rainfall data. Figure 14 shows the rainfall distribution through the study period of

station Kuta after the missed rainfall data was filled using the CCWM.

Observed and filled rainfall data at station Kuta

Figure 14: Daily rainfall after filling missed data at station Kuta for the years from 2009 to 2013. For the location of

station see Appendix V (A).

3.1.2. Consistency of the precipitation records

The double mass curve technique as described previously – section 2.1.1., was carried out to check the

quality of the meteorological stations. For that reason, high-quality assessment of the recorded rainfall data

for each meteorological station was carried out. In such a way each year from 2009-2012 was treated

independently for consistency check. It was found that fifteen stations (Bedugul, Bonganica, Buagan,

Gadungan, Kedisan, Kuta, Mambal, Pempatan, Pengotan, Sading, Selishan, Tegallalang, Tiyin Gading,

Ubung, and Sanglah) have a very good control and should be treated as reliable data. There are three stations

(Tampaksiring, Rendang, and Klungkung) that show inconsistency in the data. As the scatter plots shown

in Figure 15, the rainfall data for Bedugul and Sanglah stations have linear trends and the data do not present

0

20

40

60

80

100

120

Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13

Rai

nfa

ll (m

md

ay-1

)

RF Observed at Kuta station RF filled at Kuta station


29

a break in slope. In contrary, in the case of Rendang and Tampaksiring stations a break in slopes clearly

shown, therefore the data from the break point were adjusted using Equation 2.2.

A. Double mass curve for station Bedugulu

B. Double mass curve for station Rendang

C. Double mass curve for station Sanglah

D. Double mass curve for station Tampaksiring

Figure 15: Double mass curves of the precipitation gauges [units in mm]. The double mass curve in A & C shows

consistency in the data but B & D shows inconsistency in the data. For the location of stations see Appendix V (A).

3.1.3. Spatial data interpolation of rainfall

The spatial data interpolation was carried out in R-Software. First and for most, hypothesis test, i.e. Ho: β1

= 0 and H1: β1 ≠ 0 (Ho – null hypothesis, H1 - alternative hypothesis, and β1 - elevation) was executed to

examine whether rainfall is dependent on elevation or not. The significance test was performed for daily

rainfall records form the year 2009-2012. A sample significance test result was presented as in Figure 16 and

it was found that; p = 0.23. This p-value corresponds to the F-test (Webster & Oliver, 2007) and when p>α,

means fail to reject the Ho hypothesis. It was concluded that at the α=5% level of significance the elevation

has no significant effect on rainfall distribution. Therefore, it was not critical to include elevation as a

covariate/auxiliary variable for rainfall interpolation. By using the above results, the rainfall type in the area

may be frontal but may not be orographic type of rainfall since, in the orographic type of rainfall, large mass

of air is forced to rise over the mountain ranges and cause heavy precipitation on the windward side. In case

0

500

1000

1500

2000

2500

3000

0 500 1000 1500 2000 2500 3000 3500

Cum

ula

tive

pp

t fo

r B

edugu

l Sta

tio

n

Average cumulative ppt for a group of stations

0

500

1000

1500

2000

2500

3000

0 500 1000 1500 2000 2500 3000 3500

Cum

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tive

pp

t fo

r R

end

ang

stat

ion


0

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2500

3000

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Cum

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tive

pp

t fo

r San

glah

sta

tio

n


0

500

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1500

2000

2500

3000

0 500 1000 1500 2000 2500 3000 3500

Cum

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t fo

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amp

aksi

rin

g st

atio

n


30

of frontal rainfall, the cold air mass from northwest equatorial and the dry air mass from southeast Australia

meet and the warm air is forced to rise over the denser, colder air. As the warm air is forced to rise further

condensation occurs and rain is formed (Ahrens, 2013).

Figure 16: Sample significance test results of rainfall record on January 10, 2009.

The standardized average sample variogram was estimated by averaging the individual sample variogram

(Appendix IV). After several trial and errors, the exponential variogram model was found as the best fit

model (Figure 17). The exponential model has slightly higher nugget effect compared to the partial sill, this

might bring uncertainity in the daily rainfall interpolated map. The model bounded asymptotically and

reached the sill with some effective range (Hengl et al., 2007; Webster & Oliver, 2007; & Zhang et al., 2012).

The effective range of spatial dependency is the distance at which the semi-variance is 95% of the sill. It is

assumed that while correlations may become arbitrarily small at a large distance, they never vanish and that

spatial dependencies never fall to zero. In this case, the effective range is 17772 m; meaning that the model

will reach 95% of the sill at 17772 m.

Model Variogram

Figure 17: Standard model variogram; distance in a unit of [m] and semi-variance in a unit of [m2].

Figure 18, shows the kriged prediction and kriging variance for long-term average rainfall. The results from

ordinary kriging show that it minimized the prediction error variance and smoothing the actual variability

(Sterk & Stein, 1997; Hengl et al., 2007; & Zhang et al., 2012). The yellow and dark blue color as in Figure

18 left, shows the areas with the highest and the lowest rainfall predicted concentrations respectively.

Observations that are closer to each other had higher correlation than the observations that are far apart


31

(Webster & Oliver, 2007). The result shows that the kriged prediction has similar results in the area where

there are dense observations than sparse observations. The point where no data or very few neighboring

points (south-west to north) shows that the predictions are influenced by covariance structure. Location

with no observation alters the value of the outcome of the contribution of neighboring measured values to

the prediction.

Kriging variance is dependent on the location of prediction, location of observation point and on the

variogram model (Webster & Oliver, 2007). The kriging variance was less in the locations where there is

rain gauge observation and high in area where there is no rain gauge observation (Figure 18, right). Dark

blue color shows low kriging variance while orange to yellow has high kriging variance. Thus it can be

concluded that areas having a high kriging variance are those areas that have observation far apart (south-

west to north) whereas areas having low kriging variance are those areas that have observation close to each

other. Due to the presence of lack of a number of observation points outside of the D-T basin, there is a

substantial increase in prediction uncertainty, thereby increasing the kriging variance. Moreover, it is clearly

seen in the output that the kriging variance is almost the same for each individual day. This is because that

the ordinary kriging method used just similar variogram.

Figure 18: Kriged prediction and Kriging variance of D-T basin for long-term average rainfall from 01/01/2009 to 01/01/2012 [unit – mday-1].

3.1.4. Interception and infiltration rate

The spatially variable interception rate of D-T basin was generated using the land use map of the area. The

land use map that was collected from office locally called “BIG”. It shows that the D-T basin is mainly

covered by agriculture and it has interception rate of 14.4% (Figure 5 & 19, A). Similarly, the interception

rate of 22.4% and 6.5% was assigned for forest, grass cover respectively. Zero percent of interception rate

was assigned for buildings and bare soil. The spatiotemporal infiltration rate was calculated from

interception and rainfall map - section 2.1.3. Mathematically, the infiltration rate was calculated as Kriged

prediction rainfall – (interception rate * Kriged prediction rainfall). This can be executed either in ArcGIS

spatial analysis tools (Figure 19, B) or the mathematical formula can be written in MODFLOW-NWT.

Consequently, the latter case was used and the spatially variable interception rate and rainfall map were

imported independently into the model to maintain the mathematical expression.

32

A. Spatially variable interception rate

B. Spatially variable infiltration rate

Figure 19: Spatially variable interception (A) and infiltration rate (B) of D-T basin.

3.1.5. Potential Evapotranspiration [PET]

Due to the presence of low number of microclimatic stations (Figure 3), the correlation between Tmax, Tmin,

Tmean for the two stations namely called station Sanglah and Kuta was carried out (Figure 20). A good

coefficient of determination (R2) was found between maximum, minimum and mean temperature of the

two stations. Because of this finding the ETo that was calculated using FAO Penman-Monteith method was

considered as an average of the two stations for the entire study area. A detail explanation of ETo calculated

using FAO Penman-Monteith was shown in section 2.1.3.

Figure 20: Temperature coefficient of determination for Sanglah and Kuta stations.

R² = 0.69

15

20

25

30

35

40

15 20 25 30 35

San

glah

_st

atio

n

Kuta_station

Max Temp. 10m [ºc]

R² = 0.32

15

20

25

30

35

40

15 20 25 30 35

San

glah

_Sta

tio

n

Kuta_station

Min Temp. 10m [ºc]

R² = 0.61

15

20

25

30

35

40

15 20 25 30 35

San

glah

-sta

tio

n

Kuta_station

Mean Temp. 10m [ºc]


33

Spatially variable but temporally invariable crop coefficient, Kc and extinction depth, EXTDP were assigned

based on the dominant vegetation of the D-T basin in a similar way as interception rate (Figure 21). The

assigned crop coefficient and extinction depth were adapted from different literature (Table 2 and Table 4).

Finally, PET was calculated as the product of spatially invariable but temporally variable ETo and spatially

variable but temporally invariable crop coefficient (Kc) in MODFLOW-NWT as in Equation 2.4.

A. Crop coefficient

B. Extinction depth

Figure 21: Spatially variable crop coefficient (A) and extinction depth (B) for D-T basin.

Figure 22 shows the relation between rainfall, infiltration, interception and PET. The maximum and

minimum PET value of 6.71 mmday-1 and 1.82 mmday-1 was found for the entire simulation period. The

calculated PET was proportional to temperature (Figure 4). Therefore, PET was reasonable to be applied

in the model as a driving force. The average interception loss by the forest, agriculture and grassland were

0.085, 0.62, 0.014 mmday-1 respectively. High infiltration rate was observed during the periods with a high

rate of precipitation, the estimated infiltration rate was the highest in January 2009 with 94.9 mmday-1 (Figure

22). The estimated infiltration rate ranged from 0 to 94.9 mmday-1 with an average value of 5.7 mmday-1.

Long-term average rainfall, interception, infiltration and PET

Figure 22: Average Rainfall (P), Infiltration rate (Pr), Interception rate (I) and Potential evapotranspiration (PET) for four hydrological years from 2009 to 2012.

0

1

2

3

4

5

0

20

40

60

80

100

1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13

PE

T

P, I,

an

d P

r

P (mm/day) Pr (mm/day) I (mm/day) PET (mm/day)

34

3.1.6. Consistency of stream discharge

The consistency of stream discharges data was carried out in the same way as precipitation records. The

double mass curve between one stream discharge data and average cumulative discharge of group stations

was generated for each stream gauge. It was found that thirteen out of sixteen stations namely called Yeh

Matan, Yeh Hoo, Yeh Empass, Tukad Penat, Tukad Oos, Tukad Petan, Sangsang, Melangit, Tukad Jinah,

Tukad Unda-cegeng, Yeh Otan, Yeh Aba, and Pekerisan have a very good consistency and should be treated

as reliable data. As in the scatter plot shown in Figure 23, the sample double mass curve for Melangit and

Yeh Hoo stations have a linear trends and it does not present a break in slope. The frequency distribution

graphs were also constructed for each station to show normality of the stream gauging records (Figure 23).

The results show those 13 stream discharge records have the uniform distribution but skewed to the right.

However, the log transform gives normal distribution (Appendix V, C). Additionally, the consistency of the

records was checked based on the relation between each stream flow against rainfall recorded at the

upstream (Figure 24). The result shows a few outliers, but in general the relation between stream flow and

the upstream rainfall record gives a logical statement that the stream flow increased when the rainfall

increases and the opposite is also true. Therefore, discharge for the above records were reasonable to be

applied in the model as a state variable.

A. Double mass curve for station Melangit

B. Double mass curve for station Yeh Hoo

C. Frequency distribution for station Melangit

D. Frequency distribution for station Melangit

0

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600

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Cum

ula

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Q f

or

Yeh

Ho

o s

tati

on



35

Figure 23: Sample double mass curve and frequency distribution for the stream gauge discharge data [Q- stream

discharge in m3sec-1]. For the location of station and log transform see Appendix V.

Nevertheless, the remaining three streams gauge data, i.e. Balian, Ayung Buangga, and Badung Hilir show

inconsistency in the data (Appendix V; D, E and F). It was difficult to adjust these data since, the double

mass curve was quite erratic and there was no clear relation to apply equation 2.2. Apart from that, the graph

between stream flow and rainfall recorded at the upstream was unrelated. Such error may be due to exposure,

gauge location, or observation method. Due to the above facts, those stream gauges are not used for model

calibration rather incorporated in the model to assess the model response. Therefore, in this study only 13

out of 16 stream gauge records were used for model calibration and the remaining 3 included to see the

model response.

A. Relation between rainfall and stream discharge at station Yeh Hoo

B. Relation between rainfall and stream discharge at station Tukad Petanu

Figure 24: Relation between rainfall and stream discharge. The oval shape indicates uncertainty on the relation between

measured stream flow and rainfall pattern. [RF – rainfall and Q – stream discharge]. For the location of stream gauging

stations see Appendix V.

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Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13

Q [

m3se

c-1]

RF

[m

md

ay-1

]

Gadungan_RF Yeh_Hoo_Q

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Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13 Jul-13 Jan-14

Q [

m3se

c-1]

RF

[m

md

ay-1

]

Tegallalang_RF Tukad_Petanu_Q

36

3.2. Steady-state model calibration

This was addressed into four main parts, namely: (1) calibration head and error assessment, (2) calibrated

stream discharge, (3) hydraulic conductivity, and (4) water budget of the steady-state simulation.

3.2.1. Calibrated head and error assessment

The assigned hydraulic conductivity value has been adjusted until the simulated heads matched with

observed heads. The steady-state observed and simulated heads were tested for correlation using a scatter

plot and by calculating R2 (Figure 25). A quantitative comparison of the head data in all the observation

points indicates a good match between the simulated and observed head values. The scatter plot exhibits a

random distribution and fall close to the 1:1 solid line, which indicates a reasonable match between observed

and simulated heads. The result is in the line with the Hill (1998) suggestion, he indicated that when the

observed and simulated discharge plotted they should fall close to a 1:1 solid line and the R2 should be ≥

0.9.

The coefficient of determination (R2) between observed and simulated heads

Figure 25: Relationship between simulated and observed heads in the D-T basin during steady-state IHM for the year

from 2009 to 2012.

Assessment of errors was based on the mean error (ME), mean absolute error (MAE), and root means

square error (RMSE) calculated from equation 2.10, 2.11, and 2.12 respectively. The values of ME, MAE,

and RMSE are respectively equal to 0.1 m, 0.41 m, and 0.52 m with the associated error shown in Table 5.

The water table in the D-T basin varies between 2.5 m a.s.l. to 361.5 m a.s.l. which makes the total head loss

of 359 m in the model area. The steady-state model calibration result was in line with the Anderson and

Woessner (1992) and Mason & Hipke (2013) model error criteria, where mean absolute error is less than

2% of the total head changes (7.2 m); the maximum absolute value of model residuals (0.9 m) should be less

than 10% of the total head changes (35.9 m); the root mean square error is less than 2% of the total head

changes (7.8 m); the ratio of RMSE to the total head difference is 0.11% which is also lower than the 10%

of total head difference (35.9 m). Besides, the model also satisfied the suggested by Anderson and Woessner

(1992) when RMSE closer to zero (0.52 m) the model has reasonable performance.

Table 5: Observed and simulated head with calculated error assessment for 11 piezometers, Hobs – Observed head,

Hsim – Simulated head [units – m].


37

Observation

Points Latitude Longitude Hobs HSim

Hobs -

Hsim

|Hobs-

Hsim|

[Hobs -

Hsim]²

WL1 8°43'43.65"S 115°10'36.44"E 2.52 1.94 0.58 0.58 0.34

WL3 8°40'48.55"S 115°13'50.04"E 5.38 6.18 -0.80 0.80 0.64

WL5 8°36'58.96"S 115°05'47.79"E 12.34 12.33 0.01 0.01 0.00

BOL13 8°33'19.18"S 115°02'14.96"E 10.20 10.27 -0.07 0.07 0.00

WL4 8°38'53.06"S 115°13'23.01"E 27.27 27.56 -0.29 0.29 0.08

WL7 8°34'19.78"S 115°03'37.99"E 74.61 75.47 -0.86 0.86 0.74

WL8 8°33'41.88"S 115°16'27.71"E 98.90 99.20 -0.30 0.30 0.09

WL10 8°30'14.47"S 115°10'45.12"E 178.09 177.51 0.58 0.58 0.34

WL11 8°29'21.68"S 115°24'09.22"E 227.77 227.99 -0.22 0.22 0.05

BOL5 8°26'14.57"S 115°01'43.26"E 361.50 361.45 0.05 0.05 0.00

WL2 8°42'24.68"S 115°13'36.69"E 3.79 2.97 0.82 0.82 0.67

Sum -0.55 4.53 2.95

ME MAE RMSE

-0.05 0.41 0.52

Median -0.07 0.30 0.09

STD 0.54 0.33 0.29

Min -0.86 0.01 0.00

Max 0.82 0.86 0.74

Figure 26 shows the potentiometric surface of D-T basin for steady-state IHM. According to the

groundwater heads results, the higher heads value start from the north and the lowest heads are in the south

of the study area. Consequently, the flow direction is from the north to south.

Figure 26: Potentiometric surface with location of heads, stream segments of the D-T basin during steady-state IHM. The stream segments with black lines indicates those that were not included during model calibration. Heads in m a.s.l.

38

The potentiometric surface results of this study was compared with Nielsen & Widjaya (1989). Generally

speaking, the potentiometric surface of this study followed the general trend of their analytical results and

the hydraulic head values near coast exhibit similarity. However, the pattern of head distribution in the

current study is influenced by the SW-GW interaction. The streamlines that are perpendicular to the

equipotential lines follow an irregular line, this shows the coupling between SW-GW. Comparatively, the

Nielsen & Widjaya (1989) studies show non-irregularity in streamlines (Figure 8). Finally, the water table

depth was compared to the topographic surface to check if it did not rise above the ground surface. The

water table depth, which is the difference of Model Top or DEM and model simulated head, was everywhere

below the ground surface.

3.2.2. Calibrated stream discharges

Calibration of stream discharge has been done simultaneously with groundwater heads. The average values

of stream flows were calibrated in the steady-state model (Table 6). The task of stream flow calibration was

complicated due to the presence of 13 stream gaging stations, besides many parameters involved.

Assessment of errors was based on the relative volumetric error (RVE), Nash-Sutcliffe efficiency (NS), and

overall model performance (Y) calculated from equation 2.13, 2.14, and 2.15 respectively. The steady-state

model stream flow calibration result was within the limit of model error criteria as indicated by Nash and

Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007); Moriasi et al., (2007); & Akhtar et al., (2009).

The value of NS and RVE were equal to 0.86 and 23.4 respectively. The overall steady-state model

performance was 70%. Therefore, the model has reasonable performance.

Table 6: Observed and simulated stream discharge with calculated error assessment for 16 gauges: Qobs –observed stream discharge; and Qsim – simulated stream discharge [unit - m3day-1]. Stations that are highlighted by red colour indicate those station that are not used for model calibration and show the model response for those stations.

Station Latitude Longitude Qobs Qsim RVE

Yeh Empas 8°34'44.25"S 115°05'11.22"E 74,963.00 52,399.50 0.301

Tukad Petanu 8°31'26.49"S 115°17'15.64"E 175,055.20 160,357.30 0.084

Melangit 8°33'10.93"S 115°21'54.48"E 127,639.90 39,500.70 0.691

Yeh Hoo 8°29'15.96"S 115°04'46.26"E 155,918.40 222,631.20 -0.428

Yeh Mata 8°27'42.69"S 115°02'36.43"E 132,288.20 137,879.50 -0.042

Tukad Oos 8°33'25.08"S 115°15'20.73"E 107,896.70 534,283.00 -3.952

Sangsang 8°33'13.29"S 115°20'47.97"E 103,104.40 137,410.10 -0.333

Tukad Jinah 8°29'42.09"S 115°22'59.21"E 89,363.90 49,861.10 0.442

Tukad Penat 8°31'06.55"S 115°12'01.88"E 363,702.30 313,330.10 0.138

Tukad Unda 8°29'11.11"S 115°26'08.18"E 208,907.40 303,573.10 -0.453

Balian 8°27'23.44"S 115°00'12.94"E 544,448.80 1,077,433.50 -0.979

Yeh Otan 8°28'22.15"S 115°01'48.37"E 136,354.30 150,918.40 -0.107

Badung Hilir 8°38'57.85"S 115°12'44.89"E 1,056,475.60 333,563.90 0.684

Pekerisan 8°23'51.75"S 115°19'09.33"E 118,150.10 102,296.30 0.134

Ayung Buangga 8°25'33.59"S 115°13'55.11"E 9,716,965.30 6,385,364.80 0.343

Yeh Aba 8°34'04.29"S 115°04'18.22"E 204,233.30 194,908.20 0.046

Mean 832,216.68 637,231.92 -0.214

Calculated NS RVE Y

0.86 23.4 69.6


39

3.2.3. Hydraulic conductivities

Initially, 34 hydraulic conductivity zones were assigned in the model. The zones consisted of similarly sorted

sediments in which a given sedimentary structure was dominant. Then, through the calibration process, the

number of zones increased to 78 hydraulic conductivity zones and the spatial distribution of Kh was shown

as in Figure 27. The value of Kh varied from 0.01 to 900 mday-1 in the D-T basin unconfined aquifer. Lower

Kh was observed over the streambeds ranging from 0.01 to 0.8 mday-1. Aquifer Kh varied over several orders

of magnitude and show strong spatial variation. Higher Kh was obtained in the southern and lower Kh in

the northern part of the modeled area. Based on Kruseman and de Ridder (1971), the geological class of the

D-T basin varied from medium sands to gravel; where sand and gravel aquifer materials were found close

to the sea, coarse to medium sand materials were found at the center and over the mountain range. The

result of aquifer Kh agrees with the geological cross section map of the D-T basin that was found from

locally called "KESDM" (Figure 11). The cross section map shows that sand and gravel material was

deposited at the south Sanur, whereas sand and gravel together with tuff, lava and breccias were deposited

at the north Denpasar.

Figure 27: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after steady-state IHM [unit - mday-1].

3.2.4. Water budget of the steady-state simulation using GHB conditions at the sea coast

The water budget of the steady-state simulation using the GHB conditions at the sea coast was presented

below. The GHB conductance has a large effect on the water budget as confirmed by its sensitivity analysis

– section 3.2.6. After several trial and error, a conductance of 0.1 m2day-1 per unit length was used as an

optimal value by considering the model error as small as possible and to get reliable groundwater budget of

D-T basin. Afterward, in the GHB package the optimal conductance 0.1 m2day-1 per unit length multiplied

with defined “object section intersected length” so, the model converted it into unit of m2day-1 as in

Appendix VI, A.

Water balance of the entire model

The daily average water balance of D-T basin was calculated (Table 7) by applying equation 2.16 to 2.20.

Rainfall was the only sources of inflow to the entire system. The percent contribution of the outflow

40

components from the entire system was; 17.1% of sub-surface evapotranspiration; 12.8% of interception

loss; 65.6% of stream discharge at the outlet, and 4.7% of lateral groundwater outflow. The percent

discrepancy of 0.05 indicates the closer of the water balance for the entire model. In steady-state IHM,

groundwater evapotranspiration, ETg and unsaturated zone evapotranspiration, ETun is not distinguish

clearly, rather the model simply gives as sub-surface evapotranspiration demand. However, in the case of

transient IHM the two components considered separately (Niswonger et al., 2006).

Table 7: Total water balance of D-T basin at steady-state IHM [mmday-1].

Budget component IN Budget component OUT

Precipitation (P) 6.72 Subsurface evapotranspiration (ETss) 1.21

Interception loss (I) 0.91

Stream discharge at the outlet (q) 4.65

Lateral groundwater outflow (qg) 0.32

TOTAL 6.72 TOTAL 7.10

IN-OUT -0.35

PERCENT DISCREPANCY -4%

Water balance of land surface and unsaturated zone

The land surface and unsaturated zone water balance were calculated using Equation 2.19 in Table 8. In the

inflow, component precipitation contributed the major part 85.1% and GW exfiltration 14.9% of the total

amount of water for land surface and unsaturated zone. In the outflow component, the major part was gross

recharge 61.1%, interception loss 11.5%, and total runoff 27.4%. The water balance at the land surface and

the unsaturated zone is closed with the percent discrepancy of 0.001.

Table 8: water balance of land surface and unsaturated zone [mmday-1].


Precipitation (P) 6.72 Interception loss (I) 0.91

GW exfiltration (Exfgw) 1.17 Gross recharge (Rg) 4.82

Total runoff (Ro) 2.16


IN-OUT 0.01

PERCENT DISCREPANCY 0.1%

Water balance of the saturated zone

The groundwater/saturated zone water balance reflects the long-term average from 1st January 2009 to 31st

December 2012 water flow into and out of the D-T basin. The components of water balance that flow into

the saturated zones are gross recharge (Rg) and stream leakage to the groundwater (qsg). The components of

water balance that flow out of the saturated zones are groundwater evapotranspiration (ETg), groundwater

exfiltration (Exfgw), groundwater discharge to the streams (qgs), and lateral groundwater outflow (qg). The

saturated zone water balance was calculated using Equation 2.20 as in table 9. The gross recharge constituted

nearly all inflow to saturated zone 95%, the remaining 5% of inflow contributed by stream leakage to

groundwater. The percent contribution of groundwater outflows: sub-surface evapotranspiration 23.7%,

GW exfiltration 22.6%, groundwater flow to streams 47.8%, and lateral groundwater outflow 6.1%.


41

On average, the volumetric budget for groundwater discharge to the streams, qgs was higher than the

groundwater recharge by the streams, qsg. This shows that the interaction of the GW-SW is stream gaining

in most stream reaches and losing in few reaches. This result agrees with the Rai et al., (2015) suggestion,

who stated that stream gaining conditions is expected since most of the streams in Bali Island are perennial.

Table 9: Water balance of groundwater in steady-state IHM [mmday-1].


Stream discharge to GW (qsg) 0.25 Subsurface evapotranspiration (ETss) 1.23

Gross recharge (Rg) 4.82 GW exfiltration (Exfgw) 1.17

Stream discharge from GW (qgs) 2.47



IN-OUT -0.10

PERCENT DISCREPANCY -2%

The long term average net recharge was 2.44 mmday-1 as calculated using Equation 2.20. This value is 50.6

% of UZF recharge and 36.3% of average rainfall. The final findings of this study during the steady-state

IHM was compared with Nielsen & Widjaya (1989) and Artabudi (2012). They estimated a net recharge

value of 600 – 650 mmyear-1, whereas in this study the net recharge was 890 mmyear-1. The final finding of

this study was slightly higher than their findings. This may be due to simplification of UZF1 package in the

steady-state IHM, the package assigned the UZF recharge equals to infiltration rate. In the steady-state

model the UZF1 package does not consider storage change in either unsaturated or saturated zone and also

there is no clear difference between unsaturated zone evapotranspiration, ETun and groundwater

evapotranspiration, ETg.

The schematic representation shows the overall volumetric water budget of D-T basin (Figure 28). The

result shows the summary of the annual average flows of each water budget components for the

unconsolidated aquifer.

Figure 28: Schematic representation volumetric water budget in case of steady-state IHM for the entire model of D-T

Basin [ All units - mmyear-1].

42

3.2.5. Spatial variability of groundwater fluxes

The spatial variability of groundwater fluxes shown in Figure 29 to Figure 30. The steady-state subsurface

evapotranspiration, ETss loss varies spatially since the crop coefficient, Kc and extinction depth, EXTDP

varies through land covers. The ETss ranges from 0.0003 mmday-1 to 0.0047 mmday-1. Lower ETss was

observed in an area where there is bare soil since low Kc and EXTDP assigned whereas higher ETss demand

was observed in forest cover due to higher Kc and EXTDP assigned.

Figure 29: Spatially variable ETss of D-T Basin for calibrated steady-state IHM [Unit – mday-1].

Figure 30 shows that the distribution of groundwater gross recharge for the steady-state IHM. It was equal

to the actual infiltration rate because UZF1 package in MODFLOW-NWT over simplified the steady-state

model and gave zero unsaturated and saturated zone storage besides, no clear distinction between ETg and

ETun. The maximum gross recharge was 0.011 mmday-1 at the north, northeast of the modeled area and

minimum gross recharge was 0.0026 mmday-1 at central, south-east of the modeled area. The result shows

that the groundwater gross recharge highly influenced by the spatial distribution of rainfall and kriging

variance –section 3.1.3. Lower recharge rate that was observed may also be due to the modeled cell were

saturated and excess infiltration rate was routed as Hortonian or Dunnian flow.


43

Figure 30: Spatially variable Rg map for calibrated steady-state IHM in D-T Basin [Unit – mday-1].

3.2.6. Effects of changing GHB conductance upon lateral groundwater outflow to the ocean

Intitally, the boundary at the sea coast was defined by GHB conditions and an arbitrary value was assigned

as GHB conductance. Then, the value was calibrated through trial and error method. During the process

the effect of GHB conductance on the water budget was examined and presented as in Figure 31. The result

depicts that the head dependent boundary rate/lateral groundwater outflow increase when the GHB

conductance increases. The percent contribution of lateral groundwater outflow was more than 80% of the

incoming rainfall when the GHB conductance was higher than 12.5 m2day-1 per unit length. The remaining

20% contributed to subsurface evapotranspiration, stream leakage, and groundwater exfiltration.

Consequently, lower GHB conductance was used to get a reasonable water budget of D-T basin – section

3.2.4.

Figure 31: The relationship between GHB conductance and head dependent boundary flow rate. The GHB conductance that masked by orange circle indicate the final value that was selected. In MODFLOW-NWT the GHB conductance is calculated based on polyline objects as in Section 2.4.6.

In this study, the water budget result using GHB conditions – section 3.2.4 and CHD boundaries –section

3.2.7 were compared and similar water budget results were found at a GHB conductance of 12.5 m2day-1

per unit length. This indicates the non-uniqueness of the D-T model. However, at a low GHB conductance

the two models show quite large difference on the groundwater budget.

3.2.7. Water budget of the steady-state simulation using CHD boundaries at the sea coast

Water balance of the entire model

The daily average water balance of D-T basin for the entire area was calculated as in Appendix VII (B).

From the total incoming rainfall, the percent contribution of the outflow components was; 3.8% of sub-

0

2500

5000

7500

10000

12500

15000

17500

20000

22500

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

Hea

d d

epen

det

bo

un

dar

y ra

te p

er g

rid

cel

l [m

3 m-1

]

GHB Conductance [m2day-1 per unit length]

Head dependent Boundary rate per grid cell VS GHB conductance per unit length

44

surface evapotranspiration; 13.9% of interception loss; 10.3% of stream discharge at the outlet, and 71.9 %

of lateral groundwater outflow.

Water balance of land surface and unsaturated zone

The calculated water balance of the land surface and unsaturated zone Appendix VII (C) also shows. In the

inflow, component precipitation contributed 89.3% and GW exfiltration 10.8% of the total amount of water

for land surface and unsaturated zone. In the outflow component, the prime part was gross recharge 81.2%,

interception loss 12.1%, and total runoff 6.8%.

Water balance of the saturated zone

Table 3.6 shows the saturated zone water balance was calculated using Equation 2.26. The gross recharge

constituted nearly all in flow to saturated zone, 95.4%, and the remaining 4.6% of inflow contributed by

stream leakage to groundwater. Sub-surface evapotranspiration 3.8%, GW exfiltration 12.7%, groundwater

flow to streams 10.7 %, and lateral groundwater outflow took the major part 72.9 %. The volumetric budget

for stream leakage into the groundwater was slightly higher than the stream leakage out of the groundwater.

The result confirmed that the D-T streams gaining in some reaches and losing in other reaches.

Table 10: Water balance of groundwater in steady-state condition [mmday-1].


Stream discharge to GW (qsg) 0.27 Sub-surface evapotranspiration (ETss) 0.22

Gross recharge (Rg) 5.54 GW exfiltration (Exfgw) 0.74

Stream discharge from GW (qgs) 0.61



IN-OUT -0.01

PERCENT DISCREPANCY -0.2%

The steady-state net recharge as equation 2.26 was 4.58 mmday-1. This value is 82.7% of gross recharge and

75.3% of long-term average precipitation. The discrepancy between the inflow and outflow was within the

limit of the acceptable range, ≤ 0.2 % (Weldemichael, 2016). Hence, the numerical model error is negligible

and the water balance of the model is closed.

In the current study, groundwater budget results using the GHB condition and CHD boundaries at the sea

coast were compared. It was found that that the assigned CHD boundaries overestimated lateral

groundwater outflow and underestimated the percent contribution of groundwater evapotranspiration,

stream leakage, and groundwater exfiltration (Table 10). However, the GHB conditions control the lateral

groundwater outflow and comparatively give a reasonable water budget result of D-T basin. This finding is

in the line with Bakker et al., (2013); Durden et al., (2013); Mulligan et al., (2011); Pauw et al., (2014); &

Masterson et al., (2016) – section 2.4.6. They emphasise that GHB condition is the most widely used

boundary condition at the sea coast and it has several advantages than CHD boundaries: (1) reduced the

high contrast in hydraulic conductivity and “eliminating potential numerical problems” (2) the CHD

boundaries reduced the amplitude of heads or arise difficulty in matching the simulated and observed heads;

(3) the CHD boundaries gave incorrect simulation of fluxes and salt advection into the aquifer, salt advection

is not covered in this study; (4) CHD boundaries at the sea coast have low control on the amount of

groundwater flow from the groundwater divides to the ocean.


45

3.2.8. Sensitivity analysis

Sensitivity analysis was conducted in the steady-state IHM with the aim of assessment of groundwater in

the basin. The response of the model hydraulic head was assessed by varying model parameters as shown

in Figure 32. It was observed that the Kh and Kvun parameters showed a higher response to the model. The

Kh and Kvun follow a similar trend of the model response. The model response increase for both high and

low Kh and Kvun values. But when the two parameters are compared, the model response was higher to the

variation in the Kh parameter than the Kvun.

A. Sensitivity of Kh upon heads

B. Sensitivity of Kvun upon heads

Figure 32: Sensitivity of model for horizontal hydraulic conductivity (A) & Vertical unsaturated zone hydraulic conductivity (B).

The parameter and driving forces, i.e. infiltration rate, PET, extinction depth [EXTDP], extinction water

content [EXTWC], the Brooks-Corey-Epsilon [BC] and Saturated water content [WCsat] in the UZF1

packages were examined (Figure 33 and 34). It was observed that the infiltration rate, PET, and EXTDP

have a higher response to the model while the EXTWC, BC, and WCsat hardly showed any response. The

model was highly sensitive to infiltration rate to both higher and lower values, whereas in the case of PET

and EXTDP the model response higher to a lower value and lower response to higher values.

C. Sensitivity of EXTDP upon heads

D. Sensitivity of infiltration rate upon heads

E. Sensitivity of EXTWC upon heads F. Sensitivity of PET upon heads

0.2

0.4

0.6

0.8

1

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]

Sensitivity change factor

Kh

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

0.60

0.61

0.62

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


Kvun

0.5278

0.5280

0.5282

0.5284

0.5286

0.5288

0.5290

0.5292

0.5294

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


EXTDP

0

2

4

6

8

10

12

14

16

18

20

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


Infiltration rate

46

Figure 33: Sensitivity of model for UZF1 package parameter and driving forces: (C) extinction depth, (D) infiltration rate, (E) extinction water content, (F) potential evapotranspiration.

In general, the model is more sensitive to parameters such as Kh, Kvsun, and EXTDP and insensitive to

EXTWC, BC, and WCsat. Those the sensitive parameters are good for model calibration whereas the

insensitive may create uncertainty in the model. Therefore, more effort is required to get reliable information

about the insensitive parameters.

G. Sensitivity of BC upon heads

H. Sensitivity of WCsat upon heads

Figure 34: Sensitivity of model for (G) Brooks-Corey-Epsilon & (H) saturated water content.

3.3. Transient model calibration

Calibration of transient IHM was carried out with objectives to reproduce the pattern of stream discharges

and minimize the difference between observed and simulated stream discharges as well as heads. Due to

lack of groundwater fluctuation data, the model does not include calibration of the daily variation of heads.

It is also not constrained by groundwater abstractions. Therefore, the result of this model should be used

with caution in case future studies incorporating daily variation of groundwater heads and abstraction.

Before the transient model calibration, one-year data from 1st January 2009 to 31st December 2009 or 365

daily stress period was used as a warming period. The model with one-year data was calibrated to assess the

model response to the daily variation of 13 stream discharges. This model has used the final steady-state

heads and Kh’s as initial heads. Additionally, Sy was assigned as 0.24 for the entire modeled area – as in

section 2.4.5. At the first try, the model response was not good enough, but then the Kh, Sy and other

parameters in UZF1, as well as SFR2 packages, were adjusted. After several trial and error, the model shows

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


EXTWC

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

0.60

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


PET

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


BCE

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-30% -20% -10% 0% 10% 20% 30%

RM

SE

[m

]


WCsat


47

a reasonable response to the daily stream discharges. Then, the transient model run for four-years simulation

periods. In this study, contrary to Hassan et al., (2014), the data that was used in the warming up period was

not discarded rather three-years data from 1st January 2010 to 31st December 2012 were added into it and

in total four-year from 1st January 2009 to 31st December 2012 was considered as a transient model

simulation period. In a nutshell, the transient IHM has considered daily stream discharge records from 1st

January 2009 to 31st December 2012, this simulation period is equal to 1461 daily stress periods. The

transient model calibration having 13 streams, 11 heads and several parameters in UZF1and SFR2 packages

is complicated and time-consuming process besides, most of the input data such as rainfall, interception

rate, PET, EXTDP were spatiotemporally variable. Each calibration takes more an hour and produced huge

output files ~ 4 GB. Notepad++ was used to open the file because such file could not be open through

standard Notepad.

3.3.1. Calibration heads and error assessment

As stated earlier, the groundwater fluctuation data available neither daily nor monthly rather monitoring

records show one record per year. Hence, the final transient-state heads calibration was examined for

correlation with the observed heads using the actual date of monitoring heads (Table 11). The result shows

a good match between the simulated and observed head values since the heads fall close to the solid line

(Figure 35). The transient-state heads calibration result was in the line with Hill (1998) suggestion, who

stated based on the scatter plot that the observed and simulated heads should fall close to a line with a slope

of 1:1 and the R2 should be greater than 0.9.

Figure 35: Relationship between simulated and observed heads for the transient IHM of 11 observation points.

Table 11 shows the mean error (ME), mean absolute error (MAE), and root means square error (RMSE)

calculated from equation (2.10), (2.11), and (2.12) respectively. The values of ME, MAE, and RMSE are

respectively equal to -0.22 m, 0.57 m, and 0.6 m. The water table in the D-T basin varies between 2.5 m a.s.l.

to 361.5 m a.s.l., which makes the total head loss of 358.9 m in the model area. The transient model

calibration result fits Anderson & William, (1992) and Mason & Hipke (2013) model error criteria, where

mean absolute error is less than 2% of the total head changes (7.2 m); the maximum absolute value of model

residuals (0.9 m) should be less than 10 % of the total head changes (35.9 m); the root mean square error is

less than 2% of the total head changes (7.2 m); the ratio of RMSE to the total head difference is 0.17%

which is also lower than the 10 % of total head difference (35.9 m). The model performance with respect

to simulating groundwater heads is not as good as for the steady-state simulations possible because the

model was not calibrated sufficiently.

48

Table 11: Observed, Hobs and simulated head, Hsim with calculated error assessment for 11 piezometers. [Units – m].

Observation Points

Latitude Longitude Date of observation

Hobs Hsim Hobs.- Hsim.

|Hobs-Hsim|

[Hobs. - Hsim.]²

WL1 8°43'43.65"S 115°10'36.44"E 5-May-09 2.5 2.4 0.1 0.1 0

WL3 8°40'48.55"S 115°13'50.04"E 8-Jun-09 5.4 4.8 0.6 0.6 0.4

WL5 8°36'58.96"S 115°05'47.79"E 4-Sep-09 12.3 12.0 0.4 0.4 0.1

BOL13 8°33'19.18"S 115°02'14.96"E 13-May-09 10.2 11.1 -0.9 0.9 0.8

WL4 8°38'53.06"S 115°13'23.01"E 14-May-11 27.3 27.5 -0.2 0.2 0.1

WL7 8°34'19.78"S 115°03'37.99"E 9-May-12 74.6 75.0 -0.4 0.4 0.2

BOL3 8°33'41.88"S 115°16'27.71"E 21-Feb-09 176.8 176.0 0.7 0.7 0.6

WL10 8°30'14.47"S 115°10'45.12"E 31-Dec-09 178.1 176.8 1.3 1.3 1.6

WL11 8°29'21.68"S 115°24'09.22"E 15-May-09 227.8 227.4 0.4 0.4 0.1

BOL5 8°26'14.57"S 115°01'43.26"E 12-May-12 361.5 362.1 -0.6 0.6 0.3

WL2 8°42'24.68"S 115°13'36.69"E 6-May-11 3.8 3.2 0.6 0.6 0.4

Sum 1.9 6.2 4.5

ME MAE RMSE

0 0.1 0.6

Median 0.4 0.6 0.3

STD 0.6 0.3 0.5

Min -0.9 0.1 0

Max 1.3 1.3 1.6

Figure 36 shows the potentiometric surface of D-T basin for transient-state model simulation at the last

stress period, 31st December 2012. The potentiometric surface result was almost the same with the steady-

state potentiometric surface but slightly lower over the norther part of modeled area (Figure 25). According

to the groundwater heads result, higher heads value was observed over the mountainous area and lower

heads near to the sea coast. Consequently, the flow direction is from the north to south of the modeled area.

Figure 36: The potentiometric surface and stream segments of the D-T basin during transient model calibration at the last stress period, December 31, 2012.


49

The hydrographs of simulated groundwater heads are shown in Figure 37. In most of the monitored

piezometers, there was delayed hydrograph response to rainfall. The amplitude or the fluctuation of the

heads was higher over the north ~ 2.5 m than the south ~ 1.5 m. This fluctuation of the hydrographs is due

to the recharge of the groundwater during the rainy/wet periods from October to March.

A. Simulated head for station BOL3

B. Simulated head for WL5

C. Simulated head WL2

Figure 37: Time series for the comparison of yearly observed and daily simulated heads for D-T basin. P – rainfall, Hobs – observed heads, and Hsim – simulated heads.

0

20

40

60

80

100

120

9.5

10

10.5

11

11.5

12

12.5

13

1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12

P [

mm

day

-1]

Hea

d [

m]

P Hsim Hobs

0

20

40

60

80

100

120

0

0.5

1

1.5

2

2.5

3

3.5

4


P [

mm

day

-1]

Hea

d [

m]

P Hsim Hobs

0

20

40

60

80

100

120

175.5

176

176.5

177

177.5

178

178.5


P [

mm

day

-1]

Hea

d [

m]

P Hsim Hobs

50

3.3.2. Calibrated stream discharges

Transient-state model calibration was carried out to match the daily simulated stream discharges with the

observed stream discharges. Thirteen stream gauging station were calibrated using four-years period from

1st January 2009 to 31st December 2012. Figure 38 and Appendix VII show the hydrograph of observed and

simulated discharges in relation to daily rainfall patterns. The hydrographs of observed and simulated

discharges are reasonably fit for the year 2009 – 2012 (Figure 38). In most cases, the stream discharges

calibration result is in the line with Nash and Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007);

Moriasi et al., (2007); & Akhtar et al., (2009) model error criteria as depicted in Table 12. However, the

model has the incapability to produce peak flows, despite it gives good efficiency and model performance

for thirteen stations namely called Yeh_Empass, Yeh Matan, Yeh Hoo, Tukad Penat, Tukad Petan, Sang

Sang, Melangit, Tukad Unda-cegeng, Yeh Otan, Yeh Aba, and Pekerisan. Several reasons exist for the

incompetence of the model to simulate high flows. As model itself is the simplified representation of the

real world hydrological processes, several processes are ignored in the mathematical model for example

perched flow, macro-pore flow and other. The parameters are just the estimation of the catchment

characteristics, and may not fully consider the heterogeneity of the catchment. In addition, the

meteorological information may also not well represent the whole catchment and result in the reduced values

of peak flow.

0

40

80

120

160

2000

2

4

6

8

10

12

1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12R

F [

mm

day

-1]

Q [

m3se

c-1]

A. Station Melangit

Pengotan_RF Observed_Q Simulated_Q

0

40

80

120

160

2000

1

2

3

4

5

6


RF

[m

md

ay-1

]

Q [

m3se

c-1]

B. Station Sang Sang

Observed_Q Simulated_Q Sanglah_RF


51

0

40

80

120

160

2000

1

2

3

4

5

6

7

8


RF

[m

md

ay-1

]

Q [

m3 s

ec-1

]

C. Station Tukad Jineh

Observed_Q Simulated_Q Selishan_RF

0

40

80

120

160

2000

1

2

3

4

5

6

7

8

1-Jan-09 20-Jul-09 5-Feb-10 24-Aug-10 12-Mar-11 28-Sep-11 15-Apr-12 1-Nov-12

RF

[m

md

ay-1

]

Q [

m3se

c-1]

D. Station Tukad Oos

Observed_Q Simulated_Q Mambal_RF

0

40

80

120

160

2000

2

4

6

8

10

12

1-Jan-09 20-Jul-09 5-Feb-10 24-Aug-10 12-Mar-11 28-Sep-11 15-Apr-12 1-Nov-12

RF

[m

md

ay-1

]

Q [

m3se

c-1]

E. Station Tukad Petanu

Observed_Q Simulated_Q Tegallalang_RF

52

0

40

80

120

160

2000

1

2

3

4

5

6


RF

[m

md

ay-1

]

Q [

m3se

c-1]

F. Station Yeh Empas

Observed_Q Simulated_Q Gadungan_RF

0

40

80

120

160

2000

2

4

6

8

10

12

14


RF

[m

md

ay-1

]

Q [

m3se

c-1]

G. Station Yeh Hoo


0

40

80

120

160

2000

1

2

3

4

5

6

7


RF

[m

md

ay-1

]

Q [

m3se

c-1]

H. Station Yeh Mata

Observed_Q Simulated_Q Pempatan_RF


53

0

40

80

120

160

2000

5

10

15

20

25

30

35

40

45

50


RF

[m

md

ay-1

]

Q [

m3se

c-1]

I. Station Tukad Penat

Observed_Q Simulated_Q Tampaksiring_RF

0

40

80

120

160

2000

2

4

6

8

10

12

14

16


RF

[m

md

ay-1

]

Q [

m3se

c-1]

J. Station Tukad Unda

Observed_Q Simulated_Q Rendang_RF

0

40

80

120

160

2000

10

20

30

40

50

60

70

80


RF

[m

md

ay-1

]

Q [

m3se

c-1]

K. Station Pekerisa

Observed_Q Simulated_Q Kedisan_RF

54

Figure 38: Relationship between observed and simulated discharge in the D-T basin for the transient-state model

calibration of 13 stream gauge (2009 - 2012). For the location of gauges see Appendix V (A & B). The oval shape in

Figure 37 (J, K, and L) show that uncertainty in the measured rainfall and stream discharges. Because it is expected

that at high rainfall records, stream discharge is higher and the opposite is true. Q – stream discharge and RF – rainfall.

The oval shape in Figure 38 (A) shows that the model hardly reaches the base flows. This may be due to

that the excess rainfall was stored in the different model zones. Additionally, for station Yeh Hoo, Tukad

Penat, and Tukad Petanu the simulated stream discharge was somewhat higher than the observed stream

discharge but follow similar pattern. This may be caused by the assigned streambed top elevation, or width

in the SFR2 package, due to lack of time the result was taken as it is but for further study parameters should

be optimized for better represent with the observed stream discharges.

The model hardly performs in terms of hydrograph, model efficiency and mean difference for stations

Balian, Ayung Buanga, and Badung Hilir (Appendix VII). Nevertheless, the model represents the base flow

of those stations. For instance, in station Ayung Buanga the model reproduces the base flow from 1st January

2011 to 31st December 2012; in station Badung Hilir from 1st January 2010 to 31st December 2012, and in

station Balian from 1st January 2009 to 1st January 2010. The model performance of those stations as in

Table 12 shows very high relative volumetric error (RVE), and low Nash-Sutcliffe efficiency (NS) and overall

0

40

80

120

160

2000

5

10

15

20

25

30

35

40


RF

[m

md

ay-1

]

Q [

m3se

c-1]

L. Station Yeh Aba


0

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2000

4

8

12

16

20


RF

[m

md

ay-1

]

Q [

m3se

c-1]

M. Station Yeh Otan



55

model performance (Y), calculated from equation 2.13, 2.14, and 2.15. As stated earlier in section 3.1.6, for

those stations the hydrological information was not representative. This was discovered by the inconsistency

in the double mass curve and frequency distribution analysis (Appendix V; D, E & F). The main reason may

be due to exposure, observation method, or gauging location.

In a nutshell, the main reasons for the mismatch between observed and simulated streams discharge are due

to uncertainty in the measured stream level and groundwater heads; unaccounted surface and groundwater

abstraction, unaccounted temporal variability of land cover and heterogeneity; and also modeled grid cell

size (Mehl & Hill, 2010).

Table 12: Observed and simulated stream discharge with GHB conductance of 0.1 m2day-1 per unit length calculated error assessment for 16 gauges in m3day-1. Stations that are highlighted by red colour indicate those station that are not used for model calibration and shows the model performance for those stations.

Station Name Latitude Longitude NS RVE Y

Melangit 8°34'44.25"S 115°05'11.22"E 0.63 27.62 49.58

Sangsang 8°31'26.49"S 115°17'15.64"E 0.89 -8.67 82.13

Tukad_Jineh 8°33'10.93"S 115°21'54.48"E 0.73 17.86 61.66

Tukad_Oos 8°29'15.96"S 115°04'46.26"E -0.35 -56.44 -22.37

Tukad_Petanu 8°27'42.69"S 115°02'36.43"E 0.76 -23.32 61.75

Yeh_Empas 8°33'25.08"S 115°15'20.73"E 0.71 7.05 66.35

Yeh_Hoo 8°33'13.29"S 115°20'47.97"E 0.51 -39.66 36.78

Yeh_Mata 8°29'42.09"S 115°22'59.21"E 0.99 -2.59 96.69

Tukad_Penat 8°31'06.55"S 115°12'01.88"E 0.86 -33.26 64.77

Tukad_Unda 8°29'11.11"S 115°26'08.18"E 0.99 -4.60 94.82

Ayung Buangga 8°27'23.44"S 115°00'12.94"E -0.37 95.25 -18.74

Badung Hilir 8°28'22.15"S 115°01'48.37"E -0.38 54.33 -24.92

Balian 8°38'57.85"S 115°12'44.89"E 0.59 -28.24 46.11

Pekerisa 8°23'51.75"S 115°19'09.33"E 0.85 -63.18 52.39

Yeh_Aba 8°25'33.59"S 115°13'55.11"E 0.93 -27.86 73.10

Yeh_Otan 8°34'04.29"S 115°04'18.22"E 0.83 9.61 75.29

3.3.3. Hydraulic conductivities and specific yield

The horizontal hydraulic conductivity that was calibrated in the steady-state model was gently modified and

the result is shown in Figure 39. Generally, the spatial variability of transient Kh was almost the same as

calibrated steady-state Kh. Minor changes were made over the southern part of the basin. The value of Kh

varied from 0.01 to 580 mday-1. Riverbed hydraulic conductivity ranges from 0.01 to 0.35 mday-1.

The D-T basin aquifer materials were early Quaternary deposits. This Quaternary upper formation was

composed of different materials of volcanic origin. It includes mainly unconsolidated sand & gravel, volcanic

ash, lava flow, breccia, lahar, "pumic", clay and tuff (Nielsen & Widjaya, 1989 & Purnomo & Pichler, 2015).

The study area aquifer materials are spatially uniform so that, spatially uniform Sy, 0.24 was used during

transient model calibration. The final model parameter values and model variables that were used in the

transient calibration of the D-T basin numerical model are shown in Table 13.

56

Figure 39: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after Transient-state IHM

[unit - mday-1].

Table 13: Final calibration output for model parameters and model variables in the D-T basin: EXTDP – extinction water content; EXTWC – extinction water content; THTS – saturated volumetric water content; THTI – initial volumetric water content; STRTOP – streambed top; STRTHICK – streambed thickness; SLOPE – stream slope; STRHC1 – streambed hydraulic conductivity; WIDTH1 – stream width; Kvun – maximum unsaturated zone vertical

hydraulic conductivity; Kh – horizontal hydraulic conductivity; Sy – specific yield; and C – conductance.

Vertical zones Parameters Minimum value Maximum value Unit

Unsaturated zone EXTDP 0 2.5 m

(MODFLOW-NWT, UZF1) EXTWC 0.05 0.07 m3m-3

Kvun 0.1 0.1 mday-1

Streams THTS 0.4 0.4 -

(MODFLOW-NWT,SFR2) THTI 0.2 0.2 -

STRTOP 2.5 2.5 m

STRTHICK 0.5 0.5 m

SLOPE 0.025 0.025 -

STRHC1 0.05 0.8 mday-1

WIDTH1 2 12 m

Groundwater zone Kh 8 900 mday-1

(MODFLOW-NWT) Sy 0.24 0.24 -

C 6 44 m2day-1

3.3.4. Water budget of the transient-state simulation

The average groundwater budget during the four-year model simulation was shown in Table 14. The rainfall

recharge was the major supply to the aquifer system and Rg contributes 75% of total groundwater inflow

followed by ∆Sgin (21.4%) and qsg (3.3%). The majority of the outflow from the aquifer system was qgs

(30.4%), Exfgw (29.4%), ∆Sgout (18.94%) and ETg (14.1%) followed by 7.5% of qg. Comparatively, the

calibrated transient-state qg (7.5%) was slightly higher than the calibrated steady-state qg (6.1%). In transient-

state Rn contributes 42.4% of Rg. The Rn value is slightly lower as compared to steady-state Rn (50.6%).


57

Table 14: Long term average groundwater budget for entire model in transient-state IHM [mmday-1] for the 2009-

2012. IN – inflow to the aquifer system, OUT – outflow from the aquifer system, GW – groundwater.

IN m3day-1 OUT m3day-1

Storage 2203881 Storage 1965919

Lateral GW outflow 0 Lateral GW outflow 742374

Stream leakage 346467 stream leakage 3157223

GW ET 0 GW ET 1462588

UZF recharge 7827765 UZF recharge 0

Surface Leakage 0 Surface Leakage 3049997

TOTAL IN 10378113 TOTAL OUT 10378100

IN-OUT 13

3.3.5. Temporal variability of groundwater fluxes

The temporal variability of groundwater fluxes for gross recharge (Rg), net recharge (Rn), surface leakage

(Exfgw), and groundwater evapotranspiration (ETg) is shown in Figure 40. The net recharge was calculated as

the sum of Exfgw and ETg subtracted from the Rg. The result shown that both Rg and Rn were influenced by

the rainfall intensities. The Rn follows the Rg path for low and high values but it is influenced by ETg and

Exfgw. “Exfgw occurs whenever the altitude of the water table exceeds the soil zone and it can be lost as ETun,

qd or becomes storage in the soil zone” (Hassan et al., 2014). The temporal variability of groundwater fluxes

corresponds mainly with the seasonal variability of driving forces changing from wet to dry periods.

Figure 40: Temporal variability of groundwater fluxes in transient model calibration for gross recharge (Rg), net recharge (Rn), surface leakage (Exfgw), and groundwater evapotranspiration (ETg).

0

20

40

60

80

100

1200

1

2

3

4

5

6

7

8

9

1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13P

[m

md

ay-1

]

Rgan

d R

n[m

md

ay-1

]

Rainfall, Gross recharge and Net recharge

P Rg Rn

0

20

40

60

80

100

1200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


P [

mm

day

-1]

ET

gan

d E

xf gw

[m

md

ay-1

]

Rainfall, Gross recharge and Net recharge

P ETg Exfgw

58

Figure 41 shown the applied rainfall (P), PET, and the calculated actual infiltration rate (Pe). The result shows

that the Pe value depends on the rainfall intensities, the degree of saturation in the unsaturated zone, and the

vertical hydraulic conductivity of the soil. The peaks in the Pe rate correspond to the high P value and at

first, this water subdivided into Rg, ETun, and ETg then the remaining excess infiltration rate routed to the

streams and store in the unsaturated zone.

Figure 41: Temporal variability of rainfall, actual infiltration and PET

3.3.6. Spatial variability of groundwater fluxes

The spatial variability of groundwater fluxes was compared during dry (April – September) and wet (October

- March) periods. For comparison purpose fluxes were taken randomly from both periods. The transient-

state groundwater evapotranspiration, ETg loss varies spatially as shown in Figure 42. The ETg demand

ranging from 0.003 mmday-1 to 0.004 mmday-1 in the dry season, example in 26-July-2010. The ETg demand

ranging from 0.004 mmday-1 to 0.006 mmday-1 in the wet season, 5th-Febrary-2009. The spatial distribution

of ETg, was highly depend on land cover. For instance, lower ETg was observed in an area where there is

bare soil than forest since, low Kc and EXTDP assigned

A. Spatially variable ETg in 26-July-2010

A. Spatially variable ETg in 5-Febrary-2009

0

0.5

1

1.5

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2.5

3

3.5

4

4.5

5

0

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120

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160

1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13

PE

T [

mm

day

-1]

P a

nd

Pe

[mm

day

-1]

Rainfall (P), Actual infiltration (Pe) and PET

P Pe PET


59

Figure 42: Spatially variable ETg map for calibrated transient IHM during dry (A) and wet (B) period in D-T Basin [Unit – mday-1].

Figure 43 shows that the distribution of groundwater gross recharge for the transient-state IHM. Seasonally,

the gross recharge was higher during wet than dry season since rainfall was higher during wet season but

also during dry period (Figure 4). During the dry period, as an example in 17th – August -2009, Rg ranged

from 0.0002 mmday-1 to 0.003 mmday-1 while in the wet period, 21st –December-2009, Rg from 0.03 mmday-

1 to 0.003 mmday-1. The result shows that the spatial distribution of groundwater gross recharges was highly

influenced by the spatial distribution of rainfall and its kriging variance –section 3.1.3.

A. Spatially variable Rn in 17-August-2009 B. Spatially variable Rn in 21-December-2009

Figure 43: Spatially variable Rg map for calibrated transient IHM during dry (A) and wet (B) period in D-T Basin.

3.3.7. Yearly steady-state and transient variability of water fluxes

As stated earlier, the Newtonian formulation of MODFLOW-05 was used to run transient IHM.

MODFLOW-NWT links unsaturated and saturated zone and also simulate the interaction of GW-SW

(Niswonger et al., 2011). Initially, during transient model calibration the model stopped running and show

message “failed to meet solver convergence criteria”. This was due to UZF1 package solver criteria. In order

to solve the problem, the recommended value for flux tolerance and head tolerance as in section 2.4.5 were

increased from 500 m3day-1 and 0.0001 m into 5,000 m3day-1 and 0.001 m respectively and then model

converged.

In this study, mean of the four-year net recharge was 491 mmyear-1, this result was comparable with the

final findings of Nielsen & Widjaya (1989) who estimated groundwater recharge of southern Bali based on

(1) analysis of well hydrographs as 468 mmyear-1; (2) flow net analysis as 492 mmyear-1; (3) annual infiltration

gave 437 mmyear-1. However, the estimated net recharge of this study somewhat deviates from Nielsen &

Widjaya (1989), who estimated net recharge (1) from base flow separation as 272 mmyear-1; (2) from

analytical model using land cover map as 645 mmyear-1 in light soil, 538 mmyear-1 in the medium soil, and

376 mmyear-1 in heavy soil. In addition, the result of this study slightly varies from Artabudi (2012) final

findings, who estimated groundwater recharge as 218-220 mmyear-1 when the driving forces extracted from

satellite sensor products and as 650-660 mmyear-1 when the driving forces were obtained from in situ data.

60

Table 15: The yearly variability of driving forces and different groundwater balance components over the three hydrological periods 1st January 2009 till 31st December 2012 MODFLOW-NWT simulation period [All units in mm year-1].

where P – precipitation, PET – potential evapotranspiration, I – interception, Inf – infiltration rate, Rn – net recharge, qsg – stream leakage to the groundwater system, Rg – gross recharge, qg – lateral groundwater outflow, qgs – groundwater flow to the streams, ETg – groundwater evapotranspiration, Exfgw – surface leakage/exfiltration, ∆Sg – groundwater storage, Ro – runoff, Pe – Actual infiltration rate, ETun – Unsaturated zone evapotranspiration, and ∆Sun – Unsaturated zone storage.

Table 15 show the average yearly rainfall, PET, interception, infiltration rate, groundwater budget, and unsaturated zone budget for the simulation period from 1st

January 2009 to 31st December 2012. The result depicts that there was annual variability in groundwater fluxes and difference with the steady-state model simulation

results. The result of steady-state and the mean of the four-year transient model simulation was comparable for some flux components such as lateral groundwater

outflow and stream leakage into the groundwater. However, for the remaining fluxes, there is a dissimilarity due to oversimplification of the steady-state model;

where all the driving forces and state variables are taken as an average value. Additionally, there might be an oversimplification of UZF1 packages during steady-

state IHM in which it does not take into account the water storage, and unsaturated zone evapotranspiration. However, in the transient model simulation estimated

those groundwater budget components.

P PET I Inf Rn qsg Rg qg qgs ETg Exfgw ∆Sg Ro Pe ETun ∆Sun

Steady-state IHM 2452.8 1311.3 332.2 2120.7 890.6 91.5 1759.2 116.8 901.6 441.7 427.1 0.0 795.7 1759.2 0.0 0.0

1st Jan. 2009 – 31st Dec. 2009 2380.0 1420.6 273.7 2106.3 591.0 53.3 1343.9 119.3 476.5 258.2 494.8 48.5 281.0 2320.1 421.3 554.9

1st Jan. 2010 – 31st Dec. 2010 3206.7 1316.0 368.8 2837.9 539.1 50.7 1279.7 119.4 488.6 245.6 495.0 -18.2 420.3 2912.6 1511.1 121.8

1st Jan. 2011 – 31st Dec. 2011 2187.7 1305.7 251.6 1936.1 471.6 55.6 1214.1 120.1 480.1 241.3 501.2 -73.0 279.1 2158.2 480.8 463.3

1st Jan. 2012 – 31st Dec. 2012 2172.9 1135.3 249.9 1923.0 360.7 57.4 1074.2 120.3 478.9 207.6 505.9 -181.1 284.7 2144.3 822.8 247.3

Minimum 2172.9 1135.3 249.9 1923.0 360.7 50.7 1074.2 119.3 476.5 207.6 494.8 -181.1 279.1 2144.3 421.3 121.8

Maximum 3206.7 1420.6 368.8 2837.9 591.0 57.4 1343.9 120.3 488.6 258.2 505.9 48.5 420.3 2912.6 1511.1 554.9

Average 2486.8 1294.4 286.0 2200.8 490.6 54.3 1228.0 119.8 481.0 238.1 499.2 -55.9 316.3 2383.8 809.0 346.8

Standard deviation 423.6 102.3 48.7 374.9 86.1 2.5 100.0 0.4 4.6 18.7 4.7 84.1 60.1 313.0 433.4 171.3


61

3.3.8. Sensitivity analysis

Sensitivity analysis was conducted in the transient IHM with the aim of assessment of groundwater in the

basin. The response of the model hydraulic head was assessed by varying model parameters in the same way

as steady-state IHM (Figure 44). It was observed that the Kh and Kvun parameters showed a higher response

to the model. The Kh and Kvun follow a similar trend of the model response. The model response increase

for both high and low Kh values and to some degree for low Kvun. The model response was higher to the

variation in the Kh parameter than the Kvun. Apart from this the model hardly response for EXTDP, EXTW,

WCsat and BC values. Those the insensitive parameters may create uncertainty in the model. Therefore,

more effort is required to get reliable information about the insensitive parameters.

A. Sensitivity of Kh, Kvun, EXTDP, EXTWC, WCsat,& BC upon heads

Figure 44: Sensitivity of model for horizontal hydraulic conductivity [Kh], maximum unsaturated zone vertical hydraulic

conductivity [Kvun], extinction depth [EXTDP], extinction water content [EXTWC], Saturated water content [WCsat],

and Brooks-Corey-Epsilon [BC].

Sensitivity analysis was also conducted in the transient-state IHM with the aim of assessment of groundwater

in the basin. The response of the groundwater budget components was assessed by varying model

parameters as shown in Figure 45. It was observed that the Kvun parameter showed a higher response to the

model. The Kvun parameter has the same response to the infiltration rate and Exfgw. The response for

groundwater budget components increase for high Kvun values and decrease for low Kvun values. This is

because that when the unsaturated zone vertical hydraulic conductivity increases then the water can pass

through the soil easily than in the case of low hydraulic conductivity. Then the infiltration rate also increases.

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

-45% -30% -15% 0% 15% 30% 45%

RM

SE

[m

]


Kh

Kvun

EXTDP

EXTWC

Wcsat

BC

62

A. Sensitivity of Kvun upon Infiltration

B. Sensitivity of Kvun upon Exfgw

C. Sensitivity of EXTDP upon ETg

D. Sensitivity of GHB conductance upon qg

Figure 45: Effects of changing unsaturated zone vertical hydraulic conductivity [Kvun] upon infiltration (A) and Exfgw (B), effects of changing extinction depth [EXTDP] and GHB conductance upon ETg (C) and qg (D) respectively.

5.8

6.0

6.2

6.4

6.6

6.8

7.0

7.2

-45% -30% -15% 0% 15% 30% 45%

Infi

ltra

tio

n [

mm

day

-1]


Kvun

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

-45% -30% -15% 0% 15% 30% 45%

Ex

f gw[m

md

ay-1

]


Kvun

0.64

0.65

0.66

0.67

0.68

0.69

0.70

-45% -30% -15% 0% 15% 30% 45%

ET

g[m

md

ay-1

]


EXTDP

0.0

0.1

0.2

0.3

0.4

0.5

-45% -30% -15% 0% 15% 30% 45%

q g[m

md

ay-1

]


Conductance


63

4. CONCLUSIONS AND RECOMMENDATIONS

4.1. Conclusions

The main objective of this research was to develop an IHM of D-T basin for management purpose. For

that reason, MODFLOW-NWT under ModelMuse environment was used. MODFLOW-NWT is a

Newtonian formulation of MODFLOW-05 that with UZF1 and SFR2 packages simulates water flow

between ground surface and aquifer throughout unsaturated zone, groundwater flow and SW-GW

interaction. The steady-state and transient-state IHM was built and calibrated manually using daily data from

1st January 2009 to 31st December 2012. The most important findings of this study are listed below:

The steady-state model calibration ‘produced’ heads and stream flows with RMSE of 0.52 m and

NS of 0.86 respectively. In this model the groundwater budget components: RUZF contributed 95%

of total inflow to the aquifer system and the remaining 5% was covered by qsg. The main outflows

of the aquifer systems were and qgs and ETg which contributed 47.8% and 23.4% of total outflow

respectively. The remaining outflows were: Exfgw ~22% and qg ~6.1%.

The transient model was calibrated to reproduce patterns of stream discharge and to minimize the

difference between simulated and observed stream discharges as well as heads. The calibration

process produced stream flows with NS ranging from 0.51 to 0.99 (Table 12). Besides, the RMSE

of groundwater heads calibrated simultaneously with stream discharges was ~0.58 m.

The four-years (1st January 2009 to 31st December 2012) precipitation (P) was 6.8 mm day-1; the

corresponding groundwater fluxes were as follows: Rg=3.45 mm day-1 (50.5% of P), ETg=0.64

mmday-1 (9.5% of P), Exfgw=1.34 mmday-1 (19.7% of P), Rn 1.46 mmday-1 (21.4% of P), qgs=1.39

mmday-1 (20.4% of P); ∆S=0.11 mmday-1 (1.6% ofP), and qg=0.33 mmday-1 (4.8% of P).

The temporal variability of groundwater fluxes obtained in the transient model calibration can be

illustrated by: Rg ranging from 7.64 (January) to 2.30 mmday-1 (August) with the average value of

3.36 mmday-1; Rn ranging from 5.84 (January) to 0.26 mmday-1 (August) with the average value of

1.34 mmday-1; ETg ranging from 1.05 (February) to 0.65 mmday-1 (July) whereas, and also qgs ranging

from 1.48 (January) to 1.37 mmday-1 (August). Exfgw ranging from 1.48 (March) to 1.37 mmday-1

(December). The spatiotemporal variability of groundwater fluxes is constrained by seasonal

variability of driving forces, changing from wet season (October – March) to dry season (April –

September). The spatial variability of groundwater fluxes is mainly attributed to spatial variability

of rainfall and land cover.

The effect of boundaries at the sea coast was examined through two independent models with two

different boundary conditions at the sea coast. For the first model, the boundary was simulated by

GHB and in the second model, the CHD boundary. When the sea coast was simulated as CHD

boundary, the corresponding groundwater fluxes were as follows: Rg contributed 95%, followed by

qgs 5% of total groundwater inflow. Regarding groundwater outflow, ETg contributed 4%, Exfgw

12.7%, qgs 10.7%, and qg 72.9% of total groundwater outflow. However, when the GHB

conductance was < 12.5 m2day-1 per unit length, then the qg (5.8%) contribution was much lower

than the percent contribution of CHD boundaries besides, the percent contribution of ETg,

(33.2%), Exfgw, (12.8%) and qgs (48.3%) was reasonably higher than CHD boundaries. In a nutshell,

64

the GHB conditions at the sea coast give a more reliable water balance as compared to CHD

boundaries; this is because that at a low GHB conductance the model has a high control on the

lateral groundwater outflow to the ocean.

The UZF1 package in the steady-state IHM oversimplified UZF recharge assuming it equal to

infiltration rate. In addition to this, it lacks to estimate storage in different model zones and to

separate the sub-surface evapotranspiration, ETss into two: unsaturated evapotranspiration, ETun

and groundwater evapotranspiration, ETg. Because of that, the steady-state evapotranspiration was

higher than the transient-state groundwater evapotranspiration.

The IHM is a useful and effective tool for water resources management especially when the SW-

GW are hydraulically interconnected. It gives good results that may lead to proper planning and

management of water resources.

4.2. Recommendations

In this study, the standardized average sample variogram was estimated by averaging the individual

sample variogram. For further study, each sample and model variogram should be treated

independently for spatial data interpolation.

The temporal variability of land use map should be taken into account to assess its effect on the

groundwater budget of D-T basin.

Microclimatic data of only two stations was used to generate PET map. For further study, it is

recommended to integrate the in-situ data with satellite products, e.g. FEWSNET Global Potential

Evapotranspiration.

The effect of different density of sea water as compared to density of the fresh water at the sea

coastline, should be implemented in future model; nevertheless, quick tests with Seawater Intrusion

package [SWI2] indicated negligible impact of that condition upon the water balances of the D-T

basin.

The daily variation of groundwater fluctuation and abstraction data were not available and Ministry

of Energy and Mineral Resources of Indonesia as those data was confidential; if this data cannot

be used to upgrade this model, then such data should acquire from the field by installation of the

groundwater monitoring network.

To better close the water balance, it is recommended that model calibration should aim at both

matching hydrograph peaks and improve model overall performance (Y).


65

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Ala-aho, P., Rossi, P. M., Isokangas, E., & Klove, B. (2015). Fully integrated surface-subsurface flow modelling of groundwater-lake interaction in an esker aquifer: Model verification with stable isotopes and airborne thermal imaging. Journal of Hydrology, 522, 391–406. https://doi.org/10.1016/j.jhydrol.2014.12.054

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69

APPENDICES

APPENDIX I

D-T Basin boreholes location.

APPENDIX II

The computation equations to estimate evapotranspiration (FAO Penman-Monteith equation)

2237.3)(T

)]237.3T

T*17.27exp(*[(0.6108*4098

Δ

P*3

10* 0.664742γ

)237.3T

T*17.27exp(*0.6108(T)

0e

)100

meanRH]mean[T

0e(T)ae

5.42)z*ln(67.8

4.87ZU2U

70

Where ETo - reference evapotranspiration [mm day-1], Tmax - maximum daily air temperature [°C], Tmin -

minimum daily air temperature [°C], Ra - extraterrestrial short wave radiation [MJm-2day-1] (divide the value

by 2.45 to obtained Ra in mmday-1), Rn - net radiation at the crop surface [MJm-2 day-1], G - soil heat flux

density [MJ m-2day-1], 𝛾 - psychrometric constant [kPaoC-1], T - mean daily air temperature at 2 m height

[°C], U2 - wind speed at 2 m height [ms-1], es - vapour pressure [kPa], ea – actual vapour pressure [kPa], es-ea -

saturation vapour pressure deficit [kPa], ∆ slope vapour pressure curve [kPa°C-1]. Rn again can be calculated

using equation (2.8).

sR*α)(1lnRnsRnR

a]RN

nsbs[asR

)s(ω)cos(δcos(cos()sin(δssin(s[ωrdscGπ

24(60)aR

0.35)soR

sR)(1.35ae0.14](0.34

2

kmin,4

Tkmax,4

Tσ[lnR

where Rns - net solar or shortwave radiation [MJm-2day-1], Rln - net outgoing long wave radiation [MJm-2day-

1], Rs - solar or shortwave radiation [MJm-2day-1], Ra - extraterrestrial radiation [MJm-2day-1], Rso - clear sky

solar radiation [MJm-2day-1], Rs/Rso - relative shortwave radiation (limited to ≤ 1.0), α - albedo or canopy

reflection coefficient for the reference crop [-], n - actual duration of sunshine [hr.], N - daylight hours [hr.],

n/N - relative sunshine duration [-], Gsc - solar constant = 0.0820 [MJm-2min-1], dr - inverse relative distance

Earth-sun, ωs - sunshine hour angle [rad], ϕ - latitude [rad], δ - solar declination [rad], as - regression

constant, expressing the fraction of extraterrestrial radiation reaching the earth on overcast days (n=0), as +

bs - fraction of extraterrestrial radiation reaching the earth on clear days (i.e. n=N). In case of site specific

information, as and bs can be used as 0.25 and 0.50 respectively.

APPENDIX III

Pearson-correlation coefficient between rainfall stations in the D-T basin based on the data from 2009-2012.

Bedugul Bonganica Buagan Gadungan Kedisan

Klungkung

dpu Kuta Mambal Pempatan Pengotan Rendang Sading Selishan Tampaksiring Tegallalang

Tiying

Gading Ubung Sanglah

Bedugul 1

Bonganica 0.038 1

Buagan .135**

.215** 1

Gadungan 0.095 .297**

.323** 1

Kedisan .445**

.126*

.152**

.177** 1

Klungkung dpu .234**

.204**

.384**

.473**

.277** 1

Kuta .209**

.232**

.585**

.478**

.242**

.527** 1

Mambal .171**

.132*

.310**

.520**

.220**

.641**

.573** 1

Pempatan .130*

.242**

.131*

.239** 0.097 .210

**.232

**.284

** 1

Pengotan .359**

.195**

.324**

.303**

.488**

.396**

.437**

.374**

.192** 1

Rendang 0.072 .202**

.168**

.439**

.150**

.408**

.303**

.402**

.293**

.249** 1

Sading .129*

.165**

.489**

.605**

.194**

.674**

.593**

.727**

.265**

.439**

.370** 1

Selishan .109*

.137**

.451**

.364**

.125*

.486**

.381**

.362**

.122*

.305**

.386**

.462** 1

Tampaksiring .117*

.254**

.165**

.459**

.144**

.505**

.388**

.636**

.349**

.218**

.442**

.523**

.336** 1

Tegallalang 0.099 .185**

.231**

.537**

.180**

.532**

.399**

.671**

.278**

.324**

.574**

.559**

.375**

.643** 1

Tiying Gading .160**

.194**

.286**

.311**

.143**

.324**

.298**

.372**

.238**

.217**

.391**

.347**

.208**

.331**

.378** 1

Ubung .280**

.134*

.509**

.436**

.281**

.548**

.712**

.671**

.334**

.484**

.316**

.686**

.361**

.444**

.512**

.349** 1

Sanglah 0.119 0.061 .454**

.411** 0.113 .567

**.749

**.621

**.402

**.394

**.367

**.628

**.256

**.434

**.501

**.401

**.782

** 1


71

APPENDIX IV

Sample Variogram

Model Variogram

APPENDIX V

A. Spatial distribution of rain gauge stations with their names in the D-T basin

72

B. Stream segments overlaying the DEM of D-T basin and stream gauging stations with their names.

The yellow circle indicates three reference gauges that are not used for model calibration.

C. The log transformation of rainfall at station Melangit [units m3sec-1]


73

D. Sample double mass curve and frequency distribution for the gauge discharge data [Q - m3sec-1].

Double Mass curve for station Balian Double Mass curve for station Ayung Buangga

Frequency distribution for station Balian Frequency distribution for station Ayung

E. Relation between rainfall and stream discharge

0

20

40

60

80

100

120

140

160

180

2000

100

200

300

400

500

600

700

800

900


RF

[m

md

ay-1

]

Q [

m3se

c-1]

Station Ayung Buangga

Ayung_Q Tiying Gading_RF

0

100

200

300

400

500

600

0 200 400 600 800

Cum

ula

tive

Q f

or

Bal

ian

stat

ion


0

100

200

300

400

500

600

0 50 100 150 200 250

Cum

ula

tive

Q f

or

Ayu

ng

Buan

gga

stat

ion


74

F. Relation between rainfall and stream discharge

APPENDIX VI

A. GHB conductance at the sea coast for both steady-state and transient-state model [unit - m2day-1]

0

20

40

60

80

100

120

140

160

180

2000

10

20

30

40

50

60

70

80


RF

[m

md

ay-1

]

Q [

m3se

c-1]

Station Balian

Balian_Q Pempatan_RF


75

B. Total water balance of D-T Basin at steady-state condition using CHD boundaries [mmday-1].


Precipitation (P) 6.10 GW evapotranspiration (ETg) 0.22

Unsaturated zone ET (ETun) 0.00

Interception loss (I) 0.82

Stream discharge at the outlet (q) 0.61



IN-OUT 0.2

PERCENT DISCREPANCY 3%

C. Land surface and unsaturated zone water balance using of D-T Basin at steady-state condition using CHD boundaries

[mmday-1]. Budget component IN Budget component OUT

Precipitation (P) 6.10 Unsaturated zone ET (ETun) 0.00

GW exfiltration (Exfgw) 0.74 Interception loss (I) 0.82

Gross recharge (Rg) 5.55

Total runoff (Ro) 0.47


IN-OUT 0.01

PERCENT DISCREPANCY 0.1%

APPENDIX VII

Hydrograph of observed and simulatd stream discharges.

0

40

80

120

160

2000

100

200

300

400

500

600

700

800

900


RF

[m

md

ay-1

]

Q [

m3se

c-1]

Station Ayung Buangga

Observed_Q Simulated_Q Tiying Gading_RF

76

0

40

80

120

160

2000

20

40

60

80

100

120

140


RF

[m

md

ay-1

]

Q [

m3se

c-1]

Station Badung Hilir

Observed_Q Simulated_Q Ubung_RF

0

40

80

120

160

2000

10

20

30

40

50

60

70

80


RF

[m

md

ay-1

]

Q [

m3se

c-1]

Station Balian


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