IN DEGREE PROJECT ENVIRONMENTAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2019

HYDROLOGICAL AND CHLORIDE TRANSPORT PROCESSES IN A SMALL CATCHMENT OF THE NORRSTRÖM BASIN: A MIKE SHE MODELLING APPROACH

ZHUHUAN LIU

CHEN ZHOU

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

HYDROLOGICAL AND CHLORIDE TRANSPORT PROCESSES IN A SMALL CATCHMENT OF THE NORRSTRÖM BASIN: A MIKE SHE MODELLING APPROACH

Zhuhuan Liu & Chen Zhou

Supervisor

Zahra Kalantari

Examiner

Vladimir Cvetkovic

Degree Project in EESI (Environmental Engineering and Sustainable Infrastructure)

KTH Royal Institute of Technology

School of Architecture and Built Environment

Department of Sustainable Development, Environmental Science and Engineering

SE-100 44 Stockholm, Sweden

Abstract

Water is ubiquitous on our planet and constitutes a vital part of ecosystems. It

supports the life of all beings on the earth while simultaneously evokes water-

related issues such as water shortage, water contamination. As UN advocates, a

globally shared blueprint for available clean water is depicted in Sustainable

Development Goals (SDGs). However, there still exists a gap between current water

management situations and our sustainable goals Modelling based on Hydro-

Meteorological Data provides a way to understand regional hydrological processes

and monitor environmental chemistry changes, especially for anthropogenic

pollution. Furthermore, hydrological models make it possible to predict changes in

water quantity and quality, under the context of climate change.

The study area of this project is located in the Kringlan catchment, Norrström

basins, occupying an area of 54.5 km2. The local discharges merge into Rastälven

river and flow to the east, eventually discharging into the Baltic Sea. This project

builds up a water balance model based on the meteorological data in the time

frame from 2011 to 2012. The water balance model is calibrated to accurately

simulate realistic hydrological components interactions, during each process,

various parameters have been tested and adjusted to improve model robustness.

Meanwhile, the project tries to strike a balance between the complexity of the

model and amount of time it takes to run the model. The calibrated model is also

validated to ensure model performance using statistical analysis.

Additionally, a particle tracking model for the saturated zone is developed on the

basis of the water balance model. Chloride is chosen as the trace element due to its

feature of unreactive in ecological systems. The model results could also provide a

value to groundwater age estimation. Suggested by previous researches targeting

the area, leakage from vegetation and forest soil in this catchment have contributed

to imbalances in local Cl- budgets. An internal source of chloride from soil leaching

is specified in the model at the same time with an external source from stream

discharge.

The coupled modelling through the application of MIKE SHE software and

calibration process help us to understand dynamic processes of hydrological

modelling and chloride particle transport in the Kringlan catchment.

A future improvement to consider is extending the current model boundary to a larger area and introducing more reference data. It is also possible to establish a fully integrated solute transport model to investigate Chloride transport in the

catchment.

Key words:

MIKE SHE, Hydrological Modelling, Kringlan, Water Balance, Particle Tracking

Summary in Swedish

Vatten ersätter en viktig del av ekosystemet men det framkallar vattenrelaterade

problem som vattenbrist och vattenförorening samtidigt. Emellertid finns det

fortfarande ett gap mellan nuvarande vattenhanteringssituationer och våra

hållbara mål. Modellering baserad på meteorologiska data erbjuder en möjlighet

att förstå regionala hydrologiska processer och övervaka förändringar av

miljömässiga kemikalier, särskilt för antropogena föroreningar. Dessutom finns det

en hög potential för att förutse förändringar i vattenmängd och kvalitet med

hydrologiska modeller, i samband med klimatförändringar.

Studieområdet ligger i Kringlans upptagningsområde som ett av Norrström basins,

med en yta på 54,5 km2. De lokala utsläppen sammanfogas i Rastälven och

strömmar österut, så småningom mynnar i Östersjön. Detta projekt bygger upp en

vattenbalansmodell baserad på meteorologiska data inom tidsramen från 2011 till

2012. Vattenbalansmodellen är kalibrerad för att exakt simulera realistiska

hydrologiska komponentinteraktioner. För att förbättra modellens robusthet har

olika parametrar testats och anpassats under varje process. Samtidigt försöker

projektet att hitta en balans mellan modellens komplexitet och hur lång tid det tar

att driva modellen.

En partikelspårningsmodell för den mättade zonen har utvecklats med

utgångspunkt i vattenbalansmodellen. Klorid används som spårämne eftersom det

är inert i ekologiska system. Modellsresultaten kan också ge ett värde för

grundvattenberäkningen. Tidigare undersökningar inriktade på området föreslår

att läckage från vegetation och skogsmark i detta avrinningsområde har bidragit till

obalanser i lokala Cl- budgetar.

Med hjälp av MIKE SHE modellen har vi undersökt dynamisk process för

hydrologisk modellering och kloridpartikelspårning i Kringlan avrinningsområde.

Vad som kan gör i framtiden är att förlänga den nuvarande modellgränsen till ett

större område med mer referensdata. Det är också möjligt att upprätta en

fullständigt integrerad lösningsmodell för att undersöka kloridtransporter i ett

avrinningsområde.

Acknowledgements

We would firstly like to acknowledge our thesis advisor Zahra Kalantari (Associate Professor, Department of Physical Geography, Stockholm University). Thanks for all her patience and support during the long thesis period. It has really been our honour to be guided by her in our first hydrological study. Though it has already been a big challenge, if without her encouragement and guidance, it would be even tougher for us to embark on hydrological modelling. We would also like to thank our examiner Professor Vladimir Cvetkovic (Professor, School of Architecture and the Built Environment, KTH), who gave very insightful comments on the thesis and help us a lot with thesis improvement. What’ more, we must express our appreciation to Sten Blomgren (Client Care Manager, DHI Sverige AB), who provides us with the expensive access to MIKE SHE and MIKE Hydro.

Of course, we have to toast each other, for the company, the support, the tears, the quarrel, the improvement, for all the stories we have experienced together. Finally, our great appreciations to the families. We could never make it through without their no-string-attached love and support.

Stockholm, 10th January

Zhuhuan LIU & Chen ZHOU

CONTENTS

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

1.1 Background ....................................................................................................................................... 1

1.2 Aims and objectives ........................................................................................................................... 2

1.3 Study area ......................................................................................................................................... 3

2 METHODOLOGY .............................................................................................................. 5

2.1 Theoretical background ..................................................................................................................... 5

2.2 Data description ................................................................................................................................ 8

2.3 MIKE SHE models..............................................................................................................................16

2.4 Model calibration & validation .........................................................................................................29

3 DISCUSSION AND RESULTS ............................................................................................ 34

3.1 Water balance results .......................................................................................................................34

3.2 Particle tracking results ....................................................................................................................40

4 CONCLUSIONS ............................................................................................................... 42

4.1 Comparisons with the previous study ...............................................................................................42

4.2 Conclusions and reflections ..............................................................................................................43

REFERENCE ............................................................................................................................ 45

APPENDIX I ............................................................................................................................. 51

APPENDIX II ............................................................................................................................ 52

Abbreviations

AD: Advection-Dispersion

DEM: Digital Elevation Model

DDF: Degree-day factor

DHI: Institute for Water and Environment

ET: Evapotranspiration

GIS: Geological information system

KC: Crop coefficient

LAI: Leaf Area Index

MDGs: Millennium Development Goals

OL: Overland flow

PT: Particle tracking

RD: Root Depth

SDGs: Sustainable Development Goals

SGU: Swedish Geological Survey

SMHI: Swedish Meteorological Institute

SZ: Saturated zone

UNDP: United Nations Development Programme

USGS: U.S. Geological Survey

UZ: Unsaturated zone

Introduction | 1

1 Introduction

1.1 Background

More frequent floods and droughts have been recorded and reported in this new human-dominated epoch (Mondal A., 2016) whilst this changing situation also introduces challenges to environmental assessment and management. Besides the water shortage caused by extreme events, water availability is even more threatened by population increase, urbanisation and accelerating economic activities (Setegn, 2015). Both the quality and quantity of water resources are deteriorating on the global scale and especially compelling in some areas.

The climate change and vulnerabilities of both environmental and ecological system to this change alert human beings to reconsider water resources management (Laurent, et al., 2012). Sustainability is an essential element of environmental services and development strategies. In the autumn of 2000, a shared blueprint of global development was advocated by United Nations declaration, known as the Millennium Development Goals, and it signs that water-related issues are brought into the limelight of well-being improvements (UNDP, 2015). According to the Final MDGs Report, the population size of those who lived with poor accessibility to water and sanitation had been halved after a 15-year struggle (UNDP, 2015), The goal was reinforced with a global commitment to Sustainable Development Goals (SDGs) for the next 15 years and water stress is even more emphasized in this new pledge (UNDP, 2015). It initiates a more imperative need for sustainable water management, which should be built upon a holistic overview of water movement and water quality monitoring (Mannaerts & Meijerink, 2000).

A systematic way of achieving those goals is provided by hydrologic studies (Pan, et al., 2018). The sciences of hydrology could date back to ancient China and Egypt times when some precursors already started to record hydrologic data and

2 | Introduction

attempted to forecast floods and droughts (Ralph O. Dubayah, 2000). It is also where the concept of modern station-based hydrometeorological observation originated from. More recently, remote sensing has rejuvenated hydrological studies and inspired more potentials of hydrological modelling in response to sustainable development by augmenting the information content and expanding the scope (Ahlmer, et al., 2018). In more details, more spatial components such as topography, land use and land cover are activated in this context by remote sensing and Geographical Information Systems (GIS), and both temporal, as well as the spatial scope of the simulation, are extended (Kalantari, et al., 2017).

During the last two decades, there is a rush to develop tools and platforms for data-driven hydrological modelling (Kalantari , et al., 2014a & b; 2015; 2017). At the same time, a new interdisciplinary field of Hydro informatics, which conjugates the information technology and hydrology, hydraulics, and even broader fields of environmental sciences (Remesan & Mathew, 2015). Due to its characteristics of data-intensive and comprehensive, this emerging discipline has served as a more reliable tool to sustain the decision-making process in water management, stimulating more possibilities for future hydrological studies and sustainable development.

1.2 Aims and objectives

This study aims to serve as a guide to hydrological modelling and a better understanding of the hydrological cycle through investigating the water balance in a study area in Kringlan catchment. The distributed modelling MIKE SHE is applied to simulate groundwater, surface water, recharge and evapotranspiration (DHI, 2017).

The specific objectives of this are:

1. To set up a working climate and land environment based on local meteorological data, geological and topographical data (rainfall and snowfall, potential evapotranspiration, air temperature, vegetation type and distribution, soil distribution, digital elevation map)

2. To construct a model including unsaturated zone and saturated zone, overland flow in the working environment;

3. To draw a channel flow model in MIKE Hydro and couple it to other hydrological components with MIKE SHE;

4. To analyse and calibrate the model to fit for reference data (time-varying outlet discharge in the study area);

Introduction | 3

5. To verify the established model through simulating another period with fixed parameters and settings in the calibration stage;

6. To understand the hydraulics mechanisms and hydrological processes to explain model parameters and its performance;

7. To get a brief understanding of solute transport modelling through a simple particle tracking model of chloride in the SZ module.

The MIKE SHE model in this study mainly contains two parts:

• The water balance model: established on modules of a saturated zone, an unsaturated zone, overland flow, channel flow as well as evapotranspiration, precipitation, snow. This model is manually calibrated while using measured discharge data in Kringlan station and modelled discharge data from HYPE as a reference. Validation is conducted for another period after the time frame of calibration;

• The water quality model: a simple particle tracking model of Cl- is set up with specifying a leaching source from forest soil.

1.3 Study area

Norrström drainage basin occupies an area of 22,650 km2 and covers a mixed landscape of urban, open land, forest and wetland, which also includes two largest Swedish lakes-Lake Mälaren and Lake Hjälmaren (Pecswaterses.com, 2018). The major area of Norrström basin is located in the boreo-nemoral zone while the remaining part located in the Boreal zone. Stockholm, as the capital city of Sweden, is also situated at the outlet of this basin area with its highest population density in the whole country.

As shown in Figure 1-1, Kringlan catchment sites on the west boundary of Norrström basin with an area of 294 km2 and a sub-catchment in the southwest of Kringlan with an area of 54.5km2 is chosen as study area (Dong, 2014). The landscape of this area is dominated by lakes and plains, which is also highly afforested (about 90%). Different types of rocks like leptite rock, halle flint rock and a small amount of granite characterise the indigenous geographies (Xu, 2003). As a result, the land use is affected and somehow distributed by the specific soil type, for example, the land where is a forest is covered by sandy soil and where for agriculture is covered by clay soil. (Seibert, 1995). From the year 1981 to 2010, average precipitation is 837 mm per year while average evaporation is 459 mm per year (SMHI, 2011). Mean annual air temperature in this region is around 3.3°C, and a maximum mean monthly temperature of around 16°C occurs in July, whereas a minimum of -11°C occurs in January. (SMHI, 2018)

4 | Introduction

According to the Swedish University of Agricultural Sciences (SLU), a negative Cl- budget was occurred in Kringlan catchment. Suggested by previous researches targeting on the area, leakage from vegetation and forest soil in this catchment have contributed to imbalances in local Cl- budgets. (SLU, 2011)

Figure 1-1 Maps of the study area’s location (Xu, 2003)

Methodology | 5

2 Methodology

2.1 Theoretical background

The water cycle, or hydrological cycle, is described as the natural phenomenon of water movement and state transformation between atmosphere and earth. As shown in figure 2-1, the water cycle involves a diversity of processes, and the major components include atmospheric condensation, downward precipitation to land surface, upward evaporation and evapotranspiration, recharge from watercourses to ocean, infiltration into soil and groundwater, etc. All these involved processes occur perpetually in the hydrosphere, which is referred as the discontinuous layer where water transforms among its different phases (Britannica, 2002) and interacts with the upward atmosphere and downward lithosphere.

Figure 2-1 The Water Cycle (NASA,2019)

As the total amount of water remains constant within the water cycle, the global water cycle system is considered as a closed system (USGS, 2017). From a modelling perspective, hydrological models simulate the motion of water, the transport of mass and account for both spatial and temporal

6 | Methodology

variations (Mujumdar & Kumar, 2012) after a system boundary is defined. As the boundary information defined for a catchment, the movement of water can be clarified through inter-relationships between each hydrological component and the inter-relationship could be generalised as the following equation (Cartwright, et al., 2013):

𝑃 + 𝐺𝑊𝑖 = 𝑆𝑊𝑜 + 𝐸𝑇 + 𝐺𝑊𝑜 + ∆𝑆𝑇 (1)

Where:

P=Precipitation;

𝐺𝑊𝑖=groundwater inflow from adjacent catchments; accordingly,

𝐺𝑊𝑜=groundwater outflow from the catchment;

𝑆𝑊𝑜= surface water outflow;

𝐸𝑇=Evapotranspiration;

∆𝑆𝑇= changes in soil storage.

Regarding the broader simulation domains, the focus what hydrological models target on does not merely refer to water balance hydrograph, but the quality analysis also constitutes an irreplaceable segment. Complicated mechanisms that represent physical, chemical and biological processes outline the way how solutes transport within an aqua system (Soltani, 2017). Basically, three hierarchical mechanisms control hydrological transport, listed as follows (Soltani, 2017):

• Hydrodynamic transport, defined by physical conditions of the system such as catchment structures, hydraulic properties and boundary conditions;

• Mass transfer, indicating the exchange of solute which occurred between mobile and immobile zones;

• The mass transformation, generalised as decay and degradation.

Thus, an equation reflects mass balance could be generated in accordance with equation (1) (Cartwright, et al., 2013):

𝑃 × 𝐶𝑃 + 𝐺𝑊𝑖 × 𝐶𝐺𝑊𝑖+ Σ𝑅 = 𝑆𝑊𝑜 × 𝐶𝑆𝑊𝑜

+ 𝐺𝑊𝑖 × 𝐶𝐺𝑊𝑜+ ∆𝑆𝑇 × 𝐶𝑆𝑇 (2)

Where:

C=concentration of the Solute in different hydrological components;

𝛴𝑅=a reaction rate for all reactions that consume or produce the solute, for conservative solute,

𝛴𝑅equal to 0.

Methodology | 7

As stated in this formula, solutes in a defined water system are accumulated from precipitation; meanwhile, soil leakage and groundwater inflows from adjacent systems could also be sources of the solutes. A fraction of mass might be consumed through mineral dissolution while others would be discharged (Cartwright, et al., 2013). Figure 2-2 illustrates the hydrologic components presented in Equation (1), generalises the flow direction of each component, and also relates solutes with those components, as presented in Equation (2).

Figure 2-2 Graphical Solute Balance in a Catchment (Cartwright, et al., 2013)

Chloride is generally considered as non-reactive in ecosystems; thus, it is frequently used as a conservative solute in the field of mass balance study (Schlesinger & Bernhardt, 2013), especially to investigate transport processes. However, it is also common to notice chloride imbalances in the catchment scale, which is typically originated by complex reasons (Svensson, et al., 2012) such as dry deposition (Juang & Johnson, 1967), mineral weathering (Peters, 1991), and interactions with vegetation and soil (Öberg, 2002) (Svensson, et al., 2012). Recognised by this (Mengni, 2014) in

8 | Methodology

Kringlan catchment, a negative imbalance of chloride occurred while wet deposition could only account for less than one-third of the chloride mass. Combined with a high concentration of chloride in forest soil in Sweden tested by SLU, an internal source of chloride from soil leaching has identified to explain the imbalance.

By analysing the travel time of Cl- particle, the residence time of water in the hydrological cycle can be estimated, which can also be called water age.

The residence time of groundwater calculated by particle tracking method can be defined as Ground Water Age. Water age is widely used in the field of water management, especially in monitoring water quality.

2.2 Data description

2.2.1 Initial setup

With the considerations on processing speed and output precision, the cell size of input data is set up as 50m × 50m, with the projected coordinates system of SWEREF99 TM. The number of X columns is 180 and the number of Y columns is 262 for the case study area. All raster data are reclassified and all vector data are converted into DFS2 format with a cell size of 50m. Some initial parameters in Table 2-1 were suggested by studies of Dong (2014) and Sterte (2016) in Kringlan catchment.

Methodology | 9

Table 2-1 Initial Simulation Setup

Initial Simulation specification

Simulation period

Start date 2011/01/01

End date 2013/01/01

Time step control

Initial time step 1 hour

Max allowed OL time step 1 hour

Max allowed UZ time step 1 hour

Max allowed SZ time step 3 hours

Model domain

Map projection type SWEREF99 TM

Cell size 50m*50m

Grid (NX*NY) 180*262

10 | Methodology

2.2.2 Vegetation

The study area is covered primarily by forest, arable land, grass and lakes. As shown in Figure 2-3, the dominant vegetation type is forest, which covers near 90% of the sub-catchment area (Jutebring Sterte, 2016). The main forest types are deciduous forest, coniferous forest, and mixed forest. The main tree species are Scots pine and Norway spruce (Jutebring Sterte, 2016). Lake Sågen, the biggest lake in the region, lies on the eastern boundary of the sub-catchment, covering an area of approximately 2km2. The networks of rivers connect other lakes and discharges to lake Sågen, which is also the outlet of this sub-catchment. The number of residents in this area is negeligible, thus human activities are not included in the model.

Based on some previous researches (Butlot, 1990; DHI, 2006; F.M., Leuning, & Schulze, 1993), four factors are defined for each sort of vegetation in the module of land use and evapotranspiration: Leaf Area Index (LAI), root depth (RD), crop coefficient (Kc) and Manning’s M. Manning’s M is overall set as 20 for the entire study area and LAI, RD, Kc are set as table 2-2.

Methodology | 11

Figure 2-3 Map of Vegetation (©Naturvardsverket, 2014

Table 2-2 Evapotranspiration reference factors classified by vegetation type

Grass Lakes Arable land

Mixed forest

Deciduous forest

Coniferous forest 1

Coniferous forest 2

LAIa,b,c 2.25 0 3.5 5.25 3 7 7

RDa,b,c(m) 0.4 0 0.55 0.55 1.2 0.8 0.8

Kca,b,c 1 1 1.15 1.15 1 1 0.9

aBultot et al (1990) bDHI, (2006)

cKelliher et al., (1993)

12 | Methodology

2.2.3 Geology

In this sub-catchment, the surface soil mainly consists of peat, bedrock outcrop, fine till, clay silt and marine (Figure 2-4). The dominant soil type is clay silt, among other soil types. In the water balance model, the vertical distribution of soil types is characterized assumed by the type of surface soil. For instance, where there is 0-2m Peat above, 2-4m Middle till in mid and 4-50m Bedrock at the bottom in the unsaturated zone, the surface soil type would be characterized as peat soil. The soil profile is described more explicitly in chapter 2.3.2.

Figure 2-4 Geology map of topography (©Sveriges geologiska undersökning, 2012)

Methodology | 13

2.2.4 Climate

Figure 2-5 Precipitation 2011-2012 (©SMHI 2012a)

Figure 2-6 Temperature 2011-2012 (©SMHI 2012b)

Precipitation and air temperature are two foremost datasets used in the local meteorology module. The precipitation data from 2011/01/01 to 2012/12/31 (SMHI 2012a) presented in figure 2-5 with higher precipitation frequency in the summer, i.e., June and August, for both years. The most intensive precipitation event (29.4mm) occurred in 2012/08/22. The annual averaged precipitation of 2011, 2012 are 767 mm and 890 mm, respectively.

The temperature data is also acquired from the same station during 2011/01/01 to 2012/12/31(SMHI 2012b). Figure 2-6 shows that the temperature fluctuates between around -20℃ to 20℃. The temperature fluctuation shows similar trends, the maximums, and the minimums, occurring almost at similar periods. The annual temperature of 2011 is 4.7℃, and that of 2012 is 5.4℃. The air temperature is primary input for the snow melt calculations in the model.

0

5

10

15

20

25

30

35

2011/1/1 2011/4/1 2011/7/1 2011/10/1 2012/1/1 2012/4/1 2012/7/1 2012/10/1

Precipitation (mm) 2011-2012

-20

-10

0

10

20

30

2011/1/1 2011/4/1 2011/7/1 2011/10/1 2012/1/1 2012/4/1 2012/7/1 2012/10/1

Temperature(℃) 2011 -2012

14 | Methodology

2.2.5 Simulation reference discharge

Two sets of discharge data (Table 2-3) are derived from SMHI, serving as the reference data in the model calibration. The first one is the time-varying measurements data recorded in Kringlan meteorological station (located at the outlet of the catchment) and the second one is S-Hype (SMHI, 2011) modelled data of the midlet point, where the river of Rastälven enters lake Sången. The total discharge from 2011 to 2012 are displayed in figure 2-7 and figure 2-8. Previously mentioned initial parameters are utilzied to run the model and then subject to calibration.

Table 2-3 Reference data for Calibration

Data Type Source

Outlet discharge (Kringlan)

Station Discharge SMHI

Main river flow (Inloppet i Sången)

Model Discharge SMHI

Methodology | 15

Figure 2-7 Monthly discharge in Station No. 8981 “Utloppet av Sången”

Figure 2-8 Monthly discharge in Station No.9042 “Inloppet i Sången”

1.72 1.84

10.8

2.53

1.280.9291.75

5.104.32

2.65

4.93

7.23

2.40

4.14

2.99

4.05

1.86

3.50

2.33

3.78

9.79

7.02

3.68

20

11

-02

20

11

-03

20

11

-04

20

11

-05

20

11

-06

20

11

-07

20

11

-08

20

11

-09

20

11

-10

20

11

-11

20

11

-12

20

12

-01

20

12

-02

20

12

-03

20

12

-04

20

12

-05

20

12

-06

20

12

-07

20

12

-08

20

12

-09

20

12

-10

20

12

-11

20

12

-12

Outlet Discharge (m3/s ) 2011-2012

Total Discharge

1.22 1.50 1.88

9.89

2.021.120.793

1.87

4.87

3.76

2.20

4.86

6.15

2.11

3.752.91

3.52

1.55

3.41

2.06

3.86

8.71

6.12

3.03

20

11

-01

20

11

-02

20

11

-03

20

11

-04

20

11

-05

20

11

-06

20

11

-07

20

11

-08

20

11

-09

20

11

-10

20

11

-11

20

11

-12

20

12

-01

20

12

-02

20

12

-03

20

12

-04

20

12

-05

20

12

-06

20

12

-07

20

12

-08

20

12

-09

20

12

-10

20

12

-11

20

12

-12

Main River Flow (m3/s) 2011-2012

Total Discharge

16 | Methodology

2.3 MIKE SHE models

2.3.1 MIKE SHE

MIKE SHE by DHI (Danish Hydraulic Institute) is a deterministic distributed model system.

MIKE SHE focuses on analysis, planning and management of groundwater resources and groundwater environmental issues by processing overland flow, unsaturated flow, saturated flow, channel flow (coupling with Mike 11), precipitation and evaporation.

However, there are various existing modelling software to simulate water flow. Hydrological models through catchment can be roughly divided into a kinematic model and dynamic model. The kinematic model assumes the existence of the underlying flow field basing on theoretical approaches. The dynamic model builds on the numerical solution combining water mass balance and flow equations. (Soltani, 2017)

To elaborate the software features of MIKE SHE, another widely-used modelling software-MODFLOW by U.S. Geological Survey is taken as an example to compare (Table 2-4). Both MODFLOW and MIKE SHE dynamically executes the hydrological simulation. MODFLOW is also a three-dimensional software, but it can only simulate groundwater flow and channel flow while MIKE SHE is capable of simulating the water movement more comprehensively at the catchment scale, including overland flow, channel flow and evapotranspiration. MIKE SHE can appropriately incorporate unsaturated zone and overland flow and infiltration and recharge can be calculated from their laws (Akram, 2012). Other parameters can be input to calculate water recharge, such as snowmelt and irrigation. MIKE SHE performs in a much more integrated way than MODFLOW since it is equipped with more functional modules. On the other hand, MODFLOW has some advantages that can build a model with less data and when groundwater simulation is the main focus. MODFLOW has an auto-calibration facility which leads to less operating time. Consequently, MIKE SHE stands out and is utilized in this study, as the water balance and hydrological cycle is the main focus of this study (Kalantari et al., 2017)

Methodology | 17

Table 2-4 Model features comparisons between MIKE SHE and MODFLOW (Akram, 2012)

Criteria

MIKE SHE

(by DHI)

MODFLOW

(by USGS)

Basic modules

Five modules:

Overland Flow, Channel Flow,

Evapotranspiration,

Unsaturated Flow & Saturated

Flow

Two modules:

Channel Flow and Saturated

Flow

Recharge

Recharge by water balance

simulation

Included as an upper boundary

condition, a calibration

parameter

Grid

Square cell (Raster)

Variable finite difference

(Vector)

Model layer

The layer is characterised by

horizontal and vertical hydraulic

conductivity and a top and

bottom elevation

Confined aquifer is specified by

transmissivity value and

aquitard is specified by leakage

value. No need of elevation data

Calibration Against observed hydraulic

heads, river water level and flow

Against observed hydraulic

heads. Possible Auto Calibration

for some parameters

Water Quality Model 2D 3D

User Interface Complicated and a training

program is suggested to learn

Much easier, can be learned

quickly from the users' manual

Operation Time Long Short (Much faster)

18 | Methodology

2.3.2 Water balance model

Figure 2-9 MIKE SHE models structure (DHI, 2017)

After all meteorological and geological background are provided, the whole hydrological model will be constructed step by step in each embedded hydrological section. Figure 2-9 illustrates the simulation structures and processes originated in MIKE SHE models. Water, introduced to the system by precipitation, can flow to the ground or be intercepted by vegetation. Water on the ground could infiltrate down to unsaturated zone, flow away as overland flow or evaporate to air. The water has infiltrated to the unsaturated zone could percolate further to the saturated zone, or decurrent plants' roots could also absorb it and return to the atmosphere through evapotranspiration. Channel flow should be defined in MIKE 11 or MIKE Hydro and then cohere into MIKE SHE. The water is consistently exchanging among all phases once the simulate is initiated. (Gustafsson, et al., 2008)

Figure 2-10 and Figure 2-11 conceptualise the framework of the water balance model which is built in the following chapters. The hydrologic schematic and relevant MIKE SHE components are logically organised to explain the fundamentals of the modelling. Irrigation is excluded in this modelling work due to two reasons: first, a negeligible area of land in the study area is held by agricultural activities; second, most of the agricultural land is located around watercourses, i.e., no external irrigation source.

Methodology | 19

Figure 2-10 Water Balance Model Framework; Modified from USGS scientific investigation report (Yeung, 2005)

20 | Methodology

Figure 2-11 Hydrologic schematic applied in MIKE SHE models build-up modified from USGS (2013)

Methodology | 21

2.3.2.1 Unsaturated zone

Unsaturated zone refers to the subsurface part above the water table, which stores water, plant nutrients, and other substances. This heterogeneous zone usually is not considered as a major water storage medium but plays a vital role as a filter to remove undesirable substances when water replenish an aquifer (USGS, 2013). The aquifer recharge rate, which evaluates water flow speed through unsaturated zone downwards to the water table, is often studied as the basic for contaminants spreading rate assessment.

𝜕𝜃

𝜕𝑡=

𝜕

𝜕𝑧[𝐾(𝜃) (

𝜕𝜓

𝜕𝑧+ 1)] − 𝑆(𝑧) (3)

Where:

𝜃 = is the volumetric soil moisture

K (𝜃) = unsaturated hydraulic conductivity,

𝜓 = the matric head induced by capillary action,

z = is the elevation above a vertical datum,

S (z) = the root extraction sink, and

t = is time

To dynamically calculate the vertical flow, the method of Richards Equation is chosen out of three options in MIKE SHE. Theoretically, Richards Equation (Equation 3) was suggested by continuity law and Darcy-Buckingham Law, and the latter is a derivation of Darcy’s Law adjusted for porous unsaturated media. Therefore, gravity is considered as the main force to drive vertical flow in the unsaturated zone, and the matric head is included as well. The matric pressure represents water pressure in pore medium relative to the pressure in air, which is negative because a lower pressure in soil compared with that of air (USGS, 2013).

From the geology perspective, unsaturated zone consists of a compacted upper zone or a loamy active layer with lots of humus and other organic matters and a lower alluvial zone with interbedded clay or less weathered bedrock (DHI, 2017A). Thus, soil profile is defined in this part, which is to distribute soil layers concerning the depth and thickness of each soil type. The soil zone and vertical discretisation are established and presented in table 2-5. 6 types of soil are defined into three vertical discretisations, and whole soil profile is extended to the depth of 50m. Hydrological characteristics of each type of soil are also assigned in the profile, which is represented through the Averjanov water retention curve (obtained from Kalantari et al (2014)) and soil water capacity C in Richards Equation (DHI, 2017B).

22 | Methodology

C =∂θ

∂ψ (4)

Thus, the previous Richards Equation is calculated as:

C∂ψ

∂t=

∂

∂zK(θ) (K(θ)

∂ψ

∂z) +

∂K(θ)

∂z− S (5)

For confirming lower UZ boundary, a dynamic groundwater table must be defined saturated zone model calculation method setup, and this procedure has been repeated for several times to ensure correct UZ-SZ coupling.

Table 2-5 Soil profile and discretisation in the UZ module

Vertical

Discretization Cells Peat Fine till Marine Bedrock

outcrop Clay-silt

0m-2m 0.2m*10 Mid Till

0m-4m

Fine Till

0m-4m Coarse

Till

0m-5m

Boulder

0m-5m

Clay

0m-5m 2m-4m 0.5m*4

4m-20m 1m*16

Bedrock

4m-50m 20m-50m 2m*15

Bedrock

5m-50m

2.3.2.2 Saturated zone

Saturated zone, also called as phreatic zone, is below unsaturated zone and have pores and rock fractures filled with water (EPA, 2013). The Finite Difference method has been chosen, as a full three-dimensional flow is allowed to shift between unconfined and confined zones in the SZ. The full 3-dimensional flow is governed by Darcy’s Law and calculated numerically by an iterative implicit finite difference technique (DHI, 2017A). The governing equation (Equation 6) for 3D finite difference method is (DHI, 2017B):

𝜕

𝜕𝑥(𝐾𝑥𝑥

𝜕ℎ

𝜕𝑥) +

𝜕

𝜕𝑦(𝐾𝑦𝑦

𝜕ℎ

𝜕𝑦) +

𝜕

𝜕𝑧(𝐾𝑧𝑧

𝜕ℎ

𝜕𝑧) − 𝑄 = 𝑆

𝜕ℎ

𝜕𝑡 (6)

Where,

𝐾𝑥𝑥, 𝐾𝑦𝑦, 𝐾𝑧𝑧 = the hydraulic conductivity along the x, y, Z axes;

Methodology | 23

h = the hydraulic head;

Q = the source/sink terms;

S = the specific storage coefficient.

A geological model is required before building the computational model, and the model is characterised by layers and lenses. In this project, the computational layers are set up as same as the geological layer. As no pumping well is presented in the study area, pumping wells are excluded from the SZ dialogue while subsurface drainage is taken into consideration to ensure springs drain to streams.

Table 2-6 Soil hydraulic properties

Soil

code

Soil name Horizontal

conductivity

Vertical

conductivity

Specific

yield

Specific

storage

Porosity

1 Middle till 1e-006 1e-006 0.2 0.001 0.3

2 Silt 5e-007 5e-007 0.1 0.003 0.3

3 Fine till 1e-007 1e-007 0.03 0.001 0.3

4 Marine/till 5e-006 5e-006 0.3 0.001 0.3

5 Bedrock

outcrop

1e-010 1e-010 0.15 0.001 0.5

6 Bedrock 1e-010 1e-010 0.15 0.001 0.1

Figure 2-12 The normal condition of the lower boundary in the SZ model setup (DHI, 2017A)

24 | Methodology

Two geological layers (soil layer and bedrock layer) are defined where the upper soil layer occupied a zone extended to 5 meters below ground and bedrock layer to 100 meters, respectively. Five hydraulic properties of 6 soil files are assigned as table 2-6. When the unsaturated model is coupled with the saturated model, only the top node of the SZ model exchanges water with the UZ model (a normal vertical boundary of SZ is shown in Figure 2-12), hence, vertical arrangements of water table, UZ lower boundary and SZ’s first layer lower boundary are the primary concerns. Initial head is set as -4 meters, 1 meter higher than the upper level of the second SZ layer, to ensure the UZ model intersect water table in the first SZ layer.

Both the outer and internal boundary are specified in the following steps. A no-flow boundary condition along the entire outline of the model is specified, expect the inlet and outlet. The condition of constant head is applied according to data from Lilla Grängen for upstream and Sången for downstream. Internal boundaries are used to specify lakes that are not simulated in MIKE Hydro by applying a constant head. Moreover, an additional special boundary condition is required in MIKE SHE, i.e., groundwater drainage to represent water transferred from saturated zone to surface water, topographic depressions, or removed out of model (DHI, 2017A). Each cell is specified with a drain level and a time constant. Initially, the drainage level is set as -1 meter to the ground surface (a typical value in MIKE SHE models setup) and the time constant is attributed as 1e-7/s.

2.3.2.3 UZ-SZ coupling

The recharge process between UZ and SZ occurs when the water table rises and water table rising rate is affected by the UZ moisture profile above the water table. In MIIKE SHE, UZ and SZ are explicitly coupled, in other words, they are simulated in parallel and only exchange water in specific time spots. Thus, the specific yield of the top numerical layer of SZ is forced to be the same as that of the UZ, and it is calculated based on the grid with the specified initial water table. (DHI, 2017A)

As mentioned above, the lower boundary of UZ should be carefully checked to ensure the water table either does not drop below the first SZ layer or rise above the top of the first SZ calculation layer. It is practised as follows (DHI, 2017B):

1. a potential head map is created in the first SZ layer after a simulation;

2. a minimum potential head map is then created from the bottom of the first SZ layer;

Methodology | 25

3. the two maps are checked together. Once the difference between the two maps is smaller than 0.5m, change the bottom of the first SZ layer to be lower;

4. procedures 1 to 3 are repeated until no small difference existing.

2.3.2.4 Overland flow

Overland flow, also called as saturation excess overland flow, could be categorised into two types despite driving mechanisms (Dimitriou, 2014). The first type is accumulated by overplus infiltration when the precipitation depth exceeds soil’s infiltration capacity then extra water would amass and flow by gravity towards hydrological networks (Dimitriou, 2014) (Liu, et al., 2004). The second is generated because of groundwater uplifting causing soil saturation exceeding its upper limit (Beven, 2006).

In MIKE SHE models, the calculation of overland flow could be time-consuming during simulation and can also cause significant instabilities. The computation choice provided by MIKE SHE is a tradeoff between accuracy and simulation time. The simplified Overland Flow Routing (SOR) method has been applied in the project. This option route overland flow with the assumption that ponded water flow to the flood plain areas from upland areas in the sub-catchment, subsequently discharge the streams through a uniform pathway. Hence, a coupling between Overland Flow in MIKE SHE and MIKE Hydro River is in need as the former offers lateral runoff to the rivers. (DHI, 2017A)

Getting down to the module control, two principal parameters to control overland flow velocity are utilized to start with. The surface roughness is restricted by Manning M, which is the inverse of Manning's value. This value ranges from 10 to 100, and a reclassified map modified from land cover is utilised. Simultaneously, detention storage to guarantee ponded water will not flow to an adjacent cell before accumulating over 2mm is specified.

In order to join drainage to the recipient of MIKE Hydro River node or a model boundary, a reference system is required. Water levels are checked to make sure the destination of flow stays at a lower level than the ponded water. Then it is routed to the nearest downhill river, boundary or internal depression based on drain levels. In ponded drainage, runoff coefficient attributes the fraction of ponded water that allowed to infiltrate or how much should be drained away (DHI, 2017A). Based on annual runoff data derived from SMHI (SMHI, 2016), runoff coefficient is adjusted as 0.5 to define available ponded water volume for OL drainage calculation. A value of zero is used to define where it is not a drainage cell, while 0.5 is assigned for drainage cells.

26 | Methodology

2.3.2.5 Channel flow (MIKE Hydro)

The Channel flow is simulated by the river module of MIKE Hydro, which defines and executes one-dimensional river models in a modelling framework, which is a new generation of DHI River modelling applications and hence the successor for MIKE 11 (DHI, 2017). Compared to MIKE 11, MIKE Hydro has a more visualised interface that allows the user to explore their data with a specific view and increases the accessibility of editing.

To simulate a Channel flow, four basic parameters are required to be input, which are River network (Include Branches), Cross section, Boundary condition and HD parameter. With MIKE Hydro, the river network from ArcGIS shapefile can be input directly. Branches inside sub-catchment are defined in the model at the same time as the chainages along each branch is computed automatically by MIKE Hydro. However, defined branches need to be connected manually by adding connecting points.

As a minimal requirement, one cross-section at each branch needs to be drawn. The cross sections can be added manually by defining the cross-section line on the branch or generated automatically by defining the width of branches and interval of the cross-section. Since the cross section is calculated based on the DEM, the DEM of water body is the elevation of the surface of the water body and the subsurface data need to be assumed. AgreeDEM, which is a surface reconditioning system for DEM, is applied to adjust the surface elevation of the DEM to be consistent with a vector coverage (Hellweger, 1997). It is calculated by ArcHydro Tool in ArcMap (Esri, 2018). Thus, lakes are generalised by wider cross-section input in MIKE Hydro.

2.3.2.6 MIKE SHE and MIKE Hydro couplings

MIKE SHE and MIKE Hydro are different products of MIKE ZERO Series by DHI. To couple them together, MIKE SHE Couplings settings in MIKE Hydro need to be included, which are Overland-river exchange, River-aquifer exchange and Inundation (If flood included).

MIKE SHE and MIKE Hydro are coupled by river links. To implement conversion from vector data in MIKE Hydro to raster data in MIKE SHE, the shapes of the river are generalised to the edges of different grid cells. In MIKE SHE, the branches are located on the edges that separate adjacent grid cells. Figure 2-13 illustrates MIKE 11 hydraulic model (The predecessor of MIKE Hydro) branches with H-points and corresponding river links in a MIKE SHE hydrological model grid. The location of river links is determined by river points called digitised points (H-point). MIKE SHE and MIKE Hydro only exchange water in H-point.

Methodology | 27

Since only edges between grids contain river links, the size of grid cells will determine the precision of model geometry. With a local scale model, the grid size of 50m can reduce the discrepancies between topography and river bank elevation, leading to more accurate water exchange between MIKE SHE and MIKE Hydro River. (DHI, 2017)

Figure 2-13 MIKE 11 branches with H-points and corresponding river links in MIKE SHE (DHI, 2007)

28 | Methodology

2.3.3 Chloride particle tracking model

As DHI stated, the full AD module is constituted of four independent fractions in each of which the transport pathways are described among the hydrological cycle (DHI, 2017B). It involves particle transport in overland flow, channel flow, unsaturated zone, and groundwater. The possibilities among different components and boundaries are shown in figure 2-14.

Figure 2-14 Transport possibilities among different components and boundaries

(DHI, 2017B)

Figure 2-15 Chloride transport model framework

A complete and calibrated MIKE SHE flow model is required before water quality simulation processing. Therefore, the chloride advective-dispersive model is set based on the thorough water balance model as described in

Methodology | 29

Chapter 2.3.1. Solute transport analysis in MIKE SHE could be performed by either the advection-dispersion (AD) module or particle tracking (PT) module. A simple particle tracking module is established in this project. Figure 2-15 briefly displays the framework of the PT model.

The tracking simulation period starts from 2011/01/01 00:00 to 2061/01/01 00:00, which bases on flow results of validation period from 2011/01.01 00:00 to 2012/01/01 00:00. Random particle tracking is chosen in the model, and only SZ is included in this method. There are three particles for each cell in the initial setting, and each particle is traced with a unique ID.

Chloride is the only species added to the system, and different sources are defined in model boundary conditions setup. The time-varying inflow measurement concentration (SLU, 2012) is added to the model as well, and the solubility in surface water is set to 3.4×106μg/m3. Additionally, an initial zero chloride concentration is set to launch the model. Suggested by (Mengni, 2014), chloride came from subsurface forest soil leaching and transported to groundwater in a constant concentration of 42mg/l across the whole catchment. The primary sources are soil leakage and inlet of upstream. The soil leakage is defined between -1m~-5m relative to the ground surface in the UZ zone of the model.

2.4 Model calibration & validation

2.4.1 Early run

A hotstart file is specified from an early 6-month simulation to maintain the starting points of the ready-to-calibrated model as a relatively stable condition, whereas, this time interval is not included in the model simulation frame. The period from January/01/2011 to December/30/2011 is officially simulated as calibration time domain and another one year from January/01/2012 to December/30/2012 of validation domain.

As initially set, the early run is tested to verify the model performance, and three plots are randomly defined in the model domain to ensure geographic continuity. It is ordinary to witness the water table experiencing drastic fluctuations in the beginning and stabilising after a while. However, plot A (coordinates: 485014, 6615100) displays a ceaselessly decreasing trend (shown in figure 2-16) while another two plots stay relatively stable. The topography base map and soil hydraulics characteristics file are simultaneously checked, in accordance with outliers shown in water head result file (figure 2-17). Errors arise around the grids where the soil type alters, especially in those have high altitude which could be figured out from

30 | Methodology

DEM. It is highly possible that low-resolution ratio and inaccuracy of soil map begets those soil taxonomy errors. Based on this assumption, the soil distribution map is modified manually in order to ensure geographic continuity.

Figure 2-16 Water head changes in Plot A（485014, 6615100）during one test run

Figure 2-17 Simulation errors in the head map

2.4.2 Model adjustments

Water is initiated to exchange and cycle among all specified hydrological components and boundaries once the simulation begins. The purpose of model calibration is to assess and improve the degree of accuracy and precision to which the model simulates the realistic hydrologic processes happened in the studied catchment. A satisfactory calibration is reached when the model is capable of reproducing despite uncertainties (DHI,

Methodology | 31

2017A). Due to the high complexity and compactness of MIKE SHE models, there are several parameters and settings might cause impacts on the model performance. Indeed, some parameters could affect more than others might do (Sterte, 2016). All adjustments are practised gradually in several tests, and performance of every single trial is evaluated to make a new modification.

2.4.2.1 Simulation control

Actually, a larger grid size can smoothly accelerate model simulation. It is suggested by DHI (2017A) to do a rough calibration with a bigger grid size or less UZ elements like reducing soil types and simplifying vertical discretisation. Another option is to replace the dynamic calculation method, for instance, using Gravity Flow method rather than Richards Equation in the UZ module. Long running time also arises when MIKE Hydro River cross-sections are too close together, which could be solved with the simple routing method embedded in MIKE Hydro River. What's more, the modules could be added one by one as shown in the following table 2-7. With the SZ module being the model basic, UZ, ET, OL OC modules could be orderly extended, and it is constructive to figure out from which module the problems originate.

Table 2-7 MIKE SHE simulation controls of modules

Modules

Saturated

Flow

(SZ)

Unsaturat

ed Flow

(UZ)

Evapotran

spiration

(ET)

Overland

Flow

(OL)

Rivers and

Lakes

(OC)

Simulation 1 √

Simulation 2 √ √ √

Simulation 3 √ √ √ √

Simulation 4 √ √ √ √ √

2.4.2.2 Potential Head and Manning’s M

Both statistics maps of the potential head from simulation and the minimum potential head from the top SZ layer are subtracted and compared with each other. The difference is minimal in some grids which alludes a probability that the unsaturated zone could drop below the bottom of the first calculation layer of the saturated zone. Under these circumstances, the lower boundary of the unsaturated zone module is extended downwards. All the

32 | Methodology

above-mentioned procedures are repeated iteratively until the discrepancies reach ideal level. Eventually, the soil profile in the unsaturated zone is moved from the premier setting of 40m to 50m under the ground surface.

There are also other issues related to UZ-SZ exchanging perceived-mismatching increase in UZ and SZ storage. For example, the UZ storage increases by 102 mm while only as much as around 1/9 of the volume increased by the SZ in the same test A. Furthermore, although the peak flow occurred in spring has almost been appropriately calculated, several small bumps show on the simulation results as showing in the figure 2-18 below. To increase the results precision, precipitation measurements are checked, and it implies those outliers always appear in the advent of rainfall. It possibly indicates errors in surface infiltration which subjects to Manning’s value as well as soil hydraulics conductivity.

Consequently, a distribution map replaces the uniform Manning’s M which is fixed in the initial running. The new distribution map is reclassified from the land cover map, and the Manning’s M for each type of vegetation cover is listed in table 2-8.

Figure 2-18 Simulation test A (period from July/01/2010-December/30/2011)

Table 2-8 Reclassified Manning’s M

Vegetation Grass Lakes Arable

land Mixed forest

Deciduous forest

Coniferous forest 1

Coniferous forest 2

Manning’s' M

17 30 25 13 13 10 10

2.4.2.3 Macropore flow

Macropore flow was excluded from the simulation system in the model setting. However, an abnormally high overland flow result indicates it should be taken into consideration so as to retain water into the UZ. Simplified Macropore Flow (bypass flow) method is added to the Unsaturated Zone module. This flow is relevant to soil moisture content and calculated with the fraction of 1 when the moisture content is above the field capacity (water

Methodology | 33

would flow freely under this condition), in contrast, the fraction of 0 when moisture content falls to the wilting point (DHI, 2017A). The equation below explains the mechanism (DHI, 2017A):

𝑄𝑏𝑦𝑝𝑎𝑠𝑠 =𝑃𝑛𝑒𝑡×𝑃𝑓𝑟𝑎𝑐√𝛼10𝛽50

∆𝑡 (7)

Where:

𝑄𝑏𝑦𝑝𝑎𝑠𝑠 =the bypass flow;

𝑃𝑛𝑒𝑡=the net rainfall rate;

𝑃𝑓𝑟𝑎𝑐=the maximum fraction of the net rainfall rate under wet conditions;

𝛼10=index to reduce the bypass fraction under dry conditions depends on 10cm below the

ground surface;

𝛽50= index to reduce the bypass fraction under dry conditions depends on 50cm below the

ground surface.

2.4.2.4 Snow melting

Merely the fundamental factors about snow melting are specified in the early model. In the calibration stage, the snow melting and freezing module is crystallised. The process of melting involves multifarious mechanisms in response to several climatic conditions (DHI, 2017A). The amount of water present within a snowpack, namely Snow Water Equivalent (SWE) is one of the driving forces to determine when snow melts (CampbellScientific, 2014). The snowmelt refers to the transformation from dry snow to wet snow and introduce surface runoff once the ratio of dry to wet snow storage surpasses the maximum wet snow storage fraction (DHI, 2017A). This fraction is typically set to 10 percent according to NSIDC (NSIDC, 2016). Apparently, air temperature has strong relativeness to snow melting speed. The degree-day factor (DDF) could be a time-varying, spatially distributed DFS file. However, due to air temperature data limitations, DDF is defined as a constant index as 4.6 mm/d/℃ to calculate snow ablation suggested by Senese’s research results (Senese.A, et al., 2014).

In MIKE SHE models, this association is reduced with melting threshold temperature as the following (DHI, 2017A):

𝑀𝑇 = 𝐶𝑇 × (𝑇𝑎𝑖𝑟 − 𝑇0) (8)

Where:

𝑀𝑇=the rate of melting due to the air temperature;

𝐶𝑇= the degree-day factor for snow melting;

𝑇𝑎𝑖𝑟=air temperature in the computation cell;

34 | Discussion and results

𝑇0=the threshold melting temperature.

However, as the snow storage change listed in table 3-3, modifications of the snow melt module have made a limited change in the MIKE SHE snow component, whereas it is not intelligible since the air temperature imported in the model is daily average which obviously blurs the sensitivity of water-snow phase transition in a snowpack.

3 Discussion and results

3.1 Water balance results

The simulated outlet discharge results of the whole model are shown in figure 3-1 (calibration stage) and figure 3-2(validation stage). In the calibration stage, the features of measurement data are almost captured by the model simulation, for instance, the peak flood happened in the spring, and the dry summer, as well as the humid autumn and winter, are all reflected properly, although there is a small number of trivial fluctuations in the simulation curve during the first 2 months. Nevertheless, when it comes to the validation stage, the model is not performing as well as that in the calibration stage. The curve follows main trends of the reference data for that year and fits well during some specific time spans such as the 1/1/2012 to 3/1/2012 and 5/1/2012 to 7/1/2012, but a spring flood is incorrectly presented. However, it does not lead to the rejection of the model as the calibration merely covers one year, and it should have larger potentials if the simulation period was prolonged to comprise more meteorological changes.

Discussion and results | 35

Figure 3-1 Simulated and measurements outlet discharge in the calibration stage

Figure 3-2 Simulated and measurements outlet discharge in the validation stage

In MIKE SHE results tab, the performance of the model is evaluated statistically, listing ME (mean error, eq.9), RMSE (root mean square error, eq.10), and R (Pearson Correlation coefficient, eq.11) automatically, which are calculated based on following equations:

𝑀𝐸 =(𝑂𝑏𝑠𝑖,𝑡−𝐶𝑎𝑙𝑖,𝑡)

𝑛 (9)

𝑅𝑀𝑆𝐸 =(√Σ𝑡(𝑂𝑏𝑠𝑖,𝑡−𝐶𝑎𝑙𝑖,𝑡)2

𝑛 (10)

𝑅 = √Σ𝑡(𝐶𝑎𝑙𝑖,𝑡−𝑂𝑏𝑠𝑖)2

Σ𝑡(𝑂𝑏𝑠𝑖,𝑡−𝑂𝑏𝑠𝑖)2 (11)

Where:

0

5

10

15

20

25

1/1/11 3/1/11 5/1/11 7/1/11 9/1/11 11/1/11

Outlet Discharge 2011 (m3/s)

Simulated

Measured

0

5

10

15

20

1/1/12 3/1/12 5/1/12 7/1/12 9/1/12 11/1/12

Outlet Discharge 2012 (m3/s)

Simulated

Measured

36 | Discussion and results

ME=mean error;

RMSE=root mean square error;

R=Pearson correlation coefficient;

i=calibration point;

t=simulation time;

Obs=observed measurement;

Cal=calculated measurement

Both ME and RMSE evaluate the precision of the model, therefore, the closer the value to 0, the more precise the model result is. R, which refers to the correlation, assess the model from the other aspect of accuracy and is anticipated to reach 1 (100%) as close as possible. Using the guide from Evans (1996), the way how the correlation R reflects model performances could be interpreted as:

When R=

• 0.00-0.19, very weak

• 0.20-0.39, weak

• 0.40-0.59, moderate

• 0.60-0.79 strong

• 0.80-1.00 very strong

The model performance in calibration and validation stages is statistically evaluated, and ME, RMSE and R are calculated simultaneously for the outlet discharge and the main river flow. Results are listed in Table 3-1. The results compared with outlet discharge are attributed with higher priority due to two reasons-first, it is daily measurement data which means higher veracity than that modelled discharge; second, the outlet station located in the most downstream of entire catchment while the main river discharge data reflects more upstream conditions. Although the model performance of the calibration stage is apparently better than that of the validation stage, generally speaking, the model correlation R keeps higher than 0.80 for both years, which indicates a very strong model precision. It also tells a relatively stable and robust performance on the upstream model segment according to similar ME, RMSE and R of main river flow in 2 years. However, besides a slight incline in Pearson correlation, a significant increase in RMSE from around 0.81 to around 1.37 is also negligible. The errors are magnified to some extent because they are squared before being averaged. Since a non-

Discussion and results | 37

existing spring flood is simulated in the validation stage, RMSE is definitely rising faster than ME.

Table 3-1 Statistical evaluation of simulation stages (Calibration & Validation)

Stage ME

(m3/d)

RMSE

(m3/d)

R

Calibration (2011)

Outlet -0.236411 0.806021 0.967714

Main river flow -0.41779 0.58031 0.989443

Validation (2012)

Outlet -0.019919 1.37144 0.88792

Main river flow -0.544572 0.783201 0.971325

To analyse more details of the water balance, hydrological processes presented in simulation output files could be categorised into four components as listed in Table 3-2. Rainfall and snowfall are described in precipitation (there is no detailed snowfall data, but rainfall is converted into snowfall when it is below the threshold air temperature). Runoff refers to all flow to the river from different hydrologic systems such as overland flow to river, base flow to river as well as the SZ drain to river. Evapotranspiration includes the total amount of volumes of water in evaporation from the soil and transpiration from the plants (Gray & Norum, 1969). The effect of storage, no matter in groundwater, surface, channel flow or reservoir storage in a basin is to moderate or dampen the fluctuant inflow (Gray & Norum, 1969). Focuses here are given to snow, overland, unsaturated zone, saturated zone in the scope of storage change.

More intense precipitation occurred in 2012, 130mm higher than the value of 767 mm in 2011. There is no significant difference between total evapotranspiration amounts in two years from model results, which also suggests a larger amount of water flows out as runoff or is stored in the underground.

As expected, significant changes in both storage and runoff can be perceived from this chart. Especially, when combining UZ and SZ to take into considerations, it could be noticed that more than doubled water volume is

38 | Discussion and results

recharged into saturated zone in 2012 compared with the previous year. Meanwhile, a deficit of 28mm happened in the unsaturated zone in the calibration stage while only 12mm deficit change in validation stage. It should be pointed out that a sharp declining snow storage change is calculated out which interpreted by the lower average air temperature during the winter season in 2011, which could be explained that snowfall and the temperature below threshold value may not appear in the exact same time in a day and it means snow could not accumulate.

Discussion and results | 39

Table 3-2 Water budgets for the study area during calibration and validation periods

Water exchange

(Units: mm)

Calibration

(2011)

Validation

(2012)

Precipitation

Total 767 890

Runoff

Total 301 394

Overland to river 232 304

Base flow to river 1 1

SZ drain to river 0 1

Overland drain to river 68 88

Evapotranspiration

Total 387 388

Storage change

Total 79 15

Snow storage change 83 -35

Overland storage change -1 3

UZ storage change -28 -12

SZ storage change 25 59

40 | Discussion and results

Table 3-3 General Water Balance (1981-2010), unit: mm (SMHI, 2016)

Station Number Rainfall Evapotranspiration Runoff

8981 839 458 381

9042 837 459 378

Table 3-3 shows an annual water balance information in the study area, which is averaged from the year of 1898 to 2010. Three general water balance components with their average values are displayed. With a geological border defined around Sången Lake, the study area is modelled into two parts- "inloppet i Sången (9042)” which is in upstream and “utlppet av Sången (8981)” in downstream. It could be noticed that there is no big discrepancy in averaged water balance in those two parts.

Compared with this general water balance information in table 3-3, the model results could be roughly evaluated. The average precipitation 828.5 mm between 2011 and 2012 is used during model simulation, which is slightly smaller than earlier years. The model does a proper estimation of the component of runoff. However, there is a gap between simulated evapotranspiration value and this average number. It is highly likely caused by the background evapotranspiration input data, which is measured based on a neighbouring catchment rather than the Kringlan catchment.

3.2 Particle tracking results

A classified figure (Figure 3-3) illustrates the travel time of the Cl- particles defined in the PT model. In this figure, the particles are represented by different colours from green to red in accordance with increasing residence time.

Comparing with the figure of the vegetation, Cl- particles with a short residence time (<5 years) are mainly located in the moveable water body like watercourses and lakes, which indicates a quicker water exchange driven by the channel flow. Simultaneously, large water body like lake Sången is a stable storage area of Cl- particles. The Cl- particles located in other areas rather than surface water systems, travel much slower with residence time more than ten years. For these Cl- particles, SZ flow and base flow are the main driving force of the solute transport. Especially for the area covered by red or dark red dots, the speed of particle transportation is quite low, which

Discussion and results | 41

implies a low groundwater refresh speed and a long water age. This travel time map could also be regarded as a sensitivity map for local water systems. Once the study area was polluted, the places covered by darker dots would suffer from more profound impacts and experience a longer recovery time.

Figure 3-3 Travel time of Cl- particles after 50 years

42 | Conclusions

4 Conclusions

4.1 Comparisons with the previous study

As the same study area, Dong’s model (2014) was done separately for the period from 2000/12/31 to 2006/12/31. The discrepancies in model settings between hers and the model in this thesis result in different models’ performances. The following table compares the statistical evaluation of the validation stage for Dong’s model (2006) and the new model (2012).

Table 4-1 Comparisons of models’ statistical evaluation of the validation stage

(based on outlet data)

Models ME

(m3/d)

RMSE

(m3/d)

R

(%)

Dong’s model

(2006)

0.226 1.20 0.97

The thesis model

(2012)

-0.019 1.37 0.89

First of all, for the statistical evaluation which is automatically processed by MIKE SHE, there are two sets of reference data in contrast with the only one in hers. Besides the identical one of outlet in both models, the main river flow data is appended, which has been indicative for calibration. Through comparisons of statistics between main river flow and outlet, it is possibly to have figured out if errors happened in downstream or upstream. To get it straight, when a general better performance has shown with main river flow than outlet, it becomes logically to pay more attention on the downstream, which makes the calibration process more time-efficient as well as well-organised.

The models are also featured by different length of calibration time frame. In Dong’s model, the calibration time lasted for 5 years, which led to a higher R value of 97% in the validation stage since more hydroclimate situations were included during calibration stages. However, the calibration R value of about 89% in the thesis’s study still reflects a very strong relation, which is the same level as Dong’s model, according to the threshold guide from Evans (1996). The results could evoke a discussion about a proper calibration time frame, which always consume time and efforts. Generally speaking, a longer

Conclusions | 43

calibration frame generates a more stable validation performance while indicates a more intensive commissioning concurrently. Based on the need for the model, to shorten calibration does not necessarily mean a less reliable model performance. It is essential to synchronize time efficiency and model robustness.

4.2 Conclusions and reflections

An integrated hydrological model is developed corresponding to local climate and topography, geology in the study area, capturing water volume exchange among different hydrological components. Hydrological modelling is usually site-specific regarding the unique local environment in each study area, but the hydraulic mechanisms driving the water cycle are identical.

MIKE SHE and MIKE Hydro are implemented for the simulations such that a better understanding of the whole hydrological cycle and driving mechanisms can be attained. The model is set by separate modules of overland flow, channel flow, unsaturated zone, saturated zone but they are coupled and interacted once simulation starts. To establish those modules, it is essential to define initial conditions and boundaries, and the initial conditions are to define the starting condition of the model, whereas, the boundaries are to restrain a domain for simulation domain. Furthermore, since all modules are integrated together in the simulation, it is crucial to make sure they correspond with each other. The UZ-SZ coupling exemplifies this point with its restrictions on computational layers setting. A proper setting of UZ soil profiles, the first SZ computation layer, assures regular water exchange between both sides of the dynamic water table. It can be considered as one of the most important factors for a successful simulation.

Calibrating a MIKE SHE model is not only about improving the model quality but also evoking a better understanding of modelling itself. A poor calibration leads to an unsatisfied model quality; thus, calibration is of critical importance to improve the robustness of the model. The time frame and the reference data could be considered as two foremost points for a successful calibration. The model modification and calibration processes are done in comparison with the reference data in this model, and it is evaluated statistically. The MIKE SHE model involves a massive amount of parameters and settings, and it is doubtless that they influence the model simulation through different ways and to different degrees. Therefore, simulations in MIKE SHE could be time-consuming.

To improve time efficiency, the model could be constructed step by step, gradually increasing its completeness and complexity, whereby the calibration could become more methodic and traceable as well. In fact, the calibration reference data used in the model is not sufficient to assure the

44 | Conclusions

model's robustness. It is reasonable to consider groundwater levels as a more reliable calibration dataset since it directly reflects the dynamic water head and is more sensitive to underground water changes. Unfortunately, there is no accessible data about time-varying groundwater levels in the study area.

Furthermore, potential evapotranspiration utilised in the model setup is not accurate enough which continuously cause accumulated errors during the entire simulation time steps. The total accumulated errors in the entire simulation period are negative, implying there is a smaller amount of water flowing out of the model boundary than flowing in.

However, it is still practical to use the current model for local hydrological investigation and regional water management. The developed flow model in MIKE SHE paves a way for future solute transport analysis and integrated water management in similar basins of the Norrström catchment and beyond. .

Reference | 45

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Appendix I | 51

Appendix I

52 | Appendix II

Appendix II

TRITA TRITA-ABE-MBT-19146

www.kth.se