the integrated distributed hydrological model, …

THE INTEGRATED DISTRIBUTED

HYDROLOGICAL MODEL, ECOFLOW- A

TOOL FOR CATCHMENT MANAGEMENT

Nikolay Sokrut

June 2005

TRITA-LWR PHD 1023 ISSN 1650-8602 ISRN KTH/LWR/PHD 1023-SE ISBN 91-7178-101-3

Nikolay Sokrut TRITA LWR PHD 1023

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The Integrated Distributed Hydrological Model ECOFLOW - a Tool for Catchment Management

PREFACE

This thesis is the final part of a PhD project initiated in 1999. The first part of the project resulted in a Licentiate thesis, entitled “A distributed coupled model of surface and subsurface dynamics as a tool for catchment management ” (Sokrut, 2001). Research results are described in Paper 1 and 2. This part of the project was partly supported by VASTRA (the Swedish Water Management Research Programme). Results of the second phase of the project are presented in Papers 3 and 4. This project part was financed by SGU (Geological Survey of Sweden). Thesis structure can be described as follows: (i) An introductory part, including the state of the art in the discussed subject, purpose of the project, methodology, results, conclusions, and future research suggestions (ii) Paper I, written in cooperation with SIAE (State Institute for Applied Ecology, Moscow, Russia) and Institute of Geophysics (University of Oslo, Norway) (iii) Paper II (iv) Paper III, written in cooperation with SIAE (State Institute for Applied Ecology, Moscow, Russia) (v) Paper IV, written in cooperation with SIAE (State Institute for Applied Ecology, Moscow, Russia) In the first paper the work has been shared between KTH, SIAE, and Institute of Geophysics. The distributed hydrological model ECOMAG, originally created at SIAE by Y. Motovilov, has been complemented with a nitrogen module, developed at Institute of Geophysics by G. Skotte. Then the model has been applied to a small watershed Vemmenhög in Southern Sweden. I was primary responsible for the model application, calibration, and analyses of the results. The second paper comprises results of testing ECOMAG as a driving routine for predicting the hydraulic conductivity head field within the Vemmenhög catchment. Variations in the hydraulic conductivity values have been studied from larger scales (i.e. regional hydraulic conductivity values of the aquifer in ECOMAG) to smaller grid scales (i.e. hydraulic conductivity values used in grid cells by ECOFLOW). My part of the work included development of a mathematical algorithm and numerical modelling. The third paper encompasses a brief description of the recently developed integrated hydrological model ECOFLOW and results of the model application. The model has been tested at the Vemmenhög watershed to demonstrate the ability of the model to properly simulate both ground and surface waters in a reliable and feasible way. The work has been shared between KTH and SIAE. I carried out the integration between the ECOMAG and the groundwater model MODFLOW. I also established the conceptual hydrogeological model used in MODFLOW. The fourth paper presents an extended and updated multi-scale version of the ECOFLOW model, which has been embedded in the Arc View and applied to the Örsundaån watershed, Sweden. The paper displays and summarizes results obtained for the Dalkarl aquifer (esker), including an analysis of the groundwater behaviour and modelling of the surface and groundwater interaction. The work has been shared between KTH and SIAE. I was responsible for developing a conceptual hydrogeological model for MODFLOW as well as applying the model to the catchment.

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ACKNOWLEDGMENTS

I am indebted to my supervisor Professor Roger Thunvik from Department of Land and Water Resources Engineering, KTH (Stockholm) for his thorough and thoughtful coaching. At times it seemed as if Roger was spending as much energy reviewing the material as I was in writing it. In addition to providing the support necessary for this project, he has been an energetic leader. I owe a lot to Professor Yuri Motovilov from State Institute for Applied Ecology (Moscow) whose guidance over the last four seasons helped me to conduct research and complete this thesis. Appreciation is expressed to Oleg Borodin and the SIAE staff for assisting in creating the ECOFLOW software. This was a project that would not have been possible without the assistance and cooperation of Geological Survey of Sweden (Uppsala). I would like to acknowledge my debt to Bo Thunholm and Mats Aastrup. I am grateful to Professor Arne Gustafson, Dr. Katarina Kyllmar and Dr. Martin Larsson from Uppsala Agricultural University, as well as to SMHI (Swedish Meteorological and Hydrological Institute) for data supplied and for interesting discussions. I wish also to thank several persons from the Institute of Geophysics, University of Oslo, who have assisted me in a variety of ways: Professor Lars Gottschalk, Dr. Wai Kwok Wong, Dr. Kolbjørn Engeland, and Dr. Nils-Otto Kitterød. I am also grateful to my colleagues at LWR for making my working hours at KTH pleasant and fruitful. My friends are specially appreciated for their tolerance and patience revealed.

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TABLE OF CONTENTS

Preface............................................................................................................................................................... iii Acknowledgments...............................................................................................................................................v Table of Contents..............................................................................................................................................vii List of papers......................................................................................................................................................ix Abstract ............................................................................................................................................................... 1 1 Introduction...................................................................................................................................................... 1

1.1 The need for an integrated model.................................................................................................................. 1 1.2 Objectives of the thesis ................................................................................................................................. 2

2 Background ......................................................................................................................................................5 3 ECOFLOW - an integrated hydrological model .............................................................................................9

3.1 The hydrological model ECOMAG .............................................................................................................. 9 3.2 Structure and principles of integration......................................................................................................... 11

3.2.1 Physical principles of integration .................................................................................................................................... 12 3.2.2 Parameter downscaling .................................................................................................................................................. 15

4 Results and Discussion.................................................................................................................................. 19 4.1 Hydrological and nitrate transport simulation at the Vemmenhög watershed............................................... 19 4.2 Results of the Bayesian downscaling algorithm............................................................................................ 21 4.3 The Örsundaån case - an example of multi-scale hydrological modelling ..................................................... 22

5 Conclusions .................................................................................................................................................... 31 6 References ...................................................................................................................................................... 33

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LIST OF PAPERS

Publications included in the thesis: Sokrut, N., Motovilov, J., Thunvik, R., and G. Skotte. (2005) Simulation of nitrate transport in the Vemmenhög catchment using the distributed hydrological model ECOMAG. Submitted to Nordic Hydrology. Sokrut, N. and R. Thunvik. (2005) Evaluation of uncertainties in simulation of hydraulic head fields by means of Bayesian updating techniques. Submitted to Journal of Geophysical Research. Sokrut, N., Motovilov, J., and R. Thunvik. (2003) ECOFLOW - a Distributed Integrated Hydrological Model as a Tool for Catchment Management. Presented at the 6th International Conference "Land and Water Use Planning and Management", Albacete, 2-5 September. Sokrut, N., Motovilov, J., and R. Thunvik. (2005) Örsundaån case –an example of multiple-scale hydrological modelling. Submitted to Journal of Hydrology. Relevant publications not included in the thesis: Collentine, D., Forsman, Å., Kallner, S., Sokrut, N., and A. Ståhl-Delbanco (2000) Systematisk beslutsprocess för ett ekologiskt, socialt och ekonomiskt hållbart vattenavrinningsområde. Vatten 3. Sokrut, N. (1999) On up- and downscaling and estimation of boundary conditions for integration of different mathematical physical surface and subsurface hydrological models. Thesis Report Series 1999:15. Sokrut, N. (2001) A distributed coupled model of surface and subsurface dynamics as a tool for catchment management. TRITA AMI LIC 2077. Sokrut, N., Motovilov, J., and R. Thunvik (2001) ECOMAG-MODFLOW: example of integration of surface- and groundwater models". Paper at the conference "MODFLOW 2001 and other modelling Odysseys", Denver, 10-15 September. Sokrut, N. and R. Thunvik. (2002) ECOFLOW – an integrated tool for surface and groundwater catchment modelling (In Swedish), Grundvatten 1, SGU. Sokrut, N., and R. Thunvik. (2002) Using Bayesian updating techniques to evaluate uncertainties in hydraulic head simulation. Paper at the 27th General Assembly of the European Geophysical Society, Nice, 22-26 April.

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ABSTRACT

In order to find effective measures that meet the requirements for proper groundwater quality and quantity management, there is a need to develop a Decision Support System (DSS) and a suitable modelling tool. Central components of a DSS for groundwater management are thought to be models for surface- and groundwater flow and solute transport. The most feasible approach seems to be integration of available mathematical models, and development of a strategy for evaluation of the uncertainty propagation through these models. The physically distributed hydrological model ECOMAG has been integrated with the groundwater model MODFLOW to form a new integrated watershed modelling system - ECOFLOW. The modelling system ECOFLOW has been developed and embedded in Arc View. The multiple-scale modelling principle, combines a more detailed representation of the groundwater flow conditions with lumped watershed modelling, characterised by simplicity in model use, and a minimised number of model parameters. A Bayesian statistical downscaling procedure has also been developed and implemented in the model. This algorithm implies downscaling of the parameters used in the model, and leads to decreasing of the uncertainty level in the modelling results. The integrated model ECOFLOW has been applied to the Vemmenhög catchment, in Southern Sweden, and the Örsundaån catchment, in central Sweden. The applications demonstrated that the model is capable of simulating, with reasonable accuracy, the hydrological processes within both the agriculturally dominated watershed (Vemmenhög) and the forest dominated catchment area (Örsundaån). The results show that the ECOFLOW model adequately predicts the stream and groundwater flow distribution in these watersheds, and that the model can be used as a possible tool for simulation of surface– and groundwater processes on both local and regional scales. A chemical module ECOMAG-N has been created and tested on the Vemmenhög watershed with a highly dense drainage system and intensive fertilisation practises. The chemical module appeared to provide reliable estimates of spatial nitrate loads in the watershed. The observed and simulated nitrogen concentration values were found to be in close agreement at most of the reference points. The proposed future research includes further development of this model for contaminant transport in the surface- and ground water for point and non-point source contamination modelling. Further development of the model will be oriented towards integration of the ECOFLOW model system into a planned Decision Support System.

Key Words: Multiple-scale hydrological modelling; Bayesian algorithm; Parameter estimation; Groundwater management; Statistical analysis.

1 INTRODUCTION

The national objective adopted by RIKSDAGEN (the Swedish parliament) outlines that groundwater must provide safe and sustainable supplies of drinking water and contribute to viable habitats for flora and fauna in lakes and watercourses (Bergqvist and Kahn, 2000). Furthermore, it states that pollution levels should be sufficiently low that the groundwater meets the requirements for high-quality drinking water as defined in the drinking water regulations of the Swedish Food

Administration, and in the requirements regarding high quality groundwater status in the EC water framework directive, which takes a catchment perspective on the strategy for dealing with the water quality problems in the environment.

1.1 The need for an integrated model

In order to find effective measures that could meet the mentioned groundwater quality requirements, there is a need for developing a Decision Support System (DSS) and a suitable model tool (Keen and Scott Morton, 1978; Fredricks et al. 1998;

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Giupponi and Rosato, 2002). Central components of a DSS for groundwater management are models for surface- and groundwater flow and solute transport (Barritt-Flatt, 1991). The most feasible approach seems to be integrating available mathematical models, and developing a strategy to evaluate the uncertainty propagation through these models. The overall purpose of such integration is not only to address technical scientific problems, but also to solve them together with various social as well as economic problems for any region (Thunvik et al. 1998). Available surface and sub surface hydrological models have usually been developed for specific purposes and limited to certain problem scales. Very often the surface water and groundwater systems respond to changes in each other (Devito et al. 1996). If one of the systems is modelled independently, an algorithm must be developed to represent changes in the other system of the model, but such techniques usually have serious limitations (Mitchell-Bruker, 1993). A more accurate and sophisticated approach is to model the system as a single integrated unit, where one process changes in both the surface water and groundwater systems and their mutual interaction occurs (Viney and Sivapalan, 2004). A number of attempts have been made in recent years to integrate different surface and groundwater models. Smith and Woolhiser, 1971; Akan and Yen, 1981; Hromadka et al. 1987; De Lima and Van der Molen, 1988; Sunada and Hong, 1988; Todini and Venutelli, 1991; Govindaraju et al. 1992; Swaine and Wexler, 1996; Van der Kwaak, 1999; Andersen and Weeber, 2000; Dogrul and Kadir, 2004; and Graham, 2004 reported about development of various integrated models. An incompatibility in the spatial and temporal resolutions is a significant impediment to a robust coupling of surface and groundwater models (Abbott et al. 1986a,b; Abbott and Refsgaard, 1996; Leavesley et al. 2002; Lidén et al. 1998;

Sivapalan and Wood, 1986; Thunvik et al. 1998). Different downscaling methods could be used to overcome the problem of discrepancies in spatial discretisation schemes (Vermulst and De Lange, 1999). These approaches cannot substitute for physically based models, but can resolve variability to smaller scales than present physical models allow (Anderson and Fenske, 1993; Ferraris et al. 2003). The challenge here is to correctly represent the natural variability as large-scale data are scaled downward to spatial distributions (Andreasson et al. 2003). Statistical disaggregation techniques have been developed worldwide to deal with large-scale data in relation to point-scale soil properties such as hydraulic conductivity values. The Bayesian updating procedure can be used to downscale given regionalised value and obtain different sets of the values for a smaller scale, taking into account their spatial distribution (Freeze et al. 1990; Hachich and Vanmarcke, 1983; Massmann and Freeze, 1989). The new integrated model ECOFLOW is formed from the hydrological model ECOMAG and the groundwater model MODFLOW (McDonald and Harbaugh, 1988). The ECOMAG model has a dual structure - a drainage basin can be modelled either as a set of the Representative Elementary Areas (REA) or a regular grid (Motovilov et al. 1999a,b). Sokrut and Thunvik (2005) demonstrated the application of this Bayesian downscaling technique in the ECOMAG model (Sokrut et al. 2003; Motovilov et al. 1999a,b) using the Representative Area Principle (Beldring et al. 1999; Bloschl et al. 1995; Fan and Bras, 1995; Wood et al. 1988; Woods and Sivapalan, 1995).

1.2 Objectives of the thesis

The primary purpose of the project was to create an integrated model capable of addressing hydrological flow and transport problems simultaneously on local and regional scales. This modelling system combines the distributed watershed model,

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ECOMAG, and the groundwater-flow model MODFLOW, functioning in a GIS environment. The objectives of the research can be stated as follows:

• To modify the ECOMAG model with a new chemical module ECOMAG–N that enables nitrate transformation modelling and to test the ability of the ECOMAG model to accurately simulate hydrological and nitrate transport processes in an arable watershed with a highly dense drainage system.

• To develop a downscaling algorithm based on a Bayesian updating procedure for obtaining parameter values at every grid cell given one effective regional parameter value for the whole region and taking into account its statistical distribution.

• To perform integration between the ECOMAG and MODFLOW.

• To apply the new integrated model ECOFLOW for the Örsundaån watershed to test the reliability of the model.

The structure of the thesis is as follows: (i) Chapter 2 provides background information about the integration of surface and groundwater; (ii) Chapter 3 demonstrates general principles of the hydrological model ECOMAG; illustrates the new integrated model ECOFLOW; and gives basic information about a Bayesian downscaling procedure used in the ECOFLOW modelling routine; (iii) Chapter 4 displays major results, which are summarised and discussed; and (iv) Chapter 5 gives important conclusions and suggestions for the future work.

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2 BACKGROUND

Methods for quantifying recharge and its variations for use in groundwater modelling applications vary. The most common method is quite simple: using an averaged recharge rate that is based on literature sources for a region. This value may be adjusted during calibration or held constant while all heterogeneity and errors in magnitude are accounted for by adjustments to hydraulic conductivity (Anderson and Fenske, 1993). Other methods of quantifying the recharge include using field methods to measure the infiltration, or analytical calculations. Another method of quantifying recharge is to integrate a watershed basin model with a groundwater model to form an integrated model that simulates the entire hydrologic cycle (Anderson and Fenske, 1993). Such a model can in an interdependent way account for processes, influence the recharge to the groundwater system, such as precipitation, interception storage, runoff, evaporation, and evapotranspiration (Meigs and Bahr, 1995). Indeed, numerous surface and groundwater projects are affected by the interaction of surface water and groundwater systems where changes in one system may have a significant impact on the other one. A situation where changes in river discharges and stages affect the groundwater system near public supply wells or environmentally sensitive areas might require an integrated modelling approach. However, the magnitude of the river stage deviations also depends upon the changes occurring in the groundwater system as a result of the surface water changes (Singh and Bhallamudi, 1998). Surface water and groundwater models are limited in their ability to simulate these scenarios relative to an appropriate integrated surface water and groundwater model (Jorgensen et al. 1989 a, b). A significant number of attempts have been made in recent years to integrate different models. Smith and Woolhiser, 1971 developed an integrated model for overland flow. They solved the one-dimensional

Richards equation for the unsaturated flow in the subsurface together with the one-dimensional kinematic wave equation for surface flow. The Richards equation was solved by an implicit Crank-Nicolson finite-difference formulation. Akan and Yen, 1981 developed a sophisticated integrated model, where they solved the complete Saint-Venant equations and the two-dimensional Richards equation. Akan, 1985; Sunada and Hong, 1988; De Lima and Van der Molen, 1988; and Govindaraju et al. 1992 developed overland flow models based on the kinematic wave approximation. Hromadka et al. 1987 developed a two-dimensional diffusion wave model assuming constant effective rainfall intensity. Govindaraju et al. 1988 derived an approximate analytical solution to overland flow under a specified net lateral inflow using the diffusion wave approximation. Todini and Venutelli, 1991 also developed a similar two-dimensional diffusion wave model in which the governing equations were solved by the finite-difference as well as the finite-element methods. Vieira, 1983 conducted a comprehensive study of various approximations usually applied to the Saint-Venant equations. Although, the overland flow models based on the complete Saint-Venant equations are computationally very intensive, they are more versatile and can also act as standards for comparison of simplified models (Andreasson, 2003). Woolhiser and Liggett, 1967; Lin et al. 1973; Chow and Ben-Zvi, 1973; and Kawahara and Yokoyama, 1980 developed two-dimensional overland flow models for impervious surfaces based on the Lax-Wendroff method (Lapidus, 1967) and a finite-element method, respectively. Zhang and Cundy, 1989 developed a two-dimensional overland flow model for a temporally constant, but spatially varying infiltration. MacCormack finite-difference method was used to obtain the numerical solution. Tayfur et al. 1993 also developed a two-dimensional overland flow model based on an implicit method for solving the governing equations and applied the model to experimental hill slopes.

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Govindaraju and Kavvas, 1991 in a detailed study of hill slope hydrology through a stream flow-overland flow-subsurface flow model, used the diffusion wave approximation for the surface flow component. Presently available integrated models for the overland flow use the Richards equation in the pressure-head form, which may result in significant mass balance errors for complex subsoil conditions. Mathematical modelling of overland flow involves the solution of the governing equations for both the surface flow and the groundwater flow with seepage at the ground surface acting as the connecting link (Cunningham and Sinclair, 1979). The level of model sophistication depends on the assumptions made for simplifying the governing equations before they are solved. Many models consider only the surface flow system along with an empirical treatment of the infiltration term (Miles and Rushton, 1983). More sophisticated integrated modelling approaches have been demonstrated in the models MIKE SHE (Graham, 2004), the Integrated Hydrology Model (InHM)(Andersen and Weeber, 2000), MODBRANCH (Swaine and Wexler, 1996), and IGSM2 (Dogrul and Kadir, 2004). In the integrated model MIKE SHE the overland flow component is simulated using the diffusion wave approximation. The subsurface flow in the unsaturated zone is represented by the one-dimensional form of Richard’s equation. The surface flow equations are solved by the explicit procedure developed by Preissmann and Zaoui, 1979, while the Richard’s equation is solved by the implicit finite-difference scheme. An integrated model that links the lumped surface water model with averaged parameters HSPF (Johanson et al. 1984) and the ground water flow model MODFLOW (McDonald and Harbaugh, 1988) has been developed by Andersen and Weeber, 2000. The approach used in the InHM model is disaggregation of the basin parameters into

discrete landforms that have similar hydrologic properties. These landforms may be impervious areas, irrigated areas, areas with high or low clay or organic fractions, areas with significantly different depths to the water table, and areas with different types of land cover or different land uses. The IHM integration interprets fluxes across the model interface and storages near the interface for transfer to the appropriate model component, accounting for disparate discretisation of land segments in HSPF and grid cells in MODLFOW (Van der Kwaak, 1999). Markström et al. 2002 used algorithms from the Precipitation-Runoff Modelling System (PRMS) and the MODFLOW groundwater model to create a new integrated model. Mathematical modelling of the integrated flow implies the solution of the governing equations for both the surface flow and the groundwater flow. The level of model sophistication depends on the assumptions made in simplifying the governing equations before they are solved (Yu and Schwartz, 1998). Many models consider only the surface flow system along with an empirical treatment of the infiltration term (Ross et al. 1995). On the other hand, some models consider both the surface and the subsurface flow systems, but use either a diffusion wave or a kinematic wave approximation for modelling overland flow (Beverly et al. 1999). Using an integrated model requires a large amount of data to model both the surface water and groundwater processes within the watershed (Ridder and Zijlstra, 1994). Additional data are often required for modelling the interaction between the surface and groundwater. Therefore, an integrated model consumes more time for development, calibration, and simulation compared with a surface water or groundwater model. An advantage with an integrated model approach is that the recharge based on a from the surface modelling appears to be more accurate and reasonable than results obtained through just using a groundwater model (Efstratiadis et al. 2005).

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Spatial and temporal variations in the aquifer recharge rates represent a type of heterogeneity that may influence characterization of the magnitude and apparent heterogeneity of hydraulic conductivities of aquifers (Sivapalan et al. 2003). The influence results from direct correlation between hydraulic conductivity and the source function in the groundwater flow equation (Western and Blöschl, 1999). Scientists have faced many problems in their efforts to develop integrated models (Blöschl, 2001). A model that integrates simulations of surface water and groundwater processes must account for the different scales of the spatial and temporal variability of the surface and groundwater systems (Kandel et al. 2004). Significant shortcomings in the integrated model include: (i) incompatibility in the spatial discretisation schemes; (ii) over parameterisation; and (iii) discrepancy in the time scale of surface water and groundwater behaviour (Abbott et al. 1986a,b; Leavesley et al. 2002; Lidén et al. 1998; Sivapalan and Wood, 1986; Thunvik et al. 1998; Blöschl et al. 1995; Fan and Bras, 1995; Wood et al. 1988; De Ridder and Zijlstra, 1994; Woods and Sivapalan, 1995). Common groundwater models that implement numerical solution techniques discretise the modelling area into grid cells because the model variables (hydraulic head, solute concentration, etc) computed by the model as well as aquifer characteristics can substantially vary over short distances (Leavesley et al. 2002). Computed variables (soil moisture, runoff, etc.) and specified parameters (land use, soil, etc.) often have a different spatial scale of variation than those of the groundwater system (Sivapalan et al. 2004). At a temporal scale, surface water models often use small time increments (minutes to hours) to depict changes in the system such as large storm events or releases of water in rivers. Groundwater models, because of the naturally slower groundwater flow (laminar flow), require longer time periods (weeks to months or years) to simulate groundwater movement and solute transport (Dagan, 1986).

Different downscaling methods could be used to overcome the problem of discrepancies in spatial discretisation schemes (Vermulst and De Lange, 1999). Numerous parameter downscaling techniques have been developed to deal with applying large-scale data to small-scale point properties (Schaake and Valencia, 1972; Venugopal and Foufoula-Georgiou, 1996; Zorita and von Storch, 1997; Sauerborn et al. 1999; Deidda, 2000; Müller et al. 2000; Sivakumar et al. 2001; Stehlik and Bardossy, 2002; Koutsoyiannis et al. 2003). Statistical disaggregation techniques have been developed worldwide to deal with large-scale data in relation to point-scale soil properties, such as hydraulic conductivity. The Bayesian updating procedure can be used to for downscaling a given regionalised value and obtaining a new set of values for a smaller scale taking into account their spatial distribution (Raiffa and Schlaifer, 1961; Benjamin and Cornell, 1970; Vicens et al. 1975; Neuman, 1982; Hoeksema and Kitanidis, 1985; Kitanidis, 1986; Freeze et al. 1990). A basic assumption is that the parameter is a random variable at each point of the computational grid, and that it is log-normally distributed, forming one uniform conductivity field. Then given some measured values, the initial a priori distribution is transferred into a posteriori distribution of the hydraulic conductivity field according to Bayes' approach (Ang and Tang, 1975). During the first step, the data are used in an unconditional sense to calculate updated parameters of the posterior pdf given the prior estimation of pdf’s parameters. In the second step, the data are used in terms of conditional simulation, taking into account the measurement locations (Massmann and Freeze, 1989). During the second step, the posterior values are updated conditionally according to Hachich and Vanmarcke, 1983 and Massmann and Freeze, 1987.

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3 ECOFLOW - AN INTEGRATED

HYDROLOGICAL MODEL

In this study, we have integrated the distributed hydrological model ECOMAG with the groundwater model MODFLOW. The distributed hydrological model ECOMAG is an attempt to integrate a physically- based representation of the hydrological processes into a conceptual model; it is a compromise between complexity of the model structure and limitation of data availability (Sokrut and Thunvik, 2005). The ECOMAG model possesses properties of lumped hydrological models, characterised by simplicity in their use, and a minimised number of model parameters, but on the other hand it preserves the main features of the physically based distributed models, e.g. ability to simulate hydrological processes at a high resolution scale (Sokrut et al. 2003). Another advantage of the model is that ECOMAG was developed especially for boreal conditions, and that it can explicitly account for lakes and swamps.

3.1 The hydrological model ECOMAG

The conceptual hydrological model ECOMAG is described comprehensively in Motovilov and Belokurov, 1997; Motovilov et al. 1998; Motovilov et al. 1999a,b. The most recent version of the ECOMAG model consists of two core modules, a hydrological module and a nitrogen one. The hydrological module considers the hydrological processes in a watershed, such as infiltration, evapotranspiration, thermal and water regimes of the soil, surface and subsurface flow, snow accumulation and snowmelt (Motovilov et al. 1998). The chemical module describes the processes of contaminant transformation in river basins and contaminant transport in river networks (Sokrut et al. 2005b). The essential feature of

the model is the ability to simulate a watershed using two distinct operation strategies (Sokrut et al. 2003): a grid approach implying a 3D grid and the assigning of all model parameters on a cell-by-cell basis, and a statistical approach based upon the Representative Elementary Area (REA) principle outlined by Beldring et al. 1999; Blöschl et al. 1995; Fan and Bras, 1995; Wood et al. 1988; Woods et al. 1990; Woods and Sivapalan, 1995. The structure of the ECOMAG landscape element is illustrated in Fig.3.1 (Motovilov et al. 1999a,b): a snow cover box that occurs during cold periods, a surface box, and three boxes in the soil (horizon A, horizon B, and a bottom box, the groundwater zone). Usually horizon A is a soil box with high porosity and conductivity, while horizon B is a deeper box with much lower porosity and conductivity. The hydrological processes for a single landscape element are numerically treated in a consecutive order for each box. Each soil horizon is divided into two zones, a capillary zone and a non-capillary one (Motovilov et al. 1999a,b). If the capillary soil moisture is less than the field capacity then the infiltrated water penetrates into the capillary zone. If the soil moisture exceeds the field capacity it drains into the non-capillary zone. Surface runoff on the slopes is described by a simplified version of the kinematic wave equation, based on Rose’s approximation. The subsurface and groundwater flow is modelled as Darcy flow (Motovilov et al. 1999a,b). The primary task of the nitrogen module is to simulate the nitrogen transformation cycle within a watershed (Sokrut et al. 2005b). The chemical module ECOMAG-N is capable of modelling the following main processes (Fig. 3.2): (i) nitrogen depositions (wet and dry deposition, fertilization, litterfall, and throughfall), (ii) organic matter decomposition, and (iii) plant uptake.

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Fig. 3.1 Vertical structure of ECOMAG for a landscape element. WP is the w lting point; h is thewater level in non-capillary zone; E1-6 are evapotranspiration rates from every box forming the total evapotranspiration rate (from Motovilov et al. 1999 a)

i

River flow

precipitation

surface water storage surface water outflow

subsurface outflow horizon A

subsurface outflow horizon B

groundwater outflow

ice particles

field capacityWP

E4

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subsurface inflow horizon A

subsurface inflow horizon B

groundwater inflow

porosity

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s

lio

i

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rta

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rta

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evap

otr

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irat

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melt watersnow cover

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ow

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zonecapillary

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Each soil box contains a pool of inorganic nitrogen (INN). The model does not distinguish between nitrate and ammonium; both these compounds are in the INN pool. It is assumed that all the nitrogen in the INN pool of a soil box, is dissolved in the water, and has a uniform concentration within the entire pool. Additionally to the INN pool, horizon A consists of two

organically bounded nitrogen pools: Labile Organic Nitrogen (LON) and Refractory Organic Nitrogen (RON) (Skotte, 1999). The processes of the LON and RON mineralization as well as decomposition of organic matter (transfer nitrogen from the LON to the RON pool) are considered 1st order kinetic processes (Sokrut et al. 2005b).

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Fig. 3.2 Nitrogen input and output fluxes, nitrogen pools and vertical transport of nitrogen in ECOMAG-N. LON is a pool of Lab le Organic Nitrogen, RON is pool of Refractory OrganicNitrogen; INN is a pool of Inorgan c N trogen (ammonium + nitrate); MINLON, MINRON areamoun s of nitrogen mineralised from LON and RON pools each day; MLOM in RON is the amount of nitrogen transferred from the LON pool to the RON pool (after Skotte, 1999)

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t

We assume that the plant uptake occurs in horizon A only, and that there is no nitrogen transformation in the horizon B and groundwater boxes, which means that the nitrogen in these boxes is only subject to advective transport (Sokrut et al. 2005b). The processes of nitrification, denitrification, dissolved organic nitrogen, and ammonia volatilisation are not yet incorporated into the model (Skotte, 1999). Modification of the modelling algorithm will be one of the key issues in future work in developing the model. The ECOMAG-N module considers only the advective transport of nitrogen. Given

the nitrogen concentration in water, the nitrogen transport is calculated by the model in the horizontal direction between adjacent grid cells, and similarly in the vertical direction between boxes, according to the water mass balance (Sokrut et al. 2005b). 3.2 Structure and principles of integration

The integration of the hydrological model ECOMAG with the groundwater model MODFLOW is based upon a regular grid cell approach. The new integrated model is based on the source codes of MODFLOW-88 and ECOMAG (Sokrut et al. 2003).

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Fig. 3.3 Vertical structure of ECOFLOW for a landscape element (from Sokrut et al. 2003)

3.2.1 Physical principles of integration The cross-section of a landscape element of the new integrated model ECOFLOW is presented in Fig. 3.3. It demonstrates a grid element divided into a number of layers: a snow cover layer in the cold period, a surface layer and two soil layers (a top layer, horizon A, and a bottom layer – MODFLOW). It differs from the original version of ECOMAG (Fig. 3.1) by the substitution of horizon B and the groundwater zone for MODFLOW (Sokrut et al. 2003). In ECOFLOW the hydrological model ECOMAG deals with the unsaturated

zone and the surface processes, whereas MODFLOW operates the saturated or the groundwater zone. The vertical water flux from horizon A (penetration), is calculated by ECOMAG at every time step, and forms the groundwater recharge to all active cells of MODFLOW (Sokrut et al. 2003). The runoff values of ECOMAG are the sum of the surface water outflow (surface runoff) and the groundwater outflow (groundwater flow) (Sokrut et al. 2003). A simplified ECOFLOW structure in the form of a flowchart is presented in Fig. 3.4. In the first stage, MODFLOW checks the type of

12


simulation, the size of the modelled grid, and the solution scheme to be used, reads values of parameters, number of stress periods, initial heads, boundary conditions, allocates memory space, etc., whereas ECOMAG reads and prepares the information about meteorological and hydrological data, reads values of parameters and the number of time steps (Sokrut et al. 2003). During this operation ECOFLOW executes ECOMAG and MODFLOW simultaneously. Within the stress period loop, ECOFLOW executes the MODFLOW and ECOMAG algorithms consecutively for each stress period. At the beginning of every stress period, ECOMAG calculates and writes information about the groundwater recharge from the surface horizon into the groundwater layer to MODFLOW's input files. Finally, all the output data are saved as separate ECOMAG output files (surface and

river runoff, soil moisture, etc.) and as MODFLOW output files (heads, draw down, and volumetric budget). The overland flow is described in the model by a simplified version of the kinematic wave equation in the form of the mass conservation equation and Manning’s formula (Maidment, 1993), which can be written as:

LQLQmBRhBLhLBdtd /)0,1,1(0)0,10,1(

21

−−=+ , (1)

Q i h B n1 11 2

15 3

1= / / / , (2) where Q1 is the horizontal flux (discharge) of surface water, h1 is the depth of surface flow, R0 is the rainfall excess, which forms the overland flow. B and L are the width and length of a landscape element, respectively,

Fig. 3.4 Flowchart of the ECOFLOW program structure. The flowchart does not include Bayesian downscaling algorithm (from Sokrut et al. 2003)

Bm=(B0+BL)*0.5 is the mean width of an element, i is the slope of an element, n is the Manning’s roughness coefficient. Indices 0 and L denote the values on the upper and lower boundaries of landscape element on a plane. The effective rainfall excess R0 is calculated as R V V V Vr P0 1 2= − + − , (3) where V1 is the rain or snowmelt water flux on the surface, V2 is the infiltration rate into the soil, Vr is the rate of return inflow of subsurface water on the surface, VP is the rate of water losses in the depressions on the surface. The infiltration rate into the soil over a whole element’s area, V, can be presented in the following form (see e.g. Vinogradov, 1988):

−−=−+= ∫∫

2

12

1

000

012 exp1)ln(1

1

1

KVKdFFdFVV

V

V

F

F

α,(4)

where

13


F K K0 ( ) exp( )= −α where F0(K) is the probability of exceedance distribution function . The penetration into the capillary zone (index c) of the soil layer of a landscape element is as follows (Motovilov et al. 1999a)

V VWFCMj c j

j

j, = −

1

β

, (5)

where FCM is the maximum field capacity value of a landscape element, and Wj is the volumetric soil moisture in the capillary zone of j soil layer. The penetration into the non-capillary zone (index nc) is described as follows (Motovilov et al. 1999a)

V VWFCMj nc j

j

j, =

β

, (6)

The water, entered into the non-capillary zone, can penetrate into the deeper soil horizon with the rate Vj+1, which equals the vertical saturated hydraulic conductivity of soil (Kj+1) in horizon j+1 (Motovilov et al. 1999a). The flow of subsurface water is supposed to be Darcy flow (Motovilov et al. 1999a). The vertical saturated hydraulic conductivity of soil (Kj+1) is assumed much higher than the penetration rate Vj,nc and only part of the infiltrated water, which enters into the non-capillary zone, percolates to the groundwater level (Sokrut et al. 2005a). The penetration rate Vj,nc , simulated in ECOMAG, is input data for the recharge term Ii,j in MODFLOW (McDonald and Harbaugh, 1988; Sokrut et al. 2005a): QRi,j=Ii,j*DELRj*DELCi, (7) where Ii,j is the recharge flux in units of length of the water layer per unit time QRi,j is the flow rate applied to the model at a horizontal cell location i,j DELRj*DELCi is the area of the cell Solving the partial-differential equation of ground-water flow used in MODFLOW yields in the finite-difference equation for a cell (McDonald and Harbaugh, 1988):

( ) ( )

( ) ( )

( ) ( )

( )1

,,1

,,

,,,,,,,,,,

,,1,,

21

,,,,1,,

21

,,

,,,,1,,

21,,,,1

,,21

,,,1,,

21

,,,,1,

,21

,

−

−

++

−−

++

−−

++

−−

−−

××=++

−+−+

−+−+

−+−

mm

kjim

kjim

kjiijkjikjikjim

kji

kjim

kjim

kjikji

mkji

m

kji

kjim

kjim

kjikji

mkji

m

kji

kjim

kjim

kjikji

mkji

m

kji

tthhTHICKDELCDELRSSQhP

hhCRhhCR

hhCRhhCC

hhCRhhCR

(8) where hm i,j,k is the head at cell i,j,k at time step m (L); CV, CR, and CC are hydraulic conductances, between node i,j,k and a neighbouring node (L2/T); P i,j,k is the sum of coefficients of head from the source and sink terms (L2/T); Q i,j,k is the sum of constants from the source and sink terms, with Q i,< 0.0 for flow out of the ground-water system, and Q i,> 0.0 for flow in (L3/T); SS i,j,k is the specific storage (L-1); DELR j is the cell width of column j in all rows (L); DELC i is the cell width of row i in all columns (L); THICK is the vertical thickness of cell i,j,k (L); and tm is the time at time step m (T). When the groundwater table reaches the ground surface and incoming surface flux V1 ends up in the saturated zone (simulated in MODFLOW), the return inflow of groundwater to the surface V2,r is formed in the saturated zone (Sokrut et al. 2005a). V2,r is calculated in ECOMAG as V2,r =V2-V2,c (9) The river flow is simulated by a simplified version of the kinematic wave equation (Rose et al. 1983) in the form of the mass conservation equation and Manning’s formula (Maidment, 1993), which are written as:

( ) RLlatRLLR LQQQhBhBdtd /)(

21

,60,60,60,,6, −+=+ ,(10)

RRR nBhiQ /35

62

16 = , (11)

where

14


Q6 is the river discharge, H6 is the depth of the river flow, LR is the length of the river element, BR is the width of the river element, iR is the slope of the river element, nR is the Manning’s roughness of the river bed. Indices 0 and L denote the variables on the upper and lower boundaries of the river element on a plane.Qlat is the lateral inflow into the river element from landscape elements on both sides of the river element. Qlat is calculated as Qlat= Q1 + Q4 (12) where indexes 1 and 4 denote the lateral inflow into the river element from the neighbouring left and right landscape elements in the watershed based on the surface layer simulated by ECOMAG and groundwater zone simulated by MODFLOW (Sokrut et al. 2005a). Lateral inflow of groundwater into river element Q4 is simulated by MODFLOW (McDonald and Harbaugh, 1988) as follows: Q4=Criv (Hriv-h), (13) where h is the groundwater head at the node of the cell underlying the stream reach, Hriv is the head in the stream (river stage simulated by ECOMAG), Criv is the hydraulic conductance of the stream-aquifer interconnection, and Q4 is the flow between the stream and the aquifer.

3.2.2 Parameter downscaling There are several conceptualisation approaches in modern hydrological modelling used to describe the runoff processes, e.g. Hydrological Response Units (HRU) (Leavesley et al., 1983), Hydrologically Similar Units (HSU) (Schultz, 1996), and Representative Elementary Areas (REA) (Wood et al. 1988), which represent areas within a river basin that have a similar hydrological behaviour and can be considered as units in modelling efforts.

Using the concept of the Representative Elementary Area (REA) in the ECOMAG model is thought to be a key issue in the estimation of the water flux and the hydraulic conductivity field distribution for different spatial scales (Motovilov et al. 1998; Sokrut et al. 2003). The REA can also be considered the scale at which a statistical treatment of spatial variability can replace a deterministic description, or more broadly, where a small-scale complexity gives way to a larger-scale simplicity (Fan and Bras, 1995). The REA concept can be interpreted also as “a spatial scale over which the process representations can remain simple and at which distributed catchment behaviour can be represented without the apparently indefinable complexity of local heterogeneity” (Blöschl et al. 1995). In the ECOFLOW model modelling parameter are disaggregated given regionalised values estimated for a landscape element using the REA principle (Sokrut et al. 2003). A statistical algorithm was developed for the parameter downscaling discretisation case for the REA (Sokrut et al. 2005). The entire up-and downscaling procedure is schematically depicted in Fig. 3.4, where, the procedure is divided into four steps (Sokrut, 2001). For the downscaling procedure we use the first and second steps only. Downscaling steps can be briefly described as follows:

• Estimating the equivalent value of the parameter (e.g. hydraulic conductivity K) from the REA analysis.

• Application of unconditional and conditional simulations using the Bayesian approach to estimate the statistical distribution F of the hydraulic conductivity K

Unconditional and conditional Bayesian updating algorithms were used to develop a procedure for downscaling of the REA parameters (Fig. 3.4). Application of these techniques has been presented in Freeze at al. 1990; Hachich and Vanmarcke 1983;

15


Massmann and Freeze, 1987; Massmann and Freeze, 1989, etc. A basic assumption is that the hydraulic conductivity is a random variable at each point of the computational grid, and that it is log-normally distributed, forming one uniform conductivity field (Sokrut and Thunvik, 2005). Then given some measured values, the initial a priori distribution is transferred into a posteriori distribution of the hydraulic conductivity field according to Bayes' approach. Similarly to Freeze et al. 1990 the whole Bayesian procedure is divided into two steps (Fig. 3.5). During the first step, the data are used in an unconditional sense to calculate updated parameters of posterior pdf given the prior estimation of pdf’s parameters. In the second step, the data are used in terms of conditional simulation, taking into account the measurement locations (Massmann and Freeze 1989). During the second step the posterior values are updated conditionally according to Hachich and Vanmarcke, 1983 and Massmann and Freeze, 1987.

The main principles of the Bayesian analysis and the mathematics of the Bayesian downscaling procedure are presented below. The Bayesian updating procedure has been performed in two steps: first, the data were used in an unconditional sense to calculate updated parameters of the posterior pdf given the prior estimation of the pdf’s parameters; and then, the data were used in terms of a conditional simulation, taking into account the measurement locations (Freeze et al. 1990; Sokrut and Thunvik, 2005). In order to obtain all necessary posterior pdf parameters for the mean and variance of a normal process we considered a process, which generates Y (Y = ln K), given independent and identically distributed random variables with a normal model pdf (Hoeksema and Kitanidis, 1985):

Fig. 3.4 A statistical algorithm for parameters up-and downscaling (e.g. for hydraulic conductivity value). Steps I and II are utilised in the Bayesian downscaling algorithm. h2 Γ2) are the boundary conditions; F is the sta istical distribution function; µ, σ, λ are the parameters of the distr bution function: mean, variance, and correlation length, respectively

(t

i

( ) ( ) ( )[ ]{ }22121 2exp2, σµσπσµ −−= −−ii yyf , (14)

where Y is a set of observations of hydraulic conductivity values (y1, y2, ..., yn) µy mean of the independent normal process

2yσ variance of the normal independent

process K hydraulic conductivity The likelihood function for this particular sample is as follows (Vicens et al.1975):

( ) ( ) ( )( )[ ]{ }22221 2exp2, σµυσπσµ −+−= −− ynsYL nn , (15) It was shown by Raiffa and Schlaifer (1961) that a convenient prior pdf for µ and σ is the natural conjugate of Eq.15, a normal inverted gamma 2 pdf, i.e. when it was combined with the likelihood function (Eq.15), it yielded an analytically tractable posterior pdf. This prior pdf is a product of a normal and an inverted gamma 2 pdf :

( ) ( ) ( υσσµωσµ ,,, 25.0 sfnyff IGN ′′⋅′′ )′=′ ,(16)

where y′ posterior mean s′ prior variance parameter n′ number of prior samples υ sample degrees of freedom ω prior information

16


Fig. 3.5 Flowchart of the Bayesian procedure used in the downscaling algorithm. The flowchart inc udes unconditional and conditional updating steps and Monte Carlo simulation l

By integrating Eq.16 with respect to both unknown variables, we obtain two marginal pdf’s for µ and for σ (Vicens et al. 1975):

( ) ( )

′′′

′′=′=′ ∫∞

υµσωσµωµ ,,,2

0 nsyfdff s ,(17)

and

( ) ( ) ( υσµωσµωσ ′′′=′=′ ∫∞

∞−

,, 2 sfdff IG ) , (18)

where ′2s prior variance parameter

υ′ prior degrees of freedom Then, the data were used in terms of a conditional simulation, taking into account

the measurement locations (Hachich and Vanmarcke, 1983; Sokrut and Thunvik, 2005). The values of µY, σY

2 and ρY were recalculated into the mean, variance, and autocorrelation function with respect to K as follows:

( )[ ]221exp YYK σµµ += , (19)

[ ]( ) [ ]( )222 2exp1exp YYYK σµσσ +−= , (20)

[ ]( ) [ ]( )1exp1exp 22 −−= YYYK σσρρ , (21) where ρY posterior autocorrelation function Then the obtained set of the downscaled parameter values was assigned to the grid in the ECOFLOW model.

17


18


4 RESULTS AND DISCUSSION

This Chapter contains a summary of the modelling results that have been obtained during the project work aimed at creating a new integrated hydrological model ECOFLOW. First, a selection of results obtained for ECOMAG-N and ECOFLOW is presented. These models have been tested and applied to the Vemmenhög catchment. The results from testing a new downscaling algorithm and analysing how the hydraulic conductivity field varies from the larger regionalised ECOMAG scale to the smaller ECOFLOW grid scale are reported briefly here as well. Finally, some of the modelling results from the ECOFLOW model as applied to the Örsundaån watershed are demonstrated.

4.1 Hydrological and nitrate transport simulation at the Vemmenhög watershed

The hydrological module ECOMAG was applied to simulate the behaviour of the Vemmenhög drainage basin for a 5-year period (1991-1995 years). The main parameters of the hydrological module were manually and automatically calibrated against observed runoff time series using the Rosenbrock procedure (Rosenbrock, 1960). The calibration was carried out using the Nash-Sutcliffe R2 criterion as an objective function (Nash and Sutcliffe, 1970). Based on the R2 criterion for the hydrological module, which ranged in value from 0.78 to 0.92, we can conclude that the model

produced good results in simulating the runoff values (Sokrut et al. 2005b). A sensitivity analysis of the hydrological module revealed that the model is highly sensitive to the following parameters (Sokrut et al. 2005b): (i) porosity of both the unsaturated and groundwater zones; (ii) thickness of the unsaturated zone; (iii) horizontal hydraulic conductivity for the unsaturated zone; and (iv) maximum retention storage. The nitrogen module ECOMAG-N was calibrated manually using sparse point observations because of the absence of observed nitrate time series measurements. Analysis of the nitrogen transformation simulation has shown that the most important parameters for ECOMAG-N are (Sokrut et al. 2005b): (i) 1st order kinetic of nitrogen mineralised from both LON (Labile Organic Nitrogen), RON (Refractory Organic Nitrogen) pools; and (ii) rate of organically bounded nitrogen transferred from the LON to RON pool. The nitrogen module algorithm used a ‘single-day’ fertiliser application principle, which assumes application of the fertiliser on a certain date. This modelling approach does not reflect the reality of the agricultural practices completely and is likely to be one of the reasons for errors in the simulation results (Sokrut et al. 2005b; Motovilov, 2005). Given the absence of available data, some of the model parameters were based solely upon literature sources, instead of field observations (Gustafson et al. 1964;

.

Point No 1 2 3 4 5 6 7 8 9Measured

value128.9 77.2 200.4 143.8 39.0 123.2 24.5 110.7 12.1

Computed value

132.7 78.4 196.2 142.0 34.4 122.5 24.8 106.7 12.6

Table 4.1 Comparison of the measured and computed inorganic nitrogen concentration values CINN for the horizon A (from Sokrut et al. 2005b)

19


P o int N o 1 2 3 4 5

M e a s ure d v a lue

12 . 3 17 . 4 3 4 . 5 19 . 9 10 . 3

C o mp ut e d v a lue

12 . 9 18 . 2 3 2 . 9 2 0 . 0 9 . 8

Table 4.2 Comparison of the measured and computed inorganic nitrogen concentration valuesCINN for the groundwater horizon (from Sokrut et al. 2005b).

Wiklert et al. 1983). Observed and simulated nitrogen concentration values for the unsaturated zone (horizon A) are found to be in relatively close agreement at most of the points (Table 1). The model results were not completely satisfying at some measurement points (1, 3, 5, and 8). Results of the nitrogen concentration simulation in the groundwater are more convincing (Table 2) except for a point 3. The modelling errors in the nitrogen simulation were probably caused by sparse observation data used for the calibration. Another important error source is that the modelling algorithm does not account for the processes of denitrification, dissolved organic nitrogen, and ammonia volatilisation. Since only a negligible amount of the nitrified nitrogen (< 0.01%) is used to be as nitrous oxide (N2O) under the nitrification process (Keeney, 1986) nitrate and ammonium are treated together in the same pool (INN) and, therefore, the process of nitrification is assumed not to be a part of the modelling algorithm (Sokrut et al. 2005b; Skotte, 1999) Although denitrification is one of the most important processes of the nitrogen transport within a watershed in Southern Sweden (Arheimer and Brandt, 1998) it was found by Starr and Gillham, 1989 that denitrification mainly occur in shallow aquifers because the water percolating the groundwater table is rich in organic matter. The difference between the groundwater and the surface levels in the Vemmenhög aquifer varies between 1.5 and 4.5 m, so we supposed that within such a deep aquifer almost all the organics are dissociated before percolation to the groundwater and the process of denitrification is not of a large magnitude. Shortage of information about

the manure application within the Vemmenhög watershed makes it difficult to make conclusions about the significance of the ammonia volatilisation process. However, assuming intensive farming practices and taking into account relatively high mean pH values of the soils (7.25) we expect that ammonia volatilisation makes an important contribution to the nitrogen budget for the Vemmenhög catchment (Sommer and Hutchings, 1995). Another important process, which should be incorporated into the model, is the transport and transformation of Dissolved Organic Nitrogen (DON) (Skotte, 1999). The challenge in modelling the transport of DON will probably how to describe the organic material precipitation and dissolution processes. Excluding DON from the model obviously resulted in modelling errors but it is relatively hard to estimate the consequences associated with these errors (Sokrut et al. 2005b). A considerable fraction of the nitrogen in soil water is organically bound and some of this nitrogen may originate from the LON and RON pools due to dissolution under the mineralisation process. Mineralisation of this part of DON is accounted for in the model by mineralisation of the LON and RON pools (Skotte, 1999). However, the transport of these substances with the moving water and the loss through discharge were not modelled. The denitrification process should also be considered for inclusion in ECOMAG-N despite the fact that this will substantially increase the model complexity (Puckett, 1995). More studies should however be done to quantify the losses of nitrogen due to denitrification before the decision is made to include nitrification and

20


denitrification processes in the ECOMAG-N model (Sokrut et al. 2005b).

4.2 Results of the Bayesian downscaling algorithm

The distributed hydrological model ECOMAG was used as a driving routine for

both unconditional and conditional simulation of the hydraulic conductivity head fields. Due to absence of real observations and the high cost of new field measurements we used synthetic observational data generated by a stochastic algorithm provided by Press et al. 1996 for a single unconfined aquifer with a uniform depth of 5 meters and “no flow” boundary conditions. The synthetic data were ranged within an interval, which was based on the analysis of the local soil properties (Sokrut and Thunvik, 2005). This synthetic example was designed to satisfy the requirements of having sufficient model simplicity to allow testing without excessive computer costs while keeping a realistic representation of aquifer parameter values and boundary conditions. Analysis of how initially prescribed correlation length, prior estimate of variance in hydraulic conductivity value, and the number of measurements affect the character and magnitude of uncertainty in the hydraulic head simulation for the following functions is provided in Sokrut and Thunvik, 2005. Fig. 4.1a shows how the variance in the hydraulic head varies with the initially prescribed correlation length; Fig. 4.1b shows how the variance in the computed hydraulic head varies with the number of measurements; and Fig. 41c shows how the variance in the computed hydraulic head varies with the prior estimate of the variance in the hydraulic conductivity value. The results demonstrated in Sokrut and Thunvik, 2005 indicate that the Bayesian downscaling method may lead to a reduction in the uncertainty of the computed head values. The beneficial effect that prior information could have on the downscaling process is clear. The response of the variance in the hydraulic head primarily depends upon the prior variance of hydraulic conductivity values as well as the number of observations (Fig. 4.1 b, c). Another factor, the equivalent prior sample size, has also a crucial effect on the character of the variability of amplitude for a parameter, such as the conditional variance in the hydraulic conductivity. Sokrut and Thunvik, 2005 have

Fig. 4.1 Analysis of the Bayesian downscaling techniques: (a) variance in hydraulic head vs. initial prescribed correlation length; (b) variance in hydraulic head vs. number of measurements; (c) variance in hydraulic head vs. prior estimateof variance in hydraulic conductiv ty value (after Sokrut and Thunvik, 2005)

i

0

0,05

0,1

0,15

0,2

0,25

0 1 5 10 50 200 500

I ni t i al pr escr i bed cor r el ati on l ength, m

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

1 5 10 15 20 25

Number of measur ements

0,000

0,020

0,040

0,060

0,080

0,100

0,120

0,140

0,160

0,180

0,200

0 1 2 3 4 5

Pr i or var i ance eti mate of hydr aul i c conducti vi ty val ue, l n K

21


shown that the initial prescribed correlation length has in most cases a minor importance for the variability in the mean hydraulic conductivity values (Fig. 4.1a). The parameter uncertainty has been explicitly included in the analysis and the uncertainty in the estimation of the prior parameters was not taken into consideration. Analysis of the graph shown in Fig. 4.1b suggests that additional data might not lead to a reduction in the predictive uncertainty. This is equivalent to the question of how many samples are needed for the stipulated accuracy (Sokrut and Thunvik, 2005). In this case one cannot definitely recommend ceasing the taking of measurements after 10 due to the apparent negligible difference in the variance of the hydraulic head values beyond this point on the graph. However, an apparent stabilisation of the curve can be observed between 10 and 15 measurements, which means that there is no evident reason in collecting any additional data thereafter (Sokrut and Thunvik, 2005). The Bayesian downscaling procedure has several weaknesses. A drawback of this method is the problem of sensitivity of the Bayesian conditional updating method based on choice of the initial correlation length, as too small and too large values of the initial correlation length may cause matrix singularity and may consequently lead to instability in the numerical solutions (Sokrut and Thunvik, 2005). This problem has been encountered for simulations with a small number of observations as well. For most realisations of the hydraulic conductivity field, the hydraulic head values responded to the spatial variations in the hydraulic conductivity in terms of the magnitude of the variation in the mean conductivity of the catchment (Sokrut and Thunvik, 2005). Vicens et al. 1975 point out that prior information must come from sources statistically independent from the site data used to update the prior distribution. This makes the method less site-specific (Bogardi et al. 1982).

4.3 The Örsundaån case - an example of multi-scale hydrological modelling

The new integrated model ECOFLOW has been applied to the Örsundaån catchment. The analysis revealed that parameters like the horizontal unsaturated hydraulic conductivity and porosity, had a crucial effect on the results, whereas parameters such as the snow compaction and Manning’s roughness coefficient for the river bed had almost no effect at all on the results (Sokrut et al. 2005). The annual hydrograph generation was based on daily stream flow, which is the sum of the surface runoff generated in the watershed, and subsurface lateral flow into the stream. The stream flow integrates the hydrological responses from across the watershed and can, therefore, be used to assess the overall predictions of the model (Das Gupta, 1998). The computed stream flow has been calibrated to the observed data collected at a Härnevi gauging station for the period from 1 July 1981 to 30 June 1989. The Härnevi monitoring gauge records the stream flow data for a part (about 40%) of the whole Örsundaån basin. Fig. 4.2 shows predicted vs. measured daily stream flow for 1981-89. The parameter estimation procedure was divided into two steps and can be summarised as follows: (i) manual calibration (the adjustment of the parameters was carried out manually, by visual comparison of simulated and observed values); (ii) automatic calibration -performed using the Rosenbrock optimisation algorithm (Rosenbrock, 1960) for the Nash-Sutcliffe criterion R2 serving as an objective function (Nash and Sutcliffe, 1970). The model produced good results in simulating the daily stream flow values. The Nash-Sutcliffe efficiency R2 was 0.805, 0.826, 0.781, 0.817, 0.935, 0.912, 0.879, and 0.872 for 1981-1982, 1982-1983, 1983-1984, 1984-1984, 1984-1985, 1985-1986, 1986-1987, 1987-1988, and 1988-1989 simulation years, respectively (Sokrut et al. 2005). The best R2 criterion of 0.935 was calculated for 1985-1986, whereas the worst calibration results (R2 is 0.781) were obtained for 1983-

22


1984. Stream flow prediction during calibration period generally agreed with measured flow resulting in an average Nash-Sutcliffe efficiency R2 of 0.853 (Sokrut et al.

During

2005).

most calibration years the simulated

generally over–and underestimated,

low flow is quite close to the measurements, except for 1981-1983 and 1983-1984, where the low flow simulated by the model is

f i

.

Fig. 4.2 Comparison o the observed hydrograph (m3/s) and the hydrograph (m3/s) s mulated by ECOFLOW for the Örsundaån catchment (1981-1982, 1982-1983, 1983-1984, 1984-1985, 1985-1986, 1986-1987, 1987-1988, 1988-1989 years, respectively). 1st July is set as an initial date for all simulations (from Sokrut et al. 2005a)

23


respectively. The model describes very accurately the basin runoff for 1985-1986, 1986-1987 and 1987-1988. For 1981-1985 periods clear deviations can be seen, which might be caused by interpolation errors in the input meteorological data. With the applied set calibrated parameters, the model is capable of capturing runoff for the simulation period, while deviations are seen for accumulated runoff and partly peak flows (1983-1984, 1986-1987, 1988-1989). In general, the model described properly the increases and recessions in the river flow but the absolute peak level is either overestimated or more often underestimated at some rainfall events (Sokrut et al. 2005). The maximum absolute deviations for a storm effect are seen for 1983-1984 and 1986-1987. However, additional adjustment of parameters for simulating single storm events had adverse effects for the remaining part of the simulation period (1981-1985). Initially, the parameter calibration was performed manually by a trial-and-error

hydraulic conductivity

tate simulation at almost all

W regional scale modelling have

iagonal line

FLOW local models for the

method through visual comparison of the computed groundwater levels and the observed at the observation wells. Thereafter, the hydraulic conductivity values were automatically calibrated using PEST (Doherty, 2000). Table 4.3 demonstrates how the initial estimates of thevalues have been substantially changed after the processes of calibration. These moderate-to-high changes in the calibrated parameters might be partly explained by the high degree of anisotropy in the geological formation; the unconsolidated glaciofluvial sediments usually have a large variation in hydraulic conductivity. The uncertainty in the hydraulic conductivity accounts for two major sources of error: (i) the representation of the aquifer as a homogeneous geological layer (i.e. spatial variations are not taken into account); (ii) the calibration errors (Dee and Da Silva, 1998). Insufficient numbers of field hydraulic conductivity measurements and lack of knowledge about the aquifer aggregation has definitely resulted in considerable uncertainty when assigning the hydraulic conductivity values at the stage of

conceptual model development. In Sokrut et al. 2005a it is shown that the drawback of the PEST method is that is highly sensitive to the initial parameters values to be calibrated. Some values that caused instability of the numerical solution were neglected. The regional model has been calibrated for the steady-sobservation points except twelve wells, where the errors were outside the estimated error interval (± 1.0 m) of the observed value (Sokrut et al. 2005a). This interval represents the estimated error (±) in the observed value and was used as a calibration target. The confidence value representing the confidence in the error estimate was set to 95%. Plots related to the calibration errors of the MODFLObeen generated (Fig. 4.3). In the first plot, a symbol is drawn for each of the observation points. In the second plot, the residual errors between the computed and observed heads are shown (Sokrut et al. 2005a). Error analysis indicates that most of the points plotted on or near the dhave low error values. Only the few points that are situated relatively far from the diagonal line have larger error values. Apparently, most of the computed values are consistent with the observed ones showing very small residual errors, except for the twelve wells located in the esker area. Error statistics have also been calculated: the mean and the mean absolute errors are 0.55 m and 1.64 m, respectively (Sokrut et al. 2005a). Calibration targets of both the MODFLOW and ECOsteady-state simulation were achieved for almost all observation points except one well (EEK1999110801), at which the error was outside the estimated error interval (± 1.0 m) of the observed value (Fig. 4.3). The confidence value representing the confidence in the error estimate was set to 95%. The fact that the calibration target was not reached (the residual is 2.68 m) might be explained by the layered heterogeneity and

24


Table 4.3. Initial and calibrated hydraulic conductivity values for 31 sub areas within the local model. The values shown were automatically calibrated, using the PEST algorithm (steady-state simulation).

3 G lacio flu vial sed im en t

7.21 9.75 2.54


2.71 4.60 1.89

8 Silt 3.36 1.60 -1.769 Silt 0.10 1.35 1.25

14 Silt 0.05 1.45 1.4016 G lacio flu vial

sed im en t17.04 12.43 -4.61


3.65 5.76 2.11


9.48 6.44 -3.04

27 Silt 0.35 2.80 2.4528 G lacio flu vial

sed im en t4.03 8.21 4.18

Difference betw een initia l and automatica lly ca libra ted

v a lue , m/day

Z one M ateria l Initia l hydrau lic conductiv ity v a lue , m/day

H ydrau lic conductiv ity va lue , automatica lly ca libra ted by

PE ST m/day

complex hydrogeological conditions. The hydraulic conductivity value assigned to the cell containing the observation well has been averaged. The aquifer is confined and bounded by several clay-rich till aquitards, and is overlain by a sand aquifer, which is overlain by glacial clay/silt, which extends to the surface (Sokrut et al. 2005a). Plots related to the calibration errors of the ECOFLOW and MODFLOW local scale

els as well. The mean and the

lated

ds caused by variations in

modelling have also been computed and displayed in Fig. 4.4 and 4.5. Most of the points have residual errors less than 1.0 m, and the only one with a larger error (1.24 m) is situated far from the diagonal (Sokrut et al. 2005a). Error statistics have been calculated for both local modmean absolute errors for the ECOFLOW and MODFLOW models are -0.27 m and 1.06 m, -0.31 m and 1.16 m, respectively. The similarity between the results is not surprising because the boundaries, layer stratigraphy, and flow components of the two models are based on the same conceptual model (Sokrut et al. 2005a). The most likely reason for the delay in the recharge can be explained by an accumuwater storage in the esker and the considerable travel time from the land surface to the aquifer (the observation well is located in a confined aquifer overlain by a

thick clayey aquitard, which prevents immediate infiltration of precipitation into the aquifer and a quick response of the hydraulic heads to the fluctuations in the recharge values). None of the graphs presented demonstrates any clear trend in the seasonal variabilities of the groundwater flows. Slight seasonable recharge fluctuations resulting in short time response of the hydraulic heads have been predicted for the observation well EEK2000112001 (Fig. 4.7). The possible reason could be the superimposed effect of the changing percolation and distribution of the recharge computed by the ECOFLOW model, which resulted in significant dynamic changes and dissipation of the transient groundwater flow system directly adjacent to the Örsundaån stream water, and caused highly variable infiltration rate conditions to the shallow aquifer. No significant alteration in the simulated groundwater heathe porosity value is clearly seen. Also, no systematic changes in the simulated groundwater values affected by the variations in horizontal hydraulic conductivity are found, which indicate that these calibration parameters may be assumed valid for other periods including future predictions (Sokrut et al. 2005a).

25


Fig. 4.3 Regional model (MODFLOW): comparison of the computed and observed values of the groundwater levels (linear regression); comparison of the residuals and observed values of the groundwater levels. These plots present computed values of the groundwater levels after the process of automatical optimisation PEST (transient simulation). Mean error is -0.55 m, mean absolute error is 1.64 m (from Sokrut et al. 2005a).

Fig. 4.4 Local model (ECOFLOW): comparison of the computed and observed values of the groundwater levels (linear regression); comparison of the residuals and observed values of the groundwater levels. These plots present computed values of the groundwater levels after the process of automated optimisation PEST (transient simulation). The mean error is -0.27 m, the mean absolute error is 1.06 m (from Sokrut et al. 2005a).

26


27

The transient simulated dynamics of the deep and shallow aquifers is captured by the model at almost all observation wells (Fig. 4.6-4.9). This applies especially to the shallow aquifer (Fig. 4.7), which is more dynamic than the deep aquifer. The most likely reason for the head fluctuations in the shallow aquifer is highly permeable sandy soil and the draw- down from nearby wells (Sokrut et al. 2005a). The high potential heads of the esker do not seem to affect the heads of the shallow aquifer, which indicates that the vertical hydraulic conductivity is very low. Apparently, the simulation of head fluctuations in the esker can be better reproduced by including recharge and withdrawal rates in the model and not by further calibration of hydraulic properties like hydraulic conductivity (Sokrut et al. 2

behaviour between simulated (well No EEK2000112003) and observed (well No 20, Tärnsjö) time series of groundwater levels in the deep esker aquifer variessignificantly (Fig. 4.6 and 4.8). The overall descending trend is clear in both computed and observed time series but yearly fluctuations are not seen in the computed groundwater levels. In Sokrut et al. 2005a it was shown that the observed potential heads at the observation well No 20 (Tärnsjö) are higher than those modelled at the observation well No EEK2000112003.Probably this behaviour of the computed potential head at the EEK2000112003 observation well might be affected by higher vertical hydraulic conductivity values, obtained after the calibration process andattributed to this part of the esker.

05a).

Fig. 4.5 Local model (MODFLOW): comparison of the computed and observed values of the groundwater levels (linear regression); comparison of the residuals and observed values of the groundwater levels. These plots present computed values of the groundwater levels after theprocess of automated optimisation PEST (transient simulation). The mean error is -0.31 m, the mean absolute error is 1.16 m (from Sokrut et al. 20

005a). However, the difference in the


A closer match in the behaviour of the simulated and observed time series of the groundwater levels is seen at the observation wells EEK2000112001 and 21(Tärnsjö) (see Figs.4.7 and 4.9). These wells are located in similar geological formations and respond quickly to deviations in the recharge (Sokrut et al. 2005a). Variations in the groundwater level for both computed and observed time series are in the same range of 1.0 and 0.7 m, respectively. Seasonal patterns can be detected in both computed and observed series. Extensive rainfall periods in 1981-1983 and 1986-1987 (Sokrut et al. 2005a) caused the observation well EEK2000112003 to discharge excess water, when the groundwater table reached the soil surface.

ecause of the shallow depth of roundwater at the observation wells

nspiration from roundwater by vegetation may significantly

Sophocleous et al, 1995 the MODFLOWmodel is not good enough to deal with localphenomena related to flow near domainboundaries. To properly handle the physicof, i

BgEEK2000112001, trag

recharge on the interaction of surface water and groundwater, using a variably saturated subsurface-flow model. The results indicated that recharge is most effective where the unsaturated zone is relatively thin. Then the recharge progresses laterally over time to the areas with thicker unsaturated zones. This process has significant implications for the interaction of groundwater and surface water (Winter, 1995). Difficulties in defining spatial distribution of the saturated and unsaturated flow thickness within the Dalkarl esker domain make it hard to analyse the role of the recharge within the unsaturated zone properly and to establish recharging and discharging periods. According to Sophocleous et al, 1988; and

s n particular, stream–aquifer interactions,

intercept groundwater that would otherwise discharge partly (summer time) to the surface water (Perez et al. 1974). Heji, 1989 evaluated the effect of the distribution of

close attention must be paid to the mechanisms operating at the surface water – groundwater interface in the ECOFLOW model. This may involve addressing the

31, 2

31, 4

31, 6

31, 8

63, 9

64

64, 1

64, 2

64, 3

64, 4

64, 5

64, 6

1981-

1982

1982-

1983

1983-

1984

1984-

1985

1985-

1986

1986-

1987

1987-

1988

1988-

1989

Fig. 4.6 Time series of groundwater level (m .l.) at the observation well EEK2000112003 (located in the esker area-deep aquifer) comput y ECOFLOW for 1981-1989 years. 1st July is set as an initial date for simulations (from Sokrut et al. 2005a).

.a.sed b

Fig. 4.7 Time series of groundwater level (m.a.s.l.) at the observation well EEK2000112001 (located in the shallow aquifer) computed by ECOFLOW for 1981-1989 years. 1st July is set as an initial date for simulations (from Sokrut et al. 2005a).

30

30, 2

30, 4

30, 6

30, 8

31

1981-

1982

1982-

1983

1983-

1984

1984-

1985

1985-

1986

1986-

1987

1987-

1988

1988-

1989

28


dynamics of seepage-face boundary conditions in detail (Yan and Smith, 1994). Because the stream–aquifer seepage flow is driven by the head differential at the interface of the two systems, inaccuracies in the determination of aquifer heads on the seepage face would have impact on the seepage fluxes; this would in turn affect the stream stages (Yen and Riggins, 1991). Computing changes in the stream stages accurately should be analysed by taking into account kinematics of the stream flow in the ECOMAG model. Comparative analysis of the observed and predicted time-series for integrated outflow and distributed groundwater flows can be used to assess ECOFLOW credibility. In Sokrut et al. 2005 it was shown that the

s in the

model could adequately predict stream flow (runoff) and groundwater flow distribution. Most of the hydraulic head values computed by the ECOFLOW model at the local scale have demonstrated smaller residual errors, related to those computed by the MODFLOW model only. Using the local model, with a more detailed representation

of the esker’s complex geology and stratigraphy, resulted in a lower simulation error level. Hydraulic properties of soils play an important role in the water movement from the soil surface to the water table through the unsaturated zone and, hence, affect the runoff and groundwater recharge processes (Beven and Germann, 1982). One of these properties is the heterogeneity of the hydraulic conductivity. This parameter can vary with several orders of magnitude over short distances in the subsurface zone (Yu et al. 1998). Sensitivity analysis demonstrated that the ECOFLOW model is highly vulnerable to even small deviationvertical hydraulic conductivity values, both for the saturated and unsaturated zones, and horizontal hydraulic conductivity values for the unsaturated zones. The model’s predictive uncertainty was found to lie within tolerable limits. Predictive uncertainty has been investigated by comparison of model predictions with corresponding field observations. The model was found to predict both high and low river

Fig. 4.8 Time series of groundwater level (m.a.s.l.) at an observation well No 20 in Tärnsjö (located in the esker area-deep aquifer) for 1981-1989 years. 1st July is set as an initial date for observations (from Sokrut et al. 2005a).

70, 4

70, 6

70, 8

71

71, 2

71, 4

71, 6

71, 8

72

1981-

1982

1982-

1983

1983-

1984

1984-

1985

1985-

1986

1986-

1987

1987-

1988

1988-

1989

78

78, 2

78, 4

78, 6

78, 8

79

79, 2

79, 4

1981-

1982

1982-

1983

1983-

1984

1984-

1985

1985-

1986

1986-

1987

1987-

1988

1988-

1989

Fig. 4.9 Time series of groundwater level (m.a.s.l.) at an observation well No 21 in Tärnsjö (located in the shallow aquifer) for 1981-1989 years. 1st July is set as an initial date for observations (from Sokrut et al. 2005a).

29


stages and groundwater elevations with a reasonable degree of precision. Basically, in an integrated and distributed model it is difficult to assess the effect of single inputs or parameters on the different results from the model (Miles and Rushton, 1983). The uncertainty in the input data does not seem to be the largest source of error in the ECOFLOW model. The depth of the existing layers, aquifer boundaries, and hydraulic conductivity parameters were primarily obtained from the typical cross-section series in the geological survey and

in this particular study is

supplemented by literature sources. Complexity in the stratigraphy and the heterogeneity of layers definitely caused some unavoidable errors related to hydraulic properties of geological materials, when

many of those have been aggregated (Sokrut et al. 2005a). Another possible source of uncertainty believed to lie in the spatial interpolation of the meteorological data, which has been conducted by the ECOMAG model (Sokrut et al. 2005a). Daily precipitation, air humidity, and average temperature from only one regular recording gauge is not sufficient enough for proper modelling of the drainage basin, which has an area of 754 km2. Interpolation errors resulted in errors in the computed surface and subsurface flow, which led to the uncertainties in the recharge rates that accentuate errors in predicted hydraulic heads (Sokrut et al. 2005a).

30


5 CONCLUSIONS

Testing the integrated model ECOFLOW demonstrated that the model adequately predicts stream and groundwater level distributions, and can be a useful tool for simulation of surface– and groundwater processes at both the local and regional scales. To decrease the modelling uncertainty level on the local scale additional data must be provided in order to obtain a detailed simulation of water levels and flows. If supplementary geological data are collected and interpreted, the conceptual hydrogeological model may be extended and refined. Although hydraulic parameters are not available for each layer a further sub division is likely to improve the simulated results. The new nitrogen module ECOMAG-N appeared to provide reliable estimates of the spatial nitrate loads in the watershed. The performance of the nitrogen module ECOMAG-N is significantly affected by the availability of parameterisation data. Incorporating nitrification, denitrification, dissolved organic nitrogen, and ammonia volatilisation processes in the modelling algorithm could definitely decrease the uncertainty in the modelling results. Additional soil sample analysis is needed to obtain a more reliable basis for the initial

hat the initial prescribed correlation length had little influence in constraining uncertainty in the predictions of the hydraulic conductivity field. Proposed future research includes application of this model to contaminant transport in surface- and groundwater for point and non-point source contamination modelling. The priority in the further investigations should be given to developing an algorithm to account for the temporal discrepancies in the surface and groundwater models. Further development of the model should be oriented towards integration of the ECOFLOW modelling system into a planned Decision Support System.

values of LON and RON model parameters. Application of the ECOMAG-N model at a catchment with mixed land use would probably enable us to gain a better insight into the validity of the model. The statistical Bayesian downscaling algorithm demonstrated the ability to reduction in the uncertainty of the computed head values and to define criteria that stop the updating procedure when additional data no longer lead to reduction in the uncertainty. The uncertainty level in the obtained predictions for the hydraulic head depended to a high extent on the quality of the supplied data, as well as the number of additional measurement points. It was shown t

31


33

330.

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