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Rapporttyp Report category Licentiatavhandling Examensarbete AB-uppsats X C-uppsats D-uppsats Övrig rapport ________________ Språk Language Svenska/Swedish X Engelska/English ________________ Titel
Utveckling av en HBV/PULS-model med sammanfogade markfuktighets- och responsrutiner
Title
Development of an HBV/PULSE model with merged soil moisture and response routines
Författare
Author Karin Berg
Sammanfattning
Abstract
Soil properties affect the chemical composition of soil water. When studying transport of chemical substances through a basin, it is therefore important to know from which soil layer the main part of the runoff is generated. The aim of this study is to develop an HBV/PULSE model with merged soil moisture and response routines, which generates good approximations of groundwater levels. It should be possible to extend the model to simulate transport of substances and take into account which soil layer the groundwater level is currently in.
The hydrological version of HBV/PULSE is used since there is no need to account for pH or alcalinity at this stage. Representation of runoff is changed to an equation analogous to that of HBV-96. The unsaturated and saturated zones in the response routines are merged by associating change in groundwater storage with change in the size of the unsaturated zone. Field capacity, which is expressed in mm in the existing model, is transformed from parameter to variable. Three models are compared in this study: HBV/PULSE without any modifications, HBV/PULSE with a response function similar to that of HBV-96 and finally a model with the same response function as model two, variable field capacity, groundwater level simulation and connected soil moisture and response compartments.
Results show that runoff is simulated equally well by the two first model versions, and alomst as well by the third. Soil moisture simulations show the same patterns for all three models, but slightly different levels. Ground water storage is different in the first model compared to the others, mainly depending on the use of capillary flux and negative storage values in the unmodified model. Groundwater simulations with the third model generated results which differed much from measurements. The main problem is the magnitude of the variations which is far too small in the simulations.
Introduction of variable soil moisture in the unsaturated zone and variable soil porosity is suggested as a way of increasing the magnitude of fluctuations in groundwater storage and levels. It is also necessary to allow groundwater storage, and thereby groundwater levels, to vary equally in both directions from the initial values. If this is not possible to achieve with the new response function, it is necessary to change back to the old function despite the increase in parameters.
ISBN _____________________________________________________ ISRN LIU-ITUF/MV-C--02/02--SE _________________________________________________________________ ISSN _________________________________________________________________
Serietitel och serienummer
Title of series, numbering
Handledare Tutor Per Sandén Nyckelord Datum Date 7 June 2002
URL för elektronisk version http://www.ep.liu.se/exjobb/ituf/
Institution, Avdelning Department, Division
Institutionen för tematisk utbildning och forskning, Miljövetarprogrammet
Department of thematic studies, Environmental Science Programme
Acknowledgments
First, I would like to thank my supervisor, Per Sandén, for invaluable help. This study could not have been accomplished without it. A huge thanks to Kaj Nyström for help with technical issues, discussions and support in general. Bo Einarsson at the department of Mathematics at Linköping University is thanked for clarifying some mathematical issues. Thanks also to Per-Erik Jansson at the Royal Institute of Technology, department of Land and Water Resources, for providing the source code for the calculations part of COUPmodel.
Contents
1 Introduction 3
2 Available models 3
2.1 SOIL and COUPmodel - structure and applications . . . 3
2.2 The HBV and HBV/PULSE models . . . 4
2.2.1 Structure . . . 5
2.2.2 Soil moisture and response routines in HBV and HBV/PULSE 6 3 Method 6 3.1 Data . . . 7
3.2 Changes in soil moisture and response routines . . . 8
4 Results 9 5 Discussion 14 5.1 Advantages and disadvantages of the new response function . . . 14
5.2 Merging of soil moisture and response routines . . . 15
5.3 Simulation of groundwater levels . . . 15
5.4 Further improvements . . . 16
5.5 Alternative solutions . . . 17
1
Introduction
The use of hydrochemical models is a common method when studying the transport of solutes through water and soil. Objectives for model use are varying and include basic research on transport and transformation of chemical substances, agriculture related research, environmental issues e.g. spreading of pollutants and other sub-stances and eutrophication. Since the models have been developed for different purposes and in different research traditions, there are many variations in the struc-tures of and degree of detail in the hydrochemical models used today. Even models that claim to simulate the same processes in a similar way may differ when it comes to degree of complexity in the different parts of the models [Botterweg, 1995].
The most widely used hydrological and hydrochemical models in Sweden are the conceptual HBV model [Bergström, 1976] and the physically based SOIL model [Jansson and Haldin, 1979], and some related models such as HBV-N, HBV/PULSE [Carlsson et al, 1987], SOILN and COUPmodel [Jansson and Karlberg, 2001]. Both HBV and SOIL are hydrological models which have been extended to simulate transport of solutes, mainly nitrogen.
Soil properties affect the chemical composition of soil water. When studying transport of chemical substances through a basin, it is therefore important to know from which soil layer the main part of the runoff is generated. Variables that affect biological activity, e.g. temperature and redox conditions, are also of interest.
Groundwater levels have already been simulated with HBV/PULSE with promis-ing results. A remainpromis-ing problem is, however, that the inner structure of the model makes it difficult to extend the model to take the soil layers all the way from the surface and down to somewhere below the water table into account. The aim of this study is thus to develop a HBV/PULSE model with merged, more physically correct, soil moisture and response routines, which generates good approximations of groundwater levels. It should be possible to extend the model to simulate trans-port of substances and take into account which soil layer the main part of runoff is generated from.
2
Available models
This section gives a description of two types of models commonly used for hyd-rological and hydrochemical modelling in Sweden. Since the HBV/PULSE model will be used in this study, the HBV model and its relatives are given a quite de-tailed description with focus on the soil moisture and response routines. SOIL and COUPmodel, which are possible alternatives to HBV/PULSE, are also described, however not as thorougly as the others.
2.1 SOIL and COUPmodel - structure and applications
The SOIL model was developed by Jansson and Haldin [Jansson and Haldin, 1979] for simulation of water and heat flows in forest soils but has been generalised to
other soils [Persson, 1995]. SOILN is an extension to the SOIL model, which simulates nitrogen transport and uptake. COUPmodel includes the SOILN model, but it also contains new or modified routines [Jansson and Karlberg, 2001]. The driving variables of the models are meteorological data such as precipitation and air temperature. COUPmodel, as well as SOIL, is a numerical model which is based on two basic assumptions:
(i) The law of conservation of mass and energy
(ii) Flows occur as a result of gradients in water potential (Darcy’s Law) or tem-perature (Fourier’s law)
Unsaturated water flow is described in COUPmodel by a combination of Darcy’s law and the law of mass conservation. Heat flow is calculated by combining an equation for conduction and convection with the law of energy conservation [Jansson and Karlberg, 2001]. The soil and water properties needed in the model are included as parameter values. Plant properties are also represented as parame-ters.
The models represent a soil profile, divided into maximum 22 compartments. Thickness of the compartments is chosen to account for soil properties and numer-ical requirements [Jansson and Karlberg, 2001], but the choice can also depend on available measurements [Botterweg, 1995]. COUPmodel contains numerous switches by which the user can determine which processes to include in the simu-lation [Jansson and Karlberg, 2001]. Examples are nitrogen and carbon processes, irrigation, frost, snow vegetation, salt tracer and evaporation. Water or heat flow calculations can also be switched on and off. Efforts have recently been made to make it as easy as possible to use and develop through an object orientated design [Jansson and Moon, 2001].
The SOIL and SOILN models have been used for many purposes, e.g. predic-tion of nitrate leaching [Bergström and Jarvis, 1991], estimation of evapotranspira-tion [Persson, 1995], studies of water flow in frozen soils [Stähli et al, 1996]. Sim-ulation results from SOILN have also been used as input variables to HBV-N, in order to estimate nitrogen leakage from arable land [Arheimer and Brandt, 1998]. COUPmodel has a number of different applications, e.g. simulation of regulating factors for biological and chemical processes in the soil, simulation of coupled bi-ological and abiotic processes, assessment of the importance of different factors, and prediction of the influence of management [Jansson and Karlberg, 2001].
2.2 The HBV and HBV/PULSE models
The conceptual hydrological model HBV was developed in the 1970’s by Bergström [Bergström, 1976]. Nowadays the HBV model is widely used for simulation of runoff in Sweden and the other Nordic countries [Bergström, 1992]. HBV/PULSE was developed from HBV in order to describe the chemistry of generated runoff, in particular pH and alcalinity [Carlsson et al, 1987]. In the HBV/PULSE model
it is possible to follow each pulse caused by rainfall or snow melt through the soil [Carlsson et al, 1987].
Applications of the HBV model include hydrological forecasting, spillway de-sign, climate change studies, water balance studies and simulations of groundwater response [Bergström, 1992]. HBV/PULSE is not as widely used as HBV. It has been used e.g. for simulation of effects of liming, modelling of metal transport and pH in an old mining area, studying the impact of land use on pH and alcalinity [Carlsson et al, 1987] and groundwater modelling [Bergström and Sandberg, 1983,
Bergström et al, 1990]. Common catchment sizes for use of the HBV/PULSE model have been 0,5 - 50km2 [Carlsson et al, 1987], while the HBV model usu-ally has been applied to larger catchments [Bergström, 1992].
2.2.1 Structure
HBV is a conceptual model, which is made as simple as possible rather than de-scribing every single detail in runoff generation. The major parts of the model are snow, soil moisture and runoff response routines [Bergström, 1992]. Driv-ing variables are, as in SOIL and COUPmodel, precipitation and air temperature. Measurements of runoff are also needed for comparison with calculated values [Bergström, 1992].
The general structure of HBV/PULSE is the same as that of HBV, but there are some differences [Brandt, 1987]. In HBV it is possible to divide a basin into subbasins, and to divide the subbasins into different elevation zones. HBV/PULSE only allows division into subbasins. HBV also takes the influence of elevation on temperature and snow melt into account. In HBV-96 potential evaporation also depends on elevation [Lindström et al, 1997]. Model performance is usually eval-uteded using the R2value [Nash and Sutcliffe, 1970]:
R2=Σ( ¯Qo− Qo)
2−Σ(Q
c− Qo)2
Σ( ¯Qo− Qo)2
where Qois observed runoff, ¯Qois mean observed runoff and Qccomputed runoff.
Graphs of accumulated difference between computed and observed runoff are also useful [Bergström, 1992].
There are some differences in performance between the two models. HBV generates better simulations of floods than of lower water flow. HBV/PULSE on the other hand is better at predicting low water flows, but tend to miss the highest peaks [Carlsson et al, 1987]. The purpose when using a model determines what behaviour is acceptable. High peaks are important when making forecasts for the hydroelectric power industry, and low water flows are important when studying transport of pollutants since the highest concentrations of different substances oc-cur during drier periods. There are also differences between the models in the soil moisture and response routines [Brandt, 1987], which are described in section
2.2.2 Soil moisture and response routines in HBV and HBV/PULSE
Since the effect of soil moisture on runoff generation, rather than a description of water content at different depths in the soil, is of interest in the HBV model, a simple model based on bucket theory is sufficient to represent soil moisture dy-namics [Lindström et al, 1997]. The soil moisture storage is determined by the empirical parameters FC, BETA and LP, where FC is the field capacity, BETA de-termines the contribution from precipitation to the unsaturated and saturated zones and LP is the soil moisture level below which actual evapotranspiration is reduced [Bergström, 1992]. Increase in runoff caused by rainfall or snow melt is described by dQ dP = SM FC BETA . (1)
The unsaturated zone is similar in both HBV and HBV/PULSE with one excep-tion: capillary flow from the saturated zone is possible in HBV/PULSE, while flow occurs only from the unsaturated to the saturated zone in HBV [Brandt, 1987]. The size of the unsaturated zone is constant during simulations and it is not affected by changes in the response routine. The structure of the saturated zone differs between the two models. In HBV it is divided into two reservoirs, compared to one reser-voir in HBV/PULSE [Brandt, 1987]. In earlier HBV models and most versions of HBV/PULSE runoff from the saturated zone is generated at two and maximum four levels respectively. These are determined by different parameters. In HBV-96, however, runoff is described by a non-linear equation
QU Z= K ·U Z(ALFA+1), (2)
which allows continous drainage from the soil [Lindström et al, 1997]. This so-lution is more realistic and also demand less parameters. A similar soso-lution for HBV/PULSE is found in an application where oxygen-18 tracer was used to de-termine water transit times in a catchment [Lindström et al, 1990]. In this case, runoff (Q) was expressed as
Q(S) = K · S(1+αS) (3)
where K andαare parameters and S is water storage in soil.
3
Method
The hydrological version of HBV/PULSE is used since there is no need to account for pH or alcalinity at this stage. Three models will be compared in this study:
1. HBV/PULSE without any modifications,
2. HBV/PULSE with a response function similar to that of HBV-96 and 3. HBV/PULSE with the same response function as model 2, variable field
3.1 Data
Data from the field research area Stubbetorp were used. Stubbetorp is situated 30 km north east of Norrköping in southern Sweden (59◦44’N-16◦21’E). The main part of the Stubbetorp basin is covered with coniferous forest, the rest is tilled soil. There are no lakes in the area. The size of the catchment is 0,87 km2. When running the HBV/PULSE model it was divided into two subbasins, 0,43 and 0,44 km2respectively. Data used include precipitation, temperature and observed runoff with daily timestep. Precipitation and temperature data from 1983-09-06 to 90-12-31 and measurements of runoff between 1985-06-18 and 1990-90-12-31 are used. Groundwater levels have been measured in 14 tubes placed along a hill slope (fig.1) every two weeks between 1986-12-15 and 1991-07-14. Tubes 29 to 34 are placed near or in a wetland at the base of the hill. Values for potential evapotranspiration are available as monthly averages [Eriksson, 1981].
Figure 1: The Stubbetorp basin with groundwater tubes. 1. tubes 21-24, 2. tubes 25-28, 3. tubes 29-31, 4. tubes 32-34 and 5. automatic measurement station.
Only calibration was performed regarding runoff, soil moisture and groundwa-ter storage, since the purpose of these simulations is to compare the behaviour of the three models with each other rather than with observed values. If the groundwa-ter level simulations should prove successful, it was possible to use daily averages of hourly measurements at the automatic station (fig.1) 1993-09-01 to 1997-02-10 for model validation. No validation was performed regarding groundwater sim-ulations, however, since the calibration results showed obvious problems in the model which an extra period of validation could not clarify further. The simulation periods starts before the calibration period, in order to reduce the impact of the choice of initial values. The same initial values, for 1983-09-06, are used in all
simulations. Initial values for groundwater level are set to 1000 mm below the soil surfaace, based on earlier studies in the area [Sandén and Warfvinge, 1992].
3.2 Changes in soil moisture and response routines
The response routines for models 2 and 3 are made by changing representation of runoff to an equation analogous to that of HBV-96. Runoff generation is thus expressed as
QGEN = K · LZ(ALFA+1). (4)
In model 3, FC in the parameter file is renamed to FCPAR and described as % of
GRW instead of mm. FC, which is used in the soil routine, is still expressed in
mm and calculated as FC = GRW · FCPAR. This makes FC a variable instead of a parameter, which is more realistic since field capacity, when expressed in mm, depends on the size of the unsaturated zone. When the groundwater level rises, i.e. when the value of GRW decreases, FC will decrease and vice versa. The second and most extensive change is that the unsaturated and saturated zones in the response routines are merged (fig.2).
PRECIPITATION SNOW ROUTINE SOIL MOISTURE (SM) GROUNDWATER STORAGE (LZ) RAIN, SNOWMELT GROUNDWATER LEVEL (GRW) CONTRIBUTION TO RUNOFF (QGEN)
Figure 2: HBV/PULSE model with merged soil moisture and response routines.
The size of the unsaturated zone is equal to ground water level and labeled
GRW . The water content of the saturated zone is still represented by LZ, but now
∆LZ is connected to∆GRW through the equation
∆GRW = Y LZ − LZ
PORV OL −GRWSM (5)
where PORV OL is a parameter used to account for the porosity of the soil and
present in the pores. In other words, soil porosity and distribution of water in the unsaturated zone is simplified in the model. Equal pore volume through the whole soil and equal soil moisture at all depths in the unsaturated zone is assumed. After runoff is calculated using (4), new LZ and SM values are computed. The water available in LZ after contribution from precipitation is calculated, LZ1, is
distributed as
LZ1= LZ2+ (LZ1− LZ2) ·
SM
GRW · PORV OL+ QGEN, (6)
where LZ2is the remaining water in LZ after runoff. (LZ1− LZ2) ·GRW ·PORV OLSM is
the addition to SM which consists of the remaining water in the soil between the first and second LZ level. From (6) the following expression for calculation of LZ2
is derived:
LZ2=
LZ1 1 −GRW ·PORV OLSM − QGEN
1 −GRW ·PORV OLSM (7)
The new soil moisture value is then calculated as
SM = SM + (LZ1− LZ2) ·
SM
GRW · PORV OL (8)
Finally, GRW is computed according to (5).
The usual weighting of variables from different vegetation types and subbasins to obtain one single value representing the whole basin is not suitable for ground-water levels and similar variables. Therefore, SM, LZ, GRW and FC for the each vegetation type in all subbasins are added as output variables.
4
Results
Results from calibration of model 1 are displayed in figure3. R2= 0,68 and accu-mulated difference between calculated and observed runoff is -39,8 mm. Results from calibration of model 2 are shown in figure 4. R2 = 0,68 and accumulated difference between calculated and observed runoff is +22,5 mm. Neither of the calibration results were the best possible concerning runoff simulation, but they generated the best agreement between the models regarding internal variables such as SM (fig.6) and LZ (fig.8). This was considered more important in this case. Unfortunately, LZ behaved significantly different with the modified response func-tion compared to the original regardless of calibrafunc-tion efforts. Calibrafunc-tion of model 3 (fig. 5) yielded a lower R2value, 0,60, but also a lower accumulated difference, -5,2 mm.
Figure6shows variations in soil moisture (SM) between 1983-09-06 and 1990-12-31 in all three model versions. Variations in groundwater storage (LZ) in the same models between 1983-09-06 and 1990-12-31 can be found in figure8. Plots of SM and LZ during one year, 1986-10-01 to 1987-09-31, are shown in figures7
and9. The best agreement between simulations and measurements occurred be-tween simulated groundwater levels and measurements in groundwater tubes T25,
T26 and T28, simulation in the field part of subbasin two between 1986-12-15 and 1990-12-30 is shown as an example (fig. 10). Similar results were obtained for tubes T23 and T24, while the results were completely different when comparing simulations with measurements in tubes T29 to T31, as illustrated in figure11.
0 20 40 60 80 100 86/01/01 87/01/01 88/01/01 89/01/01 90/01/01 91/01/01 Q (l/s) Qcom Qobs
Figure 3: Calibration of model 1
0 20 40 60 80 100 86/01/01 87/01/01 88/01/01 89/01/01 90/01/01 91/01/01 Q (l/s) Qcom Qobs
0 20 40 60 80 100 86/01/01 87/01/01 88/01/01 89/01/01 90/01/01 91/01/01 Q (l/s) Qcom Qobs
Figure 5: Calibration of model 3
20 40 60 80 100 120 140 160 86/01/01 87/01/01 88/01/01 89/01/01 90/01/01 91/01/01 SM (mm) Model 1 Model 2 Model 3
20 40 60 80 100 120 140 160 861001 861101 870101 870201 870401 870501 870701 870801 SM (mm) Model 1 Model 2 Model 3
Figure 7: Soil moisture variations during one year in the three model versions.
-40 -30 -20 -10 0 10 20 30 40 50 86/01/01 87/01/01 88/01/01 89/01/01 90/01/01 91/01/01 LZ (mm) Model 1 Model 2 Model 3
-10 -5 0 5 10 15 20 25 30 35 40 861001 861101 870101 870201 870401 870501 870701 870801 LZ (mm) Model 1 Model 2 Model 3
Figure 9: Variations in groundwater storage during one year in the three model versions. -150 -100 -50 0 50 87/01/01 87/01/01 88/01/0188/01/01 89/01/0189/01/01 90/01/0190/01/01 Depth (cm) Ground level T25 T26 T28 Simulated groundwater level
Figure 10: Comparison between simulated groundwater level (model 3) and mea-sured values from tubes 25, 26 and 28.
-120 -100 -80 -60 -40 -20 0 20 40 87/01/01 87/01/01 88/01/0188/01/01 89/01/0189/01/01 90/01/0190/01/01 Depth (cm) Ground level T29 T30 T31 Simulated groundwater level
Figure 11: Comparison between simulated groundwater level (model 3) and mea-sured values from tubes 29, 30 and 31.
5
Discussion
5.1 Advantages and disadvantages of the new response function
The results show little difference between the original response routine and the HBV-96-like function regarding runoff simulation. Results are slightly better with the modified routine, but the main advantage is the decrease in parameters. There are, however, similarities and differences in the behaviour of the internal variables
SM and LZ which are more important. Simulated soil moisture with the
modi-fied response routine is generally lower and the peaks are slightly narrower (fig.6
and7). Since there are no measurements of soil moisture to compare with, it is hard to tell which of the simulations is more correct. The difference is so small that it is not considered as a problem. A more problematic feature of the new response routine is that the dynamics of LZ differ a lot from the former routine (fig.8and9). This depend on the use of capillary flux in the original model, which can lead to negative LZ values and thereby increase the fluctuations. Negative LZ values is not possible with the current implementation of (4). Since LZ in the original HBV/PULSE model was found to follow changes in groundwater levels quite well [Bergström et al, 1990], this change in dynamics might generate prob-lems with groundwater simulation. If the probprob-lems persist it could be necessary to use the old response function instead.
5.2 Merging of soil moisture and response routines
Soil moisture dynamics and simulated levels did not change compared to the model in which only the response function was modified, which in turn differed only little from the original model (fig.6 and7). This is a desirable behaviour, since HBV/PULSE has been found to simulate soil moisture quite well in earlier studies [Sandén and Warfvinge, 1992]. The dynamics of LZ are almost the same as in model 2, but, consequently, different from the original model (fig.8 and 9). LZ levels in model 3 were lower than in model 2 and some of the lower peaks simulated by model 2 does not occur in model 3. This is probably one of the reasons why the variations in simulated groundwater levels are so small. One explaination of the lower LZ levels is that some of the water which constitutes LZ in model 2 is used to increase soil moisture in model 3 (eq. 6). Larger initial values for LZ in combination with recalibration of K and ALFA should be able to compensate for the main part of this difference.
The simplification of soil porosity is expected to cause too small changes in groundwater levels when GRW is large, and too big changes when GRW is small. This will happen because the pores generally are smaller deep down in the soil than closer to the surface. A similar problem occur because of the assumed equal distribution of water in the unsaturated zone. In reality, soil water in the unsaturated zone is more abundant close to the saturated zone than near the surface. This leads to the same type of error as the soil porosity simplification. The two errors together were expected to yield a notable difference between the size of the fluctuations in simulated and measured groundwater levels. The use of PORV OL −GRWSM allows small variations in the effective porosity, but this is not enough to compensate for the above mentioned simplifications.
5.3 Simulation of groundwater levels
Even if it is hard to compare simulations with measurements every two weeks during a relatively short time period, with numerous missing values, it is obvious that groundwater fluctuations are much greater in reality than in the simulations (fig.10). This was expected, even if the magnitude of the differences was under-estimated. The dynamics seem to be roughly the same in the simulation and the measurements in the upper tubes, but different from the measurements closer to the wetland. These are however differences which the HBV/PULSE model can not be expected to simulate. It is more reasonable to compare simulation results with tubes higher in the hillslope, which is clearly a recharge area, since HBV/PULSE don’t have any routines for simulation in discharge areas. The main problem so far is the way too small variations in simulated groundwater level. Another potential problem is that fluctuations in simulated levels seem to occur mostly in one direc-tion in reladirec-tion to the chosen initial value. It is however necessary to adjust the size of the simulated variations before the extent of this problem can be assessed.
found to generate good simulations of groundwater levels [Bergström et al, 1990,
Bergström and Sandberg, 1983,Lindström and Ottosson Löfvenius, 2000]. In one study, groundwater levels were simulated in the same area and during almost the same time as the present study [Sandén and Warfvinge, 1992]. It is therefore of interest to compare the present solution for simulation of groundwater level with the solutions in the earlier studies. In one case, groundwater levels were simu-lated with a modification of HBV [Bergström and Sandberg, 1983], which can be described as an early version of HBV/PULSE. The two response boxes of HBV were replaced by one, which was divided into three levels in the same way as it is done in HBV/PULSE. Those levels, together with the recession coefficients which determine runoff from the different levels, is one way of accounting for the vary-ing porosity of the soil. It is also possible to use separate levels for the effective porosity. Groundwater level was simulated by transforming water storage (LZ) to corresponding water level by dividing water storage by the estimated effective porosity at the current depth. This is also the solution which has previously been used in Stubbetorp [Sandén and Warfvinge, 1992]. A similar approach was used by Lindström and Ottosson Löfvenius [Lindström and Ottosson Löfvenius, 2000]. In this case, groundwater level was calculated as
dG= d0+
U Z + LZ
s ,
where dG is groundwater level, d0 is a reference level, U Z and LZ are levels in
the response routine of HBV and s is the effective porosity of the soil. These are obviously fully functioning solutions for simulation of groundwater level. From the point of view of the aim of this study there are however some problems with this type of solution. The most important is that the unsaturated zone is of the same (unknown) size during the whole simulation. Thus, even if the groundwater level is simulated with satisfactory results, there is no direct connection between the groundwater and the unsaturated zone. This creates problems e.g. if one wants to introduce a more realistic representation of soil layers in or coupled to the model. The main advantage with this solution is that variations in LZ, and consequently potential variations in GRW , are larger in this model than with the alternative re-sponse function.
5.4 Further improvements
Since it is obviously possible to simulate groundwater levels with other versions of HBV/PULSE, it is meaningful to continue the modelling efforts commenced in this study even though the present groundwater simulations did not succeed. The new model is able to simulate soil moisture and other variables in the roughly the same way as previous models. The two main problems, which are closely related, is to obtain a better simulation of groundwater storage, which is now generating too low levels, and to improve the interpretation of storage to level.
In order to increase the magnitude of the simulated variations in groundwa-ter storage, variations in soil porosity need to be accounted for. If it is neces-sary to use the old response function, porosity can be included through the lev-els in this function as shown in earlier studies [Bergström and Sandberg, 1983,
Sandén and Warfvinge, 1992]. It would, however, be better if the number of pa-rameters could be kept at a minimum. One possibility is to let porosity depend on
GRW . This would probably require a couple of new parameters, but not as many
as in the old response routine. It would also be preferable to have a soil moisture that is variable with depth. Variable soil moisture is probably possible to achieve analogous to variable porosity. As discussed above, there might be a problem with variations in simulated groundwater level occurring mainly in one direction com-pared to the initial value. If this is the case even after soil moisture and porosity calculations have been changed, it is possible that this can be fixed by using larger initial values for LZ, and adjusting K and ALFA accordingly. Otherwise, the old response function may be needed again.
When groundwater levels are simulated accurately enough, soil layers need to be integrated in the model. Another possibility is to have a separate model with soil layers, temperature and chemical and biological reactions, which is con-nected to the modified HBV/PULSE model. Soil temperature, which is impor-tant for biological activity and chemical reaction rates, has not yet been integrated in the HBV/PULSE model. It has, however, been simulated in connection with HBV/PULSE [Sandén and Warfvinge, 1992]. Soil temperature was simulated by using a function of air temperature and depth, with one empirical koefficient. Air temperature was corrected if the soil was covered with snow. The thickness of snow pack was obtained from the HBV/PULSE model. This simple model was able to simulate soil temperature at different depths well [Sandén and Warfvinge, 1992]. When soil layers are introduced, this model could account for the temperature sim-ulations in those layers.
5.5 Alternative solutions
The structure of the HBV/PULSE model with merged soil moisture and response routines, with changes proposed in section5.4, will probably end up somewhere between the original HBV/PULSE model and SOIL. Modifications to SOIL or COUPmodel is therefore an obvious alternative to the present solution. SOIL and COUPmodel already contain soil layers, temperature and many other properties which affect solute transport. In this case simplifications would be needed. This study aims to develop a model which can be used on catchment scale, and the de-gree of detail and number of parameters required in the present SOIL and COUP-model is a disadvantage in such cases [Espeby and Sandén, 1992]. The question is whether it is possible to decrease the number of parameters enough to make this an attractive alternative. It would probably be hard, since the basic equations of the models themselves contain a number of parameters, and other necessary functions add even more parameters. Even if the design of COUPmodel
proba-bly would make it relatively easy to implement e.g. a weighting module similar to the weighting routines of HBV/PULSE, it is uncertain whether it is possible to modify the model to make this weighted output useful. It is considered preferable to increase the complexity of a simple model, if this is possible, rather than the opposite.
HBV/PULSE is spatially distributed to some extent by the use of subbasins and vegetation zones, but it can not make predictions for specific places in the simula-tion areas. Since this ability would be nice, I will describe briefly and discuss one model which has this feature. TOPMODEL is a physically based, semi-distributed runoff model [Beven and Kirkby, 1979]. Input requirements are low for a spatially distributed model [Seibert et al, 1997]. This is one of the reasons this model was chosen as an alternative rather than other 3D-models which aim more explicitly at simulating solute transport. Models of the latter type, e.g. the recently developed WEC-C [Croton and Barry, 2001], which belong to the same category of models as e.g. SHE [Abbot et al, 1986], is of limited interest and use here due to their extensive data requirements. TOPMODEL is a hydrological model, but it has been suggested that the properties of the model would make it suitable for transport of solutes as well [Kirkby, 1997]. So far the model has been used for hydrological purposes such as simulation of excess overland flow, soil erosion and studies of flow paths. It has also been used to simulate groundwater levels in a catchment of almost the same size as Stubbetorp [Seibert et al, 1997]. The model did not simulate groundwater levels accurately when calibrated only against precipitation data. When information on groundwater levels in the area was included in calibra-tion the simulacalibra-tions were successful at two of three measurement stacalibra-tions, but less sucessful in the third. The model assumes that levels rise and fall simultaneously throughout the whole catchment, which is not realistic [Seibert et al, 1997]. Since ability to simulate groundwater levels is regarded as important, this is a problem. Unfortunately, this property of TOPMODEL depend on one of the model’s basic assumptions [Seibert et al, 1997], which can make it difficult to change.
6
Conclusions
The HBV/PULSE model with a response function similar to that of HBV-96 works well. The major difference is that negative LZ values due to capillary flow are not possible with the current implementation of the new response function. Apart from that, inner variables and generated runoff behave equally in the models. If the difference in LZ don’t generate any problems, the new response function is preferable since it requires considerably fewer parameters.
In the third model version, when the response and soil moisture routines are merged, inner variables behave almost exactly as in the second model, but LZ levels are lower. Runoff simulation is acceptable. The R2 value is a little lower than in the other models. Simulation of groundwater levels yield far too small variations and the variations occur mainly in one direction from the initial value.
Simplifications of the representation of soil moisture in the unsaturated zone and porosity affect variations in LZ and GRW , and is one explanation of the small variations. The tendency of variations mainly in one direction is explained by the fact that LZ, with current model formulation and initial values, changes mostly in one direction.
Changes in description of soil moisture and porosity are needed in order to allow variations with depth. If the behaviour of LZ remains a problem it may be necessary to use the old response function in order to achieve sufficient variations in groundwater storage and level.
References
[Abbot et al, 1986] Abbot, M.B., Bathurst, J.C., Cunge, J.A., O’Connell, P.E. and Rasmussen, J. (1986). An introduction to the Europe Hydrological System -Systeme Hydrologique Europeen, ’SHE’ 2: structure of a physically-based, distributed modelling system. Journal of Hydrology 87, pp.61-77.
[Arheimer and Brandt, 1998] Arheimer, B. and Brandt, M. (1998). Modelling ni-trogen transport and retention in the catchments of southern Sweden. Ambio Vol.27 No.6, pp.471-480.
[Bergström and Jarvis, 1991] Bergström, L. and Jarvis, N.J. (1991). Prediction of nitrate leaching losses from arable land under different fertilization intensities using the SOIL-SOILN models. Soil Use and Management Vol.7, pp.79-85. [Bergström, 1976] Bergström, S. (1976). Development and application of a
con-ceptual runoff model for Scandinavian catchments. SMHI RHO 7, Norrkö-ping.
[Bergström and Sandberg, 1983] Bergström, S. and Sandberg, G. (1983). Simu-lation of groundwater response by conceptual models - three case studies. Nordic Hydrology, 1983, pp.71-84.
[Bergström et al, 1990] Bergström, S., Sandén, P. and Gardelin, M. (1990). Anal-ysis of climate-induced hydrochemical variations in till aquifers. SMHI RH No.1, Norrköping.
[Bergström, 1992] Bergström, S. (1992). The HBV Model - its structure and ap-plications. SMHI RH No.4, Norrköping.
[Beven and Kirkby, 1979] Beven, K.J., and Kirkby, M.J. (1979). A physically based variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24, pp.43-69.
[Botterweg, 1995] Botterweg, P. (1995). The user’s influence on model calibra-tion results: an example of the model SOIL, independently calibrated by two users. Ecological Modelling 81, pp.71-81.
[Brandt, 1987] Brandt, M. (1987). Jämförelse mellan HBV- och PULS-modellerna (A comparison between the HBV and PULSE models, in Swedish). SMHI R&D Notes No.53, Norrköping.
[Carlsson et al, 1987] Carlsson, B., Bergström, S., Brandt, M. and Lindström, G. (1987). PULS-modellen. Struktur och tillämpningar (The PULSE model. Structure and applications. In Swedish). SMHI Reports Hydrology No.8, Norrköping.
[Croton and Barry, 2001] Croton, J.T. and Barry, D.A. (2001). WEC-C: a dis-tributed, deterministic catchment model - theory, formulation and testing. Environmental Modelling & Software 16, pp.583-599.
[Eriksson, 1981] Eriksson, B. (1981). Den ’potentiella’ evapotranspirationen i Sverige (The potential evapotranspiration in Sweden, in Swedish). SMHI RMK 28, Norrköping.
[Espeby and Sandén, 1992] Espeby, B. and Sandén, P. (1992). Comparison with the soil model. In: Sandén, P. and Warfvinge, P. (eds.) Modelling groundwater response to acidification. SMHI Reports Hydrology No.5, Norrköping, pp.66-72.
[Jansson and Haldin, 1979] Jansson, P.-E. and Haldin, S. (1979). Model for the annual water and energy flow in a layered soil. In: Haldin (ed.), Compari-son of forest and energy exchange models. Society of Ecological Modelling, Copenhagen, pp.145-163.
[Jansson and Karlberg, 2001] Jansson, P.-E. and Karlberg, L. (2001). Coupled heat and mass transfer model for soil-plant-atmosphere systems. Royal Insti-tute of Technolgy, Dept of Civl and Environmental Engineering, Stockholm. [Jansson and Moon, 2001] Jansson, P.-E. and Moon, D.S. (2001). A coupled
model of water, heat and mass transfer using object orientation to improve flexibility and functionality. Environmental Modelling & Software 16, pp.37-46.
[Kirkby, 1997] Kirkby, M.J. (1997) TOPMODEL: A personal view. Hydrological Processes 11, pp.1087-1097.
[Lindström et al, 1990] Lindström, G., Rodhe, A. and de Man, B. (1990). Transit times for water in till basins estimated by a distributed model and oxygen-18. In: Sigurdsson, G. (ed.), Nordic Hydrological Conference 1990. NHP-rapport no 26, Norrköping, pp.94-103.
[Lindström et al, 1997] Lindström, G., Johansson, B., Persson, M., Gardelin, M. and Bergström, S. (1997). Development and test of the distributed HBV-96 hydrological model. Journal of Hydrology 201, pp.272-288.
[Lindström and Ottosson Löfvenius, 2000] Lindström, G. and Ottosson Löfve-nius, M. (2000). Tjäle och avrinning i Svartberget - studier med HBV-modellen (Frost and runoff in Svartberget - studies using the HBV model). SMHI Hydrology No.84, Norrköping.
[Nash and Sutcliffe, 1970] Nash, J.E. and Sutcliffe, J.V. (1970). River flow fore-casting through conceptual models. Part I: a discussion of principles. Journal of Hydrology 10, pp.282-290.
[Persson, 1995] Persson, G. (1995). Willow stand evapotranspiration simulated for Swedish soils. Agricultural Water Management 28, pp.271-293.
[Sandén and Warfvinge, 1992] Sandén, P. and Warfvinge, P. (eds.) (1992) Mod-elling groundwater response to acidification. SMHI Reports Hydrology No.5, Norrköping.
[Seibert et al, 1997] Seibert, J., Bishop, K.H. and Nyberg, L. (1997). A test of TOPMODEL’s ability to predict spatially distributed groundwater levels. Hydrological Processes Vol.11, pp.1131-1144.
[Stähli et al, 1996] Stähli, M., Jansson, P.-E. and Lundin, L.-C. (1996). Preferen-tial water flow in a frozen soil - a two-domain model approach. Hydrological Processes 10, pp.1305-1316.
