The relationship between catchment characteristics and the parameters of a conceptual runoff model: a study in the south of Sweden

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1 FRIEND: Flow Regimes from International Experimental and Network Data (Proceedings of the Braunschweie _ Conference, October 1993). IAHS Publ. no. 221, The relationship between catchment characteristics and the parameters of a conceptual runoff model: a study in the south of Sweden BARBRO JOHANSSON The Swedish Meteorological and Hydrological Institute, S Norrkôping, Sweden Abstract A conceptual model is used to calculate the weekly and monthly runoff for about 4 ungauged catchments in the southernpart of Sweden. To improve the performance of the model, a relationship is sought between model parameters and catchment characteristics. In a special study, 11 basins with a mixed geology and land use but with a low lake percentage are investigated. They are all in an area that is fairly homogeneous from a climatological point of view. Their catchment characteristics are retrieved from standard maps and meteorological data bases. Factors that affect different parts of the hydrograph, as well as the runoff volume, are isolated. Attempts are made to quantify the effects, and to relate them to the relevant model parameters. So far the attempts to improve the simulated runoff volume have been successful, while the effects of catchment characteristics on high and low flows have been difficult to discern. INTRODUCTION In the middle of the 198s the local authorities responsible for environmental control programmes started to request runoff data for a number of streams and rivers where no observations were available. Installing gauging stations at all these sites proved to be far too expensive, and instead the Swedish Meteorological and Hydrological Institute started to compute the runoff, using the conceptual HBV model (Bergstrom, 1976). At present computations are made regularly for approximately 4 catchments, mainly in the southern part of Sweden (Johansson, 1992). Traditionally the HBV model has been used for hydrological forecasting. The model parameters have then been determined by a calibration against observed runoff. When computing the runoff from ungauged catchments, a set of regional parameters have been used, parameters which, as an average, give an acceptable accuracy within the region. This means that the runoff is systematically overestimated for some catchments and underestimated for others. As the catchment area for most gauging stations is above 1 km 2, there is a mixture of different geological and physiographic conditions within each catchment. Although this has made it difficult to see any obvious connection between runoff and catchment characteristics, it has been felt that the model performance would be improved if the model parameters could be correlated to physiographic and geological variables. The aim of the project described in this paper has been to investigate the possibility of finding any such correlations, in order to improve estimates of the runoff volume as well as low flows, high flows and recession. The results presented are preliminary.

2 476 Barbro Johansson THE HBV MODEL The HBV model was developed at the Swedish Meteorological and Hydrological Institute in the 197s, and has been widely used for a number of applications (Bergstrom, 1992). Input data are daily precipitation and temperature, and monthly mean values of potential évapotranspiration. Schematically the model can be said to consist of three subroutines, the snow routine, the soil moisture routine and the response routine. The soil routine is based on two parameters controlling the contribution to the response routine and the increase in soil moisture storage from rainfall and snow melt, and one parameter controlling the évapotranspiration. The parameters have the effect that when the soil moisture content is low, there is little contribution to the runoff and little évapotranspiration. The response routine consists of one upper and one lower quasi-linear reservoir. These are the origin of the quick and slow runoff components of the hydrograph (can also be interpreted as the direct runoff and the baseflow). The outflow from the reservoirs is determined by recession coefficients. DATA The region studied in this project is the southernmost part of Sweden (Fig. 1). This area was chosen because of its relatively dense network of hydrological stations in small and medium sized catchments. These rivers are not regulated, and the lake percentage is low. However, the area is densely populated and abstraction and discharge of waste water may occur. Eleven catchments were chosen to study the runoff volume, and nine, with a lake percentage of less than 1%, to study the shape of the hydrograph. Their area ranges from 1.6 km 2 to 35 km 2. Data for the period were used. The climate in the area is fairly homogeneous, but there are some sharp gradients in precipitation. The mean annual precipitation for the investigated period and catchments is 76 mm, ranging between 56 mm and 88 mm. The mean annual runoff varies from 19 mm to 49 mm, with 36 mm as an average. Snow may occur occasionally in winter. The dominating soil type is till, which in the southern parts has a high clay content, mixed with areas of glaciofluvial deposits. The bedrock in the south consists mainly of sedimentary rocks while gneisses dominate in the north. The maximum elevation is approximately 2 m a.m.s.l. The catchment characteristics studied are those that can be easily retrieved from standard maps and hydrological and meteorological data bases (Table 1). A consequence of this restriction is that, for instance, the effect of drainage density has not been investigated. METHOD Before considering the methods, it should be pointed out that the aim of the study is not to be able to fix the parameters of the HBV model without any calibration procedure. The regional parameters must still be determined through a calibration, but it should be possible to adjust the parameters for a specific ungauged catchment according to its

3 Relationship between catchment characteristics and model parameters 477 Fig. 1 Map of the studied area. characteristics. As the model parameters of the HBV model are interdependent, several combinations of parameters may yield good calibration results for the same catchment. Therefore, no effort is made to directly correlate model parameters to catchment characteristics. Instead an indirect way is used by correlating catchment characteristics to runoff variables, and then determining subjectively which model parameters should be adjusted to achieve the desired effect on the simulated hydrograph. It is common to construct regression equations between, for instance, baseflow recession and a number of catchment characteristics. If the coefficients of such an equation are to be used to quantify the effect on a model parameter, it is important that either the characteristics included are completely independent (which they seldom are), or that they can be assumed to affect the same parameter. The runoff characteristics investigated so far are the runoff volume, the flows with a duration of 5% (Q5), 75% ( 75) and 9% (29) respectively, and, to a certain extent, the recession coefficients. As there is a fairly large variation in precipitation within the studied area, it can be assumed that the dominating factor determining the runoff volume is the amount of precipitation. In order to more clearly see the effect of other factors, the évapotranspiration was used in the correlation calculations. For the 1-year data period the mean annual évapotranspiration was computed as the difference between precipitation and runoff, neglecting the storage components of the water balance equation.

4 478 Barbro Johansson When studying the shape of the hydrograph the highest and the very lowest flows have been excluded. The lowest flows may be affected by abstraction and discharge of water, and at the highest flows the station's rating curve may be uncertain. The 5%, 75% and 9% flows have been standardized by the mean runoff (. These flow values should be related to the recession coefficients which directly correspond to model parameters. However, as there is a large time variability in the recession (see, e.g., Tallaksen, 1991), it is not obvious how to achieve a representative and consistent value. In the studied area the climate can be considered similar for all the catchments, and in a first attempt to determine the recession it was therefore assumed that the recession for high and middle flows is proportional to the slope of the duration curve. This assumption is highly disputable and other methods will be tested. The baseflow recession was determined by means of the HBV model, using an automatic calibration procedure (Harlin, 1991) for flows below a fixed level. RESULTS Correlation analysis The calculations showed a significant (on a two-tailed 5% level) correlation between évapotranspiration and OPEN, FOREST, CLAY, TILL and ROCK, but these catchment Table 1 Catchment characteristics used for correlation with runoff variables. Mean Min P Mean annual precipitation (mm) X, Y Geographical coordinates at catchment outlet AREA Catchment area (km 2 ) HMEAN Mean elevation (m a.m.s.l.) FOREST Proportion of the catchment covered by forest (%) OPEN Proportion of the catchment covered by open fields (%) MIRE Proportion of the catchment covered by swamps (%) LAKE Proportion of the catchment covered by lakes (%).6 (FOREST + OPEN + MIRE + LAKE = 1 for each catchment) SLOPE (max elevation min elevation)a/area CLAY Proportion of the catchment covered by clay or till with a high clay 3 content (%) TILL Proportion of the catchment covered by silty and sandy till (%) SAND Proportion of the catchment covered by sand and glaciofluvial deposits (%) PEAT Proportion of the catchment covered by peat ( %) (CLAY + TILL + SAND + PEAT = 1 for each catchment) ROCK Index of bedrock type: 1 = sedimentary rocks, 2 = gneisses Max

5 Relationship between catchment characteristics and model parameters 479 characteristics are all strongly correlated to each other. When a partial correlation was made, controlling for the effect of OPEN, only one other factor, HMEAN, was found to influence the évapotranspiration. OPEN alone explains 8% of the variance of the évapotranspiration (Fig. 2), and together with HMEAN 88 %. As the improvement from including HMEAN in a regression equation was marginal, an equation including only OPEN was constructed. The coefficient for OPEN was.8, i.e. for each increase in OPEN by 1 %, the evaporation decreases by.8 mm year" 1. To check on the stability of the coefficient, the regression analysis was repeated a number of times, excluding two stations at a time. The value of the coefficient remained fairly constant. OPEN was used in the regression equation, partly because it had the highest correlation with évapotranspiration, and partly because many other investigations have related the évapotranspiration to the vegetation cover. _ The correlation analysis with <25/<2, Q15IQ and Q9QIQ was more difficult to interpret. The first calculations gave a correlation between Q15IQ and FOREST, OPEN, SLOPE, SAND and ROCK, as well as between Qd5IQ and S_LOPE and SAND, all correlations significant on the 5% level. On the 5% level Q9/Q was not correlated to any of the catchment characteristics. Partial correlation controlling for SAND leaves SLOPE as the only other factor affecting Q75/Q. However, the values for one of the catchments (Sa) differ considerably from the rest, and this catchment is also by far the steepest. If it is excluded from the analysis, the correlation with SLOPE disappears. It is likely that the steepness of a catchment affects the low flows, but it is impossible to quantify the effect with any reliability, withjmly one steep catchment in the data set. SAND explains 57 % of the variance of Q75/Q and 48 % of the variance of Q5/Q, with increasing low flows and decreasing high flows as the percentage of sand increases. For the recession coefficients determined from the duration curve, no reliable correlation with any catchment characteristics could be found. The correlations deemed significant were to a too large extent affected by extreme values in single catchments. The variance of the baseflow recession, determined by means of the HBV model, was 44% explained by SAND, with a lower recession in catchments with a high percentage of sand. v Open field (%) Fig. 2 Observed évapotranspiration against percentage of open field.

6 48 Barbro Johansson Adjustment of model parameters The results from the correlation analysis justified attempts to improve the évapotranspiration and the low flows simulated by the model. As no correlation was found between high flow recession and catchment characteristics, no attempts were made to improve the simulated high flows. The coefficients of the regression equations were used to quantify the effect of OPEN and SAND. There are two possible reasons for a higher évapotranspiration from forested areas than from areas dominated by open fields. One is the higher transpiration and the other is the effect of interception. Difficulties distinguishing between these two effects made it hard to know which model parameter to adjust. Instead a factor was applied on the values of monthly mean potential evaporation, used as input data to the model. This factor was made proportional to the percentage of open field in the catchment. When the model was run with the same set of parameters for all catchments, the simulated évapotranspiration differed little between the catchments, in spite of large differences in the precipitation. The introduction of a factor on the potential evaporation improved the results considerably (Fig. 3). The average error in the estimation of mean runoff decreased from 7 % to 3 %. Attempts to improve the simulated low flows were made by relating the percentage of sand to the model parameter defining the upper limit for baseflow, and to the baseflow recession coefficient. The upper limit for the baseflow was assumed to be directly proportional to Q15IQ. As could be expected from the low correlation between low flows and catchment characteristics, the adjustment of the model parameters gave no general improvement of the simulated flows. An improvement is seen for the catchments with the highest sand percentage, but they also contain very little forest. Although no correlation could be found between vegetation cover and low flows, it is likely that the simulated lower évapotranspiration in areas dominated by open fields, leads to higher low flows during summer. The results imply that as long as no better correlation is found between low flows and catchment characteristics, it is not meaningful to adjust the model parameters governing low flow recession. DISCUSSION AND CONCLUSIONS So far the investigation has shown that it is possible to improve simulated runoff volume, by taking into consideration the vegetation cover of a catchment. In the investigated catchments the lake percentage is negligible, and there has been no success in the attempts to improve the simulated high or low flows according to other catchment characteristics. Krasovskaia (1988) investigated the spatial variation of runoff in a 4 km 2 catchment in central Sweden by means of field campaign studies. On two occasions, simultaneous runoff measurements were made in 3 sub-catchments, and the runoff was correlated to physiographic variables describing vegetation cover, relief and stream hydraulics. On the occasion with no rain in the catchment within two weeks before the campaign measurements, only the lake percentage showed a certain correlation to runoff (no geological variables were included). The results were consequently similar to the ones found in this investigation concerning the low flows, i.e. no correlation to

7 Relationship between catchment characteristics and model parameters same model parameters vised for all catchments + model parameters adjusted to percentage of open field Precipitation-runoff mm year" observed Fig. 3 Simulated against observed évapotranspiration. vegetation cover or relief. In Finland and Norway studies of the correlation between low flows and catchment characteristics have resulted in a number of regression equations for different regions (Gustard etal., 1989; Moltzau, 199; Bonsnes, 1992). They emphasize the fact that the correlation between runoff and catchment variables differ between regions, and that general relationships are hard to find. In Sweden, the effects of drainage of wetlands on high flows have recently been studied, using three different approaches (Iritz, 1993; Lundin, 1993; Johansson, 1993). The conclusion to be drawn is that, except in small basins, the effects are marginal. Krasovskaia (1988) points out the difficulties in describing meso-scale variations in runoff on the basis of a hydrological observation network. The southern part of Sweden was chosen for this investigation because of the high number of unregulated gauging stations, as compared to other parts of Sweden. Still there is a distinct feeling of lack of data, and the catchments do not cover a wide enough range of catchment characteristics. Great importance has in this study been attached to the selection of representative precipitation stations for the estimation of areal rainfall. In an area with sharp gradients in precipitation, a mistake in the selection of precipitation data probably causes a much larger error in the estimation of runoff than a mistake in the selection of model parameters. It should also be borne in mind that the errors that can be eliminated by a better selection of model parameters, are the systematic errors. Many of the large errors that occur in a model simulation appear to be random, or are caused by special climatic conditions. This is exemplified by Fig. 4, showing monthly observed and simulated runoff with two parameter sets, for one of the investigated catchments. The large differences between observed and simulated runoff are independent of which parameter set is chosen. Acknowledgements The project was financed by the Swedish Natural Science Research Council and the Swedish Meteorological and Hydrological Institute. The support from Professor Sten Bergstrom and colleagues at the SMHI is gratefully acknowledged.

8 482 Barbro Johansson 15 observed values same model parameters used for all catchments model parameters adjusted for field and sand percentage 1 - E Ë "1 5 H 1 25 I I I I II I I I II I I I! I I! I I I I I II I I I I I I I I I II I I I I I I I I I I II I! II IIII I I I t CD E "25 e Fig. 4 Simulated monthly runoff for different parameter sets. Example from one catchment (Eg). REFERENCES Bergstrom,S. (1976) Developmentand application of a conceptualrunoff model for Scandinavian catchments. SMHI Report, RHO 7. Bergstrôm, S. (1992) The HBV model - its structure and applications. SMHI Report, RH 4. Bonsnes, T. E. (1992) Analyse av fysiografiens innflytelse pâ lavvannsavlop basert pà kampanjemâlinger (Analysis of the influence of physiography on low flows, based on field campaign measurements. Hydrol. Report 29, Univ. of Oslo. Gustard, A., Roald, L. A., Demuth, S., Lumadjeng, H. S. & Gross, R. (1989). Flow Regimes from Experimental and Network Data (FREND), vol. I, chapter 6. Harlin, J. (1991) Development of a process oriented calibration scheme for the HBV hydrological model. Nordic Hydrol. 22, Iritz, L. (1993) Studying the effects of forest drainage onfloodconditions by a physically based distributed model (SHE). In manuscript, Institute of Earth Sciences, Univ. of Uppsala. lohansson, B. (1992) Runoff calculations in ungauged catchments - An evaluation of the pulse model (in Swedish, English Summary.) Vatten48, Johansson, B. (1993) Modelling the effects of wetland drainage on high flows. In manuscript, SMHI. Krasovskaia, I. (1988) A study of mesoscale runoff variability. Geogr. Ann. 7A(3), Lundin, L. (1993) Impacts of forest drainage on flood peak discharges. In manuscript, Department of Forest Soils, Swedish Univ. of Agricultural Sciences. Moltzau, B. (199) Low flow analysis: A regional approach for low flow calculations in Norway. Hydrol. Report 23, Univ. of Oslo. Tallaksen, L. (1991) Recession rate and variability with special emphasis upon the influence of évapotranspiration.hydrol. Report 25, Univ. of Oslo.