Estimation of non-stationary hydrological model parameters for the Polish Welna catchment

Traditionally, conceptual hydrological model parameters are calibrated with observed data sets, in an attempt to find a best performing (optimal) parameter set. This calibrated parameter set is unchanged when used to simulate run-off during a future period, under the assumption that optimal parameter values do not change over time. However, functioning of conceptual hydrological models is questioned when these models are used for climatic conditions that are very different from conditions encountered during the model's calibration period. This study explores the option of defining a relationship between optimal parameter values and prevalent climatic conditions, and thus create climate-dependent parameters. The Polish Welna catchment is used as a test case. The methodology is kept simple, since no research exists to support more complex methods. First, available data are divided into overlapping 5-year periods and a HBV model is calibrated for each period. This gives an optimal parameter set for each 5-year period, corresponding to climatic conditions during this period. Second, linear correlation between optimal parameter values and certain climate characteristics (such as average precipitation during the 5-year period) are calculated. Third, significant correlations that can also be explained in a hydrological way are used for linear regression analysis, to establish equations for optimal parameter values that depend on climate characteristics. A trade-off exists between goodness-of-fit of the regression and the complexity of the equation. Fourth, a regression model is selected with climate-dependent parameters estimated with regression equations and fixed parameters with recalibrated values to partly account for their interaction with climate-dependent parameters. Fifth, the functioning of the regression model is compared to the functioning of the base model. Both are used for climate change impact assessment, comparing predicted changes in run-off between periods 1971-2000 and 2071-2100. Figure 1 compares base and regression model functioning with the functioning of optimal parameter sets for all 5-year periods. The regression model is intended to improve base model functioning and its performance markers (red crosses) should thus be located between base model (black squares) and optimal performance (blue circles). This is however not the case in the majority of periods and especially so in the validation period 1-6. Base model predictions are thus considered more reliable than regression model predictions. However, the research approach and method seem promising and performance of the regression model is thus analyzed further to determine if its functioning is different from base model functioning. Figure 1: model performance results per 5-year period In four out of five climate projections, the regression model predicts smaller discharge changes than the base model. The regression model generally predicts smaller changes than the base model for winter and spring months, and slightly larger changes than the base model for summer and autumn months. However, differences in model input for the five cases lead to larger outcome differences than outcome differences between base and regression model in an arbitrary single case. Still, while practical use of this study is limited (mostly due to issues with the catchment), research methodology seems promising and can, with minor adjustments, be applied to more test cases. Since statistically significant relations have been found in this study, more research on this topic seems justified. Several recommendations are made with regard to data quality, data series length, parameter interactions and the use of climate change projections.