Using discharge data to reduce structural deficits in a hydrological model with a Bayesian inference approach and the implications for the prediction of critical source areas

Abstract

[1] A distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in Switzerland. We tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge. This learning process consisted of five steps: For the prior prediction (step 1), knowledge of the model parameters was coarse and predictions were fairly uncertain. In the second step, discharge data were used to update the prior parameter distribution. Effects of uncertainty in input data and model structure were accounted for by an autoregressive error model. This step decreased the width of the marginal distributions of parameters describing the lower boundary (percolation rates) but hardly affected soil hydraulic parameters. Residual analysis (step 3) revealed model structure deficits. We modified the model, and in the subsequent Bayesian updating (step 4) the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior. This incremental procedure led to a strong reduction in the uncertainty of the spatial prediction. Thus, despite only using spatially integrated data (discharge), the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also. The fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results. The comparison depended critically on the ratio of event to preevent water that was discharged. This ratio cannot be estimated from hydrological data only. The results demonstrate that the value of local data is strongly dependent on a correct model structure. An iterative procedure of Bayesian updating, model testing, and model modification is suggested.Citation: Frey, M. P., C. Stamm, M. K. Schneider, and P. Reichert (2011), Using discharge data to reduce structural deficits in a hydrological model with a Bayesian inference approach and the implications for the prediction of critical source areas, Water Resour.

Comparison of two stochastic techniques for reliable urban runoff prediction by modeling systematic errors

“…Adding linear state‐dependent noise in the model equations, as in the IND, has the advantage that it guarantees positive values of the model output. When modeling the errors in the output equations, as in the EBD, output transformation might be required to ensure nonnegative predictions [e.g., in Frey et al ., ; Sikorska et al ., ].…”

Physico-chemical characteristics affect the spatial distribution of pesticide and transformation product loss to an agricultural brook

“…Especially if the model is calibrated to several sub-catchments using discharge data and pesticide data in combination there is more evidence of the correctness of the spatial prediction (Nejadhashemi et al, 2011). However, the simulated spatial distribution of pesticide loss from single fields remains a hypothesis which needs to be validated by additional local information (Frey et al, 2011) but may be used as an educated guess for further analysis.…”

“…Therefore, compared to former approaches, the method of this study is mainly limited by computational power, which has a direct effect on the choice of the spatial resolution of the CSA assessment. Furthermore, uncertainty assessment of the spatial prediction, as performed by Frey et al (2011), is hardly possible since all model uncertainty estimation methods are based on a large number of model runs (Beven, 2009). …”

“…They concluded that more complex and process-based concepts gave better results (Nejadhashemi et al, 2011) and that the choice of model concepts may largely influence the estimated location of CSAs (Easton et al, 2008;Niraula et al, 2013). Three studies employed fully distributed process-based hydrological models with the aim of delineating CSAs for pesticide export (Payraudeau et al, 2009;Frey et al, 2009, Frey et al, 2011. Even though these models were able to estimate realistic catchment connectivity and fast runoff generation processes, reactive substance mobilisation and transport simulations were neglected.…”

Model bias and complexity – Understanding the effects of structural deficits and input errors on runoff predictions

“…In order to account for the heteroschedasticity of the uncertainty of model predictions, we transformed the modeled and observed response of the system (Yang et al, 2007;Frey et al, 2011;Breinholt et al, 2012;Dietzel and Reichert, 2012). As these and several other studies show, output transformation can stabilize the variance of the calibration residuals while accounting for the increase of uncertainty with higher values of the predictand (e.g., during high flow situations).…”