Generic error model for calibration and uncertainty estimation of hydrological models

Abstract

[1] Because of the necessary simplification of the complex natural processes and the limited availability of observations, model simulations are always uncertain and this uncertainty should be quantified. In this contribution, the model error is quantified using a combined procedure. For the uncertainty of discharge due to meteorological input, a stochastic simulation method is used. To quantify the effect of process representation and parameterization, a sensitivity analysis is carried out. It is assumed that the model error due to process uncertainty is proportional to the sensitivity. The final model error variance can thus be calculated from the stochastic errors and the process sensitivities. The coefficients used for the quantification are estimated simultaneously with the model parameters. The methodology presented produces error series that are normally distributed and that represent the varying importance of different processes in time. This uncertainty time series can be used as a weighting factor to normalize the model residuals during calibration so that the assumptions of least squares optimization are fulfilled. Calibration and uncertainty estimation are demonstrated with an example application of a distributed Hydrological Bureau Waterbalance (HBV) model of three watersheds in the Neckar basin in southwest Germany. The model residual distributions are presented and compared to a standard calibration method. Further, it is shown that the new methodology leads to more realistic confidence intervals for model simulations. Although applied to the HBV model as an example, the method is general and can be applied to any model and also in conjunction with other uncertainty estimation techniques.Citation: Götzinger, J., and A. Bárdossy (2008), Generic error model for calibration and uncertainty estimation of hydrological models, Water Resour. Res., 44, W00B07,

Streamflow Modelling: A Primer on Applications, Approaches and Challenges

“…A single, correct value often cannot be uniquely or reliably identified. This leads to an additional source of hydrological model uncertainty that may be closely related to process uncertainty (Götzinger and Bárdossy, 2008). When NWP output is used to drive a forecast model, parameter uncertainty may also be related to NWP uncertainty through the use of precipitation or evapotranspiration adjustment parameters (Herr et al, 2003;Carpenter and Georgakakos, 2006).…”

“…For example, Stahl et al (2008) cited available snowmelt algorithms as an important source of uncertainty in their application of the HBV-EC model to a catchment in complex terrain in BC; this source of error would likely play a central role in overall model uncertainty during winter and the spring snowmelt period, but its importance would decrease through the summer (Götzinger and Bárdossy, 2008). Likewise, the presence of glacier melt algorithms in the WaSiM-ETH model would provide little benefit to applications in watersheds without glaciers.…”

“…Different objective functions may be sensitive to different parts of the hydrograph; thus, the choice of a single function will necessarily lead to a biased calibration (Duan et al, 2007;Götzinger and Bárdossy, 2008). For example, the Nash-Sutcliffe Efficiency (NSE) emphasizes peak flow periods, whereas the NSE of the log-transformed discharge will tend to generate a parameter set with better performance during recession and low flow periods (Schnorbus et al, 2010).…”

Improving Flood Prediction Assimilating Uncertain Crowdsourced Data into Hydrological and Hydraulic Models

“…epistemic uncertainty (Merz and Thieken, 2005;Hall and Solomatine, 2008;Domeneghetti et al, 2013). Four main sources of uncertainty can be identified in the hydrological and hydraulic models used in flood forecasting systems Liu and Gupta, 2007;Götzinger and Bárdossy, 2008;Solomatine and Wagener, 2011 Other authors have also quantified uncertainty in flood plain modelling related to the uncertain operation of hydraulic structures connecting rivers and wetlands (Alfonso and Tefferi, 2015).…”

Climate uncertainty in flood protection planning

“…Thus, the parameter estimates strongly depend on the calibration period (Brigode et al, 2013). Several approaches exist to quantify the uncertainty stemming from the hydrological model (Götzinger and Bárdossy, 2008;Velázquez et al, 2013). Overall however, the error from the hydrological model is small, in particular for high flow indicators (Velázquez 5 et al, 2013).…”