Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

Abstract

[1] Meaningful quantification of data and structural uncertainties in conceptual rainfallrunoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill-posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill-posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall-runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.

Seasonal streamflow forecasting by conditioning climatology with precipitation indices

“…In Europe, teleconnections show complex patterns and a strong seasonal dependence (Ionita et al, 2015). Some studies have thus proposed conditioning past precipitation or streamflow scenarios based on previous amounts of precipitation or on previous streamflow anomalies (Sauquet et al, 2008;Svensson, 2016).…”

Quantile hydrologic model selection and model structure deficiency assessment: 1. Theory

“…The cumulative density function in turn is a function of the underlying processes and measurement errors which for given input forcings generate a time series of variable of interest such as streamflow, evaporation or storage. Its decomposition into respective components requires assumptions on the structure of processes or measurement errors [Renard et al, 2010], which we refrain from in this study. We however remark that an assumption on the structure of measurement errors is sufficient, as it reveals the distribution of measurement-error-corrected conditional distribution of y on x given F(yjx) (uncorrected conditional distribution).…”

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

“…The BATEA framework is an example of this more advanced approach (Kavetski et al, 2006a,b;Kuczera et al, 2006;Renard et al, 2010Renard et al, , 2011, and can be implemented with DREAM as well (Vrugt et al, 2008a(Vrugt et al, , 2009a. The formulation of Equation (41) is easily adapted to include errors in the calibration data as well (see Appendix B) though it remains difficult to treat epistemic errors.…”