Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation

Abstract

[1] This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data-based probability models describing uncertainties in rainfall and runoff data and incorporating them into the Bayesian total error analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall-runoff model GR4J is presented. It exploits a calibration period where dense rain gauge data are available to characterize the uncertainty in the catchment average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill-posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff, and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.

Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method

“…As a result, it can be concluded that, with certain rainfall input combination, if the rainfall center is not captured and applied to the hydrological model, a large portion of the actual rainfall will be ignored in the rainfall-runoff simulation, resulting in significant deviation in simulated runoff. Even though some methods can produce high-intensity rainfall cells in a river basin, e.g., the geostatistical conditional approach used by Vischel et al [28] and Renard et al [29], the intensity and area of the rain centers are still difficult to simulate. Therefore, to obtain more confident simulation results, higher D S must be provided to capture more accurate range of the rainfall centers.…”

“…Vischel et al [28] used this method to study the differences of simulated runoff using different simulated rainfall spatial patterns and concluded that for Hortonian runoffs, conditional simulation performs better than simply kriging station rainfall. Moreover, Renard et al [29] used the Bayesian total error analysis methodology to decompose the total uncertainty of runoff predictions into the individual contributions of rainfall, runoff and model structural errors, where the uncertainty in the basin average rainfall was characterized using the geostatistical conditional simulation. Moreover, the spatial variation of rainfall has been proved to influence not only runoff but also erosion and sediment loads.…”

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.…”

“…Various authors have therefore proposed alternative formulations of the likelihood function to extend applicability to situations where the error residuals are non-Gaussian with varying degrees of kurtosis and skewness Smith et al, 2010;Evin et al, 2013;Scharnagl et al, 2015). Latent variables can also be used to augment likelihood functions and take better consideration of forcing data and model structural error (Kavetski et al, 2006a;Vrugt et al, 2008a;Renard et al, 2011). For systems with generative (negative) feedbacks, the error in the initial states poses no harm as its effect on system simulation rapidly diminishes when time advances.…”

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

“…Uncertainty is present in all aspects of water resources management (WRM) optimisation, from problem formulation to solutions obtained (see Figure 3) and a lot of work has been published in recent years on uncertainty quantification in the water resources literature (Beven, 2006;Gupta et al, 2008;Kavetski et al, 2006a, b;Renard et al, 2011;Vrugt et al, 2005;Vrugt et al, 2008). One general source of uncertainty stems from imperfect knowledge about socioeconomic drivers in water systems, such as future water demand and population growth, and the extent to which urbanization will occur.…”