Beyond Rainfall Multipliers: Describing Input Uncertainty as an Autocorrelated Stochastic Process Improves Inference in Hydrology

Abstract:

Rainfall is the main driver of hydrological systems. Unfortunately, it is highly variable in space and time and therefore difficult to observe accurately. This poses a serious challenge to correctly estimate the catchment-averaged precipitation, a key factor for hydrological models. As biased precipitation leads to biased parameter estimation and thus to biased runoff predictions, it is very important to have a realistic description of precipitation uncertainty. Rainfall multipliers (RM), which correct each observed storm with a random factor, provide a first step into this direction. Nevertheless, they often fail when the estimated input has a different temporal pattern from the true one or when a storm is not detected by the raingauge. In this study we propose a more realistic input error model, which is able to overcome these challenges and increase our certainty by better estimating model input and parameters. We formulate the average precipitation over the watershed as a stochastic input process (SIP). We suggest a transformed Gauss-Markov process, which is estimated in a Bayesian framework by using input (rainfall) and output (runoff) data. We tested the methodology in a 28.6 ha urban catchment represented by an accurate conceptual model. Specifically, we perform calibration and predictions with SIP and RM using accurate data from nearby raingauges (R1) and inaccurate data from a distant gauge (R2). Results show that using SIP, the estimated model parameters are "protected" from the corrupting impact of inaccurate rainfall. Additionally, SIP can correct input biases during calibration (Figure) and reliably quantify rainfall and runoff uncertainties during both calibration (Figure) and validation. In our real-word application with non-trivial rainfall errors, this was not the case with RM. We therefore recommend SIP in all cases where the input is the predominant source of uncertainty. Furthermore, the high-resolution rainfall intensities obtained with this innovative technique can help validate areal rainfall estimates from other methods and constitute an important contribution towards separating predictive uncertainties.