A Data Censoring Approach for Predictive Error Modeling of Flow in Ephemeral Rivers

Abstract

Flow simulations of ephemeral rivers are often highly uncertain. Therefore, error models that can reliably quantify predictive uncertainty are particularly important. Existing error models are incapable of producing predictive distributions that contain >50% zeros, making them unsuitable for use in highly ephemeral rivers. We propose a new method to produce reliable predictions in highly ephemeral rivers. The method uses data censoring of observed and simulated flow to estimate model parameters by maximum likelihood. Predictive uncertainty is conditioned on the simulation in such a way that it can generate >50% zeros. Our method allows the setting of a censoring threshold above zero. Many conceptual hydrological models can only approach, but never equal, zero. For these hydrological models, we show that setting a censoring threshold slightly above zero is required to produce reliable predictive distributions in highly ephemeral catchments. Our new method allows reliable predictions to be generated even in highly ephemeral catchments.Plain Language Summary Many rivers cease to flow at various times. These rivers are difficult to model well, meaning that the models have a high level of uncertainty. There are no existing methods to correctly quantify the uncertainty in models of rivers that cease to flow >50% of the time. We propose a new method that can quantify the uncertainty of these models, even for rivers that cease to flow very often.Key Points:• Current hydrological error models cannot handle cases where >50% flow is zero • We introduce a new error modeling method that uses data censoring of simulations and observations • Our model produces reliable predictions even in highly ephemeral catchmentsSupporting Information:• Supporting Information S1

Bayesian LSTM With Stochastic Variational Inference for Estimating Model Uncertainty in Process‐Based Hydrological Models

“…The Box‐Cox transformation has been used to make residuals more homoscedastic (Figures 5c and 10c). Other new transformation methods such as the log‐sinh transformation (Wang et al., 2012, 2020) and the wavelet‐based variance transformation (Z. Jiang et al., 2020) have also been demonstrated to improve model inference. Heteroscedasticity may be further reduced by training and applying the residual error model separately for each season and month.…”

Propagating reliable estimates of hydrological forecast uncertainty to many lead times

“…Both the existing and restructured versions of ERRIS use the same basic procedure to estimate parameters (Li et al, 2020;Li et al, 2016;Li et al, 2017). Because the ESDS service is operated in a number of ephemeral catchments (like the Brisbane River), the ERRIS estimation procedure uses the likelihood proposed by Wang et al (2020) to allow reliable predictions in ephemeral rivers. As for many error models, ERRIS parameters are estimated by characterising errors at one lead time in advance.…”

“…where 3 m and 3 s are the mean and standard deviation of the transformed simulation 3 z (see Appendix C) and ( ) 0,1 U is a uniform distribution. This step allows >50% of the predictive uncertainty to be zero, allowing reliable ensembles to be generated even in highly ephemeral rivers (Wang et al, 2020). 5.…”

“…Following Wang et al (2020), the likelihood handles four cases, depending on whether the simulation and/or observation are equal to zero: . The arctanh transformations applied to the restructured ERRIS allow more efficient estimation of these parameters.…”

“…are not needed in subsequent stages and are discarded. Note that Eq (C13) requires a Monte Carlo integration, as detailed byWang et al (2020).…”