Examining the uncertainty estimation properties of LSTM based rainfall-runoff models

Existing studies on Long-Short Term Memory (LSTM) based rainfall-runoff modelling predominantly focus on the performance of point estimates (e.g. Kratzert et al. 2019). These estimates are by their very nature imprecise, given the uncertainty in the available information, the forcing inputs and the streamflow observations used to train the model. To account for this imprecision, the uncertainty of a given prediction can be estimated. From a technical standpoint, one solution could be to adapt the output of an LSTM so that it provides uncertainty estimates (as opposed to point predictions). This is a native property of using a general approximation approach, such as the LSTM (they also have the advantage of not requiring a-priori sampling distribution). However, these uncertainty estimates are also forms of estimates, based on the same incomplete data as any model prediction. This property can be observed when comparing ensemble-uncertainty estimations with the ones provided by a single LSTM (e.g.: Klotz et al. 2019; Fort, Hu & Lakshminarayanan 2020). The estimates of uncertainty are therefore in themselves uncertain and therefore need to be be empirically verified, as all uncertainty estimates. The goal of this contribution is thus twofold. First, we provide an intuitive exploration into how neural networks self-organize their uncertainty estimations in the context of rainfall-runoff models, so that we can leverage these principles for general hydrological uncertainty estimations. Second, we explore the role of higher-order uncertainties regarding the estimations of the uncertainties, so that we can begin to quantify the limits of this approach.