Inference of catchment areas from modeled discharge dynamics

The delineation of catchment areas from elevation is a fundamental step in lumped process-based models (PBMs). Most machine learning (ML) approaches for rainfall-runoff modeling spatially aggregate inputs to represent basin-wide processes. Elevation-based lumping, however, disregards both human interventions such as drainages and underground hydrological flows, which can lead to significant model inaccuracies. In this work, we employ DRRAiNN (Distributed Rainfall-Runoff Artificial Neural Network) – a fully distributed neural network architecture – to infer catchment areas directly from observed precipitation and discharge dynamics without prior delineations.

As a first evaluation of the potential to infer actual catchment areas with DRRAiNN, we trained the model on relatively sparse data from 2006 until 2015: Radolan-based hourly precipitation data as input with a spatial resolution of 4x4 km and only daily discharge measurements from 17 stations in the Neckar river basin as target output. Elevation and solar radition were given as additional parameterization input. As DRRAiNN is fully differentiable, we were then able to infer station-specific attribution maps via backpropagation through space and time. To evaluate the alignment between the inferred attribution maps and elevation-based catchment areas, we compute the Wasserstein distance between attributions inside and outside the catchment boundaries. A higher distance indicates better agreement. The results show that DRRAiNN learns to propagate water in a physically plausible manner. Further, we reveal deviations that indicate additional water flows that are undetectable from elevation data alone. Our findings thus suggest that DRRAiNN captures key rainfall-runoff dynamics while avoiding the limitations of lumped models.

The quantitative evaluations alongside qualitative comparisons underscore the model’s potential for uncovering hidden hydrological processes. We show that catchment area estimates can be inferred from relatively little discharge data, which may, in the future, potentially be substituted by satellite data. As a result, DRRAiNN may be applicable in ungauged catchments. Given actual discharge measurements or discharge estimations, DRRAiNN can be used to analyze the hydrological dynamics of surface and subsurface runoff as well as baseflow esimations and has the potential to uncover unexpected and unknown runoff dynamics that would not be detectable otherwise.