Evapotranspiration is a necessary input and one of the most uncertain hydrologic variables for quantifying the water balance. Key to accurately predicting hydrologic processes, particularly under data scarcity, is the development of an understanding of the regional variation of the impact of potential evapotranspiration (PET) data inputs on model performance and parametrization. This study explores this impact using four different potential evapotranspiration products (of varying quality). For each data product, a lumped conceptual rainfall–runoff model (GR4J) is tested on a sample of 57 catchments included in the MOPEX data set. Monte Carlo sampling is performed, and the resulting parameter sets are analyzed to understand how the model responds to differences in the forcings. Test catchments are classified as energy- or water-limited using the Budyko framework and by eco-region, and the results are further analyzed. While model performance (and parameterization) in water-limited sites was found to be largely unaffected by the differences in the evapotranspiration inputs, in energy-limited sites model performance was impacted as model parameterizations were clearly sensitive to evapotranspiration inputs. The quality/reliability of PET data required to avoid negatively impacting rainfall–runoff model performance was found to vary primarily based on the water and energy availability of catchments.
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems’ previous outputs. Development and implementation of linear methods are relatively simple, but they often do not capture non-linear relationships in the data. Thus, artificial neural networks (ANNs) are receiving attention from researchers in analyzing and forecasting dynamical systems. Recurrent neural networks (RNNs), derived from feed-forward ANNs, use internal memory to process variable-length sequences of inputs. This allows RNNs to be applicable for finding solutions for a vast variety of problems in spatiotemporal dynamical systems. Thus, in this paper, we utilize RNNs to treat some specific issues associated with dynamical systems. Specifically, we analyze the performance of RNNs applied to three tasks: reconstruction of correct Lorenz solutions for a system with a formulation error, reconstruction of corrupted collective motion trajectories, and forecasting of streamflow time series possessing spikes, representing three fields, namely, ordinary differential equations, collective motion, and hydrological modeling, respectively. We train and test RNNs uniquely in each task to demonstrate the broad applicability of RNNs in the reconstruction and forecasting the dynamics of dynamical systems.
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