Self-training approach to improve the predictability of data-driven rainfall-runoff model in hydrological data-sparse regions

Numerous data-driven models have been introduced to establish reliable predictions in the rainfall-runoff relationship. The majority of these models are trained using a supervised learning approach, with paired observed (i.e., labeled) samples of climate and streamflow data. However, in practice, the availability of such paired observations is often constrained due to sparse data from streamflow gauges worldwide, which typically covers only a few years/regions. This limited number of paired samples can significantly impede the learning ability of the data-driven model. To fill this gap, we present self-training, a semi-supervised learning approach that imputes the pseudo streamflows for unpaired (i.e., unlabeled) samples to increase the amount of available paired samples. To elaborate, we adopt teacher-student framework. The teacher model is first trained on (limited number of) paired samples and then works as a generator of pseudo streamflow for unpaired samples. The student model is trained on both paired and pseudo streamflow-endowed samples. Notably, our framework introduces an annealing-able loss function for training the student model, designed to compensate for the uncertainty in pseudo streamflow. To validate the effectiveness of the proposed framework, we conducted an extensive set of experiments encompassing diverse spatial and temporal controlled settings, all of which utilized the LSTM network. The experiments are based on basins from the freely available CAMELS dataset. Results indicate that the proposed framework of self-training show significantly enhanced performance compared to the baseline models built in fully-supervised manners with sparse paired observations. Results also show that the framework can serve as a viable alternative to the previously developed fully supervised approaches. Lastly, we address potential avenues for enhancing the model and provide an outline of our future research plans in this domain.