Using neural network embeddings to achieve spatial regularization in a basic streamflow forecast model

In a project with the objective of making multi-decadal streamflow projections based on climate model simulations, we developed a basic linear regression model that links anomalies of streamflow to anomalies of precipitation amounts and temperature. Regression coefficients estimated separately for each catchment and each month, however, show physically implausible spatial patterns and indicate issues with overfitting. An alternative approach is therefore explored in which all regression
coefficients are estimated simultaneously through a neural network that retains the original linear model structure, but uses embeddings to map each combination of catchment and month to a set of regression coefficients. In our setup with ~150 catchments in Brazil, this approach yields physically more plausible relationships between streamflow, precipitation amounts, and temperature than the locally fitted regression models. The resulting model was considered trustworthy enough to be driven with climate model simulations of future temperature and precipitation scenarios and to project the future potential of hydropower production in Brazil.