Multi-decadal streamflow projections for catchments in Brazil based on CMIP6 multi-model simulations and neural network embeddings for linear regression models

A linear regression model is developed to link anomalies of streamflow to anomalies of precipitation amounts and temperature with the goal of making multi-decadal streamflow projections based on CMIP6 multi-model simulations. Regression coefficients estimated separately for each catchment and each month 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. The model is demonstrated over a set of catchments in Brazil, where the estimated relationships are used to make streamflow projections for the next decades based on CMIP6 multi-model simulations. It yields physically more plausible relationships between streamflow, precipitation amounts, and temperature for our study area than the locally fitted regression models. The resulting projections indicate reduced streamflow over northern, north-eastern, central, and south-eastern Brazil, especially for the austral spring and summer season. The signal is less clear during austral winter. In southern Brazil, an increase in streamflow is expected.