Two Strategies for Avoiding Overfitting Long-Term Forecasting Models: Downsampling Predictor Fields and Shrinking Coefficients

Long-term hydrological forecasting based on sea surface temperature (SST) fields faces the large $p$ and small $n$ problem, i.e., too many potential predictors and a limited number of samples. Considering the selection of predictors will also enhance the complexity of models and lead to overfitting, in this study, two strategies are used for building forecasting models for long-term streamflow forecasting. The first strategy is to downsample the SST field and optimize its spatial resolution; the second is to shrink model coefficients based on L1 regularization. We build models based on the downsampled SST fields with different spatial resolutions. It is found that the model based on a proper spatial resolution always performs better than the model based on the raw SST field. This result suggests that it is better to treat the spatial resolution of the predictor field as a hyperparameter, which is similar to hyperparameters for controlling the complexity of many machine learning models. For applying the second strategy, L1 norm regularization models, including (1) least absolute selection and shrinkage operator (LASSO), (2) relaxed LASSO, and (3) two-step approach of LASSO and ordinary least squares regression ($\mathrm{LASSO}+\mathrm{OLS}$) are explored. We have found that the relaxed LASSO model always performs better than the ordinary LASSO, indicating that relaxed LASSO is a better shrinkage approach. Furthermore, the skills of the presented models are compared with the stepwise regression, and the lower skill of the stepwise regression based on SST fields with a high spatial resolution suggests that one should not select predictors based on fields with high resolutions considering the limited number of samples.