Investigating Predictability of the TRHR Seasonal Precipitation at Long Lead Times Using a Generalized Regression Model with Regularization

Regression has been a popular tool to relate regional precipitation to large-scale climates. However, over-fitting could largely degrade the performance, especially when dealing with the highly 'non-square' climate data. Here, we proposed a simple regression model by coupling pooling and a generalized regression with regularization and tested it in estimating the Three-Rivers Headwater Region (TRHR) wet-season precipitation using the sea surface temperatures (SSTs) at lead times of 0-24 months. The model shows better predictive skill for certain long lead times when compared with some commonly used regression methods including the Ordinary Least Squares (OLS), Empirical Orthogonal Function (EOF), and Canonical Correlation Analysis (CCA) regressions. The high skill is found to relate to the persistent regional correlation patterns between the predictand and predictors as also confirmed by a correlation analysis. Furthermore, flexibility of the model is demonstrated using a multinomial regression model which shows good skill around the long lead times of 22 months. Consistent clusters of SSTs are found to contribute to both models. Two SST indices are defined based on the major clusters of predictors and are found to be significantly correlated with the predictand at corresponding lead times. In conclusion, the proposed regression model demonstrates great flexibility and advantages in dealing with collinearity while preserving simplicity and interpretability.