Regression Techniques Used in Hydrometeorology

Regression methods play an important role in ensemble forecasting. The atmosphere-land-ocean system is complex and dynamical, which makes it difficult to predict the state of hydrometeorological variables deterministically. Consequently, stochastic approaches become useful for hydrometeorological forecasting. As forecast uncertainty is inevitable, it is of key importance to use regression approaches to extract useful information from raw observational data and forecasts from dynamical models while providing an appropriate estimation of the confidence level of the forecasts. Regression methods are usually used in two ways in ensemble forecasting. One is used as a statistical forecasting model, which accounts for the relationships between predictors and historical observation data. Another is used as a post-processor for the forecasts from dynamical models in order to correct various biases in them and to improve their reliability and skill scores. If the statistical relationships between the dynamical forecasts and the observation data exist, the systematic bias and ensemble distribution errors can be corrected, and associated uncertainty can be reduced. The two means of applying regression approaches share a common statistical foundation. This chapter will give a brief introduction to various common linear/nonlinear regression approaches that have been used or can be potentially applicable in ensemble forecasting.