Description
This thesis further develops a multivariate linear regression model for the prediction of the United States monthly precipitation anomalies: the ensemble CCA model. First, a detailed mathematical description of the model including the derivation of all important formulas is presented. The core of the model is the transformation of the optimization problem from the physical space to the spectral space. In this way, we simplify computations and reduce the model dimensionality. A new result of this thesis is the ability to express the predictand directly in dependence of the predictor in form of a simple matrix-vector product. The theoretical part is followed by the implementation of the prediction algorithm in R and the application on an example with precipitation, sea surface temperature and sea level pressure as predictor variables as well as five predictor regions. With always 20 years of training data, the monthly precipitation anomalies of the years 2002 - 2017 are forecasted. Cross validation is used to determine the prediction skill. Temporal correlations of the true and the predicted values are highest in spring and least in summer. However, spatial correlations are highest in summer. The forecast model can capture the seasonal precipitation trend very well. A smoothing effect can be observed. The model doesn’t show the ability to predict unusual deviations from the mean precipitation rates. Therefore, the usage of additional models is recommended to increase the forecast skill.
