The Application For The Partial Least-Squares Regression (PLS) In The Short-term Climate Forecast

In weather forecasting business, the regression analysis is one of the statisticanalysis and forecasting technology commonly used today, but it is fundamentallyrequested that each of the independent variable in the mode of multiple linearregression should not exist close linearity relation. But when it is too muchindependent variable related in an actual problem, it is difficult to find a groupindependent variable, in which each of them is irrelevant, and it will bring themulti-collinearity problem. And if a regression model built on the ordinary leastsquares (OLR), the parameter estimation and the steadies of the model will be poor.To solve the multi-collinearity problem, the methods popularly used in the studyof building forecasting model are the ridge regression analysis and the principlecomponents regression. The main problem exists in the ridge regression is that thechoice of value k is mostly subjectivity, while it does not consider the dependentvariable in the principle components regression, though there is of strong compositescore to system of the variable of the components gained in those way, it is short ofexplanation ability to the dependent variable. And another way is the partial leastsquares (PLS), which is an improvement of the OLS.In this paper, we try to use the PLS to build a forecasting model to study thewinter monthly mean temperature in Guangxi province. We take monthly meantemperature anomal fields of each month in winter (December, January, February)from 1959 to 2000 of 88 stations in Guangxi as the forecasted value, and take the500,100hPa monthly mean geopotential height field and monthly mean SST inPacific from 1958 to 2000 as the forecasting components to build a forecastingmodel, and then we do some forecasting test of 5 years independent samples from2001 to 2005. In the model we are not in the way that directly aims at one stationbuilding one equation, but use EOF feature reduction method, drawing the first threetime modulus of monthly mean temperature anomal field in each month containingentire 88 stations in Guangxi as forecasting component. During our building model,we find that usually only drawing three principle components in PLS, it couldcontain more than 75ï¼…information of the independent variable and about 50ï¼…information of the dependent component, which not only can summarize theinformation of the system of the independent variable, but can explain the dependent variable well. In our paper, we using the distributing from China MeteorologicalAdministration to calculate the objective grades of the forecasting result, amongthem the evaluation of the December, January, February is 75.8, 84.7, 72.6respectively, and the average fraction of the three months is 77.7, which is satisfying.In this paper, we also do some contrast tests using stepwise regression in the somecondition, the result shows that when we use regression method directly, theevaluations for the three months are: December 62.8; January 73.6; February 66.9;the average for the three months is 68.8. Contrast the forecasting results of the twomethods, PLS is obvious better than the stepwise regression in forecasting evaluation,forecasting stability, drawing the abnormal information the factors contain and soon..Further analysis shows that, as a new multiple statistic method, there is betterforecasting effect of PLS, it is mostly because that when using the PLS to draw thefactors ,it not only summarize the information in the system of the independentvariable, but also give better explanation of the dependent variable, and eliminate themulti-colliearity, and then the forecasting accuracy is improved. In the same time,during building model, PLS can realize building regression model (multiple linearregression analysis), simplify the data structure (principle component analysis) andthe relevance analysis, it is a more effective method for building model. Further more,PLS can realize the building of forecasting model even there is only a few samples.So from the result of our study, we find that using PLS to build model of monthlymean temperature is a very effective regression analysis method, which offer a newmeteorological implement to gain data and draw information, and there is a goodextending prospect in the short-term climate forecasts business of this method.