Multidimensional Functional Principal Component Regression And Its Meteorological Applicatio

Due to the complexity of meteorological data,it is difficult for traditional methods to capture the spatio-temporal correlation information while achieving dimensionality reduction,so as to achieve accurate simulation of the Earth’s climate system.In this paper,the functional data analysis method is used to provide a functional data perspective to understand the large-scale meteorological forecast factors.At the same time,the spatial information of the variables is interpreted in detail,and the correlation between the meteorological factors is further comprehensively considered and studied.Then the fusion model is established from the perspective of time,space,and multi-dimensional characteristics of variables,So as to improve the ability to predict future climate change around the world.In the second chapter of this paper,we understand the large-scale meteorological forecast factors from a new functional data perspective,establish a multi-dimensional functional downscale learning method,and realize the two-dimensional functional feature extraction of meteorological data.The statistical downscaling model based on multidimensional functional principal component analysis proposed in this part can greatly improve the accuracy of large-scale forecast of meteorological factors.The new method of feature extraction obtained by multidimensional functional downscaling model can achieve dimensionality reduction without destroying the multidimensional structure of meteorological data itself,and retain the rich spatial information.The model can find functional principal components from different dimensions,which is impossible for traditional principal component analysis.Further using the regression model,this part provides an effective meteorological prediction method.Through the analysis of precipitation in southern Australia,this part explains the relationship between the winter mean sea level pressure and precipitation in southern Australia from the perspective of functional data.Compared with the traditional feature extraction method based on principal component analysis,the multi-dimensional functional downscale model not only needs less principal components to capture most of the variance in the mean sea level pressure,but also greatly avoids the loss of spatial information.In the third chapter of this paper,the functional principal component supervised learning method of spatiotemporal data is designed to realize the coupling analysis of meteorological characteristics.In this part,a multidimensional functional downscale regression model is established by using multidimensional functional partial least squares and supervised functional principal component method,and a feature extraction method of large-scale meteorological forecast factors that can show the correlation with the forecast variables is proposed.It can provide information related to the predicted variables and fully consider the correlation between meteorological factors on the basis of finding the characteristics of large-scale meteorological forecast factors.The regression model based on this can obtain more accurate prediction results than the traditional functional downscaling model.Based on this method,the precipitation in Australia is also studied,and the regression results show that the simulated precipitation based on this method is closer to the observed value.The resulting downscaling results provide an alternative estimate of future rainfall changes due to changes in the mean field of mean sea level pressure.In the fourth chapter,a supervised weighted fusion method for constructing a class of spatiotemporal data is proposed,which enhances the interpretability of the physical mechanism of the fusion prediction model.This model further considers the weight combination of different types of functional prediction variables.It not only assigns corresponding weights to various types of functional prediction factors,but also automatically estimates the main functional principal components related to response variables,representing the main source of change of functional prediction factors.The proposed framework for calculating weights can consider two or more types of functional predictors,and simultaneously use continuous or classified scalar response variables to improve the prediction performance of the estimated functional principal component regression.The model built can weigh the explanatory variables,and the final results can be explained by the corresponding mechanism.In addition,the estimation algorithm for the model parameters is based on eigenvalue decomposition,which is easy to implement.In view of the lack of isobaric information in the sea level pressure field data in the second and third chapters,it is impossible to study the weighting problem,so this chapter also selects the summer temperature data in the Jianghuai region for example analysis,which confirms that the proposed method has better prediction performance than the unweighted supervised function principal component analysis method.In the model testing of optimal factor combinations,the proposed model has significant advantages in both higher correlation coefficients and lower mean square error.The test of independent observation samples shows that the established model has a good ability to simulate the spatial and temporal structure and change of summer temperature in the Jianghuai region.In conclusion,the proposed regression model in this paper have realized the efficient,accurate and robust prediction function under the conditions of space-time dimension and variable function characteristic dimension.In order to carry out and improve the prediction and prediction ability of climate,this will enhance the response to climate change It provides important reference basis for formulating long-term development plan.