Extended Abstract

important featur e o f a n eural n etwork is i ts ability to learn . This learning is bas ed on th esimultaneous analysis of some input a nd output samples, which are called learning samples.As a rule, a size of learning sample is equal to one third of the general sample size. Therefore,two thirds of the gen eral sample is implemented to eva luate the efficiency and accur acy of aneural network as a predictive tool. The st ructure of the hidden layers is very complicated.Each of the hidden layer modules is linked to every one of the fuzzy logic modules. The firsthidden layer output i s connected to the second fu zzy logic lay er. Its function is designed todeclassify the results o f non-linear t ransformations, w hich were ca rried out in th e hiddenlayer. Hence, t his decl assification module provides an inverse t ransformation fro m theartificial inner variables to ordinary units of meteorological parameters. The final combinationof output v ariables l eads us to t he acquis ition of the estimates of t he pred ictive va riables(surface air te mperature, etc.). E mpirical orthogonal functi ons (EO Fs) and s ingular valuedecomposition (SVD) are the most commonly used techniques (Wang, 2001) to build a phasespace. EOFs are the eigenvectors of the co variance matrix obt ained fro m calculatingcovariances of time series at different spatial points. EOFs are optimal in explaining as muchtotal variance as possible with any specific number of spatial patterns. The first EOF explainsmost of the temporal variance in the dataset among all possible spatial fields. The subsequentEOFs are mutually orthogonal (in space and time) and successfully explain less variance. TheEOF analysis is non-local in that the loading values at two various spatial points in an EOF donot simply dep end on the time series at thos e two points but dep end on the whole dataset.This c ontrasts with the one-point correlat ion analyses us ed to define teleconn ections, forwhich the patterns can be interp reted locally. A fuzzy set approach is more appropriate toapproximate the temporal and spatial modes in low dimensional phase space (Pokrovsky et al,2002). Certainly, there ar e atmosphere-ocean inter actions generating a set of forward andfeedback links. Some of them are nonlinear and cannot b e described by simplified statisticalmodels b ased on a linear regressi on. Ther efore, a multivariate self-learning n eural n etworkmodel was developed to describ e the predictiv e relationsh ips b etween evolv ing large-scalepatterns in the Northern Hemisphere sea surface temperature, surface air pressure and surfaceair t emperature fields (predi ctors) and subsequent patterns in the E urope and NorthernMediterranean surface air temperature and precipitation rate (predictands). A lead interval ofvarying length (from 1 to 6 months) is placed between a series of consecut ive pre dictorperiods and a single predictand period. Objective evaluation of strength of such relationshipsis a primary aim of this study. The glob al monthly mean sea surface temperature, surface airtemperature, rain rate and sur face air pr essure grid fields used in the pr esent stud y werederived from the NCEP/NCAR (National Center for Environment Protection/National Centerfor At mospheric R esearch) rean alysis dat a s et. The data set covers the period from January1958 to D ecember 1998. The annu al cycle and inter-annual linear trend were removed frompredictor and predictand fields. The anomalies (departure from climate means) were used i nall prediction model modifications. The data used were d ivided into training and verificationsample sets. The data contained in the verification set were used only for the evaluation of thepredictive skill. It should be pointed out that the linear trend, calculated on each grid after theremoval of the annu al cycle is related either to artificial factors ( measurement errors ) or tovariability having a l arge t ime scale (equ ivalent to long er than a c entury), which is notrelevant to the pred ictive problem considered here. The amplitude of the linear trend is verysmall. Ho wever, i t may g ive rise to a trajectory shifting in phase s pace and thus affect theselection of the nearest fuzzy set act ivated in t he nonlinear model. Th erefore, t his filteringprocedure might be considered as a necessary step in the present context.3. Fuzzy classification o f regim e ci rculation and rain rate sp atial d istribution overEurope-276-