## EOF analysis of three-dimensional subsurface temperature anomaly field of the tropical Pacific Ocean

**ZHANG Li-feng1,2,XU Jian-ping2,HE Jin-hai3(1.Hangzhou Weather Bureau,Hangzhou 310008,China;2.State Key Laoratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,SOA,Hangzhou 310012,China;3.College of Atmospheric Sciences,Nanjing University of Information Science & Technology,Nanjing 210044,China)**

A three-dimensional four-step sea temperature model low in the west and high in the east has been formed with the subsurface temperature data of the tropical Pacific Ocean.The first step is between 120° to 180oE,with the average subsurface departure between 120 m and 160 m.The second,third and fourth steps are between 175° and 140oW,135° and 120oW,115° and 80oW respectively,with average subsurface departures between 80 m and 120 m,60 m and 80 m,and 40 m and 60 m.The whole longitude ranges is from 120oE to 80oW,while the whole latitude range from 18oN to 16oS.The steps are close to the climatic thermocline,which contains not only the horizontal field information but also possible perpendicular profile information.Empirical orthogonal function(EOF)is used to make time-space division of this model matrix.And the relationship between EOF division result and ENSO cycle is discussed,and the Nino 3 departure index is predicted.It shows that accumulated variance contribution of the first and second spatial characteristic principal components in EOF division reaches 42.58%,among which the first one represents tropical Pacific warm pool-El Nino and Lanina mode and the second one represents the east-to-west movement mode of the subsurface temperature departure in the tropical Pacific Ocean.There are catastrophe and gradual change processes in the latter.The change from the cold phase to warm phase near the equator is gradual,while the change from the cold phase to warm phase near 10oS or 10oN is catastrophe.El Nino(Lanina)results from the catastrophe change of the east to west movement mode.Time lag correlation analysis and estimation of the first and second time coefficients of the EOF division and the Nino 3 sea temperature departure indexes shows that the average circulation cycle of the tropical Pacific subsurface temperature departure is 41 months,namely 3.42 years,and the phase difference between the east to west movement mode of the tropical Pacific subsurface temperature departure and warm pool-El Nino(Lanina)mode is 9.7 months on average in ENSO circulation.The stepwise regression analysis is used to build up Nino 3 index predictive equation.It is one way of the causality analysis.In this method only one variable is chosen from selectable variables according to certain significance standards and put into the regression equation in each step.It is required that the chosen variable should lead to the greatest decline of the residual variance than the other ones.In stepwise regression,the variable that comes into the regression equation becomes unobvious because of the arrival of new variable,and can be deleted in the next step.As a result,stepwise regression assures that only important variables would be in the last-formed equation.It is the method that is used here to build up three predictive equations 3、6 and 12 months in advance of the Nino 3 departure index.The prediction shows that the first and second time coefficients are valuable for Nino 3 index with one-year validity.Comparison with documents shows that EOF development of the step model of the tropical Pacific subsurface temperature departure can reveal completely the change process of tropical Pacific subsurface temperature departure as a cycle in ENSO circulation.The second spatial modal describes the movement routes of the cold and warm water more completely.All these prove that ENSO cycle is three-dimensional in the ocean.To analyze ENSO cycle from horizontal or vertical section independently will destroy this cycle.

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