The Evolutionary Modeling and Short-range Climatic Prediction for Meteorological Element Time Series K. Q. Yu, Y. H. Zhou, J. A. Yang Institute of Heavy Rain, China Meteorological Administration, Wuhan Z.Kang Computation Center, Wuhan University, Wuhan

Contents Background Methodology Experiment of The Precipitation Data Series Conclusion Remarks

Background the meteorological element series is the set of solution by integrating a perfect climatic numerical model with certain initial, boundary etc. conditions; is also the concentrated expression of all climatic factors (including itself) nonlinear interaction in the model.

the linear modeling in short-range climatic prediction operation : AR models MA models ARMA models ARIMA models.

Asking a question ! can we find out another nonlinear modeling method except climatic numerical model to simulate the change with time of meteorological element ? The evolutionary modeling (EM) has interested many researchers in various fields.

Methodology A series of observed meteorological data X (t) (x can be temperature, or pressure, or rainfall etc.) at the past m steps can be written as (1) If we can find out a higher-order ordinary differential equation which contains some arithmetic operations, logic operations and elementary functions ( + ， ― ， × ， ∕ ， sin ， cos ， exp ， ln) involving variable x * and time t ， (2)

with the initial conditions (3) minimizing the norm of n-dimensional column vector (4)

Eq. [2] is called NODE model of the meteorological data series (2) so the values of x in future can be predicted by integrating the Eq.2 based on the “ past ” and “ now ” of it.

NODE evolutionary modeling As the initial value problem of NODE with the form of Eq. [2] can be converted into a system of ordinary differential equations (SODE) (7)

with the initial conditions (8) Once a HODE is converted into a SODE, the key part of the model (or model structure) is the last (nth) equation (10)

- + * *y4y4 4 * y2y2 y3y3 t e y1y1 The binary tree in EM of a individual P i

n y initialization mutation select crossover evaluate fitness stop condition ？ end

How to use EM for Prediction of meteorological element series X (which is precipitation in flood season May---Sep. at Wuhan) observed data series annual variation series that is necessary for prediction The first-order NODE is enough !

Experiment of the precipitation data series X data series X is split into two parts : main series includes macro climatic time-scale period waves, is approximated by EM : perturbation series includes micro climatic time-scale period waves superimposed on the macro one, is approximated by Natural Fractals Model reflects the effect of multi-time scale exterior forced factors in climate system

The expressions of simulation for in EM model are complex trigonometric functions that cause the irregular waves

Sketch map of comparison between simulation (dashed line) with actual figures (solid line) for

simulation of

evaluating the forecast capability of EM

Conclusion remarks (1) For the meteorological data series that is of chaos character, it is an efficient way to split the series into two parts and to simulate them by evolutionary modeling and natural fractals respectively, the model reflects multi-time scale effects of forced factors in climate system.

Conclusion remarks ( 2) The NODE in EM can approximate more efficiently the nonlinear character of meteorological element data series but linear models can ’ t do so, and it is also of benefit to thinking over short-range climatic analysis and prediction.

Conclusion remarks (3) So far as the EM algorithms technique the EM for single element time series can be extended to the EM for several element time series because the prediction is a problem of the first-order derivative equation of meteorological element x with respect to time t ， each one in the system of ordinary differential equations Eq. [7] can denote respectively an x i of a complex climatic system. The EM algorithms are still same only with the values of those x i to be known at initial time. This is the job we are going to do.