Using Chaos Theory to Determine Average Prediction Times of Different Meteorological Variables: A Case Study in Sivas

Abstract

Processes in the atmosphere can be described by nonlinear approaches since they depend on a large number of independent variables. Even a slight change in initial conditions can cause unpredictable results. Therefore, long-term prediction is not possible to obtain. This is usually called “sensitive dependence on initial conditions”. In this study, average prediction times were determined for different meteorological variables by using a nonlinear approach. Daily values of relative humidity, air temperature, and wind speed in Sivas for the period 2006-2010 were used. To implement the method, the first step is to reconstruct the phase space. Phase space has two embedding parameters, namely time delay and embedding dimension. Mutual Information Function (MIF) can be used to determine the optimal value of the time delay. It considers both linear and nonlinear dependencies in a time series. To define phase space, embedding dimension, which is the number of state variables that define the dynamics of a system, must be identified correctly. The algorithm to describe the dimension is called False Nearest Neighbors (FNN). In the study, average prediction times of variables were calculated by using maximum Lyapunov exponents. Average prediction times for relative humidity, temperature, and wind speed were determined as 6.2, 5.8, and 2.5 days, respectively. In addition, it is found that the sensitivity of measurements increases the prediction time. For relative humidity, the average prediction time can have a 50% increase with 10 times increase of sensitivity.