Examining optimum prediction time of rainfall dynamics based on chaotic perspective at different temporal scales: a case study in Bojonegoro, Indonesia

Abstract As the driving force of the hydrological system, rain has severe impact when dealing with petroleum mining activities, especially in protecting assets and safety. Rainfall has high variability, both spatial and temporal (chaotic data). Due to this reason, ones can only create long-range prediction using the stochastic method. Here we use the Lyapunov exponent to analyze the nonlinear pattern of rainfall dynamics. This method is useful for identifying chaotic deportment in rainfall data. This study uses rainfall data for six years obtained from one of the largest petroleum mining sites in Bojonegoro, Indonesia. Rainfall dynamics have been analyzed on three different time scales, namely daily data, 5-day, and 10-day. The time delay (τ) was obtained by using the Average Mutual Information (AMI) method for the three-rainfall series (3, 2, 3, respectively). The observed rainfall data in Bojonegoro show signs of chaos as the finite correlation dimensions (m) attain values about 4 for all time scales. The maximum Lyapunov exponent λmax for each of three-rainfall series in Bojonegoro is 0.111, 0.057, 0.062, respectively. These values were analyzed to find the optimum prediction time of rainfall occurrence to perform better forecasting. The result shows that the optimum range of prediction time for daily, 5-day, and 10-day have 9, 18, and 16 times longer than their temporal scale.