A Multilayer Perceptron Model for Stochastic Synthesis

Abstract

Time series analysis is a major mathematical tool in hydrology, with the moving average being the most popular model type for this purpose due to its simplicity. During the last 20 years, various studies have focused on an important statistical characteristic, namely the long-term persistence and the simultaneous statistical consistency at all timescales, when different timescales are involved in the simulation. Though these issues have been successfully addressed by various researchers, the solutions that have been suggested are mathematically advanced, which poses a challenge regarding their adoption by practitioners. In this study, a multilayer perceptron network is used to obtain synthetic daily values of rainfall. In order to develop this model, first, an appropriate set of features was selected, and then, a custom cost function was crafted to preserve the important statistical properties in the synthetic time series. This approach was applied to two locations of different climatic conditions that have a long record of daily measurements (more than 100 years for the first and more than 40 years for the second). The results indicate that the suggested methodology is capable of preserving all important statistical characteristics. The advantage of this model is that, once it has been trained, it is straightforward to apply and can be modified easily to analyze other types of hydrologic time series.

Keywords

• time series analysis
• stochastic model
• machine learning
• genetic algorithms
• persistence
• Hurst–Kolmogorov