Comparative study of spectral methods for precipitation time series generators based on the conserving observed spatial and temporal properties

Precipitation time series are used as input for hydrological modeling. As the main driver of the hydrological cycle, they directly influence soil moisture, runoff, river flows, and groundwater recharge. High-resolution precipitation data is required to obtain accurate hydrological models. In addition, data should be available from different locations to reflect spatial dependencies in these models. As precipitation is measured only at selected locations, the simulated series can be used for design purposes.

In recent years, various models have been developed based on the Fourier Transform because of its ability to preserve desirable statistical properties. The concept is to transform the time series from the time domain to the frequency domain and calculate the two main components of the transformed series: the power spectrum (the square of the absolute values of the Fourier frequencies) and the phase spectrum (phase angle of the frequencies). The main idea behind all the Fourier-based models is to preserve the power spectrum because it relates to the autocorrelation function and overall structure.

This study compares the most common Fourier-based time series generators using different measures. As most spectral methods are iterative, this can be challenging for the precipitation time series, especially for the hourly resolution. In this regard, a non-iterative method is introduced. This method takes advantage of the Wiener–Khinchin theorem for the transformation between the autocorrelation function and the power spectrum. Another method, the Phase Annealing method, is introduced for precipitation time series generation and keeping the spatial and temporal properties. The results have been compared for the developed models and the most common Fourier-based methods.