Comparison between Weather Signal Simulation in Frequency and Time Domain
Abstract
Simulated weather time series are often used in engineering and research practice to assess radar systems behavior and/or to evaluate the performance of novel techniques. There are two main approaches to simulating weather time series. One is based on summing individual returns from a large number of distributed weather particles to create a cumulative return. The other is aimed at creating simulated random signals based on the predetermined values of radar observables and is of interest herein. So far, several methods to simulate weather time series, using the latter approach, have been proposed. All of these methods are based on applying the inverse discrete Fourier transform to the spectral model with added random fluctuations. To meet the desired simulation accuracy, such an approach typically requires generating the number of samples that is larger than the base sample number due to the discrete Fourier transform properties. In that regard, a novel method to determine simulation length is proposed. It is based on a detailed theoretical development that demonstrates the exact source of errors incurred by this approach. Furthermore, a simple method for time series simulation that is based on the autocorrelation matrix exists. This method neither involves manipulations in the spectral domain nor requires generating the number of samples larger than the base sample number. Herein, this method is suggested for weather time series simulation and its accuracy and efficiency are analyzed and compared to the spectral-based approach.
Significance Statement
All research articles published so far on the topic of weather time series simulation propose the use of inverse discrete Fourier transform (IDFT) when based on the desired Doppler moment values. Herein, a detailed theoretical development that demonstrates the exact source of errors incurred by this approach is presented. Also, a novel method to determine the simulation length that is based on the theoretical error computation is proposed. As an alternative, a computationally efficient general method (not using IDFT) previously developed for the simulation of sequences with desired properties is suggested for weather time series simulation. It is demonstrated that the latter method produces accurate results within overall shorter computational times. Moreover, it is shown that the use of graphics processing unit (GPU), ubiquitous in modern computers, significantly reduces computational times compared to the sole use of central processing unit (CPU) for all simulation-related calculations.
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