Analysis of drought characteristics using a copula-based method and a Hybrid of soft computing algorithms (case study: Qazvin station)

Introduction

Drought, a natural phenomenon, has always had negative effects. Severe changes in precipitation, including quantity, intensity, and distribution, have led to annual droughts in certain parts of the country, resulting in significant across in various dimensions (Capéraà P, et al., 1997). The onset of drought is a gradual process that slowly impacts various sectors, including water resources, agriculture, and the environment. The complex physical factors and interactions that govern these phenomena are not well understood, and there are currently no reliable mathematical or empirical models available. Therefore, statistical methods have been employed in many hydrological studies to adequately describe such phenomena. One reason for using joint probability functions is that they can simultaneously analyze two more variables while preserving the correlation between the variables in calculations. These functions use univariate distributions as marginal distributions to construct multivariate distributions. One reason for using soft computing algorithms is for prediction and estimation in such cases.

computing, including data mining techniques, has experienced significant development over the past two decades. These techniques can be used to discover and extract knowledge from a database, as well as create predictive models. Due to recent advancements, these techniques have become widely used as data mining tools. They do not incur the cost of laboratory modeling and provide much higher accuracy in less time compared to numerical modeling. In this study, the droughts of Qazvin province are created using a combination of joint probability functions and soft computing algorithms. Random data has been selected for the models.



Materials and Methods

In the present article, monthly rainfall data from January 1964 (Dey month 1342) to December 2018 (1397) were used for the Synoptic Station of Qazvin to identify its drought characteristics. The average rainfall at the Qazvin station is 304 millimeters. In this study, the meteorological drought of Qazvin province is created using a combination of copula functions and algorithms. The data is selected randomly in the models. In this research, the M5 algorithms are used to generate rainfall data. For soft computing, PSO, genetic algorithm, CART algorithm, GEP algorithm, and GMDH algorithm are used. The SPI index is used for drought analysis. Since SPI (Standardized Precipitation Index) is recognized as a suitable index for drought analysis (Hayes et al., 1999), the SPI time series based on monthly rainfall used to define and calculate drought characteristics such as duration and severity in this study. The intensity and duration play an important role in drought management (McKee et., 1993). Drought can be defined as periods when SPI falls below -1 or less. Moist and dry conditions are classified based on SPI values. It should be noted that some drought events may have long durations, but the average SPI for each period does not reach -1 or less. Cumulative SPI is lower than -1 for such events, despite the higher probability of short-term events. A drought event can defined as a continuous period with SPI below zero. The duration of drought is a continuous negative SPI period, and drought severity is calculated as cumulative SPI values during the drought period.



Results and Discussion

The amount of precipitation at the Qazvin station has been estimated and predicted using the mentioned algorithms and copula forecasting and estimation methods. For the application of joint functions and analysis of two-variable drought, the correlation between the variables should first be estimated. The comparison between observed drought variables (i.e., duration and intensity) and their corresponding fitted distributions indicates a significant correlation between the fitting distribution and the observed drought data. Modeling was performed using soft computing algorithms and using precipitation data (70% for testing and 30% for validation) and the output of the joint functions to estimate and predict the correlation and error rates with M5-PSO, M5-GA, CART, M5-GEP, and M5-GMDH algorithms. Based on the modeling performance using soft computing and statistical indicators, the M5-GEP model is the best model.



Conclusion

In this article, the analysis of meteorological drought characteristics (i.e., duration and intensity) for the Qazvin station during the years 1964 to 2018 was examined using a combination of the piecewise function with soft computing algorithms. The M5 model was used for parameter classification. One of the important steps in using the combination of algorithms with the piecewise function for analyzing hydrological issues is the appropriate estimation of the dependent parameter of the piecewise function. Therefore, inaccurate estimation of the piecewise function parameter leads to underling or overestimation in the modeling method, which was the main reason for our use of algorithms. The results showed that the M5-GEP model could be successfully used for drought modeling. The error rate and correlation coefficient of the model were RMSE=0.12 and CC=0.96, respectively, indicating that the M5-GEP model provided the best result among the models. Additionally, the CART model yielded an error rate and correlation coefficient of RMSE=0.46 and CC=0.87, respectively, for estimating drought duration and intensity, which was the worst result among the proposed models.