Desertification has been listed as one of the most critical global environmental issues, posing a significant threat to life, particularly in arid and semiarid regions. Therefore, gaining a comprehensive understanding of the present and future desertification trends becomes imperative. This study employs a feature space model, which effectively captures land surface changes related to desertification, enabling the extraction of pertinent information. Subsequently, time series models are used to determine the most accurate desertification simulation. Twenty-one ETM + sensor images were utilized to calculate the Topsoil Grain Size (TGSI) and Albedo remotely sensed indexes. Constructing the Albedo-TGSI feature space, the Desertification Degree Index (DDI) was extracted for each year. Different levels of desertification were identified by applying a natural break classification on the DDI values, and corresponding break values were obtained. The representative desertification degree for each year was determined by calculating the average of the minimum and maximum break values, resulting in the generation of five distinct time series for five desertification degrees. Different ARIMA models and wavelet transforms were selected to simulate the various desertification degrees based on the analysis of autocorrelation and partial autocorrelation functions and trial and error, respectively. The most suitable ARIMA models with the lowest errors were identified as follows: ARIMA (1,0,7) for severe desertification, ARIMA (0,1,6) for high desertification, ARIMA (0,0,7) for moderate desertification, and ARIMA (3,0,6) for non-desertification degrees. Among the various wavelet transform families tested, the Symlet family proved to be the most effective, except for the low desertification degree. The following wavelet transforms yielded the best results for each degree of desertification: Symlet3 for severe desertification, Symlet7 for high desertification, Symlet7 for moderate desertification, Daubechies 5 (db5) for low desertification, and Symlet7 for non-desertification degree simulations, all exhibiting the minimum error rates.
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