## 1 Introduction  
Semi-arid regions cover about 15% of the Earth's land surface and the spatial and temporal patterns of rainfall in these regions are very variable, which causes drastic variability in the spatiotemporal distribution, production, and development of vegetation [1, 2]. Over recent decades, many semi-arid and dryland habitats have faced greater pressuresfrom human-induced activities and climate change [3; 4; 5]. To better understand climatic change and anthropogenic impacts on dryland and semi-arid ecosystems, information on the vegetation's spatiotemporal variability is the key source. Satellite-based knowledge is an important tool in tracking vegetation variability and dynamics, with the potential for broad spatial coverage and regular explanations [6; 7]. The dataset of the spectral vegetation index is particularly well-related to the leaf area index (LAI), the abundance of chlorophyll, the absorption of gross-primary-production (GPP), and photosynthetically active radiation (PAR) [8; 9; 10]. To monitor semi-arid and dryland vegetation activity and spot changes in growth and phenology of vegetation [11; 12; 13], vegetation indices time-series have often been used [14; 15; 16; 17]. The polar-orbiting MODIS (Moderate Resolution Imaging Spectroradiometer) sensor allows for the monitoring and measurement of vegetation and environmental indices. MODIS-derived data have a superior spatial and radiometric resolution than that of the Advanced Very High-Resolution Radiometer (AVHRR) sensor and thus provides an enhanced radiometric, spatial, and spectral representation of surface vegetation conditions [18; 19]. Among the generally used datasets in the monitoring of vegetation dynamics, the normalized vegetation difference index (NDVI) time-series is noteworthy. Nevertheless, the NDVI has some restrictions relating to soil reflectance, affecting the index and contributing to different index values for various conditions of soil and moisture being observed for similar biophysical properties of the canopy [20]. A variable of soil adjustment 'L' was proposed to interpret the nonlinear, first-order, variance in radiative transmission through a canopy in the spectrum's red and NIR (near-infrared) zones. Through this, another index (i.e., SAVI, soil adjusted vegetation index) was obtained [21]. Subsequently, other soil-adjusted indices (e.g., the OSAVI, optimized soil adjusted vegetation index and the MSAVI, modified soil adjusted vegetation index) were established to optimize soil effects [22; 23]. In addition, to optimize the vegetation signal, the enhanced vegetation index (EVI) with enhanced sensitivity was developed in high-biomass areas to provide better vegetation monitoring by decoupling the background signal of the canopy and the atmospheric effects [19]. The EVI has been shown to be highly linear and closely correlated with phase and amplitude measurements of the seasonal eddy flux tower photosynthesis, surrounding a wider range of leaf area index (LAI) retrievals [24]. Vegetation indices (VIs) assessment plays a vital role in assessing the growth of vegetation in biomass diversity. EVI and NDVI obtained from MODIS surface reflectance, modified for the NBAR (nadir bidirectional reflectance distribution function), had better accuracy compared to the leaf area index when assessing the start of the season in large coniferous leaf forests [25; 26]. The EVI for monitoring the phenology of rice paddy in Asia during the monsoon was a successful vegetation index compared to in situ data [27]. Among EVI, green-red-vegetation-index (GRVI), and NDVI, it was observed that the best vegetation index was to extract seasonal variations in the GRVI, which was influenced by variations in leaf colors [28; 29; 30]. To track vegetation phenology and operation across a range of habitats, 2-band enhanced vegetation index (EVI2) was observed to be a comparatively improved index than the NDVI because of its insensitivity to context reflection [31]. A new generalized differential vegetation index (GDVI) was established [18].