The present study focuses on determining the changes in annual and seasonal variability of vegetation cover from time-series Landsat images in Kharif & Rabi seasons, especially in arid and semi-arid regions. The time series vegetation indices are effective techniques for the detection of vegetation variability which can be seen by time-series curves that comes from long-term Landsat images. The study has been carried out from June 1990 to March 2021 with the help of satellite images and satellite-derived climate parameters. The vegetation cover (June to October and November to March) is also considered and the whole command area has been selected where crops are growing in both seasons at Mashi Dam command area, Tonk, Rajasthan, India. In addition, Climate Engine is a time series web application platform for crop, vegetation, and other natural resource management applications. It's user-friendly for earth resources analysts and decision-makers. Using the Climate Engine, users can quickly process and visualize satellite images and gridded weather data for environmental monitoring and improving early warning of drought, wildfires, and crop failures. For this analysis, we have used processed time series vegetation indices (NDVI, EVI, NDWI), LST (land surface temperature), and climate variables (Precipitation, Temperature) from the Climate Engine web platform. MATLAB software was used to determine the direction of a relationship between biophysical variables and climate parameters. XLSTST trial version software was used to determine the Mann-Kendall and Sen's slope Trend between vegetation indices and climate parameters for drought analysis. This study also shows the limitation of the optical remote sensing images, when cloud cover has more prominent in the rainy season, so we have used cloud-free images which are available on the climate engine platform. These results will be helpful for the development of new indices and to characterize agriculture-climate variable relationships. This research provides an immense scope for implementing action for sustainable agriculture and prior information about crop management.