Because climate change is getting worse, we need more complex scientific tools to make correct predictions and studies. Partial Differential Equations (PDEs) and green’s capabilities are very critical to this project because they make it viable to describe the complex modifications that happen in Earth’s climate systems. This essay seems at how PDEs can be used to model essential weather change methods inside the surroundings and oceans, which includes warmness transfer, fluid dynamics, and mass motion. We investigate how inexperience’s functions are used to resolve these PDEs, especially boundary price troubles, which let us do correct fashions of ways matters affect the arena in certain regions. Our method combines these mathematical techniques with actual-global information to make models more reliable and correct. Placing collectively PDEs and green’s capabilities with laptop methods solves troubles like nonlinearity and multistate activities that come up in weather models. The effects display how important advanced clinical techniques are for developing complex weather models which are used for making coverage choices and managing the environment. This study helps make prediction models better and gives us a better understanding of the complicated processes that cause climate change and unpredictability.