what method; be it statistics, mathematical or modeling approach can I use to determine the part of a basin/watershed that is most affected by the combined impact of climate and land use change or their individual impact
Not all watersheds or basins are the same. Many papers have been prepared on BMPs and the importance of stream buffer zones. Various GIS hydroloy tools can help model flow network from digital elevation model, and it includes some buffering capacity. But if along the coast, the potential for sea level rise and salt water intrusion into freshwater areas may be the most sensitive. In the mountains, perhaps the oversteepened headwaters of unstable terrain is the most sensitive. In amother watershed, perhaps the urbanized area subject to flooding is most sensitive. There may be some models that can help assess these varied conditions, but I imagine some of this will also be experience and attention to detail specific to each watershed. In my researchgate materials, there is an example of Indian Creek Hydrologic Analysis. Perhaps some of the spatial tools available and watershed topics will help determine what area is most sensitive on your watershed of interest.
@Rajiv Pandey, thank you so much for your suggestions and article. i shall go through this article but i will also need a more physical approach because most of my data are physically based even though i know that social impacts should not be neglected. an approach that can use models (statistical, distributed or semi-distributed models etc.)