Potential evaporation (Eo) doesn't vary over short distances, so estimate Eo from somewhere similar (even if it is 500km away). Calculate the requirement from  Potential Evaporation (Eo) x % green cover /100. This provides a good estimate for short crops. Tall crops like maize can use 10 to 20% more eater, especially in windy environments. 

If you have class A pan data, Eo = pan x 0.8

best wishes

I think there are some hydro meteorological stations within the Karnali Watershed. You can get these information from DHM and use these data to get the Potential Evapotranspiration. If you don't have field based data.. may be you can use some remote sensing methods...

There are several methods for working reference evapo-transpiration for crops (FAO bulletins), which could provide you the information on potential evapo-transpiration for a specific crop, which could be used for rainfall potential. for regional estimates you have to take the weighted average over the crops covered within the region. 

the other approach could be incorporating the soil profile characteristics, on the basis of which the recharge of the profile takes place which aids in root water uptake potential for assessing the potential with reference to potential evapo-transpiration

crop simulation models viz DSSAT, APSIM, INFOCROP, SWOT, WOFOST takes care of the component of soil water balance, with a sub-routine to calculate reference evapo-transpiration

regards