In such areas, the potential rates of 'e-max' and 'e-min' will vary according to many interacting features of topography, soil condition, vegetative cover, land-uses and their varied management, broad seasonal climatic conditions, short-term rainfall-intensities etc., as affecting each identifiably-different sub-unit of land. Once you have characterised each 'homogeneous land unit', you can then begin to calculate the possible/likely rates of erosion for each, under stated conditions of environment x management, and map the results.
If - on the other hand - you want to maintain/improve the condition of the entire watershed [or: do you mean 'catchment'?] for a specific purpose (e.g. maximum annual yield of clean water for a city downstream), you would need to optimise the year-round conditions of vegetative cover (to mitigate rainfall-impact effects on the soil surfaces) and of porosity conditions (to permit water-movement downwards through the soil profiles, of the various soils. These features dictate both storage and slow-release of water down through the profile into the groundwater, and thence to river-flow or dammed storage.
If, on the other hand, the purpose of the exercise is to maximise accumulation of eroded sand and gravel for making buildings etc., then destroy the vegetative cover and enable erosion to remove all the soil, leaving the required materials to mov e downslope to the collection lion area.
Some relevant guidelines which might prove helpful as background concepts and practices relevant to land-use management can be found e.g. in the journal 'International Soil and Water Conservation Research' (ISSN 2095-6339) Volume 2, nos. 3 and 4, Sept. and Dec. 2014, and elsewhere in the literature.
While remote-sensing wizardry can produce appropriate figures for manipulation, there is no substitute for on-the ground verification as well, for building-up personal experience!