How does elevation affect the amount of rainfall received?
Elevation affects temperature which affects the amount of rain. Most raingauges around the world are within a few hundred metres of sea-level, i.e the range in which most people live. Within this range the rainfall-elevation relationship often appears to be linear. However, as the temperature gets cooler with altitude, the maximum precipitable moisture decreases drastically, so the rainfall-altitude curve reflexes back upon itself, so that there is an elevation of maximum precipitation ('EMP'). This variation variies with several factors, such as continentality, 'tropicality', aspect, rain shadow and barrier effect. Some examples of the EMP, are (in metres): Tajikistan 3800,
Alberta Canada 2360, European Alps, 2250, NW Pakistan1500, Oman 1400 to 2200, Kilimanjaro Tanzania 1500, and Hawaii 900. In the case of polar regions the EMP is ground level because the rainfall-altitude relationship is nearly always negative. Above the EMP the rainfall decreases rapidly with altitude, which is why high mountainous regions are essentially deserts. 

Wherever there is significant relief in a catchment, the first step is to determine whether the catchment is all below the EMP. The second step is to process the historic record to see if a second order, or even third order rainfall altitude regression is a significant improvement upon 'linear'. If you want further refinement the seasonal rainfalls, or rainfalls from different directions, often have markedly differing rainfall-altitude relationships. If you want to go the whole hog, and be scientific about it, then the rainfall approximates a multi-variate solution, with components of 
altitude, altitude squared, aspect, regional trend, rain shadow and barrier effect. This can be solved as an equation of the form: $$R = aH + BH^{2} + cA + dT + eS +f'BE'$$