From S.E. Palsson et al. Science of the Total Environment, Prediction of spatial variation in global fallout of 137Cs using precipitation:
The relationship between precipitation and deposition density is often inadequately characterized so that it becomes difficult to compare results between different studies. In some papers, the relationship is expressed as activity per unit area corresponding to a given rainfall (e.g. Bq m-2 per 1000 mm rain) (e.g. Cawse and Horrill, 1986). Such expressions should explicitly state the time period to which it applies. Often it is better to relate radionuclide deposition to the average annual precipitation rate (e.g. mm per rain per year) rather than cumulative precipitation (e.g. mm rain). The former expression is more appropriate because a location receiving double the average precipitation rate compared to another location is likely to have twice the radionuclide deposition density. However, for the latter expression, comparing cumulative precipitation between two sites is meaningless without referring to a given time interval.
[…] …it has to clearly state whether the estimate takes into account (i) future deposition (e.g. until the present) with estimates time corrected back to the reference date or (ii) deposition that fell to the specified year (which would normally be the case for data reported in that year.
A well established method of estimating global fallout from data on precipitation and radionuclide concentration in rain water is simply to multiply the amount of precipitation during a given time period and the activity concentration of a radionuclide in the precipitation during the same period and then to sum this over the time period being studied.
Crochet (2002) has estimated the spatial variation in average annual precipitation for Iceland using measurement data for 1971 – 2000. He used a linear model that takes the effects of topography into account and is based on precipitation, location, distance to the ocean, elevation, average and orientation of hill slope, standard deviation of elevation and hill slope orientation.
The method applied here, calculating weighting factors based on the time integrated decay corrected concentration of a radionuclide in precipitation, can be used to create a set of weighting factors at a reference site and these can be subsequently used to calculate the average annual precipitation at sites of interest.
When applying the method for estimating deposition at remote places, various factors can effect the quality of the deposition estimates. The quality of precipitation estimate is a key factor. The further away from a site where the precipitation is actually measured, the greater the uncertainty becomes. The topography of the area is also an important factor. […] Snow can be another factor causing estimation uncertainties, even at sites where precipitation is being measured.
(S.E. Palsson et al. Science of the Total Environment, Prediction of spatial variation in global fallout of 137Cs using precipitation).