The Arctic moisture budget plays a key role in the global climate system. Determining the components of the moisture budget in high latitudes is very difficult, as measurements from satellite are problematic above ice and direct measurements are very sparse or of limited reliability. Reanalyses - as the state-of-the-art depiction of atmospheric conditions - show inaccuracies in the parametrization of moisture and the still unsolved spin-up-problem. The effect of these issues on long term budgets is difficult to estimate, therefor the results have to be validated with independent data.

There exist a number of investigations on the moisture budget in the Arctic atmosphere, based on reanalysis data as well as on observational data from radiosondes. Sizable differences between reanalysis and radiosonde based atmospheric budgets have been found, e.g. by comparing the convergence of moisture flux. The differences are commonly explained by the different resolutions at which the data are present. Still, when a moisture flux convergence from radiosonde measurements is calculated, two problems have to be considered, connected on the one hand with the spatial irregularity of the observations, on the other hand with the necessity to provide a wind field which observes the continuity equation. We present a technique to solve these tasks by combining the finite-element method (FEM) with a variational approach.

The method removes the errors introduced by lacking mass consistency, thus reducing noise dramatically. Many known features of Arctic moisture flux convergence, like the mean annual cycle with a distinct maximum in summer, are well reproduced. We estimate the net water gain of the Arctic atmosphere (north of 70°) as 164mm/yr for 1979-1993, a rather small value compared to the recently published numbers. Furthermore, our method allows us to do the calculations based on radiosonde and reanalysis data on exactly the same grid, thus avoiding the problem of different resolutions.