The scenario forecasting technique for assessing changes of water balance components of the northern river basins due to possible climate change was developed. Three IPCC global emission scenarios corresponding to different possible scenarios for economic, technological, political and demographic development of the human civilization in the 21st century were chosen for generating climate change projections by an ensemble of 16 General Circulation Models with a high spatial resolution. The projections representing increments of monthly values of meteorological characteristics were used for creating 3-hour meteorological time series up to 2063 for the Northern Dvina River basin, which belongs to the pan-Arctic basin and locates at the north of the European part of Russia. The obtained time series were applied as forcing data to drive the land surface model SWAP to simulate possible changes in the water balance components due to different scenarios of climate change for the Northern Dvina River basin.
We identify some situations where mappings related to left centralizers, derivations and generalized (α, β)-derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation T, of a semiprime ring R the mapping ψ: R → R defined by ψ(x) = T(x)x − xT(x) for all x ∈ R is a free action. We also show that for a generalized (α, β)-derivation F of a semiprime ring R, with associated (α, β)-derivation d, a dependent element a of F is also a dependent element of α + d. Furthermore, we prove that for a centralizer f and a derivation d of a semiprime ring R, ψ = d ◦ f is a free action.