It is assumed that the river runoff process can be approximated by a Markov process. The process is thus described by M distribution functions:

Fn (qt, t ; qt-1; t-1;…;qt-n, t-n), t ≡ 1, 2, …, M where M is the number of time intervals within the year, n - the order of the Markov process and qt, in general, is a vector representing runoff at several sites in a river or neighbouring rivers.

Fundamental hypothesis of relations between multivariate distributions and corresponding marginal distributions is given.

A finite difference scheme for multisite and multilag generation of river runoff is derived. The derivation is based on the multivariate normal distribution.

Different methods for determination of the order of the finite difference scheme are discussed as well as the influence of model order and method of parameter estimation on properties of the model.