On stochastic properties of daily river flow processes

A study of the structure of daily river flows is made by means of the correlation theory of stochastic processes, i.e. on the basis of time functions of the first two moments: mean, variance, and autocorrelation function. The experimental basis of the study are long (over 50 years) time series of daily flows, without any gaps from five stations, with an average length of 71.2 years and areas of drainage basins ranging from 25,083 to 131,959 km2. As a result of the analysis, it can be stated that (i) days with high mean have also high variance; (ii) the coefficients of variations cannot be considered to be constant even approximately (iii) the lag 1 autocorrelation functions ρi(1), i=1,2,…,365, estimated “over realizations” have at least half of their coefficients significantly different from other coefficients; (iv) autocorrelation functions estimated “over time” are greater in the absolute value for data which have not been standardized but were initially treated with the logarithmic transformation only; (v) autocorrelation functions estimated “over realizations” are preferred to autocorrelation functions estimated “over time” because the daily river process is not ergodic. It is suggested that the description of daily flows as ergodic stochastic processes should be abandoned and the autocorrelation functions should be estimated “over realizations”. The “over time” estimated autocorrelation functions may only be treated as a very rough approximation of the “over realizations” autocorrelation functions.