Continuous Hydrological Time-Series Discretization

The available information about many continuous hydrological time series X_t is often given by continuous time records with given finite duration and in many cases (i.e. rainfall and runoff records) the autocovariance function of X_t can be approximated by a function of exponential type. Once the data have been deseasonalized, stationarity is usually assumed. A discretization technique is required to estimate the mean and the variance of X_t which implies setting a value for the lag of time, L, between any two successive observations taken from the continuous record. The greater the time lag, the smaller is the number of used X_t values, the weaker is the dependence between them and the shorter is the required computing time. The aim of this paper is to study the three effects to make possible the selection of an optimal value for L. Numerical results of general use are derived and presented. Obviously, these conclusions also can be applied to any nonhydrological time series providing the assumed statistical assumptions are acceptable.