Improving single-variable and multivariable techniques for estimating missing hydrological data

A highly efficient technique is developed to obtain the best least-squares approximation of the missing hydrological data in the single-variable case, and this is presented here, The technique is based on an appropriate weighing of the estimated values generated by two autoregressive processes operating, respectively, in the forward and backward directions of time. For the multivariable case, the originality of the work presented here consists in the use of the linear regression model with variable coefficients to estimate missing data, As for the single-variable case, two multivariable regression models are calibrated recursively on available data preceding and following the period of missing data. The use of Kalman filter (KF) has improved the accuracy in the estimation of the first missing data including the peak flow. For subsequent missing data the confidence of the estimates is greater when using a static model identified by the ordinary least squares (OLS) technique, It has been found that there is a critical rank for which there is an inversion of performance between the KF and OLS technique. When the period of missing data is smaller than the critical rank we use only KF technique, When the period of missing data extends past the critical rank, it is recommended that KF be used to estimate the first missing data and then use OLS technique to estimate data coming after the critical rank. (C) 1997 Elsevier Science B.V.