An efficient and robust method for estimating unit hydrograph ordinates

This paper describes how to take advantage of the coefficient matrix for the “normal equations” for least-squares estimates of discrete unit hydrographs (DUH) is symmetric Toeplitz to reduce both the data storage and arithmetic computation requirements of computer programs for estimating DUH's.

Abstract

The coefficient matrix for the "normal equations" for least-squares estimates of discrete unit hydrographs (DUH) is symmetric Toeplitz. This paper describes how to take advantage of this matrix structure to reduce both the data storage and arithmetic computation requirements of computer programs for estimating DUH's. The method is particularly useful for small computers when memory space is limited or when large amounts of data are involved. The algorithm can be used to provide smoothed least-squares estimates of the DUH using a single extra arithmetic addition. Estimates of DUH's for multiple-event data can easily be calculated. Computer programs are presented for both the single-event and multiple-event case. The utility of the smoothed estimates is illustrated using real data which would give unrealistic ordinary least-squares estimates.