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Reply [to “Comment on ‘Computation of optimum realizable unit hydrographs,’ by Peter S. Eagleson, Ricardo Mejia‐R, and Frederick March”]
Author(s) -
Eagleson Peter S.,
MejiaR Ricardo,
March Frederick
Publication year - 1968
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr004i001p00215
Subject(s) - citation , unit (ring theory) , computation , computer science , operations research , library science , mathematics , algorithm , mathematics education
of ho, (t) and h (t). The definition of ho, (t) recognizes the presence of nonlineartries and measurement errors by requiring that the observed input and output. data are only approximately linearly related. This controlled allowance of error ensures that the calculated ho•(t) will be both stable and realizable. If a parametric representation of ho, (t) is required, it may be carried out subsequently and with the advantage of knowing the form of the function to be fitted. On the other hand, calculation of h(t) assumes the input and output to be exactly linearly related. In particular, the method of moments suggested for this determination by Nash and O'Connor is based upon the applicability of the convolution relation. Since only the first two moments are required to fit their two parameter h(t) function, this method of fitting would seem to contain the degree of approximation necessary to ensure stable, realizable results, yet there is evidence to. the contrary. In a study of urban catchments (1) it was found that fitting the 'Nash model' by the method of moments using input and output data. very often led to physically unrealistic values of the h (t) parameters, whereas for the same events fitting the Nash h (t) to the derived ho•t (k) did not. We thank Nash and O'Connor for calling attention to our faulty reasoning in the interrelationship of equations 4 through 7. Fortunately, this has no effect on what follows, since the problem remains the solution of equation 10 for h(k) using input-output pairs that are not linearly related. The question of the area enclosed by ho•(k) is one that deserves some discussion, as the absence of any constraint thereon by the authors is intentional. The main purpose of the paper, as stated in both the Abstract and the Intro-