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Continuous Convolution With Hydrologic Data
Author(s) -
Chapman T. G.
Publication year - 1985
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/wr021i006p00847
Subject(s) - deconvolution , convolution (computer science) , mathematics , algorithm , polynomial , multiple , sampling (signal processing) , inversion (geology) , computer science , mathematical analysis , geology , arithmetic , filter (signal processing) , machine learning , artificial neural network , computer vision , paleontology , structural basin
The integral form of the convolution equation can be used for hydrologic data sampled at equal time increments if simple functional forms are assumed for the change in the hydrologic variables between sampling points. The forms studied here are a step function, linear segment, and sliding polynomial, and algorithms are presented for convolution of all combinations of these functions. The effect of the different assumptions is demonstrated by a sample data set. These algorithms have three advantages: an appropriate functional form can be selected for the two variables to be convolved, different time increments may be used for the two variables, and the output may be calculated at any point in continuous time, not just at multiples of the sampling increments. The algorithms may also be applied to deconvolution but suffer many of the difficulties of matrix inversion techniques when the data contain errors or are derived from a system which is only approximately linear.