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Unit graph estimation and stabilization using quadratic programming and difference norms
Author(s) -
Dietrich C. R.,
Chapman T. G.
Publication year - 1993
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 - 10.1029/93wr00746
Subject(s) - graph , quadratic programming , quadratic equation , unit (ring theory) , surface runoff , regression , variance (accounting) , computer science , mathematical optimization , estimation , mathematics , algorithm , statistics , theoretical computer science , engineering , geometry , ecology , mathematics education , accounting , business , biology , systems engineering
For a rainfall‐runoff event, quadratic programming is particularly suited to the estimation of unit graph as linear and positivity constraints on unit graph ordinates can be naturally implemented. In this paper, the quadratic programming framework is invoked in a novel way to stabilize the unit graph estimation procedure via the use of difference norms. The advantage of the latter over standard ridge regression is that penalties are placed on oscillations of the unit graph rather than on the size of its ordinates, Application of the methodology to real rainfall‐runoff data is provided and comparisons with existing approaches are made. The latter indicate that our approach generally yields unit graph estimates of more realistic shape and smaller variance resulting in a better fit to the runoff data.