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Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation
Author(s) -
Rupp David E.,
Keim Richard F.,
Ossiander Mina,
Brugnach Marcela,
Selker John S.
Publication year - 2009
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 - 10.1029/2008wr007321
Subject(s) - cascade , multiplicative function , scale (ratio) , intensity (physics) , dependency (uml) , mathematics , range (aeronautics) , environmental science , statistics , series (stratigraphy) , computer science , geography , geology , physics , engineering , paleontology , software engineering , chemical engineering , aerospace engineering , mathematical analysis , cartography , quantum mechanics
Multiplicative random cascades (MRCs) can parsimoniously generate highly intermittent patterns similar to those in rainfall. The elemental MRC model parameter is the cascade weight, which determines how rainfall at one scale is partitioned at the next smallest scale in the cascade. While it is known that the probability density of these weights may vary with both time scale and rainfall intensity, nearly all previous studies have considered either time scale or intensity separately. We examined the simultaneous dependency of the weights on both factors and assessed the impacts of explicitly including these dependencies in the MRC model. On the basis of the observed relationships between cascade weights and time scale and intensity, four progressively more “dependent” models were constructed to disaggregate a long time series of daily rainfall to hourly intervals. We found that inclusion of the intensity dependency on the model parameters that generate dry intervals greatly improved performance. For the relatively small range of time scales over which the rainfall was disaggregated, varying model parameters with time scale resulted in minor improvement.