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Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation

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Abstract
  • 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.
  • Keywords: dependent, multiplicative random cascade, intensity, time scale, rainfall, disaggregation
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  • Rupp, D. E., R. F. Keim, M. Ossiander, M. Brugnach, and J. S. Selker (2009), Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation, Water Resources Research, 45, W07409, doi:10.1029/2008WR007321.
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  • 45
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  • W07409
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  • Funding to continue this research was provided by New Zealand’s Foundation for Research Science and Technology through the program ‘‘Land Use Intensification: Sustainable Management of Water Quality and Quantity’’ (contract C01X0304).
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