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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-449
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-449
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 20 Sep 2019

Submitted as: research article | 20 Sep 2019

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A revised version of this preprint is currently under review for the journal HESS.

A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields

Marc Schleiss Marc Schleiss
  • Department of Geoscience & Remote Sensing, Delft University of Technology

Abstract. Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists in redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRC). This works well for slowly varying, homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, each of them containing exactly half of the original amount of water. The relative areas of the sub-grid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity dependent standard deviation. The process ends when the amount of water in each sub-grid cell is smaller than a fixed bucket capacity, at which point the output of the cascade can be re-sampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model to the presence of intermittency and to the lower variance of its generator. However, improvements are not systematic and both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale extremes and variability, the EVA model tends to produce fields that are slightly too smooth and blocky compared with observations.

Marc Schleiss

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Marc Schleiss

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Short summary
A new way to downscale rainfall fields based on the notion of equal-volume areas (EVAs) is proposed. Experiments conducted on 100 rainfall events in the Netherlands show that the EVA method outperforms classical methods based on fixed grid cell sizes, producing fields with more realistic spatial structures. The main novelty of the method lies in its adaptive sampling strategy, which avoids many of the mathematical challenges associated with the presence of zero rainfall values.
A new way to downscale rainfall fields based on the notion of equal-volume areas (EVAs) is...
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