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

Abstract

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 of redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRCs). 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, namely 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, with each of them containing exactly half of the original amount of water. The relative areas of the subgrid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity-dependent standard deviation (SD). The process ends when the amount of water in each subgrid cell is smaller than a fixed-bucket capacity, at which point the output of the cascade can be resampled 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 in the presence of intermittency and to the lower variance of its generator. However, both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale variability and extremes, the EVA model tends to produce fields that are slightly too smooth and block shaped compared to the observations. The complementary nature of the two approaches, and the fact that they produce errors of opposite signs, opens up new possibilities for quality control and bias corrections of downscaled fields.

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High Resolution Time Height Doppler Data from a Single Mobile Vertical Pointing Radar

“…Some involve smoothing [19] or Kriging of the observations [19,20]. The primary limitation of such techniques is that they are filters of the power spectra [21] leading to a reduction of information as discussed in [22]. A different approach uses the Bayesian components of the rainfall and the observed power spectrum (or correlation function for statistically homogeneous rain) to generate rain over many different scales with the appropriate statistical properties consistent with the observations [12].…”

Spatial Downscaling Model Combined with the Geographically Weighted Regression and Multifractal Models for Monthly GPM/IMERG Precipitation in Hubei Province, China

“…The fractal/multifractal phenomenon exists wildly in the natural world, such as the well-known example of the coastline of Britain, for which one can obtain diverse measurement results at different scales [34]. The evidence concerning the multiple scaling or multifractal behavior of precipitation fields has been well documented in the scientific literature, and the self-similarity-based multiplicative random cascade model was introduced into the spatial downscaling research of satellite precipitation, which is a type of weather-generator method [35][36][37]. For example, Posadas et al [38] developed a reliable spatial downscaling model for TRMM 3B42 datasets by applying the multifractal technique over the Southern Peruvian Andes.…”

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High Resolution Time Height Doppler Data from a Single Mobile Vertical Pointing Radar

“…In the literature there is an assortment of techniques for downscaling such as the socalled multiplicative cascading method [14,[14][15][16] with improvements proposed by [17].…”