Accounting for Precipitation Asymmetry in a Multiplicative Random Cascade Disaggregation Model
Authors: Maloku Kaltrina , Hingray Benoit , Evin Guillaume 
Published: February 2023

Multiplicative random cascades (MRC) have been widely used for the disaggregation of coarse-resolution time series (e.g. daily) to high-resolution ones (e.g. sub-hourly). With MRCs, the amount of precipitation at any time step is partitioned into two parts, attributed respectively to the first and second sub-division of this time step. The partition is repeated throughout the cascade levels until the final temporal resolution is achieved.In the so-called micro-canonical MRCs, the partition is conservative. The rainfall amounts R1 and R2 attributed respectively to the first and second sub-divisions of the considered time step (with rainfall amount R0), are expressed as R1=W1&#183;R0 and R2=W2&#183;R0 where the weights W1 and W2 are complementary, i.e. &#160;W1+W2=1. The possible values of W1 are:Therefore, for a given time step, the disaggregation is determined by the value of&#160; W:=W1.The probabilities p01, p10 and the distribution fW+ define the cascade generator of the MRC. For a given location, they have been found to depend on different factors. The cascade generator depends for instance on temporal scale, on precipitation intensity and on precipitation temporal asymmetry, i.e. on the temporal pattern of precipitation amounts Ri-1,Ri,Ri+1 around the amount of precipitation to disaggregate Ri (e.g. Olsson, 1998; Hingray and BenHaha, 2005). p01 tends to be higher than p10 in the case of a so-called "ascending" precipitation pattern (Ri-1<Ri<Ri+1) and,&#160;&#160;p01 tends to be smaller than p10&#160; in the case of a "so-called" descending pattern (Ri-1>Ri>Ri+1). Different models have been proposed to estimate p01,p10 and fW+ . Analytical scaling models are used very often because very convenient for simulation, but to date, they have disregarded the dependency on asymmetry (Paschalis et al., 2014).Our work presents an analytical MRC modelling framework that merges the strengths of some of the different MRC models proposed in past years, allowing the cascade generator to depend in a continuous way on temporal scales, precipitation intensity and precipitation asymmetry.We first define a precipitation asymmetry index and show how it influences the parameters of the cascade generator. This index is used to model the scaling dependency on asymmetry. We then compare four different analytical MRC models that account for the dependency on the temporal scale, precipitation intensity and/or precipitation asymmetry. An application to 81 stations in Switzerland is presented where the performance of the models is assessed. Including the asymmetry of precipitation in a model brings significant improvements in the reproduction of observed temporal persistence of precipitation in the disaggregated time series. The proposed model, with a simple parametrization, shows a great potential for regionalization, thus for the application of the approach to sites with coarse-resolution data only.&#160;ReferencesHingray, B., Ben Haha, M., 2005. Statistical performances of various deterministic and stochastic models for rainfall series disaggregation. Atmospheric Research 77, 152&#8211;175.doi:10.1016/j.atmosres.2004.10.023.Olsson, J., 1998. Evaluation of a scaling cascade model for temporal rainfall disaggregation. Hydrology and Earth System Sciences 2, 19&#8211;30. doi:10.5194/hess-2-19-1998.Paschalis, A., Molnar, P., Fatichi, S., Burlando, P., 2014. On temporal stochastic modeling of precipitation, nesting models across scales. Advances in Water Resources 63, 152&#8211;166. doi:10.1016/j.advwatres.2013.11.006.