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

Abstract

[1] 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.

Incorporating parameter dependencies into temporal downscaling of extreme rainfall using a random cascade approach

“…In some respects the results substantiate the previous results of Olsson (1998( ), Guntner et al (2001, Molnar and Burlando (2005) and Rupp et al (2009) who between them found significant dependencies on event structure, season and rainfall volume; and Licznar et al (2015) who illustrated the potential for parameter bias due to climate oscillations within a 25-year period. Another result in common with previous papers is the relative consistency of the downscaling parameters from daily scale to around 45 minutes, then greater changes from 45 minutes to ~10 minutes.…”

“…While there was some weak evidence that the probability distribution of 5 W varied over different cascade levels, Guntner et al (2001) elected to use a scale-invariance assumption, recognising the benefits of pooling more data; while Olsson (1998) focused on the levels within which scale invariance could be justified from the data. Rupp et al (2009) investigated the dependence of parameters on rainfall intensity and found that including the dependence of p(1|0) and p(0|1) in a MDRC model significantly improved performance. Olsson (1998) and Guntner et al (2001) illustrate the potential to make the microcanonical MDRC model conditional on season, rainfall volume and the presence of surrounding wet or dry intervals.…”

A homogenous daily rainfall record for the Radcliffe Observatory, Oxford, from the 1820s

“…Note that a record of hourly rainfall data is available for the Radcliffe Observatory from the British Atmospheric Data Centre for the period 1994-2005. No comparative analysis has been attempted here, but it would clearly be interesting to see how the Oxford record disaggregates to an hourly time scale [cf. Rupp et al, 2009] and whether a record of hourly rainfall could be generated for the earlier period.…”

Imperfect scaling in distributions of radar-derived rainfall fields

“…Additionally, scaling behaviour was found to differ with the intensity of storms (Venugopal et al, 2006) and thus the nonraining intervals do not scale (Olsson, 1998). These deviations from perfect scaling are further examined in Veneziano et al (2006), Serinaldi (2010), and Rupp et al (2009), who showed that it is possible to model these imperfections in scaling through empirical functions of the parameters of various downscaling models.…”

“…Serinaldi, 2010;Rupp et al, 2009;Veneziano et al, 2006). Some other studies have investigated the dependence of breakdown coefficients, i.e.…”