Multifractal modelling and simulation of rain fields exhibiting spatial heterogeneity

Pathirana, Assela; Herath, Srikantha

doi:10.5194/hess-6-695-2002

Cited by 49 publications

(69 citation statements)

References 18 publications

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“…This approach is similar to the one adopted by Jothityangkoon et al (2000) and Pathirana and Herath (2002), who modulated homogeneous spatial random cascades by means of spatial patterns obtained from long term accumulation rain fields.…”

Section: Introduction Of Local Heterogeneity In Synthetic Rainfall Fimentioning

confidence: 96%

“…The opportunity of introducing a heterogeneous component when modelling synthetic rainfall fields over land was investigated by Harris et al (1996), Jothityangkoon et al (2000), Purdy et al (2001), Pathirana and Herath (2002). Specifically Jothityangkoon et al (2000) and Pathirana and Herath (2002) analysed a 400 km×400 km area in southwestern Australia and a 128 km×128 km region centered in the Japanese archipelago, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically Jothityangkoon et al (2000) and Pathirana and Herath (2002) analysed a 400 km×400 km area in southwestern Australia and a 128 km×128 km region centered in the Japanese archipelago, respectively. In order to reproduce observed spatial heterogeneity they multiplied a homogeneous spatial random cascade by a deterministic factor depending on the spatial location without linking it to local features.…”

Section: Introductionmentioning

confidence: 99%

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Modulation of homogeneous space-time rainfall cascades to account for orographic influences

Badas

Deidda

Piga

2006

Nat. Hazards Earth Syst. Sci.

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Abstract. The development of efficient space-time rainfall downscaling procedures is highly important for the implementation of a meteo-hydrological forecasting chain operating over small watersheds. Multifractal models based on homogeneous cascade have been successfully applied in literature to reproduce space-time rainfall events retrieved over ocean, where the hypothesis of spatial homogeneity can be reasonably accepted. The feasibility to apply this kind of models to rainfall fields occurring over a mountainous region, where spatial homogeneity may not hold, is herein investigated. This issue is examined through the analysis of rainfall data retrieved by the high temporal resolution rain gage network of the Sardinian Hydrological Survey. The proposed procedure involves the introduction of a modulating function which is superimposed to homogeneous and isotropic synthetic fields to take into account the spatial heterogeneity detected in observed precipitation events. Specifically the modulating function, which reproduces the differences in local mean values of the precipitation intensity probability distribution, has been linearly related to the terrain elevation of the analysed spatial domain. Comparisons performed between observed and synthetic data show how the proposed procedure preserves the observed rainfall fields features and how the introduction of the modulating function improves the reproduction of spatial heterogeneity in rainfall probability distributions.

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Section: Introduction Of Local Heterogeneity In Synthetic Rainfall Fimentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modulation of homogeneous space-time rainfall cascades to account for orographic influences

Badas

Deidda

Piga

2006

Nat. Hazards Earth Syst. Sci.

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“…A few approaches have been proposed to adapt the stochastic generators to better capture the local variability of precipitation. Pathirana and Herath (2002) and Badas et al (2006) proposed to filter or remove the heterogeneities of the precipitation field before applying a homogeneous multifractal downscaling technique and re-adding the trend after running the stochastic simulation. A similar strategy was employed in a recent STEPS implementation, which computes the local mean and variance of the rainfall field on a regular grid to remove the local non-stationarity before adding the homogeneous stochastic perturbations (Seed et al, 2013).…”

Section: Limitation Of Current Stochastic Rainfall Generatorsmentioning

confidence: 99%

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Nerini

Bešič

Sideris

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. In this paper we present a non-stationary stochastic generator for radar rainfall fields based on the short-space Fourier transform (SSFT). The statistical properties of rainfall fields often exhibit significant spatial heterogeneity due to variability in the involved physical processes and influence of orographic forcing. The traditional approach to simulate stochastic rainfall fields based on the Fourier filtering of white noise is only able to reproduce the global power spectrum and spatial autocorrelation of the precipitation fields. Conceptually similar to wavelet analysis, the SSFT is a simple and effective extension of the Fourier transform developed for space-frequency localisation, which allows for using windows to better capture the local statistical structure of rainfall. The SSFT is used to generate stochastic noise and precipitation fields that replicate the local spatial correlation structure, i.e. anisotropy and correlation range, of the observed radar rainfall fields. The potential of the stochastic generator is demonstrated using four precipitation cases observed by the fourth generation of Swiss weather radars that display significant non-stationarity due to the coexistence of stratiform and convective precipitation, differential rotation of the weather system and locally varying anisotropy. The generator is verified in its ability to reproduce both the global and the local Fourier power spectra of the precipitation field. The SSFT-based stochastic generator can be applied and extended to improve the probabilistic nowcasting of precipitation, design storm simulation, stochastic numerical weather prediction (NWP) downscaling, and also for other geophysical applications involving the simulation of complex nonstationary fields.

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“…Multifractals have been developed and applied to analyse and simulate geophysical fields exhibiting extreme variability over a wide range of scales such as rainfall [29,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. For such fields the statistical moment of order q of a field R at the resolution λ (= L/l, where L is the outer scale of the phenomenon and l the observation scale) is a power-law behaviour related to the resolution:…”

Section: Short Recap Of Multifractals and Classical Error Metricsmentioning

confidence: 99%

Multifractal Comparison of Reflectivity and Polarimetric Rainfall Data from C- and X-Band Radars and Respective Hydrological Responses of a Complex Catchment Model

Paz

Willinger

Gires

et al. 2018

Water

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This paper presents a comparison between C-band and X-band radar data over an instrumented and regulated catchment of the Paris region. We study the benefits of polarimetry and the respective hydrological impacts with the help of rain gauge and flow measurements using a semi-distributed hydrological model. Both types of radar confirm the high spatial variability of the rainfall down to their space resolution (1 km and 250 m, respectively). Therefore, X-band radar data underscore the limitations of simulations using a semi-distributed model with sub-catchments of an average size of 2 km. The use of the polarimetric capacity of the Météo-France C-band radar was limited to corrections of the horizontal reflectivity, and its rainfall estimates are adjusted with the help of a rain gauge network. On the contrary, no absolute calibration and scanning optimisation were performed for the polarimetric X-band radar of the Ecole des Ponts ParisTech (hereafter referred to as the ENPC X-band radar). In spite of this and the fact that the catchment is much closer to the C-band radar than to the X-band radar (average distance of 15 km vs. 35 km, respectively), the latter seems to perform at least as well as the former, but with a higher spatial resolution. This was best highlighted with the help of a multifractal analysis, which also shows that the X-band radar was able to pick up a few rainfall extremes that were smoothed out by the C-band radar.

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Multifractal modelling and simulation of rain fields exhibiting spatial heterogeneity

Cited by 49 publications

References 18 publications

Modulation of homogeneous space-time rainfall cascades to account for orographic influences

Modulation of homogeneous space-time rainfall cascades to account for orographic influences

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Multifractal Comparison of Reflectivity and Polarimetric Rainfall Data from C- and X-Band Radars and Respective Hydrological Responses of a Complex Catchment Model

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