Multiscaling analysis of high resolution space-time lidar-rainfall

Mandapaka, Pradeep V.; Lewandowski, Piotr; Eichinger, W. E.; Krajewski, Witold F.

doi:10.5194/npg-16-579-2009

Cited by 25 publications

(26 citation statements)

References 22 publications

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“…The UM parameter estimates are slightly different with especially a C1 smaller than the ones usually reported at coarser resolution ( ~ 1.7-1.9, C1 ~ 0.05-0.2) by authors who studied rainfall field in space (Mandapaka et al 2009, Verrier et al 2010, Gires et al 2013. Although these authors studied rainfall fields horizontally which makes direct comparison harder (due to a possible anisotropy between the vertical and horizontal directions), this hints at a possible break between two scaling regimes, a small scales one and a large scales one, located at few tens of meters or few hundreds of meters.…”

Section: 2) Scaling Behaviourmentioning

confidence: 87%

“…Very few studies have analysed this, mainly because of the lack of rainfall data at these scales. Mandapaka et al (2009) observed on lidar data scaling on the range 1 -512 s in time and 2.5 -320 m in space. Lilley et al (2006) and Lovejoy and Schertzer (2008), using few 3D snapshots of an 8 m 3 volume with most of its drops (Desaulnier-Soucy et al 2001), reported a scaling behaviour down to few tens of cm with a dependency on the turbulence intensity and drop size.…”

Section: ) Introductionmentioning

confidence: 99%

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2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process

Gires

Tchiguirinskaia

Schertzer

et al. 2015

Journal of Hydrometeorology

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International audienceData collected during four heavy rainfall events that occurred in Ardeche (France) with the help of a 2D video disdrometer (2DVD) are used to investigate the structure of the raindrop distribution in both space and time. A first type of analysis is based on the reconstruction of 36-m-height vertical rainfall columns above the measuring device. This reconstruction is obtained with the help of a ballistic hypothesis applied to 1-ms time step series. The corresponding snapshots are analyzed with the help of universal multifractals. For comparison, a similar analysis is performed on the time series with 1-ms time steps, as well as on time series of accumulation maps of N consecutive recorded drops (therefore with variable time steps). It turns out that the drop distribution exhibits a good scaling behavior in the range 0.5-36 m during the heaviest portion of the events, confirming the lack of empirical evidence of the widely used homogenous assumption for drop distribution. For smaller scales, drop positions seem to be homogeneously distributed. The notion of multifractal singularity is well illustrated by the very high-resolution time series

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Section: 2) Scaling Behaviourmentioning

confidence: 87%

Section: ) Introductionmentioning

confidence: 99%

2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process

Gires

Tchiguirinskaia

Schertzer

et al. 2015

Journal of Hydrometeorology

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show abstract

“…The choice of such a high value of α is theoretically motivated to better assess the estimate bias resulting from the thresholding and corresponds to an upper bound of empirical estimates on portions of time series or maps where there are (almost) no zeros. For example, de Montera et al (2010) reported C 1 = 0.13 and α = 1.7 for a 30 s time series, Mandapaka et al (2009) reported C 1 = 0.18 and α = 1.9 for spatial and temporal analysis performed on high-resolution (2.5 m, 1 s) lidar data, and Verrier et al (2010) reported C 1 = 0.12 and α = 1.78 for spatial analysis of radar data (1 km resolution). Concerning the additional parameters introduced in the new model, γ 0 =0.1 and p 0 = 0.5 are tested in this section.…”

Section: Results Of Um + 0 For a Set Of Parametersmentioning

confidence: 99%

Development and analysis of a simple model to represent the zero rainfall in a universal multifractal framework

Gires

Tchiguirinskaia

Schertzer

et al. 2013

Nonlin. Processes Geophys.

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High-resolution rainfall fields contain numerous zeros (i.e. pixels or time steps with no rain) which are either real or artificial – that is to say associated with the limit of detection of the rainfall measurement device. In this paper we revisit the enduring discussion on the source of this intermittency, e.g. whether it requires specific modelling. We first review the framework of universal multifractals (UM), which are commonly used to analyse and simulate geophysical fields exhibiting extreme variability over a wide range of scales with the help of a reduced number of parameters. However, this framework does not enable properly taking into account these numerous zeros. For example, it has been shown that performing a standard UM analysis directly on the field can lead to low observed quality of scaling and severe bias in the estimates of UM parameters. In this paper we propose a new simple model to deal with this issue. It is a UM discrete cascade process, where at each step if the simulated intensity is below a given level (defined in a scale invariant manner), it only has a predetermined probability to survive and is otherwise set to zero. A threshold can then be implemented at the maximum resolution to mimic the limit of detection of the rainfall measurement device. While also imperfect, this simple model enables explanation of most of the observed behaviour, e.g. the presence of scaling breaks, or the difference between statistics computed for single events or longer periods

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“…Considering the high spatial variability of rainfall on small scales (e.g. Gires et al, 2014;Jaffrain and Berne, 2012b;Mandapaka et al, 2009), one important challenge of the method becomes obvious here. The section bounds are located at s 3 − s and s 3 + s on both sides of R 3 .…”

Section: Theoretical Frameworkmentioning

confidence: 99%

A novel approach for absolute radar calibration: formulation and theoretical validation

Merker¹,

Peters²,

Clemens³

et al. 2015

Atmos. Meas. Tech.

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Abstract. The theoretical framework of a novel approach for absolute radar calibration is presented and its potential analysed by means of synthetic data to lay out a solid basis for future practical application. The method presents the advantage of an absolute calibration with respect to the directly measured reflectivity, without needing a previously calibrated reference device. It requires a setup comprising three radars: two devices oriented towards each other, measuring reflectivity along the same horizontal beam and operating within a strongly attenuated frequency range (e.g. K or X band), and one vertical reflectivity and drop size distribution (DSD) profiler below this connecting line, which is to be calibrated. The absolute determination of the calibration factor is based on attenuation estimates.Using synthetic, smooth and geometrically idealised data, calibration is found to perform best using homogeneous precipitation events with rain rates high enough to ensure a distinct attenuation signal (reflectivity above ca. 30 dBZ). Furthermore, the choice of the interval width (in measuring range gates) around the vertically pointing radar, needed for attenuation estimation, is found to have an impact on the calibration results.Further analysis is done by means of synthetic data with realistic, inhomogeneous precipitation fields taken from measurements. A calibration factor is calculated for each considered case using the presented method. Based on the distribution of the calculated calibration factors, the most probable value is determined by estimating the mode of a fitted shifted logarithmic normal distribution function. After filtering the data set with respect to rain rate and inhomogeneity and choosing an appropriate length of the considered attenuation path, the estimated uncertainty of the calibration factor is of the order of 1 to 11 %, depending on the chosen interval width. Considering stability and accuracy of the method, an interval of eight range gates on both sides of the vertically pointing radar is most appropriate for calibration in the presented setup.

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Multiscaling analysis of high resolution space-time lidar-rainfall

Cited by 25 publications

References 22 publications

2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process

2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process

Development and analysis of a simple model to represent the zero rainfall in a universal multifractal framework

A novel approach for absolute radar calibration: formulation and theoretical validation

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