On the Importance of Statistical Homogeneity to the Scaling of Rain

Jameson, A. R.

doi:10.1175/jtech-d-18-0160.1

Cited by 5 publications

(8 citation statements)

References 38 publications

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“…In order to be able to fully scale the rain rate, R, for example, in any spatial direction, it is most useful to have access to the radial power spectra that, in the case of statistically homogeneous rain, can also be transformed into the radial correlation function. (e.g., for a discussion see Jameson, 2019). Accomplishing estimates of the rainfall rates at high resolution is a challenging task that is, perhaps, best addressed using vertical pointing Doppler radar data in rain.…”

Section: Basic Considerationsmentioning

confidence: 99%

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

Jameson¹

2022

Preprint

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Rain occurs over a wide range of spatial scales. The challenge is to connect certain fine scale needs to the available large scale observations from radars, satellites or coarse grid numerical weather predictions. This is the problem of rescaling of the rainfall. Whatever approach is used, it requires a knowledge of rainfall scales over a wide range of possible dimensions from tens of meters to kilometers. It is also desirable to have measurements at different locations and under different meteorological settings. Such measurements are not necessarily readily obtainable, requiring extensive and usually fixed and expensive networks of multiple instruments over large areas. A mobile and less expensive alternative is the, Micro-Rain Radars (MRR). We illustrate this using observations of the Doppler spectra of falling rain every 10 m vertically and 10 second temporally over intervals varying from 15 up to 41 minutes collected at Wallop’s Island Virginia and Charleston South Carolina using two different MRR. An objective method to estimate advection velocity was developed so that the time-height profiles could be transformed into height-horizontal distance profiles in order to calculate scaling relations. Thus, MRR and other Doppler radars may obviate the need for networks of instruments.

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Section: Basic Considerationsmentioning

confidence: 99%

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

Jameson¹

2022

Preprint

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“…Thus, correlation functions are usually likely to be of little use when trying to tranform rainfall rate among different time and/or different spatial scales. Nor can they be transformed into power spectra with any general applicability(e.g., see [8]) via the Wiener-Khintchine theorem [16,17]. However, the power spectra of these data fields might still serve a useful albeit more narrow purpose.…”

Section: Convective Variable Rainmentioning

confidence: 99%

“…In particular the correlation function exists only when they are independent of the origin of the calculation in space or time over the spatial-temporal domain of interest. Similarly, power spectra, whether power fits or otherwise, only have generality when the data are wide-spread statistically homogeneous and statistically stationary (WSS) as emphasized for the rainfall rate in [8]).…”

Section: Introductionmentioning

confidence: 99%

Preliminary Statistical Characterizations of the Lowest Kilometer Time-Height Profiles of the Rainfall Rate Using a Vertically Pointing Radar

Jameson¹,

Larsen²

2022

Preprint

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A realistic approach for gathering high-resolution observation of the rainfall rate, R, in the vertical plane is to use data from vertical pointing Doppler radars. After accounting for the vertical air velocity and attenuation, it is possible to determine the fine, spatially resolved drop size spectra and to calculate R for further statistical analyses. The first such results in a vertical plane are reported here. Specifically, we present results using MRR-Pro Doppler radar observations at resolutions of ten meters in height over the lowest 1.28 km as well as ten seconds in time over four sets of observations using two different radars at different locations. Both correlation functions and power spectra are useful for translating observations and numerical model outputs of R from on one scale down to other scales that may be more appropriate to particular applications such as flood warnings and soil erosion, for example. However, it was found in all cases that while locally applicable radial power spectra could be calculated, because of statistical heterogeneity, most of the power spectra lost all generality and proper correlation functions could not be computed in general except for one 17 minute interval. Nevertheless, these results are still useful since they could be combined to develop catalogs of power spectra over different meteorological conditions and in different climatological settings and locations. Furthermore, even within the limitations of these data, this approach is being used to gain a deeper understanding of rainfall to be reported in a forthcoming paper.

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“…In particular, the correlation function exists only when they (mean values and variance) are independent of the origin of their calculation in space or time over the spatial-temporal domain of interest. Similarly, power spectra, whether power fits or otherwise, exist but only have generality when the data are widespread, statistically homogeneous, and statistically stationary (WSS), as emphasized for the rainfall rate in [8]. According to the Wiener-Khintchine theorem, only when the data are WSS can one compute the auto-correlation function and proper power laws [1,2] Specifically, then, the first order of business is to see whether or not the temporalvertical MRR observations of rainfall rates are statistically homogeneous.…”

Section: Introductionmentioning

confidence: 99%

Preliminary Statistical Characterizations of the Lowest Kilometer Time–Height Profiles of Rainfall Rate Using a Vertically Pointing Radar

Jameson¹,

Larsen

2022

Atmosphere

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A realistic approach for gathering high-resolution observations of the rainfall rate, R, in the vertical plane is to use data from vertically pointing Doppler radars. After accounting for the vertical air velocity and attenuation, it is possible to determine the fine, spatially resolved drop size spectra and to calculate R for further statistical analyses. The first such results in a vertical plane are reported here. Specifically, we present results using MRR-Pro Doppler radar observations at resolutions of ten meters in height over the lowest 1.28 km, as well as ten seconds in time, over four sets of observations using two different radars at different locations. Both the correlation functions and power spectra are useful for translating observations and numerical model outputs of R from one scale down to other scales that may be more appropriate for particular applications, such as flood warnings and soil erosion, for example. However, it was found in all cases that, while locally applicable radial power spectra could be calculated, because of statistical heterogeneity most of the power spectra lost all generality, and proper correlation functions could not be computed in general except for one 17-min interval. Nevertheless, these results are still useful since they can be combined to develop catalogs of power spectra over different meteorological conditions and in different climatological settings and locations. Furthermore, even with the limitations of these data, this approach is being used to gain a deeper understanding of rainfall to be reported in a forthcoming paper.

show abstract

On the Importance of Statistical Homogeneity to the Scaling of Rain

Cited by 5 publications

References 38 publications

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

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

Preliminary Statistical Characterizations of the Lowest Kilometer Time-Height Profiles of the Rainfall Rate Using a Vertically Pointing Radar

Preliminary Statistical Characterizations of the Lowest Kilometer Time–Height Profiles of Rainfall Rate Using a Vertically Pointing Radar

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