scholarly journals Coupled Contributions in the Doppler Radar Spectrum Width Equation

2008 ◽  
Vol 25 (12) ◽  
pp. 2245-2258 ◽  
Author(s):  
Ming Fang ◽  
Richard J. Doviak
Keyword(s):  
Doppler Radar ◽  
Central Moment ◽  
Doppler Spectrum ◽  
Spectral Broadening ◽  
Theoretical Derivation ◽  
Central Moments ◽  
Spectrum Width

Abstract Contrary to accepted usage, the second central moment of the Doppler spectrum is not the sum of the second central moments of individual spectral broadening mechanisms. A rigorous theoretical derivation of the spectrum width observed with short dwell times reveals that the sum cannot strictly be taken for the variances associated with various spectral broadening mechanisms and that an added-term coupling shear with turbulence is needed. Furthermore, shear and antenna rotation are coupled. The theoretical expressions derived herein apply to radars with fixed or scanning beams.

scholarly journals Mobile Ka-band Polarimetric Doppler Radar Observations of Wildfire Smoke Plumes

2021 ◽  
Author(s):  
Taylor B. Aydell ◽  
Craig B. Clements
Keyword(s):  
Radial Velocity ◽  
Doppler Radar ◽  
Radar Reflectivity ◽  
Doppler Spectrum ◽  
Fine Scale ◽  
Prescribed Burn ◽  
Ka Band ◽  
Wildfire Smoke ◽  
Smoke Plumes ◽  
Spectrum Width

AbstractRemote sensing techniques have been used to study and track wildfire smoke plume structure and evolution, however knowledge gaps remain due to the limited availability of observational datasets aimed at understanding fine-scale fire-atmosphere interactions and plume microphysics. While meteorological radars have been used to investigate the evolution of plume rise in time and space, highly resolved plume observations are limited. In this study, we present a new mobile millimeter-wave (Ka-band) Doppler radar system acquired to sample the fine-scale kinematics and microphysical properties of active wildfire smoke plumes from both wildfires and large prescribed fires. Four field deployments were conducted in the fall of 2019 during two wildfires in California and one prescribed burn in Utah. Radar parameters investigated in this study include reflectivity, radial velocity, Doppler spectrum width, Differential Reflectivity (ZDR), and copolarized correlation coefficients (ρHV). Observed radar reflectivity ranged between -15 and 20 dBZ in plume and radial velocity ranged 0 to 16 m s-1. Dual-polarimetric observations revealed that scattering sources within wildfire plumes are primarily nonspherical and oblate shaped targets as indicated by ZDR values measuring above 0 and ρHV values below 0.8 within the plume. Doppler spectrum width maxima were located near the updraft core region and were associated with radar reflectivity maxima.

Assessing the Errors of Cloud Liquid Water and Precipitation Flux Retrievals in Marine Stratocumulus Based on Doppler Radar Parameters

2007 ◽  
Vol 8 (4) ◽  
pp. 665-677 ◽  
Author(s):  
Yefim L. Kogan ◽  
Zena N. Kogan ◽  
David B. Mechem
Keyword(s):  
Liquid Water ◽  
Doppler Radar ◽  
Radar Reflectivity ◽  
Doppler Spectrum ◽  
Doppler Velocity ◽  
Cloud Liquid Water ◽  
Eddy Simulation ◽  
Air Turbulence ◽  
Spectrum Width ◽  
Drop Size Distributions

Abstract The errors of formulations of cloud retrievals based on radar reflectivity, mean Doppler velocity, and Doppler spectrum width are evaluated under the controlled framework of the Observing System Simulation Experiments (OSSEs). Cloud radar parameters are obtained from drop size distributions generated by the high-resolution Cooperative Institute for Mesoscale Meteorological Studies (CIMMS) large-eddy simulation (LES) model with explicit microphysics. It is shown that in drizzling stratocumulus the accuracy of cloud liquid water (Ql) retrieval can be substantially increased when information on Doppler velocity or Doppler spectrum width is included in addition to radar reflectivity. In the moderate drizzle case (drizzle rate R of about 1 mm day−1) the mean and standard deviation of errors is of the order of 10% for Ql values larger than 0.2 g m−3; in stratocumulus with heavy drizzle (R > 2 mm day−1) these values are approximately 20%–30%. Similarly, employing Doppler radar parameters significantly improves the accuracy of drizzle flux retrieval. The use of Doppler spectrum width σd instead of Doppler velocity yields about the same accuracy, thus demonstrating that both Doppler parameters have approximately the same potential for improving microphysical retrievals. It is noted that the error estimates herein represent the theoretical lower bound on retrieval errors, because the actual errors will inevitably increase, first and foremost, due to uncertainties in estimation contributions from air turbulence.

scholarly journals Turbulence and Wind Shear in Layers of Large Doppler Spectrum Width in Stratiform Precipitation

2009 ◽  
Vol 26 (3) ◽  
pp. 430-443 ◽  
Author(s):  
Valery M. Melnikov ◽  
Richard J. Doviak
Keyword(s):  
Wind Shear ◽  
Weather Radar ◽  
Velocity Fields ◽  
The Other ◽  
Doppler Spectrum ◽  
Weak Turbulence ◽  
Radar Observations ◽  
Spectrum Width ◽  
Stratiform Precipitation ◽  
Radar Resolution

Abstract Weather radar observations of stratiform precipitation often reveal regions having very large measured Doppler spectrum widths, exceeding 7, and sometimes 10, m s−1. These widths are larger than those typically found in thunderstorms; widths larger than 4 m s−1 are associated with moderate or severe turbulence in thunderstorms. In this work, stratiform precipitation has been found to have layers of widths larger than 4 m s−1 in more than 80% of cases studied, wherein the shear of the wind on scales that are large compared to the dimensions of the radar resolution volume is the dominant contributor to spectrum width. Analyzed data show that if width ≤7 m s−1, and if the layers are not wavy or patchy, these layers have weak turbulence. On the other hand, regions having widths >4 m s−1 in patches or in wavelike structures are likely to have moderate to severe turbulence with the potential to be a hazard to safe flight. To separate the contributions to spectrum width from wind shear and turbulence and to evaluate the errors in turbulence estimates, data have been collected with elevation increments much less than a beamwidth. Despite beamwidth limitations, the small elevation increments reveal impressive structures in the fields. For example, the “cat’s eye” structure associated with Kelvin–Helmholtz waves is clearly exhibited in the fields of spectrum width observed at low-elevation angles, but not in the reflectivity or velocity fields. Reflectivity fields in stratiform precipitation are featureless compared to spectrum width fields.

The Performance of Mechanically Scanned Color Flow Mapping

1989 ◽  
Vol 11 (4) ◽  
pp. 227-232 ◽  
Author(s):  
C.B. Burckhardt
Keyword(s):  
Point Spread Function ◽  
Phase Variation ◽  
Doppler Spectrum ◽  
Spectral Broadening ◽  
Flow Mapping ◽  
Mean Velocity ◽  
Color Flow ◽  
Color Flow Mapping ◽  
Point Spread ◽  
Spread Function

The performance of mechanically scanned Color Flow Mapping is analysed. It is shown that the Doppler spectrum is convolved with a scaled version of the Fourier transform of the two-way point spread function of the transducer. This spectral broadening is no larger than the inherent limit of the method if the point spread function shows smooth amplitude variation and little phase variation. The spectral broadening can cause clutter from stationary objects to fall outside the MTI filter stopband and, thereby, alter the estimates of the mean velocity and turbulence. Mechanically scanned and electronically stepped Color Flow Mapping are compared.

scholarly journals On the Forward Modeling of Radar Doppler Spectrum Width From LES: Implications for Model Evaluation

2018 ◽  
Vol 123 (14) ◽  
pp. 7444-7461 ◽  
Author(s):  
Y.-S. Chen ◽  
J. Verlinde ◽  
E. E. Clothiaux ◽  
A. S. Ackerman ◽  
A. M. Fridlind ◽  
...  
Keyword(s):  
Model Evaluation ◽  
Forward Modeling ◽  
Doppler Spectrum ◽  
Spectrum Width

scholarly journals Approximation Properties of New Modified Gamma Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yun-Shun Wu ◽  
Wen-Tao Cheng ◽  
Wei-Ping Zhou ◽  
Lun-Zhi Deng
Keyword(s):  
Asymptotic Formula ◽  
Weighted Approximation ◽  
Central Moment ◽  
Sixth Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Type Approximation ◽  
Quantitative Properties ◽  
The Moment ◽  
Direct Results

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

Cirrus Microphysical Properties and Air Motion Statistics Using Cloud Radar Doppler Moments. Part I: Algorithm Description

2006 ◽  
Vol 45 (12) ◽  
pp. 1690-1709 ◽  
Author(s):  
Min Deng ◽  
Gerald G. Mace
Keyword(s):  
Particle Size ◽  
Vertical Velocity ◽  
Sample Volume ◽  
Doppler Spectrum ◽  
Convolution Integral ◽  
Mean Particle Size ◽  
Microphysical Properties ◽  
Spectrum Width ◽  
The Mean ◽  
Air Motion

Abstract The first three moments of the millimeter-wavelength radar Doppler spectrum provide valuable information regarding both cloud properties and air motion. An algorithm using these Doppler radar moments is developed to retrieve cirrus microphysical properties and the mean air vertical motion and their errors. The observed Doppler spectrum results from the convolution of a quiet-air radar reflectivity spectrum with the turbulence probability density function. Instead of expressing the convolution integral in terms of the particle fall velocity as in past studies, herein the convolution integral is integrated over the air motion so that the mean vertical velocity within the sample volume can be explicitly solved. To avoid an ill-conditioned problem, the turbulence is considered as a parameter in the algorithm and predetermined from the Doppler spectrum width and radar reflectivity based on the observation that the spread of the particle size distribution in the velocity domain dominates the Doppler spectrum width measurement for most cirrus. It is also shown that the assumed single mode functional shapes cannot reliably represent significant bimodalities. Nevertheless, the IWC can be retrieved more reliably than can the mass mean particle size. Error analysis also shows that the retrieval algorithm results are very sensitive to the power-law relationships describing the ice particle mass and the terminal velocity in terms of the particle maximum length. It is estimated that the algorithm errors will be on the order of 35%, 85%, and ±20 cm s−1 for mass mean particle size, IWC, and sample volume mean air motion, respectively. Algorithm validation with in situ data demonstrates that the algorithm can determine the cloud microphysical properties and air mean vertical velocity within the predicted theoretical error bounds.

scholarly journals Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation

2012 ◽  
Vol 12 (3) ◽  
pp. 732-766 ◽  
Author(s):  
Kannan N. Premnath ◽  
Sanjoy Banerjee
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Inertial Frame ◽  
Fluid Velocity ◽  
Central Moment ◽  
Distribution Functions ◽  
Inverse Transformation ◽  
Lattice Boltzmann Equation ◽  
Source Terms ◽  
Central Moments

AbstractWe present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.

scholarly journals A Doppler Radar Emulator with an Application to the Detectability of Tornadic Signatures

2007 ◽  
Vol 24 (12) ◽  
pp. 1973-1996 ◽  
Author(s):  
Ryan M. May ◽  
Michael I. Biggerstaff ◽  
Ming Xue
Keyword(s):  
Pulse Propagation ◽  
Doppler Radar ◽  
Doppler Spectrum ◽  
Doppler Velocity ◽  
Advanced Regional Prediction System ◽  
Adaptive Sensing ◽  
Regional Prediction ◽  
Sampling Intervals ◽  
Half Power ◽  
The Impact

Abstract A Doppler radar emulator was developed to simulate the expected mean returns from scanning radar, including pulse-to-pulse variability associated with changes in viewing angle and atmospheric structure. Based on the user’s configuration, the emulator samples the numerical simulation output to produce simulated returned power, equivalent radar reflectivity, Doppler velocity, and Doppler spectrum width. The emulator is used to evaluate the impact of azimuthal over- and undersampling, gate spacing, velocity and range aliasing, antenna beamwidth and sidelobes, nonstandard (anomalous) pulse propagation, and wavelength-dependent Rayleigh attenuation on features of interest. As an example, the emulator is used to evaluate the detection of the circulation associated with a tornado simulated within a supercell thunderstorm by the Advanced Regional Prediction System (ARPS). Several metrics for tornado intensity are examined, including peak Doppler velocity and axisymmetric vorticity, to determine the degradation of the tornadic signature as a function of range and azimuthal sampling intervals. For the case of a 2° half-power beamwidth radar, like those deployed in the first integrated project of the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA), the detection of the cyclonic shear associated with this simulated tornado will be difficult beyond the 10-km range, if standard metrics such as azimuthal gate-to-gate shear from a single radar are used for detection.

Spaceborne Doppler Radar Measurements of Rainfall: Correction of Errors Induced by Pointing Uncertainties

2005 ◽  
Vol 22 (11) ◽  
pp. 1676-1690 ◽  
Author(s):  
Simone Tanelli ◽  
Eastwood Im ◽  
Satoru Kobayashi ◽  
Roberto Mascelloni ◽  
Luca Facheris
Keyword(s):  
Doppler Radar ◽  
Sea Surface ◽  
Doppler Spectrum ◽  
Airborne Radar ◽  
Precipitation Radar ◽  
Analysis Technique ◽  
Correction Technique ◽  
Radar Echo ◽  
Radar Measurements ◽  
Nonuniform Beam

Abstract In this paper a sea surface radar echo spectral analysis technique to correct for the rainfall velocity error caused by radar-pointing uncertainty is presented. The correction procedure is quite straightforward when the radar is observing a homogeneous rainfall field. When nonuniform beam filling (NUBF) occurs and attenuating frequencies are used, however, additional steps are necessary in order to correctly estimate the antenna-pointing direction. This new technique relies on the application of the combined frequency–time (CFT) algorithm to correct for uneven attenuation effects on the observed sea surface Doppler spectrum. The performance of this correction technique was evaluated by a Monte Carlo simulation of the Doppler precipitation radar backscatter from high-resolution 3D rain fields (either generated by a cloud resolving numerical model or retrieved from airborne radar measurements). The results show that the antenna-pointing-induced error can, indeed, be reduced by the proposed technique in order to achieve 1 m s−1 accuracy on rainfall vertical velocity estimates.

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