scholarly journals Autocorrelation and Cross-Correlation Estimators of Polarimetric Variables

2007 ◽  
Vol 24 (8) ◽  
pp. 1337-1350 ◽  
Author(s):  
Valery M. Melnikov ◽  
Dusan S. Zrnić
Keyword(s):  
Correlation Coefficient ◽  
Cross Correlation ◽  
Radar Data ◽  
Lower Sensitivity ◽  
Noise Levels ◽  
Low Snr ◽  
Interference Signals ◽  
Cross Correlations ◽  
Differential Reflectivity ◽  
Thermal Radiations

Abstract Herein are proposed novel estimators of differential reflectivity ZDR and correlation coefficient ρhv between horizontally and vertically polarized echoes. The estimators use autocorrelations and cross correlations of the returned signals to avoid bias by omnipresent but varying white noise. These estimators are considered for implementation on the future polarimetric Weather Surveillance Radar-1988 Doppler (WSR-88D) network. On the current network the reflectivity factor is measured at signal-to-noise ratios (SNRs) as low as 2 dB and the same threshold is expected to hold for the polarimetric variables. At such low SNR and all the way up to SNR = 15 dB, the conventional estimators of differential reflectivity and the copolar correlation coefficient are prone to errors due to uncertainties in noise levels caused by instability of radar devices, thermal radiations of precipitation and the ground, and wideband radiation of electrically active clouds. Noise variations at SNR less than 15 dB can bias the estimates beyond apparatus accuracy. For brevity the authors refer to the estimators of ZDR and ρhv free from noise bias as the “1-lag estimators” because these are derived from 1-lag correlations. The estimators are quite robust and the only weak assumption for validity is that spectral widths of signals from vertically and horizontally polarized returns are equal. This assumption is verified on radar data. Radar observations demonstrate the validity of these estimator and lower sensitivity to interference signals than the conventional algorithms.

scholarly journals Assimilation of Polarimetric Radar Data in Simulation of a Supercell Storm with a Variational Approach and the WRF Model

2021 ◽  
Vol 13 (16) ◽  
pp. 3060
Author(s):  
Muyun Du ◽  
Jidong Gao ◽  
Guifu Zhang ◽  
Yunheng Wang ◽  
Pamela L. Heiselman ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Cross Correlation ◽  
Weather Prediction ◽  
Radar Data ◽  
Polarimetric Radar ◽  
Differential Phase ◽  
Supercell Storm ◽  
Convective Scale ◽  
Differential Reflectivity ◽  
Forward Operator

Polarimetric radar data (PRD) have potential to be used in numerical weather prediction (NWP) models to improve convective-scale weather forecasts. However, thus far only a few studies have been undertaken in this research direction. To assimilate PRD in NWP models, a forward operator, also called a PRD simulator, is needed to establish the relation between model physics parameters and polarimetric radar variables. Such a forward operator needs to be accurate enough to make quantitative comparisons between radar observations and model output feasible, and to be computationally efficient so that these observations can be easily incorporated into a data assimilation (DA) scheme. To address this concern, a set of parameterized PRD simulators for the horizontal reflectivity, differential reflectivity, specific differential phase, and cross-correlation coefficient were developed. In this study, we have tested the performance of these new operators in a variational DA system. Firstly, the tangent linear and adjoint (TL/AD) models for these PRD simulators have been developed and checked for the validity. Then, both the forward operator and its adjoint model have been built into the three-dimensional variational (3DVAR) system. Finally, some preliminary DA experiments have been performed with an idealized supercell storm. It is found that the assimilation of PRD, including differential reflectivity and specific differential phase, in addition to radar radial velocity and horizontal reflectivity, can enhance the accuracy of both initial conditions for model hydrometer state variables and ensuing model forecasts. The usefulness of the cross-correlation coefficient is very limited in terms of improving convective-scale data analysis and NWP.

scholarly journals Detrended Multiple Cross-Correlation Coefficient applied to solar radiation, air temperature and relative humidity

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andrea de Almeida Brito ◽  
Heráclio Alves de Araújo ◽  
Gilney Figueira Zebende
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Solar Energy ◽  
Correlation Coefficient ◽  
Air Temperature ◽  
Cross Correlation ◽  
Global Solar Radiation ◽  
Meteorological Variables ◽  
Hourly Data ◽  
Cross Correlations

AbstractDue to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the cross-correlations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global cross-correlation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended Cross-Correlation Coefficient, ρDCCA, and subsequently with the recently developed Multiple Detrended Cross-Correlation Coefficient, $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2. We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρDCCA was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2 to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}$$DMCx2=1 (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.

scholarly journals Validation of a Multilag Estimator on NJU-CPOL and a Hybrid Approach for Improving Polarimetric Radar Data Quality

2020 ◽  
Vol 12 (1) ◽  
pp. 180
Author(s):  
Shiqing Shao ◽  
Kun Zhao ◽  
Haonan Chen ◽  
Jianjun Chen ◽  
Hao Huang
Keyword(s):  
Theoretical Analysis ◽  
Correlation Coefficient ◽  
Hybrid Method ◽  
Radar Data ◽  
Noise Power ◽  
Signal Power ◽  
Polarimetric Radar ◽  
Moment Estimation ◽  
Spectrum Width ◽  
Differential Reflectivity

For the estimation of weak echo with low signal-to-noise ratio (SNR), a multilag estimator is developed, which has better performance than the conventional method. The performance of the multilag estimator is examined by theoretical analysis, simulated radar data and some specific observed data collected by a C-band polarimetric radar in previous research. In this paper, the multilag estimator is implemented and verified for Nanjing University C-band polarimetric Doppler weather radar (NJU-CPOL) during the Observation, Prediction and Analysis of Severe Convection of China (OPACC) field campaign in 2014. The implementation results are also compared with theoretical analysis, including the estimation of signal power, spectrum width, differential reflectivity, and copolar correlation coefficient. The results show that the improvement of the multilag estimator is little for signal power and differential reflectivity, but significant for spectrum width and copolar correlation coefficient when spectrum width is less than 2 ms−1, which implies a large correlation time scale. However, there are obvious biases from the multilag estimator in the regions with large spectrum width. Based on the performance analysis, a hybrid method is thus introduced and examined through NJU-CPOL observations. All lags including lag 0 of autocorrelation function (ACF) are used for moment estimation in this algorithm according to the maximum usable lag number. A case study shows that this hybrid method can improve moment estimation compared to both conventional estimator and multilag estimator, especially for weak weather echoes. The improvement will be significant if SNR decreases or the biases of noise power in the conventional estimator increase. In addition, this hybrid method is easy to implement on both operational and non-operational radars. It is also expected that the proposed hybrid method will have a better performance if applied to S-band polarimetric radars which have twice the maximum useable lags in the same conditions with C-band radars.

scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

The Impact of Beam Broadening on the Quality of Radar Polarimetric Data

2007 ◽  
Vol 24 (5) ◽  
pp. 729-744 ◽  
Author(s):  
Alexander V. Ryzhkov
Keyword(s):  
Correlation Coefficient ◽  
Cross Correlation ◽  
Horizontal Gradients ◽  
Analytical Formulas ◽  
Radar Resolution ◽  
Differential Reflectivity ◽  
The Impact ◽  
Nonuniform Beam ◽  
Beam Broadening

Abstract The impact of beam broadening on the quality of radar polarimetric data in the presence of nonuniform beam filling (NBF) is examined both theoretically and experimentally. Cross-beam gradients of radar reflectivity Z, differential reflectivity ZDR, and differential phase ΦDP within the radar resolution volume may produce significant biases of ZDR, ΦDP, and the cross-correlation coefficient ρhv. These biases increase with range as a result of progressive broadening of the radar beam. They are also larger at shorter radar wavelengths and wider antenna beams. Simple analytical formulas are suggested for estimating the NBF-induced biases from the measured vertical and horizontal gradients of Z, ZDR, and ΦDP. Analysis of polarimetric data collected by the KOUN Weather Surveillance Radar-1988 Doppler (WSR-88D) demonstrates that frequently observed perturbations of the radial ΦDP profiles and radially oriented “valleys” of ρhv depression can be qualitatively and quantitatively explained using the suggested NBF model.

scholarly journals Close-Range Observations of Tornadoes in Supercells Made with a Dual-Polarization, X-Band, Mobile Doppler Radar

2007 ◽  
Vol 135 (4) ◽  
pp. 1522-1543 ◽  
Author(s):  
Howard B. Bluestein ◽  
Michael M. French ◽  
Robin L. Tanamachi ◽  
Stephen Frasier ◽  
Kery Hardwick ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Cross Correlation ◽  
Doppler Radar ◽  
Dual Polarization ◽  
Radar Beam ◽  
X Band ◽  
Close Range ◽  
Debris Cloud ◽  
The Cross ◽  
Differential Reflectivity

Abstract A mobile, dual-polarization, X-band, Doppler radar scanned tornadoes at close range in supercells on 12 and 29 May 2004 in Kansas and Oklahoma, respectively. In the former tornadoes, a visible circular debris ring detected as circular regions of low values of differential reflectivity and the cross-correlation coefficient was distinguished from surrounding spiral bands of precipitation of higher values of differential reflectivity and the cross-correlation coefficient. A curved band of debris was indicated on one side of the tornado in another. In a tornado and/or mesocyclone on 29 May 2004, which was hidden from the view of the storm-intercept team by precipitation, the vortex and its associated “weak-echo hole” were at times relatively wide; however, a debris ring was not evident in either the differential reflectivity field or in the cross-correlation coefficient field, most likely because the radar beam scanned too high above the ground. In this case, differential attenuation made identification of debris using differential reflectivity difficult and it was necessary to use the cross-correlation coefficient to determine that there was no debris cloud. The latter tornado’s parent storm was a high-precipitation (HP) supercell, which also spawned an anticyclonic tornado approximately 10 km away from the cyclonic tornado, along the rear-flank gust front. No debris cloud was detected in this tornado either, also because the radar beam was probably too high.

Microphysical Insights into Ice Pellet Formation Revealed by Fully Polarimetric Ka-Band Doppler Radar

2020 ◽  
Vol 59 (10) ◽  
pp. 1557-1580
Author(s):  
Matthew R. Kumjian ◽  
Dana M. Tobin ◽  
Mariko Oue ◽  
Pavlos Kollias
Keyword(s):  
New York ◽  
Correlation Coefficient ◽  
Doppler Radar ◽  
Radar Data ◽  
Ice Crystals ◽  
Horizontal Polarization ◽  
Ka Band ◽  
Pellet Formation ◽  
Linear Depolarization Ratio ◽  
Differential Reflectivity

AbstractFully polarimetric scanning and vertically pointing Doppler spectral data from the state-of-the-art Stony Brook University Ka-band Scanning Polarimetric Radar (KASPR) are analyzed for a long-duration case of ice pellets over central Long Island in New York from 12 February 2019. Throughout the period of ice pellets, a classic refreezing signature was present, consisting of a secondary enhancement of differential reflectivity ZDR beneath the melting layer within a region of decreasing reflectivity factor at horizontal polarization ZH and reduced copolar correlation coefficient ρhv. The KASPR radar data allow for evaluation of previously proposed hypotheses to explain the refreezing signature. It is found that, upon entering a layer of locally generated columnar ice crystals and undergoing contact nucleation, smaller raindrops preferentially refreeze into ice pellets prior to the complete freezing of larger drops. Refreezing particles exhibit deformations in shape during freezing, leading to reduced ρhv, reduced co-to-cross-polar correlation coefficient ρxh, and enhanced linear depolarization ratio, but these shape changes do not explain the ZDR signature. The presence of columnar ice crystals, though apparently crucial for instigating the refreezing process, does not contribute enough backscattered power to affect the ZDR signature, either.

scholarly journals Polarimetric Tornadic Debris Signature Variability and Debris Fallout Signatures

2015 ◽  
Vol 54 (12) ◽  
pp. 2389-2405 ◽  
Author(s):  
Matthew S. Van Den Broeke
Keyword(s):  
Land Cover ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Extreme Values ◽  
Life Cycles ◽  
Areal Extent ◽  
Polarimetric Radar ◽  
Horizontal Polarization ◽  
Differential Reflectivity ◽  
Relative Flow

AbstractValues of polarimetric radar variables may vary substantially between and through tornadic debris signature (TDS) events. Tornadoes with higher intensity ratings are associated with higher average and extreme values of reflectivity factor at horizontal polarization ZHH and lower values of copolar cross-correlation coefficient ρhv. Although values of these variables often fluctuate through reported tornado life cycles, ZHH repeatably decreases and ρhv repeatably increases across the volume scan immediately following reported tornado demise. Land cover has a relatively small effect on values of the polarimetric variables within TDSs, although near-radar urban TDSs may exhibit relatively high ZHH values. TDS areal extent is typically larger aloft than near the surface, although this trend may reverse in the most intense tornadoes. Maximum altitude to which a TDS is visible is more strongly a function of tornado intensity than of land cover or ambient shear and instability. Debris often disappears once lofted but may also be observed to spread out downstream with the storm-relative flow or to fall out along the parent storm’s northwest flank in a debris fallout signature (DFS). DFS characteristics, although variable, most commonly include ZHH values of 30–35 dBZ, ρhv values of 0.60–0.80, and values of differential reflectivity ZDR that are repeatably near 0 dB.

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