scholarly journals A Gaussian mixture method for specific differential phase retrieval at X-band frequency

2019 ◽  
Vol 12 (10) ◽  
pp. 5613-5637 ◽  
Author(s):  
Guang Wen ◽  
Neil I. Fox ◽  
Patrick S. Market
Keyword(s):  
Phase Shift ◽  
Linear Regression ◽  
Gaussian Mixture ◽  
Differential Phase Shift ◽  
Band Frequency ◽  
Differential Phase ◽  
X Band ◽  
Gauge Data ◽  
Bow Echo ◽  
Expected Values

Abstract. The specific differential phase Kdp is one of the most important polarimetric radar variables, but the variance σ2(Kdp), regarding the errors in the calculation of the range derivative of the differential phase shift Φdp, is not well characterized due to the lack of a data generation model. This paper presents a probabilistic method based on the Gaussian mixture model for Kdp estimation at X-band frequency. The Gaussian mixture method can not only estimate the expected values of Kdp by differentiating the expected values of Φdp, but also obtain σ2(Kdp) from the product of the square of the first derivative of Kdp and the variance of Φdp. Additionally, the ambiguous phase and backscattering differential phase shift are corrected via the mixture model. The method is qualitatively evaluated with a convective event of a bow echo observed by the X-band dual-polarization radar in the University of Missouri. It is concluded that Kdp estimates are highly consistent with the gradients of Φdp in the leading edge of the bow echo, and large σ2(Kdp) occurs with high variation of Kdp. Furthermore, the performance is quantitatively assessed by 2-year radar–gauge data, and the results are compared to linear regression model. It is clear that Kdp-based rain amounts have good agreement with the rain gauge data, while the Gaussian mixture method gives improvements over the linear regression model, particularly for far ranges.

scholarly journals A Gaussian Mixture Method for Specific Differential Phase Retrieval at X-band Frequency

2019 ◽  
Author(s):  
Guang Wen ◽  
Neil I. Fox ◽  
Patrick S. Market
Keyword(s):  
Phase Shift ◽  
Linear Regression ◽  
Gaussian Mixture ◽  
Differential Phase Shift ◽  
Band Frequency ◽  
Differential Phase ◽  
X Band ◽  
Gauge Data ◽  
Bow Echo ◽  
Expected Values

Abstract. Specific differential phase Kdp is one of the most important polarimetric radar variables, but the variance σ2(Kdp), regarding the errors in the calculation of the range derivative of differential phase shift Φdp, is not well characterized due to the lack of a data generation model. This paper presents a probabilistic method based on Gaussian mixture model for Kdp estimation at X-band frequency. The Gaussian mixture method can not only estimate the expected values of Kdp by differentiating the expected values of Φdp, but also obtain σ2(Kdp) from the product of the square of the first derivative of Kdp and the variance of Φdp. Additionally, ambiguous Φdp and backscattering differential phase shift are corrected via the mixture model. The method is qualitatively evaluated with a convective event of a bow echo observed by the X-band dual-polarization radar in the University of Missouri. It is concluded that Kdp estimates are highly consistent with the gradients of Φdp in the leading edge of the bow echo, and large σ2(Kdp) occurs with high variation of Kdp. Furthermore, the performance is quantitatively assessed by three-year radar-gauge data, and the results are compared to linear regression model. It is clear that Kdp-based rain amounts have good agreement with the rain gauge data, while the Gaussian mixture method gives improvements over linear regression model, particularly for far ranges.

scholarly journals Characterization of Mediterranean hail-bearing storms using an operational polarimetric X-band radar

2015 ◽  
Vol 8 (11) ◽  
pp. 4681-4698 ◽  
Author(s):  
G. Vulpiani ◽  
L. Baldini ◽  
N. Roberto
Keyword(s):  
Phase Shift ◽  
Attenuation Correction ◽  
Convective System ◽  
Polarimetric Radar ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Radar Measurements ◽  
Storm Characteristics ◽  
The City

Abstract. This work documents the effective use of X-band radar observations for monitoring severe storms in an operational framework. Two severe hail-bearing Mediterranean storms that occurred in 2013 in southern Italy, flooding two important Sicilian cities, are described in terms of their polarimetric radar signatures and retrieved rainfall fields. The X-band dual-polarization radar operating inside the Catania airport (Sicily, Italy), managed by the Italian Department of Civil Protection, is considered here. A suitable processing is applied to X-band radar measurements. The crucial procedural step relies on the differential phase processing, being preparatory for attenuation correction and rainfall estimation. It is based on an iterative approach that uses a very short-length (1 km) moving window, allowing proper capture of the observed high radial gradients of the differential phase. The parameterization of the attenuation correction algorithm, which uses the reconstructed differential phase shift, is derived from electromagnetic simulations based on 3 years of drop size distribution (DSD) observations collected in Rome (Italy). A fuzzy logic hydrometeor classification algorithm was also adopted to support the analysis of the storm characteristics. The precipitation field amounts were reconstructed using a combined polarimetric rainfall algorithm based on reflectivity and specific differential phase. The first storm was observed on 21 February when a winter convective system that originated in the Tyrrhenian Sea, marginally hit the central-eastern coastline of Sicily, causing a flash flood in Catania. Due to an optimal location (the system is located a few kilometers from the city center), it was possible to retrieve the storm characteristics fairly well, including the amount of rainfall field at the ground. Extemporaneous signal extinction, caused by close-range hail core causing significant differential phase shift in a very short-range path, is documented. The second storm, on 21 August 2013, was a summer mesoscale convective system that originated from a Mediterranean low pressure system lasting a few hours that eventually flooded the city of Syracuse. The undergoing physical process, including the storm dynamics, is inferred by analyzing the vertical sections of the polarimetric radar measurements. The high registered amount of precipitation was fairly well reconstructed, although with a trend toward underestimation at increasing distances. Several episodes of signal extinction were clearly manifested during the mature stage of the observed supercells.

Investigation of the relationship between differential phase shift and path integrated attenuation in the melting layer of precipitation of X-band radar

2021 ◽  
Author(s):  
Anil Kumar Khanal ◽  
Guy Delrieu ◽  
Brice Boudevillain ◽  
Frédéric Cazenave ◽  
Nan Yu
Keyword(s):  
Phase Shift ◽  
Complex Terrain ◽  
High Mountain ◽  
Differential Phase Shift ◽  
Melting Layer ◽  
Differential Phase ◽  
Quantitative Precipitation Estimation ◽  
X Band ◽  
Precipitation Estimation ◽  
The Relationship

<p>The RadAlp experiment at the Grenoble region in the French Alps aims to advance the radar remote sensing techniques of precipitation in high mountain regions. Since 2016, two dual-polarimetric X-band radars, one on top of Mt Moucherotte (1901 m asl) and another in the Grenoble valley (220 m asl) are operated by Metro France and IGE respectively. High spatio-temporal variability of precipitation (e.g. intensity and phase) in the complex terrain requires high-resolution observations. X-band radar provides high spatial and temporal resolution imagery which makes it ideal for use in complex terrain but also comes with significant attenuation problems during heavy precipitation and in the melting layer (ML). The development of polarimetric techniques, especially differential phase shift (ϕDP) has helped to mitigate the power signal attenuation problem to a certain extent. The ϕDP is immune to attenuation due to rainfall, radar calibration errors and partial beam blockage, making it an attractive parameter for quantitative precipitation estimation (QPE) through attenuation correction of the reflectivity (Z). The ϕDP, however, is quite noisy and requires regularization. An iterative algorithm based on maximum allowed step sizes provides a robust solution in ϕDP regularization. In this study, we aim to understand the relationship between differential phase shift (ϕDP) and path integrated attenuation (PIA) at X-band. This relationship is crucial for quantitative precipitation estimation (QPE) using polarimetric techniques. Furthermore, this relationship is still poorly documented within the melting layer due to the complexity of the hydrometeors' distributions in terms of phase, size, shape and density. We use the mountain reference technique (MRT) for direct PIA estimations associated with the decrease in returns from mountain targets during precipitation events as compared to dry periods. The quasi-vertical profiles from the valley-based radar (XPORT) help to identify, characterize and follow the evolution of the melting layer. For the mountaintop radar (MOUC) stratiform events (59 days between Nov 2016 to Dec 2019) where the O° elevation angle beam passes through the melting layer are considered.  The PIA/ ϕDP ratios at different strata of the ML, snow-ML interface and ML-rain interface are studied. Initial results show that the PIA/ ϕDP ratio peaks at the levels of cross-correlation coefficient (ρHV) minima, remains strong in the upper part of the ML and tends to 0 towards the top of ML. Additionally, its value in rain (0.32 dB per deg) below the ML matches closely with the specific attenuation vs specific phase (k-KDP) relationship (0.29) derived from the disdrometer at ground level.  Its value increases steadily in the lower part of ML (peaks around 0.70 dB per deg), remains strong in the upper part of ML (0.5 - 0.6 dB per degree), and decreases rapidly to 0.13 dB per degree above the ML (in snow).</p>

X-band Polarimetric Radar Rainfall Measurements in Keys Area Microphysics Project

2006 ◽  
Vol 63 (1) ◽  
pp. 187-203 ◽  
Author(s):  
Emmanouil N. Anagnostou ◽  
Mircea Grecu ◽  
Marios N. Anagnostou
Keyword(s):  
Phase Shift ◽  
Attenuation Correction ◽  
Doppler Radar ◽  
Model Parameters ◽  
Dual Polarization ◽  
Radar Rainfall ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Filter Noise

Abstract The Keys Area Microphysics Project (KAMP), conducted as part of NASA’s Fourth Convective and Moisture Experiment (CAMEX-4) in the lower Keys area, deployed a number of ground radars and four arrays of rain gauge and disdrometer clusters. Among the various instruments is an X-band dual-polarization Doppler radar on wheels (XPOL), contributed by the University of Connecticut. XPOL was used to retrieve rainfall rate and raindrop size distribution (DSD) parameters to be used in support of KAMP science objectives. This paper presents the XPOL measurements in KAMP and the algorithm developed for attenuation correction and estimation of DSD model parameters. XPOL observations include the horizontal polarization reflectivity ZH, differential reflectivity ZDR, and differential phase shift ΦDP. Here, ZH and ZDR were determined to be positively biased by 3 and 0.3 dB, respectively. A technique was also applied to filter noise and correct for potential phase folding in ΦDP profiles. The XPOL attenuation correction uses parameterizations that relate the path-integrated specific (differential) attenuation along a radar ray to the filtered-ΦDP (specific attenuation) profile. Attenuation-corrected ZH and specific differential phase shift (derived from filtered ΦDP profiles) data are then used to derive two parameters of the normalized gamma DSD model, that is, intercept (Nw) and mean drop diameter (D0). The third parameter (shape parameter μ) is calculated using a constrained μ–Λ relationship derived from the measured raindrop spectra. The XPOL attenuation correction is evaluated using coincidental nonattenuated reflectivity fields from the Key West Weather Surveillance Radar-1988 Doppler (WSR-88D), while the DSD parameter retrievals are statistically assessed using DSD parameters calculated from the measured raindrop spectra. Statistics show that XPOL DSD parameter estimation is consistent with independent observations. XPOL estimates of water content and Nw are also shown to be consistent with corresponding retrievals from matched ER-2 Doppler radar (EDOP) profiling observations from the 19 September airborne campaign. Results shown in this paper strengthen the applicability of X-band dual-polarization high resolution observations in cloud modeling and precipitation remote sensing studies.

scholarly journals An Extended Kalman Filter Framework for Polarimetric X-Band Weather Radar Data Processing

2012 ◽  
Vol 29 (5) ◽  
pp. 711-730 ◽  
Author(s):  
Marc Schneebeli ◽  
Alexis Berne
Keyword(s):  
Kalman Filter ◽  
Phase Shift ◽  
Extended Kalman Filter ◽  
Rain Rate ◽  
Swiss Alps ◽  
Horizontal Polarization ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Attenuation Corrected

Abstract The different quantities measured by dual-polarization radar systems are closely linked to each other. An extended Kalman filter framework is proposed in order to make use of constraints on individual radar observables that are induced by these relations. This new approach simultaneously estimates the specific differential phase on propagation Kdp, the attenuation-corrected reflectivity at horizontal polarization Zh, and the attenuation-corrected differential reflectivity Zdr, as well as the differential phase shift on backscatter δhυ. In a simulation experiment it is found that Kdp and δhυ can be retrieved with higher accuracy and spatial resolution than existing estimators that solely rely on a smoothed measurement of the differential phase shift Ψdp. Attenuation-corrected Zh was retrieved with an accuracy similar to standard algorithms, but improvements were found for attenuation-corrected Zdr. In addition, the algorithm can be used for radar calibration by comparing the directly retrieved differential phase shift on propagation Φdp with the accumulated Kdp estimates. The extended Kalman filter estimation scheme was applied to data collected with an X-band polarimetric radar in the Swiss Alps in 2010. Radome attenuation appears to be significant (up to 5 dB) in moderate to intense rain events and hence needs to be corrected in order to have reliable quantitative precipitation estimates. Measurements corrected for radome and propagation attenuation were converted into rain-rate R with a newly developed relation between R, Kdp, and Zdr. The good agreement between rain-rate values inferred from ground observations and from the radar measurements confirms the reliability of the proposed radar processing technique.

scholarly journals Preliminary investigation of the relationship between differential phase shift and path-integrated attenuation at the X band frequency in an Alpine environment

2020 ◽  
Vol 13 (7) ◽  
pp. 3731-3749
Author(s):  
Guy Delrieu ◽  
Anil Kumar Khanal ◽  
Nan Yu ◽  
Frédéric Cazenave ◽  
Brice Boudevillain ◽  
...  
Keyword(s):  
Phase Shift ◽  
Ground Level ◽  
Observation System ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Total Differential ◽  
Rain Rates ◽  
The Relationship ◽  
Precipitation Events

Abstract. The RadAlp experiment aims at developing advanced methods for rainfall and snowfall estimation using weather radar remote sensing techniques in high mountain regions for improved water resource assessment and hydrological risk mitigation. A unique observation system has been deployed since 2016 in the Grenoble region of France. It is composed of an X-band radar operated by Météo-France on top of the Moucherotte mountain (1901 m  above sea level; hereinafter MOUC radar). In the Grenoble valley (220 m  above sea level; hereinafter a.s.l.), we operate a research X-band radar called XPORT and in situ sensors (weather station, rain gauge and disdrometer). In this paper we present a methodology for studying the relationship between the differential phase shift due to propagation in precipitation (Φdp) and path-integrated attenuation (PIA) at X band. This relationship is critical for quantitative precipitation estimation (QPE) based on polarimetry due to severe attenuation effects in rain at the considered frequency. Furthermore, this relationship is still poorly documented in the melting layer (ML) due to the complexity of the hydrometeors' distributions in terms of size, shape and density. The available observation system offers promising features to improve this understanding and to subsequently better process the radar observations in the ML. We use the mountain reference technique (MRT) for direct PIA estimations associated with the decrease in returns from mountain targets during precipitation events. The polarimetric PIA estimations are based on the regularization of the profiles of the total differential phase shift (Ψdp) from which the profiles of the specific differential phase shift on propagation (Kdp) are derived. This is followed by the application of relationships between the specific attenuation (k) and the specific differential phase shift. Such k–Kdp relationships are estimated for rain by using drop size distribution (DSD) measurements available at ground level. Two sets of precipitation events are considered in this preliminary study, namely (i) nine convective cases with high rain rates which allow us to study the ϕdp–PIA relationship in rain, and (ii) a stratiform case with moderate rain rates, for which the melting layer (ML) rose up from about 1000 up to 2500 m a.s.l., where we were able to perform a horizontal scanning of the ML with the MOUC radar and a detailed analysis of the ϕdp–PIA relationship in the various layers of the ML. A common methodology was developed for the two configurations with some specific parameterizations. The various sources of error affecting the two PIA estimators are discussed, namely the stability of the dry weather mountain reference targets, radome attenuation, noise of the total differential phase shift profiles, contamination due to the differential phase shift on backscatter and relevance of the k–Kdp relationship derived from DSD measurements, etc. In the end, the rain case study indicates that the relationship between MRT-derived PIAs and polarimetry-derived PIAs presents an overall coherence but quite a considerable dispersion (explained variance of 0.77). Interestingly, the nonlinear k–Kdp relationship derived from independent DSD measurements yields almost unbiased PIA estimates. For the stratiform case, clear signatures of the MRT-derived PIAs, the corresponding ϕdp value and their ratio are evidenced within the ML. In particular, the averaged PIA∕ϕdp ratio, a proxy for the slope of a linear k–Kdp relationship in the ML, peaks at the level of the copolar correlation coefficient (ρhv) peak, just below the reflectivity peak, with a value of about 0.42 dB per degree. Its value in rain below the ML is 0.33 dB per degree, which is in rather good agreement with the slope of the linear k–Kdp relationship derived from DSD measurements at ground level. The PIA∕ϕdp ratio remains quite high in the upper part of the ML, between 0.32 and 0.38 dB per degree, before tending towards 0 above the ML.

scholarly journals Characterization of Mediterranean hail-bearing storms using an operational polarimetric X-band radar

2015 ◽  
Vol 8 (7) ◽  
pp. 7201-7237
Author(s):  
G. Vulpiani ◽  
L. Baldini ◽  
N. Roberto
Keyword(s):  
Phase Shift ◽  
Convective System ◽  
Tyrrhenian Sea ◽  
Polarimetric Radar ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
X Band ◽  
Radar Measurements ◽  
Storm Characteristics ◽  
The City

Abstract. This work documents the fruitul use of X-band radar observations for the monitoring of severe storms in an operational framework. More specifically, a couple of severe hail-bearing Mediterranean storms occurred in 2013 in southern Italy, flooding two important cities of Sicily, are described in terms of their polarimetric radar signatures and retrieved rainfall fields. It is used the X-band dual-polarization radar operating inside the Catania airport (Sicily, Italy), managed by the Italian Department of Civil Protection. A suitable processing is applied to X-band radar measurements. The crucial procedural step relies on the differential phase processing based on an iterative approach that uses a very short-length (1 km) moving window allowing to properly catch the observed high radial gradients of the differential phase. The parameterization of the attenuation correction algorithm, which use the reconstructed differential phase shift, is derived from electromagnetic simulations based on 3 years of DSD observations collected in Rome (Italy). A Fuzzy Logic hydrometeor classification algorithm was also adopted to support the analysis of the storm characteristics. The precipitation fields amount were reconstructed using a combined polarimetric rainfall algorithm based on reflectivity and specific differential phase. The first considered storm was observed on the 21 February, when a winter convective system, originated in the Tyrrhenian sea, hit only marginally the central-eastern coastline of Sicily causing the flash-flood of Catania. Due to the optimal radar location (the system is located at just few kilometers from the city center), it was possible to well retrieve the storm characteristics, including the amount of rainfall field at ground. Extemporaneous signal extinction, caused by close-range hail core causing significant differential phase shift in very short range path, is documented. The second storm, occurred on 21 August 2013, is a summer mesoscale convective system originated by the temperature gradient between sea and land surface, lasted a few hours and eventually flooded the city of Siracusa. The undergoing physical process, including the storm dynamics, is inferred by analysing the vertical sections of the polarimetric radar measurements. The high registered precipitation amount was fairly well reconstructed even though with a trend to underestimation at increasing distances. Several episodes of signal extinction clearly manifested during the mature stage of the observed supercell.

scholarly journals 1310 nm differential-phase-shift QKD system using superconducting single-photon detectors

2009 ◽  
Vol 11 (4) ◽  
pp. 045020 ◽  
Author(s):  
Lijun Ma ◽  
S Nam ◽  
Hai Xu ◽  
B Baek ◽  
Tiejun Chang ◽  
...  
Keyword(s):  
Phase Shift ◽  
Single Photon ◽  
Photon Detectors ◽  
Differential Phase Shift ◽  
Differential Phase ◽  
Single Photon Detectors
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