single-Doppler Radar Observations Research Articles

A New Closure Assumption and Formulation Based on the Helmholtz Decomposition for Improving Retrievals for Vortex Circulations from Single-Doppler Radar Observations

Abstract Doppler weather radars are powerful tools for investigating the inner-core structure and intensity of tropical cyclones (TCs). The Doppler velocity can provide quantitative information on the vortex structure in the TCs. The generalized velocity track display (GVTD) technique has been used to retrieve the axisymmetric circulations and asymmetric tangential flows in the TCs from ground-based single-Doppler radar observations. GVTD can have limited applicability to asymmetric vortices due to the closure assumption of no asymmetric radial flows. The present study proposes a new closure formulation that includes asymmetric radial flows, based on the Helmholtz decomposition. Here it is assumed that the horizontal flow is predominantly rotational and expressed with a streamfunction, but limited inclusion of wavenumber-1 divergence is available. Unlike the original GVTD, the decomposition introduces consistency along the radius by solving all equations simultaneously. The new approach, named GVTD-X, is applied to analytical vortices and a real TC with asymmetric structures. This approach makes the retrieval of axisymmetric flow relatively insensitive to the contamination from asymmetric flows and to small errors in storm center location. For an analytical vortex with a wavenumber-2 asymmetry, the maximum relative error of the axisymmetric tangential wind retrieved by GVTD-X is less than 2% at the radius of the maximum wind speed. In practical applications, errors can be evaluated by comparing results for different maximum wavenumbers. When applied to a real TC, GVTD-X largely suppressed an artificial periodic fluctuation that occurs in GVTD from the aliasing of the neglected asymmetric radial flows. Significance Statement In tropical cyclone (TC) wind retrievals from single-Doppler weather radar observations, closure assumptions are required for the retrieval equations. The present study proposes a new closure allowing asymmetric radial winds and improving retrievals for TC winds in the previously developed technique. The relative error of the axisymmetric tangential wind in idealized vortices from the new approach is less than 2% at the radius of the maximum wind speed. In applying to a real TC with an elliptical eyewall, we found that the new approach can largely suppress an artificial evolution of the tangential winds in the previous retrieval technique.

Doppler Radar Analysis of the Eyewall Replacement Cycle of Hurricane Matthew (2016) in Vertical Wind Shear

AbstractHurricane Matthew (2016) was observed by ground-based polarimetric radars in Miami (KAMX), Melbourne (KMLB), and Jacksonville (KJAX) and a NOAA P3 airborne tail Doppler radar near the coast of the southeastern United States during an eyewall replacement cycle (ERC). The radar observations indicate that Matthew’s primary eyewall was replaced with a weaker outer eyewall, but unlike a classic ERC, Matthew did not reintensify after the inner eyewall disappeared. Triple Doppler analysis was calculated from the NOAA P3 airborne fore and aft radar scanning combined with the KAMX radar data during the period of secondary eyewall intensification and inner eyewall weakening from 19 UTC 6 October to 00 UTC 7 October. Four flight passes of the P3 aircraft show the evolution of the reflectivity, tangential winds, and secondary circulation as the outer eyewall became well-established. Further evolution of the ERC is analyzed from the ground-based single Doppler radar observations for 35 hours with high temporal resolution at a 5-minute interval from 19 UTC 6 October to 00 UTC 8 October using the Generalized Velocity Track Display (GVTD) technique. The single-Doppler analyses indicate that the inner eyewall decayed a few hours after the P3 flight, while the outer eyewall contracted but did not reintensify and the asymmetries increased episodically. The analysis suggests that the ERC process was influenced by a complex combination of environmental vertical wind shear, an evolving axisymmetric secondary circulation, and an asymmetric vortex Rossby wave damping mechanism that promoted vortex resiliency despite increasing shear.

Nonlinear Wind Analysis of Single-Doppler Radar Observations within a DVAD Framework

AbstractThe application of the distance velocity azimuth display (DVAD) method to the retrieval of vertical wind profiles from single-Doppler radar observations is presented in this study. It was shown that Doppler velocity observations at a constant altitude can be expressed as a single polynomial function for both linear and nonlinear wind fields in DVAD. Only a one-step least squares fitting of a polynomial function is required to obtain the vertical wind profile of a real wind field. The mathematic formulation of DVAD results in two advantages over the traditional nonlinear VAD method used for the nonlinear analysis of single-Doppler observations. First, the requirement of only one-step least squares fitting leads to robust performance when Doppler velocity observations are contaminated by unevenly distributed data noise and voids. Second, the degree of nonlinearity to properly represent a real wind field can be directly estimated in DVAD instead of being empirically determined in the traditional method. A proper nonlinear wind model for approximating the real wind field can be objectively derived using the DVAD method. The merits of DVAD as a quantitative single-Doppler analysis method were compared with the traditional method using both idealized and real datasets. Results show that the simplicity and robust performance of DVAD make it a good candidate for single-Doppler retrieval in operational use.

Distance Velocity–Azimuth Display (DVAD)—New Interpretation and Analysis of Doppler Velocity

Abstract The concept and mathematical framework of the distance velocity–azimuth display (DVAD) methodology is presented. DVAD uses rVd (Doppler velocity scaled by the distance from the radar to a gate, r) as the basis to display, interpret, and extract information from single Doppler radar observations. Both linear and nonlinear wind fields can be represented by the same Cartesian polynomial with different orders. DVAD is mathematically concise and superior to the velocity–azimuth display (VAD) in interpreting and deducing flow characteristics. The rVd pattern of a two-dimensional linear wind field is exclusively in the form of a bivariate quadratic equation representing conic sections (e.g., ellipse, parabola, and hyperbola) centered at the radar depending only on divergence and deformation. The presence of a constant background flow translates the conic sections to a different origin away from the radar. It is possible to graphically estimate the characteristics of a linear wind field from the conical sections without performing a VAD analysis. DVAD analysis can deduce quantitative flow characteristics by a least squares fitting and/or a derivative method, and is a natural way to account for nonlinearity. The rVd pattern behaves similar to a type of velocity potential in fluid mechanics where ∇(rVd) is a proxy of the true wind vector and is used to estimate the general flow pattern in the vicinity of the radar.

Kinematic features of a bow echo in southern China observed with Doppler radar

A bow echo is a type of mesoscale convective phenomenon that often induces extreme weather and appears with strong reflectivity on radar images. A strong bow echo that developed from a supercell was observed over Foshan City in southern China on 17 April 2011. The intense gusty winds and showers caused huge losses of property and severely affected human lives. This paper presents an analysis of this strong meso-β-scale convective system based on Doppler radar observations. The isolated bow echo exhibited a horizontal scale of about 80 km in terms of reflectivity above 40 dBZ, and a life span of 8 hours. The system originated from the merging of a couple of weakly organized cells in a shear line, and developed into an arch shape as it moved through the shear zone. Sufficient surface moisture supply ensured the convective instability and development of the bow echo. The low-altitude winds retrieved from single Doppler radar observations showed an obvious rear-inflow jet along the notch area. Different from the conventional definition, no bookend anticyclone was observed throughout the life cycle. Very strong slantwise updrafts and downdrafts were recognizable from the retrieved winds, even though the spatial scale of the bow echo was small. Strong winds and induced damage on the surface are considered to have been caused by the mid-level rear-inflow jet and intense convective downdrafts.

Short-Term Forecasting of a Midlatitude Convective Storm by the Assimilation of Single–Doppler Radar Observations

Abstract The McGill University radar data assimilation system is used to initialize a convective storm at high resolution (1 km) from single–Doppler radar observations. In this study, the background term in the assimilation system is improved. Specifically, by assuming the correlation of the errors of the control variables to be isotropic and homogeneous, the background error covariance matrix is modeled by a recursive filter. In addition, a 3-h-prior high-resolution model forecast is used as the background field. The analysis fields from the assimilation system successfully trigger the convective storms in the radar-observed regions from a single assimilation window. Without data assimilation, the modeled storms did not occur at the right time and place. To account for the rapid evolution of the convective storms and to correct the forecast errors with time, a cycling process is applied for a very short-term forecast. It is found that the first assimilation window can maintain the prediction of the storms for less than 1 h. The cycling process helps to maintain the intensity of the storm cells for a longer period of time. However, a comparison of radar observations with the 90-min simulation indicates an error in the position of the convective cells. The error of the radial component of the wind field between the observation and the simulation is larger at the upper levels. A wavelet analysis between the observation and simulated reflectivities indicates that the forecast is able to adequately predict the convective scale (∼10–20 km) during the first 20 min, whereas the simulation has more predictability at the longer scale (>30 km) beyond 20 min.

Descending Reflectivity Cores in Supercell Thunderstorms Observed by Mobile Radars and in a High-Resolution Numerical Simulation

Abstract This paper is motivated by the recent interest in the “descending reflectivity cores” (DRCs) that have been observed in some supercell thunderstorms prior to the development or intensification of low-level rotation. The DRCs of interest descend on the right rear flank of the storms and are small in scale, relative to the main radar echo. They are observed to descend from the echo overhang and, upon reaching low levels, have been found to contribute to the formation or evolution of hook echoes, which are perhaps the most familiar radar characteristic of supercells. Herein, observations of DRCs obtained by a mobile Doppler radar at close range are presented. The data afford higher-resolution views of DRCs and their accompanying radial velocity fields than typically are available from operational radars, although one drawback is that some of the larger-scale perspective is sacrificed (e.g., the origin of the DRC and its possible connection to the reflectivity near the updraft summit are within the cone of silence). It is found that it is difficult to generalize a relationship between the observations of DRCs and the subsequent evolution of the low-level wind field. The results of a three-dimensional numerical simulation of a supercell thunderstorm also are presented. DRCs are a common development within the simulation despite the use of a simple (warm rain) microphysics parameterization. The simulation allows for an investigation of the aspects of DRCs that cannot be ascertained using single-Doppler radar observations, for example, DRC formation mechanisms, the relationship between DRCs and the three-dimensional wind field, and the thermodynamic fields that accompany DRCs. Three different mechanisms are identified by which DRCs can develop in the model, not all of which are followed by increases in low-level rotation. This finding might account for the aforementioned difficulty in generalizing associations between DRCs and changes in the low-level wind field observed by mobile radar, as well as the fact that prior studies also have produced somewhat mixed results with respect to the potential of DRC detection to aid in the operational forecasting of tornadogenesis.

Generalized VTD Retrieval of Atmospheric Vortex Kinematic Structure. Part I: Formulation and Error Analysis

Abstract The primary circulation of atmospheric vortices, such as tropical cyclones and tornadoes, can be estimated from single-Doppler radar observations using the ground-based velocity track display (GBVTD) algorithm. The GBVTD algorithm has limitations in the following four areas: 1) distortion in the retrieved asymmetric wind fields, 2) a limited analysis domain, 3) the inability to resolve the cross-beam component of the mean wind, and 4) the inability to separate the asymmetric tangential and radial winds. This paper presents the generalized velocity track display (GVTD) algorithm, which eliminates the first two limitations inherent in the GBVTD technique and demonstrates the possibility of subjectively estimating the mean wind vector when its signature is visible beyond the influence of the vortex circulation. In this new paradigm, the GVTD algorithm fits the atmospheric vortex circulation to a new variable VdD/RT in a linear azimuth angle (θ′), rather than the Doppler velocity Vd in a nonlinear angle (ψ), which is used in GBVTD. Key vortex kinematic structures (e.g., mean wind, axisymmetric tangential wind, etc.) in the VdD/RT space simplify the interpretation of the radar signature and eliminate the geometric distortion inherent in the Vd display. This is a significant improvement in diagnosing vortex structures in both operations and research. The advantages of using VdD/RT are illustrated using analytical atmospheric vortices, and the properties are compared with GBVTD. The characteristics of the VdD/RT display of Typhoon Gladys (1994) can be approximated by a constant mean wind plus an axisymmetric vortex.

Structure and Evolution of Intense Tropical Cyclone Dina near La Réunion on 22 January 2002: GB-EVTD Analysis of Single Doppler Radar Observations

Doppler radar observations of Tropical Cyclone Dina, as its eye passed at less than 100 km from the northern coast of La Reunion Island (21°S, 55.5°E) on 22 January 2002, are analyzed using the Ground-Based Extended Velocity Track Display (GB-EVTD) technique. This method is an extension of GB-VTD and it allows one to determine the full set of wavenumber-0 and -1 components of the tangential and radial winds in a tropical cyclone from a series of observations with a ground-based Doppler radar. The results obtained for Dina reveal the presence of strong swirling winds (>65 m s−1) at 40–60-km radii from the storm center and below 3-km altitude. The observed changes in the location and intensity of the maximum winds, as well as the veering propagation of Dina, are shown to result probably from interaction between cyclonic winds and high topography of the island.

A Method for Retrieving Mean Horizontal Wind Profiles from Single-Doppler Radar Observations Contaminated by Aliasing

The velocity–azimuth display (VAD) technique was designed to estimate the areal mean vertical profile of the horizontal wind above a ground-based Doppler radar. The method uses radial velocity observations under the assumption of a linear wind field, though it encounters difficulty when the observations are contaminated by velocity ambiguities, large noise, and when viable data exist only over a restricted azimuthal range. The method suggested in this paper uses gradients of radial velocity, rather than only the velocity itself, to derive wind profiles and thus is termed the gradient velocity–azimuth display (GVAD) technique. Both the VAD and GVAD methods are tested first on simulated data to examine their sensitivity to different type of errors in radial velocity. The retrieved mean wind profiles are shown to be insensitive to random errors in radial velocity, even at large amplitude. However, the VAD method is very sensitive to systematic errors caused by velocity ambiguities. The experiments indicate that if only 3% of a full-volume scan of radial wind data is contaminated by aliasing errors, the relative rms error in the mean wind profile retrieved by VAD can reach 50%. In contrast, GVAD is very robust to such errors. Application of GVAD to Weather Surveillance Radar-1988 Doppler (WSR-88D) data collected during the 3 May 1999 tornado outbreak show that it has the ability to obtain accurate wind profiles even when the observations contain large errors caused by velocity ambiguities and random noise.

A Method for Retrieving Mean Horizontal Wind Profiles from Single-Doppler Radar Observations Contaminated by Aliasing

A Method for Retrieving Mean Horizontal Wind Profiles from Single-Doppler Radar Observations Contaminated by Aliasing

The Evolution of Low-Level Rotation in the 29 May 1994 Newcastle–Graham, Texas, Storm Complex during VORTEX

Abstract This paper reports the results of an analysis of airflow evolution in the tornadic Newcastle–Graham, Texas, storm complex of 29 May 1994. A series of seven pseudo-dual-Doppler analyses from 2242 to 2315 are performed from tail radar observations by the National Oceanic and Atmospheric Administration P-3 aircraft. Subjective analyses of quasi-horizontal single-Doppler radar observations provide a detailed look at structure and evolution of the hook echo and the low-level Newcastle mesocyclone. Special emphasis is placed on the evolution of low-level [i.e., below 1 km above ground level (AGL)] rotation of the parent mesoscale circulation of the Newcastle tornado and the origins of mesoscale rotation preceding tornadogenesis. The structure and evolution of the Newcastle and Graham mesocyclones are compared and contrasted. The airborne Doppler analyses reveal that the tornadic Newcastle cell had supercell characteristics and that the Newcastle storm circulation could be classified as a mesocyclone ba...

Tropical Cyclone Kinematic Structure Retrieved from Single-Doppler Radar Observations. Part III: Evolution and Structures of Typhoon Alex (1987)

Abstract This paper is the third of a series that focuses on the applications of the ground-based velocity track display (GBVTD) technique and the GBVTD-simplex center finding algorithm developed in the previous two papers to a real tropical cyclone (TC). The evolution and structure of Typhoon Alex (1987), including full tangential winds, mean radial winds, one component of the mean flow, and their derived axisymmetric angular momentum and perturbation pressure fields are reconstructed from 16 volume scans (6.5 h of data with a 2-h gap) from the Civil Aeronautic Administration (CAA) Doppler radar while Typhoon Alex moved across the mountainous area in northern Taiwan. This analysis retrieves a plausible and physically consistent three-dimensional primary circulation of a landfalling TC using a single ground-based Doppler radar. Highly asymmetric wind structures were resolved by the GBVTD technique where the maximum relative tangential wind at z = 2 km evolved from 52 m s−1 (before landfall), to less than ...

Tropical Cyclone Kinematic Structure Retrieved from Single-Doppler Radar Observations. Part I: Interpretation of Doppler Velocity Patterns and the GBVTD Technique

Deducing the three-dimensional primary circulation of landfalling tropical cyclones (TCs) from single ground-based Doppler radar data remains a difficult task. The evolution and structure of landfalling TCs and their interactions with terrain are left uncharted due to the lack of dual-Doppler radar observations. Existing ground-based single-Doppler radar TC algorithms provide only qualitative information on axisymmetric TC center location and intensity. In order to improve understanding of the wind structures of landfalling TCs using the widely available WSR-88D data along the U.S. coastal region, a single ground-based radar TC wind retrieval technique, the ground-based Velocity Track Display (GBVTD) technique, is developed. Part I of this paper presents 1) single-Doppler velocity patterns of analytic, asymmetric TCs, 2) derivation of the GBVTD technique, and 3) evaluation of the GBVTD-retrieved winds using analytic TCs. The Doppler velocity patterns of asymmetric TCs display more complex structure than their axisymmetric counterparts. The asymmetric structure of TCs can be inferred qualitatively from the pattern (or curvature) of the zero Doppler velocity line and the position and shape of the Doppler velocity dipole. However, without knowing the axisymmetric portion of the TC circulation, it is extremely difficult to extract quantitative information from these similar Doppler velocity patterns. Systematic evaluations on the GBVTD-retrieved winds show good agreement compared with the original analytic wind fields for axisymmetric flows plus mean wind and/or angular wavenumber 1, 2, and 3 asymmetry. It is also shown that the GBVTD technique retrieves wind maxima that are not directly observed (perpendicular to the radar beams) because the GBVTD technique uses the Doppler velocity gradient, not the observed maxima, to retrieve wind maxima. The success of the GBVTD-retrieved winds and understanding their characteristics provide the theoretical basis to nowcast TC kinematic structure.

低い山脈の風上側に形成された弱風域と上方に発達した降雪雲

When the winter monsoon prevails over the Japan Sea, many shallow convective snow clouds appear in the atmospheric mixed layer, and provide much snow over Japan. The behavior of the snow clouds and airflow affected by a complex terrain in the Tsugaru district of Japan, was studied based on single Doppler-radar observations. At ∼ 15 km upstream of the Tsugaru mountains, which is a low-altitude (200-700 m ASL) ridge, a weak-wind zone accompanied by upward developing snow clouds appeared parallel to the mountains. Above and in the lee of the Tsugaru mountains, the tops of the snow clouds were significantly lower towards the east accompanied with wind acceleration. In accordance with a theory of 2-D two-layer flow passing over a ridge, sonde-observed environmental parameters described a flow regime, where the flow is partially blocked and associated with a hydraulic lee jump. The observed flow pattern was consistent to this theoretical prediction, although the hydraulic lee jump could not be conclusively identified due to observational difficulties. Low-level wind convergence in the front of the weak-wind zone sustained the upward development of the snow clouds. The upward development of the snow clouds, however, did not lead to an obvious increase of snowfall intensity. A WSW to ENE elongated zone of increased snowfall appeared from the north of the Shirakami mountains and Mt. Iwaki (both high-altitude mountains with peaks exceeding 1000 m ASL), to Mutsu Bay, passing through a corridor of the Tsugaru mountains. The orographic effects of the Shirakami mountains, Mt. Iwaki, and the corridor of the Tsugaru mountains were examined with respect to maintaining this elongated snowfall zone.

Comments on “Single-Doppler Radar Observations of a Mini-Supercell Tornadic Thunderstorm”

Comments on “Single-Doppler Radar Observations of a Mini-Supercell Tornadic Thunderstorm”

A Variational Analysis Method for Retrieval of Three-Dimensional Wind Field from Single-Doppler Radar Data

A variational method for retrieval of the three-dimensional wind field from single-Doppler radar observations is developed and tested. The method uses the conservation equation for reflectivity and the continuity equation as a constraining model. Weak and strong constraint formalisms in data analysis am reviewed and compared using a one-dimensional advection equation for reflectivity considered as a passive tracer. The authors show that a model equation should be used as a weak constraint when the model does not predict exactly the evolution of the observations (such as the conservation equation for reflectivity). Consequently, the variational method presented here combines both formalisms: the conservation equation for reflectivity is used as a weak constraint, while the continuity equation is used as a strong constraint. The method is applied to retrieve detailed three-dimensional wind field of a microburst observed by two C-band Doppler radars during the Phoenix II Convective Boundary Layer Experiment. Retrieved wind fields are compared with dual-Doppler wind analysis. Results of experiments show that the cost function has multiple minima, and consequently retrievals are sensitive to the initial guess. To find the true minimum the retrieval is performed from large to small scale. The results are very encouraging.

Fitting Microphysical Observations of Nonsteady Convective Clouds to a Numerical Model: An Application of the Adjoint Technique of Data Assimilation to a Kinematic Model

Abstract Rapid advances in the quality and quantity of atmospheric observations have placed a demand for the development of techniques to assimilate these data sources into numerical forecasting models. Four-dimensional variational assimilation is a promising technique that has been applied to atmospheric and oceanic dynamical models, and to the retrieval of three-dimensional wind fields from single-Doppler radar observations. This study investigates the feasibility of using space–time variational assimilation for a complex discontinuous numerical model including cloud physics. Two test models were developed: a one-dimensional and a two-dimensional liquid physics kinematic microphysical model. These models were used in identical-twin experiments, with observations taken intermittently. Small random errors were introduced into the observations. The retrieval runs were initialized with a large perturbation of the observation run initial conditions. The models were able to retrieve the original initial condi...

A Method of Retrieving Turbulence Parameters from Volume Processing of Single-Doppler Radar Measurements

Abstract In previous work the derivation of turbulence parameters from single-Doppler radar observations was performed with data acquired along a horizontal circle. Here the technique is extended to all the radar data within a horizontal cylindrical slice of finite depth using the same basic assumptions of linearity of the mean wind field and horizontal homogeneity of the turbulence. The method allows the extraction of the six Reynolds stress components, together with their vertical derivatives, and the turbulent fluxes of a scalar quantity deduced from the reflectivity data. Experimental data were used for the performance evaluation of the methodology. A simple testing procedure was carried out to remove erroneous results. The statistical uncertainty in the measured Reynolds stress terms was found to be about 0.05 m2 s−2, except for the variance of the vertical component, which was poorly retrieved because of an absence of data at high elevation angles. Calculations showed that contamination of the verti...

A Midlatitude Squall Line with a Trailing Region of Stratiform Rain: Radar and Satellite Observations

Abstract A squall line exhibiting an extensive trailing region of stratiform precipitation passed over the observational network of the National Severe Storms Laboratory on 22 May 1976. Satellite imagery and conventional radar observations document its evolution from a broken line of thunderstorms to a system of mesoscale proportions, and single-Doppler radar observations describe aspects of its mature structure. Satellite measurements of cloud-top temperature showed the system to be a mesoscale convective complex (MCC). The life cycle of the system exhibited the stages of development seen in tropical cloud clusters. At maturity, two prominent mesoscale flow regimes were identified at midlevels: one marked by inflow into the system's front and continuing toward its rear, and another associated with inflow entering the extreme rear of the system. The rear inflow was associated with a cyclonic midlevel vortex in the stratiform precipitation region. It produced a concavity, or “notch”, in the back edge of th...