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Alessandro Battaglia and Pavlos Kollias

Abstract

An error budget analysis is performed for retrieval of along-track winds based on the design of a spaceborne Doppler radar using polarization diversity. The analysis is conducted within the framework of a case study of an Atlantic hurricane. The proposed concept consists of either a Ka-band or W-band stereoradar mounted on an LEO satellite equipped with both nadir- and forward-viewing beams and with an optional cross-scanning capability. Such a radar design is intended for observing the microphysical and dynamical structures of cloud systems, including disturbed mesoscale convective systems. Because of the high winds involved in such weather phenomena and because of the Doppler fading introduced by platform motion, polarization diversity is adopted. The simulation framework enables a breakdown of the Doppler velocity measurement error budget into its most important components, that is, nonuniform beamfilling, multiple scattering, and inherent signal noise. The impact of each of these error terms on the total error depends on the adopted integration length, the number of scanned tracks, and the specifics of the radar. This allows for optimally selecting an integration length suitable for minimizing the total rms velocity error. The analysis shows that the use of a large antenna could achieve impressive measurement accuracy of the along-line-of-sight wind velocities. Notably, this would be the case for integration lengths longer than 3 km, even when carrying out cross-track scanning for up to 17 separate tracks. Examples of retrieved along-track wind fields also reveal that the large antenna configurations are capable of identifying and quantifying the foremost dynamic features (e.g., vertical wind shear and convergence/divergence regions).

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Robin J. Hogan and Alessandro Battaglia

Abstract

Spaceborne lidar returns from liquid water clouds contain significant contributions from photons that have experienced many wide-angle multiple-scattering events, resulting in returns appearing to originate from far beyond the end of the cloud. A similar effect occurs for spaceborne millimeter-wave radar observations of deep convective clouds. An efficient method is described for calculating the time-dependent returns from such a medium by splitting the photons into those that have taken a near-direct path out to and back from a single backscattering event (in the case of lidar, accounting for small-angle forward scatterings on the way, as described in Part I of this paper) and those that have experienced wide-angle multiple-scattering events. This paper describes the modeling of the latter using the time-dependent two-stream approximation, which reduces the problem to solving a pair of coupled partial differential equations for the energy of the photons traveling toward and away from the instrument. To determine what fraction of this energy is detected by the receiver, the lateral variance of photon position is modeled by the Ornstein–Fürth formula, in which both the ballistic and diffusive limits of photon behavior are treated; this is considerably more accurate than simple diffusion theory. By assuming that the lateral distribution can be described by a Gaussian, the fraction of photons within the receiver field of view may be calculated. The method performs well in comparison to Monte Carlo calculations (for both radar and lidar) but is much more efficient. This opens the way for multiple scattering to be accounted for in radar and lidar retrieval schemes.

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Sergey Y. Matrosov, Alessandro Battaglia, and Peter Rodriguez

Abstract

An attenuation-based method to retrieve vertical profiles of rainfall rates from height derivatives/gradients of CloudSat nadir-pointing W-band reflectivity measurements is discussed. This method takes advantage of the high attenuation of W-band frequency signals in rain and the low variability of nonattenuated reflectivity due to strong non-Rayleigh scattering from rain drops. The retrieval uncertainties could reach 40%–50%. The suggested method is generally applicable to rainfall rates (R) in an approximate range from about 2–3 to about 20–25 mm h−1. Multiple scattering noticeably affects the gradients of CloudSat measurements for R values greater than about 5 mm h−1. To avoid a retrieval bias caused by multiple-scattering effects, a special correction for retrievals is introduced. For rainfall rates greater than about 25 mm h−1, the influence of multiple scattering gets overwhelming, and the retrievals become problematic, especially for rainfalls with higher freezing-level altitudes. The attenuation-based retrieval method was applied to experimental data from CloudSat covering the range of rainfall rates. CloudSat retrievals were compared to the rainfall estimates available from a National Weather Service ground-based scanning precipitation radar operating at S band. Comparisons between spaceborne and conventional radar rainfall retrievals were generally in good agreement and indicated the mutual consistency of both quantitative precipitation estimate types. The suggested CloudSat rainfall retrieval method is immune to the absolute calibration of the radar and to attenuation caused by the melting layer and snow regions. Since it does not require surface returns, it is applicable to measurements above both land and water surfaces.

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Daniel Watters, Alessandro Battaglia, and Richard P. Allan

Abstract

NASA Precipitation Measurement Mission observations are used to evaluate the diurnal cycle of precipitation from three CMIP6 models (NCAR-CESM2, CNRM-CM6-1, CNRM-ESM2-1) and the ERA5 reanalysis. NASA’s global-gridded IMERG product, which combines spaceborne microwave radiometer, infrared sensor and ground-based gauge measurements, provides high spatio-temporal resolution (0.1°, half-hourly) estimates that are suitable for evaluating the diurnal cycle in models, as determined against the CONUS ground-based radar network. IMERG estimates are coarsened to the spatial and hourly resolution of the state-of-the-art CMIP6 and ERA5 products, and their diurnal cycles are compared across multiple decades of June-July-August in the 60°N–S domain (IMERG and ERA5: 2000–2019; NCAR and CNRM: 1979–2008). Low precipitation regions (and weak amplitude regions when analyzing the diurnal phase) are excluded from analyses in order to assess only robust diurnal signals. Observations identify greater diurnal amplitudes over land (26–134% of the precipitation mean; 5th–95th percentile) than over ocean (14–66%). ERA5, NCAR and CNRM underestimate amplitudes over ocean, whilst ERA5 overestimates over land. IMERG observes a distinct diurnal cycle only in certain regions, with precipitation peaking broadly between 14–21 LST over land (21–6 LST over mountainous and varying-terrain regions) and 0–12 LST over ocean. The simulated diurnal cycle is unrealistically early compared with observations, particularly over land (NCAR-CESM2-AMIP: –1 hour; ERA5: –2 hours; CNRM-CM6-1-AMIP: –4 hours on average) with nocturnal maxima not well represented over mountainous regions. Furthermore, ERA5’s representation of the diurnal cycle is too simplified, with less interannual variability in the time of maximum compared to observations over many regions.

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Prabhat K. Koner, Alessandro Battaglia, and Clemens Simmer

Abstract

A dynamic regularization scheme for rain-rate retrievals from attenuated radar measurements is presented. Most regularization techniques, including the optimal estimation method, use the state-space parameters to regularize the problem, which will always lead to a bias in the solution. To avoid this problem the authors introduce an evolutionary regularization technique, which is based on the spatial derivative of the measured reflectivity profile and allows for a bias-free global solution. The regularization strength is determined by the quadratic eigenvalue solution using the regularized total least squares method. With the new method, the authors perform a retrieval of rain-rate profiles from simulated measurements of a nadir-pointing W-band (94 GHz) radar, in a configuration similar to the cloud radar employed on CloudSat. The simulations assume that multiple scattering is negligible and only liquid hydrometeors are taken into account. The authors compare the results of this method with the outcome of an optimal estimation method and demonstrate that their method is superior in terms of reliability, correlation coefficient, and dispersion to the optimal estimation method for layers experiencing high values of attenuation; therefore, the a priori bias typical for optimal estimation solutions is avoided.

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Alessandro Battaglia, Simone Tanelli, and Pavlos Kollias

Abstract

Spaceborne Doppler radars have the potential to provide key missing observations of convective vertical air motions especially over the tropical oceans. Such measurements can improve understanding of the role of tropical convection in vertical energy transport and its interaction with the environment. Several millimeter wavelength Doppler radar concepts have been proposed since the 1990s. The Earth Clouds, Aerosols, and Radiation Explorer (EarthCARE) Cloud Profiling Radar (CPR) will be the first Dopplerized atmospheric radar in space but has not been optimized for Doppler measurements in deep convective clouds.

The key challenge that constrains the CPR performance in convective clouds is the range–Doppler dilemma. Polarization diversity (PD) offers a solution to this constraint by decoupling the coherency (Doppler) requirement from the unambiguous range requirement. Careful modeling of the radar signal depolarization and its impact on radar receiver channel cross talk is needed to accurately assess the performance of the PD approach.

The end-to-end simulator presented in this work allows reproduction of the signal sensed by a Doppler radar equipped with polarization diversity when overpassing realistic three-dimensional convective cells, with all relevant cross-talk sources accounted for. The notional study highlights that multiple scattering is the primary source of cross talk, highly detrimental for millimeter Doppler velocity accuracy. The ambitious scientific requirement of 1 m s−1 accuracy at 500-m integration for reflectivities above −15 dBZ are within reach for a W-band radar with a 2.5-m antenna with optimal values of the pulse-pair interval between 20 and 30 μs but only once multiple scattering and ghost-contaminated regions are screened out. The identification of such areas is key for Doppler accuracies and can be achieved by employing an interlaced pulse-pair mode that measures the cross and the copolar reflectivities. To mitigate the impact of attenuation and multiple scattering, the Ka band has been considered as either alternative or additional to the W band. However, a Ka system produces worse Doppler performances than a W-band system with the same 2.5-m antenna size. Furthermore, in deep convection it results in similar levels of multiple scattering and therefore it does not increase significantly the depth of penetration. In addition, the larger footprint causes stronger nonuniform beam-filling effects. One advantage of the Ka-band option is the larger Nyquist velocity that tends to reduce the Doppler accuracies. More significant benefits are derived from the Ka band when observing precipitation not as intense as the deep convection is considered here.

This study demonstrates that polarization diversity indeed represents a very promising methodology capable of significantly reducing aliasing and Doppler moment estimate errors, two main error sources for Doppler velocity estimates in deep convective systems and a key step to achieving typical mission requirements for convection-oriented millimeter radar-based spaceborne missions.

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Alessandro Battaglia, Satoru Kobayashi, Simone Tanelli, Clemens Simmer, and Eastwood Im

Abstract

In this paper, two different numerical methods capable of computing multiple scattering effects in pulsed-radar systems are compared. Both methods are based on the solution of the time-dependent vectorial form of the radiative transfer equation: one exploits the successive order of scattering approximation, the other a forward Monte Carlo technique.

Different benchmark results are presented (including layers of monodisperse spherical water and ice particles), which are of specific interest for W-band spaceborne cloud radars such as CloudSat’s or EarthCARE’s cloud profiling radars. Results demonstrate a good agreement between the two methods. The pros and cons of the two models are discussed, with a particular focus on the validity of the second order of scattering approximation.

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Daniel Watters, Alessandro Battaglia, Kamil Mroz, and Frédéric Tridon

Abstract

Instantaneous surface rain rate estimates from the Global Precipitation Measurement (GPM) mission’s Dual-Frequency Precipitation Radar (DPR) and combined DPR and multifrequency microwave imager (CMB) version-5 products are compared to those from the Met Office Radarnet 4 system’s Great Britain and Ireland (GBI) radar composite product. The spaceborne and ground-based rainfall products are collocated spatially and temporally and compared at 5- and 25-km resolutions over GBI during a 3-yr period (from May 2014 to April 2017). The comparison results are evaluated as a function of both the intensity and variability of precipitation within the DPR field of view and are stratified spatially and seasonally. CMB and DPR products underestimate rain rates with respect to the Radarnet product by 21% and 31%, respectively, when considering 25-km resolution data taken within 75 km of a ground-based radar. Large variability in the discrepancies between spaceborne and ground-based rain rate estimates is the result of limitations of both systems and random errors in the collocation of their measurements. The Radarnet retrieval is affected by issues with measuring the vertical extent of precipitation at far ranges, while the GPM system struggles in properly quantifying orographic precipitation. Part of the underestimation by the GPM products appears to be a consequence of an erroneous DPR clutter identification in the presence of low freezing levels. Both products are susceptible to seasonal variations in performance and decreases in precision with increased levels of heterogeneity within the instruments’ field of view.

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Alessandro Battaglia, Elke Rustemeier, Ali Tokay, Ulrich Blahak, and Clemens Simmer

Abstract

The performance of the laser-optical Particle Size Velocity (PARSIVEL) disdrometer is evaluated to determine the characteristics of falling snow. PARSIVEL’s measuring principle is reexamined to detect its limitations and pitfalls when applied to solid precipitation. This study uses snow observations taken during the Canadian Cloudsat/Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) Validation Project (C3VP) campaign, when two PARSIVEL instruments were collocated with a single two-dimensional disdrometer (2-DVD), which allows more detailed observation of snowflakes. When characterizing the snowflake size, PARSIVEL instruments inherently retrieve only one size parameter, which is approximately equal to the widest horizontal dimension (more accurately with large snowflakes) and that has no microphysical meaning. Unlike for raindrops, the equivolume PARSIVEL diameter—the PARSIVEL output variable—has no physical counterpart for snowflakes.

PARSIVEL’s fall velocity measurement may not be accurate for a single snowflake particle. This is due to the internally assumed relationship between horizontal and vertical snow particle dimensions. The uncertainty originates from the shape-related factor, which tends to depart more and more from unity with increasing snowflake sizes and can produce large errors. When averaging over a large number of snowflakes, the correction factor is size dependent with a systematic tendency to an underestimation of the fall speed (but never exceeding 20%).

Compared to a collocated 2-DVD for long-lasting events, PARSIVEL seems to overestimate the number of small snowflakes and large particles. The disagreement between PARSIVEL and 2-DVD snow measurements can only be partly ascribed to PARSIVEL intrinsic limitations (border effects and sizing problems), but it has to deal with the difficulties and drawbacks of both instruments in fully characterizing snow properties.

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Alessandro Battaglia, Simone Tanelli, Gerald M. Heymsfield, and Lin Tian

Abstract

Deep convective systems observed by the High Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar during the 2011 Midlatitude Continental Convective Clouds Experiment (MC3E) field campaign in Oklahoma provide the first evidence of multiple-scattering effects simultaneously at Ku and Ka band. One feature is novel and noteworthy: often, in correspondence to shafts with strong convection and when moving from the top of the cloud downward, the dual wavelength ratio (DWR) first increases as usual in KuKa-band observations, but then it reaches a maximum and after that point it steadily decreases all the way to the surface, forming what will be hereinafter referred to as a knee. This DWR knee cannot be reproduced by single-scattering theory under almost any plausible cloud microphysical profile. On the other hand, it is explained straightforwardly with the help of multiple-scattering theory when simulations involving hail-bearing convective cores with large horizontal extents are performed. The DWR reduction in the lower troposphere (i.e., DWR increasing with altitude) is interpreted as the result of multiple-scattering pulse stretching caused by the highly diffusive hail layer positioned high up in the atmosphere, with Ka multiple scattering typically exceeding that occurring in the Ku channel. Since the effects of multiple scattering increase with increasing footprint size, if multiple-scattering effects are present in the aircraft measurements, they are likely to be more pronounced in the spaceborne dual-frequency Ku–Ka radar observations, envisaged for the NASA–Japan Aerospace Exploration Agency (JAXA) Global Precipitation Measurement (GPM) Mission, launched in February 2014. This notional study supports the idea that DWR knees will be observed by the GPM radar when overflying high-density ice shafts embedded in large convective systems and suggests that their explanation must not be sought in differential attenuation or differential Mie effects but via multiple-scattering effects.

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