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NASA NTRS1998

Global Studies of the Sulfur Cycle Including the Influence of DMS and Fossil Fuel Sulfur on Climate and Climate Change

The indirect effect of anthropogenic aerosols, wherein aerosol particles are thought to increase cloud droplet concentrations and cloud lifetime, is the most uncertain component of climate forcing over the past 100 years. Here, for the first time, we use a mechanistic treatment of droplet nucleation and a prognostic treatment of the number of cloud droplets to study the indirect aerosol effect from changes in carbonaceous and sulfate aerosols. Cloud droplet nucleation is parameterized as a function of total aerosol number concentration, updraft velocity and a shape parameter, which takes into account the mechanism, of sulfate aerosol formation, while cloud droplet number depends on the nucleation as well as on droplet sinks. Whereas previous treatments have predicted annual average indirect effects between -1 and -2 W/sq m, we obtain an indirect aerosol effect between -0.14 W/sq m and -0.42 W/sq m in the global mean.

Penner, Joyce E.↗
NASA NTRS1998

Total Lightning and Radar Storm Characteristics Associated with Severe Storms in Central Florida

This paper examines the three dimensional characteristics of lightning flashes and severe storms observed in Central Florida during 1997-1998. The lightning time history of severe and tornadic storms were captured during the on-going ground validation campaign supporting the Lightning Imaging Sensor (LIS) experiment on the Tropical Rainfall Measuring Mission (TRMM). The ground validation campaign is a collaborative experiment that began in 1997 and involves scientists at the Global Hydrology and Climate Center, MIT/Lincoln Laboratories, and the NWS Forecast Office at Melbourne, FL. Lightning signatures that may provide potential early warning of severe storms are being evaluated by the forecasters at the NWS/MLB office. Severe storms with extreme flash rates sometimes exceeding 300 per minute and accompanying rapid increases in flash rate prior to the onset of the severe weather (hall, damaging winds, tornadoes) have been reported by Hodanish et al. and Williams et al. (1998-this conference). We examine the co-evolving changes in storm structure (mass, echo top, shear, latent heat release) and kinematics associated with these extreme and rapid flash rate changes over time. The flash frequency and density are compared with the three dimensional radar reflectivity structure of the storm to help interpret the possible mechanisms producing the extreme and rapidly increasing flash rates. For two tornadic storms examined thus far, we find the burst of lightning is associated with the development of upper level rotation in the storm. In one case, the lightning burst follows the formation of a bounded weak echo region (BWER). The flash rates diminish with time as the rotation develops to the ground in conjunction with the decent of the reflectivity core. Our initial findings suggest the dramatic increase of flash rates is associated with a sudden and dramatic increase in storm updraft intensity which we hypothesize is stretching vertical vorticity as well as enhancing the development of the mixed phase region of the storm. We discuss the importance of these factors in producing both the observed extreme flash rates and the severe weather that follows in these storms and others to be presented.

Goodman, Steven J↗
NASA NTRS1999

Large Eddy Simulation of Cirrus Clouds

The Regional Atmospheric Modeling System (RAMS) with mesoscale interactive nested-grids and a Large-Eddy Simulation (LES) version of RAMS, coupled to two-moment microphysics and a new two-stream radiative code were used to investigate the dynamic, microphysical, and radiative aspects of the November 26, 1991 cirrus event. Wu (1998) describes the results of that research in full detail and is enclosed as Appendix 1. The mesoscale nested grid simulation successfully reproduced the large scale circulation as compared to the Mesoscale Analysis and Prediction System's (MAPS) analyses and other observations. Three cloud bands which match nicely to the three cloud lines identified in an observational study (Mace et al., 1995) are predicted on Grid #2 of the nested grids, even though the mesoscale simulation predicts a larger west-east cloud width than what was observed. Large-eddy simulations (LES) were performed to study the dynamical, microphysical, and radiative processes in the 26 November 1991 FIRE 11 cirrus event. The LES model is based on the RAMS version 3b developed at Colorado State University. It includes a new radiation scheme developed by Harrington (1997) and a new subgrid scale model developed by Kosovic (1996). The LES model simulated a single cloud layer for Case 1 and a two-layer cloud structure for Case 2. The simulations demonstrated that latent heat release can play a significant role in the formation and development of cirrus clouds. For the thin cirrus in Case 1, the latent heat release was insufficient for the cirrus clouds to become positively buoyant. However, in some special cases such as Case 2, positively buoyant cells can be embedded within the cirrus layers. These cells were so active that the rising updraft induced its own pressure perturbations that affected the cloud evolution. Vertical profiles of the total radiative and latent heating rates indicated that for well developed, deep, and active cirrus clouds, radiative cooling and latent heating could be comparable in magnitude in the cloudy layer. This implies that latent heating cannot be neglected in the construction of a cirrus cloud model. The probability density function (PDF) of w was analyzed to assist in the parameterization of cloud-scale velocities in large-scale models. For the more radiatively-driven, thin cirrus case, the PDFs are approximately Gaussian. However, in the interior of the deep, convectively unstable case, the PDFs of w are multi-modal and very broad, indicating that parameterizing cloud-scale motions for such clouds can be very challenging. The results of this research are described in detail in a paper submitted to the Journal of Atmospheric Science (Wu and Cotton, 1999), which is enclosed as Appendix 2. Using soundings extracted from a mesoscale simulation of the November 26, 1991 cirrus event, the radiative effects on vapor deposition/sublimation of ice crystals was studied using a two-dimensional cloud-resolving model (CRM) version of RAMS, coupled to an explicit bin-resolving microphysics. The CRM simulations of the November 26, 1991 cirrus event demonstrate that the radiative impact on the diffusional growth (or sublimation) of ice crystals is significant. In this case, the ice particles experienced radiative warming. Model results show that radiative feedbacks in the diffusional growth of ice particles can be very complex. Radiative warming of an ice particle will restrict the particle's diffusional growth. In the case of radiative warming, ice particles larger than a certain size will experience so much radiative warming that surface ice saturation vapor pressures become large enough to cause sublimation of the larger crystals, while smaller crystals are growing by vapor deposition. However, ice mass production can be enhanced in the case of radiative cooling of an ice particle. For the November 26, 1991 cirrus event, radiative feedback results in significant reduction in the total ice mass, especially in the production of large ice crystals, and consequently, both radiative and dynamic properties of the cirrus cloud are significantly affected. A complete description of this research has been submitted as a paper to the Journal of Atmospheric Science (Wu et al., 1999), and included as Appendix 3.

Wu, Ting↗
NASA NTRS1999

Airborne Radar Observations of Hurricane Georges during Landfall over the Dominican Republic

On 22 September 1998 hurricane Georges made landfall on the Dominican Republic (DR). Georges cost the DR at least 500 lives, made more than 155,000 people homeless and caused extensive damage to the country's main industries, tourism and agriculture. There was considerable wind damage, with wind gusts up to 58 m/s in Santa Domingo on the south coast, but most of the damage and deaths resulted from mudslides and the flooding of rivers. While this may have been the worst natural disaster to strike the DR, the sustained rapid storm movement saved the island from worse damage. Georges had previously affected several islands in the Lesser Antilles and Puerto Rico, but it had retained much of its circulation strength. Forty raingauge stations across the DR measured rainfall totals from Georges between 0.7 and 41 cm, the latter at the capital Santo Domingo, located on the south coast. At Herrera the maximum 1 h rainfall rate was 72 mm/h. It is suspected that much higher rain rates occurred in DR's mountainous interior. Before landfall the eye was clearly evident in satellite imagery. When the eye moved over southeastern DR, it filled rapidly, and the cloud top height decreased in all storm sectors except in the southern inflow sector, where a long-lived MCS, with a diameter larger than that of the eyewall, slowly became enwrapped in the hurricane circulation. The eye closure was most rapid between 16-18 UTC, when the eyewall circulation felt the mountainous terrain of the Cordillera Central, which rises up to 3,093 m. The estimated central pressure increased from 962 hPa at 15 UTC to 986 hPa at 03Z on 23 Sept, and the maximum sustained surface wind speed decreased from 54 to 36 in s-1 during the same period. The island of Hispaniola has a cross-track width of about 250 km, much wider than the diameter of the eyewall anvil (about 100 km before landfall). So the event can truly be considered to be a landfalling case, even though Georges recovered after crossing Hispaniola, albeit never to the same strength. This talk will summarize satellite and ground observations of Georges, as it passed the DR, and it will focus on EDOP data. In particular, we will try to estimate the rainfall rate over the mountainous terrain of the DR. And we will use detailed sounding data to explain the presence and characteristics of the massive MCS to the south, as well as the upper-level updrafts apparent over this MCS and over the mountains of the DR.

Geerts, B.↗
NASA NTRS1999

Lightning First Pulses Used in the "Last" (Time-of-Arrival) and "Atlas" (Single Station) Total Lightning Mapping Systems

The first RF pulse from "total lightning' discharges (cloud and ground flashes) has been used in different ways to locate the origin of flashes in two new types of lightning detection systems. The multisensor LASI time-of-arrival (TOA) system uses GPS timing of the first pulse. The ATLAS single sensor system uses the amplitude of the first pulse, which is invariant in magnitude and polarization for all lightning discharges, to determine distance from the sensor. It is significantly more accurate than past single sensor lightning mapping systems. The polarity of the first pulse generally identifies lightning type (IC or CG). Both systems utilize only the first pulse which makes signal processing much simpler than with previous lightning locating systems. Knowing the position where lightning begins (maximum electric fields, mixed phase hydrometeors and updrafts) is valuable for identifying convective cells producing the hazardous meteorological conditions caused by thunderstorms. It is also important for research studying thunderstorm electrification and associated microphysical problems.

Markson, Ralph↗
NASA NTRS1999

The Lightning Imaging Sensor

The Lightning Imaging Sensor (LIS) is a NASA Earth Observing System (EOS) instrument on the Tropical Rainfall Measuring Mission (TRMM) platform designed to acquire and investigate the distribution and variability of total lightning (i.e., cloud-to-ground and intracloud) between q35' in latitude. Since lightning is one of the responses of the atmosphere to thermodynamic and dynamic forcing, the LIS data is being used to detect deep convection without land-ocean bias, estimate the precipitation mass in the mixed phased region of thunderclouds, and differentiate storms with strong updrafts from those with weak vertical motion.

Christian, Hugh J.↗
NASA NTRS1999

Hurricane Georges' Landfall in the Dominican Republic: Detailed Airborne Doppler Radar Imagery

Current understanding of landfalling tropical cyclones is limited, especially with regard to convective scale processes. On 22 September 1998 Hurricane Georges made landfall on the island of Hispaniola, leaving behind a trail of death and devastation, largely the result of excessive rainfall, not sea level surge or wind. Detailed airborne measurements were taken as part of the Third Convection and Moisture Experiment (CAMEX-3). Of Particular interest are the ER-2 nadir X-band Doppler radar (EDOP) data, which provide a first-time high-resolution view of the precipitation and airflow changes as a hurricane interacts with mountainous terrain. The circulation of hurricane Georges underwent an obvious transition during landfall, evident in the rapid increase in minimum sea-level pressure, the subsidence of the eyewall anvil, and a decrease in average ice concentrations in the eyewall. The eye, as seen in satellite imagery, disappeared, but contrary to current understanding, this was not due to eyewall contraction but rather to convective eruption within the eye. The main convective event within the eye, with upper-level updraft magnitudes near 20 m/s and 89 GHz brightness temperatures below 100 K, occurred when the eye moved over the Cordillera Central, the island's main mountain chain. The location, intensity and evolution of this convection indicate that it was coupled to the surface orography. It is likely that surface rain rates increased during landfall, because of effective droplet collection, both in the convection and in the more widespread stratiform rainfall areas over the island. Evidence for this is the increase in radar reflectivity below the bright band of 1-2 dB/km down to ground-level. Such increase was absent offshore. Such low-level rain enhancement, which cannot be detected in satellite images of upwelling infrared or microwave radiation, must be due to the ascent of boundary-layer air over the topography.

Geerts, B.↗
NASA NTRS1998

A System Concept for the Advanced Post-TRMM Rainfall Profiling Radars

Atmospheric latent heating field is fundamental to all modes of atmospheric circulation and upper mixed layer circulations of the ocean. The key to understanding the atmospheric heating process is understanding how and where precipitation occurs. The principal atmospheric processes which link precipitation to atmospheric circulation include: (1) convective mass fluxes in the form of updrafts and downdrafts; (2) microphysical. nucleation and growth of hydrometeors; and (3) latent heating through dynamical controls on the gravitation-driven vertical mass flux of precipitation. It is well-known that surface and near-surface rainfall are two of the key forcing functions on a number of geophysical parameters at the surface-air interface. Over ocean, rainfall variation contributes to the redistribution of water salinity, sea surface temperature, fresh water supply, and marine biology and eco-system. Over land, rainfall plays a significant role in rainforest ecology and chemistry, land hydrology and surface runoff. Precipitation has also been closely linked to a number of atmospheric anomalies and natural hazards that occur at various time scales, including hurricanes, cyclones, tropical depressions, flash floods, droughts, and most noticeable of all, the El Ninos. From this point of view, the significance of global atmospheric precipitation has gone far beyond the science arena - it has a far-reaching impact on human's socio-economic well-being and sustenance. These and many other science applications require the knowledge of, in a global basis, the vertical rain structures, including vertical motion, rain intensity, differentiation of the precipitating hydrometeors' phase state, and the classification of mesoscale physical structure of the rain systems. The only direct means to obtain such information is the use of a spaceborne profiling radar. It is important to mention that the Tropical Rainfall Measuring Mission (TRMM) have made a great stride forward towards this ultimate goal. The Precipitation Radar (PR) aboard the TRMM satellite is the first ever spaceborne radar dedicated to three-dimensional, global precipitation measurements over the tropics and the subtropics, as well as the detailed synopsis of a wide range of tropical rain storm systems. In only twelve months since launch, the PR, together with other science instruments abroad the satellite have already provided unprecedented insights into the rainfall systems. It is anticipated the a lot more exciting and important rain observations would be made by TRMM throughout its mission duration. While TRMM has provided invaluable data to the user community, it is only the first step towards advancing our knowledge on rain processes and its contributions to climate variability. It is envisioned that a TRMM follow-on mission is needed in such a way to capitalize on the pioneering information provided by TRMM, and its instrument capability must be extended beyond TRMM in such a way to fully address the key science questions from microphysical to climatic time scale. In fact, a number of new and innovative mission concepts have recently put forth for this purpose. Almost all of these new concepts have suggested the utility of a more advanced, high-resolution, Doppler-enabled, vertical profiling radar that can provide multi-parameter observations of precipitation. In this paper, a system concept for a second- gene ration precipitation radar (PR-2) which addresses the above requirements will be described.

Im, Eastwood↗
NASA NTRS2000

The Estimation of Hydrometeor Profiles from Wideband Microwave Observations

Profiles of the microphysical properties of clouds and raincells are essential in many areas of atmospheric research and operational meteorology. In order to enhance the understanding of the nonlinear and underconstrained relationships between cloud and hydrometeor microphysical profiles and passive microwave brightness temperatures, estimations of cloud profiles for an anvil, a convective, and an updraft region of an oceanic squall were performed. The estimations relied on comparisons between radiative transfer calculations of incrementally estimated microphysical profiles and concurrent dual-altitude wideband brightness temperatures from the 22 February 1993 flight during TOGA-COARE. The wideband observations (10--220 GHz) are necessary for estimating cloud profiles reaching up to 20 km. The low frequencies enhance the rain and cloud water profiles, while the high frequencies are required to detail the higher altitude ice microphysics. A microphysical profile was estimated for each of the three regions of the storm. Each of the three estimated profiles produced calculated brightness temperatures within approximately 10 K of the observations. A majority, of the total iterative adjustment were to the estimated profile's frozen hydrometeor characteristics and were necessary to match the high frequency calculations with the observations. This indicates a need to validate cloud resolving models using high frequencies. Some difficulties matching the 37 GHz observation channels on the DC-8 and ER-2 aircrafts with the calculations simulated at the two aircraft heights (approximately 11 km and 20 km, respectively) were noted and potential causes presented.

Gail M Skofronick-Jackson↗
NASA NTRS2000

Passive Microwave Observations of Hurricanes Bonnie, Danielle, and Georges

During the 1998 hurricane season, three hurricanes were sampled by the Advanced Microwave Precipitation Radiometer (AMPR) which was flown aboard the National Aeronautics and Space Administration (NASA) ER-2 high altitude aircraft during the Third Convection And Moisture EXperiment (CAMEX-3). The ER-2 aircraft was deployed from Patrick Air Force Base, Florida for hurricane missions over the Atlantic Basin and Gulf of Mexico between 6 August - 23 September. Hurricanes Bonnie, Danielle and Georges were each sampled multiple times during several subsequent aircraft missions. The passive microwave observations of these hurricanes collected by the AMPR at 10.7, 19.35, 37.1, and 85.5 GHz frequencies will be presented to explain differences in precipitation features of the hurricanes. In particular, the relationship of the passive microwave signatures of precipitation-sized ice to vertical updraft strength will be examined as a possible indicator of future convective intensity. Correlating aircraft radar information will also be examined to provide further insight.

Hood, Robbie E.↗
NASA NTRS2000

Cirrus Parcel Model Comparison Project

The Cirrus Parcel Model Comparison (CPMC) is a project of the GEWEX Cloud System Study Working Group on Cirrus Cloud Systems (GCSS WG2). The primary goal of this project is to identify cirrus model sensitivities to the state of our knowledge of nucleation and microphysics. Furthermore, the common ground of the findings may provide guidelines for models with simpler cirrus microphysics modules. We focus on the nucleation regimes of the warm (parcel starting at -40 C and 340 hPa) and cold (-60 C and 170 hPa) cases studied in the GCSS WG2 Idealized Cirrus Model Comparison Project. Nucleation and ice crystal growth were forced through an externally imposed rate of lift and consequent adiabatic cooling. The background haze particles are assumed to be lognormally-distributed H2SO4 particles. Only the homogeneous nucleation mode is allowed to form ice crystals in the HN-ONLY runs; all nucleation modes are switched on in the ALL-MODE runs. Participants were asked to run the HN-lambda-fixed runs by setting lambda = 2 (lambda is further discussed in section 2) or tailoring the nucleation rate calculation in agreement with lambda = 2 (exp 1). The depth of parcel lift (800 m) was set to assure that parcels underwent complete transition through the nucleation regime to a stage of approximate equilibrium between ice mass growth and vapor supplied by the specified updrafts.

Lin, Ruei-Fong↗
NASA NTRS2000

Lightning Scaling Laws Revisited

Scaling laws relating storm electrical generator power (and hence lightning flash rate) to charge transport velocity and storm geometry were originally posed by Vonnegut (1963). These laws were later simplified to yield simple parameterizations for lightning based upon cloud top height, with separate parameterizations derived over land and ocean. It is demonstrated that the most recent ocean parameterization: (1) yields predictions of storm updraft velocity which appear inconsistent with observation, and (2) is formally inconsistent with the theory from which it purports to derive. Revised formulations consistent with Vonnegut's original framework are presented. These demonstrate that Vonnegut's theory is, to first order, consistent with observation. The implications of assuming that flash rate is set by the electrical generator power, rather than the electrical generator current, are examined. The two approaches yield significantly different predictions about the dependence of charge transfer per flash on storm dimensions, which should be empirically testable. The two approaches also differ significantly in their explanation of regional variability in lightning observations.

Boccippio, D. J.↗
NASA NTRS2000

Vertical Structure of Stratiform Rain During TEFLUN-B and TRMM-LBA as Derived From an Airborne Radar Perspective

The NASA aircraft instrumented with airborne radars overflew a number of stratiform rain systems during the Texas and Florida Underflights Experiment-B TEFLUN-B) and TRMM-LBA (LBA). TEFLUN-B was conducted near Melbourne Florida during late Summer 1998 for validation of the TRMM satellite. LBA was conducted in Rondonia, Brazil in the Amazon region. Key in these campaigns were the ER-2 and DC-8 aircraft, as well as extensive ground-validation networks including the NCAR S-band (S-POL) polarization radar and University of North Dakota Citation II in situ microphysics measurements. This paper compares the vertical structure of precipitation and vertical motions for four cases: 5 September 1998 and 13 August 1998 during TEFLUN-B and 17 February 1999 and 21 February 1999 during LBA. Both these stratiform systems were within close range of the S-POL radar, and were sampled with downlooking radars and radiometers on the ER-2 (and DC-8 during LBA). Emphasis in the paper is on statistics of the vertical hydrometeor profiles, and their relation to the vertical velocity structure deduced from the ER-2 Doppler Radar (EDOP) measurements. These profiles are used to identify whether growth regions exist as would be expected with mesoscale updrafts often associated with stratiform regions. Finally, rain rates in the stratiform rain derived from EDOP and S-POL are compared.

Heymsfield, Gerald M.↗
NASA NTRS2000

TRMM Observations of Polarization Difference in 85 GHz: Information About Hydrometeors and Rain Rate

Observations made by the Precipitation Radar (PR) and the Microwave Imager (TMI) radiometer on board the Tropical Rainfall Measuring Mission (TRMM) satellite help us to show the significance of the 85 GHz polarization difference, PD85, measured by TMI. Rain type, convective or stratiform, deduced from the PR allows us to infer that PD85 is generally positive in stratiform rain clouds, while PD85 can be markedly negative in deep convective rain clouds. Furthermore, PD85 increases in a gross manner as stratiform rain rate increases. On the contrary, in a crude fashion PD85 decreases as convective rain rate increases. From the observations of TMI and PR, we find that PD85 is a weak indicator of rain rate. Utilizing information from existing polarimetric radar studies, we infer that negative values of PD85 are likely associated with vertically-oriented small oblate or wet hail that are found in deep convective updrafts.

Prabhakara, C.↗
NASA NTRS2000

Possible Importance of Convection Near the Tropical Tropopause

Most studies of convection and its interaction with the large-scale behavior of the atmosphere focus on the convective heating and drying in the troposphere up to perhaps 15 km. Above this, effects become difficult to measure and are sometimes assumed to vanish. Here I discuss the possible effects of overshooting and irreversible mixing above the level of neutral buoyancy of convective updrafts. These effects should include cooling and drying of the atmosphere near the tropopause. Observational and model support exists for each of these. An argument can be made that the relative role played by the details of convective physics and microphysics in influencing gross atmospheric behavior may be greater and more observable near the tropopause than it is at lower levels in the troposphere where most of the attention has been directed. This has implications not only for our understanding of the tropical tropopause region, but also for where we should be looking to learn more about the physics of convection itself and to obtain observations that can usefully discriminate between different schemes for representing convection in large-scale models.

Sherwood, Steven C.↗
NASA NTRS2001

Measurement of Attenuation with Airborne and Ground-Based Radar in Convective Storms Over Land and Its Microphysical Implications

Observations by the airborne X-band Doppler radar (EDOP) and the NCAR S-band polarimetric (S-POL) radar from two field experiments are used to evaluate the Surface ref'ercnce technique (SRT) for measuring the path integrated attenuation (PIA) and to study attenuation in deep convective storms. The EDOP, flying at an altitude of 20 km, uses a nadir beam and a forward pointing beam. It is found that over land, the surface scattering cross-section is highly variable at nadir incidence but relatively stable at forward incidence. It is concluded that measurement by the forward beam provides a viable technique for measuring PIA using the SRT. Vertical profiles of peak attenuation coefficient are derived in vxo deep convective storms by the dual-wavelength method. Using the measured Doppler velocity, the reflectivities at. the two wavelengths, the differential reflectivity and the estimated attenuation coefficients, it is shown that: supercooled drops and dry ice particles probably co-existed above the melting level in regions of updraft, that water-coated partially melted ice particles probably contributed to high attenuation below the melting level, and that the data are not readil~ explained in terms of a gamma function raindrop size distribution.

Tian, Lin↗
NASA NTRS2001

Measurement of Attenuation with Airborne and Ground-Based Radar in Convective Storms Over Land Its Microphysical Implications

Observations by the airborne X-band Doppler radar (EDOP) and the NCAR S-band polarimetric (S-Pol) radar from two field experiments are used to evaluate the surface reference technique (SRT) for measuring the path integrated attenuation (PIA) and to study attenuation in deep convective storms. The EDOP, flying at an altitude of 20 km, uses a nadir beam and a forward pointing beam. It is found that over land, the surface scattering cross-section is highly variable at nadir incidence but relatively stable at forward incidence. It is concluded that measurement by the forward beam provides a viable technique for measuring PIA using the SRT. Vertical profiles of peak attenuation coefficient are derived in two deep convective storms by the dual-wavelength method. Using the measured Doppler velocity, the reflectivities at the two wavelengths, the differential reflectivity and the estimated attenuation coefficients, it is shown that: supercooled drops and (dry) ice particles probably co-existed above the melting level in regions of updraft, that water-coated partially melted ice particles probably contributed to high attenuation below the melting level.

Tian, Lin↗