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At least 289 records · Page 16

The Diurnal Cycle of Precipitation and Organized Convection in a Set of Global Mesoscale Simulations with the NASA GEOS AGCM

The NASA Global Modeling and Assimilation Office (GMAO) has conducted a series of 40-day nonhydrostatic global simulations with horizontal grid spacing ranging from 200 km to 3 km, as part of the DYAMOND model intercomparison project. The Goddard Earth Observing System (GEOS) model was run with the Grell-Freitas scale-aware convection scheme, which smoothly reduces parameterized deep convection with increasing resolution. Here we evaluate the diurnal cycle and other statistics of precipitation and organized convection as a function of resolution. For validation we use the 0.1 degree IMERG precipitation and 4 km Merged IR brightness temperature datasets, focusing on four regions: the continental United States, Amazonia, the equatorial Indian ocean, and the Maritime Continent. Early results indicate good phase agreement but excessive magnitude of the continental diurnal cycle of precipitation at coarser resolutions, with improved magnitude as resolution increases and the role of parameterization is reduced. Convective cloud clusters are identified with a brightness temperature threshold, and we find realistic numbers of the largest clusters (>10^4 km sq) at all resolutions, while the number of smaller clusters increases with resolution, approaching observations when dx=3 km. The observed diurnal cycle in the cluster size distribution is also reproduced, with realistic magnitude in the highest resolution runs. Precipitation characteristics across cluster sizes are also examined. The results show the potential for global mesoscale simulations as a community science resource, and we invite collaboration to explore these runs in greater detail.

Arnold, Nathan↗

Statistics of Cloud Optical Properties from Airborne Lidar Measurements

Cloud optical properties, such as extinction-to-backscatter ratio and depolarization ratio, have a significant impact on the accuracy of cloud extinction retrievals from lidar systems because parameterizations of these variables are often used in non-ideal conditions to determine cloud type and optical depth. Statistics and trends of these optical parameters were analyzed for four years, 2003-2007, of Cloud Physics Lidar data during five projects of varying geographic locations. Extinction-to-backscatter ratio (at 532 nm) was derived by calculating the transmission loss through the cloud layer, while depolarization ratio was computed using the parallel and perpendicular polarized 1064 nm channels. The majority of the cloud layers yielded an S-ratio between 10 and 40 sr with the S-ratio frequency distribution centered at 25 sr for ice clouds, 21 sr for mixed phase clouds, and 11 sr for water clouds. On average for ice clouds, S ratio slightly decreased with decreasing temperature, while depolarization ratio increased significantly as temperatures decreased. Trends for water and mixed phase clouds were also observed. Ultimately, these observed trends in optical properties as a function of temperature and geographic location will improve current parameterizations of extinction-to-backscatter ratio, which consequently increases accuracy in cloud optical depth and radiative forcing estimates.

Yorks, John E.↗

Tropical Oceanic Precipitation Processes over Warm Pool: 2D and 3D Cloud Resolving Model Simulations

Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere, The vertical distribution of convective latent-heat release modulates the large-scale circulations of the tropics, Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate models simulate cloud processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMS) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and cloud systems, The major objective of this paper is to investigate the latent heating, moisture and momenti,im budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (CCE) model which includes a 3-class ice-phase microphysical scheme, The model domain contains 256 x 256 grid points (using 2 km resolution) in the horizontal and 38 grid points (to a depth of 22 km depth) in the vertical, The 2D domain has 1024 grid points. The simulations are performed over a 7 day time period. We will examine (1) the precipitation processes (i.e., condensation/evaporation) and their interaction with warm pool; (2) the heating and moisture budgets in the convective and stratiform regions; (3) the cloud (upward-downward) mass fluxes in convective and stratiform regions; (4) characteristics of clouds (such as cloud size, updraft intensity and cloud lifetime) and the comparison of clouds with Radar observations. Differences and similarities in organization of convection between simulated 2D and 3D cloud systems. Preliminary results indicated that there is major differences between 2D and 3D simulated stratiform rainfall amount and convective updraft and downdraft mass fluxes.

Tao, W.- K.↗

Radiative Flux and Forcing Parameterization Error in Aerosol-Free Clear Skies

This article reports on the accuracy in aerosol- and cloud-free conditions of the radiation parameterizations used in climate models. Accuracy is assessed relative to observationally validated reference models for fluxes under present-day conditions and forcing (flux changes) from quadrupled concentrations of carbon dioxide. Agreement among reference models is typically within 1 W/m2, while parameterized calculations are roughly half as accurate in the longwave and even less accurate, and more variable, in the shortwave. Absorption of shortwave radiation is underestimated by most parameterizations in the present day and has relatively large errors in forcing. Error in present-day conditions is essentially unrelated to error in forcing calculations. Recent revisions to parameterizations have reduced error in most cases. A dependence on atmospheric conditions, including integrated water vapor, means that global estimates of parameterization error relevant for the radiative forcing of climate change will require much more ambitious calculations.

Climate↗

Assimilation of Satellite Data in Regional Air Quality Models

In terms of important uncertainty in regional-scale air-pollution models, probably no other aspect ranks any higher than the current ability to specify clouds and soil moisture on the regional scale. Because clouds in models are highly parameterized, the ability of models to predict the correct spatial and radiative characteristics is highly suspect and subject to large error. The poor representation of cloud fields from point measurements at National Weather Services stations and the almost total absence of surface moisture availability observations has made assimilation of these variables difficult to impossible. Yet, the correct inclusion of clouds and surface moisture are of first-order importance in regional-scale photochemistry.

SPATIAL DISTRIBUTION↗

FIRE Science Results 1988

FIRE (First ISCCP Regional Experiment) is a U.S. cloud-radiation program that seeks to address the issues of a basic understanding and parameterizations of cirrus and marine stratocumulus cloud systems and ISCCP data products. The papers describe research analysis of data collected at the 1986 Cirrus Intensive Field Observations (IFO), the 1987 Marine Stratocumulus IFO, and the Extended Time Observations. The papers are grouped into sessions on satellite studies, lidar/radiative properties/microphysical studies, radiative properties, thermodynamic and dynamic properties, case studies, and large scale environment and modeling studies.

Mcdougal, David S.↗

Development and Testing of Coupled Land-surface, PBL and Shallow/Deep Convective Parameterizations within the MM5

The objective of this investigation was to study the role of shallow convection on the regional water cycle of the Mississippi and Little Washita Basins using a 3-D mesoscale model, the PSUINCAR MM5. The underlying premise of the project was that current modeling of regional-scale climate and moisture cycles over the continents is deficient without adequate treatment of shallow convection. It was hypothesized that an improved treatment of the regional water cycle can be achieved by using a 3-D mesoscale numerical model having a detailed land-surface parameterization, an advanced boundary-layer parameterization, and a more complete shallow convection parameterization than are available in most current models. The methodology was based on the application in the MM5 of new or recently improved parameterizations covering these three physical processes. Therefore, the work plan focused on integrating, improving, and testing these parameterizations in the MM5 and applying them to study water-cycle processes over the Southern Great Plains (SGP): (1) the Parameterization for Land-Atmosphere-Cloud Exchange (PLACE) described by Wetzel and Boone; (2) the 1.5-order turbulent kinetic energy (TKE)-predicting scheme of Shafran et al.; and (3) the hybrid-closure sub-grid shallow convection parameterization of Deng. Each of these schemes has been tested extensively through this study and the latter two have been improved significantly to extend their capabilities.

Stauffer, David R.↗

Tropical Oceanic Precipitation Processes Over Warm Pool: 2D and 3D Cloud Resolving Model Simulations

Rainfall is a key link in the hydrologic cycle as well as the primary heat source for the atmosphere. The vertical distribution of convective latent-heat release modulates the large-scale circulations of the topics. Furthermore, changes in the moisture distribution at middle and upper levels of the troposphere can affect cloud distributions and cloud liquid water and ice contents. How the incoming solar and outgoing longwave radiation respond to these changes in clouds is a major factor in assessing climate change. Present large-scale weather and climate model simulate processes only crudely, reducing confidence in their predictions on both global and regional scales. One of the most promising methods to test physical parameterizations used in General Circulation Models (GCMs) and climate models is to use field observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and physically realistic parameterizations of cloud microphysical processes, and allow for their complex interactions with solar and infrared radiative transfer processes. The CRMs can reasonably well resolve the evolution, structure, and life cycles of individual clouds and clouds systems. The major objective of this paper is to investigate the latent heating, moisture and momentum budgets associated with several convective systems developed during the TOGA COARE IFA - westerly wind burst event (late December, 1992). The tool for this study is the Goddard Cumulus Ensemble (GCE) model which includes a 3-class ice-phase microphysics scheme.

Tao, W.-K.↗

Importance of Ice Nucleation and Precipitation on Climate With the Parameterization of Unified Microphysics Across Scales Version 1 (PUMASv1)

Cloud microphysics is critical for weather and climate prediction. In this work, we document updates and corrections to the cloud microphysical scheme used in the Community Earth System Model (CESM) and other models. These updates include a new nomenclature for the scheme, now called Parameterization of Unified Microphysics Across Scales (PUMAS), and the ability to run the scheme on graphics processing units (GPUs). The main science changes include refactoring an ice number limiter and associated changes to ice nucleation, adding vapor deposition onto snow, and introducing an implicit numerical treatment for sedimentation. We also detail the improvements in computational performance that can be achieved with GPU acceleration. We then show the impact of these scheme changes on the (a) mean state climate, (b) cloud feedback response to warming, and (c) aerosol forcing. We find that corrections are needed to the immersion freezing parameterization and that ice nucleation has important impacts on climate. We also find that the revised scheme produces less cloud liquid and ice but that this can be adjusted by changing the loss process for cloud liquid (autoconversion). Furthermore, there are few discernible effects of the PUMAS changes on cloud feedbacks but some reductions in the magnitude of aerosol–cloud interactions (ACIs). Small cloud feedback changes appear to be related to the implicit sedimentation scheme, with a number of factors affecting ACIs.

Clouds↗

The parameterization of the planetary boundary layer in the UCLA general circulation model - Formulation and results

A planetary boundary layer (PBL) parameterization for general circulation models (GCMs) is presented. It uses a mixed-layer approach in which the PBL is assumed to be capped by discontinuities in the mean vertical profiles. Both clear and cloud-topped boundary layers are parameterized. Particular emphasis is placed on the formulation of the coupling between the PBL and both the free atmosphere and cumulus convection. For this purpose a modified sigma-coordinate is introduced in which the PBL top and the lower boundary are both coordinate surfaces. The use of a bulk PBL formulation with this coordinate is extensively discussed. Results are presented from a July simulation produced by the UCLA GCM. PBL-related variables are shown, to illustrate the various regimes the parameterization is capable of simulating.

Suarez, M. J.↗

NASA Goddard Earth Sciences Graduate Student Program

The evolution of synoptic-scale dynamics associated with a middle and upper tropospheric cloud event that occurred on 26 November 1991 is examined. The case under consideration occurred during the FIRE CIRRUS-II Intensive Field Observing Period held in Coffeyville, KS during Nov. and Dec., 1991. Using data from the wind profiler demonstration network and a temporally and spatially augmented radiosonde array, emphasis is given to explaining the evolution of the kinematically-derived ageostrophic vertical circulations and correlating the circulation with the forcing of an extensively sampled cloud field. This is facilitated by decomposing the horizontal divergence into its component parts through a natural coordinate representation of the flow. Ageostrophic vertical circulations are inferred and compared to the circulation forcing arising from geostrophic confluence and shearing deformation derived from the Sawyer-Eliassen Equation. It is found that a thermodynamically indirect vertical circulation existed in association with a jet streak exit region. The circulation was displaced to the cyclonic side of the jet axis due to the orientation of the jet exit between a deepening diffluent trough and building ridge. The cloud line formed in the ascending branch of the vertical circulation with the most concentrated cloud development occurring in conjunction with the maximum large-scale vertical motion. The relationship between the large scale dynamics and the parameterization of middle and upper tropospheric clouds in large-scale models is discussed and an example of ice water contents derived from a parameterization forced by the diagnosed vertical motions and observed water vapor contents is presented.

Ackerman, Thomas P.↗

Extended field observations of cirrus clouds using a ground-based cloud observing system

The evolution of synoptic-scale dynamics associated with a middle and upper tropospheric cloud event that occurred on 26 November 1991 is examined. The case under consideration occurred during the FIRE CIRRUS-II Intensive Field Observing Period held in Coffeyville, KS during Nov. and Dec., 1991. Using data from the wind profiler demonstration network and a temporally and spatially augmented radiosonde array, emphasis is given to explaining the evolution of the kinematically-derived ageostrophic vertical circulations and correlating the circulation with the forcing of an extensively sampled cloud field. This is facilitated by decomposing the horizontal divergence into its component parts through a natural coordinate representation of the flow. Ageostrophic vertical circulations are inferred and compared to the circulation forcing arising from geostrophic confluence and shearing deformation derived from the Sawyer-Eliassen Equation. It is found that a thermodynamically indirect vertical circulation existed in association with a jet streak exit region. The circulation was displaced to the cyclonic side of the jet axis due to the orientation of the jet exit between a deepening diffluent trough and building ridge. The cloud line formed in the ascending branch of the vertical circulation with the most concentrated cloud development occurring in conjunction with the maximum large-scale vertical motion. The relationship between the large scale dynamics and the parameterization of middle and upper tropospheric clouds in large-scale models is discussed and an example of ice water contents derived from a parameterization forced by the diagnosed vertical motions and observed water vapor contents is presented.

Ackerman, Thomas P.↗

Stratiform clouds and their interaction with atmospheric motion

During 1989 and 1990, the researchers saw the publication of two papers and the submission of a third for review on work supported primarily by the previous contract, NAS8-36150; the delivery of an invited talk at the SIAM Conference on Dynamical Systems in Orlando, Florida; and the start of two new projects on the radiative effects of stratocumulus on the large-scale flow. The published papers discuss aspects of stratocumulus circulations (Laufersweiler and Shirer, 1989) and the Hadley to Rossby regime transition in rotating spherical systems (Higgins and Shirer, 1990). The submitted paper (Haack and Shirer, 1990) discusses a new nonlinear model of roll circulations that are forced both dynamically and thermally. The invited paper by H. N. Shirer and R. Wells presented an objective means for determining appropriate truncation levels for low-order models of flows involving two incommensurate periods; this work has application to the Hadley to Rossby transition problem in quasi-geostrophic flows (Moroz and Holmes, 1984). The new projects involve the development of a multi-layered quasi-geostrophic channel model for study of the modulation of the large-scale flow by stratocumulus clouds that typically develop off the coasts of continents. In this model the diabatic forcing in the lowest layer will change in response to the (parameterized) development of extensive fields of stratocumulus clouds. To guide creation of this parameterization scheme, researchers are producing climatologies of stratocumulus frequency and the authors correlate these frequencies with the phasing and amplitude of the large-scale flow pattern. Researchers discuss the above topics in greater detail.

Clark, John H. E.↗

Mesoscale Convective Systems in SCSMEX: Simulated by a Regional Climate Model and a Cloud Resolving Model

A Regional Land-Atmosphere Climate Simulation (RELACS) System is being developed and implemented at NASA Goddard Space Flight Center. One of the major goals of RELACS is to use a regional scale model with improved physical processes, in particular land-related processes, to understand the role of the land surface and its interaction with convection and radiation as well as the water and energy cycles in Indo-China/South China Sea (SCS)/China, North America and South America. The Penn State/NCAR MM5 atmospheric modeling system, a state of the art atmospheric numerical model designed to simulate regional weather and climate, has been successfully coupled to the Goddard Parameterization for Land-Atmosphere-Cloud Exchange (PLACE) land surface model, PLACE allows for the effect A vegetation, and thus important physical processes such as evapotranspiration and interception are included. The PLACE model incorporates vegetation type and has been shown in international comparisons to accurately predict evapotranspiration and runoff over a wide variety of land surfaces. The coupling of MM5 and PLACE creates a numerical modeling system with the potential to more realistically simulate the atmosphere and land surface processes including land-sea interaction, regional circulations such as monsoons, and flash flood events. RELACS has been used to simulate the onset of the South China Sea Monsoon in 1986, 1991 and 1998. Sensitivity tests on various land surface models, cumulus parameterization schemes (CPSs), sea surface temperature (SST) variations and midlatitude influences have been performed. These tests have indicated that the land surface model has a major impact on the circulation over the South China Sea. CPSs can effect the precipitation pattern while SST variation can effect the precipitation amounts over both land and ocean. RELACS has also been used to understand the soil-precipitation interaction and feedback associated with a flood event that occurred in and around China's Yantz River during 1998. The exact location (region) of the flooding can be effected by the soil-rainfall feedback. Also, the Goddard Cumulus Ensemble (GCE) model which allows for realistic moist processes as well as explicit interactions between cloud and radiation, and cloud and surface processes will be used to simulate convective systems associated with the onset of the South China Sea Monsoon in 1998. The GCE model also includes the same PLACE and radiation scheme used in the RELACS. A detailed comparison between the results from the GCE model and RELACS will be performed.

Tao, W.-K.↗

Seasonal variation of surface and atmospheric cloud radiative forcing over the globe derived from satellite data

Global distributions of surface and atmospheric cloud radiative forcing parameters have been derived using parameterized radiation models with satellite meteorological data from the International Satellite Cloud Climatology Project, and directly measured top-of-atmosphere radiative fluxes from the Earth Radiation Budget Experiment. Specifically, shortwave, longwave, and total cloud forcing at the surface, and column-averaged values of longwave cloud forcing of the atmosphere were derived for the midseasonal months of April, July, and October 1985 and January 1986, covering a complete annual cycle. Seasonal variability is illustrated by comparing the results for July 1985 and January 1986, which represent the seasonal extremes. Surface shortwave cloud forcing is always negative, representing a cooling of the surface, with strongest cooling (-120 to -180 W/sq m) occurring over midlatitude storm tracks of the summer hemisphere. Surface longwave cloud forcing is always positive, representing a warming of the surface, with strongest warming (60 to 75 W/sq m) occurring over storm tracks of the winter hemisphere. Zonal averages show the entire summer hemisphere dominated by shortwave cooling, the middle and high latitudes of the winter hemisphere dominated by longwave warming, and a broad zone of transition in between. The globally averaged total cloud forcing amounts to a cooling throughout the year, ranging from a low of about -12 W/sq m for July 1985 to a high of about -25 W/sq m for January 1986. The longwave cloud forcing of the atmosphere shows a strong warming over deep convective regions in the tropics and a moderate cooling outside the tropics, amounting to a weak cooling (-2 to -5 W/sq m) in the global average. Comparisons of the results with general circulation model simulations show broad qualitative agreement regarding the locations of prominent warming and cooling regions. Quantitative comparisons, on the other hand, show significant differences between the magnitudes of warming and cooling in these regions. Most of the larger differences can be attributed to known deficiences of the general circulation model simulations. Comparisons with satellite-derived results of other investigators show much better agreement.

Gupta, Shashi K.↗

Dependence of tropospheric temperature on the parameterization of cumulus convection in the GLAS model of the general circulation

Analysis of the simulation of seasonal change by the GLAS model of the general circulation reveals deficiencies in the simulation of tropospheric temperature and of convective cloud cover. These interrelated deficiencies are due to a spurious doubling from January to July in the convective cloud cover of the Northern Hemisphere. The spurious doubling, in turn, is due to the oversensitivity of cumulus convection, in the GLAS model, to the specific humidity of the lower atmosphere. The oversensitivity is enhanced by a feedback mechanism which perpetuates the existence of deep, penetrative convective clouds at certain preferred locations. The cumulus parameterization scheme has been modified to more realistically relate the onset of cumulus convection to the relative humidity of the lower atmosphere. The modified parameterization has improved the simulation of tropospheric temperature, planetary albedo and convective cloud cover as well as their seasonal variations. Comparison of this experiment with its control has shown a high degree of interrelation among these fields in the GLAS model and has demonstrated the sensitivity of the atmospheric heat budget to the design of the cumulus parameterization scheme. Also, the modification to the cumulus scheme has demonstrated a plausible mechanism to explain the correlation between convective cloud cover and relative humidity in the real atmosphere.

Helfand, H. M.↗

A Solar Radiation Parameterization for Atmospheric Studies

The solar radiation parameterization (CLIRAD-SW) developed at the Goddard Climate and Radiation Branch for application to atmospheric models are described. It includes the absorption by water vapor, O3, O2, CO2, clouds, and aerosols and the scattering by clouds, aerosols, and gases. Depending upon the nature of absorption, different approaches are applied to different absorbers. In the ultraviolet and visible regions, the spectrum is divided into 8 bands, and single O3 absorption coefficient and Rayleigh scattering coefficient are used for each band. In the infrared, the spectrum is divided into 3 bands, and the k-distribution method is applied for water vapor absorption. The flux reduction due to O2 is derived from a simple function, while the flux reduction due to CO2 is derived from precomputed tables. Cloud single-scattering properties are parameterized, separately for liquid drops and ice, as functions of water amount and effective particle size. A maximum-random approximation is adopted for the overlapping of clouds at different heights. Fluxes are computed using the Delta-Eddington approximation.

Chou, Ming-Dah↗

Observations and Parameterizations of Particle Size Distributions in Deep Tropical Cirrus and Stratiform Precipitation Clouds: Results from In-Situ Observations in TRMM Field Campaigns

In this study, we report on the evolution of particle size distributions (PSDs) and habits as measured during slow, Lagrangian-type spiral descents through deep subtropical and tropical cloud layers in Florida, Brazil, and Kwajalein, Marshall Islands, most of which were precipitating. The objective of the flight patterns was to learn more about how the PSDs evolved in the vertical and to obtain information of the vertical structure of microphysical properties. New instrumentation yielding better information on the concentrations of particles in the size (D) range between 0.2 and 2 cm, as well as improved particle imagery, produced more comprehensive observations for tropical stratiform precipitation regions and anvils than have been available previously. Collocated radar observations provided additional information on the vertical structure of the cloud layers sampled. Most of the spirals began at cloud top, with temperatures (T) as low as -50 C, and ended at cloud base or below the melting layer (ML). The PSDs broadened from cloud top towards cloud base, with the largest particles increasing in size from several millimeters at cloud top to one centimeter or larger towards cloud base. Some continued growth was noted in the upper part of the ML. Concentrations of particles less than 1 mm in size decreased with decreasing height. The result was a consistent change in the PSDs in the vertical. Similarly, systematic changes in the size dependence of the particle cross-sectional area was noted with decreasing height. Aggregation-as ascertained from both the changes in the PSDs and evolution of particle habits as observed in high detail with the cloud particle imager (CPI) probe-was responsible for these trends. The PSDs were generally well-represented by gamma distributions of the form N = N0 gamma D microns e- lambda gamma D that were fitted to the PSDs over 1-km horizontal intervals throughout the spirals. The intercept (N0 gamma), slope (lambda gamma), and dispersion (microns) values were derived for each PSD. Exponential curves (N = N0e- lambdaD; micron = 0) were also fitted to the distributions. The lambda gamma values for given spirals varied systematically with temperature as did the values of lambda (exponential), and the data generally conformed to values found in previous studies involving exponential fits to size distributions in mid-latitude frontal and cirrus layers. Considerable variability often noted in the PSD properties during the loops of individual spirals was manifested primarily in large changes in N0 gamma and N0, but micron, lambda gamma and lambda remained fairly stable. Temperature is not found to be the sole factor controlling lambda gamma or lambda but is a primary one. Direct relationships were found between lambda gamma and N0 gamma or lambda gamma and micron for the gamma distributions and lambda and N0 for the exponential. The latter relationship was not found as distinctly in earlier studies; observed PSDs in this study had better fidelity with less scatter. The micron values changed monotonically with T over the range of temperatures and were directly related to N0 gamma or lambda gamma, thereby reducing the number of variables in the PSD functional equation to two. In the upper part of the ML, N0 and lambda continued to decrease, and in the lower part these values began to increase as the largest particles melted. We developed general expressions relating various bulk microphysical, radar, and radiative transfer-related variables to N0 gamma and lambda gamma, useful for both tropical and mid-latitude clouds. These relationships facilitate the specification of a number of bulk properties in cloud and climate models. The results presented in this paper apply best to temperatures between 0 and -40 C, for which the measured radar reflectivities fall in the range of 0 to 25 dBZe.

Heymsfield, Andrew J.↗