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At least 289 records · Page 16
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NASA NTRS2004

Offline GCSS Intercomparison of Cloud-Radiation Interaction and Surface Fluxes

Simulations of deep tropical clouds by both cloud-resolving models (CRMs) and single-column models (SCMs) in the GEWEX Cloud System Study (GCSS) Working Group 4 (WG4; Precipitating Convective Cloud Systems), Case 2 (19-27 December 1992, TOGA-COARE IFA) have produced large differences in the mean heating and moistening rates (-1 to -5 K and -2 to 2 grams per kilogram respectively). Since the large-scale advective temperature and moisture "forcing" are prescribed for this case, a closer examination of two of the remaining external types of "forcing", namely radiative heating and air/sea hear and moisture transfer, are warranted. This paper examines the current radiation and surface flux of parameterizations used in the cloud models participating in the GCSS WG4, be executing the models "offline" for one time step (12 s) for a prescribed atmospheric state, then examining the surface and radiation fluxes from each model. The dynamic, thermodynamic, and microphysical fluids are provided by the GCE-derived model output for Case 2 during a period of very active deep convection (westerly wind burst). The surface and radiation fluxes produced from the models are then divided into prescribed convective, stratiform, and clear regions in order to examine the role that clouds play in the flux parameterizations. The results suggest that the differences between the models are attributed more to the surface flux parameterizations than the radiation schemes.

Tao, W.-K.↗
NASA NTRS2012

Impact of Land Model Calibration on Coupled Land-Atmosphere Prediction

Land-atmosphere (L-A) interactions play a critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface heat and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry and wet land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through calibration of the Noah land surface model using the new optimization and uncertainty estimation subsystem in NASA's Land Information System (LIS-OPT/UE). The impact of the calibration on the a) spinup of the land surface used as initial conditions, and b) the simulated heat and moisture states and fluxes of the coupled WRF simulations is then assessed. Changes in ambient weather and land-atmosphere coupling are evaluated along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Results indicate that the offline calibration leads to systematic improvements in land-PBL fluxes and near-surface temperature and humidity, and in the process provide guidance on the questions of what, how, and when to calibrate land surface models for coupled model prediction.

Santanello, Joseph A., Jr.↗
NASA NTRS1993

Scientific goals of the Cooperative Multiscale Experiment (CME)

Mesoscale Convective Systems (MCS) form the focus of CME. Recent developments in global climate models, the urgent need to improve the representation of the physics of convection, radiation, the boundary layer, and orography, and the surge of interest in coupling hydrologic, chemistry, and atmospheric models of various scales, have emphasized the need for a broad interdisciplinary and multi-scale approach to understanding and predicting MCS's and their interactions with processes at other scales. The role of mesoscale systems in the large-scale atmospheric circulation, the representation of organized convection and other mesoscale flux sources in terms of bulk properties, and the mutually consistent treatment of water vapor, clouds, radiation, and precipitation, are all key scientific issues concerning which CME will seek to increase understanding. The manner in which convective, mesoscale, and larger scale processes interact to produce and organize MCS's, the moisture cycling properties of MCS's, and the use of coupled cloud/mesoscale models to better understand these processes, are also major objectives of CME. Particular emphasis will be placed on the multi-scale role of MCS's in the hydrological cycle and in the production and transport of chemical trace constituents. The scientific goals of the CME consist of the following: understand how the large and small scales of motion influence the location, structure, intensity, and life cycles of MCS's; understand processes and conditions that determine the relative roles of balanced (slow manifold) and unbalanced (fast manifold) circulations in the dynamics of MCS's throughout their life cycles; assess the predictability of MCS's and improve the quantitative forecasting of precipitation and severe weather events; quantify the upscale feedback of MCS's to the large-scale environment and determine interrelationships between MCS occurrence and variations in the large-scale flow and surface forcing; provide a data base for initialization and verification of coupled regional, mesoscale/hydrologic, mesoscale/chemistry, and prototype mesoscale/cloud-resolving models for prediction of severe weather, ceilings, and visibility; provide a data base for initialization and validation of cloud-resolving models, and for assisting in the fabrication, calibration, and testing of cloud and MCS parameterization schemes; and provide a data base for validation of four dimensional data assimilation schemes and algorithms for retrieving cloud and state parameters from remote sensing instrumentation.

Cotton, William↗
NASA NTRS2012

Translation of Land Surface Model Accuracy and Uncertainty into Coupled Land-Atmosphere Prediction

Land-atmosphere (L-A) Interactions playa critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface heat and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry (2006) and wet (2007) land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through the use of a new optimization and uncertainty estimation module in NASA's Land Information System (US-OPT/UE), whereby parameter sets are calibrated in the Noah land surface model and classified according to a land cover and soil type mapping of the observation sites to the full model domain. The impact of calibrated parameters on the a) spinup of the land surface used as initial conditions, and b) heat and moisture states and fluxes of the coupled WRF Simulations are then assessed in terms of ambient weather and land-atmosphere coupling along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Finally, tradeoffs of computational tractability and scientific validity, and the potential for combining this approach with satellite remote sensing data are also discussed.

Santanello, Joseph A.↗
NASA NTRS2012

Impact of Calibrated Land Surface Model Parameters on the Accuracy and Uncertainty of Land-Atmosphere Coupling in WRF Simulations

Land-atmosphere (L-A) interactions play a critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface temperature and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry (2006) and wet (2007) land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through the use of a new optimization and uncertainty estimation module in NASA's Land Information System (LIS-OPT/UE), whereby parameter sets are calibrated in the Noah land surface model and classified according to a land cover and soil type mapping of the observation sites to the full model domain. The impact of calibrated parameters on the a) spinup of the land surface used as initial conditions, and b) heat and moisture states and fluxes of the coupled WRF simulations are then assessed in terms of ambient weather and land-atmosphere coupling along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Finally, tradeoffs of computational tractability and scientific validity, and the potential for combining this approach with satellite remote sensing data are also discussed.

Santanello, Joseph A., Jr.↗
NASA NTRS2013

A Single-column Model Ensemble Approach Applied to the TWP-ICE Experiment

Single-column models (SCM) are useful test beds for investigating the parameterization schemes of numerical weather prediction and climate models. The usefulness of SCM simulations are limited, however, by the accuracy of the best estimate large-scale observations prescribed. Errors estimating the observations will result in uncertainty in modeled simulations. One method to address the modeled uncertainty is to simulate an ensemble where the ensemble members span observational uncertainty. This study first derives an ensemble of large-scale data for the Tropical Warm Pool International Cloud Experiment (TWP-ICE) based on an estimate of a possible source of error in the best estimate product. These data are then used to carry out simulations with 11 SCM and two cloud-resolving models (CRM). Best estimate simulations are also performed. All models show that moisture-related variables are close to observations and there are limited differences between the best estimate and ensemble mean values. The models, however, show different sensitivities to changes in the forcing particularly when weakly forced. The ensemble simulations highlight important differences in the surface evaporation term of the moisture budget between the SCM and CRM. Differences are also apparent between the models in the ensemble mean vertical structure of cloud variables, while for each model, cloud properties are relatively insensitive to forcing. The ensemble is further used to investigate cloud variables and precipitation and identifies differences between CRM and SCM particularly for relationships involving ice. This study highlights the additional analysis that can be performed using ensemble simulations and hence enables a more complete model investigation compared to using the more traditional single best estimate simulation only.

numerical weather forecasting↗
NASA NTRS2002

Simulation of High-Latitude Hydrological Processes in the Torne-Kalix Basin: PILPS Phase 2(e): Equivalent Model Representation and Sensitivity Experiments - 3

The Project for Intercomparison of Land Surface Parameterization Schemes (PILPS) Phase 2(e) showed that in cold regions the annual runoff production in Land Surface Schemes (LSSs) is closely related to the maximum snow accumulation, which in turn is controlled in large part by winter sublimation. To help further explain the relationship between snow cover, turbulent exchanges and runoff production, a simple equivalent model-(SEM) was devised to reproduce the seasonal and annual fluxes simulated by 13 LSSs that participated in PILPS Phase 2(e). The design of the SEM relates the annual partitioning of precipitation and energy in the LSSs to three primary parameters: snow albedo, effective aerodynamic resistance and evaporation efficiency. Isolation of each of the parameters showed that the annual runoff production was most sensitive to the aerodynamic resistance. The SEM was somewhat successful in reproducing the observed LSS response to a decrease in shortwave radiation and changes in wind speed forcings. SEM parameters derived from the reduced shortwave forcings suggested that increased winter stability suppressed turbulent heat fluxes over snow. Because winter sensible heat fluxes were largely negative, reductions in winter shortwave radiation imply an increase in annual average sensible heat.

Bowling, Laura C.↗
NASA NTRS2001

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.↗
NASA NTRS1999

Mesoscale Simulations of a Florida Sea Breeze Using the PLACE Land Surface Model Coupled to a 1.5-Order Turbulence Parameterization

A sophisticated land-surface model, PLACE, the Parameterization for Land Atmospheric Convective Exchange, has been coupled to a 1.5-order turbulent kinetic energy (TKE) turbulence sub-model. Both have been incorporated into the Penn State/National Center for Atmospheric Research (PSU/NCAR) mesoscale model MM5. Such model improvements should have their greatest effect in conditions where surface contrasts dominate over dynamic processes, such as the simulation of warm-season, convective events. A validation study used the newly coupled model, MM5 TKE-PLACE, to simulate the evolution of Florida sea-breeze moist convection during the Convection and Precipitation Electrification Experiment (CaPE). Overall, eight simulations tested the sensitivity of the MM5 model to combinations of the new and default model physics, and initialization of soil moisture and temperature. The TKE-PLACE model produced more realistic surface sensible heat flux, lower biases for surface variables, more realistic rainfall, and cloud cover than the default model. Of the 8 simulations with different factors (i.e., model physics or initialization), TKE-PLACE compared very well when each simulation was ranked in terms of biases of the surface variables and rainfall, and percent and root mean square of cloud cover. A factor separation analysis showed that a successful simulation required the inclusion of a multi-layered, land surface soil vegetation model, realistic initial soil moisture, and higher order closure of the planetary boundary layer (PBL). These were needed to realistically model the effect of individual, joint, and synergistic contributions from the land surface and PBL on the CAPE sea-breeze, Lake Okeechobee lake breeze, and moist convection.

Lynn, Barry H.↗
NASA NTRS2003

Factors Affecting the Evolution of Hurricane Erin and the Distributions of Hydrometeors: Role of Microphysical Processes

Fine-resolution simulations of Hurricane Erin 2001 are conducted using the Penn State University/National Center for Atmospheric Research mesoscale model version 3.5 to investigate the role of thermodynamic, boundary layer and microphysical processes in Erin's growth and maintenance, and their effects on the horizontal and vertical distributions of hydrometeors. Through comparison against radar, radiometer, and dropsonde data collected during the Convection and Moisture Experiment 4, it is seen that realistic simulations of Erin are obtained provided that fine resolution simulations with detailed representations of physical processes are conducted. The principle findings of the study are as follows: 1) a new iterative condensation scheme, which limits the unphysical increase of equivalent potential temperature associated with most condensation schemes, increases the horizontal size of the hurricane, decreases its maximum rainfall rate, reduces its intensity, and makes its eye more moist; 2) in general, microphysical parameterization schemes with more categories of hydrometeors produce more intense hurricanes, larger hydrometeor mixing ratios, and more intense updrafts and downdrafts; 3) the choice of coefficients describing hydrometeor fall velocities has as big of an impact on the hurricane simulations as does choice of microphysical parameterization scheme with no clear relationship between fall velocity and hurricane intensity; and 4) in order for a tropical cyclone to adequately intensify, an advanced boundary layer scheme (e.g., Burk-Thompson scheme) must be used to represent boundary layer processes. The impacts of varying simulations on the horizontal and vertical distributions of different categories of hydrometeor species, on equivalent potential temperature, and on storm updrafts and downdrafts are examined to determine how the release of latent heat feedbacks upon the structure of Erin. In general, all simulations tend to overpredict precipitation rate and hydrometeor mixing ratios. The ramifications of these findings for quantitative precipitation forecasts (QPFs) of tropical cyclones are discussed.

McFarquhar, Greg M.↗
NASA NTRS2001

Technical Report Series on Global Modeling and Data Assimilation: The Climate of the FVCCM-3 Model - Volume 20

This document describes the climate of version 1 of the NASA-NCAR model developed at the Data Assimilation Office (DAO). The model consists of a new finite-volume dynamical core and an implementation of the NCAR climate community model (CCM-3) physical parameterizations. The version of the model examined here was integrated at a resolution of 2 degrees latitude by 2.5 degrees longitude and 32 levels. The results are based on assimilation that was forced with observed sea surface temperature and sea ice for the period 1979-1995, and are compared with NCEP/NCAR reanalyses and various other observational data sets. The results include an assessment of seasonal means, subseasonal transients including the Madden Julian Oscillation, and interannual variability. The quantities include zonal and meridional winds, temperature, specific humidity, geopotential height, stream function, velocity potential, precipitation, sea level pressure, and cloud radiative forcing.

Suarez, Max J.↗
NASA NTRS2005

A Hierarchical Modeling Study of the Interactions Among Turbulence, Cloud Microphysics, and Radiative Transfer in the Evolution of Cirrus Clouds

This project used a hierarchy of cloud resolving models to address the following science issues of relevance to CRYSTAL-FACE: What ice crystal nucleation mechanisms are active in the different types of cirrus clouds in the Florida area and how do these different nucleation processes influence the evolution of the cloud system and the upper tropospheric humidity? How does the feedback between supersaturation and nucleation impact the evolution of the cloud? What is the relative importance of the large-scale vertical motion and the turbulent motions in the evolution of the crystal size spectra? How does the size spectra impact the life-cycle of the cloud, stratospheric dehydration, and cloud radiative forcing? What is the nature of the turbulence and waves in the upper troposphere generated by precipitating deep convective cloud systems? How do cirrus microphysical and optical properties vary with the small-scale dynamics? How do turbulence and waves in the upper troposphere influence the cross-tropopause mixing and stratospheric and upper tropospheric humidity? The models used in this study were: 2-D hydrostatic model with explicit microphysics that can account for 30 size bins for both the droplet and crystal size spectra. Notably, a new ice crystal nucleation scheme has been incorporated into the model. Parcel model with explicit microphysics, for developing and evaluating microphysical parameterizations. Single column model for testing bulk microphysics parameterizations

Curry, Judith↗
NASA NTRSDate not supplied

Impacts of aerosol size-dependent below-cloud scavenging on tropospheric aerosol in the NASA GEOS model

Cloud scavenging is the major sink for a suite of tropospheric aerosols, and thus largely affects the global distribution and lifetime of aerosols as well as the formation of clouds. Simplified model parameterizations of cloud scavenging of aerosols substantially contribute to large uncertainties in the simulated aerosol burdens, spatial distributions, lifetimes, as well as aerosol radiative forcing. Here we evaluate the wet scavenging scheme in the current NASA GEOS model, develop more physically-based parameterizations of below-cloud scavenging, and assess the impacts of the new scavenging parameterizations on the GEOS simulations of aerosols. The current below-cloud scavenging (BCS; washout) scheme uses a first-order removal with a constant scavenging coefficient. We replaced the current scheme with a size-dependent parameterization of Croft et al.(Atmos. Chem. Phys., 2009; hereafter referred to as C09). The C09 BCS parameterizations calculate aerosol below-cloud scavenging coefficients based on a size-dependent collision efficiency between aerosol particles and raindrops (or snow crystals). A look-up table of compiled collision efficiencies provides values for sixty aerosol sizes and nine rain flux rates. Snow-aerosol collision efficiencies are a function of the sixty aerosol sizes only. We assume a log-normal size distribution for aerosols (bulk) in GOCART. The collision efficiencies are then calculated online using a bilinear interpolation from the look-up table for the given aerosol sizes and precipitation flux rates in the model.

aerosols↗
NASA NTRS1992

GPS meteorology - Remote sensing of atmospheric water vapor using the Global Positioning System

We present a new approach to remote sensing of water vapor based on the Global Positioning System (GPS). Geodesists and geophysicists have devised methods for estimating the extent to which signals propagating from GPS satellites to ground-based GPS receivers are delayed by atmospheric water vapor. This delay is parameterized in terms of a time-varying zenith wet delay (ZWD) which is retrieved by stochastic filtering of the GPS data. Given surface temperature and pressure readings at the GPS receiver, the retrieved ZWD can be transformed with very little additional uncertainty into an estimate of the integrated water vapor (IWV) overlying that receiver. Networks of continuously operating GPS receivers are being constructed by geodesists, geophysicists, and government and military agencies, in order to implement a wide range of positioning capabilities. These emerging GPS networks offer the possibility of observing the horizontal distribution of IWV or, equivalently, precipitate water with unprecedented coverage and a temporal resolution of the order of 10 min. These measurements could be utilized in operational weather forecasting and in fundamental research into atmospheric storm systems, the hydrologic cycle, atmospheric chemistry, and global climate change.

Bevis, Michael↗
NASA NTRS2000

Comparison of Cirrus Cloud Models: A Project of the GEWEX Cloud System Study (GCSS) Working Group on Cirrus Cloud Systems

The GEWEX Cloud System Study (GCSS, GEWEX is the Global Energy and Water Cycle Experiment) is a community activity aiming to promote development of improved cloud parameterizations for application in the large-scale general circulation models (GCMs) used for climate research and for numerical weather prediction. The GCSS strategy is founded upon the use of cloud-system models (CSMs). These are "process" models with sufficient spatial and temporal resolution to represent individual cloud elements, but spanning a wide range of space and time scales to enable statistical analysis of simulated cloud systems. GCSS also employs single-column versions of the parametric cloud models (SCMs) used in GCMs. GCSS has working groups on boundary-layer clouds, cirrus clouds, extratropical layer cloud systems, precipitating deep convective cloud systems, and polar clouds.

Starr, David O'C.↗
NASA NTRS2022

The Lithophile Element Budget of Earth’s Core

The relative composition of Earth’s core and mantle were set during core formation. By determining how elements partition between metal and silicate at high pressures and temperatures, measurements of the mantle composition and geophysical observations of the core can be used to understand the mechanisms by which Earth formed. Here we present the results of metal–silicate partitioning experiments for a range of nominally lithophile elements (Al, Ca, K, Mg, O, S, Si, Th, U) and S to 85 GPa and up to 5400 K. With our results and a compilation of literature data, we developed a parameterization for partitioning that accounts for compositional dependencies in both the metal and silicate phases. Using this parameterization in a range of planetary growth models, we find that, in general, lithophile element partitioning into the metallic phase is enhanced at high temperatures. The relative abundances of FeO, SiO2 and MgO in the mantle vary significantly between planetary growth models, and the mantle abundances of these elements can be used to provide important constraints on Earth’s accretion. To match Earth’s core mass and mantle composition, Earth’s building blocks must have been enriched in Fe and depleted in Si compared with CI chondrites. Finally, too little Mg, Si and O are partitioned into the core for precipitation of oxides to be a major source of energy for the geodynamo. In contrast, several ppb of U can be partitioned into the core at high temperatures, and this energy source must be accounted for in thermal evolution models.

dynamo↗
NASA NTRS2000

Comparison of Cirrus Cloud Models: A Project of the GEWEX Cloud System Study (GCSS) Working Group on Cirrus Cloud Systems

The GEWEX Cloud System Study (GCSS, GEWEX is the Global Energy and Water Cycle Experiment) is a community activity aiming to promote development of improved cloud parameterizations for application in the large-scale general circulation models (GCMs) used for climate research and for numerical weather prediction (Browning et al, 1994). The GCSS strategy is founded upon the use of cloud-system models (CSMs). These are "process" models with sufficient spatial and temporal resolution to represent individual cloud elements, but spanning a wide range of space and time scales to enable statistical analysis of simulated cloud systems. GCSS also employs single-column versions of the parametric cloud models (SCMs) used in GCMs. GCSS has working groups on boundary-layer clouds, cirrus clouds, extratropical layer cloud systems, precipitating deep convective cloud systems, and polar clouds.

Starr, David OC.↗
NASA NTRS2003

Precipitation Processes Developed During ARM (1997), TOGA COARE (1992), GATE (1974), SCSMEX (1998), and KWAJEX (1999): Consistent 2D, Semi-3D and 3D Cloud Resolving Model Simulations

Real clouds and cloud systems are inherently three-dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical cloud systems with large horizontal domains at the National Center for Atmospheric Research (NACAR) and at NASA Goddard Space Flight Center . At Goddard, a 3D Goddard Cumulus Ensemble (GCE) model was used to simulate periods during TOGA COARE, SCSMEX and KWAJEX using 512 by 512 km domain (with 2 km resolution). The results indicate that surface precipitation and latent heating profiles are very similar between the 2D and 3D GCE model simulations. The reason for the strong similarity between the 2D and 3D CRM simulations is that the same observed large-scale advective tendencies of potential temperature, water vapor mixing ratio, and horizontal momentum were used as the main focusing in both the 2D and 3D models. Interestingly, the 2D and 3D versions of the CRM used at CSU showed significant differences in the rainfall and cloud statistics for three ARM cases. The major objectives of this paper are: (1) to assess the performance of the super-parameterization technique, (2) calculate and examine the surface energy (especially radiation) and water budgets, and (3) identify the differences and similarities in the organization and entrainment rates of convection between simulated 2D and 3D cloud systems.

Tao, W-K.↗