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NASA NTRS2022

Updraft Dynamics and Microphysics: On the Added Value of the Cumulus Thermal Reference Frame in Simulations of Aerosol–Deep Convection Interactions

One fundamental question about atmospheric moist convection processes that remains debated is whether or under what conditions a relevant variability in background aerosol concentrations may have a significant dynamical impact on convective clouds and their associated precipitation. Furthermore, current climate models must parameterize both the microphysical and the cumulus convection processes, but this is usually implemented separately, whereas in nature there is a strong coupling between them. As a first step to improve our understanding of these two problems, we investigate how aerosol concentrations modify key properties of updrafts in eight large-eddy permitting regional simulations of a case study of scattered convection over Houston, Texas, in which convection is explicitly simulated and microphysical processes are parameterized. Dynamical and liquid-phase microphysical responses are investigated using two different reference frames: static cloudy-updraft grid cells versus tracked cumulus thermals. In both frameworks we observe the expected microphysical responses to higher aerosol concentrations, such as higher cloud number concentrations and lower rain number concentrations. In terms of the dynamical responses, both frameworks indicate weak impacts of varying aerosol concentrations relative to the noise between simulations over the observationally derived range of aerosol variability for this case study. On the other hand, results suggest that thermals are more selective than cloudy-updraft grid cells in terms of sampling the most active convective air masses. For instance, vertical velocity from thermals is significantly higher at upper levels than when sampled from cloudy-updraft grid points, and several microphysical variables have higher average values in the cumulus thermal framework than in the cloudy-updraft framework. In addition, the thermal analysis is seen to add rich quantitative information about the rates and covariability of microphysical processes spatially and throughout tracked thermal lifecycles, which can serve as a stronger foundation for improving subgrid-scale parameterizations.

Daniel Hernandez-Deckers↗

NASA NTRS2013

Development of Two-Moment Cloud Microphysics for Liquid and Ice Within the NASA Goddard Earth Observing System Model (GEOS-5)

This work presents the development of a two-moment cloud microphysics scheme within the version 5 of the NASA Goddard Earth Observing System (GEOS-5). The scheme includes the implementation of a comprehensive stratiform microphysics module, a new cloud coverage scheme that allows ice supersaturation and a new microphysics module embedded within the moist convection parameterization of GEOS-5. Comprehensive physically-based descriptions of ice nucleation, including homogeneous and heterogeneous freezing, and liquid droplet activation are implemented to describe the formation of cloud particles in stratiform clouds and convective cumulus. The effect of preexisting ice crystals on the formation of cirrus clouds is also accounted for. A new parameterization of the subgrid scale vertical velocity distribution accounting for turbulence and gravity wave motion is developed. The implementation of the new microphysics significantly improves the representation of liquid water and ice in GEOS-5. Evaluation of the model shows agreement of the simulated droplet and ice crystal effective and volumetric radius with satellite retrievals and in situ observations. The simulated global distribution of supersaturation is also in agreement with observations. It was found that when using the new microphysics the fraction of condensate that remains as liquid follows a sigmoidal increase with temperature which differs from the linear increase assumed in most models and is in better agreement with available observations. The performance of the new microphysics in reproducing the observed total cloud fraction, longwave and shortwave cloud forcing, and total precipitation is similar to the operational version of GEOS-5 and in agreement with satellite retrievals. However the new microphysics tends to underestimate the coverage of persistent low level stratocumulus. Sensitivity studies showed that the simulated cloud properties are robust to moderate variation in cloud microphysical parameters. However significant sensitivity in ice cloud properties was found to variation in the dispersion of the ice crystal size distribution and the critical size for ice autoconversion. The implementation of the new microphysics leads to a more realistic representation of cloud processes in GEOS-5 and allows the linkage of cloud properties to aerosol emissions.

Aerosol-Cloud Interactions↗

NASA NTRS2009

Multiscale Cloud System Modeling

The central theme of this paper is to describe how cloud system resolving models (CRMs) of grid spacing approximately 1 km have been applied to various important problems in atmospheric science across a wide range of spatial and temporal scales and how these applications relate to other modeling approaches. A long-standing problem concerns the representation of organized precipitating convective cloud systems in weather and climate models. Since CRMs resolve the mesoscale to large scales of motion (i.e., 10 km to global) they explicitly address the cloud system problem. By explicitly representing organized convection, CRMs bypass restrictive assumptions associated with convective parameterization such as the scale gap between cumulus and large-scale motion. Dynamical models provide insight into the physical mechanisms involved with scale interaction and convective organization. Multiscale CRMs simulate convective cloud systems in computational domains up to global and have been applied in place of contemporary convective parameterizations in global models. Multiscale CRMs pose a new challenge for model validation, which is met in an integrated approach involving CRMs, operational prediction systems, observational measurements, and dynamical models in a new international project: the Year of Tropical Convection, which has an emphasis on organized tropical convection and its global effects.

Tao, Wei-Kuo↗

NASA NTRS1993

Incorporation of the planetary boundary layer in atmospheric models

The topics discussed include the following: perspectives on planetary boundary layer (PBL) measurements; current problems of PBL parameterization in mesoscale models; and convective cloud-PBL interactions.

Moeng, Chin-Hoh↗

NASA NTRS2005

A New Approach to using a Cloud-Resolving Model to Study the Interactions between Clouds, Precipitation and Aerosols

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically-based parameterizations for climate models and numerical weather prediction models. A review of developments and applications of cloud models in the past, present and future will be presented in this talk. In particular, a new approach to using cloud-resolving models to study the interactions between clouds, precipitation and aerosols will be presented.

Tao, Wei-Kuo↗

NASA NTRS2005

A New Approach to Using a Cloud-resolving Model to Study the Interactions Between Clouds, Precipitation and Aerosols

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as l0,OOO km in two-dimensions, and 1,OOO x 1,OOO km2 in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically-based parameterizations for climate models and numerical weather prediction models. A review of developments and applications of cloud models in the past, present and future will be presented in this talk. In particular, a new approach to using cloud-resolving models to study the interactions between clouds, precipitation and aerosols will be presented.

Tao, Wei-Kuo↗

NASA NTRS2005

A New Approach to using a Cloud-Resolving Model to Study the Interactions between Clouds, Precipitation and Aerosols

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically-based parameterizations for climate models and numerical weather prediction models. A review of developments and applications of cloud models in the past, present and future will be presented in this talk. In particular, a new approach to using cloud-resolving models to study the interactions between clouds, precipitation and aerosols will be presented.

Tao, Wei-Kuo↗

NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial-lkm scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard wlll be is presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

NASA NTRS2006

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 sq km in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

NASA NTRS2013

The MJO Transition from Shallow to Deep Convection in CloudSat/CALIPSO Data and GISS GCM Simulations

The relationship between convective penetration depth and tropospheric humidity is central to recent theories of the Madden-Julian oscillation (MJO). It has been suggested that general circulation models (GCMs) poorly simulate the MJO because they fail to gradually moisten the troposphere by shallow convection and simulate a slow transition to deep convection. CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) data are analyzed to document the variability of convection depth and its relation to water vapor during the MJO transition from shallow to deep convection and to constrain GCM cumulus parameterizations. Composites of cloud occurrence for 10MJO events show the following anticipatedMJO cloud structure: shallow and congestus clouds in advance of the peak, deep clouds near the peak, and upper-level anvils after the peak. Cirrus clouds are also frequent in advance of the peak. The Advanced Microwave Scanning Radiometer for EarthObserving System (EOS) (AMSR-E) columnwater vapor (CWV) increases by;5 mmduring the shallow- deep transition phase, consistent with the idea of moisture preconditioning. Echo-top height of clouds rooted in the boundary layer increases sharply with CWV, with large variability in depth when CWV is between;46 and 68 mm. International Satellite Cloud Climatology Project cloud classifications reproduce these climatological relationships but correctly identify congestus-dominated scenes only about half the time. A version of the Goddard Institute for Space Studies Model E2 (GISS-E2) GCM with strengthened entrainment and rain evaporation that produces MJO-like variability also reproduces the shallow-deep convection transition, including the large variability of cloud-top height at intermediate CWV values. The variability is due to small grid-scale relative humidity and lapse rate anomalies for similar values of CWV. 1.

DelGenio, Anthony G.↗

NASA NTRS1994

Ozone formation during an episode over Europe: A 3-D chemical/transport model simulation

A 3-D regional photochemical tracer/transport model for Europe and the Eastern Atlantic has been developed based on the NASA/GISS CTM. The model resolution is 4x5 degrees latitude and longitude with 9 layers in the vertical (7 in the troposphere). Advective winds, convection statistics and other meteorological data from the NASA/GISS GCM are used. An extensive gas-phase chemical scheme based on the scheme used in our global 2D model has been incorporated in the 3D model. In this work ozone formation in the troposphere is studied with the 3D model during a 5 day period starting June 30. Extensive local ozone production is found and the relationship between the source regions and the downwind areas are discussed. Variations in local ozone formation as a function of total emission rate, as well as the composition of the emissions (HC/NO(x)) ratio and isoprene emissions) are elucidated. An important vertical transport process in the troposphere is by convective clouds. The 3D model includes an explicit parameterization of this process. It is shown that this process has significant influence on the calculated surface ozone concentrations.

Berntsen, Terje↗

NASA NTRS2013

Cloud Simulations in Response to Turbulence Parameterizations in the GISS Model E GCM

The response of cloud simulations to turbulence parameterizations is studied systematically using the GISS general circulation model (GCM) E2 employed in the Intergovernmental Panel on Climate Change's (IPCC) Fifth Assessment Report (AR5).Without the turbulence parameterization, the relative humidity (RH) and the low cloud cover peak unrealistically close to the surface; with the dry convection or with only the local turbulence parameterization, these two quantities improve their vertical structures, but the vertical transport of water vapor is still weak in the planetary boundary layers (PBLs); with both local and nonlocal turbulence parameterizations, the RH and low cloud cover have better vertical structures in all latitudes due to more significant vertical transport of water vapor in the PBL. The study also compares the cloud and radiation climatologies obtained from an experiment using a newer version of turbulence parameterization being developed at GISS with those obtained from the AR5 version. This newer scheme differs from the AR5 version in computing nonlocal transports, turbulent length scale, and PBL height and shows significant improvements in cloud and radiation simulations, especially over the subtropical eastern oceans and the southern oceans. The diagnosed PBL heights appear to correlate well with the low cloud distribution over oceans. This suggests that a cloud-producing scheme needs to be constructed in a framework that also takes the turbulence into consideration.

Yao, Mao-Sung↗

NASA NTRS2004

Florida Thunderstorms: A Faucet of Reactive Nitrogen to the Upper Troposphere

During the NASA Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) enhanced mixing ratios of nitric oxide were measured in the anvils of thunderstorms and in clear air downwind of storm systems on flights of a Wl3-57F high-altitude aircraft. Mixing ratios greater than l0 - 20 times background were readily observed over distances of 25-120 km due to lightning activity. In many of the Florida storms deposition of NO occurred up to near the tropopause but major deposition usually occurred 1 - 2 km below the tropopause, or mostly within the visible anvil volume formed prior to storm decay. Observations from two storms of very different anvil size and electrical activity allowed estimates of the total mass of NO, vented to the middle and upper troposphere. Using the cloud-to ground (CG) flash accumulations from the National Lightning Detection Network, climatological intra-cloud (IC) to CG ratios, and assuming that CG and IC flashes were of equivalent efficiency for NO production, the ranges of production per flash for a moderate-sized and a large storm were (0.51 - 1.0) x l0(exp 26) and (2.3 - 3.1) x 10(exp 26) molecules NO/flash, respectively. Using the recently determined average global flash rate of 44 8, a gross extrapolation of these two storms to represent possible global annual production rates yield 1.6 - 3.2 and 7.3 - 9.9 Tg(N)/yr, respectively. If the more usual assumption is made that IC efficiency is l/l0th that of CG activity, the ranges of production for the moderate-sized and large storm were (1.3 - 2.7) x l0(exp 26) and (6.0 - 8.1) x l0(exp 26) molecules NO/CG flash, respectively. The estimates from the large storm may be high because there is indirect evidence that the IC/CG ratio was larger than would be derived from climatology. These two storms and others studied did not have flash rates that scaled as approx. H(sup 5) where H is the cloud top altitude. The observed CG flash accumulations and NO(x) mass production estimate for the month of July over the Florida area were compared with a representative 3D global Chemistry-Transport Model (CTMJ that uses the Price et al. lightning parameterization. For two land grid points representing the Florida peninsula the model compared well with the observations: CG flash rates were low by only a factor of approx. 2. When the model grid points included the coastal regions of Florida the flash accumulations were lower than observed by a factor of 3.4 - 4.6. It is recommended that models using the Price et al. parameterization allow any global coastal grid point to maintain the land rather than the marine flash rate parameterization. The convection in this CTM underestimated the actual cloud top heights over Florida by 1 - 2 km and thus the total lightning flash rates and the altitude range of reactive nitrogen deposition. Broad scale (20 - 120 km) median mixing ratios of NO within anvils over Florida were significantly larger than in storms previously investigated over Colorado and New Mexico.

Ridley, B.↗

NASA NTRS2007

Using Multi-scale Modeling Systems to Study the Precipitation Processes

Tao, Wei-Kuo↗

NASA NTRS2008

A Multi-Scale Modeling System with Unified Physics

Tao, Wei-Kuo↗

NASA NTRS2019

Extratropical Cyclone Clouds in the GFDL Climate Model: Diagnosing Biases and the Associated Causes

The clouds in southern hemisphere extratropical cyclones generated by the GFDL climate model are analyzed against MODIS, CloudSat and CALIPSO cloud and precipitation observations. Two model versions are used: one is a developmental version of AM4, a model GFDL will utilize for CMIP6, the other is the same model with a different parameterization of moist convection. Both model versions predict a realistic top-of-atmosphere cloud cover in the southern oceans, within 5% of the observations. However, an examination of cloud cover transects in extratropical cyclones reveals a tendency in the models to overestimate high-level clouds (by differing amounts) and underestimate cloud cover at low-levels (again by differing amounts), especially in the post-cold frontal (PCF) region, when compared to observations. Focusing on only the models, their differences in high and mid-level clouds are consistent with their differences in convective activity and relative humidity (RH), but the same is not true for the PCF region. In this region, RH is higher in the model with less cloud fraction. These seemingly contradictory cloud and RH differences can be explained by differences in the cloud parameterization tuning parameters that ensure radiative balance. In the PCF region, the model cloud differences are smaller than either of the model biases with respect to observations, suggesting other physics changes are needed to address the bias. The process-oriented analysis used to assess these model differences will soon be automated and shared.

Catherine M Naud↗

NASA NTRS1972

Design of the UCLA general circulation model

An edited version is reported of notes distributed at the Summer Workshop on the UCLA General Circulation Model in June 1971. It presents the computational schemes of the UCLA model, along with the mathematical and physical principles on which these schemes are based. Included are the finite difference schemes for the governing fluid-dynamical equations, designed to maintain the important integral constraints and dispersion characteristics of the motion. Also given are the principles of parameterization of cumulus convection by an ensemble of identical clouds. A model of the ground hydrology, involving the liquid, ice and snow states of water, is included. A short summary is given of the scheme for computing solar and infrared radiation transfers through clear and cloudy air.

Arakawa, A.↗