Engineering topics

Simpson, Joanne

Publications and source records attributed to Simpson, Joanne.

At least 19 records

NASA NTRS2012

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Recently, a detailed spectral-bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (GCE) model. Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and summertime convection over a mid-latitude continent with different concentrations of CCN: a low clean concentration and a high dirty concentration. The impact of atmospheric aerosol concentration on cloud and precipitation will be investigated.

cloud-resolving model↗

NASA NTRS2010

The Role of Atmospheric Aerosol Concentration on Deep Convective Precipitation: Cloud-Resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 2001]. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds NRC [2001]." The aerosol effect on Clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path and the "semi-direct" effect on cloud coverage. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect, is even more complex, especially for mixed-phase convective clouds. In this paper, a cloud-resolving model (CRM) with detailed spectral-bin microphysics was used to examine the effect of aerosols on three different deep convective cloud systems that developed in different geographic locations: South Florida, Oklahoma and the Central Pacific, In all three cases, rain reaches the ground earlier for the low CCN (clean) case. Rain suppression is also evident in all three cases with high CCN (dirty) case. However, this suppression only occurs during the first hour of the simulations. During the mature stages of the simulations, the effects of increasing aerosol concentration range from rain suppression in the Oklahoma case, to almost no effect in the Florida case, to rain enhancement in the Pacific case. These results show the complexity of aerosol interactions with convection. The model results suggest that evaporative cooling is a key process in determining whether high CCN reduces or enhances precipitation. Stronger evaporative cooling can produce a stronger cold pool and thus stronger low-level convergence through interactions with the low-level wind shear. Consequently, precipitation processes can be more vigorous. For example,, the evaporative cooling is more than two times stronger in the lower troposphere with high CCN for the Pacific case. Sensitivity tests also suggest that ice processes are crucial for suppressing precipitation in the Oklahoma case with high CCN.

Tao, Wei-Kuo↗

NASA NTRS2009

Diagnosing the Ice Crystal Enhancement Factor in the Tropics

Recent modeling studies have revealed that ice crystal number concentration is one of the dominant factors in the effect of clouds on radiation. Since the ice crystal enhancement factor and ice nuclei concentration determine the concentration, they are both important in quantifying the contribution of increased ice nuclei to global warming. In this study, long-term cloud-resolving model (CRM) simulations are compared with field observations to estimate the ice crystal enhancement factor in tropical and midlatitudinal clouds, respectively. It is found that the factor in tropical clouds is ~10 3-104 times larger than that of mid-latitudinal ones, which makes physical sense because entrainment and detrainment in the Tropics are much stronger than in middle latitudes. The effect of entrainment/detrainment on the enhancement factor, especially in tropical clouds, suggests that cloud microphysical parameterizations should be coupled with subgrid turbulence parameterizations within CRMs to obtain a more accurate depiction of cloud-radiative forcing.

Zeng, Xiping↗

NASA NTRS2009

A Multiscale Modeling System: Developments, Applications, and Critical Issues

The foremost challenge in parameterizing convective clouds and cloud systems in large-scale models are the many coupled dynamical and physical processes that interact over a wide range of scales, from microphysical scales to the synoptic and planetary scales. This makes the comprehension and representation of convective clouds and cloud systems one of the most complex scientific problems in Earth science. During the past decade, the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) has pioneered the use of single-column models (SCMs) and cloud-resolving models (CRMs) for the evaluation of the cloud and radiation parameterizations in general circulation models (GCMs; e.g., GEWEX Cloud System Science Team 1993). These activities have uncovered many systematic biases in the radiation, cloud and convection parameterizations of GCMs and have led to the development of new schemes (e.g., Zhang 2002; Pincus et al, 2003; Zhang and Wu 2003; Wu et al. 2003; Liang and Wu 2005; Wu and Liang 2005, and others). Comparisons between SCMs and CRMs using the same large-scale forcing derived from field campaigns have demonstrated that CRMs are superior to SCMs in the prediction of temperature and moisture tendencies (e.g., Das et al. 1999; Randall et al 2003b; Xie et al. 2005).

Tao, Wei-Kuo↗

NASA NTRS2009

Sensitivity of a Cloud-Resolving Model to Bulk and Explicit Bin Microphysical Schemes: Cloud Microphysics and Storm Dynamics Interactions - Part 2

Part I of this paper compares two simulations, one using a bulk and the other a detailed bin microphysical scheme, of a long-lasting, continental mesoscale convective system with leading convection and trailing stratiform region. Diagnostic studies and sensitivity tests are carried out in Part II to explain the simulated contrasts in the spatial and temporal variations by the two microphysical schemes and to understand the interactions between cloud microphysics and storm dynamics. It is found that the fixed raindrop size distribution in the bulk scheme artificially enhances rain evaporation rate and produces a stronger near surface cool pool compared with the bin simulation. In the bulk simulation, cool pool circulation dominates the near-surface environmental wind shear in contrast to the near-balance between cool pool and wind shear in the bin simulation. This is the main reason for the contrasting quasi-steady states simulated in Part I. Sensitivity tests also show that large amounts of fast-falling hail produced in the original bulk scheme not only result in a narrow trailing stratiform region but also act to further exacerbate the strong cool pool simulated in the bulk parameterization. An empirical formula for a correction factor, r(q(sub r)) = 0.11q(sub r)(exp -1.27) + 0.98, is developed to correct the overestimation of rain evaporation in the bulk model, where r is the ratio of the rain evaporation rate between the bulk and bin simulations and q(sub r)(g per kilogram) is the rain mixing ratio. This formula offers a practical fix for the simple bulk scheme in rain evaporation parameterization.

Li, Xiaowen↗

NASA NTRS2008

On the Sensitivity of Atmospheric Ensembles to Cloud Microphysics in Long-Term Cloud-Resolving Model Simulations

Month-long large-scale forcing data from two field campaigns are used to drive a cloud-resolving model (CRM) and produce ensemble simulations of clouds and precipitation. Observational data are then used to evaluate the model results. To improve the model results, a new parameterization of the Bergeron process is proposed that incorporates the number concentration of ice nuclei (IN). Numerical simulations reveal that atmospheric ensembles are sensitive to IN concentration and ice crystal multiplication. Two- (2D) and three-dimensional (3D) simulations are carried out to address the sensitivity of atmospheric ensembles to model dimensionality. It is found that the ensembles with high IN concentration are more sensitive to dimensionality than those with low IN concentration. Both the analytic solutions of linear dry models and the CRM output show that there are more convective cores with stronger updrafts in 3D simulations than in 2D, which explains the differing sensitivity of the ensembles to dimensionality at different IN concentrations.

Zeng, Xiping↗

NASA NTRS2008

The Impact of Aerosols on Cloud and Precipitation Processes: Cloud-Resolving Model Simulations

Aerosols and especially their effect on clouds are one of the key components of the climate system and the hydrological cycle [Ramanathan et al., 2001]. Yet, the aerosol effect on clouds remains largely unknown and the processes involved not well understood. A recent report published by the National Academy of Science states "The greatest uncertainty about the aerosol climate forcing - indeed, the largest of all the uncertainties about global climate forcing - is probably the indirect effect of aerosols on clouds [NRC, 2001]." The aerosol effect on clouds is often categorized into the traditional "first indirect (i.e., Twomey)" effect on the cloud droplet sizes for a constant liquid water path [Twomey, 1977] and the "semi-direct" effect on cloud coverage [e.g., Ackerman et al ., 2001]." Enhanced aerosol concentrations can also suppress warm rain processes by producing a narrow droplet spectrum that inhibits collision and coalescence processes [e.g., Squires and Twomey, 1961; Warner and Twomey, 1967; Warner, 1968; Rosenfeld, 19991. The aerosol effect on precipitation processes, also known as the second type of aerosol indirect effect [Albrecht, 1989], is even more complex, especially for mixed-phase convective clouds. Table 1 summarizes the key observational studies identifying the microphysical properties, cloud characteristics, thermodynamics and dynamics associated with cloud systems from high-aerosol continental environments. For example, atmospheric aerosol concentrations can influence cloud droplet size distributions, warm-rain process, cold-rain process, cloud-top height, the depth of the mixed phase region, and occurrence of lightning. In addition, high aerosol concentrations in urban environments could affect precipitation variability by providing an enhanced source of cloud condensation nuclei (CCN). Hypotheses have been developed to explain the effect of urban regions on convection and precipitation [van den Heever and Cotton, 2007 and Shepherd, 2005]. Please see Tao et al. (2007) for more detailed description on aerosol impact on precipitation. Recently, a detailed spectral-bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (GCE) model. Atmospheric aerosols are also described using number density size-distribution functions. A spectral-bin microphysical model is very expensive from a computational point of view and has only been implemented into the 2D version of the GCE at the present time. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and summertime convection over a mid-latitude continent with different concentrations of CCN: a low "clean" concentration and a high "dirty" concentration. The impact of atmospheric aerosol concentration on cloud and precipitation will be investigated.

Tao, Wei-Kuo↗

NASA NTRS2007

Microphysical Timescales in Clouds and their Application in Cloud-Resolving Modeling

Independent prognostic variables in cloud-resolving modeling are chosen on the basis of the analysis of microphysical timescales in clouds versus a time step for numerical integration. Two of them are the moist entropy and the total mixing ratio of airborne water with no contributions from precipitating particles. As a result, temperature can be diagnosed easily from those prognostic variables, and cloud microphysics be separated (or modularized) from moist thermodynamics. Numerical comparison experiments show that those prognostic variables can work well while a large time step (e.g., 10 s) is used for numerical integration.

Zeng, Xiping↗

NASA NTRS2006

Evaluating Clouds in Long-Term Cloud-Resolving Model Simulations with Observational Data

Two 20-day, continental midlatitude cases are simulated with a three-dimensional (3D) cloud-resolving model (CRM) and compared to Atmospheric Radiation Measurement (ARM) data. This evaluation of long-term cloud-resolving model simulations focuses on the evaluation of clouds and surface fluxes. All numerical experiments, as compared to observations, simulate surface precipitation well but over-predict clouds, especially in the upper troposphere. The sensitivity of cloud properties to dimensionality and other factors is studied to isolate the origins of the over prediction of clouds. Due to the difference in buoyancy damping between 2D and 3D models, surface precipitation fluctuates rapidly with time, and spurious dehumidification occurs near the tropopause in the 2D CRM. Surface fluxes from a land data assimilation system are compared with ARM observations. They are used in place of the ARM surface fluxes to test the sensitivity of simulated clouds to surface fluxes. Summertime simulations show that surface fluxes from the assimilation system bring about a better simulation of diurnal cloud variation in the lower troposphere.

Zeng, Xiping↗

NASA NTRS2006

Structure of Highly Sheared Tropical Storm Chantal during CAMEX-4

Tropical Storm Chantal during August 2001 was a storm that failed to intensify over the few days prior to making landfall on the Yucatan Peninsula. An observational study of Tropical Storm Chantal is presented using a diverse dataset including remote and in situ measurements from the NASA ER-2 and DC-8 and the NOAA WP-3D N42RF aircraft and satellite. The authors discuss the storm structure from the larger-scale environment down to the convective scale. Large vertical shear (850-200-hPa shear magnitude range 8-15 m/s) plays a very important role in preventing Chantal from intensifying. The storm had a poorly defined vortex that only extended up to 5-6-km altitude, and an adjacent intense convective region that comprised a mesoscale convective system (MCS). The entire low-level circulation center was in the rain-free western side of the storm, about 80 km to the west-southwest of the MCS. The MCS appears to have been primarily the result of intense convergence between large-scale, low-level easterly flow with embedded downdrafts, and the cyclonic vortex flow. The individual cells in the MCS such as cell 2 during the period of the observations were extremely intense, with reflectivity core diameters of 10 km and peak updrafts exceeding 20 m/s. Associated with this MCS were two broad subsidence (warm) regions, both of which had portions over the vortex. The first layer near 700 hPa was directly above the vortex and covered most of it. The second layer near 500 hPa was along the forward and right flanks of cell 2 and undercut the anvil divergence region above. There was not much resemblance of these subsidence layers to typical upper-level warm cores in hurricanes that are necessary to support strong surface winds and a low central pressure. The observations are compared to previous studies of weakly sheared storms and modeling studies of shear effects and intensification. The configuration of the convective updrafts, low-level circulation, and lack of vertical coherence between the upper- and lower-level warming regions likely inhibited intensification of Chantal. This configuration is consistent with modeled vortices in sheared environments, which suggest the strongest convection and rain in the downshear left quadrant of the storm, and subsidence in the upshear right quadrant. The vertical shear profile is, however, different from what was assumed in previous modeling in that the winds are strongest in the lowest levels and the deep tropospheric vertical shear is on the order of 10-12 m/s.

Heymsfield, G. M.↗

NASA NTRS2006

A Multi-scale Modeling System: Developments, Applications and Critical Issues

A multi-scale modeling framework (MMF), which replaces the conventional cloud parameterizations with a cloud-resolving model (CRM) in each grid column of a GCM, constitutes a new and promising approach. The MMF can provide for global coverage and two-way interactions between the CRMs and their parent GCM. The GCM allows global coverage and the CRM allows explicit simulation of cloud processes and their interactions with radiation and surface processes. A new MMF has been developed that is based the Goddard finite volume GCM (fvGCM) and the Goddard Cumulus Ensemble (GCE) model. This Goddard MMF produces many features that are similar to another MMF that was developed at Colorado State University (CSU), such as an improved .surface precipitation pattern, better cloudiness, improved diurnal variability over both oceans and continents, and a stronger, propagating Madden-Julian oscillation (MJO) compared to their parent GCMs using conventional cloud parameterizations. Both MMFs also produce a precipitation bias in the western Pacific during Northern Hemisphere summer. However, there are also notable differences between two MMFs. For example, the CSU MMF simulates less rainfall over land than its parent GCM. This is why the CSU MMF simulated less overall global rainfall than its parent GCM. The Goddard MMF overestimates global rainfall because of its oceanic component. Some critical issues associated with the Goddard MMF are presented in this paper.

Tao, Wei-Kuo↗

NASA NTRS2004

Microphysical Timescales in Clouds and their Application in Cloud-Resolving Modeling

Computational phenomena (i.e., spurious supersaturation and negative mixing ratio of cloud water) usually exist in cloud-resolving models when the time step for explicit integration is larger than a microphysical timescale in clouds. In this paper, the microphysical timescales in clouds are studied, showing that the timescale of water vapor condensation (or cloud water evaporation) is smaller than 10 s - the order of a typical time step for cloud-resolving models. To avoid spurious computational phenomena in cloud-resolving modeling, it is suggested that moist entropy be used as a prognostic thermodynamic variable, and temperature be diagnosed from that and other prognostic variables. A simple numerical model with moist entropy as a prognostic variable, for example, is presented to show that spurious computational phenomena are removed when moist entropy is used as a prognostic variable.

Zeng, Xi-Ping↗

NASA NTRS2004

Implementation of a Message Passing Interface into a Cloud-Resolving Model for Massively Parallel Computing

The capability for massively parallel programming (MPP) using a message passing interface (MPI) has been implemented into a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model. The design for the MPP with MPI uses the concept of maintaining similar code structure between the whole domain as well as the portions after decomposition. Hence the model follows the same integration for single and multiple tasks (CPUs). Also, it provides for minimal changes to the original code, so it is easily modified and/or managed by the model developers and users who have little knowledge of MPP. The entire model domain could be sliced into one- or two-dimensional decomposition with a halo regime, which is overlaid on partial domains. The halo regime requires that no data be fetched across tasks during the computational stage, but it must be updated before the next computational stage through data exchange via MPI. For reproducible purposes, transposing data among tasks is required for spectral transform (Fast Fourier Transform, FFT), which is used in the anelastic version of the model for solving the pressure equation. The performance of the MPI-implemented codes (i.e., the compressible and anelastic versions) was tested on three different computing platforms. The major results are: 1) both versions have speedups of about 99% up to 256 tasks but not for 512 tasks; 2) the anelastic version has better speedup and efficiency because it requires more computations than that of the compressible version; 3) equal or approximately-equal numbers of slices between the x- and y- directions provide the fastest integration due to fewer data exchanges; and 4) one-dimensional slices in the x-direction result in the slowest integration due to the need for more memory relocation for computation.

Juang, Hann-Ming Henry↗

NASA NTRS2004

Sensitivity of a Cloud-Resolving Model to the Bulk and Explicit Bin Microphysical Schemes: Validations with a PRE-STORM Case - Part 1

A cloud-resolving model is used to study sensitivities of two different microphysical schemes, one is the bulk type, and the other is an explicit bin scheme, in simulating a mid-latitude squall line case (PRE-STORM, June 10-11, 1985). Simulations using different microphysical schemes are compared with each other and also with the observations. Both the bulk and bin models reproduce the general features during the developing and mature stage of the system. The leading convective zone, the trailing stratiform region, the horizontal wind flow patterns, pressure perturbation associated with the storm dynamics, and the cool pool in front of the system all agree well with the observations. Both the observations and the bulk scheme simulation serve as validations for the newly incorporated bin scheme. However, it is also shown that, the bulk and bin simulations have distinct differences, most notably in the stratiform region. Weak convective cells exist in the stratiform region in the bulk simulation, but not in the bin simulation. These weak convective cells in the stratiform region are remnants of the previous stronger convections at the leading edge of the system. The bin simulation, on the other hand, has a horizontally homogeneous stratiform cloud structure, which agrees better with the observations. Preliminary examinations of the downdraft core strength, the potential temperature perturbation, and the evaporative cooling rate show that the differences between the bulk and bin models are due mainly to the stronger low-level evaporative cooling in convective zone simulated in the bulk model. Further quantitative analysis and sensitivity tests for this case using both the bulk and bin models will be presented in a companion paper.

Li, Xiao-Wen↗

NASA NTRS2004

A Study of the Response of Deep Tropical Clouds to Mesoscale Processes: Sensitivities to Microphysics, Radiation, and Surface Fluxes - Part 2

The Goddard Cumulus Ensemble (GCE) model is used to examine the sensitivities of surface fluxes, explicit radiation, and ice microphysical processes on multi-day simulations of deep tropical convection over the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE). The simulations incorporate large-scale advective temperature and moisture forcing, as well as large-scale momentum, that are updated every time step on a periodic lateral boundary grid. This study shows that when surface fluxes are eliminated, the mean atmosphere is much cooler and drier, convection and CAPE are much weaker, precipitation is less, and cloud coverage in stratiform regions much greater. Surface fluxes using the TOGA COARE flux algorithm are weaker than with the aerodynamic formulation, but closer to the observed fluxes. In addition, similar trends noted above for the case without surface fluxes are produced for the TOGA flux case, albeit to a much lesser extent. The elimination of explicit shortwave and longwave radiation is found to have only minimal effects on the mean thermodynamics, convection, and precipitation. However explicit radiation does have a significant impact on cloud temperatures and structure above 200 mb and on the overall mean vertical circulation. The removal of ice processes produces major changes in the structure of the cloud. Much of the liquid water is transported aloft and into anvils above the melting layer (600 mb), leaving narrow, but intense bands of rainfall in convective regions. The elimination of melting processes leads to greater hydrometeor mass below the melting layer, and produces a much warmer and moister boundary layer, leading to a greater mean CAPE. Finally, the elimination of the graupel species has only a small impact on mean total precipitation, thermodynamics, and dynamics of the simulation, but does produce much greater snow mass just above the melting layer. Some of these results differ from previous CRM studies of tropical systems, which is likely due to the type of simulated system, total time integration, and model setup.

Johnson, Daniel↗

NASA NTRS2004

Structure of the Highly Sheared Tropical Storm Chantal During CAMEX-4

NASA's 4th Convection and Moisture Experiment (CAMEX-4) focused on Atlantic hurricanes during the 2001 hurricane season and it involved both NASA and NOAA participation. The NASA ER-2 and DC-8 aircraft were instrumented with unique remote sensing instruments to help increase the overall understanding of hurricanes. This paper is concerned about one of the storms studied, Tropical Storm Chantal, that was a weak storm which failed to intense into a hurricane. One of the practical questions of high importance is why some tropical sto~ins intensify into hurricanes, and others remain weak or die altogether. The magnitude of the difference between the horizontal winds at lower levels and upper altitudes in a tropical storm, i.e., the wind shear, is one important quantity that can affect the intensification of a tropical storm. Strong shear as was present during Tropical Storm Chantal s lifetime and it was detrimental to its intensification. The paper presents an analysis of unique aircraft observations collected from Chantal including an on-board radar, radiometers, dropsondes, and flight level measurements. These measurements have enabled us to examine the internal structure of the winds and thermal structure of Chantal. Most of the previous studies have involved intense hurricanes that overcame the effects of shear and this work has provided new insights into what prevents a weaker storm from intensifying. The storm had extremely intense thunderstorms and rainfall, yet its main circulation was confined to low levels of the atmosphere. Chantal's thermal structure was not configured properly for the storm to intensify. It is most typical that huricanes have a warm core structure where warm temperatures in upper levels of a storm s circulation help intensify surface winds and lower its central pressure. Chantal had two weaker warm layers instead of a well-defined warm core. These layers have been related to the horizontal and vertical winds and precipitation structure and have helped us learn more about why this storm didn't develop.

Heymsfield, G. M.↗

NASA NTRS2004

Sensitivity of a Cloud-Resolving Model to the Bulk and Explicit Bin Microphysical Schemes

A cloud-resolving model is used to study sensitivities of two different microphysical schemes, one is the traditional bulk type, and the other is an explicit bin scheme, in simulating a mid-latitude squall line case (PRE-STORM, June 10-1 1,1985). Simulations using different microphysical schemes are compared with each other and also with the observations. Both the bulk and bin models reproduce the general features during the developing and mature stage of the system. Furthermore, the observations and the well-proven bulk scheme simulation serve as validations for the newly incorporated bin scheme. However, it is also shown that the bulk and bin simulations have distinct differences, most notably in the stratiform region of the squall line system. Weak convective cells exist in the stratiform region in the bulk simulation, but not in the bin simulation. These weak convective cells in the stratiform region simulated in the bulk scheme model are remnants of the stronger convections previously at the leading edge of the system, sustained by horizontal vorticity generated by its own cool pool near the surface. The bin simulation, on the other hand, has a horizontally homogeneous stratiform cloud structure, which agrees better with the observations. Examinations of the downdraft core strength, the potential temperature perturbation, and the evaporative cooling rate show that the differences between the bulk and bin models are due mainly to the stronger low-level evaporative cooling in the convective zone simulated in the bulk microphysical scheme, which is unrealistic because of the assumptions made in raindrop size distribution. Further sensitivity tests that reduce the evaporation rate in bulk scheme artificially produce more upright convective core and less weak cores in stratiform region. However, they produce weaker upper level outflow and consequently less stratiform rain area. The addition of a more realistic raindrop breakup scheme in the bin scheme results more realistic radar reflectivity and stronger surface rainfall. Despite the increase of the rain evaporation and strengthening of the near surface cool pool, bin scheme with rain breakup shows homogeneous stratiform rain. These sensitivity tests prove the robustness of the bin microphysical scheme and the difficulty of tuning the limited parameters in the bulk microphysical scheme to realistically reproduce detail structures in a mid-latitude squall line case study.

Li, Xiao-Wen↗

NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗