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NASA NTRS2014

Development of Super Ensemble-Based Aviation Turbulence Guidance (SEATG) for Air Traffic Management

A new method for forecasting turbulence is developed and evaluated using the high resolution weather model and in situ turbulence observations from commercial aircraft. The new method is an ensemble of various turbulence metrics from multiple time-lagged ensemble forecasts created using a sequence of four procedures. These include weather modeling, calculation of turbulence metrics, mapping the metrics into a common turbulence-scale, and production of final forecast. The new method uses similar methodology as current operational turbulence forecast with three improvements. First, it uses a higher resolution ((delta)x = 3 km) weather model to capture cloud resolving scale phenomena. Second, it computes the metrics for multiple forecasts that are combined at the same valid time resulting in a time-lagged ensemble of multiple turbulence metrics. Finally, it provides both deterministic and probabilistic turbulence forecasts. Results show the new forecasts match well with observed radar reflectivity along a surface front as well as convectively induced turbulence outside the clouds on research period. Overall performance skill of the new turbulence forecast compared with the observed EDR data during the research period is superior to any single turbulence metric. The probabilistic turbulence forecast is used in an example air traffic management application for creating a wind-optimal route considering turbulence information. The wind-optimal route passing through areas of 50% potential for moderate-or-greater turbulence and the lateral turbulence avoidance routes starting from three different waypoints along the wind-optimal route from Los Angeles international airport to John F. Kennedy international airport are calculated using different turbulence forecasts. This example shows additional flight time is required to avoid potential turbulence encounters.

modeling↗

NASA NTRS1991

Optically thin cirrus clouds over oceans and possible impact on sea surface temperature of warm pool in western Pacific

Over the convectively active tropical ocean regions, the measurement made from space in the IR and visible spectrum have revealed the presence of optically thin cirrus clouds, which are quite transparent in the visible and nearly opaque in the IR. The Nimbus-4 IR Interferometer Spectrometer (IRIS), which has a field of view (FOV) of approximately 100 km, was utilized to examine the IR optical characteristics of these cirrus clouds. From the IRIS data, it was observed that these optically thin cirrus clouds prevail extensively over the warm pool region of the equatorial western Pacific, surrounding Indonesia. It is found that the seasonal cloud cover caused by these thin cirrus clouds exceeds 50 percent near the central regions of the warm pool. For most of these clouds, the optical thickness in the IR is less than or = 2. It is deduced that the dense cold anvil clouds associated with deep convection spread extensively and are responsible for the formation of the thin cirrus clouds. This is supported by the observation that the coverage of the dense anvil clouds is an order of magnitude less than that of the thin cirrus clouds. From these observations, together with a simple radiative-convective model, it is inferred that the optically thin cirrus can provide a greenhouse effect, which can be a significant factor in maintaining the warm pool. In the absence of fluid transports, it is found that these cirrus clouds could lead to a runaway greenhouse effect. The presence of fluid transport processes, however, act to moderate this effect. Thus, if a modest 20 W/sq m energy input is considered to be available to warm the ocean, then it is found that the ocean mixed-layer of a 50-m depth will be heated by approximately 1 C in 100 days.

Prabhakara, C.↗

NASA NTRS2009

Distribution and Radiative Forcing of Tropical Thin Cirrus Clouds

To understand the radiative impact of tropical thin cirrus clouds, the frequency of occurrence and optical depths of these clouds have been derived. Thin cirrus clouds are defined here as being those that are not detected by the operational Moderate Resolution Imaging Spectroradiometer (MODIS) cloud mask, corresponding to an optical depth value of approximately 0.3 or smaller, but that are detectable in terms of the cirrus reflectance product based on the MODIS 1.375-micron channel. With such a definition, thin cirrus clouds were present in more than 40% of the pixels flagged as clear sky by the operational MODIS cloud mask algorithm. It is shown that these thin cirrus clouds are frequently observed in deep convective regions in the western Pacific. Thin cirrus optical depths were derived from the cirrus reflectance product. Regions of significant cloud fraction and large optical depths were observed in the Northern Hemisphere during the boreal spring and summer and moved southward during the boreal autumn and winter. The radiative effects of tropical thin cirrus clouds were studied on the basis of the retrieved cirrus optical depths, the atmospheric profiles derived from the Atmospheric Infrared Sounder (AIRS) observations, and a radiative transfer model in conjunction with a parameterization of ice cloud spectral optical properties. To understand how these clouds regulate the radiation field in the atmosphere, the instantaneous net fluxes at the top of the atmosphere (TOA) and at the surface were calculated. The present study shows positive and negative net forcings at the TOA and at the surface, respectively. The positive (negative) net forcing at the TOA (surface) is due to the dominance of longwave (shortwave) forcing. Both the TOA and surface forcings are in a range of 0-20 W/sq m, depending on the optical depths of thin cirrus clouds.

THIN CIRRUS CLOUDS↗

NASA NTRS2014

Thermodynamics in the Suppressed Phase of the Madden-Julian Oscillation Using a Multiplatform Strategy

The Madden-Julian Oscillation (MJO) represents a prominent mode of intraseasonal tropical variability. It is manifest by coherent large-scale changes in atmospheric circulation, convection, and thermodynamic processes. Preconditioning of the environment prior to the active phase of the MJO has been noted, but the balance of theorized mechanisms to accomplish this process remains unresolved. Further, there is a lack of consensus on the means by which primary initiation of an MJO event occurs. Observational and modeling efforts have recently been undertaken to advance our understanding of the physical underpinnings governing MJO development. However these intensive studies are often limited in space and/or time and are potentially subject to model deficiencies. Satellite observations, especially those providing vertical resolution of temperature and moisture, provide an opportunity to expand our knowledge of processes critical to MJO initiation and preconditioning. This work will provide an analysis of suppressed phase thermodynamics with an emphasis on the use of a complementary suite of satellite observations including AIRS/AMSU-A profiles, CERES radiative fluxes, and cloud properties observed by MODIS. Emphasis of this work will regard the distribution of cloud regimes, their radiative-convective effects, and their relationship to moist static energy during the recharge and suppressed stages of MJO initiation and eastward propagation. The analyses will make use of cloud regimes from MODIS observations to provide a compositing technique that enables the identification of systematic connections between different cloud regimes and the larger scale environment. Within these cloud regimes, the relationship between the associated cloud-radiative effects observed by CERES, vertically-resolved and vertically-integrated thermodynamics using AIRS/AMSU-A observations, and atmospheric boundary layer fluxes will be demonstrated.

Roberts, J. Brent↗

NASA NTRS1994

Forecast skill of a high-resolution real-time mesoscale model designed for weather support of operations at Kennedy Space Center and Cape Canaveral Air Station

NASA funded Mesoscale Environmental Simulations and Operations (MESO), Inc. to develop a version of the Mesoscale Atmospheric Simulation System (MASS). The model has been modified specifically for short-range forecasting in the vicinity of KSC/CCAS. To accomplish this, the model domain has been limited to increase the number of horizontal grid points (and therefore grid resolution) and the model' s treatment of precipitation, radiation, and surface hydrology physics has been enhanced to predict convection forced by local variations in surface heat, moisture fluxes, and cloud shading. The objective of this paper is to (1) provide an overview of MASS including the real-time initialization and configuration for running the data pre-processor and model, and (2) to summarize the preliminary evaluation of the model's forecasts of temperature, moisture, and wind at selected rawinsonde station locations during February 1994 and July 1994. MASS is a hydrostatic, three-dimensional modeling system which includes schemes to represent planetary boundary layer processes, surface energy and moisture budgets, free atmospheric long and short wave radiation, cloud microphysics, and sub-grid scale moist convection.

Taylor, Gregory E.↗

NASA NTRS1986

Mesoscale waves as a probe of Jupiter's deep atmosphere

Search of the Voyager images of Jupiter reveals a class of mesoscale waves occurring near the extrema of the zonal velocity profile between latitudes 30 deg S and 30 deg N. The average horizontal wavelength is 300 km, compared to an atmospheric scale height of 20 km; the standard deviation about the mean is only 20 percent. The alignment of most wave trains is nearly zonal, i.e., wave crests are north-south. A typical wave packet is 20 wave crests in length and 1300 km wide. Modeling shows that the waves propagate in a duct below the ammonia condensation level (the visible clouds). For selection of one dominant mode, the Richardson number in the duct must be of order unity; this is the first quantitative determination that has ever been made of the stability of Jupiter's atmosphere below its clouds. The duct is topped by a trapping layer, the ammonia clouds, where the Richardson number is less than 0.25. Meridional trapping of the wave packets is due to the shear in the zonal wind. It is speculated that the period of the waves is diurnal and that they do not propagate poleward of latitudes + or - 30 deg because the Coriolis frequency exceeds the duct Brunt frequency. The waves might be excited by diurnal variations of moist convective activity in the ammonia clouds.

Flasar, F. M.↗

NASA NTRS1986

Satellite contributions to convective scale weather analysis and forecasting

Severe weather phenomena which are amenable to remote sensing by satellite instruments and having resolution fine enough to discern mesoscale features are described. GOES satellites acquire imagery with 1 km resolution in the visible band and 8 km at IR wavelengths. Animation of the images allows tracking the evolution and motions of clouds, which are the prime indicators of convective activity. Sample satellite imagery of sea, lake and river breezes which reveal differential heating processes, the effect of early morning cloud cover, thunderstorm outflow processes, and mesoscale convective systems are provided. Techniques for analyzing the satellite data to predict the onset of severe weather are discussed.

Purdom, James F. W.↗

NASA NTRS2020

An Overview of CMIP5 and CMIP6 Simulated Cloud Ice, Radiation Fields, Surface Wind Stress, Sea Surface Temperatures and Precipitation over Tropical and Subtropical Oceans

The potential links between ice water path (IWP), radiation, circulation, sea surface temperature (SST) and precipitation over the Pacific and Atlantic Oceans resulting from the falling ice radiative effects (FIREs) are examined from present day model outputs of CMIP5 and CMIP6. The latter is divided into two subsets with (SON6) and without FIREs (NOS6) as more models with FIREs are included in CMIP6 than in CMIP5. Improvement in floating cloud ice (~20 g m-2) is noticeable over convective regions in CMIP6 relative to CMIP5. The inclusion of FIREs in SON6 subset may contribute to reduce biases of overestimated outgoing longwave radiation and downward surface shortwave and overestimated reflected shortwave at the top of the atmosphere (TOA) by magnitudes of 4?8 W m-2 over convective regions against CERES, compared to NOS6 subset. The reduced biases in radiative fluxes in convective regions stabilize the atmosphere and lead to circulation, SST, cloud and precipitation changes over the trade-wind regions, as seen from improved radiative fluxes (4?15 W m-2), surface wind stress biases, SST (0.2?0.8 K) and precipitation (1 mm day-1) biases. The significant improvement from NOS6 to SON6 leads to improved multi-model means for CMIP6 relative to CMIP5 for radiation fields over the trade wind regions but the degradation over convective zones is attributed to NOS6 subset. The results suggest that other sources of uncertainty and deficiencies in climate models may play significant roles for reducing discrepancies although FIREs, via radiation-circulation coupling, may be one of the factors that help to reduce regional biases.

Jui-Lin F Li↗

NASA NTRS2018

Microphysical Variability of Amazonian Deep Convective Cores Observed by CloudSat and Simulated by a Multi-Scale Modeling Framework

Recently launched cloud observing satellites provide information about the vertical structure of deep convection and its microphysical characteristics. In this study, CloudSat reflectivity data is stratified by cloud type, and the contoured frequency by altitude diagrams reveal a doublearc structure in deep convective cores (DCCs) above 8 km. This suggests two distinct hydrometeor modes (snow versus hail/graupel) controlling variability in reflectivity profiles. The day–night contrast in the double arcs is about four times larger than the wet–dry season contrast. Using QuickBeam, the vertical reflectivity structure of DCCs is analyzed in two versions of the Superparameterized Community Atmospheric Model (SP-CAM) with single-moment (no graupel) and double-moment (with graupel) microphysics. Doublemoment microphysics shows better agreement with observed reflectivity profiles; however, neither model variant captures the double-arc structure. Ultimately, the results show that simulating realistic DCC vertical structure and its variability requires accurate representation of ice microphysics, in particular the hail/graupel modes, though this alone is insufficient.

Dodson, J. Brant↗

NASA NTRS2002

Mesoscale Convective Systems During SCSMEX: Simulations with a Regional Climate Model and a Cloud-Resolving Model

The South China Sea Monsoon Experiment (SCSMEX) was conducted in May-June 1998. One of its major objectives is to better understand the key physical processes for the onset and evolution of the summer monsoon over Southeast Asia and southern China. Multiple observation platforms (e.g., upper-air soundings, Doppler radar, ships, wind profilers, radiometers, etc.) during SCSMEX provided a first attempt at investigating the detailed characteristics of convection and circulation changes associated with monsoons over the South China Sea region. SCSMEX also provided precipitation derived from atmospheric budgets and comparison to those obtained from the Tropical Rainfall Measuring Mission (TRMM). In this paper, a regional scale model (with grid size of 20 km) and Goddard Cumulus Ensemble (GCE) model (with 1 km grid size) are used to perform multi-day integration to understand the precipitation processes associated with the summer monsoon over Southeast Asia and southern China. The regional climate model is used to understand the soil-precipitation interaction and feedback associated with a flood event that occurred in and around China's Yantz River during SCSMEX Sensitivity tests on various land surface models, sea surface temperature (SST) variations, and cloud processes are performed to understand the precipitation processes associated with the onset of the monsoon over the S. China Sea during SCSMEX. These tests have indicated that the land surface model has a major impact on the circulation over the S. China Sea. Cloud processes can effect the precipitation pattern while SST variation can effect the precipitation amounts over both land and ocean. The exact location (region) of the flooding can be effected by the soil-rainfall feedback. The GCE-model results captured many observed precipitation characteristics because it used a fine grid size. For example, the model simulated rainfall temporal variation compared quite well to the sounding-estimated rainfall. The results show there are more latent heat fluxes prior to the onset of the monsoon. However, more rainfall was simulated after the onset of the monsoon. This modeling study indicates the latent heat fluxes (or evaporation) have more of an impact on precipitation processes and rainfall in the regional climate model simulations than in the cloud-resolving model simulations. Research is underway to determine if the difference in the grid sizes or the moist processes used in these two models is responsible for the differing influence of surface fluxes an precipitation processes.

Tao, W.-K.↗

NASA NTRS1987

Factors leading to the formation of arc cloud complexes

A total of 12 mesoscale convective systems (MCSs) were investigated. The duration of the gust front, produced by each MCS, was used to classify the MCSs. Category 1 MCSs were defined as ones that produced a gust front and the gust front lasted for more than 6 h. There were 7 category 1 MCSs in the sample. Category 2 MCSs were defined as ones that produced a gust front and the gust front lasted for 6 h or less. There were 4 category 2 MCSs. The MCS of Case 12 was not categorized because the precipitation characteristics were similar to a squall line, rather than an MCS. All of the category 1 MCSs produced arc cloud complexes (ACCs), while only one of the category 2 MCSs produced an ACC. To determine if there were any differences in the characteristics between the MCSs of the two categories, composite analyses were accomplished. The analyses showed that there were significant differences in the characteristics of category 1 and 2 MCSs. Category 1 MCSs, on average, had higher thunderstorm heights, greater precipitation intensities, colder cloud top temperatures and produced larger magnitudes of surface divergence than category 2 MCSs.

Welshinger, Mark John↗

NASA NTRS1993

Planetary circulations in the presence of transient and self-induced heating

The research program focuses on large-scale circulations and their interaction with the global convective pattern. An 11-year record of global cloud imagery and contemporaneous fields of motion and temperature have been used to investigate organized convection and coherent variability of the tropical circulation operating on intraseasonal time scales. This study provides a detailed portrait of tropical variability associated with the so-called Madden-Julian Oscillation (MJO). It reveals the nature, geographical distribution, and seasonality of discrete convective signal, which is a measure of feedback between the circulation and the convective pattern. That discrete spectral behavior has been evaluated in light of natural variability of the ITCZ associated with climatological convection. A composite signature of the MJO, based on cross-covariance statistics of cloud cover, motion, and temperature, has been constructed to characterize the lifecycle of the disturbance in terms of these properties. The composite behavior has also been used to investigate the influence the MJO exerts on the zonal-mean circulation and the involvement of the MJO in transfers of momentum between the atmosphere and the solid Earth. The aforementioned observational studies have led to the production of two animations. One reveals the convective signal in band-pass filtered OLR and compares it to climatological convection. The other is a 3-dimensional visualization of the composite lifecycle of the MJO. With a clear picture of the MJO in hand, feedback between the circulation and the convective pattern can be diagnosed meaningfully in numerical simulations. This process is being explored in calculations with the linearized primitive equations on the sphere in the presence of realistic stability and shear. The numerical framework represents climatological convection as a space-time stochastic process and wave-induced convection in terms of the vertically-integrated moisture flux convergence. In these calculations, frictional convergence near the equator emerges as a key to feedback between the circulation and the convective pattern. At low latitudes, nearly geostrophic balance in the boundary layer gives way to frictional balance. This shifts the wave-induced convection into phase with the temperature anomaly and allows the attending heating to feed back positively onto the circulation. The calculations successfully reproduce the salient features of the MJO. They are being used to understand the growth and decay phases of the composite lifecycle and the conditions that favor amplification of the MJO.

Salby, Murry L.↗

NASA NTRS1983

Diagnosing convective instability using VAS data

The utility of combining visible and various infrared images from the VAS to produce a forecasting tool, that can be available on a near real time basis, to predict severe weather development is shown. Areas where dry air in the midtroposphere overlays substantial moisture at low levels are used to diagnose mesoscale regions that have the potential for being convectively unstable before the onset of severe convection. Specifically, 6.7 micron water vapor imagery, used for isolating regions of substantial midlevel dryness, are combined with images of low level clouds or with split-window low level moisture images to delineate regions that have the potential for convective instability. In areas where scattered low level clouds are present, computer generated, color image combinations are used to isolate those warm, low level clouds that are in potential convectively unstable environments from clouds that exist under a deeply moist atmosphere. In clear regions, the split window technique is used for delineating areas of substantial boundary layer moisture. These images are again computer overlayed by the midlevel dryness to produce a color coded image of potential convective instability.

Petersen, R. A.↗

NASA NTRS2015

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Precipitation↗

NASA NTRS2019

The Impact of Neglecting Ice Phase on Cloud Optical Depth Retrievals from AERONET Cloud Mode Observations

Clouds present many challenges to climate modelling. To develop and verify the parameterisations needed to allow climate models to represent cloud structure and processes, there is a need for high-quality observations of cloud optical depth from locations around the world. Retrievals of cloud optical depth are obtainable from radiances measured by Aerosol Robotic Network (AERONET) radiometers in “cloud mode” using a two-wavelength retrieval method. However, the method is unable to detect cloud phase, and hence assumes that all of the cloud in a profile is liquid. This assumption has the potential to introduce errors into long term statistics of retrieved optical depth for clouds that also contain ice. Using a set of idealized cloud profiles we find that, for optical depths above 20, the fractional error in retrieved optical depth is a linear function of the fraction of the optical depth that is due to the presence of ice cloud (“ice fraction”). Clouds that are entirely ice have positive errors with magnitudes of the order of 55% to 70 %. We derive a simple linear equation that can be used as a correction at AERONET sites where ice fraction can be independently estimated. Using this linear equation, we estimate the magnitude of the error for a set of cloud profiles from five sites of the Atmospheric Radiation Measurement programme. The dataset contains separate retrievals of ice and liquid retrievals; hence ice fraction can be estimated. The magnitude of the error at each location was related to the relative frequencies of occurrence in thick frontal cloud at the mid-latitude sites and of deep convection at the tropical sites – that is, of deep cloud containing both ice and liquid particles. The long-term mean optical depth error at the five locations spans the range 2– 4, which we show to be small enough to allow calculation of top-of-atmosphere flux to within 10% and surface flux to about 15 %.

Shonk, Jonathan K. P.↗

NASA NTRS2007

Low-Level Cloud Variability over the Equatorial Cold Tongue in Observations and Models

A fourth paper now in press is, Low-level cloud variability over the equatorial cold tongue in observations and models, by D. K. Mansbach and J. R. Norris (2007, J. Climate). This study examined cloud and meteorological observations from satellite, surface, and reanalysis datasets and fount that monthly anomalies in low-level cloud amount and near-surface temperature advection are strongly negatively correlated on the southern side of the equatorial Pacific cold tongue. This inverse correlation occurs independently of relationships between cloud amount and sea surface temperature (SST) or lower tropospheric static stability (LTS) and the combination of advection plus SST or LTS explains significantly more interannual cloud variability in a multilinear regression than does SST or LTS alone. Warm anomalous advection occurs when the equatorial cold tongue is well defined and the southeastern Pacific trade winds bring relatively warm air over colder water. Ship meteorological reports and soundings show that the atmospheric surface layer becomes stratified under these conditions, thus inhibiting the upward mixing of moisture needed to sustain cloudiness against subsidence and entrainment drying. Cold anomalous advection primarily occurs when the equatorial cold tongue is weak or absent and the air-sea temperature difference is substantially negative. These conditions favor a more convective atmospheric boundary layer, greater cloud amount, and less frequent occurrence of clear sky. Examination of output from global climate models developed by the Geophysical Fluid Dynamics Laboratory (GFDL) and the National Center for Atmospheric Research (NCAR) indicates that both models generally fail to simulate the cloud-advection relationships observed on the northern and southern sides of the equatorial cold tongue. Although the GFDL atmosphere model does reproduce the expected signs of cloud-advection correlations when forced with prescribed historical SST variations, it does not consistently do so when coupled to an ocean model. The NCAR model has difficulty reproducing the observed correlations in both atmosphere-only and coupled versions. This suggests that boundary layer cloud parameterizations could be improved through better representation of the effects of advection over varying SST.

Mansbach, David K.↗

NASA NTRS1990

Gravity wave initiated convection

The vertical velocity of convection initiated by gravity waves was investigated. In one particular case, the convective motion-initiated and supported by the gravity wave-induced activity (excluding contributions made by other mechanisms) reached its maximum value about one hour before the production of the funnel clouds. In another case, both rawinsonde and geosynchronous satellite imagery were used to study the life cycles of severe convective storms. Cloud modelling with input sounding data and rapid-scan imagery from GOES were used to investigate storm cloud formation, development and dissipation in terms of growth and collapse of cloud tops, as well as, the life cycles of the penetration of overshooting turrets above the tropopause. The results based on these two approaches are presented and discussed.

Hung, R. J.↗

NASA NTRS2000

Diurnal Variability of the Hydrologic Cycle and Radiative Fluxes: Comparisons Between Observation and a GCM

The simulated diurnal cycle is in many ways an ideal test bed for new physical parameterizations. The purpose of this paper is to compare observations from the Tropical Rainfall Measurement Mission, the Earth Radiation Budget Experiment, the International Satellite Cloud Climatology Project, the Clouds and the Earth's Radiant Energy System Experiment, and the Anglo-Brazilian Amazonian Climate Observation Study with the diurnal variability of the Amazonian hydrologic cycle and radiative energy budget as simulated by the Colorado State University general circulation model, and to evaluate improvements and deficiencies of the model physics. The model uses a prognostic cumulus kinetic energy (CKE) to relax the quasi-equilibrium closure of the Arakawa-Schubert cumulus parameterization. A parameter, alpha, is used to relate the CKE to the cumulus mass flux. This parameter is expected to vary with cloud depth, mean shear, and the level of convective activity, but up to now a single constant value for all cloud types has been used. The results of the present study show clearly that this approach cannot yield realistic simulations of both the diurnal cycle and the monthly mean climate state. Improved results are obtained using a version of the model in which alpha is permitted to vary with cloud depth.

Lin, Xin↗