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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
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NASA NTRS1990

Radiatively driven stratosphere-troposphere interactions near the tops of tropical cloud clusters

Results are presented of two numerical simulations of the mechanism involved in the dehydration of air, using the model of Churchill (1988) and Churchill and Houze (1990) which combines the water and ice physics parameterizations and IR and solar-radiation parameterization with a convective adjustment scheme in a kinematic nondynamic framework. One simulation, a cirrus cloud simulation, was to test the Danielsen (1982) hypothesis of a dehydration mechanism for the stratosphere; the other was to simulate the mesoscale updraft in order to test an alternative mechanism for 'freeze-drying' the air. The results show that the physical processes simulated in the mesoscale updraft differ from those in the thin-cirrus simulation. While in the thin-cirrus case, eddy fluxes occur in response to IR radiative destabilization, and, hence, no net transfer occurs between troposphere and stratosphere, the mesosphere updraft case has net upward mass transport into the lower stratosphere.

Churchill, Dean D.↗
NASA NTRS1994

A global numerical study of radon-222 and lead-210 in the atmosphere using the AES and York University CDT General Circulation Model (AYCG)

The Canadian Climate Center (CCC) GCM has been modified to allow its use for studies in atmospheric chemistry. The initial experiments reported here have been run to test and allow sensitivity studies of the new transport module. The impact of different types of parameterization for the convective mixing have been studied based on the large scale evolution of Rn-222 and Pb-210. Preliminary results have shown that the use of a scheme, which mixes unstable columns over a very short time scale, produces a global distribution of lead that agrees in some aspects with observations. The local impact of different mixing schemes on a short lived tracer like the radon is very important.

Beagley, Stephen R.↗
NASA NTRS2001

Sensitivity of the Tropical Atmospheric Energy Balance to ENSO-Related SST Changes: Comparison of Climate Model Simulations to Observed Responses

This paper focuses on how fresh water and radiative fluxes over the tropical oceans change during ENSO warm and cold events and how these changes affect the tropical energy balance. At present, ENSO remains the most prominent known mode of natural variability at interannual time scales. While this natural perturbation to climate is quite distinct from possible anthropogenic changes in climate, adjustments in the tropical water and energy budgets during ENSO may give insight into feedback processes involving water vapor and cloud feedbacks. Although great advances have been made in understanding this phenomenon and realizing prediction skill over the past decade, our ability to document the coupled water and energy changes observationally and to represent them in climate models seems far from settled (Soden, 2000 J Climate). In a companion paper we have presented observational analyses, based principally on space-based measurements which document systematic changes in rainfall, evaporation, and surface and top-of-atmosphere (TOA) radiative fluxes. Here we analyze several contemporary climate models run with observed SSTs over recent decades and compare SST-induced changes in radiation, precipitation, evaporation, and energy transport to observational results. Among these are the NASA / NCAR Finite Volume Model, the NCAR Community Climate Model, the NCEP Global Spectral Model, and the NASA NSIPP Model. Key disagreements between model and observational results noted in the recent literature are shown to be due predominantly to observational shortcomings. A reexamination of the Langley 8-Year Surface Radiation Budget data reveals errors in the SST surface longwave emission due to biased SSTs. Subsequent correction allows use of this data set along with ERBE TOA fluxes to infer net atmospheric radiative heating. Further analysis of recent rainfall algorithms provides new estimates for precipitation variability in line with interannual evaporation changes inferred from the da Silva, Young, Levitus COADS analysis. The overall results from our analysis suggest an increase (decrease) of the hydrologic cycle during ENSO warm (cold) events at the rate of about 5 W/sq m per K of SST change. Model results agree reasonably well with this estimate of sensitivity. This rate is slightly less than that which would be expected for constant relative humidity over the tropical oceans. There remain, however, significant quantitative uncertainties in cloud forcing changes in the models as compared to observations. These differences are examined in relationship to model convection and cloud parameterizations Analysis of the possible sampling and measurement errors compared to systematic model errors is also presented.

Robertson, Franklin R.↗
DOE OSTI2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗
DOE OSTI2020

Interpreting and Stabilizing Machine-Learning Parametrizations of Convection

Neural networks are a promising technique for parameterizing subgrid-scale physics (e.g., moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption. For instance, it is not fully understood why neural network parameterizations often cause dramatic instability when coupled to atmospheric fluid dynamics. This paper introduces tools for interpreting their behavior that are customized to the parameterization task. First, we assess the nonlinear sensitivity of a neural network to lower-tropospheric stability and the midtropospheric moisture, two widely studied controls of moist convection. Second, we couple the linearized response functions of these neural networks to simplified gravity wave dynamics, and analytically diagnose the corresponding phase speeds, growth rates, wavelengths, and spatial structures. To demonstrate their versatility, these techniques are tested on two sets of neural networks, one trained with a super-parameterized version of the Community Atmosphere Model (SPCAM) and the second with a near-global cloud-resolving model (GCRM). Additionally, even though the SPCAM simulation has a warmer climate than the cloud-resolving model, both neural networks predict stronger heating/drying in moist and unstable environments, which is consistent with observations. Moreover, the spectral analysis can predict that instability occurs when GCMs are coupled to networks that support gravity waves that are unstable and have phase speeds larger than 5 m s -1 . In contrast, standing unstable modes do not cause catastrophic instability. Using these tools, differences between the SPCAM-trained versus GCRM-trained neural networks are analyzed, and strategies to incrementally improve both of their coupled online performance unveiled.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Moist Physics Parameterization Based on Deep Learning

Abstract Current moist physics parameterization schemes in general circulation models (GCMs) are the main source of biases in simulated precipitation and atmospheric circulation. Recent advances in machine learning make it possible to explore data‐driven approaches to developing parameterization for moist physics processes such as convection and clouds. This study aims to develop a new moist physics parameterization scheme based on deep learning. We use a residual convolutional neural network (ResNet) for this purpose. It is trained with 1‐year simulation from a superparameterized GCM, SPCAM. An independent year of SPCAM simulation is used for evaluation. In the design of the neural network, referred to as ResCu, the moist static energy conservation during moist processes is considered. In addition, the past history of the atmospheric states, convection, and clouds is also considered. The predicted variables from the neural network are GCM grid‐scale heating and drying rates by convection and clouds, and cloud liquid and ice water contents. Precipitation is derived from predicted moisture tendency. In the independent data test, ResCu can accurately reproduce the SPCAM simulation in both time mean and temporal variance. Comparison with other neural networks demonstrates the superior performance of ResNet architecture. ResCu is further tested in a single‐column model for both continental midlatitude warm season convection and tropical monsoonal convection. In both cases, it simulates the timing and intensity of convective events well. In the prognostic test of tropical convection case, the simulated temperature and moisture biases with ResCu are smaller than those using conventional convection and cloud parameterizations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Implicit learning of convective organization explains precipitation stochasticity

Accurate prediction of precipitation intensity is crucial for both human and natural systems, especially in a warming climate more prone to extreme precipitation. Yet, climate models fail to accurately predict precipitation intensity, particularly extremes. One missing piece of information in traditional climate model parameterizations is subgrid-scale cloud structure and organization, which affects precipitation intensity and stochasticity at coarse resolution. Here, using global storm-resolving simulations and machine learning, we show that, by implicitly learning subgrid organization, we can accurately predict precipitation variability and stochasticity with a low-dimensional set of latent variables. Using a neural network to parameterize coarse-grained precipitation, we find that the overall behavior of precipitation is reasonably predictable using large-scale quantities only; however, the neural network cannot predict the variability of precipitation (R 2 ~ 0.45) and underestimates precipitation extremes. The performance is significantly improved when the network is informed by our organization metric, correctly predicting precipitation extremes and spatial variability (R 2 ~ 0.9). The organization metric is implicitly learned by training the algorithm on a high-resolution precipitable water field, encoding the degree of subgrid organization. The organization metric shows large hysteresis, emphasizing the role of memory created by subgrid-scale structures. We demonstrate that this organization metric can be predicted as a simple memory process from information available at the previous time steps. These findings stress the role of organization and memory in accurate prediction of precipitation intensity and extremes and the necessity of parameterizing subgrid-scale convective organization in climate models to better project future changes of water cycle and extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

The Strong Impact of Weak Horizontal Convergence on Continental Shallow Convection

Idealized large-eddy simulation (LES) is a basic tool for studying three-dimensional turbulence in the planetary boundary layer. LES is capable of providing benchmark solutions for parameterization development efforts. However, real small-scale atmospheric flows develop in heterogeneous and transient environments with locally varying vertical motions inherent to open multiscale interactive dynamical systems. These variations are often too subtle to detect them by state-of-the-art remote and in situ measurements, and are typically excluded from idealized simulations. The present study addresses the impact of weak [i.e., O(10-6) s-1] short-lived low-level large-scale convergence/divergence perturbations on continental shallow convection. The results show a strong response of shallow nonprecipitating convection to the applied weak large-scale dynamical forcing. Evolutions of CAPE, mean liquid water path, and cloud-top heights are significantly affected by the imposed convergence/divergence. In contrast, evolving cloud-base properties, such as the area coverage and mass flux, are only weakly affected. To contrast those impacts with microphysical sensitivity, the baseline simulations are perturbed assuming different observationally based cloud droplet number concentrations and thus different rainfall. For the tested range of microphysical perturbations, the imposed convergence/divergence provides significantly larger impact than changes in the cloud microphysics. Simulation results presented here provide a stringent test for convection parameterizations, especially important for large-scale models progressing toward resolving some nonhydrostatic effects.

Meteorology & Atmospheric Sciences↗
DOE OSTI2021

Using Radiative Convective Equilibrium to Explore Clouds and Climate in the Community Atmosphere Model

Abstract Characteristics of, and fundamental differences between, the radiative‐convective equilibrium (RCE) climate states following the Radiative‐Convective Equilibrium Model Intercomparison Project (RCEMIP) protocols in the Community Atmosphere Model version 5 (CAM5) and version 6 (CAM6) are presented. This paper explores the characteristics of clouds, moisture, precipitation and circulation in the RCE state, as well as the tropical response to surface warming, in CAM5 and CAM6 with different parameterizations. Overall, CAM5 simulates higher precipitation rates that result in larger global average precipitation, despite lower outgoing longwave radiation compared to CAM6. Differences in the structure of clouds, particularly the amount and vertical location of cloud liquid, exist between the CAM versions and can, in part, be related to distinct representations of shallow convection and boundary layer processes. Both CAM5 and CAM6 simulate similar peaks in cloud fraction, relative humidity, and cloud ice, linked to the usage of a similar deep convection parameterization. These anvil clouds rise and decrease in extent in response to surface warming. More generally, extreme precipitation, aggregation of convection, and climate sensitivity increase with warming in both CAM5 and CAM6. This analysis provides a benchmark for future studies that explore clouds, convection, and climate in CAM with the RCEMIP protocols now available in the Community Earth System Model. These results are discussed within the context of realistic climate simulations using CAM5 and CAM6, highlighting the usefulness of a hierarchical modeling approach to understanding model and parameterization sensitivities to inform model development efforts.

Reed, Kevin A.↗
NASA NTRS2013

Characteristics of Mesoscale Organization in WRF Simulations of Convection during TWP-ICE

Compared to satellite-derived heating profiles, the Goddard Institute for Space Studies general circulation model (GCM) convective heating is too deep and its stratiform upper-level heating is too weak. This deficiency highlights the need for GCMs to parameterize the mesoscale organization of convection. Cloud-resolving model simulations of convection near Darwin, Australia, in weak wind shear environments of different humidities are used to characterize mesoscale organization processes and to provide parameterization guidance. Downdraft cold pools appear to stimulate further deep convection both through their effect on eddy size and vertical velocity. Anomalously humid air surrounds updrafts, reducing the efficacy of entrainment. Recovery of cold pool properties to ambient conditions over 5-6 h proceeds differently over land and ocean. Over ocean increased surface fluxes restore the cold pool to prestorm conditions. Over land surface fluxes are suppressed in the cold pool region; temperature decreases and humidity increases, and both then remain nearly constant, while the undisturbed environment cools diurnally. The upper-troposphere stratiform rain region area lags convection by 5-6 h under humid active monsoon conditions but by only 1-2 h during drier break periods, suggesting that mesoscale organization is more readily sustained in a humid environment. Stratiform region hydrometeor mixing ratio lags convection by 0-2 h, suggesting that it is strongly influenced by detrainment from convective updrafts. Small stratiform region temperature anomalies suggest that a mesoscale updraft parameterization initialized with properties of buoyant detrained air and evolving to a balance between diabatic heating and adiabatic cooling might be a plausible approach for GCMs.

Del Genio, Anthony D.↗
DOE OSTI2023

Diurnal cycle of precipitation over the tropics and central United States: intercomparison of general circulation models

Diurnal precipitation is a fundamental mode of variability that climate models have difficulty in accurately simulating. Here, in this work, the diurnal cycle of precipitation (DCP) in participating climate models from the Global Energy and Water Exchanges' DCP project is evaluated over the tropics and central United States. Common model biases such as excessive precipitation over the tropics, too frequent light-to-moderate rain, and the failure to capture propagating convection in the central United States still exist. Over the central United States, the issues of too weak rainfall intensity in climate runs is well improved in their hindcast runs with initial conditions from numerical weather prediction analyses. But the improvement is minimal over the central Amazon. Incorporating the role of the large-scale environment in convective triggering processes helps resolve the phase-locking issue in many models where precipitation often incorrectly peaks near noon due to maximum insolation over land. Allowing air parcels to be lifted above the boundary layer improves the simulation of nocturnal precipitation which is often associated with the propagation of mesoscale systems. Including convective memory in cumulus parameterizations acts to suppress light-to-moderate rain and promote intense rainfall; however, it also weakens the diurnal variability. Simply increasing model resolution (with cumulus parameterizations still used) cannot fully resolve the biases of low-resolution climate models in DCP. The hierarchy modeling framework from this study is useful for identifying the missing physics in models and testing new development of model convective processes over different convective regimes.

58 GEOSCIENCES↗
DOE OSTI2021

A Statistical Evaluation of WRF-LES Trace Gas Dispersion Using Project Prairie Grass Measurements

In recent years, new measurement systems have been deployed to monitor and quantify methane emissions from the natural gas sector. Large-eddy simulation (LES) has complemented measurement campaigns by serving as a controlled environment in which to study plume dynamics and sampling strategies. However, with few comparisons with controlled-release experiments, the accuracy of LES for modeling natural gas emissions is poorly characterized. In this paper, we evaluate LES from the Weather Research and Forecasting (WRF) Model against Project Prairie Grass campaign measurements and surface layer similarity theory. Using WRF-LES, we simulate continuous emissions from 30 near-surface trace gas sources in two stability regimes: strong convection and weak convection. We examine the impact of grid resolutions ranging from 6.25 to 52 m in the horizontal dimension on model results. We evaluate performance in a statistical framework, calculating fractional bias and conducting Welch’s t tests. WRF-LES accurately simulates observed surface concentrations at 100 m and beyond under strong convection; simulated concentrations pass t tests in this region irrespective of grid resolution. However, in weakly convective conditions with strong winds, WRF-LES substantially overpredicts concentrations—the magnitude of fractional bias often exceeds 30%, and all but one t test fails. The good performance of WRF-LES under strong convection correlates with agreement with local free convection theory and a minimal amount of parameterized turbulent kinetic energy. The poor performance under weak convection corresponds to misalignment with Monin–Obukhov similarity theory and a significant amount of parameterized turbulent kinetic energy.

17 WIND ENERGY↗
DOE OSTI2022

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 which 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 the following 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.

54 ENVIRONMENTAL SCIENCES↗
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 which 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 the following 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.

aerosols↗
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↗
DOE OSTI2025

Navigating the Noise: Bringing Clarity to ML Parameterization Design With O $\boldsymbol{\mathcal{O}}$(100) Ensembles

Abstract Machine‐learning (ML) parameterizations of subgrid processes (here of turbulence, convection, and radiation) may one day replace conventional parameterizations by emulating high‐resolution physics without the cost of explicit simulation. However, uncertainty about the relationship between offline and online performance (i.e., when integrated with a large‐scale general circulation model) hinders their development. Much of this uncertainty stems from limited sampling of the noisy, emergent effects of upstream ML design decisions on downstream online hybrid simulation. Our work rectifies the sampling issue via the construction of a semi‐automated, end‐to‐end pipeline for size ensembles of hybrid simulations, revealing important nuances in how systematic reductions in offline error manifest in changes to online error and online stability. For example, removing dropout and switching from a Mean Squared Error to a Mean Absolute Error loss both reduce offline error, but they have opposite effects on online error and online stability. Other design decisions, like incorporating memory, converting moisture input from specific humidity to relative humidity, using batch normalization, and training on multiple climates do not come with any such compromises. Finally, we show that ensemble sizes of may be necessary to reliably detect causally relevant differences online. By enabling rapid online experimentation at scale, we can empirically settle debates regarding subgrid ML parameterization design that would have otherwise remained unresolved in the noise.

Lin, Jerry [Department of Earth System Sciences Un↗
NASA NTRS1995

Modeling of shallow and inefficient convection in the outer layers of the Sun using realistic physics

In an attempt to understand the properties of convective energy transport in the solar convective zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, nonmagnetic, gravitationally stratified medium using a realistic equation of state and realistic opacities. The time-dependent, three-dimensional hydrodynamic equations are solved with minimal simplifications. The statistical information obtained from the present simulation provides an improved undserstanding of solar photospheric convection. The characteristics of solar convection in shallow regions is parameterized and compared with the results of Chan & Sofia's (1989) simulations of deep and efficient convection. We assess the importance of the zones of partial ionization in the simulation and confirm that the radiative energy transfer is negliglble throughout the region except in the uppermost scale heights of the convection zone, a region of very high superadiabaticity. When the effects of partial ionization are included, the dynamics of flows are altered significantly. However, we confirm the Chan & Sofia result that kinetic energy flux is nonnegligible and can have a negative value in the convection zone.

Kim, Yong-Cheol↗