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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Coupled fvGCM-GCE Modeling System: TRMM Latent Heating and Cloud Library

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. A seed fund is available at NASA Goddard to build a MMF based on the 2D GCE model and the Goddard finite volume general circulation model (fvGCM). A prototype MMF will be developed by the end of 2004 and production runs will be conducted at the beginning of 2005. The purpose of this proposal is to augment the current Goddard MMF and other cloud modeling activities. In this talk, I will present: (1) A summary of the second Cloud Modeling Workshop took place at NASA Goddard, (2) A summary of the third TRMM Latent Heating Workshop took place at Nara Japan, (3) A brief discussion on the GCE model on developing a global cloud simulator.

Tao, Wei-Kuo↗
NASA NTRS2018

Climate Lecture 4: Atmospheric Radiation

The climate system is well known for its great complexity and complex interactions that involve dynamic, thermodynamic, radiative, chemical, biological and human-driven processes. This view of the climate system has emerged from detailed measurements, meticulous record keeping, and theoretical analyses arising from, and made possible by the science and technology revolution that greatly advanced our understanding the role of physical processes that operate in the global climate system. These measurements also show very clearly that the global surface temperature has been rising over the past century, and that this is a consequence of human industrial activity.

Oinas, Valdar↗
NASA NTRS1977

Accretion of rotating fluids by barytropes - Numerical results for white-dwarf models

Numerical sequences of rotating axisymmetric nonmagnetic equilibrium models are constructed which represent the evolution of a barytropic star as it accretes material from a rotating medium. Two accretion geometries are considered - one approximating accretion from a rotating cloud and the other, accretion from a Keplerian disk. It is assumed that some process, such as Ekman spin-up or nonequilibrium oscillations, maintains nearly constant angular velocity along cylinders about the rotation axis. Transport of angular momentum in the cylindrically radial direction by viscosity is included. Fluid instabilities and other physical processes leading to enhancement of this transport are discussed. Particular application is made to zero-temperature white-dwarf models, using the degenerate electron equation of state. An initially nonrotating 0.566-solar-mass white dwarf is followed during the accretion of more than one solar mass of material. Applications to degenerate stellar cores, to mass-transfer binary systems containing white dwarfs, such as novae and dwarf novae, to Type I supernovae, and to galactic X-ray sources are considered.

Durisen, R. H.↗
NASA NTRS1991

Derivation of sequential, real-time, process-control programs

The use of weakest-precondition predicate transformers in the derivation of sequential, process-control software is discussed. Only one extension to Dijkstra's calculus for deriving ordinary sequential programs was found to be necessary: function-valued auxiliary variables. These auxiliary variables are needed for reasoning about states of a physical process that exists during program transitions.

Marzullo, Keith↗
NASA NTRS2023

Electrification Within Wintertime Stratiform Regions Sampled During the 2020/2022 NASA IMPACTS Field Campaign

Two nor'easter events—sampled during the NASA Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) field campaign—were examined to characterize the microphysics in relation to the underlying electrification processes within wintertime stratiform regions. A theoretical model was developed to determine whether accretion or diffusion growth regimes were preferential during periods of greatest electrification. Model simulation with electrification parameterization was used to provide supplemental context to the physical processes of in-cloud microphysics and electrification. The strongest electric fields (i.e., ∼80 V m −1 at 20 km) during the 2020 NASA IMPACTS deployment was associated with large non-rimed ice crystals colliding with each other. During the 29–30 January 2022 science flight, the NASA P-3 microphysical probe data demonstrated that non-inductive charging was possible off the coastline of Cape Cod, Massachusetts. Later in the science flight, when the NASA P-3 and ER-2 were coordinating with each other, measured electric fields consistently were less than 8 V m −1 and electrification was subdued owing to reduced concentrations of graupel and large ice hydrometeors. Altogether, the in-situ observations provide evidence for the non-riming collisional charging mechanism and demonstrates that graupel and supercooled liquid water may not be necessary for weak electrification within wintertime stratiform regions. Model output from simulation of both events suggested that the main synoptic snowbands were associated with elevated hydrometeor snow charge density and electric fields.

snowfall↗
NASA NTRS2024

Understanding the Variability of Helium Abundance in the Solar Corona Using Three Fluid Modeling and Ultraviolet Observations

The variability of helium abundance in the solar corona and the solar wind is an important signature of solar activity, solar cycle, and solar wind sources, as well as coronal heating processes. Motivated by recently reported remote-sensing UV imaging observations by Helium Resonance Scattering in the Corona and Heliosphere payload sounding rocket of helium abundance in the inner corona on 2009 September 14 near solar minimum, we present the results of the first three-dimensional three-fluid (electrons, protons, and alpha particles) model of tilted coronal streamer belt and slow solar wind that illustrates the various processes leading to helium abundance differentiation and variability. We find good qualitative agreement between the three-fluid model and the coronal helium abundance variability deduced from UV observations of streamers, providing insight on the effects of the physical processes, such as heating, gravitational settling, and interspecies Coulomb friction in the outflowing solar wind that produce the observed features. The study impacts our understanding of the origins of the slow solar wind.

Leon Ofman↗
NASA NTRS2009

Prominence Structure and Dynamics

Nonerupting prominences are not dull, static objects. Rather, they are composed of fine-scale blobs and threads that are highly dynamic, often appearing to travel in opposite directions on adjacent tracks (denoted counterstreaming). Because the plasma is largely constrained to travel along the magnetic field, these cool, dense features can serve as tracers of the prominence magnetic structure, a valuable resource in view of the long-standing difficulty of observing the coronal field. Conversely, greater understanding of the fundamental magnetic geometry of filament channels can provide important constraints on the physical processes governing the accumulation, support, motion, and eruption of the cool plasma. Despite over a century of detailed observations, large gaps remain in our knowledge of filament channel/plasma formation and evolution. Resolving these issues will shed light on the physics of coronal heating, helicity transport throughout the solar cycle, and the origins of eruptive activity on the Sun. I will discuss the leading models for the magnetic and plasma structure, and outline how new observations and theory /modeling could solve long-standing uncertainties regarding this majestic solar phenomenon.

Karpen, Judy T.↗
NASA NTRS2014

The Deuterium to Hydrogen Ratio in the Water that Formed the Yellowknife Bay Mudstones in Gale Crater

A suite of isotope ratios of light elements in the present martian atmosphere (13C/12C, 15N/14N, 18O/16O, 38Ar/36Ar, and D/H) are all substantially enriched in the heavy element suggesting atmospheric loss to space over the past billions of years with preferential loss of the lighter isotope from each pair. In situ measurements from MSL's Sample Analysis at Mars (SAM) instrument [e.g. 1,2,3] have considerably refined previous measurements from the Viking mass spectrometers [e.g. 4], from remote spectroscopic observations [e.g. 5,6], and from martian meteorite studies [e.g. 7,8]. The persistence of habitable environments such as the ancient Yellowknife Bay lake recently revealed by measurements from the Curiosity rover [9] depends on the surface temperatures and the duration of an atmosphere thicker than that at present. Current and planned measurements from orbit with the Mars Express and MAVEN missions respectively intend to study the processes of atmospheric escape including solar wind interaction, sputtering, thermal escape, and dissociative recombination, and determine or refine the current rate of atmospheric loss caused by these and other mechanisms. The goal of these programs is to understand the physical processes sufficiently well so that robust extrapolations over the past billions of years can be made D/H is measured by both the Tunable Laser Spectrometer (TLS) and the Quadrupole Mass Spectrometer (QMS) of the SAM suite. to predict the atmospheric and surface conditions on early Mars. However, the study of the history of martian atmospheric evolution will be greatly facilitated if we are able to also directly measure the isotopic composition of volatiles captured in rocks that are representative of the ancient atmosphere. To date, D/H is one of the most promising candidates for this study since water is the most abundant volatile thermally released from the Yellowknife Bay phylosilicates discovered by the SAM and CheMin experiments of MSL and its

Yellowknife Bay↗
NASA NTRS2001

Venus Multiprobe Mission

A summary of the proposal for the Discovery Program Venus Multiprobe Mission (VMPM) which was submitted in 1994 will be presented. The major goal of the mission was to provide sufficient observations of winds and thermal structure in the Venus atmosphere that the mechanism producing the atmospheric superrotation could be identified. The superrotation has been a major unsolved problem of planetary science for over 30 years. In spite of many theoretical efforts and many spacecraft missions to Venus, the principal driving mechanism(s) remain undetermined. Sixteen small probes, modeled after the Pioneer Venus small probes, would enter the Venus atmosphere, and measure winds, temperatures, and pressures from 60 km to the surface. Towards the bottom of the atmosphere, measurements would be made at 10 meter intervals. Temperature and pressure measurements are similar to those used on Pioneer Venus, but are four times more sensitive. Winds would be obtained by dual-frequency, differential. long-baseline interferometry, using S- and X-band transmitters on the probes, and four receiving telescopes round the Pacific rim. The precision of wind measurements is 0.05 ms- 1 or better, at least twenty times more precise than for Pioneer Venus. Ground based observations occurring in conjunction with the multiprobe entries would provide a temporal context for the upper boundary to the probe observations. UV and near IR features would be tracked for periods of hours to weeks to obtain cloud level zonal mean and transient eddy circulations with accuracies of 10 /ms or better. The data would be processed into wind and opacity maps. A hierarchy of atmospheric numerical models would be used to distinguish different dynamical elements existing in the data. Primary among the models was the development of a Venus general circulation model containing all known physical processes.

Young, Richard E.↗
NASA NTRS1999

Friction Stir Welding of Curved Plates

Friction stir welding (FSW) is a remarkable technology for making butt and lap joints in aluminum alloys. The process operates by passing a rotating tool between two closely butted plates. This process generates heat and the heated material is stirred from both sides of the plates to generate a high quality weld. Application of this technique has a very broad field for NASA. In particular, NASA is interested in using this welding process to manufacture tanks and curved elements. Therefore, this research has been oriented to the study the FSW of curved plates. The study has covered a number of topics that are important in the model development and to uncover the physical process involve in the welding itself. The materials used for the experimental welds were as close to each other as we could possibly find, aluminum 5454-0 and 5456-0 with properties listed at http://matweb.com. The application of FSW to curved plates needs to consider the behavior that we observed in this study. There is going to be larger force in the normal direction (Fz) as the curvature of the plate increases. A particular model needs to be derived for each material and thickness. A more complete study should also include parameters such as spin rate, tool velocity, and power used. The force in the direction of motion (Fx) needs to be reconsidered to make sure of its variability with respect to other parameters such as velocity, thickness, etc. It seems like the curvature does not play a role in this case. Variations in temperature were found with respect to the curvature. However, these changes seem to be smaller than the effect on Fz. The temperatures were all below the melting point. We understand now that the process of FSW produces a three dimensional flow of material that takes place during the weld. This flow needs to be study in a more detailed way to see in which directions the flow of material is stronger. It could be possible to model the flow using a 2-dimensional model in the particular directions where the flow moves faster. More experimental information is required to enrich the knowledge about FSW, and from this point, derive useful mathematical formulas to optimize the process and the design of the machines that will perform it. More experiments and experimental equipment are required to uncover the mathematics of the process.

Sanchez, Nestor↗
NASA NTRS2010

Studies of 21st-Century Precipitation Trends Over West Africa

West Africa includes a semi-arid zone between the Sahara Desert and the humid Gulf of Guinea coast, approximately between 10 N and 20 N, which is irrigated by summer monsoon rains. This article refers to the region as the Sahel. Rain-fed agriculture is the primary sustenance for Sahel populations, and severe droughts (in the 1970s and 1980s), therefore, have devastating negative societal impacts. The future frequency of Sahel droughts and the evolution of its hydrological balance are therefore of great interest. The article reviews 10 recent research studies that attempt to discover how climate changes will affect the hydrology of the Sahel throughout the 21st century. All 10 studies rely on atmosphere ocean global climate model (AOGCM) simulations based on a range of greenhouse gas emissions scenarios. Many of the simulations are contained in the Intergovernmental Panel on Climate Change archives for Assessment Reports #3 and #4. Two of the studies use AOGCM data to drive regional climate models. Seven studies make projections for the first half of the 21st century and eight studies make projections for the second half. Some studies make projections of wetter conditions and some predict more frequent droughts, and each describes the atmospheric processes associated with its prediction. Only one study projects more frequent droughts before 2050, and that is only for continent-wide degradation in vegetation cover. The challenge to correctly simulate Sahel rainfall decadal trends is particularly daunting because multiple physical mechanisms compete to drive the trend upwards or downwards. A variety of model deficiencies, regarding the simulation of one or more of these physical processes, taints models climate change projections. Consequently, no consensus emerges regarding the impact of anticipated greenhouse gas forcing on the hydrology of the Sahel in the second half of the 21st century.

Druyan, Leonard M.↗
NASA NTRS2019

Cluster Analysis of Spectroscopic Line Profiles and EUV Emission in RMHD Simulations and Observations of the Solar Atmosphere

Spatially-resolved observations from the IRIS, SDO/AIA, and other space mission and ground-based telescopes, coupled with realistic 3D RMHD simulations, are a powerful tool for analysis of processes in the solar atmosphere. To better understand the dynamical and thermodynamic properties in the simulation data and their connection to observations, it is essential to determine similarities in the behaviors of the synthesized and observed emission. However, the complexity of observational data and physical processes makes comparison of observations and modeling results difficult. In this work, we show the initial results of application of K-Means clustering (unsupervised machine learning) algorithm to two different problems: 1) recognition of the typical spectroscopic line profiles observed by IRIS during solar flares and their typical dynamic behavior; 2) recognition of shocks and heating events in synthetic AIA emission data obtained from StellarBox quiet-Sun simulations. The average silhouette width technique for the KMeans algorithm is utilized in different ways to obtain optimal numbers of clusters. We discuss application of the emission clustering to visualizations of the computational volume, understanding its evolutionary trends and behavior patterns, and inversion (reconstruction) of physical properties of the solar atmosphere from synthesizes emission data.

Sadykov, Viacheslav↗
NASA NTRS2006

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CFWs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1 998 and 1999). In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗
NASA NTRS1994

Numerical modeling studies of wake vortex transport and evolution within the planetary boundary layer

The proposed research involves four tasks. The first of these is to simulate accurately the turbulent processes in the atmospheric boundary layer. TASS was originally developed to study meso-gamma scale phenomena, such as tornadic storms, microbursts and windshear effects in terminal areas. Simulation of wake vortex evolution, however, will rely on appropriate representation of the physical processes in the surface layer and mixed layer. This involves two parts. First, a specified heat flux boundary condition must be implemented at the surface. Using this boundary condition, simulation results will be compared to experimental data and to other model results for validation. At this point, any necessary changes to the model will be implemented. Next, a surface energy budget parameterization will be added to the model. This will enable calculation of the surface fluxes by accounting for the radiative heat transfer to and from the ground and heat loss to the soil rather than simple specification of the fluxes. The second task involves running TASS with prescribed wake vortices in the initial condition. The vortex models will be supplied by NASA Langley Research Center. Sensitivity tests will be performed on different meteorological environments in the atmospheric boundary layer, which include stable, neutral, and unstable stratifications, calm and severe wind conditions, and dry and wet conditions. Vortex strength may be varied as well. Relevant non-dimensional parameters will include the following: Richardson number or Froude number, Bowen ratio, and height to length scale ratios. The model output will be analyzed and visualized to better understand the transport, decay, and growth rates of the wake vortices. The third task involves running simulations using observed data. MIT Lincoln Labs is currently planning field experiments at the Memphis airport to measure both meteorological conditions and wake vortex characteristics. Once this data becomes available, it can be used to validate the model for vortex behavior under different atmospheric conditions. The fourth task will be to simulate the wake in a more realistic environment covering a wider area. This will involve grid nesting, since high resolution will be required in the wake region but a larger total domain will be used. During the first allocation year, most of the first task will be accomplished.

Lin, Yuh-Lang↗
NASA NTRS2001

Representation of Stormflow and a More Responsive Water Table in a TOPMODEL-Based Hydrology Model

This study presents two new modeling strategies. First, a methodology for representing the physical process of stormflow within a TOPMODEL framework is developed. In using this approach, discharge at quickflow time scales is simulated and a fuller depiction of hydrologic activity is brought about. Discharge of water from the vadose zone is permitted in a physically realistic manner without a priori assumption of the level within the soil column at which stormflow saturation can take place. Determination of the stormflow contribution to discharge is made using the equation for groundwater flow. No new parameters are needed. Instead, regions of near saturation that develop during storm events, producing vertical recharge, are allowed to contribute to soil column discharge. These stormflow contributions to river runoff, as for groundwater flow contributions, are a function of catchment topography and local hydraulic conductivity at the depth of these regions of near saturation. The second approach improves groundwater flow response through a reduction of porosity and field capacity with depth in the soil column. Large storm events are better captured and a more dynamic water table develops with application of this modified soil column profile (MSCP). The MSCP predominantly reflects soil depth differences in upland and lowland regions of a watershed. Combined, these two approaches - stormflow and the MSCP - provide a more accurate representation of the time scales at which soil column discharge responds and a more complete depiction of hydrologic activity. Storm events large and small are better simulated, and some of the biases previously evident in TOPMODEL simulations are reduced.

Shaman, Jeffrey↗
NASA NTRS2005

CFD Multiphysics Tool

The recent bold initiatives to expand the human presence in space require innovative approaches to the design of propulsion systems whose underlying technology is not yet mature. The space propulsion community has identified a number of candidate concepts. A short list includes solar sails, high-energy-density chemical propellants, electric and electromagnetic accelerators, solar-thermal and nuclear-thermal expanders. For each of these, the underlying physics are relatively well understood. One could easily cite authoritative texts, addressing both the governing equations, and practical solution methods for, e.g. electromagnetic fields, heat transfer, radiation, thermophysics, structural dynamics, particulate kinematics, nuclear energy, power conversion, and fluid dynamics. One could also easily cite scholarly works in which complete equation sets for any one of these physical processes have been accurately solved relative to complex engineered systems. The Advanced Concepts and Analysis Office (ACAO), Space Transportation Directorate, NASA Marshall Space Flight Center, has recently released the first alpha version of a set of computer utilities for performing the applicable physical analyses relative to candidate deep-space propulsion systems such as those listed above. PARSEC, Preliminary Analysis of Revolutionary in-Space Engineering Concepts, enables rapid iterative calculations using several physics tools developed in-house. A complete cycle of the entire tool set takes about twenty minutes. PARSEC is a level-zero/level-one design tool. For PARSEC s proof-of-concept, and preliminary design decision-making, assumptions that significantly simplify the governing equation sets are necessary. To proceed to level-two, one wishes to retain modeling of the underlying physics as close as practical to known applicable first principles. This report describes results of collaboration between ACAO, and Embry-Riddle Aeronautical University (ERAU), to begin building a set of level-two design tools for PARSEC. The "CFD Multiphysics Tool" will be the propulsive element of the tool set. The name acknowledges that space propulsion performance assessment is primarily a fluid mechanics problem. At the core of the CFD Multiphysics Tool is an open-source CFD code, HYP, under development at ERAU. ERAU is renowned for its undergraduate degree program in Aerospace Engineering the largest in the nation. The strength of the program is its applications-oriented curriculum, which culminates in one of three two-course Engineering Design sequences: Aerospace Propulsion, Spacecraft, or Aircraft. This same philosophy applies to the HYP Project, albeit with fluid physics modeling commensurate with graduate research. HYP s purpose, like the Multiphysics Tool s, is to enable calculations of real (three-dimensional; geometrically complex; intended for hardware development) applications of high speed and propulsive fluid flows.

Perrell, Eric R.↗
NASA NTRS2007

A Coupled GCM-Cloud Resolving Modeling System, and a Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a superparameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (2ICE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generatio11 regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗
NASA NTRS2006

A Coupled GCM-Cloud Resolving Modeling System, and A Regional Scale Model to Study Precipitation Processes

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. The Goddard MMF is based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM), and it has started production runs with two years results (1998 and 1999). Also, at Goddard, we have implemented several Goddard microphysical schemes (21CE, several 31CE), Goddard radiation (including explicitly calculated cloud optical properties), and Goddard Land Information (LIS, that includes the CLM and NOAH land surface models) into a next generation regional scale model, WRF. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes (microphysical and land processes), (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), and preliminary results (the comparison with traditional GCMs), and (3) A discussion on the Goddard WRF version (its developments and applications).

Tao, Wei-Kuo↗