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Tonlé Sap Food Security and Agriculture II: Evaluating Changes in Ecosystem Vitality and Freshwater Healthin the Tonlé Sap Basin using Remotely Sensed Data

The Tonlé Sap Lake and river basin in central Cambodia provide critical ecosystem services to the region, including fisheries, agricultural irrigation, hydropower, and biodiverse habitats. Deforestation, increased pumping for farming, and effects of climate change such as droughts and forest fires threaten the health of the lake and food security in the region. This project built upon the previous term through a partnership with Conservation International (CI), the Cambodian Ministry of Water Resources and Meteorology, and the Tonlé Sap Authority to assess ecosystem vitality and implement CI’s Freshwater Health Index (FHI) tool, in an effort to prioritize resource expenditure and highlight areas of concern. Due to the COVID-19 pandemic and related travel restrictions, partners had not been able to readily collect in situ data for the past year, which make up the majority of FHI inputs. To help fill this data gap, we developed a methodology for using Gravity Recovery and Climate Experiment (GRACE) satellite data to calculate groundwater storage depletion, and a Python Application Programming Interface for processing and formatting remotely-sensed data for the Soil and Water Assessment Tool (SWAT) model. We then used SWAT to model nutrient flows and of phosphorous, nitrogen and suspended sediments amounts in the basin from October 2000 to December 2020. These outputs served as inputs for the FHI and provided policy makers with robust monitoring information to aid decision-making in the area and safeguard the lake’s vital fisheries and biodiversity.

Justine Spore↗

Tonlé Sap Food Security & Agriculture III: Evaluating Changes in Ecosystem Vitality and Freshwater Health in the Tonlé Sap Basin using Remotely Sensed Data

Tonlé Sap Lake, located in Cambodia, Southeast Asia, is one of the most productive inland fisheries in the world. With the unique reverse flow hydrology of the Tonlé Sap River, this freshwater system contains rich biodiversity and provides critical freshwater resources for the local community. Overfishing, stronger seasonality, drought, dam construction, forest fires, and untreated industrial domestic sewage threaten the ecosystem vitality and economic success of Tonlé Sap. In collaboration with Conservation International and the Cambodian Ministry of Water Resources and Meteorology’s Tonlé Sap Authority, we calibrated and finalized remotely-sensed proxies for sub-indicators of the Freshwater Health Index (FHI). We used NASA Earth observation data from Moderate Resolution Imaging Spectroradiometer (MODIS), and the Gravity Recovery and Climate Experiment (GRACE). These datasets were used in RS proxies and a Soil and Water Assessment Tool (SWAT) model that previous teams developed for sub-indicators of FHI. They included landcover, bank modification, and water quality metrics. It was determined that the ground water storage in Tonlé Sap Lake exhibited a slight declining trend over from April 1st, 2002 to February 3rd, 2017. To calculate chlorophyll-a concentration in the Tonlé Sap Lake, we used Copernicus Global Land Service mission data which provided a Trophic State Index of the lake. Between January 1st, 2000 and December 31st, 2020, the lake and surrounding region within the study area boundary displayed a slight decrease in vegetation density and consistently high chlorophyll-a concentrations. The SWAT model calculated nitrogen and phosphorus content measured in outlet points of the lake. We demonstrated that remotely sensed data is valuable for providing additional information for the FHI, but is not fully capable of replacing its in situ counterpart. We also concluded the water quantity is on a slowly declining trend within the basin.

Joey Lindsay↗

Simultaneous Aerosol and Ocean Polarimeter Products Using Coupled Atmosphere-Ocean Vector Radiative Transfer and Neural Networks: The PACE-MAPP Algorithm

We describe the PACE-MAPP algorithm that simultaneously retrieves aerosol and ocean optical parameters using multiangle and multi-channel polarimeter measurements from the SPEXone, Hyper-Angular Rainbow Polarimeter 2 (HARP2), and Ocean Color Instrument (OCI) instruments onboard the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) observing system PACE-MAPP is adapted from the Research Scanning Polarimeter (RSP) Microphysical Aerosol Properties from Polarimetry (RSP-MAPP) algorithm. A key feature of the MAPP family of algorithms is the use of a coupled vector radiative transfer model such that the atmosphere and ocean are always considered together as one system. Consequently, conservation of energy ensures that negative water-leaving radiances do not occur. PACE-MAPP uses optimal estimation to simultaneously characterize the optical and microphysical properties of aerosol and ocean constituents, find the optimal solution, and reliably account for the uncertainties of each parameter. This coupled approach, together with multiangle, multi-channel polarimeter measurements, will enable retrievals of aerosol and water properties across the Earth’s oceans. The PACE-MAPP algorithm provides aerosol and ocean products for both the open ocean and coastal areas and is designed to be accurate, modular, and efficient by using fast neural networks that replace the time-consuming vector radiative transfer calculations. We provide an overview of the PACE-MAPP framework and also describe its modular components including its aerosol and hydrosol models, ocean bio-optical models, and thin cirrus model.

Snorre Stamnes↗

Assessing the Needs of NASA's Near Real-Time Earth Observation Products

"The 2017-2027 Decadal Survey for Earth Science and Applications from Space stated that NASA's Earth Science with planned implementation of applications provides sustained earth observations for societal benefits [1]. The Decadal Survey indicated that data latency is invaluable for time-sensitive applications including disaster risk reduction, wildland fire carbon emissions quantification, real-time measurements of the state of the hydrologic systems and many more. Data latency refers to the time between earth observation and data products available to users. During the past 13 years, NASA's Land, Atmosphere Near Real-Time Capability for Earth Observing Systems (LANCE) continues to provide free access to earth observation products that are made available much quicker than routine processing allows. The latency of most LANCE data products is Near Real-time (NRT) which is defined as less than three hours from satellite observations [2]. LANCE is managed by the Earth Science Data and Information System (ESDIS) Project at NASA Goddard Space Flight Center [3], and a User Working Group (UWG) is responsible for providing guidance to LANCE. LANCE data are used by direct users and brokers who add value to the data [4]. NASA Earth Applied Sciences Program (ASP) is one of the primary users of LANCE, which collaborates with partner organizations and provides support to scientists to solve problems in applications of earth observations. ASP promotes the use of LANCE NRT data products to demonstrate applications in decision making, facilitates end-user feedback to the science team to improve data products, and provides information on future demands for research. LANCE supports applications that need a rapid response including detecting wildland fires and volcanic eruptions, tracking smoke, ash and dust plumes, monitoring air quality and tracking extreme weather events such as hurricanes, landslides, and floods. To gather feedback regarding the availability, accessibility and actionability of NASA's NRT data products for societal benefit, three surveys and a few discussions with experts involved in the topic within ASP were conducted from the perspective of users. Feedback has been collected from users who are interested in using low latency NASA data within application communities of agriculture, disasters, water resources, health and air quality, ecological conservation, wildland fires and capacity building. Analysis-ready NRT data products in a variety of formats have been mentioned many times in the collected feedback, especially for applied users with little to no experience using research-grade earth observation products. Users prefer to have products that can be easily integrated into their existing workflows and take their analysis to the data. HDF5 is a commonly used data format for research, but typically requires some conversion to a more friendly format for applications and regular use in decision-making. Users prefer the GeoTIFF data format that can be directly ingested into a GIS mapping software and platform for data analysis and visualization. For example, LANCE’s fire, flood, SO2 and Black Marble Nighttime Blue/Yellow Composite data products have been integrated into NASA Disasters Mapping Portal, which is an GIS-based open data portal, for users in the disaster management community. There are 291 LANCE NRT layers available through GIBS and Worldview, where users can download a snapshot in GeoTIFF format. Operational users expect data to be processed as close to the user as possible. The collected feedback indicates that LANCE fire products within 3 hours latency would meet the needs of the wildland fire community. The ideal latency for volcanic application is 10-15 minutes. Users in Volcanic Ash Advisory Centers (VAAC) reported that the first forecast volcanic product should be issued within 75 minutes from the volcano eruption [5]. Overall, for disaster applications, data latency within 3 hours is useful while latency greater than 12 hours is not timely enough for operational use. Capacity building and training are critical for users to be able to access, interpret and use data products and tools for their decision making, especially for applied users with limited experience using earth observation products. LANCE data products have been used in a number of capacity building projects domestically and internationally [6]. As LANCE continues to bring new products into the system, users request training to utilize LANCE new and upcoming data products and capabilities in their applications. Due to the limitation of bandwidth and downstream flow paths, users in some developing countries need tools to select and download data for a specific area of interest instead of bulk downloads. The collected feedback also shows the lack of available SAR satellite low latency data products. The advantages of SAR to monitor conditions and changes on the ground through darkness, clouds, volcanic ash, and other atmospheric conditions, are appealing to low latency users. For example, terabytes of low latency but cloudy optical images are not helpful in rapidly identifying the extent of flood or fire impacts. LANCE could be complemented with low latency measurements via the upcoming NASA-ISRO Synthetic Aperture Radar (NISAR) mission [7]. Requests for higher spatial resolution products are expressed. A user from the wildland fire management community reported that products with 30-m spatial resolution could be used to detect small fires. The 30-m Landsat OLI fire data is now part of NASA’s Fire Information for Resource Management System (FIRMS) US/Canada [8]. Within the open and free NASA resources, LANCE disseminates NRT data products in a manner that allows them to be accessible and understandable to both scientific and applied users. In many application areas, latency plays an important or even decisive role where low latency earth observations help people to observe areas of interest, detect and track changes in the environment and make timely decisions. NASA’s Earth Applied Sciences Program promotes the use of LANCE NRT products and builds a bridge between application users and research teams. The collected feedback indicates data latency within 3 hours is useful for most of the applications, and shows the needs of user-friendly, analysis-ready products, and requests training on LANCE’s new and upcoming data products. User feedback has been provided to LANCE UWG for guidance and recommendations, and for translating findings into something actionable.

Tian Yao↗

Evaluating Changes in Freshwater Health in the Tonlé Sap Basin using Remotely Sensed Data

The Tonlé Sap lake and river basin provide freshwater resources to about 4.5 million people in central Cambodia. Accelerating dam construction, intensifying agriculture, deforestation, and changing climate patterns threaten the health of the lake and the food security of nearby communities. NASA DEVELOP collaborated with Conservation International to calculate multiple components of the ecosystem vitality indicator of the Freshwater Health Index for Tonlé Sap lake from 2000 – 2020 using remote sensing. Landcover classifications, lake level altimetry, groundwater storage and nutrient flows were derived from multiple satellites including Landsat 5, Landsat 7, Landsat 8, Sentinel-2, the Global Precipitation Measurement (GPM)mission, and the Gravity Recovery and Climate Experiment (GRACE). Additionally, the Soil and Water Assessment Tool (SWAT) was used to analyze nutrient flow and water quality in the basin. A breakdown in the volume and regularity of annual lake levels from 2000-2020 was observed, reflecting increased pressure on water supply and agricultural productivity. A decrease in landcover naturalness was also observed and at least 8% of forested areas in the basin were lost while rice harvest intensity increased throughout the study period. Additionally, an initial water quality analysis was demonstrated using SWAT. Continued collaboration with Conservation International and local representatives will guide the remaining water quality analyses and allow them to make informed decisions regarding freshwater management and resource allocation in the Tonlé Sap lake and river basin.

Adriana Le Compte↗

Estimating Evapotranspiration Using an Observation Based Terrestrial Water Budget

Evapotranspiration (ET) is difficult to measure at the scales of climate models and climate variability. While satellite retrieval algorithms do exist, their accuracy is limited by the sparseness of in situ observations available for calibration and validation, which themselves may be unrepresentative of 500m and larger scale satellite footprints and grid pixels. Here, we use a combination of satellite and ground-based observations to close the water budgets of seven continental scale river basins (Mackenzie, Fraser, Nelson, Mississippi, Tocantins, Danube, and Ubangi), estimating mean ET as a residual. For any river basin, ET must equal total precipitation minus net runoff minus the change in total terrestrial water storage (TWS), in order for mass to be conserved. We make use of precipitation from two global observation-based products, archived runoff data, and TWS changes from the Gravity Recovery and Climate Experiment satellite mission. We demonstrate that while uncertainty in the water budget-based estimates of monthly ET is often too large for those estimates to be useful, the uncertainty in the mean annual cycle is small enough that it is practical for evaluating other ET products. Here, we evaluate five land surface model simulations, two operational atmospheric analyses, and a recent global reanalysis product based on our results. An important outcome is that the water budget-based ET time series in two tropical river basins, one in Brazil and the other in central Africa, exhibit a weak annual cycle, which may help to resolve debate about the strength of the annual cycle of ET in such regions and how ET is constrained throughout the year. The methods described will be useful for water and energy budget studies, weather and climate model assessments, and satellite-based ET retrieval optimization.

Rodell, Matthew↗

On the effect of using the Shapiro filter to smooth winds on a sphere

Spatial differencing schemes which are not enstrophy conserving nor implicitly damping require global filtering of short waves to eliminate the build-up of energy in the shortest wavelengths due to aliasing. Takacs and Balgovind (1983) have shown that filtering on a sphere with a latitude dependent damping function will cause spurious vorticity and divergence source terms to occur if care is not taken to ensure the irrotationality of the gradients of the stream function and velocity potential. Using a shallow water model with fourth-order energy-conserving spatial differencing, it is found that using a 16th-order Shapiro (1979) filter on the winds and heights to control nonlinear instability also creates spurious source terms when the winds are filtered in the meridional direction.

Takacs, L. L.↗

Freshwater Requirements of Large-Scale Bioenergy Plantations for Limiting Global Warming to 1.5°C

Limiting mean global warming to well below 2 °C will probably require substantial negative emissions (NEs) within the 21st century. To achieve these, bioenergy plantations with subsequent carbon capture and storage (BECCS) may have to be implemented at a large scale. Irrigation of these plantations might be necessary to increase the yield, which is likely to put further pressure on already stressed freshwater systems. Conversely, the potential of bioenergy plantations (BPs) dedicated to achieving NEs through CO2 assimilation may be limited in regions with low freshwater availability. This paper provides a first-order quantification of the biophysical potentials of BECCS as a negative emission technology contribution to reaching the 1.5 °C warming target, as constrained by associated water availabilities and requirements. Using a global biosphere model, we analyze the availability of freshwater for irrigation of BPs designed to meet the projected NEs to fulfill the 1.5 °C target, spatially explicitly on areas not reserved for ecosystem conservation or agriculture. We take account of the simultaneous water demands for agriculture, industries, and households and also account for environmental flow requirements (EFRs) needed to safeguard aquatic ecosystems. Furthermore, we assess to what extent different forms of improved water management on the suggested BPs and on cropland may help to reduce the freshwater abstractions. Results indicate that global water withdrawals for irrigation of BPs range between ~400 and ~3000 km(exp 3) yr(exp -1), depending on the scenario and the conversion efficiency of the carbon capture and storage process. Consideration of EFRs reduces the NE potential significantly, but can partly be compensated for by improved on-field water management.

Stenzel, Fabian↗

Water sprays in space retrieval operations

Experiments were conducted in a ground based vacuum chamber to determine physical properties of water-ice in a space-like environment. Additional ices, alcohol and ammonia, were also studied. An analytical analysis based on the conservation of angular momentum, resulted in despin performance parameters, i.e., total water mass requirements and despin times. The despin and retrieval of a disabled spacecraft was considered to illustrate a potential application of the water spray technique.

Freesland, D. C.↗

Water sprays in space retrieval operations

Recent experiments involving liquid jets exhausting into a vacuum have led to significant conclusions regarding techniques for detumbling and despinning disabled spacecraft during retrieval operations. A fine water spray directed toward a tumbling or spinning object may quickly form ice over its surface. The added mass of water will absorb angular momentum and slow the vehicle. As this ice sublimes it carries momentum away with it. Thus, a complete detumble or despin is possible by simply spraying water at a disabled vehicle. Experiments were conducted in a ground based vacuum chamber to determine physical properties of water-ice in a space-like environment. Additional ices, alcohol and ammonia, were also studied. An analytical analysis based on the conservation of angular momentum, resulted in despin performance parameters, i.e., total water mass requirements and despin times. The despin and retrieval of a disabled spacecraft was considered to illustrate a potential application of the water spray technique.

Freesland, D. C.↗

Firex Water Tank, SWMU 069, Confirmatory Sampling Report

The National Aeronautics and Space Administration (NASA) Resource Conservation and Recovery Act (RCRA) permit requires identification and evaluation of known Solid Waste Management Units (SWMU) located at the Kennedy Space Center (KSC). Firex Water Tank (FWT), or the “site,” is designated as SWMU 069 under the NASA RCRA permit. This report summarizes the results of the Confirmatory Sampling (CS) field activities carried out during Fall 2021, at FWT, SWMU 069, KSC, Florida. Three locations of concern (LOCs) were identified by screening historical sample results to current State of Florida soil cleanup target levels (SCTL). A total of 18 soil samples were collected to investigate the historical exceedance locations. Samples at LOC 1 and 2 were analyzed for arsenic and the results for all were below the SCTL. Samples at LOC 3 were analyzed for polynuclear aromatic hydrocarbons and it was determined that certain locations have results that remain above the SCTL. The current land use controls will remain in place at FWT to mitigate potential risks.

Firex↗

Remote Sensing and Modeling for Improving Operational Aquatic Plant Management

The California Sacramento-San Joaquin River Delta is the hub for California’s water supply, conveying water from Northern to Southern California agriculture and communities while supporting important ecosystem services, agriculture, and communities in the Delta. Changes in climate, long-term drought, water quality changes, and expansion of invasive aquatic plants threatens ecosystems, impedes ecosystem restoration, and is economically, environmentally, and sociologically detrimental to the San Francisco Bay/California Delta complex. NASA Ames Research Center and the USDA-ARS partnered with the State of California and local governments to develop science-based, adaptive-management strategies for the Sacramento-San Joaquin Delta. The project combines science, operations, and economics related to integrated management scenarios for aquatic weeds to help land and waterway managers make science-informed decisions regarding management and outcomes. The team provides a comprehensive understanding of agricultural and urban land use in the Delta and the major water sheds (San Joaquin/Sacramento) supplying the Delta and interaction with drought and climate impacts on the environment, water quality, and weed growth. The team recommends conservation and modified land-use practices and aids local Delta stakeholders in developing management strategies. New remote sensing tools have been developed to enhance ability to assess conditions, inform decision support tools, and monitor management practices. Science gaps in understanding how native and invasive plants respond to altered environmental conditions are being filled and provide critical biological response parameters for Delta-SWAT simulation modeling. Operational agencies such as the California Department of Boating and Waterways provide testing and act as initial adopter of decision support tools. Methods developed by the project can become routine land and water management tools in complex river delta systems.

Agriculture↗

Adaptive Management Methods to Protect the California Sacramento-San Joaquin Delta Water Resource

The California Sacramento-San Joaquin River Delta is the hub for California's water supply, conveying water from Northern to Southern California agriculture and communities while supporting important ecosystem services, agriculture, and communities in the Delta. Changes in climate, long-term drought, water quality changes, and expansion of invasive aquatic plants threatens ecosystems, impedes ecosystem restoration, and is economically, environmentally, and sociologically detrimental to the San Francisco Bay/California Delta complex. NASA Ames Research Center and the USDA-ARS partnered with the State of California and local governments to develop science-based, adaptive-management strategies for the Sacramento-San Joaquin Delta. The project combines science, operations, and economics related to integrated management scenarios for aquatic weeds to help land and waterway managers make science-informed decisions regarding management and outcomes. The team provides a comprehensive understanding of agricultural and urban land use in the Delta and the major water sheds (San Joaquin/Sacramento) supplying the Delta and interaction with drought and climate impacts on the environment, water quality, and weed growth. The team recommends conservation and modified land-use practices and aids local Delta stakeholders in developing management strategies. New remote sensing tools have been developed to enhance ability to assess conditions, inform decision support tools, and monitor management practices. Science gaps in understanding how native and invasive plants respond to altered environmental conditions are being filled and provide critical biological response parameters for Delta-SWAT simulation modeling. Operational agencies such as the California Department of Boating and Waterways provide testing and act as initial adopter of decision support tools. Methods developed by the project can become routine land and water management tools in complex river delta systems.

Agriculture↗

Seasonal Phytoplankton Dynamics in the Eastern Tropical Atlantic

The coastal zone color scanner (CZCS) that operated aboard the Nimbus 7 satellite provided extensive coverage of phytoplankton pigment concentrations in the surface waters of the eastern tropical Atlantic (ETA) from March 1979 to February 1980 and coincided with four major research cruises to this region. Total primary production within the ETA (5 deg N-10 deg S, 25 deg W-10 deg E) was determined from CZCS pigment estimates and an empirical algorithm derived from concurrent in situ data taken along 4 deg W that relates near-surface chlorophyll concentration and integrated primary production. We estimated an average annual production for the ETA of 2.3 Gt C/yr with an associated 3.5-fold seasonal variation in the magnitude of this production. We describe the principal physical mechanisms controlling seasonal phytoplankton dynamics within the ETA and propose that in addition to seasonal change in the thermocline depth, one must also consider changes in the depth of the equatorial under current. An extensive validation effort indicates that the standard CZCS global products are a conservative estimate of pigment concentrations in ETA surface waters. Significant underestimates by the CZCS global products were observed in June and July which we attributed, in part, to aerosol correction errors and, more importantly, to errors caused by a significant reduction in the concentration of near-surface dissolved organic matter that resulted from strong equatorial upwelling.

Monger, Bruce↗

Florida Water Resources: Assessing Coastal Resiliency Across Florida's Aquatic Preserves Response To Hurricane Forces

Intensifying weather events, sea level rise, and extensive coastal development in Southwestern Florida are escalating the need for Florida’s mangrove conservation. These mangroves are imperative for coastline stabilization, habitat provision for native species, and water quality management. Our partner, the Florida Department of Environmental Protection (FDEP), Office of Resilience and Coastal Protection is tasked with monitoring and conserving the Charlotte Harbor, Estero Bay, Rookery Bay, and Pinellas County Aquatic Preserves. We developed the Growth, Resilience, and Optical Vegetation Evaluator (GROVE) Google Earth Engine toolset for partners to determine mangrove forest extent through time, analyze mangrove forest health, and collect several water quality parameters within the preserves from January 2002–August 2022. The toolset provides easily accessible data from Landsat 7 Enhanced Thematic Mapper Plus (ETM+), Landsat 8 Operational Land Imager (OLI), Landsat 9 Operational Land Imager 2 (OLI-2), and the Shuttle Radar Topography Mission (SRTM). Using training datasets of known mangrove forest locations, we also established a machine learning approach to create mangrove extent maps. Maps from all four preserves indicated migration of mangrove forests inland as the greatest areas of change were transitional zones. Additionally, normalized difference vegetation index (NDVI), normalized difference turbidity index (NDTI), and chlorophyll-a maps were generated for the partners. This project provides decision makers with a useful tool for understanding temporal changes in Florida’s aquatic preserves, identifying areas of ecological stress, and providing actionable data to make informed plans for mangrove preservation.

Samuel Perrello↗

Florida Water Resources: Assessing Coastal Resiliency Across Florida's Aquatic Preserves in Response to Hurricane Forces

Intensifying weather events, sea level rise, and extensive coastal development in Southwestern Florida are escalating the need for Florida’s mangrove conservation. These mangroves are imperative for coastline stabilization, habitat provision for native species, and water quality management. Our partner, the Florida Department of Environmental Protection (FDEP), Office of Resilience and Coastal Protection is tasked with monitoring and conserving the Charlotte Harbor, Estero Bay, Rookery Bay, and Pinellas County Aquatic Preserves. We developed the Growth, Resilience, and Optical Vegetation Evaluator (GROVE) Google Earth Engine toolset for partners to determine mangrove forest extent through time, analyze mangrove forest health, and collect several water quality parameters within the preserves from January 2002–August 2022. The toolset provides easily accessible data from Landsat 7 Enhanced Thematic Mapper Plus (ETM+), Landsat 8 Operational Land Imager (OLI), Landsat 9 Operational Land Imager 2 (OLI-2), and the Shuttle Radar Topography Mission (SRTM). Using training datasets of known mangrove forest locations, we also established a machine learning approach to create mangrove extent maps. Maps from all four preserves indicated migration of mangrove forests inland as the greatest areas of change were transitional zones. Additionally, normalized difference vegetation index (NDVI), normalized difference turbidity index (NDTI), and chlorophyll-a maps were generated for the partners. This project provides decision makers with a useful tool for understanding temporal changes in Florida’s aquatic preserves, identifying areas of ecological stress, and providing actionable data to make informed plans for mangrove preservation.

Remote sensing↗

Interaction of a cumulus cloud ensemble with the large-scale environment. IV - The discrete model

The Arakawa-Schubert (1974) parameterization is applied to a prognostic model of large-scale atmospheric circulations and used to analyze data in a general circulation model (GCM). The vertical structure of the large-scale model and the solution for the cloud subensemble thermodynamical properties are examined to choose cloud levels and representative regions. A mass flux distribution equation is adapted to formulate algorithms for calculating the large-scale forcing and the mass flux kernel, using either direct solution or linear programming. Finally, the feedback of the cumulus ensemble on the large-scale environment for a given subensemble mass flux is calculated. All cloud subensemble properties were determined from the conservation of mass, moist static energy, and total water.

Lord, S. J.↗