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All sources NASA NTRS DOE OSTI

DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Direct Phase-Angle Detection for Three-Phase Inverters in Asymmetrical Power Grids

This paper introduces a signal reformation based direct phase-angle detection (DPD-SR) technique for three-phase inverters supporting asymmetrical grids. Asymmetries in three-phase systems may happen because of unbalanced three-phase loads, which can lead to the voltage asymmetry at the terminals of grid-tied inverters. The proposed DPD-SR technique can detect the voltage phase-angle under asymmetrical conditions. The DPD-SR technique also offers precise and rapid phase-angle detection via signal reformation and trigonometric functions. In essence, the phase-angle detection is directly derived from the trigonometric properties of the line-line voltages, while signal reformation is implemented to handle asymmetrical voltages. The proposed method measures two line-line voltages and detects the phase-angle of a three-phase system under both symmetrical and asymmetrical conditions. Unlike classical phase-locked loop (PLL) techniques, DPD-SR does not need any closed-loop PI controller, which significantly reduces the complexity and the delay in detecting the phase-angle. In this paper, the efficacy of the proposed technique is examined in comparison with the state-of-the-art PLLs under asymmetrical conditions via a set of laboratory experiments. Here, the performance of the phase-angle detection is also tested as part of an inverter feeding an asymmetrical grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Microstructure‐Dependent Sodium Storage Mechanisms in Hard Carbon Anodes

Sustainable energy storage is essential to support the transition to renewables and meet the increasing demand for energy. Sodium‐ion batteries (NIBs) are attractive for grid‐scale energy storage due to the abundance and low cost of sodium, sustainability of other battery components, and electrochemical performance. Hard carbon (HC) is a leading anode material for NIBs, but its complex microstructure complicates the understanding of sodium storage mechanisms. Using X‐ray total scattering and density functional theory calculations, this study clarifies how HC's microstructural variations influence sodium storage across the slope (high potential) and plateau (low potential) regions of the potential capacity curve. In the slope region, sodium initially adsorbs at high‐binding energy defect sites and subsequently intercalates between graphene layers, adsorbing at low‐binding energy defect sites, correlating with different slopes observed during initial sodiation. Initial irreversibility arises from sodium trapping at surface defects and solid electrolyte interface formation. In the plateau region, sodium simultaneously intercalates and fills pores, influenced by pore size, interlayer spacing, and defect concentration. HCs with larger pore sizes form larger sodium clusters. In conclusion, the proposed mechanism underscores the role of microstructure engineering in enhancing HC performance and advancing NIBs for grid‐scale energy storage.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Modeling and Visualizing Uncertainty in Continuous Variables Predicted using Remotely Sensed Data

The use of remotely sensed images to map continuous biophysical variables, such as those related to terrestrial vegetation amount, sea surface temperature, and many other targets of NASA s Earth Observing System (EOS), includes variable, parametric, positional, spatial support and structural sources of uncertainty. A complete description of uncertainty will lead to a probability distribution at each location, allowing the exploration of the spatial dimension of uncertainty, that is, where the field is not well quantified. To achieve this purpose, convenient visualization tools are required. We have produced such a tool, called PDFVis, that facilitates the display of probability density functions (pdfs) on a per-grid-cell basis. The density estimate from Monte-Carlo generated realizations is interactively displayed as well as parametric and non-parametric summaries of the pdf field (such as mean, median, quartiles, standard deviation, number of modes, and locations of modes). Shaded surface renderings of pdfs along a transect can also be projected onto a plane. This tool will become more useful as richer descriptions of spatial uncertainty become available.

Dungan, Jennifer L.↗

DOE OSTI2025

Application of Cyber-Informed Engineering for Protecting BESS

This white paper synthesizes an array of crucial grid services provided by BESS technology, assesses its architecture and communications, and presents a case study for analysis against the principles introduced by Cyber-Informed Engineering (CIE). Furthermore, in walking through the analysis, this paper presents a framework to evaluate risks and solutions when considering BESS components. Asset owners and buyers could perform this analysis to assess their BESS product implementations, alternative inverter-based resources (IBR), and energy management systems (EMS). Battery systems fulfill various roles contingent on the unique market demands and the specific challenges presented by regional grid infrastructures. These roles also vary due to the differing utility models for ownership and operation, which are adapted to meet regional and local capabilities and requirements. Concerns have been raised regarding the potential for adversaries to exploit knowledge of battery operational patterns to orchestrate decisive attacks. However, the security of operational data for these systems may not be the primary vulnerability, as much of this information is already well-understood within the community. Applying a modest degree of subject matter expertise can often yield valuable predictions regarding how a battery will respond under certain conditions, such as grid emergencies, high or low-temperature days, Public Safety Power Shutoff (PSPS) events, and outages. The operational characteristics of batteries are well-documented, and their capabilities, including the risks associated with misoperation and the resulting consequences, are published and understood within the industry. CIE practices represent the next step in gaining functional assurance and providing an acceptable level of risk, regardless of whether a battery vendor can support a trusted and validated supply chain. While this issue has exacerbated supply chain challenges, it is not an isolated condition. This foreign supply route is the primary source of BESS for the U.S. market. Significant efforts are underway through the Bipartisan Infrastructure Law (BIL) to change that. Still, strategic short-term operational mitigations are needed to ensure the security of our operational technology (OT) systems, which are enhanced by instilling trust and are separate from vendors implementing CIE principles.

25 ENERGY STORAGE↗

DOE OSTI2022

A Medium Voltage Testbed for the Performance and Function Tests of a 13.8 kV Power Conditioning System Converter

Medium voltage SiC devices facilitate the development of medium voltage grid-connected power electronics converters. However, it is difficult to test these converters directly on the real medium voltage grid, especially considering abnormal grid conditions, such as grid voltage and frequency variation, and different converter operation modes, such as grid-connected mode and islanded mode. This paper introduces the design and implementation of a medium voltage testbed, which supports tests of medium voltage converters in both grid-connected and islanded mode tests. In the grid-connected mode, the testbed can provide up to 13.8 kV grid voltage, can support the four-quadrant operation, and can emulate different grid conditions, such as voltage and frequency variation. In the islanded mode, the converter under test works as a voltage source and the testbed emulates a three-phase balanced or unbalanced load. Experiment test results are provided to validate the design and capability of the testbed.

Li, Haiguo↗

NASA NTRS2011

NEXT Propellant Management System Integration With Multiple Ion Thrusters

As a critical part of the NEXT test validation process, a multiple-string integration test was performed on the NEXT propellant management system and ion thrusters. The objectives of this test were to verify that the PMS is capable of providing stable flow control to multiple thrusters operating over the NEXT system throttling range and to demonstrate to potential users that the NEXT PMS is ready for transition to flight. A test plan was developed for the sub-system integration test for verification of PMS and thruster system performance and functionality requirements. Propellant management system calibrations were checked during the single and multi-thruster testing. The low pressure assembly total flow rates to the thruster(s) were within 1.4 percent of the calibrated support equipment flow rates. The inlet pressures to the main, cathode, and neutralizer ports of Thruster PM1R were measured as the PMS operated in 1-thruster, 2-thruster, and 3-thruster configurations. It was found that the inlet pressures to Thruster PM1R for 2-thruster and 3-thruster operation as well as single thruster operation with the PMS compare very favorably indicating that flow rates to Thruster PM1R were similar in all cases. Characterizations of discharge losses, accelerator grid current, and neutralizer performance were performed as more operating thrusters were added to the PMS. There were no variations in these parameters as thrusters were throttled and single and multiple thruster operations were conducted. The propellant management system power consumption was at a fixed voltage to the DCIU and a fixed thermal throttle temperature of 75 C. The total power consumed by the PMS was 10.0, 17.9, and 25.2 W, respectively, for single, 2-thruster, and 3-thruster operation with the PMS. These sub-system integration tests of the PMS, the DCIU Simulator, and multiple thrusters addressed, in part, the NEXT PMS and propulsion system performance and functionality requirements.

Sovey, James S.↗

DOE OSTI2023

Distribution Grid Management in the Presence of Distributed Energy Resources

The global concerns over climate change, government policies, and incentives in support of distributed energy resources (DERs) are accelerating the growth of DERs in distribution networks. The growth in DER penetration levels can create various issues such as over/under voltages, reverse power flows, overloading, and protection miscoordination. State-of-the-art grid automation solutions such as advanced distribution management systems (ADMS) and distributed energy resource management systems (DERMS) can leverage the DERs to improve distribution grid operations. The ADMS offers advanced grid management functions such as Volt-VAR optimization (VVO), fault management, and outage management to the distribution operator to improve situational awareness and optimize network operations. The DERMS solutions aggregate the small-scale BTM DERs to provide grid services including demand response, voltage regulation, and situational awareness. In this presentation, distribution grid management approaches in the presence of DERs using ADMS and DERMS will be discussed.

ADMS↗

DOE OSTI2021

A Novel Three Phase Oak Ridge DC / AC Converter for Wireless Grid Tied Applications

In this study, a novel three phase oak ridge dc to ac converter is introduced for wireless mobility energy storage (WMES) applications to support the grid demand during peak times. The proposed topology can be used in a bi-directional operation between ac grid and dc terminals of energy storage by accomplishing unity power factor. Inherent merit of the technology can directly merge dc input to the high frequency and 60 Hz grid frequency by superimposing through the wireless coils. Theoretical and simulation results are validated by the simulation analysis for 20 kW output power. The functionality of the proposed three phase system is established by using 6 inches air gap between the couplers with the input of 675 V DC and output of 277 V AC, RMS . The system overall design analysis is demonstrated for simulation analysis and simulation results are presented achieving 3% current total harmonic distortion (THD) and 0.99 power factor (PF) at full load 20 kW wireless power transfer.

Asa, Erdem↗

NASA NTRS2016

FUN3D Analyses in Support of the Second Aeroelastic Prediction Workshop

This paper presents the computational aeroelastic results generated in support of the second Aeroelastic Prediction Workshop for the Benchmark Supercritical Wing (BSCW) configurations and compares them to the experimental data. The computational results are obtained using FUN3D, an unstructured grid Reynolds- Averaged Navier-Stokes solver developed at NASA Langley Research Center. The analysis results include aerodynamic coefficients and surface pressures obtained for steady-state, static aeroelastic equilibrium, and unsteady flow due to a pitching wing or flutter prediction. Frequency response functions of the pressure coefficients with respect to the angular displacement are computed and compared with the experimental data. The effects of spatial and temporal convergence on the computational results are examined.

Chwalowski, Pawel↗

DOE OSTI2024

Response of salt intrusion in a tidal estuary to regional climatic forcing

Abstract Salinity distribution in a large tidal estuary is subject to estuarine adjustment under the influences of multiple physical drivers such as freshwater pulses and sea level rise, and is crucial to upstream water quality, aquaculture, and ecosystem functions of the estuary. To better understand the estuarine salinity response to climate change, the unstructured-grid Finite Volume Community Ocean Model was implemented to simulate the salt intrusion in the Delaware Bay Estuary. The model was first validated by multiple observational data sets and subsequently applied in an idealized setting to examine the response of salt front to freshwater pulses in high flow conditions, followed by a long-term drought condition supported by a multi-decadal streamflow drought analysis in the estuary. The model results showed that after the freshwater pulses the salt front location moved further upstream with sea level rise. Under the simulated long-term drought condition, the adjustment timescale of salt intrusion varies nonlinearly with sea level rise. With a significant increase in sea level rise, the adjustment timescale starts to decrease. This shift suggests a transition into a different regime where the estuary becomes more stratified, as indicated by an increasing bulk Simpson number with rising sea levels.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Response Of Salt Intrusion In A Tidal Estuary To Regional Climatic Forcing (FVCOM Output for the baseline scenario)

Salinity distribution in a large tidal estuary is subject to estuarine adjustment under the influences of multiple physical drivers such as freshwater pulses and sea level rise, and is crucial to upstream water quality, aquaculture, and ecosystem functions of the estuary. To better understand the estuarine salinity response to climate change, the unstructured-grid Finite Volume Community Ocean Model was implemented to simulate the salt intrusion in the Delaware Bay Estuary. The model was first validated by multiple observational data sets and subsequently applied in an idealized setting to examine the response of salt front to freshwater pulses in high flow conditions, followed by a long-term drought condition supported by a multi-decadal streamflow drought analysis in the estuary. The model results showed that after the freshwater pulses the salt front location moved further upstream with sea level rise. Under the simulated long-term drought condition, the adjustment timescale of salt intrusion varies nonlinearly with sea level rise. With a significant increase in sea level rise, the adjustment timescale starts to decrease. This shift suggests a transition into a different regime where the estuary becomes more stratified, as indicated by an increasing bulk Simpson number with rising sea levels. These findings have been summarized into a journal manuscript. The data included in this information release request are FVCOM model output associated with the numerical simulations described in the journal manuscript.

Liu, Jinliang↗

DOE OSTI2025

Testbed and Experiments for Quantum-Conventional Networking

The realization of quantum networks requires the development of devices and methods unprecedented in conventional networks, and yet they critically depend on the latter for implementing foundational blocks and essential operations. We describe a testbed to support the development and testing of their functionality and performance by providing quantum and conventional data planes and devices, together with a secure conventional control plane. It incorporates a variety of entangled photon sources, qubit technologies, detector technologies, photonic components, and supporting conventional switches and workstations. It implements a novel fiber telescoping scheme that provides suites of connections using fiber spools and inground-aerial fiber loops. We briefly summarize a variety of experiments conducted over this testbed including: (i) flex-grid quantum connection experiments, (ii) quantum state and channel tomography, (iii) utilization of quantum key distribution keys to secure conventional encryption and firewall devices, (iv) comparative study of analytical capacity estimates and entanglement throughput, (v) deployed squeezing coexisting with conventional communications, and (iv) measurement of polarization time variation.

Rao, Nageswara [ORNL] (ORCID:0000000234085941)↗

DOE OSTI2024

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe–Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn–Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2018

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗

DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Novel Three-Phase Oak Ridge AC / AC Converter for Wireless Mobility Energy Storage System (WMESS) Connectivity

In this study, a novel three-phase Oak Ridge ac to ac converter is introduced for wireless mobility energy storage system (WMESS) applications for grid support or ancillary service applications. The proposed topology can be used in bidirectional operation between ac grid and ac terminals of energy storage (output of the ESS inverter) by accomplishing unity power factor. Inherent merit of the technology is that it can directly merge ac input 60 Hz grid frequency with the high frequency by superimposing them with the Oak Ridge Converter (ORC) and through the wireless coils. Theoretical and simulation results are provided for 10 kW output power. The functionality of the proposed three-phase system is demonstrated with the coupling coils separated by 6 inches of air gap with the input / output of 277 V AC,RMS . The system overall design is presented, and simulation results demonstrate achieving 3% current total harmonic distortion (THD) and 0.99 power factor (PF) at full load of 10 kW wireless power transfer.

Asa, Erdem↗

NASA NTRS1993

A Regional Analysis of Cloudy Mean Spherical Albedo over the Marine Stratocumulus Region and the Tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. This study examines the relationships between cloud properties and cloud fraction in order to supplement grid scale parameterizations. The satellite data used in this study is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.50 x 2.50 latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakleys (1991) theory of reflection for uniform and broken layered cloud and to Kedem, et al.(1990) findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 in) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al. theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗