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NASA NTRS2019

Atmospheric Research 2018 Technical Highlights

Highlights↗

NASA NTRS2008

Contributions of TRMM and GPM to GEOSS

Two international satellite missions have a major role in the development of global precipitation data under the auspices of the Global Earth Observation System of Systems (GEOSS) to meet the needs of several Societal Benefit Areas set forth by the Group on Earth Observations (GEO). One is the joint U.S.-Japan Tropical Rainfall Measuring Mission (TRMM), launched in 1997, which provides combined radar/radiometer measurements to serve as a benchmark for tropical precipitation measurements by passive microwave radiometers and has played a key role in the development of the current generation of multi-satellite global rainfall products. The other is the Global Precipitation Measurement (GPM) Mission, an international satellite mission to be launched in 2013 to deliver the next-generation global precipitation observations from a constellation of dedicated and operational microwave sensors. GPM is a science mission with integrated applications goals aimed at (1) advancing the knowledge of the global water/energy cycle variability and freshwater availability and (2) improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM Mission is currently a partnership between NASA and the Japan Aerospace Exploration Agency (JAXA), with additional partners in satellite constellation and ground validation under discussion. With NASA and JAXA science team activities providing the framework and infrastructures for international collaboration on satellite inter-calibration, retrieval algorithm development, and ground validation, GPM has been identified as the cornerstone for the development of the Precipitation Constellation for the Committee on Earth Observation Satellites (CEOS). An overview of current accomplishments by TRMM and anticipated contributions by GPM to GEOSS activities will be presented.

Hou, Arthur Y.↗

NASA NTRS2015

Atmospheric Research 2014 Technical Highlights

Atmospheric research in the Earth Sciences Division (610) consists of research and technology development programs dedicated to advancing knowledge and understanding of the atmosphere and its interaction with the climate of Earth. The Division's goals are to improve understanding of the dynamics and physical properties of precipitation, clouds, and aerosols; atmospheric chemistry, including the role of natural and anthropogenic trace species on the ozone balance in the stratosphere and the troposphere; and radiative properties of Earth's atmosphere and the influence of solar variability on the Earth's climate. Major research activities are carried out in the Mesoscale Atmospheric Processes Laboratory, the Climate and Radiation Laboratory, the Atmospheric Chemistry and Dynamics Laboratory, and the Wallops Field Support Office. The overall scope of the research covers an end-to-end process, starting with the identification of scientific problems, leading to observation requirements for remote-sensing platforms, technology and retrieval algorithm development; followed by flight projects and satellite missions; and eventually, resulting in data processing, analyses of measurements, and dissemination from flight projects and missions. Instrument scientists conceive, design, develop, and implement ultraviolet, infrared, optical, radar, laser, and lidar technology to remotely sense the atmosphere. Members of the various Laboratories conduct field measurements for satellite sensor calibration and data validation, and carry out numerous modeling activities. These modeling activities include climate model simulations, modeling the chemistry and transport of trace species on regional-to-global scales, cloud resolving models, and developing the next-generation Earth system models. Satellite missions, field campaigns, peer-reviewed publications, and successful proposals are essential at every stage of the research process to meeting our goals and maintaining leadership of the Earth Sciences Division in atmospheric science research. Figure 1.1 shows the 20-year record of peer-reviewed publications and proposals among the various Laboratories. This data shows that the scientific work being conducted in the Laboratories is competitive with the work being done elsewhere in universities and other government agencies. The office of Deputy Director for Atmospheric Research will strive to maintain this record by rigorously monitoring and promoting quality while emphasizing coordination and integration among atmospheric disciplines. Also, an appropriate balance will be maintained between the scientists' responsibility for large collaborative projects and missions and their need to carry out active science research as a principal investigator. This balance allows members of the Laboratories to improve their scientific credentials, and develop leadership potentials. Interdisciplinary research is carried out in collaboration with other laboratories and research groups within the Earth Sciences Division, across the Sciences and Exploration Directorate, and with partners in universities and other government agencies. Members of the Laboratories interact with the general public to support a wide range of interests in the atmospheric sciences. Among other activities, the Laboratories raise the public's awareness of atmospheric science by presenting public lectures and demonstrations, by making scientific data available to wide audiences, by teaching, and by mentoring students and teachers. The Atmosphere Laboratories make substantial efforts to attract and recruit new scientists to the various areas of atmospheric research. We strongly encourage the establishment of partnerships with Federal and state agencies that have operational responsibilities to promote the societal application of our science products. This report describes our role in NASA's mission, provides highlights of our research scope and activities, and summarizes our scientists' major accomplishments during calendar year 2014. The composition of the organization is shown in Figure 1.2 for each code. This report is published in a printed version with an electronic version on our atmospheres Web site, http://atmospheres.gsfc.nasa.gov/.

Technical↗

NASA NTRS1991

Investigation of Advanced Counterrotation Blade Configuration Concepts for High Speed Turboprop Systems. Task 2: Unsteady Ducted Propfan Analysis

The primary objective was the development of a time dependent 3-D Euler/Navier-Stokes aerodynamic analysis to predict unsteady compressible transonic flows about ducted and unducted propfan propulsion systems at angle of attack. The resulting computer codes are referred to as Advanced Ducted Propfan Analysis Codes (ADPAC). A computer program user's manual is presented for the ADPAC. Aerodynamic calculations were based on a four stage Runge-Kutta time marching finite volume solution technique with added numerical dissipation. A time accurate implicit residual smoothing operator was used for unsteady flow predictions. For unducted propfans, a single H-type grid was used to discretize each blade passage of the complete propeller. For ducted propfans, a coupled system of five grid blocks utilizing an embedded C grid about the cowl leading edge was used to discretize each blade passage. Grid systems were generated by a combined algebraic/elliptic algorithm developed specifically for ducted propfans. Numerical calculations were compared with experimental data for both ducted and unducted flows.

Hall, Edward J.↗

NASA NTRS1998

Optical Detection of Lightning from Space

Optical sensors have been developed to detect lightning from space during both day and night. These sensors have been fielded in two existing satellite missions and may be included on a third mission in 2002. Satellite-hosted, optically-based lightning detection offers three unique capabilities: (1) the ability to reliably detect lightning over large, often remote, spatial regions, (2) the ability to sample all (IC and CG) lightning, and (3) the ability to detect lightning with uniform (i.e., not range-dependent) sensitivity or detection efficiency. These represent significant departures from conventional RF-based detection techniques, which typically have strong range dependencies (biases) or range limitations in their detection capabilities. The atmospheric electricity team of the NASA Marshall Space Flight Center's Global Hydrology and Climate Center has implemented a three-step satellite lightning research program which includes three phases: proof-of-concept/climatology, science algorithm development, and operational application. The first instrument in the program, the Optical Transient Detector (OTD), is deployed on a low-earth orbit (LEO) satellite with near-polar inclination, yielding global coverage. The sensor has a 1300 x 1300 sq km field of view (FOV), moderate detection efficiency, moderate localization accuracy, and little data bias. The OTD is a proof-of-concept instrument and its mission is primarily a global lightning climatology. The limited spatial accuracy of this instrument makes it suboptimal for use in case studies, although significant science knowledge has been gained from the instrument as deployed.

Boccippio, Dennis J.↗

NASA NTRS2011

Passive Microwave Remote Sensing of Falling Snow and Associated GPM Field Campaigns

Retrievals of falling snow from space represent one of the next important challenges for the atmospheric, hydrological, and energy budget scientific communities. Historically, retrievals of falling snow have been difficult due to the relative insensitivity of satellite rain-based channels as used in the past. We emphasize the use of high frequency passive microwave channels (85-200 GHz) since these are more sensitive to the ice in clouds and have been used to estimate falling snow from space. While satellite-based remote sensing provides global coverage of falling snow events and the science is relatively new, retrievals are still undergoing development with challenges remaining. There are several current satellite sensors, though not specifically designed for estimating falling snow, are capable of measuring snow from space. These include NOAA's AMSU-B, the MHS sensors, and CloudSat radar. They use high frequency (greater than 85 GHz) passive and active microwave and millimeter-wave channels that are sensitive to the scattering from ice and snow particles in the atmosphere. Sensors with water vapor channels near 183 GHz center line provide opaqueness to the Earth's surface features that can contaminate the falling snow signatures, especially over snow covered surface. In addition, the Global Precipitation Measurement (GPM) mission scheduled for launch in 2013 is specifically designed to measure both liquid rain and frozen snow precipitation. Since falling snow from space is the next precipitation measurement challenge from space, information must be determined in order to guide retrieval algorithm development for these current and future missions. This information includes thresholds of detection for various sensor channel configurations, snow event system characteristics, and surface types. For example, can a lake effect snow system with low cloud tops having an ice water content (IWC) at the surface of 1.0 gram per cubic meter be detected? If this information is known, we can focus retrieval efforts on detectable storms and concentrate advances on achievable results. In this work, the focus is to determine thresholds of detection for falling snow for various snow conditions over land and lake surfaces. The results rely on simulated Weather Research Forecasting (WRF) simulations of falling snow cases [9] since simulations provide all the information to determine the measurements from space and the ground truth. This analysis relies on data from the Canadian CloudSat/CALIPSO Validation Program (C3VP) field campaign held from October 31, 2006 through March 1, 2007. In January 2012 GPM will return to the C3VP area for the GPM Cold Precipitation Experiment (GCPEx). This presentation will describe the thresholds-of-detection procedure and results, as well as the field campaign details.

Skofronick-Jackson, Gail↗

NASA NTRS1990

A method of determining attitude from magnetometer data only

Presented here is a new algorithm to determine attitude using only magnetometer data under the following conditions: (1) internal torques are known and (2) external torques are negligible. Torque-free rotation of a spacecraft in thruster firing acquisition phase and its magnetic despin in the B-dot mode give typical examples of such situations. A simple analytical formula has been derived in the limiting case of a spacecraft rotating with constant angular velocity. The formula has been tested using low-frequency telemetry data for the Earth Radiation Budget Satellite (ERBS) under normal conditions. Observed small oscillation of body-fixed components of the angular velocity vector near their mean values result in relatively minor errors of approximately 5 degrees. More significant errors come from processing digital magnetometer data. Higher resolution of digitized magnetometer measurements would significantly improve the accuracy of this deterministic scheme. Tests of the general version of the developed algorithm for a free-rotating spacecraft and for the B-dot mode are in progress.

Natanson, G. A.↗

NASA NTRS2003

Shuttle Payload Ground Command and Control: An Experiment Implementation Combustion Module-2 Software Development, STS-107

This presentation covers the design of a command and control architecture developed by the author for the Combustion Module-2 microgravity experiment, which flew aboard the STS-107 Shuttle mission, The design was implemented to satisfy a hybrid network that utilized TCP/IP for both the onboard segment and ground segment, with an intermediary unreliable transport for the space to ground segment. With the infusion of Internet networking technologies into Space Shuttle, Space Station, and spacecraft avionics systems, comes the need for robust methodologies for ground command and control. Considerations of high bit error links, and unreliable transport over intermittent links must be considered in such systems. Internet protocols applied to these systems, coupled with the appropriate application layer protections, can provide adequate communication architectures for command and control. However, there are inherent limitations and additional complexities added by the use of Internet protocols that must be considered during the design. This presentation will discuss the rationale for the: framework and protocol algorithms developed by the author. A summary of design considerations, implantation issues, and learned lessons will be will be presented. A summary of mission results using this communications architecture will be presented. Additionally, areas of further needed investigation will be identified.

Carek, David Andrew↗

NASA NTRSDate not supplied

Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory

One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.

Uncertainty Quantification↗

NASA NTRS1999

SHADOZ (Southern Hemisphere ADditional OZonesondes): A New Ozonesonde Data Set for the Earth Science Community

In the past several years, new tropical tropospheric ozone data products have been developed from TOMS and other satellites. Global chemical-transport models have been developed for interpretation of satellite data and to predict future ozone levels in the troposphere and stratosphere. However, the lack of ozone profile measurements for validation and evaluation of these data sets and models is critical in regions like the tropics. In 1998 NASA/Goddard Space Flight Center, in partnership with NOAA/CMDL (Climate Monitoring and Diagnostics Lab) and other nations, began a 2-year project to collect weekly ozonesonde measurements at southern hemisphere tropical sites and make the data available to the scientific community at a single electronic location: http://code9lQ.gsfc.nasa.gov/Data services/Shadoz/shadoz hmpq2.htmi A summary of data from the SHADOZ sites will be presented: Ascension Island, Fiji, Tahiti, Galapagos, American Samoa, Natal (Brazil), Reunion Island, Watukosek (Java), Nairobi and Irene, South Africa. SHADOZ is designed to meet other needs: (1) Provide the first climatology of tropical ozone along the equatorial zone for the wave-one pattern in total ozone; (2) Supplement field project observations. (3) Guide algorithm development for future satellite instruments; (4) Train scientists and educators in southern hemisphere tropical locations. From time to time, intensive tropical campaigns are making data available to SHADOZ. Data from the first half of 1999 will include INDOEX (Indian Ocean Experiment), SOWER (Stratospheric Ozone and Water in the Equatorial Region) at Christmas Island (2N, 157W), and a cruise from Norfolk, Virginia to Cape Town and Mauritius on NOAA's RN 'Ronald H Brown.'

Witte, J. C.↗

NASA NTRS2012

Accelerated Aging in Electrolytic Capacitors for Prognostics

The focus of this work is the analysis of different degradation phenomena based on thermal overstress and electrical overstress accelerated aging systems and the use of accelerated aging techniques for prognostics algorithm development. Results on thermal overstress and electrical overstress experiments are presented. In addition, preliminary results toward the development of physics-based degradation models are presented focusing on the electrolyte evaporation failure mechanism. An empirical degradation model based on percentage capacitance loss under electrical overstress is presented and used in: (i) a Bayesian-based implementation of model-based prognostics using a discrete Kalman filter for health state estimation, and (ii) a dynamic system representation of the degradation model for forecasting and remaining useful life (RUL) estimation. A leave-one-out validation methodology is used to assess the validity of the methodology under the small sample size constrain. The results observed on the RUL estimation are consistent through the validation tests comparing relative accuracy and prediction error. It has been observed that the inaccuracy of the model to represent the change in degradation behavior observed at the end of the test data is consistent throughout the validation tests, indicating the need of a more detailed degradation model or the use of an algorithm that could estimate model parameters on-line. Based on the observed degradation process under different stress intensity with rest periods, the need for more sophisticated degradation models is further supported. The current degradation model does not represent the capacitance recovery over rest periods following an accelerated aging stress period.

Celaya, Jose R.↗

NASA NTRS2000

Radiative Transfer and Satellite Remote Sensing of Cirrus Clouds Using FIRE-2-IFO Data

Under the support of the NASA grant, we have developed a new geometric-optics model (GOM2) for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. From comparisons with the results computed by the finite difference time domain (FDTD) method, we show that the novel geometric-optics can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as approximately 6. We demonstrate that the present model converges to the conventional ray tracing method for large size parameters and produces single-scattering results close to those computed by the FDTD method for size parameters along the minimum dimension smaller than approximately 20. We demonstrate that neither the conventional geometric optics method nor the Lorenz-Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20. On the satellite remote sensing algorithm development and validation, we have developed a numerical scheme to identify multilayer cirrus cloud systems using AVHRR data. We have applied this scheme to the satellite data collected over the FIRE-2-IFO area during nine overpasses within seven observation dates. Determination of the threshold values used in the detection scheme are based on statistical analyses of these satellite data.

Source record↗

NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

NASA NTRS1993

Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS)

This effort involves development of a calibrated, pulsed coherent CO2 Doppler lidar, followed by a carefully-planned and -executed program of multi-dimensional wind velocity and aerosol backscatter measurements from the NASA DC-8 research aircraft. The lidar, designated as the Multi-center Airborne Coherent Atmospheric Wind Sensor (MACAWS), will be applicable to two research areas. First, MACAWS will enable specialized measurements of atmospheric dynamical processes in the planetary boundary layer and free troposphere in geographic locations and over scales of motion not routinely or easily accessible to conventional sensors. The proposed observations will contribute fundamentally to a greater understanding of the role of the mesoscale, helping to improve predictive capabilities for mesoscale phenomena and to provide insights into improving model parameterizations of sub-grid scale processes within large-scale circulation models. As such, it has the potential to contribute uniquely to major, multi-institutional field programs planned for the mid 1990's. Second, MACAWS measurements can be used to reduce the degree of uncertainty in performance assessments and algorithm development for NASA's prospective Laser Atmospheric Wind Sounder (LAWS), which has no space-based instrument heritage. Ground-based lidar measurements alone are insufficient to address all of the key issues. To minimize costs, MACAWS is being developed cooperatively by the lidar remote sensing groups of the Jet Propulsion Laboratory, NOAA Wave Propagation Laboratory, and MSFC using existing lidar hardware and manpower resources. Several lidar components have already been exercised in previous airborne lidar programs (for example, MSFC Airborne Doppler Lidar System (ADLS) used in 1981,4 Severe Storms Wind Measurement Program; JPL Airborne Backscatter Lidar Experiment (ABLE) used in 1989,90 Global Backscatter Experiment Survey Missions). MSFC has been given responsibility for directing the overall program of instrument development and scientific measurement. The focus of current research and plans for next year are presented.

Rhothermel, Jeffry↗

NASA NTRS2018

Polarimetric Remote Sensing of Atmospheric Aerosols: Instruments, Methodologies, Results, and Perspectives

Polarimetry is one of the most promising types of remote sensing for improved characterization of atmospheric aerosol. Indeed, aerosol particles constitute a highly variable atmospheric component characterized by a large number of parameters describing particle sizes, morphologies (including shape and internal structure), absorption and scattering properties, amounts, horizontal and vertical distribution, etc. Reliable monitoring of all these parameters is very challenging, and therefore the aerosol effects on climate and environment are considered to be among the most uncertain factors in climate and environmental research. In this regard, observations that provide both the angular distribution of the scattered atmospheric radiation as well as its polarization state at multiple wavelengths covering the UV–SWIR spectral range carry substantial implicit information on the atmospheric composition. Therefore, high expectations in improving aerosol characterization are associated with detailed passive photopolarimetric observations. The critical need to use space-borne polarimetry for global accurate monitoring of detailed aerosol properties was first articulated in the late 1980s and early 1990s. By now, several orbital instruments have already provided polarization observations from space, and a number of advanced missions are scheduled for launch in the coming years by international and national space agencies. The first and most extensive record of polarimetric imagery was provided by POLDER-I, POLDER-II, and POLDER/PARASOL multi-angle multi-spectral polarization sensors. Polarimetric observations with the POLDER-like design intended for collecting extensive multi-angular multi-spectral measurements will be provided by several instruments, such as the MAI/TG-2, CAPI/TanSat, and DPC/GF-5 sensors recently launched by the Chinese Space Agency. Instruments such as the 3MI/MetOp-SG, MAIA, SpexOne and HARP2 on PACE, POSP, SMAC, PCF, DPC–Lidar, ScanPol and MSIP/Aerosol-UA, MAP/Copernicus CO2 Monitoring, etc. are planned to be launched by different space agencies in the coming decade. The concepts of these future instruments, their technical designs, and the accompanying algorithm development have been tested intensively and analyzed using diverse airborne prototypes. Certain polarimetric capabilities have also been implemented in such satellite sensors as GOME-2/MetOp and SGLI/GCOM-C.

Aerosols↗

NASA NTRSDate not supplied

3D Lightning Geolocation With the CubeSpark Constellation

The new CubeSpark mission concept is being developed as a constellation of up to six satellites for high-resolution 3D lightning mapping. Each satellite in low-Earth orbit (LEO) will use optical and radio frequency (RF) sensors to geolocate individual sources from lightning flashes. The purpose of this study is to evaluate the potential accuracies and feasibilities of RF-based geolocation methods. This is done using a robust simulation framework to accurately depict the ionosphere’s effect on propagating RF signals, using their arrival times at each station to reconstruct source locations. We identified the primary sources of error as geometric, ionospheric, and instrumental. These are each analyzed to determine their quantitative effect on geolocation uncertainty. CubeSpark’s science objectives include mapping thundercloud charge regions and even individual flash channel structure for applications across a wide range of fields from climatology to hydrology. These applications require geolocation accuracy better than 1-2 km in each dimension, thus special care must be taken to optimize constellation design, minimize the main sources of error, and maximize CubeSpark’s potential. The algorithms developed in this study show promising results, with large regions having both horizontal and vertical uncertainties less than 1 km. After the removal of the Lightning Imaging Sensor from the International Space Station, an observational gap has been left for lightning observers from LEO. It therefore becomes increasingly vital to evaluate and improve on the current state of lightning mapping to prepare for the next generation of 3D lightning geolocation.

lightning↗

NASA NTRSDate not supplied

3D Lightning Geolocation with the CubeSpark Constellation

lightning↗

NASA NTRS2009

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Johnson, W. L.↗