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At least 361 records · Page 20

Development and Validation of a Slosh-Based Ullage Collapse Model

Ullage collapse modeling is an essential tool for the success of spacecraft powered by cryogenic propellants. The degree of ullage collapse can have a major impact on the design of cryogenic propellant tanks as well as the mission’s concept of operations. Additional commodities (e.g., helium gas for pressure control) and their quantities are dependent on the amount of heat transfer and phase change of propellants expected during flight. Currently, high-fidelity computational fluid dynamics (CFD) with heat transfer and phase change is the most accurate method for predicting ullage collapse. CFD simulations of this kind, however, can become very costly for problems requiring large domains, long simulation times, or significant liquid motion. Consequently, there is a need for a reduced order model to provide fast responses which can be used in engineering design decisions. The proposed numerical model is a nodal approach, augmented by outputs from CFD analyses that are generated rapidly and reliably. These outputs include transient values for liquid-vapor interface area, interface velocity, and liquid position using a volume of fluid (VoF) method. There are several benefits of combining a nodal approach with slosh predictions from CFD simulations: leveraging of the Loci/STREAM-VoF solver that has been validated in high-g and low-g environments, rapid modeling of VoF with isothermal propellant simplifications and relatively coarse meshes, and improved model predictions from the nodal tool. The nodal approach, informed by the slosh predictions from CFD, assumes uniform conditions in the liquid and gas domains. Modifications to account for temperature stratification in the liquid and gas may be implemented as a future improvement. Thermodynamic changes within the tank are solved at user-defined timesteps. First, impacts due to mass entering or leaving the control volume are captured. Second, heat transfer impacts are accounted for by tracking the volume of the gas which has been contacted by liquid in that timestep and rebalancing the internal energy. Finally, phase change is approximated using the area and velocity of the interface. The tank conditions are re-computed by conserving mass and energy. Calibration of the model to several test flights and experiments are required to baseline the predictive power and uncertainty. The final product will enable designers and engineers to create quick-turnaround predictions for ullage collapse and inform design feasibility.

Computational Fluid Dynamics↗

Evidence from the limb infrared monitor of the stratosphere for nonlocal thermodynamic equilibrium in the nu2 mode of mesospheric water vapour and the nu3 mode of stratospheric nitrogen dioxide

Data from the 6.9-micron H2O channel and the 6.2-micron NO2 channel of the Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) have been used to investigate the daytime enhancement to H2O; the high concentration of H2O sometimes observed in the polar night mesosphere; and the high ratio of daytime to nighttime NO2 in the upper stratosphere. These three phenomena deviate noticeably from the predictions of photochemical theory. The 20 to 30 percent diurnal variation in stratospheric H2O apparent in LIMS data cannot be reconciled with a photochemical lifetime in excess of four months. This is attributed to departure from local thermodynamic equilibrium of daytime emission which had not been accounted for in retrievals. Speculative possibilities of NLTE emission from the H2O nu2 and NO2 nu3 hot bands are discussed. It is found that the nonthermal emission from NO2 significantly affects retrieval of H2O in the polar nighttime and NO2 in the daytime stratosphere at low latitudes.

Kerridge, Brian J.↗

Validation of Thermodynamic Vent System Performance using Thermal Desktop

Cryogenic fluid management (CFM) for in-space propulsion systems is crucial to enabling future space missions. A means to control the pressure inside a propellant tank is necessary to prevent the venting of liquid propellant in microgravity environments. A thermodynamic vent system (TVS) is one way to regulate the pressure and temperature of the fluid inside a tank. A previous study created a simplified model of a TVS in a two-phase cryogenic heat exchanger. The TVS expands the working fluid across a Joule-Thomson (J-T) device and routes the cooled fluid through the heat exchanger to remove heat from the surrounding fluid. The model was able to predict the TVS heat extraction performance and was validated against experimental data using the same hardware. This study expands the model of the TVS into Thermal Desktop (TD) and recreates the results from both the original model and the experimental data. This new TD model has the potential to be used to predict TVS heat extraction performance in cryogenic propellant tanks for future space missions.

Cryogenic Fluid Management↗

Spatial and Temporal Distribution of Clouds as Observed by MODIS Onboard the Terra and Aqua Satellites

The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4, 2002. It achieved its final orbit and began Earth observations on February 24,2000 for Terra and June 24,2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, and fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. Over the last year, extensive improvements and enhancements in the global cloud products have been implemented, and reprocessing of all MODIS data on Terra has commenced since first light in February 2000. In the cloud mask algorithm, the most extensive improvements were in distinguishing clouds at nighttime, including the challenging polar darkness regions of the world. Additional improvements have been made to properly distinguish sunglint from clouds in the tropical ocean regions, and to improve the identification of clouds from snow during daytime in Polar Regions. We will show global monthly mean cloud fraction for both Terra and Aqua, and show how similar the global daytime cloud fraction is from these morning and afternoon orbits, respectively. We will also show the zonal distribution of cloud fraction over land and ocean regions for both Terra and Aqua, and show the time series of global cloud fraction from July 2002 through June 2006.

King, Michael D.↗

Validation of a Two-Phase CFD Model for Autogenous Pressurization and Expulsion

This paper presents a two-phase computational fluid dynamics (CFD) model for simulating autogenous pressurization and expulsion in a cryogenic liquid hydrogen storage tank, utilizing a volume-of-fluid (VOF) approach combined with the kinetics-based Schrage equation to accurately capture the phase boundary and interfacial heat, mass, and momentum transfer between liquid and vapor phases. The model is validated against experimental data from NASA's K-site tank facility, specifically experimental case 225, which involved pressurization and controlled expulsion of liquid hydrogen. Various turbulence models are evaluated to assess their influence on model accuracy. The CFD simulations successfully replicate key thermodynamic behaviors observed during the experiments, including pressure evolution, temperature profiles, and phase-change dynamics at the vapor-liquid interface. The predicted tank pressures, temperatures, and pressurant requirements agree with experimental data, with pressurant mass predictions within 16\% of observed values. This study highlights the importance of selecting appropriate turbulence models to accurately simulate complex flow and heat transfer phenomena during tank pressurization and expulsion. By enhancing the accuracy and reliability of CFD models for liquid hydrogen under cryogenic conditions, this research contributes to developing efficient cryogenic propellant management strategies for future space missions.

Computational Fluid Dynamics↗

Validation of a Two-Phase CFD Model for Autogenous Pressurization and Expulsion

This paper presents a two-phase computational fluid dynamics (CFD) model for simulating autogenous pressurization and expulsion in a cryogenic liquid hydrogen storage tank, utilizing a volume-of-fluid (VOF) approach combined with the kinetics-based Schrage equation to accurately capture the phase boundary and interfacial heat, mass, and momentum transfer between vapor and liquid phases. The model is validated against experimental data from NASA's K-site tank facility, specifically experimental case 225, which involved autogenous pressurization and controlled expulsion of liquid hydrogen. Various turbulence models are evaluated to assess their influence on model accuracy. The CFD simulations successfully replicate key thermodynamic behaviors observed during the experiments, including pressure evolution, temperature profiles, and phase-change dynamics at the vapor-liquid interface. The predicted tank pressures and temperatures agree well with experimental data, whereas the pressurant mass predictions are within 16% of observed values. This study emphasizes the importance of selecting appropriate turbulence models to accurately simulate the complex flow and heat transfer phenomena during tank autogenous pressurization and expulsion. By improving the accuracy and reliability of CFD models for these processes, this research contributes to developing efficient cryogenic propellant management strategies for future space missions.

Computational Fluid Dynamics↗

NLTE model stellar atmospheres with line blanketing near the series limits

In this paper we study the influence of line-merging regions at the intermediate long-wavelength side of a continuum threshold on the computed model atmosphere structure and predicted spectrum. In order to model these regions sufficiently accurately, we have developed two concepts. First, we have extended the occupation probability formalism of Hummer and Mihalas to non-local thermodynamic equilibrium (non-LTE) plasmas. Second, in order to treat the very complicated opacity in the line merging region, we have generalized the concept of opacity distribution functions to treat non-LTE situations. All Rydberg states are consistently included within this framework, so that no arbitrary cutoff of high (LTE) levels is made. We have calculated several pure hydrogen models atmospheres for two effective temperatures, T(sub eff) = 20000 and 35000 K, and discussed the differences between models calculated with various treatments of the line merging. In particular, we have shown that the error in the predicted profiles of Balmer lines resulting from the neglect of line merging is typically of the order of 3-4%, while the errors in the far-UV portion of the Balmer continuum reaches 15-35%. The errors generally decrease with increasing effective temperature. At the same time, the internal accuracy of the models is shown to be about or below 0.5% for all predicted spectral features. We conclude that for interpreting current high-accuracy spectrophotometric observations models including the line merging are necessary, and that the formalism developed in this paper is capable of providing a sufficiently accurate and robust modeling technique.

Hubeny, I.↗

Evaluation of a GCM cirrus parameterization using satellite observations

This study applies a simple yet effective methodology to validate a general circulation model parameterization of cirrus ice water path. The methodology combines large-scale dynamic and thermodynamic fields from operational analyses with prescribed occurrence of cirrus clouds from satellite observations to simulate a global distribution of ice water path. The predicted cloud properties are then compared with the corresponding satellite measurements of visible optical depth and infrared cloud emissivity to evaluate the reliability of the parameterization. This methodology enables the validation to focus strictly on the water loading side of the parameterization by eliminating uncertainties involved in predicting the occurrence of cirrus internally within the parameterization. Overall the parameterization performs remarkably well in capturing the observed spatial patterns of cirrus optical properties. Spatial correlations between the observed and the predicted optical depths are typically greater than 0.7 for the tropics and northern hemisphere midlatitudes. The good spatial agreement largely stems from the strong dependence of the ice water path upon the temperature of the environment in which the clouds form. Poorer correlations (r approximately 0.3) are noted over the southern hemisphere midlatitudes, suggesting that additional processes not accounted for by the parameterization may be important there. Quantitative evaluation of the parameterization is hindered by the present uncertainty in the size distribution of cirrus ice particles. Consequently, it is difficult to determine if discrepancies between the observed and the predicted optical properties are attributable to errors in the parameterized ice water path or to geographic variations in effective radii.

Soden, B. J.↗

Radiometric Modeling and Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)Ground Based Measurement Experiment

The ultimate remote sensing benefits of the high resolution Infrared radiance spectrometers will be realized with their geostationary satellite implementation in the form of imaging spectrometers. This will enable dynamic features of the atmosphere s thermodynamic fields and pollutant and greenhouse gas constituents to be observed for revolutionary improvements in weather forecasts and more accurate air quality and climate predictions. As an important step toward realizing this application objective, the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) Engineering Demonstration Unit (EDU) was successfully developed under the NASA New Millennium Program, 2000-2006. The GIFTS-EDU instrument employs three focal plane arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The GIFTS calibration is achieved using internal blackbody calibration references at ambient (260 K) and hot (286 K) temperatures. In this paper, we introduce a refined calibration technique that utilizes Principle Component (PC) analysis to compensate for instrument distortions and artifacts, therefore, enhancing the absolute calibration accuracy. This method is applied to data collected during the GIFTS Ground Based Measurement (GBM) experiment, together with simultaneous observations by the accurately calibrated AERI (Atmospheric Emitted Radiance Interferometer), both simultaneously zenith viewing the sky through the same external scene mirror at ten-minute intervals throughout a cloudless day at Logan Utah on September 13, 2006. The accurately calibrated GIFTS radiances are produced using the first four PC scores in the GIFTS-AERI regression model. Temperature and moisture profiles retrieved from the PC-calibrated GIFTS radiances are verified against radiosonde measurements collected throughout the GIFTS sky measurement period. Using the GIFTS GBM calibration model, we compute the calibrated radiances from data collected during the moon tracking and viewing experiment events. From which, we derive the lunar surface temperature and emissivity associated with the moon viewing measurements.

Tian, Jialin↗

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗

GMS-based"Future Time" Rainfall Data Assimilation for Mesoscale Weather Prediction over Korean Peninsula and Future Prospects with GPM Satellite Measurements

This study examines the use of satellite-derived nowcasted (short-term forecasted) rainfall over 3-hour time periods to gain an equivalent time increment in initializing a nonhydrostatic mesoscale model used for predicting convective rainfall events over the Korean peninsula. Infrared (IR) window measurements from the Japanese Geostationary Meteorological Satellite (GMS) are used to specify latent heating for a spinup period of the model - but in future time -- thus initializing in advance of actual time in the framework of a prediction scenario. The main scientific objective of the study is to investigate the strengths and weaknesses of this approach insofar as data assimilation, in which the nowcasted assimilation data are derived independently of the prognostic model itself. Although there have been various recent improvements in formulating the dynamics, thermodynamics, and microphysics of mesoscale models, as well as computer advances which allow the use of high resolution cloud-resolving grids and explicit latent heating over regional domains, spinup remains at the forefront of unresolved mesoscale modeling problems. In general, non-realistic spinup limits the skill in predicting the spatial-temporal distribution of convection and precipitation, primarily in the early hours of a. forecast, stemming from standard prognostic variables not representing the initial diabatic heating field produced by the ambient convection and cloud fields. The long-term goal of this research is to improve short-range (12-hour) quantitative precipitation forecasting (QPF) over the Korean peninsula through the use of innovative data assimilation methods based on geosynchronous satellite measurements. As a step in th~s direction, a non-standard data assimilation experiment in conjunction with GMS-retrieved nowcasted rainfall information introduced to the mesoscale model is conducted. The 3-hourly precipitation forecast information is assimilated through nudging the associated diabatic heating during the early stages of a forecast period. This procedure is expected to enhance details in the moisture field during model integration, and thus improve spinup performance, assuming the errors in the future time latent heating data ate less than intrinsic model background errors.

Smith, Eric A.↗

Toward a dynamic-thermodynamic assimilation of satellite surface temperature in numerical atmospheric models

An assimilation technique is described in which satellite-observed surface skin temperature tendencies are used in a model surface energy budget so that the predicted rate of temperature change in the model more closely agrees with the satellite observations. Both visible and infrared GOES satellite data are used in the assimilation. The technique is based on analytically recovering surface moisture from similarity expressions derived from an evapotranspiration residual obtained as a difference between the unadjusted model evapotranspiration and the satellite-inferred evapotranspiration. The technique has application in regional-scale models where surface parameters such as root zone moisture, soil moisture, etc., are unknown. It is assumed that the largest error in the surface energy budget is in the evapotranspiration term. Two tests are given for the technique, first, a one-dimensional test against FIFE data and, second, a three-dimensional test over Oklahoma. In these cases the technique appears to correctly adjust the model response to agree better with observations.

Mcnider, Richard T.↗

Effects of physical aging on long-term behavior of composites

The HSCT plane, envisioned to have a lifetime of over 60,000 flight hours and to travel at speeds in excess of Mach 2, is the source of intensive study at NASA. In particular, polymer matrix composites are being strongly considered for use in primary and secondary structures due to their high strength to weight ratio and the options of property tailoring. However, an added difficulty in the use of polymer based materials is that their properties change significantly over time, especially at the elevated temperatures that will be experienced during flight, and prediction of properties based on irregular thermal and mechanical loading is extremely difficult. This study focused on one aspect of long-term polymer composite behavior: physical aging. When a polymer is cooled to below its glass transition temperature, the material is not in thermodynamic equilibrium and the free volume and enthalpy evolve over time to approach their equilibrium values. During this time, the mechanical properties change significantly and this change is termed physical aging. This work begins with a review of the concepts of physical aging on a pure polymer system. The effective time theory, which can be used to predict long term behavior based on short term data, is mathematically formalized. The effects of aging to equilibrium are proven and discussed. The theory developed for polymers is then applied first to a unidirectional composite, then to a general laminate. Comparison to experimental data is excellent. It is shown that the effects of aging on the long-term properties of composites can be counter-intuitive, stressing the importance of the development and use of a predictive theory to analyze structures.

Brinson, L. Catherine↗

Effect of humidity on jet engine axial-flow compressor performance

Two problems related to the ingestion of humid air into jet engine axial compressors have been studied: (1) the changes in the performance of the compressor in the absence of condensation and (2) the changes in the entry conditions to the compressor when condensation occurs. Regarding the first, the extent of changes are predicted and also measured in the case of a six-stage compressor operated with air-methane gas mixture utilizing the similarities in the thermodynamic properties between water vapor and methane. For the condensation process in an inlet, a model is described that takes into account the presence of micro particulates and the flow field changes in the vicinity of the inlet wall. Finally, the effects of humidity on engine performance are discussed in relation to engine trim and control schemes.

Ehresman, C. M.↗

[Two-phase Interfaces in Weak External Fields]

Our aim has been that of understanding from first principles the behavior of two-phase interfaces in the absence of gravitational constraints. This is fundamental to our ability to deal with the fluid structures that abound in the real biological, chemical, and physical world. A substantial effort was mounted to determine how familiar hydrodynamic concepts have to be modified and interpreted to make them appropriate to the multi-level structure alluded to above. This was primarily in the context of the microscopic symmetric pressure tensor, which was, for the first time, expressed in the invaluable density functional format, and the used to follow the predictions of popular microscopic models of the energetics of interfacial systems. In the course of these investigations, the previous murky relation between pressure tensor and thermodynamics was completely clarified. The process of extending thermodynamic information to interfacial dynamics was initiated along two paths. One was from the viewpoint of an inertialess lattice gas, resulting in the surprising conclusion that at this level, all transport is governed by precisely the thermodynamic free energy, albeit with a non-trivial effective particle mobility. The other aimed at understanding the fashion in which slow macroscopic motions, accounted for by a time-varying microscopic energy, generate effective hydrodynamic parameters. By examining a solvable model system, it was found that all current procedures for doing so are deficient, and suitable alleviation suggested. The major effect of this project was to set the stage for the analysis of the substantial dynamical regimes in which extensive equilibrium information provides the dominant background. This produces a smooth junction to the models of Araki and Munakata, Giacomin and Lebowitz, and Oxtoby. It is also crucial to our understanding of the complex interfacial equilibrium configurations required for intermediate stages of two-phase separation, for which the "phase-field" techniques we have been developing are uniquely effective. And it puts us within striking range of the physical experiments that can provide incisive tests of the theoretical framework.

Percus, J. K.↗

Global Multispectral Cloud Retrievals from MODIS

The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4,2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua, and will show characteristics of cloud optical and microphysical properties as a function of latitude for land and ocean separately, and contrast the statistical properties of similar cloud types in various parts of the world.

King, Michael D.↗

Global Multispectral Cloud Retrievals from MODIS

The Moderate Resolution Imaging Spectroradiometer (MODIS) was developed by NASA and launched onboard the Terra spacecraft on December 18,1999 and Aqua spacecraft on May 4,2002. It achieved its final orbit and began Earth observations on February 24, 2000 for Terra and June 24, 2002 for Aqua. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate change studies, climate modeling, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. We will describe the various cloud properties being analyzed on a global basis from both Terra and Aqua, and will show characteristics of cloud optical and microphysical properties as a function of latitude for land and ocean separately, and contrast the statistical properties of similar cloud types in various parts of the world.

King, Michael D.↗

Multi-Spectral Cloud Retrievals from Moderate Image Spectrometer (MODIS)

MODIS observations from the NASA EOS Terra spacecraft (1030 local time equatorial sun-synchronous crossing) launched in December 1999 have provided a unique set of Earth observation data. With the launch of the NASA EOS Aqua spacecraft (1330 local time crossing! in May 2002: two MODIS daytime (sunlit) and nighttime observations are now available in a 24-hour period allowing some measure of diurnal variability. A comprehensive set of remote sensing algorithms for cloud masking and the retrieval of cloud physical and optical properties has been developed by members of the MODIS atmosphere science team. The archived products from these algorithms have applications in climate modeling, climate change studies, numerical weather prediction, as well as fundamental atmospheric research. In addition to an extensive cloud mask, products include cloud-top properties (temperature, pressure, effective emissivity), cloud thermodynamic phase, cloud optical and microphysical parameters (optical thickness, effective particle radius, water path), as well as derived statistics. An overview of the instrument and cloud algorithms will be presented along with various examples, including an initial analysis of several operational global gridded (Level-3) cloud products from the two platforms. Statistics of cloud optical and microphysical properties as a function of latitude for land and Ocean regions will be shown. Current algorithm research efforts will also be discussed.

Platnick, Steven↗