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NASA NTRS1976

Sea ice studies in the Spitsbergen-Greenland area

The author has identified the following significant results. Detailed information on the outflow through the Fram Strait of ice from the Polar Ocean over shorter periods was obtained. It is found that the speed of the outflow may vary about 100% over periods of a few days. The core of the East Greenland Current is found between 2 deg E and 4 deg W. The speed of the surface water at 81 deg N is for a calm period estimated to be about 10 cm/s. A new surging glacier was discovered and new fronts of several glaciers were determined. The variation of the snow line with respect to distance from the coast was for the first time determined for the southern part of Spitsbergen. Great variations were observed, from 200 m in east to 550 m in the central area of the island.

Vinje, T. E.↗

NASA NTRS2003

Differential Velocity Between Solar Wind Protons and Alpha Particles in Pressure Balance Structures

Pressure balance structures (PBSs) are a common high plasma beta feature in high latitude, high speed solar wind. They have been proposed as remnants of coronal plumes. If true, they should reflect the observation that plumes are rooted in unipolar magnetic flux concentrations in the photosphere and are heated as oppositely directed flux is advected into and reconnects with the flux concentration. A minimum variance analysis (MVA) of magnetic discontinuities in PBSs showed there is a larger proportion of tangential discontinuities than in the surrounding high speed wind, supporting the hypothesis that plasmoids or extended current sheets are formed during reconnection at the base of plumes. To further evaluate the character of magnetic field discontinuities in PBSs, differential streaming between alpha particles and protons is analyzed here for the same sample of PBSs used in the MVA. Alpha particles in high speed wind generally have a higher radial flow speed than protons. However, if the magnetic field is folded back on itself, as in a large amplitude Alfven wave, alpha particles will locally have a radial flow speed less than protons. This characteristic is used here to distinguish between folded back magnetic fields (which would contain rotational discontinuities) and tangential discontinuities using Ulysses high latitude, high speed solar wind data. The analysis indicates that almost all reversals in the radial magnetic field in PBSs are folded back field lines. This is found to also be true outside PBSs, supporting existing results for typical high speed, high latitude wind. There remains a small number of cases that appear not to be folds in the magnetic field and which may be flux tubes with both ends rooted in the Sun. The distinct difference in MVA results inside and outside PBSs remains unexplained.

Yamauchi, Y.↗

NASA NTRS2004

Solar Wind Stream Interaction Regions without Sector Boundaries

During periods of high solar activity when there are many sources of solar wind on the solar disk, a spacecraft occasionally encounters consecutive solar wind streams with the same magnetic polarity. The low-speed wind in the region of interaction between the two streams exhibits many of the same features as, but has some differences from, the low-speed wind that includes crossings of the heliospheric current sheet (HCS) where the direction of the heliospheric magnetic field reverses. The non-HCS slow wind exhibits many of the same small-scale structures usually associated with the slow wind around the HCS; these include discontinuous stream interfaces and other discontinuities, magnetic holes, and low-entropy structures. These entropy holes do not appear to have the same origin as the plasma sheets observed near the HCS, however. The helium abundances and heavy ion charge states in the non-HCS regions are not significantly different from those in HCS-associated regions. Some of the dynamical properties of the non-HCS regions differ from those found near the HCS; the regions between leading and trailing stream interfaces have a shorter duration or scale size, greater minimum speed, and lower peak and average densities. No correlation could be found between the non-HCS slow wind and visible coronal streamers.

interaction regions↗

NASA NTRS2004

Differential Velocity between Solar Wind Protons and Alpha Particles in Pressure Balance Structures

Pressure balance structures (PBSs) are a common high-plasma beta feature in high-latitude, high-speed solar wind. They have been proposed as remnants of coronal plumes. If true, they should reflect the observation that plumes are rooted in unipolar magnetic flux concentrations in the photosphere and are heated as oppositely directed flux is advected into and reconnects with the flux concentration. A minimum variance analysis (MVA) of magnetic discontinuities in PBSs showed there is a larger proportion of tangential discontinuities than in the surrounding high-speed wind, supporting the hypothesis that plasmoids or extended current sheets are formed during reconnection at the base of plumes. To further evaluate the character of magnetic field discontinuities in PBSs, differential streaming between alpha particles and protons is analyzed here for the same sample of PBSs used in the MVA. Alpha particles in high-speed wind generally have a higher radial flow speed than protons. However, if the magnetic field is folded back on itself, as in a large-amplitude Alfven wave, alpha particles will locally have a radial flow speed less than protons. This characteristic is used here to distinguish between folded back magnetic fields (which would contain rotational discontinuities) and tangential discontinuities using Ulysses high-latitude, high-speed solar wind data. The analysis indicates that almost all reversals in the radial magnetic field in PBSs are folded back field lines. This is found to also be true outside PBSs, supporting existing results for typical high-speed, high-latitude wind. There remains a small number of cases that appear not to be folds in the magnetic field and which may be flux tubes with both ends rooted in the Sun. The distinct difference in MVA results inside and outside PBSs remains unexplained.

Yamauchi, Yohei↗

DOE OSTI2022

Measuring characteristic differences between high- and low-performing discharges on the MegaJOuLe Neutron Imaging Radiography (MJOLNIR) DPF

A dense plasma focus (DPF) is a compact coaxial plasma gun, which completes its discharge as a Z-pinch, producing short (<100 ns) pulses of ions, x rays, and/or neutrons. Lawrence Livermore National Laboratory recently constructed and began operating a new device, the MJOLNIR (MegaJOuLe Neutron Imaging Radiography) DPF, which is designed for single-pulse flash neutron radiography. This device has achieved neutron yields of up to 4.1×10 11 neutrons/pulse at 3.3 MA peak current, and higher-current commissioning is under way. Like most DPFs, MJOLNIR exhibits variable yields in some configurations. Here, we present evidence of the role of parasitic current paths within the gun in stochastically influencing the yield. First through “conditioning shots,” where new hardware has been introduced, we show that increased run-down and run-in speeds correlate with higher yields. These observations are consistent with current being delivered to the electrodes but not to the main plasma sheath, degrading the implosion-driving force. Once nominal conditions are established, we correlate low-performing discharges with smaller current dip and associated voltage spike for a fixed machine configuration. A snow-plow model is able to recreate small-magnitude current dips through the introduction of a parasitic current path, and particle-in-cell simulations establish how parasitic current paths lower the ion beam energy available to produce neutrons. Finally, we observe an increased likelihood of shots with low yield and smaller current dip with increasing fill pressure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Synoptic maps of solar wind parameters from in situ spacecraft observations

Solar wind observations from the Interplanetary Monitoring Platform-8 (IMP-8) and Pioneer Venus Orbiter (PVO) spacecraft from 1982 until 1988 are combined to construct synoptic maps of solar wind parameters near 1 AU. Each map consists of 6 months of hourly averaged solar wind data, binned by heliographic latitude and Carrington longitude and projected back to the Sun. These maps show the structure and time evolution of solar wind streams near 1 AU in the heliographic latitudes of +/- 7.25 deg and provide and explicit picture of several phenomena, such as gradients, changes in the inclination of the heliospheric current sheet, and the relative positions of various structures in the inner heliosphere, that is difficult to obtain from single-spacecraft observations. The stream structure varied significantly during the last solar cycle. Between 1982 and early 1985, solar wind parameters did not depend strongly on heliographic latitude. During the last solar minimum, the solar wind developed significant latitudinal structure, and high-speed streams were excluded from the vicinity of the solar equator. The interplanetary magnetic field was strongly correlated with the coronal field, and the current sheet tended to coincide with the coronal neutral line. The solar wind speed showed the expected correlations with temperature, interplanetary magnetic field, and distance from the current sheet. The solar wind speed was anticorrelated with density, but the regions of highest density occurred east of the heliospheric current sheet and the regions of lowest solar wind speed. This is consistent with compression at the leading edge of high-speed streams.

Gazis, P. R.↗

NASA NTRS2006

Lightning Return-Stroke Current Waveforms Aloft, from Measured Field Change, Current, and Channel Geometry

Three-dimensional reconstructions of six rocket-triggered lightning channels are derived from stereo photographs. These reconstructed channels are used to infer the behavior of the current in return strokes above the ground from current waveforms measured at the channel base and electric-field-change waveforms measured at a range of 5.2 kilometers for 24 return strokes in these channels. Streak photographs of 14 of the same strokes are analyzed to determine the rise times, propagation speeds, and amplitudes of relative light intensity for comparison with the electrical inferences. Results include the following: 1) The fine structure of the field-change waveforms that were radiated by these subsequent return strokes can be explained, in large part, by channel geometry. 2) The average 10 - 90% rise time of the stroke current increased by about a factor of seven in our sample, from an observed 0.31 plus or minus 0.17 microseconds at the surface to an inferred 2.2 plus or minus 0.5 microcseconds at 1 kilometer path length above the surface. 3) The three-dimensional propagation speed of the current front averaged 1.80 plus or minus 0.24 X 10(exp 8) meters per second over channel lengths typically greater than 1 kilometer. 4) Assuming that the measured current was entirely due to the return stroke forced an unreasonably large and abrupt reduction in inferred current amplitude over the first few tens of meters above the surface, especially in cases when the leader was bright relative to its stroke. Therefore, a significant fraction of the current at the surface was probably due to the leader, at least in such cases. 5) Peak return-stroke currents decreased by approximately 37 plus or minus 12% from 100 meters to 1 kilometer of path length above the surface. Because of uncertainty about how to partition the measured current between leader and return stroke, we are unable to infer the variation of current amplitude near the ground.

Willett, J. C.↗

NASA NTRS1985

Commutating Permanent-Magnet Motors At Low Speed

Circuit provides forced commutation during starting. Forced commutation circuit diverts current from inverter SCR's and turns SCR's off during commutation intervals. Silicon controlled rectifier in circuit unnecessary when switch S10 replaced by high-current, high-voltage transistor. At present, high-current, low-voltage device must suffice.

Dolland, C.↗

DOE OSTI2022

High-Speed Diagnostic and Simulation Capabilities for Reacting Hypersonic Reentry Flows (LDRD Final Report)

High-enthalpy hypersonic flight represents an application space of significant concern within the current national-security landscape. The hypersonic environment is characterized by high-speed compressible fluid mechanics and complex reacting flow physics, which may present both thermal and chemical nonequilibrium effects. We report on the results of a three-year LDRD effort, funded by the Engineering Sciences Research Foundation (ESRF) investment area, which has been focused on the development and deployment of new high-speed thermochemical diagnostics capabilities for measurements in the high-enthalpy hypersonic environment posed by Sandia's free-piston shock tunnel. The project has additionally sponsored model development efforts, which have added thermal nonequilibrium modeling capabilities to Sandia codes for subsequent design of many of our shock-tunnel experiments. We have cultivated high-speed, chemically specific, laser-diagnostic approaches that are uniquely co-located with Sandia's high-enthalpy hypersonic test facilities. These tools include picosecond and nanosecond coherent anti-Stokes Raman scattering at 100-kHz rates for time-resolved thermometry, including thermal nonequilibrium conditions, and 100-kHz planar laser-induced fluorescence of nitric oxide for chemically specific imaging and velocimetry. Key results from this LDRD project have been documented in a number of journal submissions and conference proceedings, which are cited here. The body of this report is, therefore, concise and summarizes the key results of the project. The reader is directed toward these reference materials and appendices for more detailed discussions of the project results and findings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

How Snow Aggregate Ellipsoid Shape and Orientation Variability Affects Fall Speed and Self-Aggregation Rates

Snow aggregate shapes and orientations have long been known to exhibit substantial variability. Despite this observed variability, most weather and climate prediction models use fixed power-law functions that deterministically map particle size to mass and fall speed. As such, integrated quantities like precipitation and self-aggregation rates currently ignore nonlinear effects resulting from variation in shape and orientation for aggregates of the same size. This study therefore develops an analytic framework that couples an empirically based bivariate distribution of ellipsoid shapes to classical hydrodynamic theory so as to capture an appropriate dispersion of masses, projected areas, and fall speeds for an assumed size distribution. For a fixed aggregate size, shape variations produce approximately ±0.13 m s -1 standard deviation of fall speed which increases the mass flux fall speed dispersion by more than 100% over traditional microphysics models. This increased fall speed dispersion results predominantly from shape-induced mass dispersion whereas orientation and drag dispersion play a lesser role. Shape variations can increase mass- and reflectivity-weighted fall speeds by up to 60% of traditional models whereas self-aggregation rates can increase by a factor of 100 for very small slope parameters. This implies that aggregate shape variations effectively forestall the theorized onset of fall speed distribution narrowing and subsequent quenching of the aggregation process. As a result, it is likely that secondary ice formation is necessary to prevent an ever decreasing slope parameter. The mathematical theory presented in this study is used to develop simple correction factors for snow forecast and climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

A new approach to high-speed flow measurements using constant voltage anemometry

The paper addresses the basic features of conventional instrumentation, such as the constant temperature (CTA) and the constant current (CCA) anemometers, their limitations, and describes a totally new approach to high-speed dynamic measurements using a constant voltage anemometer (CVA). The paper describes the design features of a newly developed CVA and compares preliminary results obtained with CVA and conventional anemometry in low- and high-speed flows.

Mangalam, S. M.↗

NASA NTRS2016

Development of an Interval Management Algorithm Using Ground Speed Feedback for Delayed Traffic

One of the goals of NextGen is to enable frequent use of Optimized Profile Descents (OPD) for aircraft, even during periods of peak traffic demand. NASA is currently testing three new technologies that enable air traffic controllers to use speed adjustments to space aircraft during arrival and approach operations. This will allow an aircraft to remain close to their OPD. During the integration of these technologies, it was discovered that, due to a lack of accurate trajectory information for the leading aircraft, Interval Management aircraft were exhibiting poor behavior. NASA's Interval Management algorithm was modified to address the impact of inaccurate trajectory information and a series of studies were performed to assess the impact of this modification. These studies show that the modification provided some improvement when the Interval Management system lacked accurate trajectory information for the leading aircraft.

Barmore, Bryan E.↗

NASA NTRS1981

Coronal streamers in the solar wind at 1 AU

Virtually all solar wind observing groups have reported substantial variations in the solar wind helium-hydrogen abundance ratio (A(He)). A study of Los Alamos Imp solar wind data has revealed an association between low A(He) and high proton density that occurs at low flow speeds and that is correlated with polarity reversals of the interplanetary magnetic field. The current investigation has the objective to present further examples of the low A(He), high proton density, low speed, magnetic field polarity association, and to document the common occurrence of multiple events lasting approximately 3-7 days. The results are presented of attempts to relate these events directly to maps or isophotes of solar coronal brightness at 1.5 solar radii. The results of the investigation suggest that a substantial fraction of the low-speed solar wind originates in coronal streamers, particularly near solar minimum.

Gosling, J. T.↗

NASA NTRS1995

Comparison of tropical pacific temperature and current simulations with two vertical mixing schemes embedded in an ocean general circulation model and reference to observations

The Pacanowski-Philander (PP) and Mellor-Yamada (MY) parameterization models of vertical mixing by turbulent processes were embedded in the Geophysical Fluid Dynamics Laboratory high-resolution ocean general circulation model of the tropical Pacific Ocean. All other facets of the numerical simulations were the same. Simulations were made for the 1987-1988 period. At the equator the MY simulation produced near-surface temperatures more uniform with depth, a deeper thermocline, a deeper core speed of the Equatorial Undercurrent, and a South Equatorial Current with greater vertical thickness compared with that computed with the PP method. Along 140 deg W, between 5 deg N and 10 deg N, both simulations were the same. Moored buoy current and temperature observations had been recorded by the Pacific Marine Environmental Laboratory at three sites (165 deg E, 140 deg W, 110 deg W) along the equator and at three sites (5 deg N, 7 deg N, 9 deg N) along 140 deg W. Simulated temperatures were lower than those observed in the near-surface layer and higher than those observed in the thermocline. Temperature simulations were in better agreement with observations compared to current simulations. At the equator, PP current and temperature simulations were more representative of the observations than MY simulations.

Halpern, David↗

DOE OSTI2022

Electric Drive Technologies Research: Bottom-Up Soft Magnetic Composites (FY2022 Annual Progress Report)

In order to meet 2025 goals for enhanced peak power (100 kW), specific power (50 kW/L), and reduced cost (3.3 $\$$/kW) in a motor that can operate at ≥ 20,000 rpm, improved soft magnetic materials must be developed. Better performing soft magnetic materials will also enable rare earth free electric motors. In fact, replacement of permanent magnets with soft magnetic materials was highlighted in the Electrical and Electronics Technical Team (EETT) Roadmap as a R&D pathway for meeting 2025 targets. Eddy current losses in conventional soft magnetic materials, such as silicon steel, begin to significantly impact motor efficiency as rotational speed increases. Soft magnetic composites (SMCs), which combine magnetic particles with an insulating matrix to boost electrical resistivity (ρ) and decrease eddy current losses, even at higher operating frequencies (or rotational speeds), are an attractive solution. Today, SMCs are being fabricated with values of ρ ranging between 10 -3 to 10 -1 μohm∙m, which is significantly higher than 3% silicon steel (~0.05 μohm∙m). The isotropic nature of SMCs is ideally suited for motors with 3D flux paths, such as axial flux motors. Additionally, the manufacturing cost of SMCs is low and they are highly amenable to advanced manufacturing and net-shaping into complex geometries, which further reduces manufacturing costs. There is still significant room for advancement in SMCs, and therefore additional improvements in electrical machine performance. For example, despite the inclusion of a non-magnetic insulating material, the electrical resistivities of SMCs are still far below that of soft ferrites (10 – 10 8 μohm∙m).

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS2003

Brayton Power Conversion Unit Tested: Provides a Path to Future High-Power Electric Propulsion Missions

Closed-Brayton-cycle conversion technology has been identified as an excellent candidate for nuclear electric propulsion (NEP) power conversion systems. Advantages include high efficiency, long life, and high power density for power levels from about 10 kWe to 1 MWe, and beyond. An additional benefit for Brayton is the potential for the alternator to deliver very high voltage as required by the electric thrusters, minimizing the mass and power losses associated with the power management and distribution (PMAD). To accelerate Brayton technology development for NEP, the NASA Glenn Research Center is developing a low-power NEP power systems testbed that utilizes an existing 2- kWe Brayton power conversion unit (PCU) from previous solar dynamic technology efforts. The PCU includes a turboalternator, a recuperator, and a gas cooler connected by gas ducts. The rotating assembly is supported by gas foil bearings and consists of a turbine, a compressor, a thrust rotor, and an alternator on a single shaft. The alternator produces alternating-current power that is rectified to 120-V direct-current power by the PMAD unit. The NEP power systems testbed will be utilized to conduct future investigations of operational control methods, high-voltage PMAD, electric thruster interactions, and advanced heat rejection techniques. The PCU was tested in Glenn s Vacuum Facility 6. The Brayton PCU was modified from its original solar dynamic configuration by the removal of the heat receiver and retrofitting of the electrical resistance gas heater to simulate the thermal input of a steady-state nuclear source. Then, the Brayton PCU was installed in the 3-m test port of Vacuum Facility 6, as shown. A series of tests were performed between June and August of 2002 that resulted in a total PCU operational time of about 24 hr. An initial test sequence on June 17 determined that the reconfigured unit was fully operational. Ensuing tests provided the operational data needed to characterize PCU performance over its full operating range. The primary test variables used in operating the Brayton PCU were heater input power and rotor speed. Testing demonstrated a maximum steady-state alternating-current power output of 1835 W at a gas heater power of 9000 W and a rotor speed of 52000 rpm. The corresponding measured turbine inlet gas temperature was 1076 K, and the compressor inlet gas temperature was 282 K. When insulation losses from the gas heater were neglected, the Brayton cycle efficiency for the maximum power point was calculated to be 24 percent. The net direct-current power output was 1750 W, indicating a PMAD efficiency of about 95 percent.

Mason, Lee S.↗

NASA NTRS2000

Experiments on the Richtmyer-Meshkov Instability of Incompressible Fluids

Richtmyer-Meshkov (R-M) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and possibly become turbulent given the proper initial conditions. R-M instability is similar to the Rayleigh-Taylor (R-T) instability, which is generated when the two fluids undergo a constant acceleration. R-M instability is a fundamental fluid instability that is important to fields ranging from astrophysics to high-speed combustion. For example, R-M instability is currently the limiting factor in achieving a net positive yield with inertial confinement fusion. The experiments described here utilize a novel technique that circumvents many of the experimental difficulties previously limiting the study of the R-M instability. A Plexiglas tank contains two unequal density liquids and is gently oscillated horizontally to produce a controlled initial fluid interface shape. The tank is mounted to a sled on a high speed, low friction linear rail system, constraining the main motion to the vertical direction. The sled is released from an initial height and falls vertically until it bounces off of a movable spring, imparting an impulsive acceleration in the upward direction. As the sled travels up and down the rails, the spring retracts out of the way, allowing the instability to evolve in free-fall until impacting a shock absorber at the end of the rails. The impulsive acceleration provided to the system is measured by a piezoelectric accelerometer mounted on the tank, and a capacitive accelerometer measures the low-level drag of the bearings. Planar Laser-Induced Fluorescence is used for flow visualization, which uses an Argon ion laser to illuminate the flow and a CCD camera, mounted to the sled, to capture images of the interface. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. The amplitude of the disturbance during the experiment is measured and compared to theory. The results show good agreement (within 10%) with linear stability theory up to nondimensional amplitude ka = 0.7 (wavenumber x amplitude). These results hold true for an initial ka (before acceleration) of -0.7 less than ka less than -0.06, while the linear theory was developed for absolute value of ka much less than 1. In addition, a third order weakly nonlinear perturbation theory is shown to be accurate for amplitudes as large as ka = 1.3, even though the interface becomes double-valued at ka = 1.1. As time progresses, the vorticity on the interface concentrates, and the interface spirals around the alternating sign vortex centers to form a mushroom pattern. At higher Reynolds Number (based on circulation), an instability of the vortex cores has been observed. While time limitations of the apparatus prevent determination of a critical Reynolds Number, the lowest Reynolds Number this vortex instability has been observed at is 5000.

Jacobs, J.↗

NASA NTRS2008

Simulation of the Impact of New Aircraft and Satellite-Based Ocean Surface Wind Measurements on H*Wind Analyses

Accurate observations of surface ocean vector winds (OVW) with high spatial and temporal resolution are required for understanding and predicting tropical cyclones. As NASA's QuikSCAT and Navy's WindSat operate beyond their design life, many members of the weather and climate science communities recognize the importance of developing new observational technologies and strategies to meet the essential need for OVW information to improve hurricane intensity and location forecasts. The Hurricane Imaging Radiometer (HIRAD) is an innovative technology development which offers new and unique remotely sensed satellite observations of both extreme oceanic wind events and strong precipitation. It is based on the airborne Stepped Frequency Microwave Radiometer (SFMR), which is the only proven remote sensing technique for observing tropical cyclone (TC) ocean surface wind speeds and rain rates. The proposed HIRAD instrument advances beyond the current nadir viewing SFMR to an equivalent wide-swath SFMR imager using passive microwave synthetic thinned aperture radiometer (STAR) technology. This sensor will operate over 4-7 GHz (C-band frequencies) where the required TC remote sensing physics has been validated by both SFMR and WindSat radiometers. The instrument is described in more detail in a paper by Jones et al. presented to the Tropical Meteorology Special Symposium at this AMS Annual Meeting. Simulated HIRAD passes through a simulation of hurricane Frances are being developed to demonstrate HIRAD estimation of surface wind speed over a wide swath in the presence of heavy rain. These are currently being used in "quick" OSSEs (Observing System Simulation Experiments) with H'Wind analyses as the discriminating tool. The H'Wind analysis, a product of the Hurricane Research Division of NOAA's Atlantic , Oceanographic and Meteorological Laboratory, brings together wind measurements from a variety of observation platforms into an objective analysis of the distribution of wind speeds in a tropical cyclone. This product is designed to improve understanding of the extent and strength of the wind field, and to improve the assessment of hurricane intensity. See http://www.aoml.noaa._ov/hrd/data sub/wind.html. Observations have been simulated from both aircraft altitudes and space. The simulated flight patterns for the aircraft platform cases have been designed to duplicate the timing and flight patterns used in routine NOAA and USAF hurricane surveillance flights, and the spaceborne case simulates a TRMM orbit and altitude.

Miller, TImothy L.↗