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A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3

An improved model of Earth's gravitational field, Goddard Earth Model T-3 (GEM-T3), has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM-T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM-T3 uses altimeter data from GEOS 3 (1975-1976), Seasat (1978) and Geosat (1986-1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long-wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes Tracking Network (TRANET) Doppler, optical, and satellite-to-satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM-T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65 deg N and 60 deg S latitudes in GEM-T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long-wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM-T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM-T3.

Lerch, F. J.↗

Quantifying Interannual Variability of the UTLS Ozone Using Assimilation of Satellite Data

An accurate representation of spatial and temporal variability of the Upper Troposphere Lower Stratosphere (UTLS) ozone is essential for understanding both the tropospheric ozone budget and ozone s contribution to radiative forcing. The complex, dynamically driven structure of trace gas fields in the UTLS presents a challenge to data-based and modelling studies. Small features are not fully resolved in data from limb-sounding instruments such as the Microwave Limb Sounder on EOS-Aura (the EOS-MLS), but are captured in assimilation of those data as vertical structure is added from the assimilated meteorology. This will be demonstrated using a multi-year assimilation of EOS-MLS observations in the Goddard Earth Observing System, Version 5 (GEOS-5) data assimilation system. The results demonstrate the realism of the seasonal and year to year variability of laminar structures in the mid-latitudinal ozone field between years 2005-2007, for which independent validation data are available from the HIRDLS instrument. The analysis is done in the context of the underlying large scale dynamics. The lifetimes of most research instruments are too short for them to be used throughout the duration of long-term (at least 3 decades) reanalyses. For example, the EOS-MLS instrument has operated since mid-2004 until present. By contrast, Solar Backscatter Ultra Violet (SBUV) measurements provide continuous data since late 1978, but their vertical resolution is insufficient to represent the profile shape in the UTLS. Assimilation of these SBUV/2 observations in the GEOS-5 data assimilation system has hitherto not captured a realistic ozone structure in the UTLS, even though transport studies using GEOS-5 wind fields do show such structures. We show that careful construction of the background error covariance structure in GEOS-5 can lead to more realistic UTLS ozone fields when assimilating SBUV/2 observations. The reasoning behind this will be discussed, emphasizing the need to retain the sharp gradient of ozone concentrations across the tropopause. We analyze the UTLS ozone distributions in multi-year SBUV/2 assimilation experiments, comparing the results against the independent HIRDLSdataset and, for a longer period, with the MLS assimilation and discuss the consequences for tropospheric ozone and radiative forcing.

Wargan, K.↗

On-Orbit Multi-Field Wavefront Control with a Kalman Filter

A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system alignment when WFC alone cannot effectively align the system.

Lou, John↗

Validation and Error Characterization for the Global Precipitation Measurement

The Global Precipitation Measurement (GPM) is an international effort to increase scientific knowledge on the global water cycle with specific goals of improving the understanding and the predictions of climate, weather, and hydrology. These goals will be achieved through several satellites specifically dedicated to GPM along with the integration of numerous meteorological satellite data streams from international and domestic partners. The GPM effort is led by the National Aeronautics and Space Administration (NASA) of the United States and the National Space Development Agency (NASDA) of Japan. In addition to the spaceborne assets, international and domestic partners will provide ground-based resources for validating the satellite observations and retrievals. This paper describes the validation effort of Global Precipitation Measurement to provide quantitative estimates on the errors of the GPM satellite retrievals. The GPM validation approach will build upon the research experience of the Tropical Rainfall Measuring Mission (TRMM) retrieval comparisons and its validation program. The GPM ground validation program will employ instrumentation, physical infrastructure, and research capabilities at Supersites located in important meteorological regimes of the globe. NASA will provide two Supersites, one in a tropical oceanic and the other in a mid-latitude continental regime. GPM international partners will provide Supersites for other important regimes. Those objectives or regimes not addressed by Supersites will be covered through focused field experiments. This paper describes the specific errors that GPM ground validation will address, quantify, and relate to the GPM satellite physical retrievals. GPM will attempt to identify the source of errors within retrievals including those of instrument calibration, retrieval physical assumptions, and algorithm applicability. With the identification of error sources, improvements will be made to the respective calibration, assumption, or algorithm. The instrumentation and techniques of the Supersites will be discussed. The GPM core satellite, with its dual-frequency radar and conically scanning radiometer, will provide insight into precipitation drop-size distributions and potentially increased measurement capabilities of light rain and snowfall. The ground validation program will include instrumentation and techniques commensurate with these new measurement capabilities.

Bidwell, Steven W.↗

Sonic Boom Pressure Signature Uncertainty Calculation and Propagation to Ground Noise

The objective of this study was to outline an approach for the quantification of uncertainty in sonic boom measurements and to investigate the effect of various near-field uncertainty representation approaches on ground noise predictions. These approaches included a symmetric versus asymmetric uncertainty band representation and a dispersion technique based on a partial sum Fourier series that allows for the inclusion of random error sources in the uncertainty. The near-field uncertainty was propagated to the ground level, along with additional uncertainty in the propagation modeling. Estimates of perceived loudness were obtained for the various types of uncertainty representation in the near-field. Analyses were performed on three configurations of interest to the sonic boom community: the SEEB-ALR, the 69o DeltaWing, and the LM 1021-01. Results showed that representation of the near-field uncertainty plays a key role in ground noise predictions. Using a Fourier series based dispersion approach can double the amount of uncertainty in the ground noise compared to a pure bias representation. Compared to previous computational fluid dynamics results, uncertainty in ground noise predictions were greater when considering the near-field experimental uncertainty.

West, Thomas K., IV↗

Atmospheric response to variations in sea surface temperature

An extended range prediction experiment was performed with the GISS atmospheric model on a global data to test the sensitivity of the model to sea surface temperature (SST) variation over a two-week forecast period. The use of an initial observed SST field in place of the climatological monthly mean sea temperatures for surface flux calculations in the model was found to have a significant effect on the predicted precipitation over the ocean, with enhanced convection computed over areas where moderately large warm SST anomalies are found. However, there was no detectable positive effect of the SST anomaly field on forecast quality. The influence of the SST anomalies on the daily predicted fields of pressure and geopotential is relatively insignificant up to about one week compared with the growth of prediction error, and is no greater over a two-week period than that resulting from random errors in the initial meteorological state. The 14-day average fields of sea level pressure and 500-mb height predicted by the model, appear to be similarly insensitive to anomalies of sea surface temperature.

Spar, J.↗

Model studies of the beam-filling error for rain-rate retrieval with microwave radiometers

Low-frequency (less than 20 GHz) single-channel microwave retrievals of rain rate encounter the problem of beam-filling error. This error stems from the fact that the relationship between microwave brightness temperature and rain rate is nonlinear, coupled with the fact that the field of view is large or comparable to important scales of variability of the rain field. This means that one may not simply insert the area average of the brightness temperature into the formula for rain rate without incurring both bias and random error. The statistical heterogeneity of the rain-rate field in the footprint of the instrument is key to determining the nature of these errors. This paper makes use of a series of random rain-rate fields to study the size of the bias and random error associated with beam filling. A number of examples are analyzed in detail: the binomially distributed field, the gamma, the Gaussian, the mixed gamma, the lognormal, and the mixed lognormal ('mixed' here means there is a finite probability of no rain rate at a point of space-time). Of particular interest are the applicability of a simple error formula due to Chiu and collaborators and a formula that might hold in the large field of view limit. It is found that the simple formula holds for Gaussian rain-rate fields but begins to fail for highly skewed fields such as the mixed lognormal. While not conclusively demonstrated here, it is suggested that the notionof climatologically adjusting the retrievals to remove the beam-filling bias is a reasonable proposition.

Ha, Eunho↗

Application of 3-signal coherence to core noise transmission

A method for determining transfer functions across turbofan engine components and from the engine to the far-field is developed. The method is based on the three-signal coherence technique used previously to obtain far-field core noise levels. This method eliminates the bias error in transfer function measurements due to contamination of measured pressures by nonpropagating pressure fluctuations. Measured transfer functions from the engine to the far-field, across the tailpipe, and across the turbine are presented for three turbofan engines.

Krejsa, E. A.↗

Application of 3-signal coherence to core noise transmission

A method for determining transfer functions across turbofan engine components and from the engine to the far-field is developed. The method is based on the 3-signal coherence technique used previously to obtain far-field core noise levels. This method eliminates the bias error in transfer function measurements due to contamination of measured pressures by nonpropagating pressure fluctuations. Measured transfer functions from the engine to the far-field, across the tailpipe, and across the turbine are presented for three turbofan engines.

Krejsa, E. A.↗

Development of a Shuttle Infrared Telescope Facility /SIRTF/ fine guidance sensor

Fine guidance technology development for the Shuttle Infrared Telescope Facility (SIRTF) centers upon the use of a single multiple-star-tracking sensor to provide the position information necessary to produce three-axis attitude control signals for precision payload pointing. The effort described in this paper is concerned with the development of a fine guidance sensor that employs a high-density charge-coupled imaging device for producing position information signals by using star fields. Multiple star position information produces three-axis position error signals that are used to update inertial reference gyros. The sensor employs advanced position interpolation algorithms to enhance field-of-view resolution and to correct for optical aberrations inherent in spatially chopped star images resulting from the telescope's movable secondary mirror. Operation of the sensor is under the control of a high-performance microcomputer that provides both autonomy and flexibility in a guidance application.

Salomon, P. M.↗

Performance of a 2-micrometer coherent Doppler lidar for wind measurements

Measurements of boundary layer winds are presented using a 2-micrometer coherent Doppler lidar and the optimal performance of the maximum likelihood estimator. The systematic error for single-shot estimates was estimated as 3.6 cm/s using measurements from a stationary hard target. The estimation error for measurements of the radial component of the wind field was determined, as well as the fraction of the estimates that are randomly distributed over the velocity search space, when the signal power is low and speckle fading is important. The results from actual data are compared with the results from ideal simulations. The first direct estimation of the spatial structure function of the radial wind field and of the energy dissipation rate is presented for both horizontal and vertical directions of propagation. The rms estimation error of the velocity estimates is found to be within 30% of ideal performance based on simulation.

Frehlich, Rod↗

EOS radiometer concepts for soil moisture remote sensing

Preliminary work with aperture synthesis concepts for EOS is reported. The effects of nonvanishing bandwidths on image reconstruction in aperture synthesis system was studied. It is found that nonvanishing bandwidths introduce errors in off-axis pixels when naive Fourier processing is used. The net effect is for bandwidth to limit sensor field-of-view. To quantify this effect a computer program was written which is documented. Example runs are included which illustrate the resultant radiometric errors and effective fields-of-view for a plausible simple sensor.

Carr, J.↗

Error analyses for a gravity gradiometer mission

This paper addresses the usefulness of an orbiting gravity gradiometer as a sensor for mapping the fine structure of the earth gravity field. The exact knowledge of this field is essential for studies of the solid earth and the dynamics of the oceans. Although the earth gravity tensor, measured by a gradiometer assembly, has nine components, only five components are independent. This latter fact is as a consequence of the symmetry and conservative nature of the earth's gravity field. The most dominant component is the radial one. The error analyses considered here are therefore based only upon a single axis gradiometer sensing this radial component. The expected global gravity and geoid errors for a 50 x 50-km (1/2 x 1/2 deg) area utilizing a spaceborne gradiometer with a precision of 0.001 EU in a 160-km circular polar orbit are about 3 mGAL and 5 cm, respectively.

Kahn, W. D.↗

Sun compass error model

An error model is described for the Apollo 15 sun compass, a contingency navigational device. Field test data are presented along with significant results of the test. The errors reported include a random error resulting from tilt in leveling the sun compass, a random error because of observer sighting inaccuracies, a bias error because of mean tilt in compass leveling, a bias error in the sun compass itself, and a bias error because the device is leveled to the local terrain slope.

Blucker, T. J.↗

Simulated measurement of power flow in structures near to simple sources and simple boundaries

Advances in electronics technology along with the advent of low cost multichannel Fast Fourier analyzers have made it practical to use higher order central difference formulas to measure power flow in 1- and 2-D structures. The method discussed uses five point differencing for the spatial derivatives in 1-D and a thirteen point difference pattern for the spatial derivatives in 2-D plates and shells. It is assumed that the measuring transducers are accelerometers. An analytical study of the higher order differencing method and the conventional two accelerometer method was performed as a preliminary to the application of these methods to actual aircraft structures. Some classical problems were analyzed in order to simulate and compare the performance of the two methods under near field measurement conditions. These near field conditions include examples of power flows near simple sources and simple boundaries. The estimates produced by the two methods were compared to the exact solution in each example. Presented are the theory and selected results of the study, which indicate that the bias errors of the two accelerometer method under near field measurement conditions may be much larger than previous studies have suggested.

Mcgary, Michael C.↗

A comparison of vertical velocity in cirrus obtained from aircraft and lidar divergence measurements during FIRE

Techniques are presented to obtain vertical velocity in cirrus clouds from in situ aircraft lateral wind measurements and from ground-based remote Doppler lidar measurements. The approach used is to calculate w from the integral of the divergence of the horizontal velocity around a closed path. Divergence measurements from both aircraft and Doppler lidar are discussed. The principal errors in the calculation of w from aircraft lateral wind measurements are bias in the lateral wind, ground speed errors, and error due to vertical shear of the horizontal wind. For Doppler lidar measurements the principal errors are in the estimate of mean terminal velocity and the zeroth order coefficients of the Fourier series that is fitted to the data. The technique is applied to a cirrus cloud investigated during the FIRE (First International Satellite Cloud Climatology Regional Experiment) Cirrus Intensive Field Observation Program. The results indicate that the error in w is about + or - 14 cm/s from the aircraft technique; this can be reduced to about + or - 2 to 3 cm/s with technical improvements in both ground speed and lateral velocity measurements. The error in w from Doppler lidar measurements, which is about + or - 8 cm/s, can be reduced to about + or - 5 cm/s by improvements in the Doppler velocity measurements with technology that is currently available.

Gultepe, Ismail↗

Physical Simulation of Rocket Exhaust Aerodynamics Using Heated Ethane: Conceptual Foundations

Heated ethane (C2H6) has been proposed as an alternative to inert gases for use as a motive fluid in the experimental simulation of rocket exhaust plumes. By adjusting stagnation temperature, the isentropic exponent of ethane can be tuned to approximate those produced by common rocket propellants including hydrogen, hypergols, alcohols, and hydrocarbons. As a result, ethane can be made to follow a nozzle expansion process which is nearly identical to realistic rocket engine flow fields. Additionally, its high auto-ignition temperature and resistance to condensation enable the testing of expansion ratios much larger than conventional inertgas testing. NASA SSC has performed quasi-one-dimensional analyses using the Chemical Equilibrium with Applications (CEA) code as a preliminary means to compare flow fields produced by non-reacting ethane to those of reacting combustion products. A LO2/LH2 rocket engine operating at a chamber pressure of 5.0 MPa and a mixture ratio of 6.1 was used as an example case to demonstrate ethane’s efficacy as a simulant. Errors for key similarity parameters were compared to legacy cold-flow test methods. Additional errors induced by machining tolerances and chemical impurities were also examined. Results suggest that at a 3% geometric scale and ~500 K ethane stagnation temperature, an error of less than 2.5% throughout the flow field is realistically achievable along the dimensions of Mach number, Reynolds number, pressure ratio, and isentropic exponent. The development of an experimental test bed for validation of this configuration is currently underway.

Jones, Daniel R.↗