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NASA NTRS1977

Quantitative analysis of aircraft multispectral-scanner data and mapping of water-quality parameters in the James River in Virginia

Statistical analysis techniques were applied to develop quantitative relationships between in situ river measurements and the remotely sensed data that were obtained over the James River in Virginia on 28 May 1974. The remotely sensed data were collected with a multispectral scanner and with photographs taken from an aircraft platform. Concentration differences among water quality parameters such as suspended sediment, chlorophyll a, and nutrients indicated significant spectral variations. Calibrated equations from the multiple regression analysis were used to develop maps that indicated the quantitative distributions of water quality parameters and the dispersion characteristics of a pollutant plume entering the turbid river system. Results from further analyses that use only three preselected multispectral scanner bands of data indicated that regression coefficients and standard errors of estimate were not appreciably degraded compared with results from the 10-band analysis.

Johnson, R. W.↗
NASA NTRS1979

Application of non-attenuating frequency radars for prediction of rain attenuation and space diversity performance

In order to establish transmitter power and receiver sensitivity levels at frequencies above 10 GHz, the designers of earth-satellite telecommunication systems are interested in cumulative rain fade statistics at variable path orientations, elevation angles, climatological regions, and frequencies. They are also interested in establishing optimum space diversity performance parameters. In this work are examined the many elements involved in the employment of single non-attenuating frequency radars for arriving at the desired information. The elements examined include radar techniques and requirements, phenomenological assumptions, path attenation formulations and procedures, as well as error budgeting and calibration analysis. Included are the pertinent results of previous investigators who have used radar for rain attenuation modeling. Suggestions are made for improving present methods.

Goldhirsh, J.↗
NASA NTRS1993

AVHRR Surface Temperature and Narrow-Band Albedo Comparison with Ground Measurements for the Greenland Ice Sheet

An ice-surface temperature retrieval algorithm for the Greenland ice sheet was developed using NOAA 11 thermal radiances from channels 4 and 5. Temperature, pressure and humidity profiles, cloud observations and skin temperatures from the Swiss Federal Institute of Technology (ETH) camp, located at the equilibrium line altitude at 49 deg17 min W, 69 deg 34 min N, were used in the LOWTRAN 7 model. Through a statistical analysis of daily clear sky profiles, the coefficients that correct for the atmospheric effects were determined for the ETH-Camp field season (May to August). Surface temperatures retrieved by this method were then compared against the in situ observations with a maximum difference of 0.6 K. The NOAA 11 narrow-band planetary albedo values for channels 1 and 2 were calculated using pre-launch calibration coefficients. Scattering and absorption by the atmosphere were modelled with LOWTRAN 7. Then, narrow-band albedo values for the AVHRR visible and near infrared channels were compared with in situ high resolution spectral reflectance measurements. In the visible band (580-680 nm), AVHRR-derived narrow-band albedo and the in situ measurements corrected with radiative transfer model LOWTRAN 7 showed a difference of less than 2%. For the near infrared channel (725-1100 nm) the difference between the measured and modelled narrow-band albedo was 14%. These discrepancies could be either the result of inaccurate aerosol scattering modelling (lack of the in situ observation), or the result of sensor drift due to degradation.

Haefliger, M.↗
NASA NTRS2017

Classifying Multi-Model Wheat Yield Impact Response Surfaces Showing Sensitivity to Temperature and Precipitation Change

Crop growth simulation models can differ greatly in their treatment of key processes and hence in their response to environmental conditions. Here, we used an ensemble of 26 process-based wheat models applied at sites across a European transect to compare their sensitivity to changes in temperature (minus 2 to plus 9 degrees Centigrade) and precipitation (minus 50 to plus 50 percent). Model results were analysed by plotting them as impact response surfaces (IRSs), classifying the IRS patterns of individual model simulations, describing these classes and analysing factors that may explain the major differences in model responses. The model ensemble was used to simulate yields of winter and spring wheat at four sites in Finland, Germany and Spain. Results were plotted as IRSs that show changes in yields relative to the baseline with respect to temperature and precipitation. IRSs of 30-year means and selected extreme years were classified using two approaches describing their pattern. The expert diagnostic approach (EDA) combines two aspects of IRS patterns: location of the maximum yield (nine classes) and strength of the yield response with respect to climate (four classes), resulting in a total of 36 combined classes defined using criteria pre-specified by experts. The statistical diagnostic approach (SDA) groups IRSs by comparing their pattern and magnitude, without attempting to interpret these features. It applies a hierarchical clustering method, grouping response patterns using a distance metric that combines the spatial correlation and Euclidian distance between IRS pairs. The two approaches were used to investigate whether different patterns of yield response could be related to different properties of the crop models, specifically their genealogy, calibration and process description. Although no single model property across a large model ensemble was found to explain the integrated yield response to temperature and precipitation perturbations, the application of the EDA and SDA approaches revealed their capability to distinguish: (i) stronger yield responses to precipitation for winter wheat than spring wheat; (ii) differing strengths of response to climate changes for years with anomalous weather conditions compared to period-average conditions; (iii) the influence of site conditions on yield patterns; (iv) similarities in IRS patterns among models with related genealogy; (v) similarities in IRS patterns for models with simpler process descriptions of root growth and water uptake compared to those with more complex descriptions; and (vi) a closer correspondence of IRS patterns in models using partitioning schemes to represent yield formation than in those using a harvest index. Such results can inform future crop modelling studies that seek to exploit the diversity of multi-model ensembles, by distinguishing ensemble members that span a wide range of responses as well as those that display implausible behaviour or strong mutual similarities.

Classification; Climate change; Crop model; Ensemb↗
NASA NTRS1995

Calibration of the NOAA 11 solar backscatter ultraviolet (SBUV/2) ozone data set from 1989 to 1993 using in-flight calibration data and SSBUV

Total ozone and ozone profiles are currently being measured by solar backscatter ultraviolet (SBUV/2) instruments onboard NOAA polar orbiting spacecraft using the backscattered ultraviolet technique. The NOAA 11 SBUV/2 operational data set, reprocessed from January 1989 to May 1993 (version 6), includes an updated algorithm and revised prelaunch and postlaunch calibrations of the geometrical albedo observations used to derive ozone values. The postlaunch calibration revisions remove time dependent errors in the ozone amounts due to instrument drift, while the revised prelaunch calibration corrects the absolute value of retrieved ozone. The prelaunch corrections are a result of calibration checks from in-orbit comparisons of ultraviolet geometric albedos measured by shuttle SBUV (SSBUV) and the NOAA 11 SBUV/2. Geometric albedo comparison data are further corrected using a radiative transfer code to account for the small difference in observing conditions between the two spacecraft. The postlaunch corrections rely on in-flight calibration and solar irradiance data to account for time dependent changes in instrument gain, thermal response, and instrument diffuser degradation over time. Comparison of data from three SSBUV flights, which occurred about one year apart, with concurrent SBUV/2 data provided an independent check of the time dependent change derived from the in-flight calibration data. Time independent corrections result in an increase of about 1% for total ozone, 5% for ozone at 1 mbar, and near 0% at 15 mbar. The time dependent corrections amount to an increase of 2% for total ozone, 10% for ozone near 1 mbar, and 3% at 15 mbar at the end of the current record in May 1993. Recent laboratory studies indicate that the absolute radiance calibrations may still be in error by a few percent which results in ozone profile values that are too low. The SBUV/2 total and ozone profile data are compared to the Nimbus SBUV data during the period when the data overlapped. Total ozone values agree to about 1%, while ozone profile differences range from -4% to +6%, depending on latitude and altitude, relative to SBUV. These differences are not statistically significant given the uncertainties of the two data sets.

Hilsenrath, E.↗
NASA NTRS1994

The optical and near-infrared colors of galaxies, 1: The photometric data

We present optical and near-infrared photometry and spectroscopic redshifts of a well defined sample of 171 field galaxies selected from three high galactic latitude fields. This data set forms the basis for subsequent studies to characterize the trends, dispersion, and evolution of rest-frame colors and image structure. A subset of 143 galaxies constitutes a magnitude-limited sample to B approx. 19.9-20.75 (depending on field), with a median redshift of 0.14, and a maximum redshift of 0.54. This subset is statistically representative in its sampling of the apparent color distribution of galaxies. Thirty six galaxies were selected to have the reddest red-optical colors in two redshift intervals between 0.2 less than z less than 0.3. Photometric passbands are similar to U, B, V, I, and K, and sample galaxy spectral energy distributions between 0.37 and 2.2 micrometers in the observed frame, or down to 0.26 micrometers in the rest frame for the most distant galaxies. B and K images of the entire sample are assembled to form the first optical and near-infrared atlas of a statistically-representative sample of field galaxies. We discuss techniques for faint field-galaxy photometry, including a working definition of a total magnitude, and a method for matching magnitudes in different passbands and different seeing conditions to ensure reliable, integrated colors. Photographic saturation, which substantially affects the brightest 12% of our sample in the optical bands, is corrected with a model employing measured plate-density distributions for each galaxy, calibrated via similar measurements for stars as a function of known saturation level. Both the relative and absolute calibration of our photometry are demonstrated.

Bershady, Matthew A.↗
NASA NTRS2000

Operational Assimilation of GOES Data into a Mesoscale Model

A technique has been developed for assimilating GOES-derived skin temperature tendencies and insolation into the surface energy budget equation of a mesoscale model so that the simulated rate of temperature change closely agrees with the satellite observations. A critical assumption of the technique is that the availability of moisture (either from the soil or vegetation) is the least known term in the model's surface energy budget. Therefore, the simulated latent heat flux, which is a function of surface moisture availability, is adjusted based upon differences between the modeled and satellite- observed skin temperature tendencies. An advantage of this technique is that satellite temperature tendencies are assimilated in an energetically consistent manner that avoids energy imbalances and surface stability problems that arise from direct assimilation of surface shelter temperatures. The fact that the rate of change of the satellite skin temperature is used rather than the absolute temperature means that sensor calibration is not as critical. The technique has been employed on a semi-operational basis at the Global Hydrology and Climate Center (GHCC) within the Penn State/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Model (MM5) since 1 November 1998. We performed the assimilation on a model grid centered over the Southeastern US. In addition, a control run without assimilation was performed to provide insight into the performance of the assimilation technique. Bulk verification statistics (BIAS and RMSE) of surface air temperature and relative humidity of more than 250 case days has been performed to date. Results show that assimilation of the satellite data results reduces both the bias and RMSE for simulations of surface air temperature and relative humidity. We are working with forecasters at the National Weather Service Forecast Office located in Birmingham, AL to evaluate the impact of the assimilation on precipitation forecasts. In addition, work is currently underway to determine the ability of both the assimilation technique and Early Eta to sense the significant changes that occur in both leaf expansion and soil moisture conditions during the Spring-Summer of 1999. This will be accomplished via examination of the simulated surface energy budgets from both modeling systems.

Lapenta, William↗
NASA NTRS2017

Land Surface Temperature Product Validation Best Practice Protocol Version 1.0 - October, 2017

The Global Climate Observing System (GCOS) has specified the need to systematically generate andvalidate Land Surface Temperature (LST) products. This document provides recommendations on goodpractices for the validation of LST products. Internationally accepted definitions of LST, emissivity andassociated quantities are provided to ensure the compatibility across products and reference data sets. Asurvey of current validation capabilities indicates that progress is being made in terms of up-scaling and insitu measurement methods, but there is insufficient standardization with respect to performing andreporting statistically robust comparisons.Four LST validation approaches are identified: (1) Ground-based validation, which involvescomparisons with LST obtained from ground-based radiance measurements; (2) Scene-based intercomparisonof current satellite LST products with a heritage LST products; (3) Radiance-based validation,which is based on radiative transfer calculations for known atmospheric profiles and land surface emissivity;(4) Time series comparisons, which are particularly useful for detecting problems that can occur during aninstrument's life, e.g. calibration drift or unrealistic outliers due to undetected clouds. Finally, the need foran open access facility for performing LST product validation as well as accessing reference LST datasets isidentified.

best practice↗
NASA NTRS2021

Assessing Sensitivity of MERRA-2 to AMSU-A in the Upper Stratosphere

Microwavetemperaturesounders provide key observationsin data assimilation, both in the 9current and historical global observing systems, as they provide the largest amount of horizontal and vertical temperature information due to their insensitivity to clouds. In the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2),microwave sounder radiances from the Advanced Microwave Sounding Unit-A (AMSU-A)are assimilated beginning with NOAA-15and continuing through the current period. The time series of observation minus background statistics forAMSU-A channels sensitive to upper stratosphere and lower mesosphere show variabilities due to changes in AMSU-A constellation in the early AMSU-A period.Noted discrepancies are seen at the onset and exit of AMSU-A observations on the NOAA-15, NOAA-16, NOAA-17, and NASA EOS Aqua satellites.This effort characterizesthesensitivity, both in terms of the observations and the MERRA-2 analysis. Furthermore, it exploresthe use of reprocessed and inter-calibrated datasets to evaluatewhether these homogenized observations can reduce the disparity due to change in instrumental biases against the model background. The results indicate that the AMSU-A radiances used in MERRA-2 are the fundamental cause of this inter-platform sensitivitywhich can be mitigated by using reprocessed data.The results explore the importance of the reprocessing of the AMSU-A radiances as well as their inter-calibration.

MERRA-2↗
NASA NTRS1973

Engineering studies related to geodetic and oceanographic remote sensing using short pulse techniques

For the Skylab S-193 radar altimeter, data processing flow charts and identification of calibration requirements and problem areas for defined S-193 altimeter experiments are presented. An analysis and simulation of the relationship between one particular S-193 measurement and the parameter of interest for determining the sea surface scattering cross-section are considered. For the GEOS-C radar altimeter, results are presented for system analyses pertaining to signal-to-noise ratio, pulse compression threshold behavior, altimeter measurement variance characteristics, desirability of onboard averaging, tracker bandwidth considerations, and statistical character of the altimeter data in relation to harmonic analysis properties of the geodetic signal.

Miller, L. S.↗
NASA NTRS2023

Fitting Leak Test Report: Ground-Based Cryogenic Leak Test of Fittings for Cryogenic Fluid Management

EXECUTIVE SUMMARY Mechanically connected joints used in cryogenic fluid lines as part of space flight elements need to survive launch vibrations and remain leak-free to minimize the loss of on-board commodity and hazardous gas accumulation. In 2020, a cryogenic test apparatus was developed which can evaluate the leak performance of pressurized threaded fluid fittings. The fittings were mounted in the TVAC and cooled to cryogenic test temperature and pressurized with helium while the leak rate was measured using a calibrated GHe leak detector. The test articles for the initial proof of concept testing were ¼ and 1 inch Swagelok VCR fittings with three different types of seal rings copper, nickel, and Ni. Each fitting configuration (size/seal material) was subjected to two consecutive cryogenic thermal cycles, followed by exposure to a launch vibration profile at ambient temperature, after which two additional TVAC cycle tests were performed. The testing reported here is a continuation of the 2020 tests with a statistically significant large number of samples and test runs. Three Swagelok VCR fitting sizes were tested ¼, ½ and 1 inch, and five (5) samples of each fitting size, each sample was tested with SST and Ni seal rings (Total of 30 unique test articles). Each test article was subjected to four (4) thermal cycles. Half of these cycles were performed before vibration testing and half were performed after vibration testing. The vibration testing was performed to evaluate the ability of the fittings to survive launch-type vibration profiles and remain leak-free. Leak checking of each fitting was completed at temperatures between 20K – 30K. The test procedure in Section 8.0 was designed to facilitate a qualification test program by allowing a higher test throughput rate coupled with repeatable test profiles. Results were very positive and show that out of the 30 samples they all passed with leak rates a factor of 2-3 lower than the established 10-6sccs GHe leak threshold. The result showed the Ni seals had lower leak rate, but the SST was more rugged. There were two deviations where damage to the Ni seal ring during assembly resulted in a leaky fitting, this is discussed in Section 10.7 Test Deviations. These fittings show great promise for space flight use and further testing is recommended to fully qualify the fittings per the ASTM F1387-19 and/or other relevant NASA specifications. The test equipment hardware and software capability developed for this testing is generic and not restricted to VCR fittings. It can be employed to evaluate/qualify the leak performance of other types of fittings and a wide range of other cryogenic fluid components such as valves, gages, connectors, etc.

Cryogenic↗
NASA NTRS2019

Satellite Mapping of PM2.5 Episodes in the Wintertime San Joaquin Valley: A "Static" Model Using Column Water Vapor

The use of satellite Aerosol Optical Thickness (AOT) from imaging spectrometers has been successful in quantifying and mapping high PM2.5 (particulate matter mass <2.5µm diameter) episodes for pollution abatement and health studies. However, some regions have high PM2.5 but poor estimation success. The challenges in using Aerosol Optical Thickness (AOT) from imaging spectrometers to characterize PM2.5 worldwide was especially evident in the wintertime San Joaquin Valley (SJV). The SJV's attendant difficulties of high-albedo surfaces and very shallow, variable vertical mixing also occur in other significantly polluted regions around the world. We report on more accurate PM2.5 maps for the whole-winter period in the SJV, Nov 14, 2012?Dec 11, 2013. Intensive measurements by including NASA aircraft were made for several weeks in that winter, the DISCOVER-AQ California mission.We found success with a relatively simple method based on calibration and checking with surface monitors and a characterization of vertical mixing, and incorporating specific understandings of the region's climatology. We estimate PM2.5 to within ~7µgm?3 RMSE and with R values of ~0.9, based on remotely sensed MAIAC (Multi-Angle Implementation of Atmospheric Correction) observations, and that certain further work will improve that accuracy. Mapping is at 1km resolution. This allows a time sequence of mapped aerosols at 1km for cloud-free days. We describe our technique as a "static estimation". Estimation procedures like this one, not dependent on well-mapped source strengths or on transport error, should help full source-driven simulations by deconstructing processes. They also provide a rapid method to create a long-term climatology.Essential features of the technique are (a) daily calibration of the AOT to PM2.5 using available surface monitors, and (b) characterization of mixed-layer dilution using column water vapor (CWV, otherwise "precipitable water"). We noted that on multi-day timescales both water vapor and particles share near-surface sources and both fall to very low values with altitude; indeed, both are largely removed by precipitation. The existence of layers of H2O or aerosol not within the mixed layer adds complexity, but mixed-effects statistical regression captures essential proportionality of PM2.5 and the ratio variable (AOT/CWV). Accuracy is much higher than previous statistical models, and can be extended to the whole Aqua-satellite data record. The maps and time-series we show suggest a repeated pattern for large valleys like the SJV ? progressive stabilization of the mixing height after frontal passages: PM2.5 is somewhat more determined by day-by-day changes in mixing than it is by the progressive accumulation of pollutants (revealed as increasing AOT).

Chatfield, Robert B.↗
NASA NTRSDate not supplied

NASA’s Orbital Debris Optical Program: ES-MCAT Nearing Full Operational Capability (FOC)

The NASA JAO/ES-MCAT (Eugene Stansbery Meter Class Autonomous Telescope) Facility is nearing Full Operational Capability, or FOC. ES-MCAT is now fully capable of autonomously running all observations, including: (a) monitoring weather and closing when conditions are not safe, as well as halting observations when conditions are not suitable (e.g. too cloudy) for operations, (b) start-up/shut-down nightly tasking, (c) collecting calibration data and survey or TLE-tracked data, and (d) processing all collected data, including on-chip photometry and astrometry calibrations using the GAIA star catalogue. The processed data are then further analyzed at NASA Johnson Space Center to correlate detections with known objects in the Space Surveillance Network (SSN) catalogue. MCAT can collect data of specific objects with known orbits or can search for objects with orbits similar to those of spacecraft or rocket bodies that have recently broken up. However, the primary goal for ES-MCAT is to survey the geosynchronous (GEO) belt to provide a statistical sample of the GEO debris environment for both engineering models for spacecraft designers and long-term environment evolutionary purposes. The approach for sweeping the sky to statistically survey GEO has been investigated and updated from past surveys taken by NASA and will be reported, herein referred to as the Candy Cane method. ES-MCAT’s optical performance and the limiting magnitude for the full optical system will be discussed. An analysis used to determine which filter to use for GEO surveys (SDSS r′) includes combining the reflectivity of the primary and secondary mirrors, transmission of the field corrector and CCD window, and the quantum efficiency of the CCD detector, resulting in throughput of the full optical path. This throughput is then combined with the expected typical transparency of the atmosphere at ES-MCAT’s altitude/location for the Sloan Digital Sky Survey (SDSS) g′r′i′z′ and Johnson/Kron-Cousins BVRI filters to yield expected relative throughput.

S. M. Lederer↗
NASA NTRS1991

Gas and dust production by Comet P/Halley (1910 II)

Selected long-slit spectrograms of Comet P/Halley, photographed during the postperihelion period between April 16 and June 3, 1910 have been quantitatively analyzed for comparison with the 1985/86 apparition. The Fe-V-Na spark spectrum was used to determine characteristic curves for these plates, and flux calibrations based on contemporaneous broad-band photometric measurements were applied. Haser model production rates for C2 and values Afp were computed for each of the nights selected and compared with the photometric observations obtained by Schleicher et al. (1987) during the comparable postperihelion period of the 1985/86 apparition. As found for the 1985/86 apparation, the gas and dust production in 1910 varied in phase, but the rates of production were higher than observed in 1986 by a small but statistically significant amount.

Howell, Ellen S.↗
NASA NTRS1995

The velocity and vorticity fields of the turbulent near wake of a circular cylinder

The purpose of this research is to provide a detailed experimental database of velocity and vorticity statistics in the very near wake (x/d less than 10) of a circular cylinder at Reynolds number of 3900. This study has determined that estimations of the streamwise velocity component in flow fields with large nonzero cross-stream components are not accurate. Similarly, X-wire measurements of the u and v velocity components in flows containing large w are also subject to the errors due to binormal cooling. Using the look-up table (LUT) technique, and by calibrating the X-wire probe used here to include the range of expected angles of attack (+/- 40 deg), accurate X-wire measurements of instantaneous u and v velocity components in the very near wake region of a circular cylinder has been accomplished. The approximate two-dimensionality of the present flow field was verified with four-wire probe measurements, and to some extent the spanwise correlation measurements with the multisensor rake. Hence, binormal cooling errors in the present X-wire measurements are small.

Wallace, James↗
NASA NTRS1997

Report to TRMM

The effort involved three elements all related to the measurement of rain and clouds using microwaves: (1) Examine recently proposed techniques for measuring rainfall rate and rain water content using data from ground-based radars and the TRMM microwave link in order to develop improved ground validation and radar calibration techniques; (2) Develop dual-polarization, multiple frequency radar techniques for estimating rain water content and cloud water content to interpret the vertical profiles of radar reflectivity factors (Z) measured by the TRMM Precipitation Radar; and (3) Investigate theoretically and experimentally the potential biases in TRMM Z measurements due to spatial inhomogeneities in precipitation. The research succeeded in addressing all of these topics, resulting in several referred publications. addition, the research indicated that the effects of non-Rayleigh statistics resulting from the nature of the precipitation inhomogeneities will probably not result in serious errors for the TRMM radar Measurements, but the TRMM radiometers may be subject to significant bias due to the inhomogeneities.

Jameson, Arthur R.↗
NASA NTRS1979

A review of the application of nonattenuating frequency radars for estimating rain attenuation and space-diversity performance

Cumulative rain fade statistics are used by space communications engineers to establish transmitter power and receiver sensitivities for systems operating under various geometries, climates, and radio frequencies. Space-diversity performance criteria are also of interest. This work represents a review, in which are examined the many elements involved in the employment of single nonattenuating frequency radars for arriving at the desired information. The elements examined include radar techniques and requirements, phenomenological assumptions, path attenuation formulations and procedures, as well as error budgeting and calibration analysis. Included are the pertinent results of previous investigators who have used radar for rain-attenuation modeling. Suggestions are made for improving present methods.

Goldhirsh, J.↗
NASA NTRS1997

Report to TRMM

The effort involved three elements all related to the measurement of rain and clouds using microwaves: (1) Examine recently proposed techniques for measuring rainfall rate and rain water content using data from ground-based radars and the TRMM microwave link in order to develop improved ground validation and radar calibration techniques; (2) Develop dual-polarization, multiple frequency radar techniques for estimating rain water content and cloud water content to interpret the vertical profiles of radar reflectivity factors (Z) measured by the TRMM Precipitation Radar; and (3) Investigate theoretically and experimentally the potential biases in TRMM Z measurements due to spatial inhomogeneities in precipitation. The research succeeded in addressing all of these topics, resulting in several refereed publications. In addition, the research indicated that the effects of non-Rayleigh statistics resulting from the nature of the precipitation inhomogeneities will probably not result in serious errors for the TRMM radar measurements, but the TRMM radiometers may be subject to significant bias due to the inhomogeneities.

Jameson, Arthur R.↗