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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Finite Element Model Calibration Approach for Area I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of non-conventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pretest predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.↗
NASA NTRS2011

Meteorological Necessities for the Stratospheric Observatory for Infrared Astronomy

The Stratospheric Observatory for Infrared Astronomy (SOFIA) is joint program with NASA and DLR (German Aerospace Center) of a highly modified Boeing 747-SP. The purpose of this modification is to include a 2.5 m infrared telescope in a rear bulkhead of the airplane, with a retractable door open to the atmosphere. The NASA Dryden Flight Research Center (DFRC) is responsible for verifying that the aerodynamics, acoustics, and flying qualities of the modified aircraft stay within safe limits. Flight testing includes determining meteorological limitations of the aircraft, which is done by setting strict temporary operating limits and verifying through data analysis, what conditions are acceptable. Line operations are calibration tests of various telescope instruments that are done on the ground prior to flights. The method in determining limitations for this type of operation is similar to that of flight testing, but the meteorological limitations are different. Of great concern are the particulates near the surface that could cause damage to the telescope, as well as condensation forming on the mirror. Another meteorological involvement for this program is the process of obtaining Reduced Vertical Separation Minimums (RVSM) Certification from the FAA. This heavily involves obtaining atmospheric data pertinent to the flight, analyzing data to actual conditions for validity, and computing necessary results for comparison to aircraft instrumentation.

Houtas, Franzeska↗
NASA NTRS2010

Finite Element Model Calibration Approach for Ares I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.↗
DOE OSTI2015

FermI large area telescope third source catalog

We present the third Fermi Large Area Telescope (LAT) source catalog (3FGL) of sources in the 100 MeV–300 GeV range. Based on the first 4 yr of science data from the Fermi Gamma-ray Space Telescope mission, it is the deepest yet in this energy range. Relative to the Second Fermi LAT catalog, the 3FGL catalog incorporates twice as much data, as well as a number of analysis improvements, including improved calibrations at the event reconstruction level, an updated model for Galactic diffuse γ-ray emission, a refined procedure for source detection, and improved methods for associating LAT sources with potential counterparts at other wavelengths. The 3FGL catalog includes 3033 sources above 4σ significance, with source location regions, spectral properties, and monthly light curves for each. Of these, 78 are flagged as potentially being due to imperfections in the model for Galactic diffuse emission. Twenty-five sources are modeled explicitly as spatially extended, and overall 238 sources are considered as identified based on angular extent or correlated variability (periodic or otherwise) observed at other wavelengths. For 1010 sources we have not found plausible counterparts at other wavelengths. More than 1100 of the identified or associated sources are active galaxies of the blazar class; several other classes of non-blazar active galaxies are also represented in the 3FGL. Pulsars represent the largest Galactic source class. From source counts of Galactic sources we estimate that the contribution of unresolved sources to the Galactic diffuse emission is ∼3% at 1 GeV.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2011

Application of Temperature Sensitivities During Iterative Strain-Gage Balance Calibration Analysis

A new method is discussed that may be used to correct wind tunnel strain-gage balance load predictions for the influence of residual temperature effects at the location of the strain-gages. The method was designed for the iterative analysis technique that is used in the aerospace testing community to predict balance loads from strain-gage outputs during a wind tunnel test. The new method implicitly applies temperature corrections to the gage outputs during the load iteration process. Therefore, it can use uncorrected gage outputs directly as input for the load calculations. The new method is applied in several steps. First, balance calibration data is analyzed in the usual manner assuming that the balance temperature was kept constant during the calibration. Then, the temperature difference relative to the calibration temperature is introduced as a new independent variable for each strain--gage output. Therefore, sensors must exist near the strain--gages so that the required temperature differences can be measured during the wind tunnel test. In addition, the format of the regression coefficient matrix needs to be extended so that it can support the new independent variables. In the next step, the extended regression coefficient matrix of the original calibration data is modified by using the manufacturer specified temperature sensitivity of each strain--gage as the regression coefficient of the corresponding temperature difference variable. Finally, the modified regression coefficient matrix is converted to a data reduction matrix that the iterative analysis technique needs for the calculation of balance loads. Original calibration data and modified check load data of NASA's MC60D balance are used to illustrate the new method.

Ulbrich, N.↗
NASA NTRS2002

Data Analysis for the SOLIS Vector Spectromagnetograph

The National Solar Observatory's SOLIS Vector Spectromagnetograph (VSM), which will produce three or more full-disk maps of the Sun's photospheric vector magnetic field every day for at least one solar magnetic cycle, is in the final stages of assembly. Initial observations, including cross-calibration with the current NASA/NSO spectromagnetograph (SPM) will soon be carried out at a test site in Tucson. This paper discusses data analysis techniques for reducing the raw data, calculation of line-of-sight magnetograms and both quick-look and high-precision inference of vector fields from Stokes spectral profiles. Existing SPM algorithms, suitably modified to accomodate the cameras, scanning pattern, and polarization calibration optics for the VSM, will be used to "clean" the raw data and to process line-of-sight, magnetograms. A recent. version of the High Altitude Observatory Milne-Eddington (HAO-ME) inversion code (Skumanich and Lites; 1987, 11)J 322, p. 473) will he used for high-precision vector fields since the algorithm has been extensively tested, is well understood, and is fast enough to complete data analysis within 24 hours of data acquisition. The simplified inversion algorithm of Auer, Heasley. arid House (1977, Sol. Phys. 55, p. 47) forms the initial guess for this version of the HAO-ME code and will be used for quick-look vector analysis of VSM data since its performance on simulated Stokes profiles is better than other candidate methods. Improvements (e.g., principal components analysis or neural networks) are under consideration and will be straightforward to implement. However, current resources are sufficient to store the original Stokes profiles only long enough for high-precision analysis. Retrospective reduction of Stokes data with improved methods will not be possible, and modifications will only be introduced when the advantages of doing so are compelling enough to justify discontinuity in the long-term data stream.

Jones, Harrison P.↗
DOE OSTI2018

Linearized Boltzmann-Langevin model for heavy quark transport in hot and dense QCD matter

In relativistic heavy-ion collisions, the production of heavy quarks at large transverse momenta is strongly suppressed compared to proton-proton collisions. In addition, an unexpectedly large azimuthal anisotropy was observed for the emission of charmed hadrons in noncentral collisions. Both observations pose challenges to the theoretical understanding of the coupling between heavy quarks and the quark-gluon plasma produced in these collisions. Transport models for the evolution of heavy quarks in a QCD medium offer the opportunity to study these effects; two of the most successful approaches are based on the linearized Boltzmann transport equation and the Langevin equation. In this work, we develop a hybrid transport model that combines the strengths of both of these approaches: Heavy quarks scatter with medium partons using matrix-elements calculated in perturbative QCD, while between these discrete hard scatterings they evolve using a Langevin equation with empirical transport coefficients to capture the nonperturbative soft part of the interaction. With the hybrid transport model coupled to a state-of-the-art event-by-event bulk evolution model based on 2+1D relativistic viscous fluid dynamics, we study the azimuthal anisotropy and nuclear modification factor of heavy quarks in Pb+Pb collisions at √s = 5.02 TeV. The parameters related to heavy-flavor transport are calibrated using a Bayesian analysis comparing them to available D -meson and B -meson data at the Large Hadron Collider. Lastly, using the calibrated model, we study the implications on heavy-flavor transport properties and predict observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1972

Neutron die-away experiment for remote analysis of the surface of the moon and the planets, phase 3

Continuing work on the two die-away measurements proposed to be made in the combined pulsed neutron experiment (CPNE) for analysis of lunar and planetary surfaces is described. This report documents research done during Phase 3. A general exposition of data analysis by the least-squares method and the related problem of the prediction of variance is given. A data analysis procedure for epithermal die-away data has been formulated. In order to facilitate the analysis, the number of independent material variables has been reduced to two: the hydrogen density and an effective oxygen density, the latter being determined uniquely from the nonhydrogeneous elemental composition. Justification for this reduction in the number of variables is based on a set of 27 new theoretical calculations. Work is described related to experimental calibration of the epithermal die-away measurement. An interim data analysis technique based solely on theoretical calculations seems to be adequate and will be used for future CPNE field tests.

Mills, W. R.↗
DOE OSTI2023

Extraction of branching ratios from HERFD data

A quantitative analysis method has been developed that allows the cross calibration of separate Uranium M 4 and M 5 X-ray absorption spectra (XAS), in particular those collected with the new High Energy Resolution Fluorescence Detection (HERFD) method. With this method, it is now possible to generate experimental Branching Ratio (BR) values from the U M 4,5 XAS HERFD data.

36 MATERIALS SCIENCE↗
NASA NTRS2021

Triply eclipsing triple stars in the northern TESS fields: TICs 193993801, 388459317, and 52041148

In this work we report the discovery and analysis of three new triply eclipsing triple star systems found with the TESS mission during its observations of the northern skies: TICs 193993801, 388459317, and 52041148. We utilized the TESS precision photometry of the binary eclipses and third-body eclipsing events, ground-based archival and follow-up photometric data, eclipse timing variations, archival spectral energy distributions, as well as theoretical evolution tracks in a joint photodynamical analysis to deduce the system masses and orbital parameters of both the inner and outer orbits. In one case (TIC 193993801) we also obtained radial velocity measurements of all three stars. This enabled us to `calibrate' our analysis approach with and without `truth' (i.e., RV) data. We find that the masses are good to 1-3% accuracy with RV data and 3-10% without the use of RV data. In all three systems we were able to find the outer orbital period before doing any detailed analysis by searching for a longer-term periodicity in the ASAS-SN archival photometry data -- just a few thousand ASAS-SN points enabled us to find the outer periods of 49.28 d, 89.86 d, and 177.0 d, respectively. From our full photodynamical analysis we find that all three systems are coplanar to within 1 ∘ −3 ∘ . The outer eccentricities of the three systems are 0.003, 0.10, and 0.62, respectively (i.e., spanning a factor of 200). The masses of the three stars {Aa, Ab, and B} in the three systems are: {1.31, 1.19, 1.34}, {1.82, 1.73, 2.19}, and {1.62, 1.48, 2.74} M ⊙ , respectively.

Tamás Borkovits↗
NASA NTRS1984

An emulator for minimizing computer resources for finite element analysis

A computer code, SCOPE, has been developed for predicting the computer resources required for a given analysis code, computer hardware, and structural problem. The cost of running the code is a small fraction (about 3 percent) of the cost of performing the actual analysis. However, its accuracy in predicting the CPU and I/O resources depends intrinsically on the accuracy of calibration data that must be developed once for the computer hardware and the finite element analysis code of interest. Testing of the SCOPE code on the AMDAHL 470 V/8 computer and the ELAS finite element analysis program indicated small I/O errors (3.2 percent), larger CPU errors (17.8 percent), and negligible total errors (1.5 percent).

Melosh, R.↗
NASA NTRS2024

The Radio Fundamental Catalogue. I. Astrometry

We present the all-sky catalogue of absolute positions and estimates of correlated flux density of 21,942 compact radio sources determined from processing interferometric visibility data of virtually all VLBI observing sessions at 2 to 23~GHz from 72 programs suitable for absolute astrometry collected for 30 years. We used a novel technique of generation of a dataset of fused observables that allowed us to incorporate all available data in our analysis. The catalogue is the most complete and most precise to date. It forms the foundation and reference for positional astronomy, space geodesy, space navigation, population analysis of active galactic nuclei (AGNs), and provides calibrators for phase-referencing for differential astrometry and VLBI astrophysical observations. Its accuracy was evaluated through a detailed accounting systematic errors, rigorous decimation tests, comparison of different datasets, and comparison with other catalogues. The catalogue samples preferentially the AGNs with a strong contemporary parsec-scale synchrotron emission. Its milliarcsecond level positional accuracy allows association of these AGNs with detections in a wide range of the electromagnetic spectrum from low-frequency radio to gamma-rays and high energy neutrinos. We describe the innovative data processing and calibration technique in full detail, report the in depth analysis of random and systematic positional errors, and provide the list of associations with large surveys at different wavelengths.

Astronomy↗
DOE OSTI2012

LOW-FREQUENCY IMAGING OF FIELDS AT HIGH GALACTIC LATITUDE WITH THE MURCHISON WIDEFIELD ARRAY 32 ELEMENT PROTOTYPE

The Murchison Widefield Array (MWA) is a new low-frequency, wide-field-of-view radio interferometer under development at the Murchison Radio-astronomy Observatory in Western Australia. We have used a 32 element MWA prototype interferometer (MWA-32T) to observe two 50 Degree-Sign diameter fields in the southern sky, covering a total of {approx}2700 deg{sup 2}, in order to evaluate the performance of the MWA-32T, to develop techniques for epoch of reionization experiments, and to make measurements of astronomical foregrounds. We developed a calibration and imaging pipeline for the MWA-32T, and used it to produce {approx}15' angular resolution maps of the two fields in the 110-200 MHz band. We perform a blind source extraction using these confusion-limited images, and detect 655 sources at high significance with an additional 871 lower significance source candidates. We compare these sources with existing low-frequency radio surveys in order to assess the MWA-32T system performance, wide-field analysis algorithms, and catalog quality. Our source catalog is found to agree well with existing low-frequency surveys in these regions of the sky and with statistical distributions of point sources derived from Northern Hemisphere surveys; it represents one of the deepest surveys to date of this sky field in the 110-200 MHz band.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Measuring the neutrino-oxygen neutral current quasielastic cross section using the accelerator neutrino neutron interaction experiment

The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a 26-ton gadolinium-doped water Cherenkov detector located on-axis to Fermilab’s Booster Neutrino Beam (BNB). ANNIE is uniquely positioned to perform high-statistics measurements of neutrino-nucleus interactions in water, benefiting from a large neutrino flux due to a short (100-meter) baseline. A central focus of ANNIE’s physics program is the measurement of both charged current (CC) and neutral current (NC) cross sections on water, including neutral current quasielastic (NCQE) and CC-inclusive channels. The NCQE measurement is particularly critical for constraining uncertainties in rare-event searches such as the Diffuse Supernova Neutrino Background (DSNB), where atmospheric $\nu$NCQE interactions constitute a significant and poorly constrained background. This dissertation presents a measurement of the flux-averaged neutrino-oxygen neutral current quasielastic ($\nu$NCQE) cross section using $2.573 \times 10^{20}$~POT of BNB exposure from the 2022 and 2023 beam years. The $\nu$NCQE interaction is identified through the primary $\gamma$-rays produced by nuclear de-excitation of the residual $^{15}$N$^*$ or $^{15}$O$^*$ nucleus following nucleon knockout from $^{16}$O. A dedicated Monte Carlo (MC) re-tuning campaign was conducted using an americium-beryllium (AmBe) calibration source, Michel electrons from stopped muons, and throughgoing dirt muons originating upstream of the detector. This multi-sample approach provided a wide-ranging $\mathcal{O}(\text{MeV})$--$\mathcal{O}(\text{GeV})$ dataset for tuning the simulated detector response, which was subsequently validated against AmBe neutron and Michel electron data for use in the $\nu$NCQE analysis. A dedicated laser calibration campaign was carried out to reduce timing uncertainties across the PMT system, enabling reconstruction of the BNB bunch substructure with sufficient resolution to serve as a background rejection tool. By selecting events in-time with individual neutrino bunches, beam-correlated $\nu$NCQE events are separated from diffuse and accelerator-induced backgrounds, notably skyshine neutrons and externally-originating events, that would otherwise dominate traditional charge-based selections within a small-scale, surface-level, short-baseline detector. A data-driven estimation of the skyshine neutron and external background rates was performed and incorporated into the systematic uncertainty budget. The flux-averaged $\nu$NCQE cross section on oxygen is measured to be $1.57 \pm 0.06\,(\text{stat.})$ $^{+0.91}_{-0.67}\,(\text{syst.})$ $\times 10^{-38}\ \text{cm}^{2}$. A full systematic budget is constructed by propagating uncertainties in the secondary hadronic interaction modeling, background cross section normalizations, detector response, neutrino flux, and the primary $\gamma$-ray emission probabilities from oxygen nuclear de-excitation. An idealized de-excitation model, constructed from existing measurements in the literature is developed to benchmark the predictions of the \textsc{GENIE} event generator. A comparison reveals that \textsc{GENIE} systematically overpredicts the primary $\gamma$-ray emission probability from oxygen de-excitation by a factor of $1.49\times$ for $E_\gamma > 6$~MeV and $3.07\times$ in the $3$--$6$~MeV band. This comparison motivates the dominant systematic uncertainty in this analysis, where a conservative uncertainty of $^{+39.9\%}_{-0\%}$ on the primary $\gamma$-ray signal prediction is assigned. The ANNIE result is consistent with and complementary to existing flux-averaged $\nu$NCQE cross section measurements from T2K and Super-Kamiokande, providing an independent measurement with a different detector, neutrino beam, and analysis methodology. Looking ahead, an upgrade to the ANNIE DAQ infrastructure enabling continuous extended readout will allow a complementary $\nu$NCQE neutron multiplicity measurement, directly relevant to constraining the NCQE background in DSNB searches, competitive with the recent T2K measurement at SK-Gd. The planned Super-SANDI upgrade, deploying a large Water-based Liquid Scintillator (WbLS) volume, will further extend ANNIE's reach to hadronic final states and exclusive NC channels, and enable joint measurements with liquid argon detectors sharing the BNB beamline ahead of DUNE and Hyper-Kamiokande.

Doran, Steven [Iowa State U.]↗
NASA NTRS1994

(abstract) Tropospheric Calibration for the Mars Observer Gravity Wave Experiment

In spring 1993, microwave radiometer-based tropospheric calibration was provided for the Mars Observer gravitational wave search. The Doppler shifted X-band radio signals propagating between Earth and the Mars Observer satellite were precisely measured to determine path length variations that might signal passage of gravitational waves. Experimental sensitivity was restricted by competing sources of variability in signal transit time. Principally, fluctuations in the solar wind and ionospheric plasma density combined with fluctions in tropospheric refractivity determined the detection limit. Troposphere-induced path delay fluctions are dominated by refractive changes caused by water vapor inhomogeneities blowing through the signal path. Since passive microwave remote sensing techniques are able to determine atmospheric propagation delays, radiometer-based tropospheric calibration was provided at the Deep Space Network Uranus tracking site (DSS-15). Two microwave water vapor radiometers (WVRs), a microwave temperature profiler (MTP), and a ground based meterological station were deployed to determine line-of-sight vapor content and vertical temperature profile concurrently with Mars Observer tracking measurements. This calibration system provided the capability to correct Mars Observer Doppler data for troposphere-induced path variations. We present preliminary analysis of the Doppler and WVR data sets illustrating the utility of WVRs to calibrate Doppler data. This takes an important step toward realizing the ambitious system required to support future Ka-band Cassini satellite gravity wave tropospheric calibration system.

atmospheric water vapor microwave remote sensing↗
NASA NTRS2001

POLAR/CEPPAD Data Analysis

This a report on the Comprehensive Energetic Particle Pitch Angle Distribution (CEPPAD) experiment of POLAR. Dr. Baker has been active in the design and calibration of the CEPPAD sensors and is now heavily involved in the analysis and interpretation of the data. Baker and his team have developed analysis and data display software and continue to support all aspects of the CEPPAD program.

Baker, D. N.↗
NASA NTRS2012

Optical Density Analysis of X-Rays Utilizing Calibration Tooling to Estimate Thickness of Parts

This process is designed to estimate the thickness change of a material through data analysis of a digitized version of an x-ray (or a digital x-ray) containing the material (with the thickness in question) and various tooling. Using this process, it is possible to estimate a material's thickness change in a region of the material or part that is thinner than the rest of the reference thickness. However, that same principle process can be used to determine the thickness change of material using a thinner region to determine thickening, or it can be used to develop contour plots of an entire part. Proper tooling must be used. An x-ray film with an S-shaped characteristic curve or a digital x-ray device with a product resulting in like characteristics is necessary. If a film exists with linear characteristics, this type of film would be ideal; however, at the time of this reporting, no such film has been known. Machined components (with known fractional thicknesses) of a like material (similar density) to that of the material to be measured are necessary. The machined components should have machined through-holes. For ease of use and better accuracy, the throughholes should be a size larger than 0.125 in. (.3 mm). Standard components for this use are known as penetrameters or image quality indicators. Also needed is standard x-ray equipment, if film is used in place of digital equipment, or x-ray digitization equipment with proven conversion properties. Typical x-ray digitization equipment is commonly used in the medical industry, and creates digital images of x-rays in DICOM format. It is recommended to scan the image in a 16-bit format. However, 12-bit and 8-bit resolutions are acceptable. Finally, x-ray analysis software that allows accurate digital image density calculations, such as Image-J freeware, is needed. The actual procedure requires the test article to be placed on the raw x-ray, ensuring the region of interest is aligned for perpendicular x-ray exposure capture. One or multiple machined components of like material/ density with known thicknesses are placed atop the part (preferably in a region of nominal and non-varying thickness) such that exposure of the combined part and machined component lay-up is captured on the x-ray. Depending on the accuracy required, the machined component fs thickness must be carefully chosen. Similarly, depending on the accuracy required, the lay-up must be exposed such that the regions of the x-ray to be analyzed have a density range between 1 and 4.5. After the exposure, the image is digitized, and the digital image can then be analyzed using the image analysis software.

Grau, David↗
NASA NTRS1999

Tropical Rainfall Analysis Using TRMM in Combination With Other Satellite Gauge Data: Comparison with Global Precipitation Climatology Project (GPCP) Results

This paper describes recent results of using Tropical Rainfall Measuring Mission (TRMM) information as the key calibration tool in a merged analysis on a 1 deg x 1 deg latitude/longitude monthly scale based on multiple satellite sources and raingauge analysis. The procedure used to produce the GPCP data set is a stepwise approach which first combines the satellite low-orbit microwave and geosynchronous IR observations into a "multi-satellite" product and than merges that result with the raingauge analysis. Preliminary results produced with the still-stabilizing TRMM algorithms indicate that TRMM shows tighter spatial gradients in tropical rain maxima with higher peaks in the center of the maxima. The TRMM analyses will be used to evaluate the evolution of the 1998 ENSO variations, again in comparison with the GPCP analyses.

Adler, Robert F.↗