Search NASA⌕ Search

SEARCH · Search NASA

Results for “Deep uncertainty”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

The NASA Energy and Water Cycle Extreme (NEWSE) Integration Project

Skillful predictions of water and energy cycle extremes (flood and drought) are elusive. To better understand the mechanisms responsible for water and energy extremes, and to make decisive progress in predicting these extremes, the collaborative NASA Energy and Water cycle Extremes (NEWSE) Integration Project, is studying these extremes in the U.S. Southern Great Plains (SGP) during 2006-2007, including their relationships with continental and global scale processes, and assessment of their predictability on multiple space and time scales. It is our hypothesis that an integrative analysis of observed extremes which reflects the current understanding of the role of SST and soil moisture variability influences on atmospheric heating and forcing of planetary waves, incorporating recently available global and regional hydro- meteorological datasets (i.e., precipitation, water vapor, clouds, etc.) in conjunction with advances in data assimilation, can lead to new insights into the factors that lead to persistent drought and flooding. We will show initial results of this project, whose goals are to provide an improved definition, attribution and prediction on sub-seasonal to interannual time scales, improved understanding of the mechanisms of decadal drought and its predictability, including the impacts of SST variability and deep soil moisture variability, and improved monitoring/attributions, with transition to applications; a bridging of the gap between hydrological forecasts and stakeholders (utilization of probabilistic forecasts, education, forecast interpretation for different sectors, assessment of uncertainties for different sectors, etc.).

House, P. R.↗
NASA NTRS2020

Evaluation of global terrestrial evapotranspiration using state-of-the-art approaches in remote sensing, machine learning and land surface modeling

Evapotranspiration (ET) is critical in linking global water, carbon and energy cycles. However, direct measurement of global terrestrial ET is not feasible. Here, we first reviewed the basic theory and state-of-the-art approaches for estimating global terrestrial ET, including remote-sensing-based physical models, machine-learning algorithms and land surface models (LSMs). We then utilized 4 remote-sensing-based physical models, 2 machine-learning algorithms and 14 LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the ensemble means of annual global terrestrial ET estimated by these three categories of approaches agreed well, with values ranging from 589.6 mm/yr (6.56×10^4 cu.km/yr) to 617.1 mm/yr (6.87×10^4 cu.km/yr). For the period from 1982 to 2011, both the ensembles of remote-sensing-based physical models and machine-learning algorithms suggested increasing trends in global terrestrial ET (0.62 mm/sq.yr with a significance level of p<0.05 and 0.38 mm yr−2 with a significance level of p<0.05, respectively). In contrast, the ensemble mean of the LSMs showed no statistically significant change (0.23 mm/sq.yr, p>0.05), although many of the individual LSMs reproduced an increasing trend. Nevertheless, all 20 models used in this study showed that anthropogenic Earth greening had a positive role in increasing terrestrial ET. The concurrent small interannual variability, i.e., relative stability, found in all estimates of global terrestrial ET, suggests that a potential planetary boundary exists in regulating global terrestrial ET, with the value of this boundary being around 600 mm/yr. Uncertainties among approaches were identified in specific regions, particularly in the Amazon Basin and arid/semiarid regions. Improvements in parameterizing water stress and canopy dynamics, the utilization of new available satellite retrievals and deep-learning methods, and model–data fusion will advance our predictive understanding of global terrestrial ET.

surface modeling↗
NASA NTRSDate not supplied

Exploring Radiation, Water and Energy Closure in Key Deep Tropical Regions Over the Last 3 Decades

The closure of global energy and water budgets at various time scales depends heavily upon the on the processes of water and energy exchange in the deep tropics. A key process observed is the change in convection regimes from disorganized convection to organized deep convection. During these periods an imbalance in key tropical regions is observed of water budget terms between observations and atmospheric reanalysis systems, implying that processes are not simulated well. For instance, periods of imbalance in the water budget may be at least partly attributed to precipitation estimates due to the transition between cloud and precipitation systems in which ice cloud affects microwave radar estimates (Lietmann-Niimi et al. 2024, submitted). A recent paper by Hsaio et al (2023, pre-published version) found that the transition process is characterized by wind shear and longwave cloud radiative feedback signatures as well. This is just one example how these processes also affect the radiative fluxes and thus the energy budget at the TOA. In this presentation, we assess the net radiative budget and components in the deep tropics by comparing multiple data products (GEWEX SRB Rel4IP, CERES EBAF/SYN1deg Ed4.2, ISSCP FH, etc.) and describing the temporal variability of energy balance terms across the deep tropics for the period from 1988 to near present in six key oceanic regions. These six key tropical oceanic regions are West Indian Ocean, the south Indian Ocean east, tropical western, central and eastern Pacific Ocean, and Tropical Atlantic Ocean. In these regions we assess the sensitivity of the fluxes as a function of fluctuations in cloud types in response to various larger scale atmospheric processes (e.g. El Niño, Indian Ocean Dipole). We assess this variability of the radiative flux anomalies (including the net TOA, surface and the atmospheric divergence fluxes) against water vapor divergence, cloud properties (include ISCCP “Weather States, Tselioudis et al. 2021) and larger scale wind shear to assess the uncertainties of energy closure in these regions. These are contrasted against the modeled radiative fluxes from ERA-5 and MERRA-2. Ocean buoy measurements of radiative fluxes are utilized to help assess data radiative flux uncertainty over the nearly 40 year period. In general, the variability for overlap periods of these various data products agrees well, but there are significant differences in the net fluxes that vary according to the rendering of surface, atmospheric, aerosol and cloud properties. These differences also affect closure terms and inferences on systematic uncertainties within the observational estimates. We conclude with recommendations for continuing work

Radiation budget↗
NASA NTRS1974

Tracking system analytic calibration activities for the Mariner Mars 1971 mission

This report describes the functions of the Tracking System Analytic Calibration activity for Mariner Mars 1971 (MM'71), its objectives for this and future missions, and the support provided to the MM'71 Navigation Team during operations. The support functions encompass calibration of tracking data by estimating physical parameters whose uncertainties represent limitations to navigational accuracy, and detailed analysis of the tracking data to uncover and resolve any anomalies. Separate articles treat the activities and results of producing calibrations for the various error sources: Deep Space Station Locations, timing and polar motion, charged particles, and the troposphere. Two other articles are also included dis- - cussing the effects of the media error sources on orbit determination and the merits of the smoothing technique used for DRIVID.

Facilities↗
NASA NTRS1974

The tracking system analytic calibration activity for Mariner Mars 1971: Its function and scope

The functions of the Tracking System Analytic Calibration activity for Mariner Mars 1971 (MM'71), its objectives for this and future missions, and the support provided to the MM'71 Navigation Team during operations are described. Support functions encompass calibration of tracking data by estimating physical parameters whose uncertainties represent limitations to navigational accuracy, and detailed analysis of the tracking data to uncover and resolve any anomalies. Separate articles treat the activities and results of producing calibrations for the various error sources: Deep Space Station Locations, timing and polar motion, charged particles, and the troposphere. Two other articles are also included discussing the effects of the media error sources on orbit determination and the merits of the smoothing technique used for DRIVID.

Madrid, G. A.↗
NASA NTRS2017

Advances in Medical Analytics Solutions for Autonomous Medical Operations on Long-Duration Missions

A review will be presented on the progress made under STMDGame Changing Development Program Funding towards the development of a Medical Decision Support System for augmenting crew capabilities during long-duration missions, such as Mars Transit. To create an MDSS, initial work requires acquiring images and developing models that analyze and assess the features in such medical biosensor images that support medical assessment of pathologies. For FY17, the project has focused on ultrasound images towards cardiac pathologies: namely, evaluation and assessment of pericardial effusion identification and discrimination from related pneumothorax and even bladder-induced infections that cause inflammation around the heart. This identification is substantially changed due to uncertainty due to conditions of fluid behavior under space-microgravity. This talk will present and discuss the work-to-date in this Project, recognizing conditions under which various machine learning technologies, deep-learning via convolutional neural nets, and statistical learning methods for feature identification and classification can be employed and conditioned to graphical format in preparation for attachment to an inference engine that eventually creates decision support recommendations to remote crew in a triage setting.

Medical Decision Support Systems↗
NASA NTRS1988

Determination of the inner planet frame tie using VLBI data

The problem of connecting the independent reference frames formed by the planetary ephemeris and the radio source catalog is one of growing importance to spacecraft navigation. Using quasar-relative VLBI delay data collected by the Deep Space Network, and Soviet coherent data from the Venus flyby of the Soviet Vega 1 and 2 spacecraft, a self-consistent estimate of the frame tie offset has been found, along with its uncertainty.

Mcelrath, Timothy P.↗
NASA NTRS2016

The Calibration of the DSCOVR EPIC Multiple Visible Channel Instrument Using MODIS and VIIRS as a Reference

The Deep Space Climate Observatory (DSCOVR), launched on 11 February 2015, is a satellite positioned near the Lagrange-1 (L1) point, carrying several instruments that monitor space weather, and Earth-view sensors designed for climate studies. The Earth Polychromatic Imaging Camera (EPIC) onboard DSCOVR continuously views the sun-illuminated portion of the Earth with spectral coverage in the UV, VIS, and NIR bands. Although the EPIC instrument does not have any onboard calibration abilities, its constant view of the sunlit Earth disk provides a unique opportunity for simultaneous viewing with several other satellite instruments. This arrangement allows the EPIC sensor to be inter-calibrated using other well-characterized satellite instrument reference standards. Two such instruments with onboard calibration are MODIS, flown on Aqua and Terra, and VIIRS, onboard Suomi-NPP. The MODIS and VIIRS reference calibrations will be transferred to the EPIC instrument using both all-sky ocean and deep convective clouds (DCC) ray-matched EPIC and MODIS/VIIRS radiance pairs. An automated navigation correction routine was developed to more accurately align the EPIC and MODIS/VIIRS granules. The automated navigation correction routine dramatically reduced the uncertainty of the resulting calibration gain based on the EPIC and MODIS/VIIRS radiance pairs. The SCIAMACHY-based spectral band adjustment factors (SBAF) applied to the MODIS/ VIIRS radiances were found to successfully adjust the reference radiances to the spectral response of the specific EPIC channel for over-lapping spectral channels. The SBAF was also found to be effective for the non-overlapping EPIC channel 10. Lastly, both ray-matching techniques found no discernable trends for EPIC channel 7 over the year of publically released EPIC data.

Haney, Conor↗
NASA NTRS2020

MODIS TEB Calibration Algorithm Improvements for Future L1B Collection

Terra and Aqua MODIS have provided continuous global observations for scientific applications for more than 20 and 18 years, respectively. The radiometric calibration of the MODIS thermal emissive bands (TEB) is based on a quadratic approximation of the instrument response. The calibration coefficients look-up tables (LUTs) are updated using the response of the MODIS on-board blackbody (BB)with the response background subtracted by space view. The quarterly on-board BB warm-up and cool-down activity temperature ranges from 270 K to 315 K, and the derived offset has a relatively large uncertainty. Electronic cross-talk, an artifact that affects both instrument calibration and Earth view (EV) radiance retrievals, is corrected based on lunar observations. Calibration assessments using EV observations (e.g. ocean, desert, Antarctic Dome Concordia, and deep convective clouds) provide useful information to evaluate the impact of the Terra safe mode (February 2016) and Aqua MODIS formatter reset (January 2018) events on both MODIS instruments. This study focuses on the TEB radiometric calibration algorithm improvements for future collections based on calibration assessments using EV measurements and analytical modeling. Measurement stability and consistency over specific Earth scenes with a wide temperature range, as well as their brightness temperature (BT) dependency, are used for bias estimations in the calibration coefficients. Calibration coefficients are derived and updated after adjusting the current fitting algorithm. Thereafter, using the test LUTs, their impact on the Level 1B (L1B) data for different EV scenes is analyzed.

MODIS↗
NASA NTRS2003

The Galileo Probe: How it Has Changed Our Understanding of Jupiter

The Galileo Mission to Jupiter, which arrived in December of 1995, provided the first study by an orbiter, and the first in-situ sampling via an entry probe, of an outer planet atmosphere. The rationale for an entry probe is that, even from an orbiter, remote sensing of the jovian atmosphere could not adequately retrieve the information desired. This paper provides a current summary of the most significant aspects of the data returned from the Galileo entry probe. As a result of the probe measurements, there has been a reassessment of our understanding of outer planet formation and evolution of the solar system. The primary scientific objective of the Galileo probe was to determine the composition of the jovian atmosphere, which from remote sensing remained either very uncertain, or completely unknown, with respect to several key elements. The probe found that the global He mass fraction is. significantly above the value reported from the Voyager Jupiter flybys but is slightly below the protosolar value, implying that there has been some settling of He to the deep jovian interior. The probe He measurements have also led to a reevaluation of the Voyager He mass fraction for Saturn, which is now determined to be much closer to that of Jupiter. The elements C, N, S, Ar, Kr, Xe were all found to have global abundances approximately 3 times their respective solar abundances. This result has raised a number of fundamental issues with regard to properties of planetesimals and the solar nebula at the time of giant planet formation. Ne, on the other hand, was found to be highly depleted, probably as the result of it being carried along with helium as helium settles towards the deep interior. The global abundance of O was not obtained by the probe because of the influence of local processes at the probe entry site (PES), processes which depleted condensible species, in this case H2O, well below condensation levels. Other condensible species, namely NH3 and H2S, were similarly affected but attained their deep equilibrium mixing ratios before the maximum depth sampled by the probe. Processes that might be capable of producing such effects on the condensibles are still under investigation. Measured isotopic ratios of noble gases and other heavy elements are solar, and (D + (Sup 3)He)/H is the same to within measurement uncertainties as in the local interstellar medium. No thick clouds were detected, and in particular no significant water cloud, but the PES location clearly affected the probe measurements of clouds. In fact, the probe data must be understood in the context of the location of the PES, which was within what is termed a 5 micron hot spot, a local clearing in the clouds that is bright near the 5 microns spectral region. The thermal structure at the PES was determined from approximately 1000 km above the 1 bar pressure level (10(exp -9 bars)) to 132 km 1 bar (22bars). The probe showed the atmosphere to have a generally sub-adiabatic temperature gradient (static stability) of = 0.1 K/km to as deep as the probe made measurements. In the upper atmosphere the probe derived a maximum positive vertical temperature gradient of approximately 5 K/km, and maximum temperature of = 900 K. The energy sources producing the warm upper atmosphere have yet to be completely identified. At first glance, Doppler tracking of the probe indicates that the long observed cloud level zonal winds extend to levels at least as deep as the probe made measurements. Zonal wind increases from = 80 m/s at pressures less than a bar to about 180 m/s near 5 bars, and remains approximately constant with depth thereafter. However, there is a question as to whether the winds measured from probe tracking are representative of the general wind field, or are considerably influenced by localized winds associated with the PES.

Young, Richard E.↗
NASA NTRS2023

Broader Impacts and Outreach Videos on Ocean Physics and Biogeochemistry

This is just a preliminary NF1676 in advance of filming for a project....A convergent team of experts in biology, chemistry, physics, engineering, mathematics, and computational modeling examine how dynamic and coupled phytoplankton-pathogen-particle-predator linkages coalesce to explain the observed high spatial variability in the efficiency of the export of particulate organic carbon (POC) to the deep ocean. They elucidate and quantify the linkages between viruses and ballast minerals to increase understanding of carbon cycling in the oceanic biological carbon pump and the impact of viruses within it. By providing knowledge than can be used to improve the parameterization of carbon export in Earth system models, the project will help reduce uncertainty in regional marine biogeochemical projections, potentially improving marine ecosystem and fisheries management on timescales from seasons to decades. The project includes activities that provide teaching resources and hands-on training to educators within a ‘Tools of Science’ program that provides a simple and succinct way to communicate the process of scientific research to students in a way that is useful to teachers. The project couples laboratory-based experiments on model host-virus-grazer systems with extensive field based observational and manipulative studies on natural populations of diatoms and coccolithophores, the two phytoplankton groups that account for most of the estimated particulate organic matter flux to the deep ocean. Experiments and measurements integrate diagnostic biological and chemical controls on infection and particle coagulation theory with microscale physics and grazing to quantify links to each hypothesized export mechanism under field-relevant turbulent conditions. Cutting-edge engineering and analytical tools are used to diagnose and track infection dynamics while characterizing and quantifying particle aggregation and disaggregation, mineral dissolution, sinking dynamics, grazing rates, and fecal pellet production at unprecedented resolution and under well-defined, microscale physical regimes. Field campaigns elucidate the relative efficiency of hypothesized mechanisms in stimulating POC export in natural blooms, while providing bulk and size-resolved estimates of POC flux.

Daniel B Whitt↗
NASA NTRS1979

Oceanic geoid and tides derived from GEOS 3 satellite data in the Northwestern Atlantic Ocean

Two sets of GEOS 3 altimeter data which fall within about a 2.5-deg width are analyzed for ocean geoid and tides. One set covers a path from Newfoundland to Cuba, and the other a path from Puerto Rico to the North Carolina coast. Forty different analyses using various parameters are performed in order to investigate convergence. Profiles of the geoid and four tides, M2, O1, S2, and K1, are derived along the two strips. While the analyses produced convergent solutions for all 40 cases, the uncertainty caused by the linear orbital bias error of the satellite is too large to claim that the solutions represent the true ocean tides in the area. A spot check of the result with the Mode deep-sea tide gauge data shows poor agreement. A positive conclusion of this study is that despite the uncertain orbital error the oceanic geoid obtained through this analysis can improve significantly the short-wavelength structure over existing spherical harmonic geoid models.

Won, I. J.↗
NASA NTRS2004

Deep Convective Cloud Top Heights and Their Thermodynamic Control During CRYSTAL-FACE

Infrared (11 micron) radiances from GOES-8 and local radiosonde profiles, collected during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) in July 2002, are used to assess the vertical distribution of Florida-area deep convective cloud top height and test predictions as to its variation based on parcel theory. The highest infrared tops (Z(sub 11)) reached approximately to the cold point, though there is at least a 1-km uncertainty due to unknown cloud-environment temperature differences. Since lidar shows that visible 'tops' are 1 km or more above Z(sub 11), visible cloud tops frequently penetrated the lapse-rate tropopause (approx. 15 km). Further, since lofted ice content may be present up to approx. 1 km above the visible tops, lofting of moisture through the mean cold point (15.4 km) was probably common. Morning clouds, and those near Key West, rarely penetrated the tropopause. Non-entraining parcel theory (i.e., CAPE) does not successfully explain either of these results, but can explain some of the day-to-day variations in cloud top height over the peninsula. Further, moisture variations above the boundary layer account for most of the day-today variability not explained by CAPE, especially over the oceans. In all locations, a 20% increase in mean mixing ratio between 750 and 500 hPa was associated with about 1 km deeper maximum cloud penetration relative to the neutral level. These results suggest that parcel theory may be useful for predicting changes in cumulus cloud height over time, but that parcel entrainment must be taken into account even for the tallest clouds. Accordingly, relative humidity above the boundary layer may exert some control on the height of the tropical troposphere.

Sherwood, Steven C.↗
NASA NTRSDate not supplied

A Deep Neural Network for Achieving Spectrally Consistent and Seamless Infrared Radiance Measurements Across Geostationary Satellite Domains

The NASA Clouds and the Earth's Radiant Energy System (CERES) project provides the scientific community with observed top-of-atmosphere (TOA) shortwave and longwave fluxes for climate monitoring and climate model validation. To achieve this goal, CERES relies on TOA broadband fluxes derived from geostationary satellite (GEO) imagery to account for the diurnal flux variations between the CERES observation intervals. Consistent global flux derivation depends on accurate and consistent cloud retrievals. Scene-dependent spectral measurement inconsistency of the instruments that make up the contiguous ring of GEO observations (GEO-Ring), as well as limb darkening effects, can cause discontinuities in derived cloud properties and radiative fluxes at the boundaries of adjacent imager domains. Although the algorithms utilize radiative transfer models to account for instrument-band-dependent atmospheric correction and viewing zenith angle (VZA) dependency, small discontinuities may persist due to uncertainties inherent to the multiple imager-specific algorithms. Furthermore, while hyperspectral-instrument-based spectral band adjustment factors may effectively account for spectrally induced bias, they are less effective at reducing variance owed to the specific composition of the viewed scene, which is challenging to robustly characterize. As such, this article highlights the use of a deep neural network (DNN) to resolve spectral-and VZA-induced biases between GEO-Ring imagers. The DNN uses available infrared (IR) channels from the GEO instruments, along with viewing and solar illumination geometry, to estimate homogenized, VIIRS-like IR radiances for use in the GEO cloud algorithm. This approach is effective at mitigating scene-dependent spectral variance and VZA dependency, resulting in consistent radiance measurements across the GEO-Ring, thereby leading toward a more seamless global cloud assessment.

deep learning↗
NASA NTRS1984

Interplanetary navigation

The evolution of NASA's planetary navigation techniques is traced, and radiometric and optical data types are described. Doppler navigation; the Deep Space Network; differenced two-way range techniques; differential very long base interferometry; and optical navigation are treated. The Doppler system enables a spacecraft in cruise at high absolute declination to be located within a total angular uncertainty of 1/4 microrad. The two-station range measurement provides a 1 microrad backup at low declinations. Optical data locate the spacecraft relative to the target to an angular accuracy of 5 microrad. Earth-based radio navigation and its less accurate but target-relative counterpart, optical navigation, thus form complementary measurement sources, which provide a powerful sensory system to produce high-precision orbit estimates.

Stuart, J. R.↗
NASA NTRSDate not supplied

Generation of Continental Scale Percent Tree Cover Product Using Deep-learning and Multi-scale Remote Sensing Data

Spatially explicit percent tree cover (TC) estimation is critical for mapping forest aboveground biomass and its dynamics. While various TC products have been developed, there has not been a generalized framework that can be applied to diverse terrestrial ecosystems due to underlain extreme complexities. Deep learning algorithms can learn a spatial pattern and radiometric characteristics of tree canopy as a robust approximation of physical or empirical models, and thus have emerged as promising and efficient tools for large-scale TC mapping. In this study, we synergistically use very high-resolution aerial imageries (National Agriculture Imagery Program, NAIP) and medium resolution Landsat data to map continental-scale TC (CONUS and Mexico) through a hierarchical deep learning approach (Convolutional Neural Network), i.e., NAIP TC generated from a NAIP model is utilized to train a Landsat model. The produced TC product (hereafter, NEX-TC) is able to capture the spatial pattern of TC distribution and its changes driven by natural disturbance and human land management. We further explore and analyze the reliability and potential uncertainty of the NEX-TC by comparing it to lidar- (lidar-TC), National Land Cover Database (NLCD-TC), and MODIS Vegetation Continuous Field (MODIS-TC). This evaluation practice reveals that TC products based on passive optical sensors tend to underestimate TC across all land cover types while Landsat-based TCs (i.e., NEX-TC & NLCD-TC) perform better than the coarser MODIS TC estimate. Our results show that the NEX-TC is generally comparable to NLCD-TC but it particularly outperforms NLCD-TC and MODIS-TC over the dense forests where lidar-TC indicates >80% TC. These results indicate that our hierarchical deep learning approach and TC product will be effective and useful for characterizing large-scale tree cover and possibly associated carbon dynamics.

Landsat↗
NASA NTRS1984

Arcsecond Positions for Milliarcsecond VLBI Nuclei of Extragalactic Radio Sources, Part 2: 207 Sources

Very long base interferometry measurements of time delay and fringe frequency at 2.29 GHz on baselines of 10,000 km between Deep Space Network stations were used to determine the positions of the milliarcsecond nuclei in 207 extragalactic radio sources. Estimated accuracies generally range from approximately 0.1 to approximately 1.0, in both right ascension and declination, with all sources having uncertainties 4" in both coordinates. The observed sources are part of an all-sky VLBI catalog of milliarcsecond radio sources. Arcsecond positions are now determined for 752 of these sources. Arcsecond positions serve as a useful starting point in the construction of high-precision VLBI reference frames and are also important for unambiguous determination of optical counterparts to compact radio sources.

Morabito, D. D.↗
NASA NTRS1988

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Lerch, F. J.↗