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NASA NTRS1998

Estimation of Soil Moisture Profile using a Simple Hydrology Model and Passive Microwave Remote Sensing

Soil moisture is an important component of analysis in many Earth science disciplines. Soil moisture information can be obtained either by using microwave remote sensing or by using a hydrologic model. In this study, we combined these two approaches to increase the accuracy of profile soil moisture estimation. A hydrologic model was used to analyze the errors in the estimation of soil moisture using the data collected during Huntsville '96 microwave remote sensing experiment in Huntsville, Alabama. Root mean square errors (RMSE) in soil moisture estimation increase by 22% with increase in the model input interval from 6 hr to 12 hr for the grass-covered plot. RMSEs were reduced for given model time step by 20-50% when model soil moisture estimates were updated using remotely-sensed data. This methodology has a potential to be employed in soil moisture estimation using rainfall data collected by a space-borne sensor, such as the Tropical Rainfall Measuring Mission (TRMM) satellite, if remotely-sensed data are available to update the model estimates.

Soman, Vishwas V.↗
NASA NTRS2000

Stress Recovery and Error Estimation for 3-D Shell Structures

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Riggs, H. R.↗
NASA NTRS2000

Effect of Medium Symmetries in Limiting the Number of Parameters Estimated with Polarimetric Interferometry

The addition of interferometric backscattering pairs to the conventional polarimetric SAR data over forests and other vegetated areas increases the dimensionality of the data space, in principle enabling the estimation of a larger number of vegetation parameters. Without regard to the sensitivity of these data to vegetation scattering parameters, this paper poses the question: Will increasing the data channels as such result in a one-to-one increase in the number of parameters that can be estimated, or do vegetation and data properties inherently limit that number otherwise? In this paper, the complete polarimetric interferometric covariance matrix is considered and various symmetry properties of the scattering medium are used to study whether any of the correlation pairs can be eliminated. The number of independent pairs has direct consequences in their utility in parameter estimation schemes, since the maximum number of parameters that can be estimated cannot exceed the number of unique measurements. The independent components of the polarimetric interferometric SAR (POL/INSAR) data are derived for media with reflection, rotation, and azimuth symmetries, which are often encountered in vegetated surfaces. Similar derivations have been carried out before for simple polarimetry, i.e., zero baseline. This paper extends those to the interferometric case of general nonzero baselines. It is shown that depending on the type of symmetries present, the number of independent available measurements that can be used to estimate medium parameters will vary. In particular, whereas in the general case there are 27 mathematically independent measurements possible from a polarimetric interferometer, this number can be reduced to 15, 9, and 6 if the medium has reflection, rotation, or azimuthal symmetries, respectively. The results can be used in several ways in the interpretation of SAR data and the development of parameter estimation schemes, which will be discussed at the presentation. Recent POL/INSAR data from the JPL AIRSAR over a forested area will be used to demonstrate the results of this derivation. This work was performed by the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, under contract from the National Aeronautics and Space Administration.

Moghaddam, Mahta↗
NASA NTRS2000

Sampling Errors of SSM/I and TRMM Rainfall Averages: Comparison with Error Estimates from Surface Data and a Sample Model

Quantitative use of satellite-derived maps of monthly rainfall requires some measure of the accuracy of the satellite estimates. The rainfall estimate for a given map grid box is subject to both remote-sensing error and, in the case of low-orbiting satellites, sampling error due to the limited number of observations of the grid box provided by the satellite. A simple model of rain behavior predicts that Root-mean-square (RMS) random error in grid-box averages should depend in a simple way on the local average rain rate, and the predicted behavior has been seen in simulations using surface rain-gauge and radar data. This relationship was examined using satellite SSM/I data obtained over the western equatorial Pacific during TOGA COARE. RMS error inferred directly from SSM/I rainfall estimates was found to be larger than predicted from surface data, and to depend less on local rain rate than was predicted. Preliminary examination of TRMM microwave estimates shows better agreement with surface data. A simple method of estimating rms error in satellite rainfall estimates is suggested, based on quantities that can be directly computed from the satellite data.

Bell, Thomas L.↗
NASA NTRS2002

TRMM Science Highlights and 3-hr Quasi-global Precipitation Estimates

The Tropical Rainfall Measuring Mission (TRMM) has completed more than four years in orbit. A summary of research highlights will be presented focusing on application of TRMM data to topics ranging over climate analysis, improving forecasts, precipitation processes and non-precipitation applications. One focus of the talk will be the quasi-global TRMM real-time merged rainfall analysis with 3-hr resolution, which uses TRMM to calibrate estimates from other polar-orbit and geosynchronous satellites. These rainfall estimates provide useful information for applications for assimilation into numerical models and for hydrological studies. The status of precipitation estimates from different TRMM instruments and algorithms will be described. Monthly surface rainfall estimates over the ocean based on different instruments on TRMM currently differ by 20% in overall mean. In addition, time changes in global ocean rainfall between El Nino and La Nina conditions show differences between the active and passive microwave products. Improved versions of algorithms will shortly resolve most of these differences. The TRMM rainfall estimates are intercompared among themselves and with other estimates, including those of the standard, monthly Global Precipitation Climatology Project (GPCP) analysis. A four-year TRMM rainfall climatology is presented, including anomaly fields related to the changing ENSO situation during the mission. The evolution of precipitation analysis incorporating Advanced Microwave Scanning Radiometer (AMSR) data on AQUA and ADEOS II and eventually data from the Global Precipitation Mission (GPM) will also be described.

Adler, Robert F.↗
NASA NTRS2003

Estimation of Model Error Variances During Data Assimilation

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

Dee, Dick↗
NASA NTRS2003

Limitation of Ground-based Estimates of Solar Irradiance Due to Atmospheric Variations

The uncertainty in ground-based estimates of solar irradiance is quantitatively related to the temporal variability of the atmosphere's optical thickness. The upper and lower bounds of the accuracy of estimates using the Langley Plot technique are proportional to the standard deviation of aerosol optical thickness (approx. +/- 13 sigma(delta tau)). The estimates of spectral solar irradiance (SSI) in two Cimel sun photometer channels from the Mauna Loa site of AERONET are compared with satellite observations from SOLSTICE (Solar Stellar Irradiance Comparison Experiment) on UARS (Upper Atmospheric Research Satellite) for almost two years of data. The true solar variations related to the 27-day solar rotation cycle observed from SOLSTICE are about 0.15% at the two sun photometer channels. The variability in ground-based estimates is statistically one order of magnitude larger. Even though about 30% of these estimates from all Level 2.0 Cimel data fall within the 0.4 to approx. 0.5% variation level, ground-based estimates are not able to capture the 27-day solar variation observed from SOLSTICE.

Wen, Guoyong↗
NASA NTRS2002

Analysis of TRMM 3-Hourly Multi-Satellite Precipitation Estimates Computed in Both Real and Post-Real Time

Satellite data form the core of the information available for estimating precipitation on a global basis. While it is possible to create such estimates solely from one sensor, researchers have increasingly moved to using combinations of sensors in an attempt to improve accuracy, coverage, and resolution. This poster updates a long-term project in which the authors are working to provide routine combined-sensor estimates of precipitation over the entire globe at relatively fine time and space intervals. The goal is to produce these globally complete precipitation estimates on a 25-km grid every 3 hours. Since late January 2002 we have been estimating precipitation for the latitude band 50 degrees N-S within about 6 hours of observation time. This work is 1 of only 2 or 3 such efforts in the world. Now we are preparing to provide similar estimates for the last 5 years. All of this work is being carried out as part of the Tropical Rainfall Measuring Mission (TRMM). Initially, TRMM was focused on providing excellent long-term averages of precipitation in tropical regions, but since its launch in November 1997 continued research has allowed the same satellite and data system to be used for addressing weather-scale problems as well.

Huffman, George J.↗
NASA NTRS2004

Kernel PLS Estimation of Single-trial Event-related Potentials

Nonlinear kernel partial least squaes (KPLS) regressior, is a novel smoothing approach to nonparametric regression curve fitting. We have developed a KPLS approach to the estimation of single-trial event related potentials (ERPs). For improved accuracy of estimation, we also developed a local KPLS method for situations in which there exists prior knowledge about the approximate latency of individual ERP components. To assess the utility of the KPLS approach, we compared non-local KPLS and local KPLS smoothing with other nonparametric signal processing and smoothing methods. In particular, we examined wavelet denoising, smoothing splines, and localized smoothing splines. We applied these methods to the estimation of simulated mixtures of human ERPs and ongoing electroencephalogram (EEG) activity using a dipole simulator (BESA). In this scenario we considered ongoing EEG to represent spatially and temporally correlated noise added to the ERPs. This simulation provided a reasonable but simplified model of real-world ERP measurements. For estimation of the simulated single-trial ERPs, local KPLS provided a level of accuracy that was comparable with or better than the other methods. We also applied the local KPLS method to the estimation of human ERPs recorded in an experiment on co,onitive fatigue. For these data, the local KPLS method provided a clear improvement in visualization of single-trial ERPs as well as their averages. The local KPLS method may serve as a new alternative to the estimation of single-trial ERPs and improvement of ERP averages.

Rosipal, Roman↗
NASA NTRS2001

The Spatial Distribution of Forest Biomass in the Brazilian Amazon: A Comparison of Estimates

The amount of carbon released to the atmosphere as a result of deforestation is determined, in part, by the amount of carbon held in the biomass of the forests converted to other uses. Uncertainty in forest biomass is responsible for much of the uncertainty in current estimates of the flux of carbon from land-use change. We compared several estimates of forest biomass for the Brazilian Amazon, based on spatial interpolations of direct measurements, relationships to climatic variables, and remote sensing data. We asked three questions. First, do the methods yield similar estimates? Second, do they yield similar spatial patterns of distribution of biomass? And, third, what factors need most attention if we are to predict more accurately the distribution of forest biomass over large areas? Amazonian forests (including dead and below-ground biomass) vary by more than a factor of two, from a low of 39 PgC to a high of 93 PgC. Furthermore, the estimates disagree as to the regions of high and low biomass. The lack of agreement among estimates confirms the need for reliable determination of aboveground biomass over large areas. Potential methods include direct measurement of biomass through forest inventories with improved allometric regression equations, dynamic modeling of forest recovery following observed stand-replacing disturbances (the approach used in this research), and estimation of aboveground biomass from airborne or satellite-based instruments sensitive to the vertical structure plant canopies.

Houghton, R. A.↗
NASA NTRS1995

Estimates of volumetric bone density from projectional measurements improve the discriminatory capability of dual X-ray absorptiometry

To determine whether estimates of volumetric bone density from projectional scans of the lumbar spine have weaker associations with height and weight and stronger associations with prevalent vertebral fractures than standard projectional bone mineral density (BMD) and bone mineral content (BMC), we obtained posteroanterior (PA) dual X-ray absorptiometry (DXA), lateral supine DXA (Hologic QDR 2000), and quantitative computed tomography (QCT, GE 9800 scanner) in 260 postmenopausal women enrolled in two trials of treatment for osteoporosis. In 223 women, all vertebral levels, i.e., L2-L4 in the DXA scan and L1-L3 in the QCT scan, could be evaluated. Fifty-five women were diagnosed as having at least one mild fracture (age 67.9 +/- 6.5 years) and 168 women did not have any fractures (age 62.3 +/- 6.9 years). We derived three estimates of "volumetric bone density" from PA DXA (BMAD, BMAD*, and BMD*) and three from paired PA and lateral DXA (WA BMD, WA BMDHol, and eVBMD). While PA BMC and PA BMD were significantly correlated with height (r = 0.49 and r = 0.28) or weight (r = 0.38 and r = 0.37), QCT and the volumetric bone density estimates from paired PA and lateral scans were not (r = -0.083 to r = 0.050). BMAD, BMAD*, and BMD* correlated with weight but not height. The associations with vertebral fracture were stronger for QCT (odds ratio [QR] = 3.17; 95% confidence interval [CI] = 1.90-5.27), eVBMD (OR = 2.87; CI 1.80-4.57), WA BMDHol (OR = 2.86; CI 1.80-4.55) and WA-BMD (OR = 2.77; CI 1.75-4.39) than for BMAD*/BMD* (OR = 2.03; CI 1.32-3.12), BMAD (OR = 1.68; CI 1.14-2.48), lateral BMD (OR = 1.88; CI 1.28-2.77), standard PA BMD (OR = 1.47; CI 1.02-2.13) or PA BMC (OR = 1.22; CI 0.86-1.74). The areas under the receiver operating characteristic (ROC) curves for QCT and all estimates of volumetric BMD were significantly higher compared with standard PA BMD and PA BMC. We conclude that, like QCT, estimates of volumetric bone density from paired PA and lateral scans are unaffected by height and weight and are more strongly associated with vertebral fracture than standard PA BMD or BMC, or estimates of volumetric density that are solely based on PA DXA scans.

Non-NASA Center↗
NASA NTRS2002

Estimate of Top-of-Atmosphere Albedo for a Molecular Atmosphere over Ocean using Clouds and the Earth's Radiant Energy System (CERES) Measurements

The shortwave broadband albedo at the top of a molecular atmosphere over ocean between 40deg N and 40deg S is estimated using radiance measurements from the Clouds and the Earth's Radiant Energy System (CERES) instrument and the Visible Infrared Scanner (VIRS) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. The albedo monotonically increases from 0.059 at a solar zenith angle of 10deg to 0.107 at a solar zenith angle of 60deg. The estimated uncertainty in the albedo is 3.5 x 10(exp -3) caused by the uncertainty in CERES-derived irradiances, uncertainty in VIRS-derived aerosol optical thicknesses, variations in ozone and water vapor, and variations in surface wind speed. The estimated uncertainty is similar in magnitude to the standard deviation of 0.003 that is derived from 72 areas divided by 20deg latitude by 20deg longitude grid boxes. The empirically estimated albedo is compared with the modeled albedo using a radiative transfer model combined with an ocean surface bidirectional reflectivity model. The modeled albedo with standard tropical atmosphere is 0.061 and 0.111 at the solar zenith angles of 10deg and 60deg, respectively. This empirically estimated albedo can be used to estimate the direct radiative effect of aerosols at the top of the atmosphere over oceans.

Kato, S.↗
NASA NTRS2005

Comparison of TRMM Ground Validation and Satellite Rain Intensity Estimates

The Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) Program began in the late 1980's and has provided a wealth of data and resources for validating TRMM satellite estimates. The TRMM GV program's main operational task is to provide rainfall products for four sites: Darwin, Australia (DARW); Houston, Texas (HSTN); Kwajalein, Republic of the Marshall Islands (KWAJ); and, Melbourne, Florida (MELB). A comparison between TRMM Ground Validation (Version 5) and Satellite (Version 6) rain intensity estimates is presented. The full suite of Version 6 satellite data is currently being generated by the TRMM Science Data and Information System (TSDIS) and should be completed some time near the end of 2005. The gridded satellite product (3G68) will be compared to GV Level II rain-intensity and -type maps (2A53 and 2A54, respectively). The 3G68 product represents a 0.5 deg x 0.5 deg data grid providing estimates of rain intensities from the TRMM Precipitation Radar (PR), Microwave Imager (TMI) and Combined (COM) algorithms. The comparisons will be sub-setted according to geographical type (land, coast and ocean). A bias statistic will be presented that provides quantification of the relative differences between the various estimators. Previous comparisons of an interim satellite product (Version 6a) showed that all of the estimates (GV and satellite) are converging, with some expected discrepancies. The convergence of the GV and satellite estimates bodes well for expectations for the proposed Global Precipitation Measurement (GPM) program and this study and others are being leveraged towards planning GV goals for GPM.

Wolff, David B.↗
NASA NTRS2005

Hubble Space Telescope Angular Velocity Estimation During the Robotic Servicing Mission

During the Hubble Robotic Servicing Mission, the Hubble Space Telescope (HST) attitude and rates are necessary to achieve the capture of HST by the Hubble Robotic Vehicle (HRV). The attitude and rates must be determined without the HST gyros or HST attitude estimates. The HRV will be equipped with vision-based sensors, capable of estimating the relative attitude between HST and HRV. The HST attitude is derived from the measured relative attitude and the HRV computed inertial attitude. However, the relative rate between HST and HRV cannot be measured directly. Therefore, the HST rate with respect to inertial space is not known. Two approaches are developed to estimate the HST rates. Both methods utilize the measured relative attitude and the HRV inertial attitude and rates. First, a nonlinear estimator is developed. The nonlinear approach estimates the HST rate through an estimation of the inertial angular momentum. Second, a linearized approach is developed. The linearized approach is based on more traditional Extended Kalman filter techniques. Simulation test results for both methods are given.

Thienel, Julie K.↗
NASA NTRS2005

Hubble Space Telescope Angular Velocity Estimation During the Robotic Servicing Mission

In 2004 NASA began investigation of a robotic servicing mission for the Hubble Space Telescope (HST). Such a mission would require estimates of the HST attitude and rates in order to achieve a capture by the proposed Hubble robotic vehicle (HRV). HRV was to be equipped with vision-based sensors, capable of estimating the relative attitude between HST and HRV. The inertial HST attitude is derived from the measured relative attitude and the HRV computed inertial attitude. However, the relative rate between HST and HRV cannot be measured directly. Therefore, the HST rate with respect to inertial space is not known. Two approaches are developed to estimate the HST rates. Both methods utilize the measured relative attitude and the HRV inertial attitude and rates. First, a non-linear estimator is developed. The nonlinear approach estimates the HST rate through an estimation of the inertial angular momentum. Second, a linearized approach is developed. The linearized approach is a pseudo-linear Kalman filter. Simulation test results for both methods are given. Even though the development began as an application for the HST robotic servicing mission, the methods presented are applicable to any rendezvous/capture mission involving a non-cooperative target spacecraft.

Thienel, Julie K.↗
NASA NTRS2005

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Lee-Rausch, E. M.↗
NASA NTRS2005

Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

Simon, Dan↗
NASA NTRS2005

Data-Rate Estimation for Autonomous Receiver Operation

In this article, we present a series of algorithms for estimating the data rate of a signal whose admissible data rates are integer base, integer powered multiples of a known basic data rate. These algorithms can be applied to the Electra radio currently used in the Deep Space Network (DSN), which employs data rates having the above relationship. The estimation is carried out in an autonomous setting in which very little a priori information is assumed. It is done by exploiting an elegant property of the split symbol moments estimator (SSME), which is traditionally used to estimate the signal-to-noise ratio (SNR) of the received signal. By quantizing the assumed symbol-timing error or jitter, we present an all-digital implementation of the SSME which can be used to jointly estimate the data rate, SNR, and jitter. Simulation results presented show that these joint estimation algorithms perform well, even in the low SNR regions typically encountered in the DSN.

Tkacenko, A.↗