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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Estimating regression coefficients from clustered samples: Sampling errors and optimum sample allocation

A number of surveys were conducted to study the relationship between the level of aircraft or traffic noise exposure experienced by people living in a particular area and their annoyance with it. These surveys generally employ a clustered sample design which affects the precision of the survey estimates. Regression analysis of annoyance on noise measures and other variables is often an important component of the survey analysis. Formulae are presented for estimating the standard errors of regression coefficients and ratio of regression coefficients that are applicable with a two- or three-stage clustered sample design. Using a simple cost function, they also determine the optimum allocation of the sample across the stages of the sample design for the estimation of a regression coefficient.

Kalton, G.↗
NASA NTRS2012

Achieving Accuracy Requirements for Forest Biomass Mapping: A Spaceborne Data Fusion Method for Estimating Forest Biomass and Lidar Sampling Error

The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission (+/-20 Mg/ha or 20%, the greater of the two, for at least 80% of grid cells). A data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional-global extents. A general framework for mapping above ground live forest biomass density (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify contiguous areas (>0.5 ha) that are relatively homogenous in remote sensing metrics (forest patches). We used this image-derived data with simulated spaceborne LiDAR derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (LVIS) to compute AGB and estimate LiDAR sampling error for forest patches and 100 m, 250 m, 500 m, and 1 km grid cells. At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. First, this data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting. Second, a data fusion approach for estimating AGB using simulated spaceborne LiDAR with SAR and passive optical image combinations reduced forest AGB sampling errors 12%-38% from those where LiDAR is used with SAR or passive optical alone. In absolute terms, sampling errors were reduced from 14-40 Mg/ha to 11-28 Mg/ha across all grid scales and prediction methods, where minimum sampling errors were 11, 15, 18, and 22 Mg/ha for 1 km, 500 m, 250 m, and 100 m grid scales, respectively. Third, spaceborne global scale accuracy requirements were achieved whereby at least 80% of the grid cells at 100 m, 250 m, 500 m, and 1 km grid levels met AGB accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500 m and 250 m grid level, respectively..

LiDAR↗
NASA NTRS2012

Achieving Accuracy Requirements for Forest Biomass Mapping: A Data Fusion Method for Estimating Forest Biomass and LiDAR Sampling Error with Spaceborne Data

The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission. This data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional - global extents. A general framework for mapping above ground live forest biomass (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify forest patches, and used image and simulated spaceborne LiDAR data to compute AGB and estimate LiDAR sampling error for forest patches and 100m, 250m, 500m, and 1km grid cells. Forest patches were delineated with Landsat-derived data and airborne SAR imagery, and simulated spaceborne LiDAR (SSL) data were derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (L VIS). At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. This data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting, and that combining simulated spaceborne LiDAR with SAR and passive optical data are most useful for estimating AGB when measurements from LiDAR are limited because they minimized forest AGB sampling errors by 15 - 38%. Furthermore, spaceborne global scale accuracy requirements were achieved. At least 80% of the grid cells at 100m, 250m, 500m, and 1km grid levels met AGB density accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500m and 250m grid level, respectively.

Montesano, P. M.↗
NASA NTRS2000

Sampling Errors in Monthly Rainfall Totals for TRMM and SSM/I, Based on Statistics of Retrieved Rain Rates and Simple Models

Estimates from TRMM satellite data of monthly total rainfall over an area are subject to substantial sampling errors due to the limited number of visits to the area by the satellite during the month. Quantitative comparisons of TRMM averages with data collected by other satellites and by ground-based systems require some estimate of the size of this sampling error. A method of estimating this sampling error based on the actual statistics of the TRMM observations and on some modeling work has been developed. "Sampling error" in TRMM monthly averages is defined here relative to the monthly total a hypothetical satellite permanently stationed above the area would have reported. "Sampling error" therefore includes contributions from the random and systematic errors introduced by the satellite remote sensing system. As part of our long-term goal of providing error estimates for each grid point accessible to the TRMM instruments, sampling error estimates for TRMM based on rain retrievals from TRMM microwave (TMI) data are compared for different times of the year and different oceanic areas (to minimize changes in the statistics due to algorithmic differences over land and ocean). Changes in sampling error estimates due to changes in rain statistics due 1) to evolution of the official algorithms used to process the data, and 2) differences from other remote sensing systems such as the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I), are analyzed.

Bell, Thomas L.↗
NASA NTRS1988

Sampling error study for rainfall estimate by satellite using a stochastic model

In a parameter study of satellite orbits, sampling errors of area-time averaged rain rate due to temporal sampling by satellites were estimated. The sampling characteristics were studied by accounting for the varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates. For a satellite of nominal Tropical Rainfall Measuring Mission (Thiele, 1987) carrying an ideal scanning microwave radiometer for precipitation measurements, it is found that sampling error would be about 8 to 12 pct of estimated monthly mean rates over a grid box of 5 X 5 degrees. It is suggested that an observation system based on a low inclination satellite combined with a sunsynchronous satellite simultaneously might be the best candidate for making precipitation measurements from space.

Shin, Kyung-Sup↗
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 NTRS1990

Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model

Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.

Bell, Thomas L.↗
NASA NTRS1987

Sampling errors in satellite estimates of tropical rain

The GATE rainfall data set is used in a statistical study to estimate the sampling errors that might be expected for the type of snapshot sampling that a low earth-orbiting satellite makes. For averages over the entire 400-km square and for the duration of several weeks, strong evidence is found that sampling errors less than 10 percent can be expected in contributions from each of four rain rate categories which individually account for about one quarter of the total rain.

Mcconnell, Alan↗
NASA NTRS1991

Spatial sampling errors for a satellite-borne scanning radiometer

The Clouds and Earth's Radiant Energy System (CERES) scanning radiometer is planned as the Earth radiation budget instrument for the Earth Observation System, to be flown in the late 1990's. In order to minimize the spatial sampling errors of the measurements, it is necessary to select design parameters for the instrument such that the resulting point spread function will minimize spatial sampling errors. These errors are described as aliasing and blurring errors. Aliasing errors are due to presence in the measurements of spatial frequencies beyond the Nyquist frequency, and blurring errors are due to attenuation of frequencies below the Nyquist frequency. The design parameters include pixel shape and dimensions, sampling rate, scan period, and time constants of the measurements. For a satellite-borne scanning radiometer, the pixel footprint grows quickly at large nadir angles. The aliasing errors thus decrease with increasing scan angle, but the blurring errors grow quickly. The best design minimizes the sum of these two errors over a range of scan angles. Results of a parameter study are presented, showing effects of data rates, pixel dimensions, spacecraft altitude, and distance from the spacecraft track.

Manalo, Natividad D.↗
NASA NTRS2002

SPECIAL SESSION: (H21) on Global Precipitation Mission for Hydrology and Hydrometeorology. Sampling-Error Considerations for GPM-Era Rainfall Products

The proposed Global Precipitation Mission (GPM) builds on the success of the Tropical Rainfall Measuring Mission (TRMM), offering a constellation of microwave-sensor-equipped smaller satellites in addition to a larger, multiply-instrumented "mother" satellite that will include an improved precipitation radar system to which the precipitation estimates of the smaller satellites can be tuned. Coverage by the satellites will be nearly global rather than being confined as TRMM was to lower latitudes. It is hoped that the satellite constellation can provide observations at most places on the earth at least once every three hours, though practical considerations may force some compromises. The GPM system offers the possibility of providing precipitation maps with much better time resolution than the monthly averages around which TRMM was planned, and therefore opens up new possibilities for hydrology and data assimilation into models. In this talk, methods that were developed for estimating sampling error in the rainfall averages that TRMM is providing will be used to estimate sampling error levels for GPM-era configurations. Possible impacts on GPM products of compromises in the sampling frequency will be discussed.

Bell, Thomas L.↗
NASA NTRS1998

Flux Sampling Errors for Aircraft and Towers

Various errors and influences leading to differences between tower- and aircraft-measured fluxes are surveyed. This survey is motivated by reports in the literature that aircraft fluxes are sometimes smaller than tower-measured fluxes. Both tower and aircraft flux errors are larger with surface heterogeneity due to several independent effects. Surface heterogeneity may cause tower flux errors to increase with decreasing wind speed. Techniques to assess flux sampling error are reviewed. Such error estimates suffer various degrees of inapplicability in real geophysical time series due to nonstationarity of tower time series (or inhomogeneity of aircraft data). A new measure for nonstationarity is developed that eliminates assumptions on the form of the nonstationarity inherent in previous methods. When this nonstationarity measure becomes large, the surface energy imbalance increases sharply. Finally, strategies for obtaining adequate flux sampling using repeated aircraft passes and grid patterns are outlined.

Mahrt, Larry↗
NASA NTRS1991

Compensating sampling errors in stabilizing helmet-mounted displays using auxiliary acceleration measurements

A method based on complementary filtering is shown to be effective in compensating for the image stabilization error due to sampling delays of HMD position and orientation measurements. These delays would otherwise have prevented the stabilization of the image in HMDs. The method is also shown to improve the resolution of the head orientation measurement, particularly at low frequencies, thus providing smoother head control commands, which are essential for precise head pointing and teleoperation.

Merhav, S.↗
NASA NTRS1982

Sampling errors in the estimation of empirical orthogonal functions

Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close' to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

North, G. R.↗