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All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Global-Scale Comparison of Passive (SMOS) and Active (ASCAT) Satellite Based Microwave Soil Moisture Retrievals with Soil Moisture Simulations (MERRA-Land)

Global surface soil moisture (SSM) datasets are being produced based on active and passive microwave satellite observations and simulations from land surface models (LSM). This study investigates the consistency of two global satellite-based SSM datasets based on microwave remote sensing observations from the passive Soil Moisture and Ocean Salinity (SMOS;SMOSL3 version 2.5) and the active Advanced Scatterometer (ASCAT; version TUWien- WARP 5.5) with respect to LSM SSM from the MERRA-Land data product. The relationship between the global-scale SSM products was studied during the 2010-2012 period using (1) a time series statistics (considering both original SSM data and anomalies), (2) a space-time analysis using Hovmoller diagrams, and (3) a triple collocation error model. The SMOSL3 and ASCAT retrievals are consistent with the temporal dynamics of modeled SSM (correlation R (is) greater than 0.70 for original SSM) in the transition zones between wet and dry climates, including the Sahel, the Indian subcontinent, the Great Plains of North America, eastern Australia, and southeastern Brazil. Over relatively dense vegetation covers, a better consistency with MERRA-Land was obtained with ASCAT than with SMOSL3. However, it was found that ASCAT retrievals exhibit negative correlation versus MERRA-Land in some arid regions (e.g., the Sahara and the Arabian Peninsula). In terms of anomalies, SMOSL3 better captures the short term SSM variability of the reference dataset (MERRA-Land) than ASCAT over regions with limited radio frequency interference (RFI) effects (e.g., North America, South America, and Australia). The seasonal and latitudinal variations of SSM are relatively similar for the three products, although the MERRALand SSM values are generally higher and their seasonal amplitude is much lower than for SMOSL3 and ASCAT. Both SMOSL3 and ASCAT have relatively comparable triple collocation errors with similar spatial error patterns: (i) lowest errors in arid regions (e.g., Sahara and Arabian Peninsula), due to the very low natural variability of soil moisture in these areas, and Central America, and (ii) highest errors over most of the vegetated regions (e.g., northern Australia, India, central Asia, and South America). However, the ASCAT SSM product is prone to larger random errors in some regions (e.g., north-western Africa, Iran, and southern South Africa). Vegetation density was found to be a key factor to interpret the consistency with MERRA-Land between the two remotely sensed products (SMOSL3 and ASCAT) which provides complementary information on SSM. This study shows that both SMOS and ASCAT have thus a potential for data fusion into long-term data records.

ASCAT↗
NASA NTRS1979

Methodology for error analysis and simulation of lidar aerosol measurements

A methodology is presented for objective and automated determination of the uncertainty in lidar aerosol measurements. This methodology is based on standard error-propagation procedures, a large data base on atmospheric behavior, and long experience in lidar data processing. Algebraic expressions for probable error are derived as a function of the relevant parameters. The validity of these expressions is then tested by making simulated measurements and analyses in which random errors of appropriate size are injected at proper steps of the measurement and analysis process. An illustrative example is given where the methodology is applied to a new lidar system now being used for airborne measurements of the stratospheric aerosol.

Russell, P. B.↗
NASA NTRS1988

Nimbus-7 global cloud climatology. I - Algorithms and validation

An improved version of the Nimbus-7 cloud retrieval algorithm was validated using data from Nimbus-7 Temperature Humidity Infrared Radiometer and Total Ozone Mapping Spectrometer to determine cloudiness parameters for the globe. Quantitative validation of total cloud amount was performed by comparing the algorithm results with estimates derived from GOES images and auxiliary meteorological data. The systematic errors of the Nimbus-7 total cloud-amount algorithm, relative to the GOES-derived estimates, were found to be less than 10 percent. The random errors of daily estimates ranged between 7 and 16 percent, day or night.

Stowe, L. L.↗
NASA NTRS2007

Derivation and Application of a Global Albedo yielding an Optical Brightness To Physical Size Transformation Free of Systematic Errors

Orbital object data acquired via optical telescopes can play a crucial role in accurately defining the space environment. Radar systems probe the characteristics of small debris by measuring the reflected electromagnetic energy from an object of the same order of size as the wavelength of the radiation. This signal is affected by electrical conductivity of the bulk of the debris object, as well as its shape and orientation. Optical measurements use reflected solar radiation with wavelengths much smaller than the size of the objects. Just as with radar, the shape and orientation of an object are important, but we only need to consider the surface electrical properties of the debris material (i.e., the surface albedo), not the bulk electromagnetic properties. As a result, these two methods are complementary in that they measure somewhat independent physical properties to estimate the same thing, debris size. Short arc optical observations such as are typical of NASA's Liquid Mirror Telescope (LMT) give enough information to estimate an Assumed Circular Orbit (ACO) and an associated range. This information, combined with the apparent magnitude, can be used to estimate an "absolute" brightness (scaled to a fixed range and phase angle). This absolute magnitude is what is used to estimate debris size. However, the shape and surface albedo effects make the size estimates subject to systematic and random errors, such that it is impossible to ascertain the size of an individual object with any certainty. However, as has been shown with radar debris measurements, that does not preclude the ability to estimate the size distribution of a number of objects statistically. After systematic errors have been eliminated (range errors, phase function assumptions, photometry) there remains a random geometric albedo distribution that relates object size to absolute magnitude. Measurements by the LMT of a subset of tracked debris objects with sizes estimated from their radar cross sections indicate that the random variations in the albedo follow a log-normal distribution quite well. In addition, this distribution appears to be independent of object size over a considerable range in size. Note that this relation appears to hold for debris only, where the shapes and other properties are not primarily the result of human manufacture, but of random processes. With this information in hand, it now becomes possible to estimate the actual size distribution we are sampling from. We have identified two characteristics of the space debris population that make this process tractable and by extension have developed a methodology for performing the transformation.

Mulrooney, Dr. Mark K.↗
NASA NTRS1990

Imaging other planetary systems from the moon

This paper studies the problem of using a telescope like the HST, only larger and sensitive to a wider range of wavelengths, to image systems of planets like the solar system around other stars. Both reflected starlight and thermal radiation from the planets are treated. The instrumental effects of aperture diffraction, scattering due to the power spectral density of telescope mirror surface errors, and telescope thermal emission are included. The integration time required to achieve a signal-to-noise ratio is computed at 5 for photon-statistical random errors only, which is a necessary but not sufficient criterion for detection at a confidence level of five standard deviations. A cold telescope on the moon with 16m aperture and the optical quality of HST could detect and characterize planets around nearby stars.

Brown, Robert A.↗
NASA NTRS2010

Using MERRA Gridded Innovations for Quantifying Uncertainties in Analysis Fields and Diagnosing Observing System Inhomogeneities

MERRA is a NASA reanalysis for the satellite era using a major new version of the Goddard Earth Observing System Data Assimilation System Version 5 (GEOS-5). The project focuses on historical analyses of the hydrological cycle on a broad range of weather and climate time scales and places the NASA EOS suite of observations in a climate context. The characterization of uncertainty in reanalysis fields is a commonly requested feature by users of such data. While intercomparison with reference data sets is common practice for ascertaining the realism of the datasets, such studies typically are restricted to long term climatological statistics and seldom provide state dependent measures of the uncertainties involved. In principle, variational data assimilation algorithms have the ability of producing error estimates for the analysis variables (typically surface pressure, winds, temperature, moisture and ozone) consistent with the assumed background and observation error statistics. However, these "perceived error estimates" are expensive to obtain and are limited by the somewhat simplistic errors assumed in the algorithm. The observation minus forecast residuals (innovations) by-product of any assimilation system constitutes a powerful tool for estimating the systematic and random errors in the analysis fields. Unfortunately, such data is usually not readily available with reanalysis products, often requiring the tedious decoding of large datasets and not so-user friendly file formats. With MERRA we have introduced a gridded version of the observations/innovations used in the assimilation process, using the same grid and data formats as the regular datasets. Such dataset empowers the user with the ability of conveniently performing observing system related analysis and error estimates. The scope of this dataset will be briefly described. We will present a systematic analysis of MERRA innovation time series for the conventional observing system, including maximum-likelihood estimates of background and observation errors, as well as global bias estimates. Starting with the joint PDF of innovations and analysis increments at observation locations we propose a technique for diagnosing bias among the observing systems, and document how these contextual biases have evolved during the satellite era covered by MERRA.

da Silva, Arlindo↗
NASA NTRS1972

Data smoothing and error detection based on linear interpolation

A method is presented, based on linear interpolation, for detecting and correcting bad data points in a set of data without contaminating the good data points. The method used is not concerned with the small random errors usually attributed to a noisy system. It assumes that the data points which are in error are relatively isolated from each other and that the number of such points is small compared to the total number of data points.

Guerra, V. M.↗
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 NTRS1989

On the decoder error probability of linear codes

By using coding and combinatorial techniques, an approximate formula for the weight distribution of decodable words of most linear block codes is evaluated. This formula is then used to give an approximate expression for the decoder error probability P(sub E)(u) of linear block codes, given that an error pattern of weight u has occurred. It is shown that P(sub E)(u) approaches the constant Q as u gets large, where Q is the probability that a completely random error pattern will cause decoder error.

Cheung, K.-M.↗
NASA NTRS1961

A Study of the Effect of Errors in Measurement of Velocity and Flight-Path Angle on the Guidance of a Space Vehicle Approaching the Earth

An analysis was made of the guidance of a space vehicle approaching the earth at supercircular velocity through an entrance corridor containing a desired perigee altitude. Random errors were assumed in the measurement of velocity and flight-path angle and in obtaining the desired thrust impulse. The method described in NASA Technical Note D-191 of scheduling corrections at different values of the angle between perigee and the vehicle's position vector and a slight modification of this method were investigated as a means of correcting perigee altitude when the vehicle's predicted position was at programmed correction points not within a specified deadband about the desired perigee altitude. The study showed that modifying the angular method of NASA Technical Note D-191 by adding another correction near the initial point did not improve the efficiency and accuracy of the angular method. It was found that in some cases the use of a correction procedure which included a deadband could be more costly in total corrective velocity than a procedure which neglected the deadband. This was especially true if a large degree of confidence was required in the total corrective velocity. It was apparent from the results that a correction with a deadband limit in the guidance scheme was more sensitive to the initial conditions, the corrective procedure, the deadband, and the degree of confidence required than a correction without a deadband limit.

White, Jack A.↗
NASA NTRS1980

An error analysis of basic kinematic quantities

A description is presented of the computational procedures used to obtain spatial fields of relative vorticity, advection of vorticity, horizontal divergence, and vertical motion. An investigation is conducted of the effectiveness of these procedures to reduce the effects of deliberately introduced random errors, giving attention to the confidence which can be placed on values of the derived parameters. It is concluded that fields of 500 mb vorticity and 700 mb vertical velocity, which are frequently used in synoptic scale forecasting schemes, show minimal effects of the deliberately introduced errors. Vorticity advection is found to be the most sensitive term to input data errors. Large fluctuations in fields of this parameter are evident both statistically and qualitatively.

Berecek, E. M.↗
NASA NTRS1994

Cirrus cloud retrieval using infrared sounding data: Multilevel cloud errors

In this study we perform an error analysis for cloud-top pressure retrieval using the High-Resolution Infrared Radiometric Sounder (HIRS/2) 15-microns CO2 channels for the two-layer case of transmissive cirrus overlying an overcast, opaque stratiform cloud. This analysis includes standard deviation and bias error due to instrument noise and the presence of two cloud layers, the lower of which is opaque. Instantaneous cloud pressure retrieval errors are determined for a range of cloud amounts (0.1-1.0) and cloud-top pressures (850-250 mb). Large cloud-top pressure retrieval errors are found to occur when a lower opaque layer is present underneath an upper transmissive cloud layer in the satellite field of view (FOV). Errors tend to increase with decreasing upper-cloud effective cloud amount and with decreasing cloud height (increasing pressure). Errors in retrieved upper-cloud pressure result in corresponding errors in derived effective cloud amount. For the case in which a HIRS FOV has two distinct cloud layers, the difference between the retrieved and actual cloud-top pressure is positive in all cases, meaning that the retrieved upper-cloud height is lower than the actual upper-cloud height. In addition, errors in retrieved cloud pressure are found to depend upon the lapse rate between the low-level cloud top and the surface. We examined which sounder channel combinations would minimize the total errors in derived cirrus cloud height caused by instrument noise and by the presence of a lower-level cloud. We find that while the sounding channels that peak between 700 and 1000 mb minimize random errors, the sounding channels that peak at 300-500 mb minimize bias errors. For a cloud climatology, the bias errors are most critical.

Baum, Bryan A.↗
NASA NTRS2010

SIM-Lite Mission Spectral Calibration Sensitivities and Refinements

SIM-Lite missions will perform astrometry at microarcsecond accuracy using star light interferometry. For typical baselines that are shorter than 10 meters, this requires to measure optical path difference (OPD) accurate to tens of picometers calling for highly accurate calibration. A major challenge is to calibrate the star spectral dependency in fringe measurements -- the spectral calibration. Previously, we have developed a spectral calibration and estimation scheme achieving picometer level accuracy. In this paper, we present the improvements regarding the application of this scheme from sensitivity studies. Data from the SIM Spectral Calibration Development Unit (SCDU) test facility shows that the fringe OPD is very sensitive to pointings of both beams from the two arms of the interferometer. This sensitivity coupled with a systematic pointing error provides a mechanism to explain the bias changes in 2007. Improving system alignment can effectively reduce this sensitivity and thus errors due to pointing errors. Modeling this sensitivity can lead to further improvement in data processing. We then investigate the sensitivity to a model parameter, the bandwidth used in the fringe model, which presents an interesting trade between systematic and random errors. Finally we show the mitigation of calibration errors due to system drifts by interpolating instrument calibrations. These improvements enable us to use SCDU data to demonstrate that SIM-Lite missions can meet the 1pm noise floor requirement for detecting earth-like exoplanets.

wave front aberration↗
NASA NTRS2000

Global Warming Estimation from MSU: Correction for Drift and Calibration Errors

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz), made in the nadir direction from sequential, sun-synchronous, polar-orbiting NOAA morning satellites (NOAA 6, 10 and 12 that have about 7am/7pm orbital geometry) and afternoon satellites (NOAA 7, 9, 11 and 14 that have about 2am/2pm orbital geometry) are analyzed in this study to derive global temperature trend from 1980 to 1998. In order to remove the discontinuities between the data of the successive satellites and to get a continuous time series, first we have used shortest possible time record of each satellite. In this way we get a preliminary estimate of the global temperature trend of 0.21 K/decade. However, this estimate is affected by systematic time-dependent errors. One such error is the instrument calibration error. This error can be inferred whenever there are overlapping measurements made by two satellites over an extended period of time. From the available successive satellite data we have taken the longest possible time record of each satellite to form the time series during the period 1980 to 1998 to this error. We find we can decrease the global temperature trend by about 0.07 K/decade. In addition there are systematic time dependent errors present in the data that are introduced by the drift in the satellite orbital geometry arises from the diurnal cycle in temperature which is the drift related change in the calibration of the MSU. In order to analyze the nature of these drift related errors the multi-satellite Ch 2 data set is partitioned into am and pm subsets to create two independent time series. The error can be assessed in the am and pm data of Ch 2 on land and can be eliminated. Observations made in the MSU Ch 1 (50.3 GHz) support this approach. The error is obvious only in the difference between the pm and am observations of Ch 2 over the ocean. We have followed two different paths to assess the impact of the errors on the global temperature trend. In one path the entire error is placed in the am data while in the other it is placed in the pm data. Global temperature trend is increased or decreased by about 0.03 K/decade depending upon this placement. Taking into account all random errors and systematic errors our analysis of MSU observations leads us to conclude that a conservative estimate of the global warming is 0. 11 (+-) 0.04 K/decade during 1980 to 1998.

Prabhakara, C.↗
NASA NTRS1972

Error analysis in the Mariner 6 and 7 occultation experiments

The Mariner 6 and 7 occultation experiments provide sets of Doppler residuals from which physical properties of the Martian atmosphere may be derived, such as the ionospheric electron density distribution and the lower atmosphere temperature profile. The Doppler residuals contain both systematic and random errors. The former are removed during the data reduction, and the latter are analyzed to yield error limits on the derived physical properties of the atmosphere.

Stewart, R. W.↗
NASA NTRS1990

Custom CMOS Reed Solomon coder for the Hubble Space Telescope

A VLSI coder is presented that can function either as an encoder or decoder for Reed-Solomon codes. VLSI is one approach to implementing high-performance Reed-Solomon decoders. There are three VLSI technologies that could be used: gate arrays, standard cells, and full custom. The first two approaches are relatively easy to implement, but are limited in both performance and density. Full-custom VLSI is used to achieve both circuit density and speed, and allows control of the amount of interconnect. Speed, which is a function of capacitance, which is a function of interconnect, is an important parameter in high-performance VLSI. A single 8.2 mm x 8.4 mm, 200,000 transistor CMOS chip implementation of the Reed-Solomon code required by the Hubble Space Telescope is reported. The chip features a 10-MHz sustained byte rate independent of error pattern. The 1.6-micron CMOS integrated circuit has complete decoder and encoder functions and uses a single data/system clock. Block lengths up to 255 bytes and shortened codes are supported with no external buffering. Erasure corrections and random error corrections are supported with programmable correction of up to 10 symbol errors. Correction time is independent of error pattern and the number of errors in the incoming message.

Whitaker, S.↗
NASA NTRS2000

Global Warming Estimation from MSU: Correction for Drift and Calibration Errors

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz), made in the nadir direction from sequential, sun-synchronous, polar-orbiting NOAA morning satellites (NOAA 6, 10 and 12 that have approximately 7am/7pm orbital geometry) and. afternoon satellites (NOAA 7, 9, 11 and 14 that have approximately 2am/2pm orbital geometry) are analyzed in this study to derive global temperature trend from 1980 to 1998. In order to remove the discontinuities between the data of the successive satellites and to get a continuous time series, first we have used shortest possible time record of each satellite. In this way we get a preliminary estimate of the global temperature trend of 0.21 K/decade. However, this estimate is affected by systematic time-dependent errors. One such error is the instrument calibration error eo. This error can be inferred whenever there are overlapping measurements made by two satellites over an extended period of time. From the available successive satellite data we have taken the longest possible time record of each satellite to form the time series during the period 1980 to 1998 to this error eo. We find eo can decrease the global temperature trend by approximately 0.07 K/decade. In addition there are systematic time dependent errors ed and ec present in the data that are introduced by the drift in the satellite orbital geometry. ed arises from the diurnal cycle in temperature and ec is the drift related change in the calibration of the MSU. In order to analyze the nature of these drift related errors the multi-satellite Ch 2 data set is partitioned into am and pm subsets to create two independent time series. The error ed can be assessed in the am and pm data of Ch 2 on land and can be eliminated. Observation made in the MSU Ch 1 (50.3 GHz) support this approach. The error ec is obvious only in the difference between the pm and am observations of Ch 2 over the ocean. We have followed two different paths to assess the impact of the error ec on the global temperature trend. In one path the entire error ec is placed in the am data while in the other it is placed in the pm data. Global temperature trend is increased or decreased by approximately 0.03 K/decade depending upon this placement. Taking into account all random errors and systematic errors our analysis of MSU observations leads us to conclude that a conservative estimate of the global warming is 0. 11 (+/-) 0.04 K/decade during 1980 to 1998.

Prabhakara, C.↗
NASA NTRS2004

Why Is Rainfall Error Analysis Requisite for Data Assimilation and Climate Modeling?

Given the large temporal and spatial variability of precipitation processes, errors in rainfall observations are difficult to quantify yet crucial to making effective use of rainfall data for improving atmospheric analysis, weather forecasting, and climate modeling. We highlight the need for developing a quantitative understanding of systematic and random errors in precipitation observations by examining explicit examples of how each type of errors can affect forecasts and analyses in global data assimilation. We characterize the error information needed from the precipitation measurement community and how it may be used to improve data usage within the general framework of analysis techniques, as well as accuracy requirements from the perspective of climate modeling and global data assimilation.

Hou, Arthur Y.↗