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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Highlights of TOMS Version 9 Total Ozone Algorithm

The fundamental basis of TOMS total ozone algorithm was developed some 45 years ago by Dave and Mateer. It was designed to estimate total ozone from satellite measurements of the backscattered UV radiances at few discrete wavelengths in the Huggins ozone absorption band (310-340 nm). Over the years, as the need for higher accuracy in measuring total ozone from space has increased, several improvements to the basic algorithms have been made. They include: better correction for the effects of aerosols and clouds, an improved method to account for the variation in shape of ozone profiles with season, latitude, and total ozone, and a multi-wavelength correction for remaining profile shape errors. These improvements have made it possible to retrieve total ozone with just 3 spectral channels of moderate spectral resolution (approx. 1 nm) with accuracy comparable to state-of-the-art spectral fitting algorithms like DOAS that require high spectral resolution measurements at large number of wavelengths. One of the deficiencies of the TOMS algorithm has been that it doesn't provide an error estimate. This is a particular problem in high latitudes when the profile shape errors become significant and vary with latitude, season, total ozone, and instrument viewing geometry. The primary objective of the TOMS V9 algorithm is to account for these effects in estimating the error bars. This is done by a straightforward implementation of the Rodgers optimum estimation method using a priori ozone profiles and their error covariances matrices constructed using Aura MLS and ozonesonde data. The algorithm produces a vertical ozone profile that contains 1-2.5 pieces of information (degrees of freedom of signal) depending upon solar zenith angle (SZA). The profile is integrated to obtain the total column. We provide information that shows the altitude range in which the profile is best determined by the measurements. One can use this information in data assimilation and analysis. A side benefit of this algorithm is that it is considerably simpler than the present algorithm that uses a database of 1512 profiles to retrieve total ozone. These profiles are tedious to construct and modify. Though conceptually similar to the SBUV V8 algorithm that was developed about a decade ago, the SBUV and TOMS V9 algorithms differ in detail. The TOMS algorithm uses 3 wavelengths to retrieve the profile while the SBUV algorithm uses 6-9 wavelengths, so TOMS provides less profile information. However both algorithms have comparable total ozone information and TOMS V9 can be easily adapted to use additional wavelengths from instruments like GOME, OMI and OMPS to provide better profile information at smaller SZAs. The other significant difference between the two algorithms is that while the SBUV algorithm has been optimized for deriving monthly zonal means by making an appropriate choice of the a priori error covariance matrix, the TOMS algorithm has been optimized for tracking short-term variability using month and latitude dependent covariance matrices.

Bhartia, Pawan↗
NASA NTRS1991

Optimum data weighting and error calibration for estimation of gravitational parameters

A new approach has been developed for determining consistent satellite-tracking data weights in solutions for the satellite-only gravitational models. The method employs subset least-squares solutions of the satellite data contained within the complete solution and requires that the differences of the parameters of subset solutions and the complete solution to be in agreement with their error estimates by adjusting the data weights. GEM-T2 model was recently computed and adjusted through a direct application of this method. The estimated data weights are markedly smaller than the weights implied by the formal uncertainties of the measurements. Orbital arc tests as well as surface gravity comparisons show significant improvements for solutions when more realistic data weighting is achieved.

Lerch, Francis J.↗
NASA NTRS1979

Natural sampling strategy

A natural stratum-based sampling scheme and the aggregation procedures for estimating wheat area, yield, and production and their associated prediction error estimates are described. The methodology utilizes LANDSAT imagery and agrophysical data to permit an improved stratification in foreign areas by ignoring political boundaries and restratifying along boundaries that are more homogeneous with respect to the distribution of agricultural density, soil characteristics, and average climatic conditions. A summary of test results is given including a discussion of the various problems encountered.

Hallum, C. R.↗
NASA NTRS1985

Theoretical and experimental investigations of sensor location for optimal aeroelastic system state estimation

One of the major concerns in the design of an active control system is obtaining the information needed for effective feedback. This involves the combination of sensing and estimation. A sensor location index is defined as the weighted sum of the mean square estimation errors in which the sensor locations can be regarded as estimator design parameters. The design goal is to choose these locations to minimize the sensor location index. The choice of the number of sensors is a tradeoff between the estimation quality based upon the same performance index and the total costs of installing and maintaining extra sensors. An experimental study for choosing the sensor location was conducted on an aeroelastic system. The system modeling which includes the unsteady aerodynamics model developed by Stephen Rock was improved. Experimental results verify the trend of the theoretical predictions of the sensor location index for different sensor locations at various wind speeds.

Liu, G.↗
NASA NTRS2015

Predicting Space Weather Effects on Close Approach Events

The NASA Robotic Conjunction Assessment Risk Analysis (CARA) team sends ephemeris data to the Joint Space Operations Center (JSpOC) for conjunction assessment screening against the JSpOC high accuracy catalog and then assesses risk posed to protected assets from predicted close approaches. Since most spacecraft supported by the CARA team are located in LEO orbits, atmospheric drag is the primary source of state estimate uncertainty. Drag magnitude and uncertainty is directly governed by atmospheric density and thus space weather. At present the actual effect of space weather on atmospheric density cannot be accurately predicted because most atmospheric density models are empirical in nature, which do not perform well in prediction. The Jacchia-Bowman-HASDM 2009 (JBH09) atmospheric density model used at the JSpOC employs a solar storm active compensation feature that predicts storm sizes and arrival times and thus the resulting neutral density alterations. With this feature, estimation errors can occur in either direction (i.e., over- or under-estimation of density and thus drag). Although the exact effect of a solar storm on atmospheric drag cannot be determined, one can explore the effects of JBH09 model error on conjuncting objects' trajectories to determine if a conjunction is likely to become riskier, less risky, or pass unaffected. The CARA team has constructed a Space Weather Trade-Space tool that systematically alters the drag situation for the conjuncting objects and recalculates the probability of collision for each case to determine the range of possible effects on the collision risk. In addition to a review of the theory and the particulars of the tool, the different types of observed output will be explained, along with statistics of their frequency.

Space Weather↗
NASA NTRS2016

An Optimal-Estimation-Based Aerosol Retrieval Algorithm Using OMI Near-UV Observations

An optimal-estimation(OE)-based aerosol retrieval algorithm using the OMI (Ozone Monitoring Instrument) near-ultraviolet observation was developed in this study. The OE-based algorithm has the merit of providing useful estimates of errors simultaneously with the inversion products. Furthermore, instead of using the traditional lookup tables for inversion, it performs online radiative transfer calculations with the VLIDORT (linearized pseudo-spherical vector discrete ordinate radiative transfer code) to eliminate interpolation errors and improve stability. The measurements and inversion products of the Distributed Regional Aerosol Gridded Observation Network campaign in northeast Asia (DRAGON NE-Asia 2012) were used to validate the retrieved aerosol optical thickness (AOT) and single scattering albedo (SSA). The retrieved AOT and SSA at 388 nm have a correlation with the Aerosol Robotic Network (AERONET) products that is comparable to or better than the correlation with the operational product during the campaign. The OEbased estimated error represented the variance of actual biases of AOT at 388 nm between the retrieval and AERONET measurements better than the operational error estimates. The forward model parameter errors were analyzed separately for both AOT and SSA retrievals. The surface reflectance at 388 nm, the imaginary part of the refractive index at 354 nm, and the number fine-mode fraction (FMF) were found to be the most important parameters affecting the retrieval accuracy of AOT, while FMF was the most important parameter for the SSA retrieval. The additional information provided with the retrievals, including the estimated error and degrees of freedom, is expected to be valuable for relevant studies. Detailed advantages of using the OE method were described and discussed in this paper.

Air Pollution↗
NASA NTRS2004

Estimation of Aperture Errors with Direct Interferometer-Output Feedback for Spacecraft Formation Control

Long-baseline space interferometers involving formation flying of multiple spacecraft hold great promise as future space missions for high-resolution imagery. The major challenge of obtaining high-quality interferometric synthesized images from long-baseline space interferometers is to control these spacecraft and their optics payloads in the specified configuration accurately. In this paper, we describe our effort toward fine control of long-baseline space interferometers without resorting to additional sensing equipment. We present an estimation procedure that effectively extracts relative x/y translational exit pupil aperture deviations from the raw interferometric image with small estimation errors.

Lu, Hui-Ling↗
NASA NTRS2003

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Salem, Jonathan A.↗
NASA NTRS2017

What is the Uncertainty in MODIS Aerosol Optical Depth in the Vicinity of Clouds?

MODIS dark-target (DT) algorithm retrieves aerosol optical depth (AOD) using a Look Up Table (LUT) approach. Global comparison of AOD (Collection 6 ) with ground-based sun photometer gives an Estimated Error (EE) of +/-(0.04 + 10%) over ocean. However, EE does not represent per-retrieval uncertainty. For retrievals that are biased high compared to AERONET, here we aim to closely examine the contribution of biases due to presence of clouds and per-pixel retrieval uncertainty. We have characterized AOD uncertainty at 550 nm, due to standard deviation of reflectance in 10 km retrieval region, uncertainty related to gas (H2O, O3) absorption, surface albedo, and aerosol models. The uncertainty in retrieved AOD seems to lie within the estimated over ocean error envelope of +/-(0.03+10%). Regions between broken clouds tend to have higher uncertainty. Compared to C6 AOD, a retrieval omitting observations in the vicinity of clouds (< or = 1 km) is biased by about +/- 0.05. For homogeneous aerosol distribution, clear sky retrievals show near zero bias. Close look at per-pixel reflectance histograms suggests retrieval possibility using median reflectance values.

Patadia, Falguni↗
NASA NTRS2011

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Keppenne, Christian↗
NASA NTRS1984

Accuracy of velocity and power determination by the Doppler method

When designing a Mesosphere-Stratosphere-Troposphere (MST) radar antenna one has to trade between the choices to optimize the effective aperture or to optimize the sidelobe suppression. An optimization of the aperture increases the sensitivity. Suppression of side-lobes by tapering attenuates undesirable signals which spoil the estimates of reflectivity and velocity. Generally, any sidelobe effects are equivalent to a broadening of the antenna beam. The return signal is due to a product of the antenna pattern with the varying atmospheric reflectivity structures. Thus, knowing the antenna pattern, it is in principle possible to find the signal spectra, which, however, may be a tedious computational and ambiguous procedure. For vertically pointing main beams the sidelobe effects are efficiently suppressed because of the aspect sensitivity. It follows that sidelobes are a minor problem for spaced antenna methods. However, they can be crucial for Doppler methods, which need off-vertical beams. If a sidelobe is pointing towards the zenith a larger power may be received from the vertical than off-vertical directions, but quantitative estimates of this effect are not yet known. To get an error estimate of sidelobe effects with an off-vertical main beam a 1-dimensional example is considered.

Rottger, J.↗
NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗
NASA NTRS1995

An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Fukumori, Ichiro↗
NASA NTRS1995

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Kalman filter smoother modeling ocean simulation↗
NASA NTRS1994

An Approximate Kalman Filter for Ocean Data Assimilation; An Example with an Idealized Gulf Stream Model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady-state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudo measurements is examined, including velocity, density, and volume transport at localized arrays, and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform a previous study that used an empirical nudging scheme. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

['Kalman↗
NASA NTRSDate not supplied

Hybrid Flush and Synthetic Air Data Filter for Entry Vehicle Atmospheric State Estimation

A hybrid flush/synthetic air data sensing filter for entry vehicle atmosphere estimation is developed. The approach makes use of a Kalman-Schmidt and Rauch-Tung-Streibel smoother. The filter/smoother blends information from pressure sensors distributed on the heatshield with pseudo-measurements of the vehicle aerodynamic forces and moments computed from mass properties and inertial measurement unit data, and prior estimates of the atmosphere. The filter produces estimates of the atmospheric conditions along the entry trajectory, and systematic error estimates to reconcile differences between the pressure and aerodynamic data sources. The filter is applied to data acquired during the Mars 2020 entry, descent, and landing at Jezero crater on February 18th, 2021. The final paper will also include results from the Mars Science Laboratory entry, descent, and landing.

Chris D. Karlgaard↗