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NASA NTRS1993

AVIRIS calibration and application in coastal oceanic environments - Tracers of soluble and particulate constituents of the Tampa Bay coastal plume

AVIRIS is a testbed for future spacecraft sensors (such as HIRIS and MODIS) planned for the Earth Observing System. Model-derived absorption coefficients at 415 nm, a(415), and back-scattering coefficients at 671 nm, b sub b (671) for Tampa Bay waters were used to create images from AVIRIS data of the dissolved component of a(415) due to gelbstoff, a sub g (415), and salinity. Images of a sub g (415), salinity, and b sub b (671) were used to depict the distribution of dissolved and particulate constituents, respectively, for Tampa Bay plume during late, ebb-tidal conditions. Salinity covaried with a sub g (415), which provided a means of mapping salinity from the a sub g (415) imagery. The concentration of suspended particles, as inferred from b sub g (671), was extremely variable in the shallow regions where waves and currents interacted. Pollutants covarying with fresh water or suspended sediments can be mapped from a sub g (415) and b sub b (671) images, respectively.

Carder, K. L.↗
NASA NTRS1993

Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

Yueh, Simon H.↗
NASA NTRS1993

Estimating the instabilities of N clocks by means of comparison measurements

The estimation of individual instabilities of N clocks, compared by measuring the differences of their readings, is considered without assuming a priori any hypotheses on their uncorrelation. Instabilities of the N clocks are described by a complete (non-diagonal) N x N covariance matrix R. Only differences of clock readings are available in order to estimate R. Statistical processing of these data allows one to calculate the (N-1)x(N-l) covariance matrix S of the differences relative to the N-th(reference) clock. By analyzing the relationships tying R and S, several pieces of information can be inferred and, in particular, the conditions for the validity of the uncorrelation hypothesis are established. The estimation of R from S is not unique: in any case R must be positive definite. A theorem states that R is positive definite if and only if its determinant is positive. Nevertheless infinitely many acceptable choices of R still fulfill the condition of positive definiteness. This paper shows that, by increasing the number N of compared clocks, the amount of arbitrariness in estimating R is reduced. The analysis of some experimental data illustrates the capability of the method.

Premoli, Amedeo↗
NASA NTRS1994

Performance analysis of an integrated GPS/inertial attitude determination system

The performance of an integrated GPS/inertial attitude determination system is investigated using a linear covariance analysis. The principles of GPS interferometry are reviewed, and the major error sources of both interferometers and gyroscopes are discussed and modeled. A new figure of merit, attitude dilution of precision (ADOP), is defined for two possible GPS attitude determination methods, namely single difference and double difference interferometry. Based on this figure of merit, a satellite selection scheme is proposed. The performance of the integrated GPS/inertial attitude determination system is determined using a linear covariance analysis. Based on this analysis, it is concluded that the baseline errors (i.e., knowledge of the GPS interferometer baseline relative to the vehicle coordinate system) are the limiting factor in system performance. By reducing baseline errors, it should be possible to use lower quality gyroscopes without significantly reducing performance. For the cases considered, single difference interferometry is only marginally better than double difference interferometry. Finally, the performance of the system is found to be relatively insensitive to the satellite selection technique.

Sullivan, Wendy I.↗
NASA NTRS1994

Spacecraft-spacecraft radio-metric tracking: Signal acquisition requirements and application to Mars approach navigation

Doppler and ranging measurements between spacecraft can be obtained only when the ratio of the total received signal power to noise power density (P(sub t)/N(sub 0)) at the receiving spacecraft is sufficiently large that reliable signal detection can be achieved within a reasonable time period. In this article, the requirement on P(sub t)/N(sub 0) for reliable carrier signal detection is calculated as a function of various system parameters, including characteristics of the spacecraft computing hardware and a priori uncertainty in spacecraft-spacecraft relative velocity and acceleration. Also calculated is the P(sub t)/N(sub 0) requirements for reliable detection of a ranging signal, consisting of a carrier with pseudonoise (PN) phase modulation. Once the P(sub t)/N(sub 0) requirement is determined, then for a given set of assumed spacecraft telecommunication characteristics (transmitted signal power, antenna gains, and receiver noise temperatures) it is possible to calculate the maximum range at which a carrier signal or ranging signal may be acquired. For example, if a Mars lander and a spacecraft approaching Mars are each equipped with 1-m-diameter antennas, the transmitted power is 5 W, and the receiver noise temperatures are 350 K, then S-band carrier signal acquisition can be achieved at ranges exceeding 10 million km. An error covariance analysis illustrates the utility of in situ Doppler and ranging measurements for Mars approach navigation. Covariance analysis results indicate that navigation accuracies of a few km can be achieved with either data type. The analysis also illustrates dependency of the achievable accuracy on the approach trajectory velocity.

Kahn, R. D.↗
NASA NTRS1994

Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude

Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.

Sedlak, J.↗
NASA NTRS1994

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗
NASA NTRS1993

Polarimetric radar data decomposition and interpretation

Significant efforts have been made to decompose polarimetric radar data into several simple scattering components. The components which are selected because of their physical significance can be used to classify SAR (Synthetic Aperture Radar) image data. If particular components can be related to forest parameters, inversion procedures may be developed to estimate these parameters from the scattering components. Several methods have been used to decompose an averaged Stoke's matrix or covariance matrix into three components representing odd (surface), even (double-bounce) and diffuse (volume) scatterings. With these decomposition techniques, phenomena, such as canopy-ground interactions, randomness of orientation, and size of scatters can be examined from SAR data. In this study we applied the method recently reported by van Zyl (1992) to decompose averaged backscattering covariance matrices extracted from JPL SAR images over forest stands in Maine, USA. These stands are mostly mixed stands of coniferous and deciduous trees. Biomass data have been derived from field measurements of DBH and tree density using allometric equations. The interpretation of the decompositions and relationships with measured stand biomass are presented in this paper.

Sun, Guoqing↗
NASA NTRS1994

A geopotential model from satellite tracking, altimeter, and surface gravity data: GEM-T3

An improved model of Earth's gravitational field, Goddard Earth Model T-3 (GEM-T3), has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM-T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM-T3 uses altimeter data from GEOS 3 (1975-1976), Seasat (1978) and Geosat (1986-1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long-wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes Tracking Network (TRANET) Doppler, optical, and satellite-to-satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM-T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65 deg N and 60 deg S latitudes in GEM-T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long-wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM-T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM-T3.

Lerch, F. J.↗
NASA NTRS1994

Shortwave feedbacks and El Nino-Southern Oscillation: Forced ocean coupled ocean-atmosphere experiments

Changes in tropical sea surface temperature (SST) can produce changes in cloudiness that modify incoming solar shortwave (SW) radiation, which in turn affects SST. The effects of this negative feedback on Pacific interannual variability are examined in forced ocean model and hybrid coupled ocean-atmosphere model simulations. Two empirical schemes are used to model the large-scale, low-frequency response of surface SW to SST anomalies. The first scheme attempts to account for the nonlocal nature of the atmospheric response to SST based patterns of covariability analyzed through singular value decomposition. In the observations the primary coupled mode of variability is composed of a SW anomaly in the central Pacific that covaries with anomalous SST in the eastern Pacific. This is applied in the model as a nonlocal feedback. The second scheme examines the effects of a purely local feedback with a spatially varying coefficient of magnitude chosen similar to the first scheme. In almost all cases the second scheme behaved similarly to the first, presumably because the correlation scale of SST is large enough for El Nino-Southern Oscillation (ENSO) dynamics that there is little sensitivity to the local approximation in the SW feedback. In simulations forced by time series of observed wind stress the SW feedback induced very minor SST damping. Results for a simpified heat budget analysis showed that while the SW feedback increased the local heat flux damping on SST, it also induced a mean shallowing of the mixed layer. The resulting changes in both the local mean vertical temperature gradient and the zonal velocity response to the wind stress acted to oppose the local heat flux damping effects. When the observed SW anomalies were applied to forced simulations, the simulated SST anomalies were modified as expected, and agreement with observed SST improved. In coupled simulations the SW feedbacks had greater impact than in the case of specified stress. The main effects were to decrease the magnitude of the warm and cold SST anomalies in the central Pacific, while leaving the pattern and evolution of ENSO anomalies essentially unchanged elsewhere. The SW feedbacks thus produce a modest improvement of the model ENSO SST pattern compared with observations, although they tended to shorten the period of the model ENSO cycle. Overall the results suggest that large-scale SW feedbacks are of quantitative importance to simulating some aspects of the ENSO cycle but are not critical to the overall occurrence of the phenomenon.

Waliser, Duane E.↗
NASA NTRS1995

Another look at the UBV variability of T Tauri stars

The UBV variability of classical T Tauri stars is investigated using a large data set compiled by Herbst et al. (1994). The analysis is based on the covariance of the UBV colors, which is independent of the obscuration and the temporal sampling, and is a powerful tool for finding trends that otherwise would be hidden in the complex time-dependence of the data. I find that there are two types of UBV variability and introduce the nomenclature 'ortho-' and 'para-UBV' variations, or in short 'type-O' and 'type-P' variations. Objects with a predominance of ortho-UBV variability show strong variability in both the Balmer and Paschen continua, whereas objects dominated by para-UBV changes vary mostly in the Paschen continuum. I show that type-O variations can be explained in terms of rotating spots, variable obscuration, or changes intrinsic to the source that obey the law Delta T(sub S)/T(sub S) varies as Delta n(sub H)/n(sub H), where T(sub S) and n(sub H) are, respectively, the gas temperature and the number density of hydrogen nuclei. Type-P variations can be explained only by changes intrinsic to the source with Delta T(sub S)/T(sub S) varies as - Delta n(sub H)/n(sub H), and I speculate on a possible origin for these changes. The covariance ellipse of the UBV colors is a versatile tool for studying the connection between variability and other spectral signatures of classical T Tauri stars; its use for this purpose is illustrated by studying the correlation between the presence of CO first-overtone bands in emission and the type of variability. I find that objects with CO band emission are also those with type-P variability and propose an observational test to validate this conclusion.

Safier, Pedro N.↗
NASA NTRS1996

Conflict Probability Estimation for Free Flight

The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.

Paielli, Russell A.↗
NASA NTRS1996

Multilevel Algorithm for Atmospheric Data Assimilation

A multiscale algorithm for the problem of optimal statistical interpolation of observed data has been developed. This problem includes the calculation of the vector of the 'analyzed' (best estimated) atmosphere flow field w(sup a) by the formula: w(sup a) = w(sup f) + P(sup f) H(sup T) y, where the quantity y is defined by the equation (H P(sup f) H(sup T) + R)y = w(sup o) - H w(sup f), using the given model forecast first guess w(sup f) and the vector of observations w(sup o); H is an interpolation operator from the regular grid to the observation network, P(sup f) is the forecast error covariance matrix, and R is the observation error covariance matrix. At this initial stage the case of univariate analysis of single level radiosonde height data is considered. The matrix R is assumed to be diagonal, and the matrix P(sup f) is assumed to be given by the formula P(sub ij)(sup f) = sigma(sub i)(sup f) mu(sub ij) sigma(sub j)(sub f), where mu(sub ij) is a smooth, decreasing function of the distance between the i-th and the j-th points. In this paper we describe a multiscale iterative process based on a multiresolution, simultaneous displacement technique and a localized variational calculation of iteration parameters.

Brandt, Achi↗
NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗
NASA NTRS1997

A Predictive Attitude Determination Algorithm

In this paper, a new and efficient algorithm is developed for attitude determination from vector observations. The new algorithm, called the Predictive Attitude Determination (PAD) algorithm, is derived from a general nonlinear predictive filter approach. Traditional deterministic algorithms are shown to be suboptimal for anisotropic measurement errors. The major advantage of the PAD algorithm is that it can be easily applied to the case where anisotropic measurement errors exist. Also, an analytical expression is derived for the steady-state attitude error covariance, which is shown to be equivalent to the optimal covariance derived from maximum likelihood techniques. Simulation studies indicate that the new algorithm is able to accurately determine the attitude of a spacecraft, even for radically anisotropic measurement errors.

Markley, F. Landis↗
NASA NTRS1998

Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation

A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.

Chang, Lang-Ping↗
NASA NTRS1998

Efficient Methods to Assimilate Satellite Retrievals Based on Information Content: Suboptimal Retrieval Assimilation - Part 2

One of the outstanding problems in data assimilation has been and continues to be how best to utilize satellite data while balancing the tradeoff between accuracy and computational cost. A number of weather prediction centers have recently achieved remarkable success in improving their forecast skill by changing the method by which satellite data are assimilated into the forecast model from the traditional approach of assimilating retrievals to the direct assimilation of radiances in a variational framework. The operational implementation of such a substantial change in methodology involves a great number of technical details, e.g., pertaining to quality control procedures, systematic error correction techniques, and tuning of the statistical parameters in the analysis algorithm. Although there are clear theoretical advantages to the direct radiance assimilation approach, it is not obvious at all to what extent the improvements that have been obtained so far can be attributed to the change in methodology, or to various technical aspects of the implementation. The issue is of interest because retrieval assimilation retains many practical and logistical advantages which may become even more significant in the near future when increasingly high-volume data sources become available. The central question we address here is: how much improvement can we expect from assimilating radiances rather than retrievals, all other things being equal? We compare the two approaches in a simplified one-dimensional theoretical framework, in which problems related to quality control and systematic error correction are conveniently absent. By assuming a perfect radiative transfer model and perfect knowledge of radiance and background error covariances, we are able to formulate a nonlinear local error analysis for each assimilation method. Direct radiance assimilation is optimal in this idealized context, while the traditional method of assimilating retrievals is suboptimal because it ignores the cross-covariances between background errors and retrieval errors. We show that interactive retrieval assimilation (where the same background used for assimilation is also used in the retrieval step) is equivalent to direct assimilation of radiances with suboptimal analysis weights. We illustrate and extend these theoretical arguments with several one-dimensional assimilation experiments, where we estimate vertical atmospheric profiles using simulated data from both the High-resolution InfraRed Sounder 2 (HIRS2) and the future Atmospheric InfraRed Sounder (AIRS).

Joiner, J.↗
NASA NTRS1998

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗