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NASA NTRS2019

Prior biosphere model impact on global terrestrial CO2 fluxes estimated from OCO-2 retrievals

This study assesses the impact of different state of the art global biospheric CO2 flux models, when applied as prior information, on inverse model “top-down” estimates of terrestrial CO2 fluxes obtained when assimilating Orbiting Carbon Observatory 2 (OCO-2) observations. This is done with a series of observing system simulation experiments (OSSEs) using synthetic CO2 column-average dry air mole fraction (XCO2) retrievals sampled at the OCO-2 satellite spatiotemporal frequency. The OSSEs utilized a 4-D variational (4D-Var) assimilation system with the GEOS-Chem global chemical transport model (CTM) to estimate CO2 net ecosystem exchange (NEE) fluxes using synthetic OCO-2 observations. The impact of biosphere models in inverse model estimates of NEE is quantified by conducting OSSEs using the NASA-CASA, CASA-GFED, SiB-4, and LPJ models as prior estimates and using NEE from the multi-model ensemble mean of the Multiscale Synthesis and Terrestrial Model Intercomparison Project as the “truth”. Results show that the assimilation of simulated XCO2 retrievals at OCO-2 observing modes over land results in posterior NEE estimates which generally reproduce “true” NEE globally and over terrestrial TransCom-3 regions that are well-sampled. However, we find larger spread among posterior NEE estimates, when using different prior NEE fluxes, in regions and seasons that have limited OCO-2 observational coverage and a large range in “bottom-up” NEE fluxes. Seasonally averaged posterior NEE estimates had standard deviations (SD) of ∼10 % to ∼50 % of the multi-model-mean NEE for different TransCom-3 land regions with significant NEE fluxes (regions/seasons with a NEE flux ≥0.5 PgC/yr). On a global average, the seasonally averaged residual impact of the prior model NEE assumption on the posterior NEE spread is ∼10 %–20 % of the posterior NEE mean. Additional OCO-2 OSSE simulations demonstrate that posterior NEE estimates are also sensitive to the assumed prior NEE flux uncertainty statistics, with spread in posterior NEE estimates similar to those when using variable prior model NEE fluxes. In fact, the sensitivity of posterior NEE estimates to prior error statistics was larger than prior flux values in some regions/times in the tropics and Southern Hemisphere where sufficient OCO-2 data were available and large differences between the prior and truth were evident. Overall, even with the availability of spatiotemporally dense OCO-2 data, noticeable residual differences (up to ∼20 %–30 % globally and 50 % regionally) in posterior NEE flux estimates remain that were caused by the choice of prior model flux values and the specification of prior flux uncertainties.

Sajeev Philip↗

NASA NTRSDate not supplied

Development of the GeoNEX Level 2G Products: Exploiting the Diurnal Variability of TOA Reflectance in Atmospheric Correction

This study develops a new atmospheric correction algorithm to generate the Level 2G products, in particular the gap-filled Surface Reflectance at 10-minute time steps, for the Geostationary-NASA Earth Exchange (GeoNEX) project. The algorithm is based on the MODIS MAIAC (Multi-Angle Implementation of Atmospheric Correction) framework but with significant modifications to exploit angular/temporal information from the diurnal variability of the GeoNEX L1G TOA (Top-of-Atmosphere) reflectance. The algorithm starts by evaluating the roughness/smoothness of the diurnal time series of the TOA reflectance. Because rapid changes in TOA reflectance are generally caused by passing clouds or shadows, rough segments of the time series are automatically filtered out while the smooth segments are further tested for brightness and temperature to identify clear-sky and snow-free observations. Next the algorithm runs the MAIAC RTM (Radiative Transfer Model) to retrieve the Ross-Thick-Li-Sparse (RTLS) BRDF model parameters and the daily-mean atmospheric optical depth (AOD) that allow the RTM to optimally simulate the observed diurnal variability of clear-sky TOA reflectance. Once the initial RTLS parameters are retrieved after the algorithm’s burn-in period, they are used as the prior information to predict the AOD level for the next days, while the subsequent clear-sky observations are used to make necessary adjustments to the RTLS parameters in an continuous fashion. This “prediction-analysis” cycle is then iterated to process the full time series of the L1G data, skipping only total-cloudy days or when surface snow is detected. We tested the algorithm over a list of selected AERONET sites. The retrieved results (the daily mean AOD and the RTLS parameters) reasonably agree with the ground-based measurements. Importantly, the results indicate that the diurnal cycles of surface reflectance are continuous functions of the illumination-view geometry. Thus we can use the retrieved RTLS model to accurately fill in data gaps on partial cloudy days. Also, our algorithm is totally independent from the traditional approaches based on the use of spectral band ratios between the shortwave infrared (e.g., 2.2µm) and the visible (e.g., 0.47µm and 0.64µm) bands. Our results thus demonstrate that the high-frequent diurnal geostationary observations contain unique information that helps us improve atmospheric correction of remote sensing data.

GeoNEX↗

NASA NTRS2010

Simulation of Micron-Sized Debris Populations in Low Earth Orbit

The update of ORDEM2000, the NASA Orbital Debris Engineering Model, to its new version ORDEM2010, is nearly complete. As a part of the ORDEM upgrade, this paper addresses the simulation of micro-debris (greater than 10 m and smaller than 1 mm in size) populations in low Earth orbit. The principal data used in the modeling of the micron-sized debris populations are in-situ hypervelocity impact records, accumulated in post-flight damage surveys on the space-exposed surfaces of returned spacecrafts. The development of the micro-debris model populations follows the general approach to deriving other ORDEM2010-required input populations for various components and types of debris. This paper describes the key elements and major steps in the statistical inference of the ORDEM2010 micro-debris populations. A crucial step is the construction of a degradation/ejecta source model to provide prior information on the micron-sized objects (such as orbital and object-size distributions). Another critical step is to link model populations with data, which is rather involved. It demands detailed information on area-time/directionality for all the space-exposed elements of a shuttle orbiter and damage laws, which relate impact damage with the physical properties of a projectile and impact conditions such as impact angle and velocity. Also needed are model-predicted debris fluxes as a function of object size and impact velocity from all possible directions. In spite of the very limited quantity of the available shuttle impact data, the population-derivation process is satisfactorily stable. Final modeling results obtained from shuttle window and radiator impact data are reasonably convergent and consistent, especially for the debris populations with object-size thresholds at 10 and 100 m.

Xu, Y.-L.↗

NASA NTRS2010

Simulation of Micron-Sized Debris Populations in Low Earth Orbit

The update of ORDEM2000, the NASA Orbital Debris Engineering Model, to its new version . ORDEM2010, is nearly complete. As a part of the ORDEM upgrade, this paper addresses the simulation of micro-debris (greater than 10 micron and smaller than 1 mm in size) populations in low Earth orbit. The principal data used in the modeling of the micron-sized debris populations are in-situ hypervelocity impact records, accumulated in post-flight damage surveys on the space-exposed surfaces of returned spacecrafts. The development of the micro-debris model populations follows the general approach to deriving other ORDEM2010-required input populations for various components and types of debris. This paper describes the key elements and major steps in the statistical inference of the ORDEM2010 micro-debris populations. A crucial step is the construction of a degradation/ejecta source model to provide prior information on the micron-sized objects (such as orbital and object-size distributions). Another critical step is to link model populations with data, which is rather involved. It demands detailed information on area-time/directionality for all the space-exposed elements of a shuttle orbiter and damage laws, which relate impact damage with the physical properties of a projectile and impact conditions such as impact angle and velocity. Also needed are model-predicted debris fluxes as a function of object size and impact velocity from all possible directions. In spite of the very limited quantity of the available shuttle impact data, the population-derivation process is satisfactorily stable. Final modeling results obtained from shuttle window and radiator impact data are reasonably convergent and consistent, especially for the debris populations with object-size thresholds at 10 and 100 micron.

Xu, Y.-L.↗

NASA NTRS1975

Estimating proportions of objects from multispectral scanner data

Progress is reported in developing and testing methods of estimating, from multispectral scanner data, proportions of target classes in a scene when there are a significiant number of boundary pixels. Procedures were developed to exploit: (1) prior information concerning the number of object classes normally occurring in a pixel, and (2) spectral information extracted from signals of adjoining pixels. Two algorithms, LIMMIX and nine-point mixtures, are described along with supporting processing techniques. An important by-product of the procedures, in contrast to the previous method, is that they are often appropriate when the number of spectral bands is small. Preliminary tests on LANDSAT data sets, where target classes were (1) lakes and ponds, and (2) agricultural crops were encouraging.

Horwitz, H. M.↗

NASA NTRS1981

Texture measurements from Seasat - SAR images for urban land use interpretation

Different grey tones in Seasat Synthetic Aperture Radar (SAR) images for the same type of urban land cover considerably impair the possibilities of establishing automatic classification procedures for these types of data. Since the orientation of the main features like street patterns and buildings with respect to the azimuth angle of the radar antenna is the crucial factor for the observed differences in grey tone, prior information on these elements and special processing of the data would be required to eliminate this effect. Another approach suggested in this paper is to make use of the textural information in the image rather than of its grey tone. For different study sites within the Los Angeles urbanized area texture measures could be derived which result in characteristic values for specific types of land cover and are largely independent of the azimuth angle effect. At the same time the results for the study area indicate an improvement of the overall separability for the different land cover types included in the analysis.

Fasler, F.↗

NASA NTRS1981

ICAP - An Interactive Cluster Analysis Procedure for analyzing remotely sensed data

An Interactive Cluster Analysis Procedure (ICAP) was developed to derive classifier training statistics from remotely sensed data. ICAP differs from conventional clustering algorithms by allowing the analyst to optimize the cluster configuration by inspection, rather than by manipulating process parameters. Control of the clustering process alternates between the algorithm, which creates new centroids and forms clusters, and the analyst, who can evaluate and elect to modify the cluster structure. Clusters can be deleted, or lumped together pairwise, or new centroids can be added. A summary of the cluster statistics can be requested to facilitate cluster manipulation. The principal advantage of this approach is that it allows prior information (when available) to be used directly in the analysis, since the analyst interacts with ICAP in a straightforward manner, using basic terms with which he is more likely to be familiar. Results from testing ICAP showed that an informed use of ICAP can improve classification, as compared to an existing cluster analysis procedure.

Wharton, S. W.↗

NASA NTRS1983

Design criteria and eigensequence plots for satellite computed tomography

The use of the degrees of freedom for signal is proposed as a design criteria for comparing different designs for satellite and other measuring systems. It is also proposed that certain eigensequence plots be examined at the design stage along with appropriate estimates of the parameter lambda playing the role of noise to signal ratio. The degrees of freedom for signal and the eigensequence plots may be determined using prior information in the spectral domain which is presently available along with a description of the system, and simulated data for estimating lambda. This work extends the 1972 work of Weinreb and Crosby.

Wahba, G.↗

NASA NTRS1985

Design criteria and eigensequence plots for satellite-computed tomography

Wahba, G.↗

NASA NTRS1985

The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Bloxham, J.↗

NASA NTRS1987

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios↗

NASA NTRS1987

Spherical harmonic expansion of the Levitus Sea surface topography

Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.

Engelis, Theodossios↗

NASA NTRS1988

On the simultaneous improvement of a satellite orbit and determination of sea surface topography using altimeter data

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface toography with minimum wavelengths of about 500 km and to reduce the radial orbit errors caused by geopotential uncertainties. The modeling of these errors is made using the linearized Lagrangian perturbation theory. Observation equations are developed using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information can then provide estimates of parametrs representing the sea surface topography and corrections to the orbit. The potential of the method is demonstrated in a solution where simulated geopotential errors and the Levitus sea surface topography are used to generate the observables for a Seasat 3 day arc. The simulation results suggest that the method can be used to efficiently process real altimeter data.

Engelis, Theodossios↗

NASA NTRS1989

Confidence set inference with a prior quadratic bound

Backus, George E.↗

NASA NTRS1988

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Backus, George E.↗

NASA NTRS1989

Confidence set interference with a prior quadratic bound

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

Backus, George E.↗

NASA NTRS1989

Adaptive control: Stability, convergence, and robustness

The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.

Sastry, Shankar↗

NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗