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NASA NTRS2012

A Practical Methodology for Quantifying Random and Systematic Components of Unexplained Variance in a Wind Tunnel

This paper documents a check standard wind tunnel test conducted in the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3M TCT) that was designed and analyzed using the Modern Design of Experiments (MDOE). The test designed to partition the unexplained variance of typical wind tunnel data samples into two constituent components, one attributable to ordinary random error, and one attributable to systematic error induced by covariate effects. Covariate effects in wind tunnel testing are discussed, with examples. The impact of systematic (non-random) unexplained variance on the statistical independence of sequential measurements is reviewed. The corresponding correlation among experimental errors is discussed, as is the impact of such correlation on experimental results generally. The specific experiment documented herein was organized as a formal test for the presence of unexplained variance in representative samples of wind tunnel data, in order to quantify the frequency with which such systematic error was detected, and its magnitude relative to ordinary random error. Levels of systematic and random error reported here are representative of those quantified in other facilities, as cited in the references.

Deloach, Richard↗
NASA NTRS2012

Characterization of Turbulent Latent and Sensible Heat Flux Exchange Between the Atmosphere and Ocean in MERRA

Turbulent fluxes of heat and moisture across the atmosphere-ocean interface are fundamental components of the Earth's energy and water balance. Characterizing both the spatiotemporal variability and the fidelity of these exchanges of heat and moisture is critical to understanding the global water and energy cycle variations, quantifying atmosphere-ocean feedbacks, and improving model predictability. This study examines the veracity of the recently completed NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) product with respect to its representation of the surface turbulent heat fluxes. A validation of MERRA turbulent heat fluxes and near-surface bulk variables at local, high-resolution space and time scales is achieved by making comparisons to a large suite of direct observations. Both in situ and satellite-observed gridded surface heat flux estimates are employed to investigate the spatial and temporal variability of the surface fluxes with respect to their annual mean climatologies, their seasonal covariability of near-surface bulk parameters, and their representation of extremes. The impact of data assimilation on the near-surface parameters is assessed through evaluation of incremental analysis update tendencies produced by the assimilation procedure. It is found that MERRA turbulent surface heat fluxes are relatively accurate for typical conditions but have systematically weak vertical gradients in moisture and temperature and have a weaker covariability between the near-surface gradients and wind speed than found in observations. This results in an underestimate of the surface latent and sensible heat fluxes over the western boundary current and storm track regions. The assimilation of observations mostly acts to bring MERRA closer to observational products by increasing moisture and temperature near the surface and decreasing the near-surface wind speeds. The major patterns of spatial and temporal variability of the turbulent heat fluxes produced by MERRA compare favorably to observationally based estimates. However, MERRA is distinct in terms of amplitude. These results suggest that MERRA is likely to be a valuable resource for a number of research applications though, as with all turbulent flux estimates, systematic issues should be taken into account

Robert, J. Brent↗
NASA NTRS2012

Characterization of Turbulent Latent and Sensible Heat Flux Exchange Between the Atmosphere and Ocean in MERRA

Turbulent fluxes of heat and moisture across the atmosphere-ocean interface are fundamental components of the Earth s energy and water balance. Characterizing both the spatiotemporal variability and the fidelity of these exchanges of heat and moisture is critical to understanding the global water and energy cycle variations, quantifying atmosphere-ocean feedbacks, and improving model predictability. This study examines the veracity of the recently completed NASA Modern-Era Retrospective analysis for Research and Applications (MERRA) product with respect to its representation of the surface turbulent heat fluxes. A validation of MERRA turbulent heat fluxes and near-surface bulk variables at local, high-resolution space and time scales is achieved by making comparisons to a large suite of direct observations. Both in situ and satellite-observed gridded surface heat flux estimates are employed to investigate the spatial and temporal variability of the surface fluxes with respect to their annual mean climatologies, their seasonal covariability of near-surface bulk parameters, and their representation of extremes. The impact of data assimilation on the near-surface parameters is assessed through evaluation of incremental analysis update tendencies produced by the assimilation procedure. It is found that MERRA turbulent surface heat fluxes are relatively accurate for typical conditions but have systematically weak vertical gradients in moisture and temperature and have a weaker covariability between the near-surface gradients and wind speed than found in observations. This results in an underestimate of the surface latent and sensible heat fluxes over the western boundary current and storm track regions. The assimilation of observations mostly acts to bring MERRA closer to observational products by increasing moisture and temperature near the surface and decreasing the near-surface wind speeds. The major patterns of spatial and temporal variability of the turbulent heat fluxes produced by MERRA compare favorably to observationally based estimates. However, MERRA is distinct in terms of amplitude. These results suggest that MERRA is likely to be a valuable resource for a number of research applications though, as with all turbulent flux estimates, systematic issues should be taken into account.

Roberts, J. Brent↗
NASA NTRS2012

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

Ghrist, Richard W.↗
NASA NTRS2012

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

Mashiku, Alinda K.↗
NASA NTRS2012

Adaptive Sampling of Time Series During Remote Exploration

This work deals with the challenge of online adaptive data collection in a time series. A remote sensor or explorer agent adapts its rate of data collection in order to track anomalous events while obeying constraints on time and power. This problem is challenging because the agent has limited visibility (all its datapoints lie in the past) and limited control (it can only decide when to collect its next datapoint). This problem is treated from an information-theoretic perspective, fitting a probabilistic model to collected data and optimizing the future sampling strategy to maximize information gain. The performance characteristics of stationary and nonstationary Gaussian process models are compared. Self-throttling sensors could benefit environmental sensor networks and monitoring as well as robotic exploration. Explorer agents can improve performance by adjusting their data collection rate, preserving scarce power or bandwidth resources during uninteresting times while fully covering anomalous events of interest. For example, a remote earthquake sensor could conserve power by limiting its measurements during normal conditions and increasing its cadence during rare earthquake events. A similar capability could improve sensor platforms traversing a fixed trajectory, such as an exploration rover transect or a deep space flyby. These agents can adapt observation times to improve sample coverage during moments of rapid change. An adaptive sampling approach couples sensor autonomy, instrument interpretation, and sampling. The challenge is addressed as an active learning problem, which already has extensive theoretical treatment in the statistics and machine learning literature. A statistical Gaussian process (GP) model is employed to guide sample decisions that maximize information gain. Nonsta tion - ary (e.g., time-varying) covariance relationships permit the system to represent and track local anomalies, in contrast with current GP approaches. Most common GP models are stationary, e.g., the covariance relationships are time-invariant. In such cases, information gain is independent of previously collected data, and the optimal solution can always be computed in advance. Information-optimal sampling of a stationary GP time series thus reduces to even spacing, and such models are not appropriate for tracking localized anomalies. Additionally, GP model inference can be computationally expensive.

Thompson, David R.↗
NASA NTRS2013

Adaptive Sampling of Spatiotemporal Phenomena with Optimization Criteria

This work was designed to find a way to optimally (or near optimally) sample spatiotemporal phenomena based on limited sensing capability, and to create a model that can be run to estimate uncertainties, as well as to estimate covariances. The goal was to maximize (or minimize) some function of the overall uncertainty. The uncertainties and covariances were modeled presuming a parametric distribution, and then the model was used to approximate the overall information gain, and consequently, the objective function from each potential sense. These candidate sensings were then crosschecked against operation costs and feasibility. Consequently, an operations plan was derived that combined both operational constraints/costs and sensing gain. Probabilistic modeling was used to perform an approximate inversion of the model, which enabled calculation of sensing gains, and subsequent combination with operational costs. This incorporation of operations models to assess cost and feasibility for specific classes of vehicles is unique.

Chien, Steve A.↗
NASA NTRS2012

Momentum Flux Determination Using the Multi-beam Poker Flat Incoherent Scatter Radar

In this paper, we develop an estimator for the vertical flux of horizontal momentum with arbitrary beam pointing, applicable to the case of arbitrary but fixed beam pointing with systems such as the Poker Flat Incoherent Scatter Radar (PFISR). This method uses information from all available beams to resolve the variances of the wind field in addition to the vertical flux of both meridional and zonal momentum, targeted for high-frequency wave motions. The estimator utilises the full covariance of the distributed measurements, which provides a significant reduction in errors over the direct extension of previously developed techniques and allows for the calculation of an error covariance matrix of the estimated quantities. We find that for the PFISR experiment, we can construct an unbiased and robust estimator of the momentum flux if sufficient and proper beam orientations are chosen, which can in the future be optimized for the expected frequency distribution of momentum-containing scales. However, there is a potential trade-off between biases and standard errors introduced with the new approach, which must be taken into account when assessing the momentum fluxes. We apply the estimator to PFISR measurements on 23 April 2008 and 21 December 2007, from 60-85 km altitude, and show expected results as compared to mean winds and in relation to the measured vertical velocity variances.

Momentum flux↗
NASA NTRS2010

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Solar Dynamics Observatory-Helioseismic and Magnetic Imager Time-Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a time - distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time - distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference traveltime perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.

HMI↗
NASA NTRS2013

High-degree Gravity Models from GRAIL Primary Mission Data

We have analyzed Ka‒band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance‒component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root‒mean‒square error in the gravity anomalies computed from the error covariance to 320×320 is 0.77 mGal, compared to 29.0 mGal with the pre‒GRAIL model derived with the SELENE mission data, SGM150J, only to 140×140. The global correlations with the Lunar Orbiter Laser Altimeter‒derived topography are larger than 0.985 between l = 120 and 330. The free‒air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre‒GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit‒track‒related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S‒band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 micrometers/s for GRGM420A and from 0.03 to 0.06 micrometers/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615+/-0.0000914, k21=0.023915+/-0.0000132, and k22=0.024852+/-0.0000167, and a preliminary solution for the k30 Love number of k30=0.00734+/-0.0015, where the Love number error sigmas are those obtained with VCE.

Primary 1↗
NASA NTRS2014

Orbit Determination Accuracy Analysis of the Magnetospheric Multiscale Mission During Perigee Raise

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will provide orbit determination and prediction support for the Magnetospheric Multiscale (MMS) mission during the missions commissioning period. The spacecraft will launch into a highly elliptical Earth orbit in 2015. Starting approximately four days after launch, a series of five large perigee-raising maneuvers will be executed near apogee on a nearly every-other-orbit cadence. This perigee-raise operations concept requires a high-accuracy estimate of the orbital state within one orbit following the maneuver for performance evaluation and a high-accuracy orbit prediction to correctly plan and execute the next maneuver in the sequence. During early mission design, a linear covariance analysis method was used to study orbit determination and prediction accuracy for this perigee-raising campaign. This paper provides a higher fidelity Monte Carlo analysis using the operational COTS extended Kalman filter implementation that was performed to validate the linear covariance analysis estimates and to better characterize orbit determination performance for actively maneuvering spacecraft in a highly elliptical orbit. The study finds that the COTS extended Kalman filter tool converges on accurate definitive orbit solutions quickly, but prediction accuracy through orbits with very low altitude perigees is degraded by the unpredictability of atmospheric density variation.

Determination↗
NASA NTRS2014

Orbit Determination Accuracy Analysis of the Magnetospheric Multiscale Mission During Perigee Raise

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will provide orbit determination and prediction support for the Magnetospheric Multiscale (MMS) mission during the mission's commissioning period. The spacecraft will launch into a highly elliptical Earth orbit in 2015. Starting approximately four days after launch, a series of five large perigee-raising maneuvers will be executed near apogee on a nearly every-other-orbit cadence. This perigee-raise operations concept requires a high-accuracy estimate of the orbital state within one orbit following the maneuver for performance evaluation and a high-accuracy orbit prediction to correctly plan and execute the next maneuver in the sequence. During early mission design, a linear covariance analysis method was used to study orbit determination and prediction accuracy for this perigee-raising campaign. This paper provides a higher fidelity Monte Carlo analysis using the operational COTS extended Kalman filter implementation that was performed to validate the linear covariance analysis estimates and to better characterize orbit determination performance for actively maneuvering spacecraft in a highly elliptical orbit. The study finds that the COTS extended Kalman filter tool converges on accurate definitive orbit solutions quickly, but prediction accuracy through orbits with very low altitude perigees is degraded by the unpredictability of atmospheric density variation.

Multiscale↗
NASA NTRS2013

Assessing the Impact of Pre-gpm Microwave Precipitation Observations in the Goddard WRF Ensemble Data Assimilation System

The forthcoming Global Precipitation Measurement (GPM) Mission will provide next generation precipitation observations from a constellation of satellites. Since precipitation by nature has large variability and low predictability at cloud-resolving scales, the impact of precipitation data on the skills of mesoscale numerical weather prediction (NWP) is largely affected by the characterization of background and observation errors and the representation of nonlinear cloud/precipitation physics in an NWP data assimilation system. We present a data impact study on the assimilation of precipitation-affected microwave (MW) radiances from a pre-GPM satellite constellation using the Goddard WRF Ensemble Data Assimilation System (Goddard WRF-EDAS). A series of assimilation experiments are carried out in a Weather Research Forecast (WRF) model domain of 9 km resolution in western Europe. Sensitivities to observation error specifications, background error covariance estimated from ensemble forecasts with different ensemble sizes, and MW channel selections are examined through single-observation assimilation experiments. An empirical bias correction for precipitation-affected MW radiances is developed based on the statistics of radiance innovations in rainy areas. The data impact is assessed by full data assimilation cycling experiments for a storm event that occurred in France in September 2010. Results show that the assimilation of MW precipitation observations from a satellite constellation mimicking GPM has a positive impact on the accumulated rain forecasts verified with surface radar rain estimates. The case-study on a convective storm also reveals that the accuracy of ensemble-based background error covariance is limited by sampling errors and model errors such as precipitation displacement and unresolved convective scale instability.

microwave observations↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2013

On Using Intensity Interferometry for Feature Identification and Imaging of Remote Objects

We derive an approximation to the intensity covariance function of two scanning pinhole detectors, facing a distant source (e.g., a star) being occluded partially by an absorptive object (e.g., a planet). We focus on using this technique to identify or image an object that is in the line-of-sight between a well-characterized source and the detectors. We derive the observed perturbation to the intensity covariance map due to the object, showing that under some reasonable approximations it is proportional to the real part of the Fourier transform of the source's photon-flux density times the Fourier transform of the object's intensity absorption. We highlight the key parameters impacting its visibility and discuss the requirements for estimating object-related parameters, e.g., its size, velocity or shape. We consider an application of this result to determining the orbit inclination of an exoplanet orbiting a distant star. Finally, motivated by the intrinsically weak nature of the signature, we study its signal-to-noise ratio and determine the impact of system parameters.

quantum optics↗
NASA NTRS2015

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Grauer, Jared A.↗
NASA NTRS2016

Predicting Transition from Laminar to Turbulent Flow over a Surface

A prediction of whether a point on a computer-generated surface is adjacent to laminar or turbulent flow is made using a transition prediction technique. A plurality of instability modes are obtained, each defined by one or more mode parameters. A vector of regressor weights is obtained for the known instability growth rates in a training dataset. For an instability mode in the plurality of instability modes, a covariance vector is determined. A predicted local instability growth rate at the point is determined using the covariance vector and the vector of regressor weights. Based on the predicted local instability growth rate, an n-factor envelope at the point is determined.

Rajnarayan, Dev↗
NASA NTRS2016

Does a Relationship Between Arctic Low Clouds and Sea Ice Matter?

Arctic low clouds strongly affect the Arctic surface energy budget. Through this impact Arctic low clouds influence important aspects of the Arctic climate system, namely surface and atmospheric temperature, sea ice extent and thickness, and atmospheric circulation. Arctic clouds are in turn influenced by these elements of the Arctic climate system, and these interactions create the potential for Arctic cloud-climate feedbacks. To further our understanding of potential Arctic cloudclimate feedbacks, the goal of this paper is to quantify the influence of atmospheric state on the surface cloud radiative effect (CRE) and its covariation with sea ice concentration (SIC). We build on previous research using instantaneous, active remote sensing satellite footprint data from the NASA A-Train. First, the results indicate significant differences in the surface CRE when stratified by atmospheric state. Second, there is a weak covariation between CRE and SIC for most atmospheric conditions. Third, the results show statistically significant differences in the average surface CRE under different SIC values in fall indicating a 3-5 W m(exp -2) larger LW CRE in 0% versus 100% SIC footprints. Because systematic changes on the order of 1 W m(exp -2) are sufficient to explain the observed long-term reductions in sea ice extent, our results indicate a potentially significant amplifying sea ice-cloud feedback, under certain meteorological conditions, that could delay the fall freeze-up and influence the variability in sea ice extent and volume. Lastly, a small change in the frequency of occurrence of atmosphere states may yield a larger Arctic cloud feedback than any cloud response to sea ice.

Taylor, Patrick C.↗