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NASA NTRS2013

Ensemble Data Assimilation Without Ensembles: Methodology and Application to Ocean Data Assimilation

Two methods to estimate background error covariances for data assimilation are introduced. While both share properties with the ensemble Kalman filter (EnKF), they differ from it in that they do not require the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The first method is referred-to as SAFE (Space Adaptive Forecast error Estimation) because it estimates error covariances from the spatial distribution of model variables within a single state vector. It can thus be thought of as sampling an ensemble in space. The second method, named FAST (Flow Adaptive error Statistics from a Time series), constructs an ensemble sampled from a moving window along a model trajectory. The underlying assumption in these methods is that forecast errors in data assimilation are primarily phase errors in space and/or time.

Data Assimilation↗

NASA NTRS2013

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 boundary-layer properties at the point are obtained from a steady-state solution of a fluid flow in a region adjacent to the point. 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 each instability mode in the plurality of instability modes, a covariance vector is determined, which is the covariance of a predicted local growth rate with the known instability growth rates. Each covariance vector is used with the vector of regressor weights to determine a predicted local growth rate at the point. Based on the predicted local growth rates, an n-factor envelope at the point is determined.

Rajnarayan, Dev↗

NASA NTRS2018

Intercomparison of Evapotranspiration Measurement Methods for Vegetable Crops in California

Recent drought events in California and legislation passed with the goal of increasing the sustainability of groundwater supplies have led to increased interest in tools to optimize irrigation schedules and increase on-farm water used efficiency. With more than 400 different crops produced in California, evapotranspiration-based irrigation scheduling is a promising and well-established approach. However, there is a need for accurate methods to estimate crop evapotranspiration (ET(sub c)) across the diverse range of crops grown, coupled with cost-effective methods for quantifying the accuracy of these tools. In this study, we evaluated remotely sensed estimates of ET(sub c) and associated crop water requirements from NASA's Satellite Irrigation Support (SIMS) system for two vegetable crops and measured crop evapotranspiration ET(sub c) using multiple methods, including weighing lysimeters, eddy covariance towers (EC), and surface renewal stations. We compared ET(sub c) data from these measurements with remotely sensed basal crop evapotranspiration (ET(sub cb)) data from SIMS as well as ET(sub c) data from a standard FAO-56 crop coefficient approach. Studies were conducted for sugar beets in Five Points, CA from 2014 to 2015 and studies are ongoing for fresh market tomatoes in Firebaugh, CA. We present results from these intercomparison studies and describe implications for future studies to quantify the accuracy of remotely sensed measures of ET(sub c). Highlights from results to date include strong correlations between ET measured with both surface renewal instrumentation and eddy covariance calculations using a 3D sonic anemometer and ET(sub c) data measured with the weighing lysimeter, with respective R2 values of 0.7964 (surface renewal) and 0.8034 (eddy covariance). This study provides insights into agreement between different approaches for monitoring evapotranspiration and provides another reference point for the community working to develop accurate and cost-effective tools that support growers in optimizing irrigation management.

Measurement↗

NASA NTRS2021

Integrating continuous atmospheric boundary layer and tower-based flux measurements to advance understanding of land-atmosphere interactions

The atmospheric boundary layer mediates the exchange of energy, matter, and momentum between the land surface and the free troposphere, integrating a range of physical, chemical, and biological processes and is defined as the lowest layer of the atmosphere (ranging from a few meters to 3 km). In this review, we investigate how continuous, automated observations of the atmospheric boundary layer can enhance the scientific value of co-located eddy covariance measurements of land-atmosphere fluxes of carbon, water, and energy, as are being made at FLUXNET sites worldwide. We highlight four key opportunities to integrate tower-based flux measurements with continuous, long-term atmospheric boundary layer measurements: (1) to interpret surface flux and atmospheric boundary layer exchange dynamics and feedbacks at flux tower sites, (2) to support flux footprint modelling, the interpretation of surface fluxes in heterogeneous and mountainous terrain, and quality control of eddy covariance flux measurements, (3) to support regional-scale modeling and upscaling of surface fluxes to continental scales, and (4) to quantify land-atmosphere coupling and validate its representation in Earth system models. Adding a suite of atmospheric boundary layer measurements to eddy covariance flux tower sites, and supporting the sharing of these data to tower networks, would allow the Earth science community to address new emerging research questions, better interpret ongoing flux tower measurements, and would present novel opportunities for collaborations between FLUXNET scientists and atmospheric and remote sensing scientists.

Manuel Helbig↗

NASA NTRSDate not supplied

Is There A Relationship Between Cornered-Hat Methods and A Residual Approach to Estimate System Uncertainty?

Recently a relationship has been established between a now traditional residual diagnostic used to estimate observation, background and analysis error covariances of interest to data assimilation and the three-cornered hat (3CH) method. An existing extension of the traditional residual diagnostic uses residuals from a fixed lag-1 Kalman smoother to retrieve system (model) error covariance. It is thus natural to ask if an additional relationship can be established between this extended residual method and some form of cornered--hat method. The answer might seem straightforward. Unlike in the standard residual estimation case, attempting to estimate model error amounts to estimating the statistics of a residual quantity itself. As shown in this presentation, in such cases the 3CH method becomes trivial: the sought out uncertainty can be derived directly from the covariance of the residual quantity at hand. In the particular case of estimating model error, one of the corners would have to be composed of vectors providing estimates of model error; these are not typically available in practice. Therefore, at first glance the present work finds no relationship between the lag-1 smoother residual diagnostic for system error estimation and cornered--hat methods. However, the work suggests that a two-tiered 3CH might be all that is necessary for system uncertainty to be obtained with 3CH.

Ricardo Todling↗

NASA NTRS2024

Evaluation of Sex Differences in Physiologic Responses to Submaximal Cycling Under Normoxic and Hypoxic Conditions

BACKGROUND: During Lunar missions, astronauts may live and operate in conditions where altered atmospheric pressure and oxygen concentrations may result in a mildly hypoxic environment. While the compensatory hemodynamic mechanisms ensuring adequate oxygen delivery to contracting muscles during exercise in hypoxic conditions are well-studied, less research has focused on potential sex differences in the responses to hypoxia exposure during exercise. As female astronauts make up half of the Artemis astronaut corps, understanding whether physiologic responses in a hypoxic environment differ between sexes may inform recommendations for exercising safely in exploration environments. METHODS: Fourteen subjects (7M/7F) from NASA’s Exploration Atmosphere Study performed two submaximal cycle exercise trials (10 min of exercise at 40% peak aerobic capacity [VO 2 pk]) ergometer under normobaric normoxic gas (21% O 2 ) and normobaric hypoxic (18% O 2 and balanced N 2 ) conditions in randomized order. Linear mixed models with Bonferroni post hoc corrections (fixed effects: condition, sex, VO 2 pk [covariate], body mass [BM, covariate]; random effects: subject, mission) were performed to evaluate the effect of condition and sex on physiologic responses to exercise (oxygen uptake [VO 2 ], carbon dioxide production [VCO 2 ], ventilation [VE], oxygen saturation [SpO 2 ], and heart rate [HR]). RESULTS: Males were comparable to females for age (36.6±4.7 vs 36.4±9.3 yrs; p>0.05) but had greater BM (87.3±10.9 vs 64.5±7.4 kg; p<0.001) and absolute VO2pk (3.5±0.6 vs 2.4±4.7 L/min; p<0.001). Additionally, males had higher VO2 (p=0.005), VCO2 (p=0.02), and VE (p=0.01) during exercise trials, independent of condition; however, when VO 2 pk was added as a covariate, the effect of sex was no longer significant. SpO 2 was reduced during hypoxic exercise compared to the normoxic condition (p<0.001), but neither sex nor environmental condition impacted HR. CONCLUSIONS: Though most physiologic responses to submaximal, short-duration exercise between normoxia and mild hypoxia were similar, females exhibited lower VO 2 , VCO 2 , and VE during both conditions, likely driven by lower aerobic capacity. Future research is needed to determine whether similar findings result from multiday hypobaric hypoxia experienced during missions.

N C Strock↗

NASA NTRSDate not supplied

NASA CARA Tools

The NASA Conjunction Assessment Risk Analysis (CARA) team has created and posted to GitHub a set of MATLAB software tools for collision assessment (CA) analysis. The software is provided to the public under a NASA Open-Source Software Agreement and is maintained/updated by the CARA Analysis team. Capabilities provided within the toolset include algorithms in assessing probability of collision (Pc), collision consequence, covariance realism, Orbit Determination (OD) quality assessment, and single covariance max Pc. Additionally, a set of utilities are provided for astrodynamics topics closely related to CA, such as: Conjunction Data Message (CDM) parsing, covariance transformations, coordinate system transformations, etc. The repository is regularly updated on a monthly basis and new functionality will be added as algorithms are approved for public release. This presentation will provide a brief introduction to the toolset, highlight some of the key components which can be used in operations, and will present information on algorithms that are in the release pipeline and can be expected soon. This software will enable operators to independently perform CA calculations using the same core algorithms that CARA uses in operations.

L. Baars↗

NASA NTRS2022

Deep Interacting Multiple Model Filtering

In this paper, a deep learning-based multiple model estimation framework is presented for the state estimation of hybrid dynamical systems from high dimensional observations such as camera images. A low dimensional vector which represents the measurement of the latent dynamical system and its corresponding variance are learned using a deep encoder neural network. An Interacting Multiple Model (IMM) filter is used to generate the latent state estimates and covariances using multiple dynamical models, which can be learned using backpropagation through time. The state estimates of the dynamical system and the corresponding covariance matrix are generated from the latent state estimates and covariance using a deep decoder neural network. The whole network is trained in an end-to-end manner using a loss function which minimizes the negative log-likelihood of the neural network parameters. Simulation results are presented using a 2D bouncing ball example and estimation error statistics are computed which demonstrates the accuracy and consistency of the estimation.

Ghananeel Rotithor↗

NASA NTRSDate not supplied

NASA CARA Tools

Luis Baars↗

NASA NTRS1965

Study to investigate the stability in orbit determination technical summary report, 16 apr. 1964 - 15 apr. 1965

Kalman-Schmidt filter stability in orbit calculation, dependence on transition matrix, initial covariance matrix, observations, and covariance of noise in measurements

COVARIANCE↗

NASA NTRS2013

Integrated Model Reduction and Control of Aircraft with Flexible Wings

This paper presents an integrated approach to the modeling and control of aircraft with exible wings. The coupled aircraft rigid body dynamics with a high-order elastic wing model can be represented in a nite dimensional state-space form. Given a set of desired output covariance, a model reduction process is performed by using the weighted Modal Cost Analysis (MCA). A dynamic output feedback controller, which is designed based on the reduced-order model, is developed by utilizing output covariance constraint (OCC) algorithm, and the resulting OCC design weighting matrix is used for the next iteration of the weighted cost analysis. This controller is then validated for full-order evaluation model to ensure that the aircraft's handling qualities are met and the uttering motion of the wings suppressed. An iterative algorithm is developed in CONDUIT environment to realize the integration of model reduction and controller design. The proposed integrated approach is applied to NASA Generic Transport Model (GTM) for demonstration.

AEROELASTIC↗

NASA NTRS2017

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

assimilation↗

NASA NTRS2019

Modeling Phenological Controls on Carbon Dynamics in Dryland Sagebrush Ecosystems

Dryland ecosystems play an important role in determining how precipitation anomalies affect terrestrial carbonfluxes at regional to global scales. Thus, to understand how climate change may affect the global carbon cycle,we must also be able to understand and model its effects on dryland vegetation. Dynamic Global VegetationModels (DGVMs) are an important tool for modeling ecosystem dynamics, but they often struggle to reproduceseasonal patterns of plant productivity. Because the phenological niche of many plant species is linked to bothtotal productivity and competitive interactions with other plants, errors in how process-based models representphenology hinder our ability to predict climate change impacts. This may be particularly problematic in drylandecosystems where many species have developed a complex phenology in response to seasonal variability in bothmoisture and temperature. Here, we examine how uncertainty in key parameters as well as the structure ofexisting phenology routines affect the ability of a DGVM to match seasonal patterns of leaf area index (LAI) andgross primary productivity (GPP) across a temperature and precipitation gradient. First, we optimized modelparameters using a combination of site-level eddy covariance data and remotely-sensed LAI data. Second, wemodified the model to include a semi-deciduous phenology type and added flexibility to the representation ofgrass phenology. While optimizing parameters reduced model bias, the largest gains in model performance wereassociated with the development of our new representation of phenology. This modified model was able to bettercapture seasonal patterns of both leaf area index (R2=0.75) and gross primary productivity (R2=0.84), thoughits ability to estimate total annual GPP depended on using eddy covariance data for optimization. The new modelalso resulted in a more realistic outcome of modeled competition between grass and shrubs. These findingsdemonstrate the importance of improving how DGVMs represent phenology in order to accurately forecastclimate change impacts in dryland ecosystems.

Ecosystem model Phenology Parameter optimization E↗

NASA NTRS2019

Modeling Phenological Controls on Carbon Dynamics in Dryland Sagebrush Ecosystems

Dryland ecosystems play an important role in determining how precipitation anomalies affect terrestrial carbon fluxes at regional to global scales. Thus, to understand how climate change may affect the global carbon cycle, we must also be able to understand and model its effects on dryland vegetation. Dynamic Global Vegetation Models (DGVMs) are an important tool for modeling ecosystem dynamics, but they often struggle to reproduce seasonal patterns of plant productivity. Because the phenological niche of many plant species is linked to both total productivity and competitive interactions with other plants, errors in how process-based models represent phenology hinder our ability to predict climate change impacts. This may be particularly problematic in dryland ecosystems where many species have developed a complex phenology in response to seasonal variability in both moisture and temperature. Here, we examine how uncertainty in key parameters as well as the structure of existing phenology routines affect the ability of a DGVM to match seasonal patterns of leaf area index (LAI) and gross primary productivity (GPP) across a temperature and precipitation gradient. First, we optimized model parameters using a combination of site-level eddy covariance data and remotely-sensed LAI data. Second, we modified the model to include a semi-deciduous phenology type and added flexibility to the representation of grass phenology. While optimizing parameters reduced model bias, the largest gains in model performance were associated with the development of our new representation of phenology. This modified model was able to better capture seasonal patterns of both leaf area index (R(exp 2) = 0.75) and gross primary productivity (R(exp 2) = 0.84), though its ability to estimate total annual GPP depended on using eddy covariance data for optimization. The new model also resulted in a more realistic outcome of modeled competition between grass and shrubs. These findings demonstrate the importance of improving how DGVMs represent phenology in order to accurately forecast climate change impacts in dryland ecosystems.

Ecosystem model↗

NASA NTRS2022

Low-Earth Orbit Trajectory Optimization in the Presence of Atmospheric Uncertainty

The previous 20 to 25 years have seen a tremendous increase in space exploration, and with that an increase in the level of logistics planning needed to ensure mission success. For spacecraft that are designed to be periodically re-supplied, a key logistics consumable is propellant, as it constitutes the greatest up-mass on re-supply vehicles. A trajectory design strategy is therefore desired that minimizes propellant usage in order to ease the demand for propellant re-supply missions. This thesis develops such a strategy in three stages, and uses the International Space Station (ISS) as its testbed, as no other LEO spacecraft is more challenging from a space logistics standpoint. First, the ISS trajectory planning problem is formulated as a constrained burn optimization problem assuming a deterministic atmosphere. The cost function is total ∆v, with constraints imposed on longitude of ascending viii node (LAN) and semi-major axis (SMA) altitude. Analytic derivatives are constructed for both the cost and constraints, which are necessary given the 6-week to 2-year time frames being considered. A gradient-based optimizer is then utilized to find locally-optimal solutions to real-world ISS trajectory planning problems. Second, atmospheric uncertainty is addressed by constructing a probabilistic model of space weather data using Gaussian Processes (GPs). Bayesian inference is performed using the GP model to generate mean and covariance estimates for space weather predictions, whose pedigree is assessed against test data. The predictions are then mapped into atmospheric density via the analytic Jacchia-Roberts density model, and the effect of space weather uncertainty on orbital lifetime is examined. Third, an ISS burn execution uncertainty model is developed. This model, along with the space weather uncertainty model, are deployed in a linear covariance analysis to ascertain their combined effect on LAN and SMA altitude dispersions. The deterministic constraints from the original problem are re-formulated as stochastic constraints, where now the constraint uncertainty interval is required to fall within specified bounds. An updated optimization framework is constructed using the original ∆v cost function along with the stochastic constraints to solve the trajectory optimization problem under atmospheric uncertainty. Finally, the complete architecture is summarized for deployment in an operational setting.

Trajectory Optimization↗

NASA NTRSDate not supplied

Copernicus-LinCov (COPCOV) Software Integration in Support of Robust Trajectory Optimization

Robust trajectory optimization is the process of optimizing a trajectory while accounting for system uncertainty due to a variety of potential error sources. This work highlights the development and features of a novel tool known as CopCov to support robust trajectory optimization efforts. CopCov acts as an interface between Copernicus, a generalized trajectory design and optimization tool, and LinCov, a linear covariance analysis tool. By having a direct interface between these two software packages, Copernicus can receive covariance information from LinCov through a direct feedback loop, thus enabling optimization of a trajectory that is robust to trajectory dispersions and navigation errors. This paper details the architecture of CopCov and its flexibility to operate under varying configurations, including with both tools running locally or alternatively with the tools communicating via a remote connection. Additionally, the CopCov tool is demonstrated on a simple Hohmann transfer reference trajectory with varying numbers of Trajectory Correction Maneuvers (TCMs) and varying problem formulations. This example scenario is used to highlight how the inclusion of the CopCov interface affects burn placement of both major burns and minor burns (i.e., TCMs) in the optimized solution. Results are compared against analytical solutions and against a Genetic Algorithm (GA) optimizer for independent verification and validation.

Copernicus↗

NASA NTRSDate not supplied

Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.

Linear Covariance Analysis↗

NASA NTRS1969

Product mean values and convection speed

Applying relationship of beam intensity covariances and local extinction coefficient covariances to calculation of convection velocity in crossed-beam methodology

Heybey, W. H.↗