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NASA NTRS2017

Effective Assimilation of SMAP Observations Using Statistical Techniques

Statistical techniques permit the retrieval of soil moisture estimates in a model climatology while retaining the spatial and temporal signatures of the satellite observations. As a consequence, the need for bias correction prior to an assimilation of these estimates is reduced, which could result in a more effective use of the independent information provided by the satellite observations. In this study, a statistical neural network (NN) retrieval algorithm is calibrated using SMAP brightness temperature observations and modeled soil moisture estimates (similar to those used to calibrate the SMAP Level 4 DA system). Daily values of surface soil moisture are estimated using the NN and then assimilated into the NASA Catchment model. The skill of the assimilation estimates is assessed based on a comprehensive comparison to in situ measurements from the SMAP core and sparse network sites as well as the International Soil Moisture Network. The NN retrieval assimilation is found to significantly improve the model skill, particularly in areas where the model does not represent processes related to agricultural practices. Additionally, the NN method is compared to assimilation experiments using traditional bias correction techniques. The NN retrieval assimilation is found to more effectively use the independent information provided by SMAP resulting in larger model skill improvements than assimilation experiments using traditional bias correction techniques.

Kolassa, J.↗

NASA NTRS2019

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a pilot flying an airplane; in this case, activities with distinct visual signatures might be things like communicating, navigating, monitoring, etc. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. We compare, not individual fixations, but groups of fixations aggregated over a fixed time interval (Tau). We assume that the environment has been divided into a finite set of discrete areas-of-interest (AOIs). For a given time interval, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector, where N is the number of AOIs. These proportions can be converted to integer counts by multiplying by Tau divided by the average fixation duration, a parameter that we fix at 283 milliseconds. We compare different intervals by computing the chi-squared statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We cluster the intervals, first by merging adjacent intervals that are sufficiently similar, optionally shifting the boundary between non-merged intervals to maximize the difference. Then we compare and cluster non-adjacent intervals. The method is evaluated using synthetic data generated by a hand-crafted set of activities. While the method generally finds more activities than put into the simulation, we have obtained agreement as high as 80 percent between the inferred activity labels and ground truth.

Eye Movements↗

NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗

NASA NTRS2018

Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom PredictionWorkshop

A summary is provided for the Second AIAA Sonic Boom Workshop held 8–9 January 2017 in conjunction with AIAA SciTech 2017. The workshop used three required models of increasing complexity: an axisymmetric body, a wing body, and a complete configuration with flow-through nacelle. An optional complete configuration with propulsion boundary conditions is also provided. These models are designed with similar nearfield signatures to isolate geometry and shock/expansion interaction e ects. Eleven international participant groups submitted nearfield signatures with forces, pitching moment, and iterative convergence norms. Statistics and grid convergence of these nearfield signatures are presented. These submissions are propagated to the ground, and noise levels are computed. This allows the grid convergence and the statistical distribution of a noise level to be computed. While progress is documented since the first workshop, improvement to the analysis methods for a possible subsequent workshop are provided. The complete configuration with flow-through nacelle showed the most dramatic improvement between the two workshops. The current workshop cases are more relevant to vehicles with lower loudness and have the potential for lower annoyance than the first workshop cases. The models for this workshop with quieter ground noise levels than the first workshop exposed weaknesses in analysis, particularly in convective discretization.

Park, Michael A.↗

NASA NTRSDate not supplied

Applying NASA-STD-7009 Standard for Models and Simulations to Surrogate and Other Statistical Models

NASA-STD-7009A, Standard for Models and Simulations, contains a worthy and insightfully-crafted credibility assessment. That set of metrics is intended to accumulate and communicate information that can be critical for users and their customers in evaluating findings due to a model or simulation. Was the model designed for the present use? Is it validated in the domain it’s being applied to? And so on. The standard was originally focused on physics-based models, but it can be applied more generally. It can – and should – be applied to high-impact statistical models, including surrogate models based on larger models and sims and regression models based directly on data. A key issue with many of such models is their relative simplicity compared to most M&S despite their use in high-risk engineering decisions. This report will make a case for using this Standard for a wider class of models, and how it might actually add value in excess of its cost for not only stakeholders, but modelers themselves. A rough example showing compliance for a statistical model is included.

K L Johnson↗

NASA NTRS2019

Statistical optical link budget analysis

In this paper, we describe work on extending statistical analysis methods to optical communications links, with a primary focus on intensity modulated, direct detected photon-counting channel utilizing pulse-position-modulation (PPM). We performed analysis on the relationship between bit error rate (BER) requirement, statistical characteristics of the received signal power and noise power, and the coded performance curves. We presented link analysis results with preliminary uncertainty quantifications of signal power and noise power. We used the Consultative Committee for Space Data Systems (CCSDS) Serially Concatenated convolutionally coded Pulse Position Modulation (SCPPM) prototype software [1] to obtain coded performance curves under different operating conditions with varying signal power, background noise power, code rates,and PPM modulation orders. Comparison with traditional, deterministic analysis shows that extra margin needs to be reserved to compensate for the performance losses caused by uncertainties of the link parameters.

Cheung, Kar-Ming↗

NASA NTRSDate not supplied

Delta Method Application for the Correlation of IR Detector Thermal Parasitic Loads with Statistically Accurate Results

The Linear Etalon Imaging Spectral Array (LEISA) is a cryogenic IR detector that is passively cooled below 110K. LEISA is part of the L’Ralph instrument, which is going on the Lucy mission, with planned flyby’s of the Trojan asteroids around 5.5 AU. One of the primary thermal challenges is to successfully quantify each significant parasitic heat flow value with statistical certainty.Simulation of flight-like thermal environments and correlation of thermal models is an important part of this challenge, which can be critical for thermally sensitive systems such as cryogenic detectors that are passively cooled. It is common practice during TVAC to achieve several thermal balance points and then to correlate several design variables in order to achieve the closest match to all balance points tested. This approach lends itself to high levels of uncertainty in the correlated values due to the cumulative effect of absolute temperature uncertainty and differences between the sensors used for the measurement. Accuracy can be improved with the use of more accurate sensors, by calibrating all sensors with respect to each other, and by using Zero-Q methodologies, all of which add cost and complexity to the test.The Delta Method uses the difference in temperature caused by the changes in the boundary conditions to calculate heat flows and/or thermal resistances across temperature differentials. This eliminates the problem of high uncertainties with absolute temperature measurements, and yields statistically accurate results down to the sensor resolution of 1mK at < 100K, by taking the sensor’s calibration errors out of the equation. During testing, this method relies on parametric variations around an initial balance point, by varying the boundary conditions of the different parasitic heat sources. The Delta Method, as well as its application on the LEISA thermal test, will be discussed in detail.

Daniel G. Bae↗

NASA NTRS2021

Statistical Error Analysis on White-Light Filter Ratio Experiments to Measure Electron Parameters

The Filter ratio technique to remotely measure electron temperature and speed using four color filters in visible light and a polarization camera was described in detail in four articles by Reginald et al., Solar physics, (2018, 2019a, 2019b, 2020). In these four articles we quantified the systematic error associated with using models of symmetric corona to interpret results from asymmetric corona. We also showed the criteria applied to select the bandwidths of filters, and the pros and cons of replacing the traditional linear polarizer with a polarization camera to measure pB. What started in 1990s as ground experiments conducted during total solar eclipses that lasted for a few minutes lead to a balloon borne experiment lasting eight hours in 2019 and will blossom into a space experiment on the International Space Station in 2023. Due to constraints on the bandwidths of the four filters, a successful mission requires quantification of the statistical error using Monte Carlo simulation to generate two feasibility profiles, which are unique to the design parameters of the coronagraph, to comprehend the feasibility to measure temperature and speed within the desired temporal and spatial resolutions. For the statistical error analysis, we use modeled K and F corona profiles, representative theoretical diffraction, scattering, and vignetting profiles, assumed efficiencies for lenses, mirrors, and polarizers, assumed detector properties on quantum efficiency, full well depth, dark noise, and read noise, and assumed instrument properties on aperture diameter, solid angle, and pixel resolution. We hope future white-light coronagraphs will exhibit capabilities to measure electron density, temperature, and speed.

Nelson Reginald↗

NASA NTRS2022

An Algorithm for Statistical Audibility Prediction (SAP) of an Arbitrary Signal in the Presence of Noise

A method for predicting the audibility of an arbitrary time-varying noise (signal) in the presence of masking noise has been developed. The statistical audibility prediction (SAP) method relies on the specific loudness, or loudness perceived through the individual auditory filters, for accurate statistical estimation of audibility vs. time. More recent development has focused on derivation and inclusion of frequency-dependent correction factors in SAP’s model to account for the ability to hear signals below the level of the masking noise. Audibility prediction vs. time is intuitive since it captures changes in audibility with time as it occurs, which is critical for the study of human response to noise. Concurrently time-frequency prediction of audibility may also provide valuable information about the root cause(s) for audibility useful for the design and operation of sources of noise. Empirical data, gathered under a three-alternative forced-choice (3AFC) test paradigm for low-frequency sound, has been used to examine the accuracy of SAP.

audibility↗

NASA NTRS2022

Statistical study of favorable foreshock ion properties for the formation of hot flow anomalies and foreshock bubbles

Hot flow anomalies (HFAs) and foreshock bubbles (FBs) are frequently observed in Earth's foreshock, which can significantly disturb the bow shock and therefore the magnetosphere-ionosphere system and can accelerate particles. Previous statistical studies have identified the solar wind conditions (high solar wind speed and high Mach number, etc.) that favor their generation. However, backstreaming foreshock ions are expected to most directly control how HFAs and FBs form, whereas the solar wind may partake in the formation process indirectly by determining foreshock ion properties. Using Magnetospheric Multiscale mission and Time History of Events and Macroscale Interactions during Substorms mission, we perform a statistical study of foreshock ion properties around 275 HFAs and FBs. We show that foreshock ions with a high foreshock-to-solar wind density ratio (>∼3%), high kinetic energy (>∼600 eV), large ratio of kinetic energy to thermal energy (>∼0.1), and large ratio of perpendicular temperature to parallel temperature (>∼1.4) favor HFA and FB formation. We also examine how these properties are related to solar wind conditions: high solar wind speed and oblique bow shock (angle between the interplanetary magnetic field and the bow shock normal 𝜃Bn∼45°) favor high kinetic energy of foreshock ions; foreshock ions have large ratio of kinetic energy to thermal energy at large 𝐴𝐴𝐴𝐴Bn (>30°); small 𝐴𝐴𝐴𝐴Bn (<30°), high Mach number, and closeness to the bow shock favor a high foreshock-to-solar wind density ratio. Our results provide further understanding of HFA and FB formation.

Terry Z. Liu↗

NASA NTRSDate not supplied

Effect of Flight on Turbulence Statistics and Noise Sources in a Round Turbulent Jet

Turbulence statistics relevant to noise modeling and prediction are computed in a near-sonic, unheated round jet in the presence of a flight stream using Large Eddy Simulation. The Naval Research Laboratory’s Jet Engine Noise REduction (JENRE) code is used to obtain unsteady flow solutions which are post-processed for single- and two-point, space-time statistical quantities, including the nominal noise sources from an acoustic analogy formulation. Jets subject to three different flight-stream speeds, along with a baseline static case, are considered. The impact of flight-stream speed on mean flow and turbulence profiles and the amplitudes, length and time scales of Reynolds-stress auto co-variances are determined and scalings for representing the flight stream effect are explored. The implications for source modeling in jet mixing noise predictions within an acoustic analogy formulation are discussed.

Jet noise, flight effects, aircraft noise↗

NASA NTRSDate not supplied

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗

NASA NTRSDate not supplied

Statistically Consistent Dispersions of Line Loads to Uncertain Integrated Forces and Moments

This work presents a method to generate line loads that are consistent with integrated force and moment constraints, while also following the statistical distribution underlying known line load data. The motivation for this method is to address a particular problem that can arise during the pre-flight analysis of an ascent vehicle. That problem is constructing separate databases, for line loads and integrated aerodynamic coefficients, that contain different data and thus different amounts of quantified uncertainty. A dispersed line load method is described and applied to a data set generated by 29 computational fluid dynamics simulations at various angles of attack and sideslip. The statistical similarity of the generated line loads to the known data is confirmed by using the Maximum Mean Discrepancy 2-sample test. The promising results from this novel method are compared against results from applying an existing line load adjustment procedure to the same data set. Finally, potential future avenues of research are briefly discussed.

Aaron C. Burkhead↗

NASA NTRS2023

The Statistical Emulators of GGCMI Phase 2: Responses of Year-to-Year Variation of Crop Yield to CO 2 , Temperature, Water and Nitrogen Perturbations

Understanding the impact of climate change on year-to-year variation of crop yield is critical to global food stability and security. While crop model emulators are believed to be lightweight tools to replace the models, few emulators have been developed to capture such interannual variation of crop yield in response to climate variability. In this study, we developed a statistical emulator with a machine learning algorithm to reproduce the response of year-to-year variation of four crop yields to CO 2 (C), temperature (T), water (W), and nitrogen (N) perturbations defined in the Global Gridded Crop Model Intercomparison Project (GGCMI) phase 2. The emulators were able to explain more than 52 % of the variance of simulated yield and performed well in capturing the year-to-year variation of global average and gridded crop yield over current croplands in the baseline. With the changes in CO 2 –temperature–water–nitrogen (CTWN) perturbations, the emulators could reproduce the year-to-year variation of crop yield well over most current cropland. The variation of R and the mean absolute error was small under the single CTWN perturbations and dual-factor perturbations. These emulators thus provide statistical response surfaces of yield, including both its mean and interannual variability, to climate factors. They could facilitate spatiotemporal downscaling of crop model simulation, projecting the changes in crop yield variability in the future and serving as a lightweight tool for multi-model ensemble simulation. The emulators enhanced the flexibility of crop yield estimates and expanded the application of large-ensemble simulations of crop yield under climate change.

Climate change↗

NASA NTRSDate not supplied

Effect of Flight on Turbulence Statistics and Noise Sources in a Round Turbulent Jet

Turbulence statistics relevant to noise modeling and prediction are computed in a series near-sonic, unheated round jets in the presence of a flight stream using Large Eddy Simulation. The Naval Research Laboratory’s Jet Engine Noise REduction (JENRE®) code is used to obtain unsteady flow solutions which are post-processed for single- and two-point, space-time statistical quantities, including the nominal noise sources from an acoustic analogy formulation. Jets subject to three different flight-stream speeds, along with a baseline static case, are considered. The impact of flight-stream speed on mean flow and turbulence profiles and the amplitudes, length and time scales of Reynolds-stress auto co-variances are determined and scalings for representing the flight-stream effect are explored. The implications for source modeling in jet mixing noise predictions within an acoustic analogy formulation are discussed.

Jet noise↗

NASA NTRSDate not supplied

Effect of Flight on Turbulence Statistics and Noise Sources in a Round Turbulent Jet

Turbulence statistics relevant to noise modeling and prediction are computed in a series near-sonic, unheated round jets in the presence of a flight stream using Large Eddy Simulation. The Naval Research Laboratory’s Jet Engine Noise REduction (JENRE) code is used to obtain unsteady flow solutions which are post-processed for single- and two-point, space-time statistical quantities, including the nominal noise sources from an acoustic analogy formulation. Jets subject to three different flight-stream speeds, along with a baseline static case, are considered. The impact of flight-stream speed on mean flow and turbulence profiles and the amplitudes, length and time scales of Reynolds-stress auto co-variances are determined and scalings for representing the flight-stream effect are explored. The implications for source modeling in jet mixing noise predictions within an acoustic analogy formulation are discussed.

Jet noise↗

NASA NTRS2023

Finding the magnetopause location using soft X-ray observations and a statistical inverse method

Variability in the location and shape of the dayside magnetopause is attributed to magnetic reconnection, a fundamental process that enables the transfer of mass, energy, and momentum from the solar wind into the magnetosphere. The spatial and temporal properties of the magnetopause, under varying solar and magnetospheric conditions, remain largely unknown because empirical studies using in-situ observations are challenging to interpret. Global wide field-of-view (FOV) imaging is the only means to simultaneously observe the spatial distribution of the plasma properties over the vast dayside magnetospheric region and, subsequently, quantify the energy transport from the interplanetary medium into the terrestrial magnetosphere. Two upcoming missions, ESA/CAS SMILE and NASA’s LEXI will provide wide-field imagery of the dayside magnetosheath in soft X-rays, an emission generated by charge exchange interactions between high charge-state heavy ions of solar wind origin and exospheric neutral atoms. High-cadence two-dimensional observations of the magnetosheath will allow the estimation of dynamic properties of its inner boundary, the magnetopause, and enable studies of its response to changes in the solar wind dynamic pressure and interplanetary magnetic field orientation. This work introduces a statistically-based estimation approach based on inverse theory to estimate the spatial distribution of magnetosheath soft X-ray emissivities and, with this, identify the location of the magnetopause over the Sun−Earth line. To do so, we simulate the magnetosheath structure using the MHD-based OpenGGCM model and generate synthetic soft X-ray images using LEXI’s orbit and attitude information. Our results show that 3-D estimations using the described statistically-based technique are robust against Poisson-distributed shot noise inherent to soft X-ray images. Also, our proposed methodology shows that the accuracy of both three-dimensional (3-D) estimation and the magnetopause standoff distance calculation highly depends on the observational point.

Gonzalo Cucho-Padin↗

NASA NTRSDate not supplied

Statistical Analysis of Recent Go Around Flight Data to Study and Evaluate Skilled Pilot Monitoring

A statistical analysis was performed on a batch of recent go-around flight data of a few major US airlines spanning a one year period. The statistical analysis investigates a few select relevant aspects of these go arounds, such as initiation altitude and altitude change, aircraft configuration, deviation from the flightpath, and energy state. These data show that only one third of the landings are aborted below 400ft, but the majority of the go arounds occur at significantly higher altitudes. Current go-around training is specifically focused on the final approach and landing phase at low altitudes and low speeds. The results of this study will support the development of a broader set of relevant scenarios for an FAA simulator experiment to study and evaluate the skills of the pilots who monitor this wide spectrum of diverse go-around conditions, with the ultimate goal to help improve pilot go-around training and technologies.

go around↗