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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Liu, Zhaoyan↗
DOE OSTI2025

Leveraging transfer learning and leaf spectroscopy for leaf trait prediction with broad spatial, species, and temporal applicability

Accurate and reliable prediction of leaf traits is crucial for understanding plant adaptations to environmental variation, monitoring terrestrial ecosystems, and enhancing comprehension of functional diversity and ecosystem functioning. Currently, various approaches (e.g., statistical, physical models) have been developed to estimate leaf traits through hyperspectral remote sensing and leaf spectroscopy. However, the absence of high-performing, transferable, and stable models across various domains of space, plant functional types (PFTs) and seasons hinder our ability to quantify and comprehend spatiotemporal variations in leaf traits. This study proposes robust and highly transferable models for better predicting leaf traits with hyperspectral reflectance. Initially, three datasets were assembled, pairing common leaf traits — chlorophyll (Chla+b), carotenoids (Ccar), leaf mass per area (LAM), equivalent water thickness (EWT) — with leaf spectra measurements collected across diverse geographic locations in the U.S. and Europe, PFTs, and seasons. Measurements were acquired using spectroradiometers (e.g., ASD FieldSpec 3/4/Pro and SVC HR-1024i) with integrating spheres, leaf clips, and contact probes. Here, we then developed transfer learning-based hybrid models that incorporated the domain knowledge of radiative transfer models (RTMs) through pretraining processes and were well-constrained by fine-tuning with field measurements. Through comparison with other state-of-the-art statistical models, including partial-least squares regression (PLSR) and Gaussian Process Regression (GPR), as well as pure physical models, we found that the proposed transfer learning models achieved better predictive performance and higher transferability. Specifically, compared to other statistical models and pure RTMs, the transfer learning model exhibited higher coefficient of determination (R 2 ) values with range of 0.01 to 0.79, lower normalized root mean square error (NRMSE) with range of 0.06 % to 33.25 % in model performance. Additionally, the models exhibited improved transferability, with higher R 2 values range from 0.04 to 0.32, lower NRMSE range from 0.08 % to 30.81 %. The findings underscore that transfer learning models through integrating domain knowledge from RTMs and limited observations, can harness the advantages of both RTMs and statistical models and serve as a promising approach for effectively predicting leaf traits.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

On the utility of GPU accelerated high-order methods for unsteady flow simulations: A comparison with industry-standard tools

First- and second-order accurate numerical methods, implemented for CPUs, underpin the majority of industrial CFD solvers. Whilst this technology has proven very successful at solving steady-state problems via a Reynolds Averaged Navier–Stokes approach, its utility for undertaking scale-resolving simulations of unsteady flows is less clear. High-order methods for unstructured grids and GPU accelerators have been proposed as an enabling technology for unsteady scale-resolving simulations of flow over complex geometries. In this study we systematically compare accuracy and cost of the high-order Flux Reconstruction solver PyFR running on GPUs and the industry-standard solver STAR-CCM+ running on CPUs when applied to a range of unsteady flow problems. Specifically, we perform comparisons of accuracy and cost for isentropic vortex advection (EV), decay of the Taylor–Green vortex (TGV), turbulent flow over a circular cylinder, and turbulent flow over an SD7003 aerofoil. We consider two configurations of STAR-CCM+: a second-order configuration, and a third-order configuration, where the latter was recommended by CD-adapco for more effective computation of unsteady flow problems. Results from both PyFR and STAR-CCM+ demonstrate that third-order schemes can be more accurate than second-order schemes for a given cost e.g. going from second- to third-order, the PyFR simulations of the EV and TGV achieve 75× and 3× error reduction respectively for the same or reduced cost, and STAR-CCM+ simulations of the cylinder recovered wake statistics significantly more accurately for only twice the cost. Moreover, advancing to higher-order schemes on GPUs with PyFR was found to offer even further accuracy vs. cost benefits relative to industry-standard tools.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Estimating uncertainties in statistics computed from direct numerical simulation

Rigorous assessment of uncertainty is crucial to the utility of direct numerical simulation (DNS) results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier–Stokes equations. Due to the presence of non-trivial sampling error, standard techniques for estimating discretization error (such as Richardson extrapolation) fail or are unreliable. This work provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as part of a Bayesian extension of Richardson extrapolation in order to characterize the discretization error. These methods are tested using the Lorenz equations and are shown to perform well. These techniques are then used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow at Reτ ≈ 180. Both small (Lx/δ × Lz/δ = 4π × 2π) and large (Lx/δ × Lz/δ = 12π × 4π) domain sizes are investigated. For each case, a sequence of meshes was generated by first designing a “nominal” mesh using standard heuristics for wall-bounded simulations. These nominal meshes were then coarsened to generate a sequence of grid resolutions appropriate for the Bayesian Richardson extrapolation method. In addition, the small box case is computationally inexpensive enough to allow simulation on a finer mesh, enabling the results of the extrapolation to be validated in a weak sense. For both cases, it is found that while the sampling uncertainty is large enough to make the order of accuracy difficult to determine, the estimated discretization errors are quite small. This indicates that the commonly used heuristics provide adequate resolution for this class of problems. However, it is also found that, for some quantities, the discretization error is not small relative to sampling error, indicating that the conventional wisdom that sampling error dominates discretization error for this class of simulations needs to be reevaluated.

Oliver, Todd A.↗
DOE OSTI2015

Improved estimates of the Milky Way’s stellar mass and star formation rate from hierarchical Bayesian meta-analysis

We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields an SFR for the Galaxy of M-dot {sub ⋆}=1.65±0.19 M{sub ⊙} yr{sup −1}, assuming a Kroupa initial mass function (IMF). By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, R{sub 0}, the exponential scale length of the disk, L{sub d}, and the local surface density of stellar mass, Σ{sub ⋆}(R{sub 0}), we show that the mass of the Galactic bulge+bar is M{sub ⋆}{sup B}=0.91±0.07×10{sup 10} M{sub ⊙}, the disk mass is M{sub ⋆}{sup D}=5.17±1.11×10{sup 10} M{sub ⊙}, and their combination yields a total stellar mass of M{sub ⋆}=6.08±1.14×10{sup 10} M{sub ⊙} (assuming a Kroupa IMF and an exponential disk profile). This analysis is based upon a new compilation of literature bulge mass estimates, normalized to common assumptions about the stellar IMF and Galactic disk properties, presented herein. We additionally find a bulge-to-total mass ratio for the Milky Way of B/T=0.150{sub −0.019}{sup +0.028} and a specific SFR of M-dot {sub ⋆}/M{sub ⋆}=2.71±0.59×10{sup −11} yr{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Self-replication with magnetic dipolar colloids

Colloidal self-replication represents an exciting research frontier in soft matter physics. Currently, all reported self-replication schemes involve coating colloidal particles with stimuli-responsive molecules to allow switchable interactions. In this paper, we introduce a scheme using ferromagnetic dipolar colloids and preprogrammed external magnetic fields to create an autonomous self-replication system. Interparticle dipole-dipole forces and periodically varying weak-strong magnetic fields cooperate to drive colloid monomers from the solute onto templates, bind them into replicas, and dissolve template complexes. We present three general design principles for autonomous linear replicators, derived from a focused study of a minimalist sphere-dimer magnetic system in which single binding sites allow formation of dimeric templates. We show via statistical models and computer simulations that our system exhibits nonlinear growth of templates and produces nearly exponential growth (low error rate) upon adding an optimized competing electrostatic potential. Lastly, we devise experimental strategies for constructing the required magnetic colloids based on documented laboratory techniques. We also present qualitative ideas about building more complex self-replicating structures utilizing magnetic colloids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

SOC Microstructural Property Estimator

This pre-trained ML model is a tool that uses basic compositional parameters for porous solid oxide cell (SOC) electrodes - the phase fractions and mean particle/pore diameters – as inputs and uses them to estimate additional electrochemical performance parameters: active (i.e., connected) TPB density, all tortuosity factors, and phase pair specific interfacial areas. The electrode is assumed to be composed of two solid phases and a pore phase. The property calculations are performed using neural network regression models trained on a large bank of synthetic electrode microstructural data that NETL has generated using the program DREAM3D (that bank is also hosted on EDX: https://edx.netl.doe.gov/dataset/soc-synthetic-microstructure-bank). This means the generated parameters are based on training from actual measured properties from 3D microstructures, not estimated from geometric simplifications. This tool was developed and is intended to replace percolation theory calculations in models that use hypothetical electrode properties. An example use case would be running SOC performance simulations across a parametric sweep of electrode designs (e.g., varying phase fractions and particle sizes) and assessing how it impacts the electrochemical performance of the SOC. Within the parameter space of the training data (statistics of that parameter space is provided in the readme file), this model achieves sub-5% mean absolute percent errors, an order of magnitude less error than percolation theory across the same parameter space. However, be aware that this tool was developed with parametric simulations in mind, and users are encouraged to assess accuracy for their own specific use case rather than taking accuracy metrics at face value. More info, including a usage guide, is in the included readme file. This tool should be cited with the DOI number provided.

Electrode Microstructure↗
DOE OSTI2014

Advanced Small Modular Reactor Economics Model Development

The US Department of Energy Office of Nuclear Energy’s Advanced Small Modular Reactor (SMR) research and development activities focus on four key areas: Developing assessment methods for evaluating advanced SMR technologies and characteristics; and Developing and testing of materials, fuels and fabrication techniques; and Resolving key regulatory issues identified by US Nuclear Regulatory Commission and industry; and Developing advanced instrumentation and controls and human-machine interfaces. This report focuses on development of assessment methods to evaluate advanced SMR technologies and characteristics. Specifically, this report describes the expansion and application of the economic modeling effort at Oak Ridge National Laboratory. Analysis of the current modeling methods shows that one of the primary concerns for the modeling effort is the handling of uncertainty in cost estimates. Monte Carlo–based methods are commonly used to handle uncertainty, especially when implemented by a stand-alone script within a program such as Python or MATLAB. However, a script-based model requires each potential user to have access to a compiler and an executable capable of handling the script. Making the model accessible to multiple independent analysts is best accomplished by implementing the model in a common computing tool such as Microsoft Excel. Excel is readily available and accessible to most system analysts, but it is not designed for straightforward implementation of a Monte Carlo–based method. Using a Monte Carlo algorithm requires in-spreadsheet scripting and statistical analyses or the use of add-ons such as Crystal Ball. An alternative method uses propagation of error calculations in the existing Excel-based system to estimate system cost uncertainty. This method has the advantage of using Microsoft Excel as is, but it requires the use of simplifying assumptions. These assumptions do not necessarily bring into question the analytical results. In fact, the analysis shows that the propagation of error method introduces essentially negligible error, especially when compared to the uncertainty associated with some of the estimates themselves. The results of these uncertainty analyses generally quantify and identify the sources of uncertainty in the overall cost estimation. The obvious generalization—that capital cost uncertainty is the main driver—can be shown to be an accurate generalization for the current state of reactor cost analysis. However, the detailed analysis on a component-by-component basis helps to demonstrate which components would benefit most from research and development to decrease the uncertainty, as well as which components would benefit from research and development to decrease the absolute cost.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Travel Patterns And Characteristics Of Transit Users In New York State

This research is a detailed examination of the travel behaviors and patterns of transit users within New York State (NYS), primarily based on travel data provided by the National Household Travel Survey (NHTS) in 2009 and the associated Add-on sample households purchased by the New York State Department of Transportation (NYSDOT). Other data sources analyzed in this study include: NYS General Transit Feed Specification (GTFS) to assist in analyzing spatial relationships for access to transit and the creation of Transit Shed geographic areas of 1, 2.5, and 5 miles from transit stop locations, LandScan population database to understand transit coverage, and Census Bureau s American Community Survey (ACS) data to examine general transit patterns and trends in NYS over time. The majority of analyses performed in this research aimed at identifying transit trip locations, understanding differences in transit usage by traveler demographics, as well as producing trip/mode-specific summary statistics including travel distance, trip duration, time of trip, and travel purpose of transit trips made by NYS residents, while also analyzing regional differences and unique travel characteristics and patterns. The analysis was divided into two aggregated geographic regions: New York Metropolitan Transportation Council (NYMTC) and NYS minus NYMTC (Rest of NYS). The inclusion of NYMTC in all analysis would likely produce misleading conclusions for other regions in NYS. TRANSIT COVERAGE The NYS transit network has significant coverage in terms of transit stop locations across the state s population. Out of the 19.3 million NYS population in 2011, about 15.3 million (or 79%) resided within the 1-mile transit shed. This NYS population transit coverage increased to 16.9 million (or 88%) when a 2.5-mile transit shed was considered; and raised to 17.7 million (or 92%) when the 5-mile transit shed was applied. KEY FINDINGS Based on 2009 NHTS data, about 40% of NYMTC households used transit as their means of transportation on any typical day; while only 4% of households located elsewhere in NYS did the same. Regardless of geographic regions, 45% of the transit users came from households with income under $40,000, while 20% of transit users were from the top income group of $100,000 plus households. Travel made by NYMTC transit users were nearly twice as likely to be for work trips as compared to their counterpart non-transit users. Transit users in NYS generally made more trips but with shorter distances; they also drove less, which resulted in fewer miles. Furthermore, NYS transit users spent more time on each trip than their counterpart non-transit users. Because of the intensity of transit network services within NYMTC, 88% of the households reside within the 1-mile transit shed. Outside the NYMTC, however, only 54% of the region s households are located within the same distance. Impact to vehicle ownership was clearly evidenced. Nearly all people from zero-vehicle households in NYMTC lived within a 1-mile radius of transit stops. Elsewhere in NYS, 74% of residents from zero-vehicle households resided within the 1-mile transit shed. Close proximity to transit has a significant impact on increasing transit uses. Transit mode share, as a main mode, was higher for NYS residents that lived within the 1-mile transit shed than others. Based on ACS data, over the period from 2005 to 2013, the total number of NYMTC workers increased more than 9%, while transit commuting grew at a higher rate of more than 15% during the same period. REMARKS Note that transit use in areas outside the NYMTC region generally is not common, resulting in a smaller sample size of transit users in the Rest of NYS region. Caution should be exercised for statistics produced based on small sample sizes that tend to be less precise (i.e., with a larger margin of error). Furthermore, standardized transit network data were not available prior to 2005; comparable analyses using 2001 NHTS therefore was not feasible. As a result, this study focused on examining travel behaviors of transit users using 2009 NHTS data only.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Cosmological Constraints from Combining Photometric Galaxy Surveys and Gravitational Wave Observatories

Spatial variations in survey properties due to selection effects generate substantial systematic errors in large-scale structure measurements in optical galaxy surveys on very large scales. On such scales, the statistical sensitivity of optical surveys is also limited by their finite sky coverage. By contrast, gravitational wave (GW) sources appear to be relatively free of these issues, provided the angular sensitivity of GW experiments can be accurately characterized. We quantify the expected cosmological information gain from combining the forecast LSST 3$\times$2pt analysis (combination of three 2-point correlations of galaxy density and weak lensing shear fields) with the large-scale auto-correlation of GW sources from proposed next-generation GW experiments. We find that in $\Lambda$CDM and $w$CDM models, there is no significant improvement in cosmological constraints from combining GW with LSST 3$\times$2pt over LSST alone, due to the large shot noise for the former; however, this combination does enable a $\sim6\%$ constraint on the linear galaxy bias of GW sources. More interestingly, the optical-GW data combination provides tight constraints on models with primordial non-Gaussianity (PNG), due to the predicted scale-dependent bias in PNG models on large scales. Assuming that the largest angular scales that LSST will probe are comparable to those in Stage III surveys ($\ell_{\rm min}\sim50$), the inclusion of next-generation GW measurements could improve constraints on the PNG parameter $f_{\rm NL}$ by up to a factor of $\simeq6.6$ compared to LSST alone, yielding $\sigma(f_{\rm NL})=8.5$. These results assume the expected capability of a network of Einstein Telescope-like GW observatories, with a detection rate of $10^6$ events/year. We investigate the sensitivity of our results to different assumptions about future GW detectors as well as different LSST analysis choices.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Comparative Performance of Gaussian Plume and Backward Lagrangian Stochastic Models for Near-Field Methane Emission Estimation Using a Single Controlled Release Experiment

Methane (CH 4 ) is a major component of natural gas and a potent greenhouse gas. Increasing atmospheric methane concentrations are attributed to emissive anthropogenic activities by an average of 13 ppb per yr since 2020 and are linked to a changing global climate. Mitigating CH 4 emissions from oil and gas production sites has recently become a target to reduce overall greenhouse gas emissions; however, monitoring the efficacy of mitigation strategies depends on accurate quantification of CH 4 emissions at the facility-level. Near-field quantification of methane (CH 4 ) emissions from oil and gas (O&G) facilities remains challenging due to the effects of atmospheric variability and sensor configuration on atmospheric dispersion models. This study evaluates the performance of two atmospheric dispersion models, the Gaussian plume (GP) and backward Lagrangian stochastic (bLS), by comparing calculated CH 4 emissions to controlled single-point emissions between 0.4 and 5.2 kg CH 4 h −1 . Emissions were calculated by both models using 121 individual sets of measurements comprising five-minute averaged downwind methane mixing ratios and matching meteorological data. The comparison shows that the bLS approach achieved a higher proportion of emission estimates within a factor of two (FAC2) of the known emission rates compared to the GP approach. The emissions calculated by the bLS model also had a lower multiplicative error and reduced bias relative to GP. Other error-based metrics further confirmed the bLS model performed better, as it yielded lower RMSE and MAE than GP. Statistical analysis of the emission data shows that the lateral and vertical alignment of the source and the sensor plays a critical role in emission estimations, as measurements made closer to the plume centerline and at a distance between 40 and 80 m downwind yielded the best FAC2 agreement. High wind meander degraded the ability of both approaches to generate representative emissions, particularly with the GP approach, as it violates the modeling approach’s assumption of steady-state emissions. Data suggest emissions calculated by the bLS model are comprehensively in better agreement, but the computational demands of the modeling approach and integration into fenceline systems limit real-time applicability. While these results provide insight into model performance under controlled near-field conditions, their applicability to more complex or heterogeneous oil and gas production environments (e.g., the regions Marcellus or Unita Basins) remains limited and uncertain.

gaussian plume↗
DOE OSTI2022

Characterizing the Reproducibility of Noisy Quantum Circuits

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Extreme metrics from large ensembles: investigating the effects of ensemble size on their estimates

Abstract. We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a number of extreme metrics. While we exploit existing large ensembles, our perspective is that of a modeling center wanting to estimate a priori such sizes on the basis of an existing small ensemble (we assume the availability of only five members here). We therefore ask if such a small-size ensemble is sufficient to estimate accurately the population variance (i.e., the ensemble internal variability) and then apply a well-established formula that quantifies the expected error in the estimation of the population mean (i.e., the forced component) as a function of the sample size n, here taken to mean the ensemble size. We find that indeed we can anticipate errors in the estimation of the forced component for temperature and precipitation extremes as a function of n by plugging into the formula an estimate of the population variance derived on the basis of five members. For a range of spatial and temporal scales, forcing levels (we use simulations under Representative Concentration Pathway 8.5) and two models considered here as our proof of concept, it appears that an ensemble size of 20 or 25 members can provide estimates of the forced component for the extreme metrics considered that remain within small absolute and percentage errors. Additional members beyond 20 or 25 add only marginal precision to the estimate, and this remains true when statistical inference through extreme value analysis is used. We then ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation and – importantly – about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings. Using the F test, we find that estimates on the basis of only 5 or 10 ensemble members accurately represent the full ensemble variance even when the analysis is conducted at the grid-point scale. The detection of changes in the variance when comparing different times along the simulation, especially for the precipitation-based metrics, requires larger sizes but not larger than 15 or 20 members. While we recognize that there will always exist applications and metric definitions requiring larger statistical power and therefore ensemble sizes, our results suggest that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members. This invites consideration of the possibility of exploring additional sources of uncertainty, such as physics parameter settings, when designing ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1975

Sequential Least-Squares Using Orthogonal Transformations

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission.

Bierman, G. J.↗
NASA NTRS1976

Statistics of the radiated field of a space-to-earth microwave power transfer system

Statistics such as average power density pattern, variance of the power density pattern and variance of the beam pointing error are related to hardware parameters such as transmitter rms phase error and rms amplitude error. Also a limitation on spectral width of the phase reference for phase control was established. A 1 km diameter transmitter appears feasible provided the total rms insertion phase errors of the phase control modules does not exceed 10 deg, amplitude errors do not exceed 10% rms, and the phase reference spectral width does not exceed approximately 3 kHz. With these conditions the expected radiation pattern is virtually the same as the error free pattern, and the rms beam pointing error would be insignificant (approximately 10 meters).

Stevens, G. H.↗