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NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗
DOE OSTI2025

Transfer learning of neural surrogates on multifidelity groundwater simulations

Multifidelity data used in the paper published in Advances in Water Resources 206 (2025) 105140, https://doi.org/10.1016/j.advwatres.2025.105140 The code used to process the data is openly available on GitHub at https://github.com/Model-Reduction-and-UQ-Group/Transfer_Learning_K_reconstruction Computationally inexpensive surrogates of process-based models, such as deep neural networks, enable ensemble-based computations used in risk assessment, data assimilation, etc. However, generation of large datasets required to train a neural network can be as expensive as the ensemble simulations themselves. We ameliorate this challenge by using data from multifidelity (MF) groundwater simulations and transfer learning (TL) to reduce data generation costs while maintaining model accuracy. As a computational example, we train a deep convolutional neural network (CNN) to reconstruct permeability fields from saturation maps derived from a multiphase flow model. Starting with very low- and low-fidelity data generated on increasingly coarse meshes, we pretrain the CNN, followed by output-layer training and fine-tuning using only a limited number of high-fidelity samples. We demonstrate the surrogate’s robustness when interpreting low-quality inputs—such as interpolated maps or data affected by noise—which has strong implications for the applicability in practical hydrogeological scenarios. This multilevel MF-TL strategy achieves a favorable trade-off between computational efficiency and predictive accuracy, significantly outperforming high-fidelity-only approaches under the same computational budget.

Chiofalo, Alessia [University of Bologna] (ORCID:0↗
DOE OSTI2026

Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parametrizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion-ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the 78 Kr and 124 Xe projectiles. The resulting parameter trends are then propagated to the 92 Mo and 144 Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.

Bayesian methods↗
NASA NTRS1971

Determination of stratospheric temperature and height gradients from nimbus 3 radiation data

To improve the specification of stratospheric horizontal temperature and geopotential height fields from satellite radiation data, needed for high flying aircraft, a technique was derived to estimate data between satellite tracks using interpolated IRIS 15-micron data from Nimbus III. The interpolation is based on the observed gradients of the MRIR 15-micron radiances between subsatellite tracks. The technique was verified with radiosonde data taken within 6 hours of the satellite data. The sample varied from 1126 pairs at low levels to 383 pairs at 10 mb using northern hemisphere data for June 15 to July 20, 1969. The data were separated into five latitude bands. The Rms temperature differences were generally from 2 to 5 C for all levels above 300 mb. From 500 to 300 mb RMS differences vary from 4 to 9C except at high latitudes which show values near 3C. The RMS differences between radiosonde heights and those calculated hydrostatically from the surface were from 30 to 280 meters increasing from the surface to 10 mb. Integration starting at 100 mb reduced the RMS difference in the stratosphere to 20 to 120 meters from 70 to 10 mb. From a comparison with actual operational maps at 50 and 10 mb, it appears the techniques developed produce analyses in general agreement with those from radiosonde data. In addition, they are able to indicate details over areas of sparse data not shown by conventional techniques.

Nicholas, G. W.↗
DOE OSTI2021

DSGAN

This study develops a neural network-based approach for emulating high-resolution modeled precipitation data with comparable statistical properties but at greatly reduced computational cost. The key idea is to use combination of low-and high- resolution simulations to train a neural network to map from the former to the latter. Specifically, we define two types of CNNs, one that stacks variables directly and one that encodes each variable before stacking, and we train each CNN type both with a conventional loss function, such as mean square error (MSE), and with a conditional generative adversarial network (CGAN), for a total of four CNN variants. We compare the four new CNN-derived high-resolution precipitation results with precipitation generated from original high resolution simulations, a bilinear interpolater and the state-of-the-art CNN-based super-resolution (SR) technique. Results show that the SR technique produces results similar to those of the bilinear interpolator with smoother spatial and temporal distributions and smaller data variabilities and extremes than the original high resolution simulations. While the new CNNs trained by MSE generate better results over some regions than the interpolator and SR technique do, their predictions are still not as close as the original high resolution simulations. The CNNs trained by CGAN generate more realistic and physically reasonable results, better capturing not only data variability in time and space but also extremes such as intense and long-lasting storms. The new proposed CNN-based downscaling approach can downscale precipitation from 50~km to 12~km in 14~min for 30~years

LIU, ZHENGCHUN↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
NASA NTRS2004

High-Order Simulation of Non-Linear Oscillations and Shocks in the Solar Atmosphere

The solar atmosphere presents a rich source of highly non-linear magneto-hydrodynamic phenomena: strong gradients and forcing terms result in both large shocks and oscillations. The additional requirements of energy balance and initialization in hydrostatic equilibrium compound the challenge of this problem. A wealth of observational data allows us to check the results of our simulations. The problem of simulating the solar atmosphere provides, in addition to an interesting system in its own right, a challenging testbed for high-order shock-capturing methods. We discuss the challenge of simulating solar atmospheric phenomena, concentrating on various high-order central methods ranging from second to fourth order. Our method is based on the central-upwind scheme of Kurganov, Noelle and Petrova, which we extend to high order via various interpolants. We investigate various initial data for our simulations, corresponding to observed conditions in different regions of the solar surface: the normal quiet sun and sunspots. When non-oscillatory using second- and third-order methods, we are able to reproduce non-trivial observational results. In particular we find a correlation between initial data and both the shock speeds and particle oscillation spectra that match observations in the corresponding regions. When using fourth-order WENO interpolants, we find that while the individual shock profiles at any given time appear non-oscillatory, spurious oscillations appear in the fields after long time integrations. The issue of initialization in hydrostatic equilibrium raises difficult issues. Careful treatment of the gravitational source term can reduce violations of hydrostatic equilibrium, but difficulties remain, primarily due to discontinuities in the piecewise-polynomial reconstructions. In the case of the Euler equations in gravity, the use of high-order methods reduces the violation of hydrostatic equilibrium to a sufficiently low level for the above described results to be obtained. Including various energy flux terms in the equations, however, leads to severe instability when hydrostatic balance is violated. We discuss various strategies to address this problem, including adaptive grid methods.

Bryson, S.↗
DOE OSTI2020

Super resolution for root imaging

Premise High‐resolution cameras are very helpful for plant phenotyping as their images enable tasks such as target vs. background discrimination and the measurement and analysis of fine above‐ground plant attributes. However, the acquisition of high‐resolution images of plant roots is more challenging than above‐ground data collection. An effective super‐resolution (SR) algorithm is therefore needed for overcoming the resolution limitations of sensors, reducing storage space requirements, and boosting the performance of subsequent analyses. Methods We propose an SR framework for enhancing images of plant roots using convolutional neural networks. We compare three alternatives for training the SR model: (i) training with non‐plant‐root images, (ii) training with plant‐root images, and (iii) pretraining the model with non‐plant‐root images and fine‐tuning with plant‐root images. The architectures of the SR models were based on two state‐of‐the‐art deep learning approaches: a fast SR convolutional neural network and an SR generative adversarial network. Results In our experiments, we observed that the SR models improved the quality of low‐resolution images of plant roots in an unseen data set in terms of the signal‐to‐noise ratio. We used a collection of publicly available data sets to demonstrate that the SR models outperform the basic bicubic interpolation, even when trained with non‐root data sets. Discussion The incorporation of a deep learning–based SR model in the imaging process enhances the quality of low‐resolution images of plant roots. We demonstrate that SR preprocessing boosts the performance of a machine learning system trained to separate plant roots from their background. Our segmentation experiments also show that high performance on this task can be achieved independently of the signal‐to‐noise ratio. We therefore conclude that the quality of the image enhancement depends on the desired application.

Ruiz‐Munoz, Jose F.↗
DOE OSTI2021

Fast and accurate learned multiresolution dynamical downscaling for precipitation

Abstract. This study develops a neural-network-based approach for emulating high-resolution modeled precipitation data with comparable statistical properties but at greatly reduced computational cost. The key idea is to use combination of low- and high-resolution simulations (that differ not only in spatial resolution but also in geospatial patterns) to train a neural network to map from the former to the latter. Specifically, we define two types of CNNs, one that stacks variables directly and one that encodes each variable before stacking, and we train each CNN type both with a conventional loss function, such as mean square error (MSE), and with a conditional generative adversarial network (CGAN), for a total of four CNN variants. We compare the four new CNN-derived high-resolution precipitation results with precipitation generated from original high-resolution simulations, a bilinear interpolater and the state-of-the-art CNN-based super-resolution (SR) technique. Results show that the SR technique produces results similar to those of the bilinear interpolator with smoother spatial and temporal distributions and smaller data variabilities and extremes than the original high-resolution simulations. While the new CNNs trained by MSE generate better results over some regions than the interpolator and SR technique do, their predictions are still biased from the original high-resolution simulations. The CNNs trained by CGAN generate more realistic and physically reasonable results, better capturing not only data variability in time and space but also extremes such as intense and long-lasting storms. The new proposed CNN-based downscaling approach can downscale precipitation from 50 to 12 km in 14 min for 30 years once the network is trained (training takes 4 h using 1 GPU), while the conventional dynamical downscaling would take 1 month using 600 CPU cores to generate simulations at the resolution of 12 km over the contiguous United States.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗
DOE OSTI2023

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper considers the dual-weighted residual (DWR) error estimate for pROMs and compares it to another promising pROM error estimate, machine learned error models (MLEM). Here, we show how DWR can be applied to ROMs and then evaluate DWR on two partial differential equations (PDEs): a two-dimensional linear convection–reaction–diffusion equation, and a three-dimensional static hyper-elastic beam. It is shown that DWR is able to estimate errors for pROMs extrapolating outside of their training set while MLEM is best suited for pROMs used to interpolate within the pROM training set.

42 ENGINEERING↗
DOE OSTI2023

Energy Exascale Earth System Model v2.1.0

First release of version 2.1 of the Energy Exascale Earth System Model. [ATM] The atmosphere component remains EAM. There are no major changes in the default configuration since 2.0. New features include: A semi-lagrangian tracer transport for theta-l dycore, a new algorithm for finding the tropopause, new RRM mesh configurations. Add and update SSP370 and SSP585 cases. Restore the FIDEAL case. [LAND] The land component is ELM. There are no major changes in the default configuration since 2.0. Several option features have been added including: implementation of topography-based subgrid structure (topounits) and accompanying parameterizations and atmospheric forcing downscaling methods; a new plant hydraulics scheme; two-way land-river hydrological coupling through the infiltration of floodplain water; an implementation of perennial crops; updates to the SNICAR-AD snow radiative transfer model; and implementation of soil erosion and sediment yield in ELM-Erosion. Each of these new changes is modular in design and can be turned on or off as the user specifies; they are currently being tested in different “BGC” configurations. [OCEAN] The ocean component remains MPAS-Ocean. Major change since version 2.0 include the addition of the Fox-Kemper et al. 2011 parameterization for submesocale eddies, a correction for barotropic thickness consistency that reduces divergence noise, and the addition of an ocean carbon conservation analysis member. [SEAICE] The sea-ice component remains MPAS-Seaice. Major changes since version 2.0 include: A correction to how shortwave parameters are interpolated in the snicar-ad 5-band radiation scheme, the addition of a sea ice carbon conservation analysis member, updates to the default sea ice biogeochemistry namelist parameters to be consistent with version 2.0 improvements to nitrogen cycling and a correction in the ice-ocean dissolved organic nitrogen coupling. [LAND ICE] The land-ice component remains MPAS-Albany-landIce (MALI). Major changes since 2.0 include an update to the MALI version and the Greenland mesh.[RIVER] The river model is MOSART. There are no major changes in the default configuration since 2.0. A major new optional feature is two-way river-ocean hydrological coupling between MOSART and MPAS-O. This change can be turned on or off as the user specifies, and is being tested in different configurations. [COUPLER] The coupler remains cpl7/MCT. Major changes since version 2.0 include: Carbon budget calculated when heat/water budgets active. Fix a bug in land-atm fluxes for tri-grid configurations. [OTHER] a small bug in the zenith angle calculation was fixed in the data models.

ECP↗
NASA NTRS1996

Optimization of Orifice Geometry for Cross-Flow Mixing in a Cylindrical Duct

Mixing of gaseous jets in a cross-flow has significant applications in engineering, one example of which is the dilution zone of a gas turbine combustor. Despite years of study, the design of the jet injection in combustors is largely based on practical experience. The emergence of NO(x) regulations for stationary gas turbines and the anticipation of aero-engine regulations requires an improved understanding of jet mixing as new combustor concepts are introduced. For example, the success of the staged combustor to reduce the emission of NO(x) is almost entirely dependent upon the rapid and complete dilution of the rich zone products within the mixing section. It is these mixing challenges to which the present study is directed. A series of experiments was undertaken to delineate the optimal mixer orifice geometry. A cross-flow to core-flow momentum-flux ratio of 40 and a mass flow ratio of 2.5 were selected as representative of a conventional design. An experimental test matrix was designed around three variables: the number of orifices, the orifice length-to- width ratio, and the orifice angle. A regression analysis was performed on the data to arrive at an interpolating equation that predicted the mixing performance of orifice geometry combinations within the range of the test matrix parameters. Results indicate that the best mixing orifice geometry tested involves eight orifices with a long-to-short side aspect ratio of 3.5 at a twenty-three degree inclination from the center-line of the mixing section.

Kroll, J. T.↗
NASA NTRS1996

Atmospheric Pre-Corrected Differential Absorption Techniques to Retrieve Columnar Water Vapor: Theory and Simulations

Two different approaches exist to retrieve columnar water vapor from imaging spectrometer data: (1) Differential absorption techniques based on: (a) Narrow-Wide (N/W) ratio between overlapping spectrally wide and narrow channels; (b) Continuum Interpolated Band Ratio (CIBR) between a measurement channel and the weighted sum of two reference channels. (2) Non-linear fitting techniques which are based on spectral radiative transfer calculations. The advantage of the first approach is computational speed and of the second, improved retrieval accuracy. Our goal was to improve the accuracy of the first technique using physics based on radiative transfer. Using a modified version of the Duntley equation, we derived an "Atmospheric Pre-corrected Differential Absorption" (APDA) technique and described an iterative scheme to retrieve water vapor on a pixel-by-pixel basis. Next we compared both, the CIBR and the APDA using the Duntley equation for MODTRAN3 computed irradiances, transmissions and path radiance (using the DISORT option). This simulation showed that the CIBR is very sensitive to reflectance effects and that the APDA performs much better. An extensive data set was created with the radiative transfer code 6S over 379 different ground reflectance spectra. The calculated relative water vapor error was reduced significantly for the APDA. The APDA technique had about 8% (vs. over 35% for the CIBR) of the 379 spectra with a relative water vapor error of greater than +5%. The APDA has been applied to 1991 and 1995 AVIRIS scenes which visually demonstrate the improvement over the CIBR technique.

Borel, Christoph C.↗
DOE OSTI2022

Machine learning the metastable phase diagram of covalently bonded carbon

Abstract Conventional phase diagram generation involves experimentation to provide an initial estimate of the set of thermodynamically accessible phases and their boundaries, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to experimentally inaccessible regions. Such an approach, combined with high throughput first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases (e.g. compatible with the CALPHAD method), albeit focused on the reduced set of phases observed at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local (metastable) free energy minimum, which may exhibit desirable properties. Here, we introduce an automated workflow that integrates first-principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases to construct “metastable” phase diagrams for materials far-from-equilibrium. Using carbon as a prototypical system, we demonstrate automated metastable phase diagram construction to map hundreds of metastable states ranging from near equilibrium to far-from-equilibrium (400 meV/atom). We incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for efficient construction of metastable phase diagrams. We use the metastable phase diagram and identify domains of relative stability and synthesizability of metastable materials. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy (HRTEM) confirm our metastable phase predictions. In particular, we identify the previously ambiguous structure of n -diamond as a cubic-analog of diaphite-like lonsdaelite phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2018

Polarization Ray Tracing and Polarization Aberration Compensation in Reflective Astronomical Telescopes

Assessing and optimizing polarization performance in the context of ray-based optical design can be challenging. We describe an approach to this problem that decouples polarization effects from optical system geometry for reflective systems. Each surface's polarization properties are parameterized in terms of their impact on retardance and diattenuation in the small angle-of-incidence limit, separating polarization assessment from the task of coating design. A low-resolution ray trace of the system is adequate to determine ray geometry at each interface, which can then be interpolated to rapidly evaluate net Jones Matrix pupil functions. Coating behavior can be easily varied using the ellipsometric parameters to investigate impacts and compensation. Desired values of these parameters can then be specified as constraints in coating design. Investigation with candidate telescope optical designs for LUVOIR show baseline root-mean-square wavefront errors in the nm range for the on-diagonal Jones matrix component, and throughputs of tens of parts per million. Promising possibilities for compensation using a purpose-designed coating on the secondary mirror are discussed, which reduce the on-diagonal wavefront error by a factor 20, with accompanying but more modest reductions in coupling into off-diagonal terms.

Sabatke, Derek↗
NASA NTRS2013

Geostationary Enhanced Temporal Interpolation for CERES Flux Products

The Clouds and the Earth's Radiant Energy System (CERES) instruments on board the Terra and Aqua spacecraft continue to provide an unprecedented global climate record of the earth's top-of-atmosphere (TOA) energy budget since March 2000. A critical step in determining accurate daily averaged flux involves estimating the flux between CERES Terra or Aqua overpass times. CERES employs the CERES-only (CO) and the CERES geostationary (CG) temporal interpolation methods. The CO method assumes that the cloud properties at the time of the CERES observation remain constant and that it only accounts for changes in albedo with solar zenith angle and diurnal land heating, by assuming a shape for unresolved changes in the diurnal cycle. The CG method enhances the CERES data by explicitly accounting for changes in cloud and radiation between CERES observation times using 3-hourly imager data from five geostationary (GEO) satellites. To maintain calibration traceability, GEO radiances are calibrated against Moderate Resolution Imaging Spectroradiometer (MODIS) and the derived GEO fluxes are normalized to the CERES measurements. While the regional (1 deg latitude x 1 deg longitude) monthly-mean difference between the CG and CO methods can exceed 25 W m(sub -2) over marine stratus and land convection, these regional biases nearly cancel in the global mean. The regional monthly CG shortwave (SW) and longwave (LW) flux uncertainty is reduced by 20%, whereas the daily uncertainty is reduced by 50% and 20%, respectively, over the CO method, based on comparisons with 15-min Geostationary Earth Radiation Budget (GERB) data.

Doelling, David R.↗
NASA NTRS2009

Conical-Domain Model for Estimating GPS Ionospheric Delays

The conical-domain model is a computational model, now undergoing development, for estimating ionospheric delays of Global Positioning System (GPS) signals. Relative to the standard ionospheric delay model described below, the conical-domain model offers improved accuracy. In the absence of selective availability, the ionosphere is the largest source of error for single-frequency users of GPS. Because ionospheric signal delays contribute to errors in GPS position and time measurements, satellite-based augmentation systems (SBASs) have been designed to estimate these delays and broadcast corrections. Several national and international SBASs are currently in various stages of development to enhance the integrity and accuracy of GPS measurements for airline navigation. In the Wide Area Augmentation System (WAAS) of the United States, slant ionospheric delay errors and confidence bounds are derived from estimates of vertical ionospheric delay modeled on a grid at regularly spaced intervals of latitude and longitude. The estimate of vertical delay at each ionospheric grid point (IGP) is calculated from a planar fit of neighboring slant delay measurements, projected to vertical using a standard, thin-shell model of the ionosphere. Interpolation on the WAAS grid enables estimation of the vertical delay at the ionospheric pierce point (IPP) corresponding to any arbitrary measurement of a user. (The IPP of a given user s measurement is the point where the GPS signal ray path intersects a reference ionospheric height.) The product of the interpolated value and the user s thin-shell obliquity factor provides an estimate of the user s ionospheric slant delay. Two types of error that restrict the accuracy of the thin-shell model are absent in the conical domain model: (1) error due to the implicit assumption that the electron density is independent of the azimuthal angle at the IPP and (2) error arising from the slant-to-vertical conversion. At low latitudes or at mid-latitudes under disturbed conditions, the accuracy of SBAS systems based upon the thin-shell model suffers due to the presence of complex ionospheric structure, high delay values, and large electron density gradients. Interpolation on the vertical delay grid serves as an additional source of delay error. The conical-domain model permits direct computation of the user s slant delay estimate without the intervening use of a vertical delay grid. The key is to restrict each fit of GPS measurements to a spatial domain encompassing signals from only one satellite. The conical domain model is so named because each fit involves a group of GPS receivers that all receive signals from the same GPS satellite (see figure); the receiver and satellite positions define a cone, the satellite position being the vertex. A user within a given cone evaluates the delay to the satellite directly, using (1) the IPP coordinates of the line of sight to the satellite and (2) broadcast fit parameters associated with the cone. The conical-domain model partly resembles the thin-shell model in that both models reduce an inherently four-dimensional problem to two dimensions. However, unlike the thin-shell model, the conical domain model does not involve any potentially erroneous simplifying assumptions about the structure of the ionosphere. In the conical domain model, the initially four-dimensional problem becomes truly two-dimensional in the sense that once a satellite location has been specified, any signal path emanating from a satellite can be identified by only two coordinates; for example, the IPP coordinates. As a consequence, a user s slant-delay estimate converges to the correct value in the limit that the receivers converge to the user s location (or, equivalently, in the limit that the measurement IPPs converge to the user s IPP).

Sparks, Lawrence↗