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At least 343 records · Page 19

Reducing the error of geoid undulation computations by modifying Stokes' function

The truncation theory as it pertains to the calculation of geoid undulations based on Stokes' integral, but from limited gravity data, is reexamined. Specifically, the improved procedures of Molodenskii et al. are shown through numerical investigations to yield substantially smaller errors than the conventional method that is often applied in practice. In this improved method, as well as in a simpler alternative to the conventional approach, the Stokes' kernel is suitably modified in order to accelerate the rate of convergence of the error series. These modified methods, however, effect a reduction in the error only if a set of low-degree potential harmonic coefficients is utilized in the computation. Consider, for example, the situation in which gravity anomalies are given in a cap of radius 10 deg and the GEM 9 (20,20) potential field is used. Then, typically, the error in the computed undulation (aside from the spherical approximation and errors in the gravity anomaly data) according to the conventional truncation theory is 1.09 m; with Meissl's modification it reduces to 0.41m, while Molodenskii's improved method gives 0.45 m. A further alteration of Molodenskii's method is developed and yields an RMS error of 0.33 m. These values reflect the effect of the truncation, as well as the errors in the GEM 9 harmonic coefficients. The considerable improvement, suggested by these results, of the modified methods over the conventional procedure is verified with actual gravity anomaly data in two oceanic regions, where the GEOS-3 altimeter geoid serves as the basis for comparison. The optimal method of truncation, investigated by Colombo, is extremely ill-conditioned. It is shown that with no corresponding regularization, this procedure is inapplicable.

Jekeli, C.↗

Navigational utility of high-precision radio interferometer for Galileo's approach to Jupiter

The effect of very long baseline interferometry (VLBI) measurements of 2-nanoradian (nrad) accuracy has been studied for use in Galileo's approach to Jupiter's moon Io. Of particular interest is reducing the error in the minimum altitude above Io's surface. The nominal tracking strategy includes Doppler, range, and onboard optical data, in addition to VLBI data with 25-nrad accuracy. For nominal data, the altitude error is approximately 250 km with a data cutoff of 19 days before closest approach to Io. A limited number (two to four) of 2-nrad VLBI measurements, simulating a demonstration of improved VLBI data, were found to reduce the altitude error by 10 to 40 percent. Improving the accuracy of the VLBI measurements of the nominal tracking strategy to 2 nrads, to simulate the results from an operational few-nrad VLBI capability, was found to reduce the altitude error by an approximate factor of four. This reduction in altitude error is attributed to the ability that VLBI data give to help determine the along-track component of Jupiter's ephemeris. This capability complements the ability of the onboard optical data to determine the radial and cross-track components of Jupiter's ephemeris.

Folkner, W. M.↗

Evaluating the WFIP2 updates to the HRRR model using scanning Doppler lidar measurements in the complex terrain of the Columbia River Basin

The wind-energy (WE) industry relies on numerical weather prediction (NWP) forecast models as foundational or base models for many purposes, including wind-resource assessment and wind-power forecasting. During the Second Wind Forecast Improvement Project (WFIP2) in the Columbia River Basin of Oregon and Washington, a significant effort was made to improve NWP forecasts through focused model development, to include experimental refinements to the High Resolution Rapid Refresh (HRRR) model physics and horizontal grid spacing. In this study, the performance of an experimental version of HRRR that includes these refinements is tested against a control version, which corresponds to that of the operational HRRR run by National Oceanic and Atmospheric Administration/National Centers for Environmental Protection at the outset of WFIP2. Furthermore, the effects of horizontal grid resolution were also tested by comparing wind forecasts from the HRRR (with 3-km grid spacing) with those from a finer-resolution HRRR nest with 750-m grid spacing. Model forecasts are validated against accurate wind-profile measurements by three scanning, pulsed Doppler lidars at sites separated by a total distance of 71 km. Model skill and improvements in model skill, attributable to physics refinements and improved horizontal grid resolution, varied by season, by site, and during periods of atmospheric phenomena relevant to WE. In general, model errors were the largest below 150 m above ground level (AGL). Experimental HRRR refinements tended to reduce the mean absolute error (MAE) and other error metrics for many conditions, but degradation in skill (increased MAE) was noted below 150 m AGL at the two lowest-elevation sites at night. Finer resolution was found to produce the most significant reductions in the error metrics.

17 WIND ENERGY↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme

The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector. *************************************** AUTHOR = Slater, Bethany University of Liverpool b.slater2@liverpool.ac.uk TITLE = Enhancing Sterile Neutrino Oscillation Sensitivities using SBND-PRISM at the Short-Baseline Neutrino Programme PAGES = 218 NOTE = Ph.D. University of Liverpool March 2026 ABSTRACT = The Short-Baseline Neutrino (SBN) Programme at Fermilab is comprised of two detectors, SBND and ICARUS, placed at $110$\,m and $600$\,m along the Booster Neutrino Beam at Fermilab. The key physics aim of the programme is to definitively test the sterile neutrino hypothesis, a proposed fourth flavour of neutrino that may explain certain experimental anomalies seen regarding standard model neutrino oscillations. To be able to detect the existence of sterile neutrinos, the uncertainties of the programme must be well constrained. To enable this, a robust analysis must be constructed that can consistently identify the correct values of systematic parameters and generate accurate predictions of what the neutrino energy spectrum at ICARUS should look like. SBND's design allows for the introduction of a technique called PRISM. In PRISM, the detector is divided into regions of different off axis angles from the beam, forming different samples where systematics impact each one in a distinct way. This allows any fits performed to obtain a better understanding of the correct value of the systematic parameters. The first analysis included in this thesis focuses on the improvements seen to the sensitivity of SBN to sterile oscillation parameters when using a PRISM configuration instead of treating SBND as a single whole. Focusing on the $5\sigma$ exclusion contour from the $\numu$ disappearance channel using three PRISM samples, an improvement on the order of $30$\,\% is seen, extending the parameter space for which the null hypothesis can be excluded. This thesis also presents a series of mock data studies comparing the abilities of SBND and PRISM analyses, concluding that in the case of simple changes between Monte Carlo (MC) and data, PRISM produces predictions of the ICARUS event rate spectrum that are more accurate and have smaller uncertainties. When moving to more realistic mock data, using different models to create the mock data than were used for the MC, the postfit predictions at ICARUS had a smaller difference between the postfit and mock data reconstructed energy spectra across all mock data samples tested. Finally, a covariance matrix defined by the maximum discrepancy between the postfit and mock data spectra at ICARUS from each of the SBND and PRISM fits across all the samples was constructed. The resultant $1\sigma$ fractional error induced by this bias systematic on the postfit spectrum has a smaller magnitude for PRISM than SBND, with the improvements ranging from $2.21$\,\% to $6.26$\,\% depending on the mock data samples. This summarises the reduction in systematic error when using PRISM instead of treating SBND as a single detector.

Slater, Bethany [Liverpool U.]↗

Effect of Body Mass Index on Magnitude of Setup Errors in Patients Treated With Adjuvant Radiotherapy for Endometrial Cancer With Daily Image Guidance

Purpose: To determine the impact of body mass index (BMI) on daily setup variations and frequency of imaging necessary for patients with endometrial cancer treated with adjuvant intensity-modulated radiotherapy (IMRT) with daily image guidance. Methods and Materials: The daily shifts from a total of 782 orthogonal kilovoltage images from 30 patients who received pelvic IMRT between July 2008 and August 2010 were analyzed. The BMI, mean daily shifts, and random and systematic errors in each translational and rotational direction were calculated for each patient. Margin recipes were generated based on BMI. Linear regression and spearman rank correlation analysis were performed. To simulate a less-than-daily IGRT protocol, the average shift of the first five fractions was applied to subsequent setups without IGRT for assessing the impact on setup error and margin requirements. Results: Median BMI was 32.9 (range, 23-62). Of the 30 patients, 16.7% (n = 5) were normal weight (BMI <25); 23.3% (n = 7) were overweight (BMI {>=}25 to <30); 26.7% (n = 8) were mildly obese (BMI {>=}30 to <35); and 33.3% (n = 10) were moderately to severely obese (BMI {>=} 35). On linear regression, mean absolute vertical, longitudinal, and lateral shifts positively correlated with BMI (p = 0.0127, p = 0.0037, and p < 0.0001, respectively). Systematic errors in the longitudinal and vertical direction were found to be positively correlated with BMI category (p < 0.0001 for both). IGRT for the first five fractions, followed by correction of the mean error for all subsequent fractions, led to a substantial reduction in setup error and resultant margin requirement overall compared with no IGRT. Conclusions: Daily shifts, systematic errors, and margin requirements were greatest in obese patients. For women who are normal or overweight, a planning target margin margin of 7 to 10 mm may be sufficient without IGRT, but for patients who are moderately or severely obese, this is insufficient.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

Methods to Improve the Maintenance of the Earth Catalog of Satellites During Severe Solar Storms

The objective of this thesis is to investigate methods to improve the ability to maintain the inventory of orbital elements of Earth satellites during periods of atmospheric disturbance brought on by severe solar activity. Existing techniques do not account for such atmospheric dynamics, resulting in tracking errors of several seconds in predicted crossing time. Two techniques are examined to reduce of these tracking errors. First, density predicted from various atmospheric models is fit to the orbital decay rate for a number of satellites. An orbital decay model is then developed that could be used to reduce tracking errors by accounting for atmospheric changes. The second approach utilizes a Kalman filter to estimate the orbital decay rate of a satellite after every observation. The new information is used to predict the next observation. Results from the first approach demonstrated the feasibility of building an orbital decay model based on predicted atmospheric density. Correlation of atmospheric density to orbital decay was as high as 0.88. However, it is clear that contemporary: atmospheric models need further improvement in modeling density perturbations polar region brought on by solar activity. The second approach resulted in a dramatic reduction in tracking errors for certain satellites during severe solar Storms. For example, in the limited cases studied, the reduction in tracking errors ranged from 79 to 25 percent.

Wilkin, Paul G.↗

Results of scatterometer systems analysis for NASA/MSC Earth observation sensor evaluation program

A systems evaluation of the 13.3 GHz scatterometer system is presented. The effects of phase error between the scatterometer channels, antenna pattern deviations, aircraft attitude deviations, environmental changes, and other related factors such as processing errors, system repeatability, and propeller modulation, are established. Furthermore, the reduction in system errors and calibration improvement is investigated by taking into account these parameter deviations. Typical scatterometer data samples are presented.

Krishen, K.↗

Results of scatterometer systems analysis for NASA/MSC Earth Observation Sensor Evaluation Program.

Radar scatterometers have applications in the NASA/MSC Earth Observation Aircraft Program. Over a period of several years, several missions have been flown over both land and ocean. In this paper a system evaluation of the NASA/MSC 13.3-GHz Scatterometer System is presented. The effects of phase error between the Scatterometer channels, antenna pattern deviations, aircraft attitude deviations, environmental changes, and other related factors such as processing errors, system repeatability, and propeller modulation, were established. Furthermore, the reduction in system errors and calibration improvement was investigated by taking into account these parameter deviations. Typical scatterometer data samples are presented.

Krishen, K.↗

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection↗

Statistics of cold cumulonimbus anvils based on enhanced infrared photographs

Infrared photographs from the Atlantic Geosynchronous Satellite, enhanced to resolve cold anvil temperatures of tropical clouds, are analyzed statistically to determine their spatial-temporal variability during the NASA-U2 Flight Experiment of 1980. Diurnal dependence varies regionally, indicating topographic control via low level convergence and release of convective instability. Anvil growth rates, area covered and duration are discussed for individual and merging anvil systems. Gradients of anvil temperatures implied by infrared photographs are shown to be caused, in part, by radial decrease in anvil depth, i.e., to emissivities less than 1. An error in cloud top temperature of 10C is caused by 10% reduction in emissivity. Errors are near zero in dense, actively growing portions of the anvil.

Danielsen, E. F.↗

Error minimization using redundant gravity measurements

This paper addresses the problem of redundant gravity measurements for reduction of measurement errors. The approach exploits constraints imposed upon the components of the gravity gradient tensor by the conditions of integrability needed for reconstruction of the gravity potential. It has been demonstrated that the total error of noisy measurements can be reduced by 25% using the best fit into the integrability constraints.

gravity gradiometry↗

Estimating PV power from aggregate power measurements within the distribution grid

The increased integration of photovoltaic (PV) systems in distribution grids reduces visibility and situational awareness for utilities because the PV systems' power production is usually not monitored by them. To address this problem, a method called Contextually Supervised Source Separation (CSSS) has been recently adapted for real-time estimation of aggregate PV active power generation from aggregate net active and reactive power measurements at a point in a radially configured distribution grid (e.g., substation). In its original version, PV disaggregation is formulated as an optimization problem that fits linear regression models for the aggregate PV active power generation and true substation active power load. This paper extends the previous work by adding regularization terms in the objective function to capture additional contextual information such as smoothness, by adding new constraints, by introducing new regressors such as ambient temperature, and by investigating the use of time-varying regressors. Furthermore, we perform extensive parametric analysis to study tuning of the objective function weighting factors in a way that maximizes performance and robustness. The proposed PV disaggregation method can be applied to networks with either a single PV system (e.g., megawatt scale) or many distributed ones (e.g., residential scale) connected downstream of the substation. Simulation studies with real field recorded data show that the enhancements of the proposed method reduce disaggregation error by 58% in winter and 35% in summer compared to previous CSSS-based work. When compared against a commonly used transposition model based approach, the reduction in disaggregation error is more pronounced (78% reduction in winter and 45% in summer). Additional simulations indicate that the proposed algorithm is also applicable for PV systems with time-varying power factors. In conclusion, overall, our results show that—with appropriate modeling and tuning—it is possible to accurately estimate the aggregated PV active power generation of a distribution feeder with minimal or no additional sensor deployment.

14 SOLAR ENERGY↗

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗

On the dosimetric effect and reduction of inverse consistency and transitivity errors in deformable image registration for dose accumulation

Purpose: Deformable image registration (DIR) is necessary for accurate dose accumulation between multiple radiotherapy image sets. DIR algorithms can suffer from inverse and transitivity inconsistencies. When using deformation vector fields (DVFs) that exhibit inverse-inconsistency and are nontransitive, dose accumulation on a given image set via different image pathways will lead to different accumulated doses. The purpose of this study was to investigate the dosimetric effect of and propose a postprocessing solution to reduce inverse consistency and transitivity errors. Methods: Four MVCT images and four phases of a lung 4DCT, each with an associated calculated dose, were selected for analysis. DVFs between all four images in each data set were created using the Fast Symmetric Demons algorithm. Dose was accumulated on the fourth image in each set using DIR via two different image pathways. The two accumulated doses on the fourth image were compared. The inverse consistency and transitivity errors in the DVFs were then reduced. The dose accumulation was repeated using the processed DVFs, the results of which were compared with the accumulated dose from the original DVFs. To evaluate the influence of the postprocessing technique on DVF accuracy, the original and processed DVF accuracy was evaluated on the lung 4DCT data on which anatomical landmarks had been identified by an expert. Results: Dose accumulation to the same image via different image pathways resulted in two different accumulated dose results. After the inverse consistency errors were reduced, the difference between the accumulated doses diminished. The difference was further reduced after reducing the transitivity errors. The postprocessing technique had minimal effect on the accuracy of the DVF for the lung 4DCT images. Conclusions: This study shows that inverse consistency and transitivity errors in DIR have a significant dosimetric effect in dose accumulation; Depending on the image pathway taken to accumulate the dose, different results may be obtained. A postprocessing technique that reduces inverse consistency and transitivity error is presented, which allows for consistent dose accumulation regardless of the image pathway followed.

61 RADIATION PROTECTION AND DOSIMETRY↗