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NASA NTRS2024

Quantifying Volumetric Scattering Bias in ICESat-2 and Operation IceBridge Altimetry Over Greenland Firn and Aged Snow

The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) mission has collected surface elevation measurements for over 5 years. ICESat-2 carries an instrument that emits laser light at 532 nm, and ice and snow absorb weakly at this wavelength. Previous modeling studies found that melting snow could induce significant bias to altimetry signals, but there is no formal assessment on ICESat-2 acquisitions during the melting season. We performed two case studies over the Greenland Ice Sheet to quantify bias in ICESat-2 signals over snow: one to validate Airborne Topographic Mapper (ATM) data against Next Generation Airborne Visible/Infrared Imaging Spectrometer (AVIRIS-NG) grain sizes, and a second to estimate ICESat-2 bias relative to ATM. We used snow optical grain sizes derived from ATM and AVIRIS-NG to attribute altimetry bias to snowpack properties. For the first case study, the mean and standard deviation of optical grain sizes were 340 ± 65 µm (AVIRIS-NG) and 670 ± 420 µm (ATM). A mean altimetry bias of 4.81 ± 1.76 cm was found for ATM, with larger biases linked to increases in grain size. In the second case study, we found a mean grain size of 910 ± 381 µm and biases of 6.42 ± 1.77 cm (ICESat-2) and 9.82 ± 0.97 cm (ATM). The grain sizes and densities needed to recreate biases with a model are uncommon in nature, so we propose that additional surface attributes must be considered to characterize ICESat-2 bias over snow. The altimetry biases are within the accuracy requirements of the ICESat-2 mission, but we cannot rule out more significant errors over coarse-grained snow.

Zachary Fair↗
DOE OSTI2024

Causes of and Solutions to Wind Speed Bias in NREL's 2020 Offshore Wind Resource Assessment for the California Pacific Outer Continental Shelf

This report provides the results of a detailed analysis into the causes of high wind speed bias in the 20-year wind resource data set for offshore California the National Renewable Energy Laboratory (NREL) released in 2020, herein called CA20. The data set was developed using the state-of-the-art Weather Research and Forecasting (WRF) model. Notably, no floating lidars were available at the time in offshore California to validate offshore hub-height wind speeds. In late 2020, the Pacific Northwest National Laboratory (PNNL) deployed two floating lidars in the California outer continental shelf (OCS), near the Bureau of Ocean Energy Management (BOEM) call areas of Humboldt and Morro Bay. Using these observations through 2021, NREL found considerable bias in modeled hub-height winds at both locations: up to +2 m/s at Humboldt over a 6-month period, and up to +1 m/s at Morro Bay over a one-year period. Upon the discovery of this bias, the Department of Energy (DOE) and BOEM funded NREL and PNNL to investigate the causes of, impacts of, and solutions to the bias in the CA20 data set. This report summarizes the findings of this research. We first investigated whether different WRF model setups could lead to reduced bias. We found that the choice of planetary boundary layer (PBL) scheme - which controls the vertical turbulent mixing of momentum, heat, and moisture in the lowermost part of the atmosphere - greatly affected hub-height wind speeds in the region. Specifically, switching from the Mellor-Yamada-Nakanishi-Niino (MYNN) scheme used in CA20 (and widely used across a range of operational and research weather models) to the less common Yonsei University (YSU) scheme nearly eliminated the bias at both the Humboldt and Morro Bay lidar locations. The large discrepancy between the MYNN- and YSU-modeled hub-height winds pointed towards the role of atmospheric stability. In general, PBL schemes agree well in conditions of high turbulence and mixing, normally referred to as "unstable" conditions. By contrast, PBL schemes start to diverge in "stable" conditions, where turbulence is low and thermal stratification (i.e., higher temperature air sitting on top of colder air) greatly suppresses vertical mixing. Under such conditions, winds aloft can decouple from surface effects and greatly accelerate, causing high wind speeds at hub-height and frequent low-level jets (LLJs). We determined that these stable conditions are in fact dominant in offshore California. The region is characterized by moderate-to-extreme stable stratification with a LLJ on average around 200 meters above sea-level. To our knowledge, no wind energy area globally has as strongly stable stratification as offshore California. Under these extreme conditions, we determined that the MYNN scheme models higher stability than YSU, resulting in less vertical turbulent mixing than YSU, allowing for the acceleration of hub-height winds, more intense LLJs, and higher-amplitude inertial oscillations. Using surface observations, we found that MYNN overestimates near-surface stability, whereas YSU tends to model stability better. We then considered several short-term case studies to assess additional meteorological drivers of the bias at Humboldt. We found that during synoptic scale northerly flows driven by the North Pacific High and inland thermal low, a coastal warm bias in the MYNN case studies contributes to the modeled wind speed bias by altering the boundary layer thermodynamics via a thermal wind mechanism. Given the strong performance of the YSU-based runs in offshore California, NREL has produced and published an updated version of the CA20 data set with YSU as the PBL scheme. This updated data set is now part of NREL's 2023 National Offshore Wind (NOW-23) data set, which covers all the U.S. offshore waters. The development and final validation of the NOW-23 data set in offshore California is documented in this report.

17 WIND ENERGY↗
DOE OSTI2018

CAUSES: Diagnosis of the Summertime Warm Bias in CMIP5 Climate Models at the ARM Southern Great Plains Site

Abstract All the weather and climate models participating in the Clouds Above the United States and Errors at the Surface project show a summertime surface air temperature (T2 m) warm bias in the region of the central United States. To understand the warm bias in long‐term climate simulations, we assess the Atmospheric Model Intercomparison Project simulations from the Coupled Model Intercomparison Project Phase 5, with long‐term observations mainly from the Atmospheric Radiation Measurement program Southern Great Plains site. Quantities related to the surface energy and water budget, and large‐scale circulation are analyzed to identify possible factors and plausible links involved in the warm bias. The systematic warm season bias is characterized by an overestimation of T2 m and underestimation of surface humidity, precipitation, and precipitable water. Accompanying the warm bias is an overestimation of absorbed solar radiation at the surface, which is due to a combination of insufficient cloud reflection and clear‐sky shortwave absorption by water vapor and an underestimation in surface albedo. The bias in cloud is shown to contribute most to the radiation bias. The surface layer soil moisture impacts T2 m through its control on evaporative fraction. The error in evaporative fraction is another important contributor to T2 m. Similar sources of error are found in hindcast from other Clouds Above the United States and Errors at the Surface studies. In Atmospheric Model Intercomparison Project simulations, biases in meridional wind velocity associated with the low‐level jet and the 500 hPa vertical velocity may also relate to T2 m bias through their control on the surface energy and water budget.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Spillover as a cause of bias in baseline evaluation methods for demand response programs

Prior research has shown load reduction estimates from residential event-driven demand response programs (e.g., Critical Peak Pricing)using X of the highest Y days with a weather adjustment method are the best performing within the class of currently used baseline methods. However, they are still biased relative to estimates produced from randomized control trials (RCTs), the unbiased “gold standard” evaluation method. In this paper we identify underlying factors that cause some of the bias found in one commonly used baseline method. Rather than simply quantifying bias, our research provides a deeper understanding of what causes the bias and thus can be used to develop more accurate methods that are not subject to these underlying factors. Previous studies have compared various baseline methods relative to each other; however, because all baseline methods are biased, it is impossible to determine the true bias that exists in them. We have access to a unique RCT dataset: the Sacramento Municipal Utility District's study of critical peak pricing. Our analysis of 23 event days over two summers allows us to identify the true bias on load reduction estimates by using the RCT estimates as the unbiased gold standard against which we compare the estimates from the baseline methods. We found that spillover of energy reductions, from hours targeted by a program onto other hours, is one underlying factor that is a major cause of bias in baseline methods. We discuss alternative baseline methods that may not be subject to this same bias.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Reduction of Pacific Double‐ITCZ Bias by Convection Parameterization in NCAR CESM2.2

Abstract The impact of convective closure on the double‐ITCZ bias in the NCAR CESM2.2 is investigated in this study. The standard CESM2.2 simulates a remarkable double‐ITCZ bias in the central and eastern Pacific, especially in boreal winter and spring. Modifications to the closure in convection parameterization scheme greatly reduce the double‐ITCZ bias in all seasons, demonstrating that convection parameterization can substantially influence the double‐ITCZ bias in CESM2.2. Further analyses suggest that convection parameterization can modulate the tropical atmosphere‐ocean feedback processes, through which it influences the SST in the southern ITCZ region and hence the double‐ITCZ bias. The changes in the upper ocean temperature advection induced by modified convective closure plays important roles in reducing the warm SST bias and double‐ITCZ precipitation bias in the southern ITCZ region. The modified convective closure improves the low‐level cloud and shortwave cloud radiative forcing in the southeastern Pacific. However, surface heat flux plays only a limited role in reducing warm SST bias and double ITCZ bias because the impacts of shortwave radiation changes are largely canceled by changes in longwave radiation and latent heat flux.

Song, Xiaoliang [Scripps Institution of Oceanograp↗
DOE OSTI2022

Photometric redshift estimation with convolutional neural networks and galaxy images: Case study of resolving biases in data-driven methods

Deep-learning models have been increasingly exploited in astrophysical studies, but these data-driven algorithms are prone to producing biased outputs that are detrimental for subsequent analyses. In this work, we investigate two main forms of biases: class-dependent residuals, and mode collapse. We do this in a case study, in which we estimate photometric redshift as a classification problem using convolutional neural networks (CNNs) trained with galaxy images and associated spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multichannel outputs, balancing the training data, and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshift or photometric redshift, and the biases with respect to these two definitions are incompatible and should be treated individually. We suggest that a prerequisite for resolving biases in photometric space is resolving biases in spectroscopic space. Experiments show that our methods can better control biases than benchmark methods, and they are robust in various implementing and training conditions with high-quality data. Our methods hold promises for future cosmological surveys that require a good constraint of biases, and they may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance tradeoff and the requirement of sufficient statistics suggest that we need better methods and optimized data usage strategies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Transient plasma potential in pulsed dual frequency inductively coupled plasmas and effect of substrate biasing

An electron emitting probe in saturated floating potential mode has been used to investigate the temporal evolution of plasma potential and the effect of substrate RF biasing on it for pulsed dual frequency (2 MHz/13.56 MHz) inductively coupled plasma (ICP) source. The low frequency power (P{sub 2MHz}) has been pulsed at 1 KHz and a duty ratio of 50%, while high frequency power (P{sub 13.56MHz}) has been used in continuous mode. The substrate has been biased with a separate bias power at (P{sub 12.56MHz}) Argon has been used as a discharge gas. During the ICP power pulsing, three distinct regions in a typical plasma potential profile, have been identified as ‘initial overshoot’, pulse ‘on-phase’ and pulse ‘off-phase’. It has been found out that the RF biasing of the substrate significantly modulates the temporal evolution of the plasma potential. During the initial overshoot, plasma potential decreases with increasing RF biasing of the substrate, however it increases with increasing substrate biasing for pulse ‘on-phase’ and ‘off-phase’. An interesting structure in plasma potential profile has also been observed when the substrate bias is applied and its evolution depends upon the magnitude of bias power. The reason of the evolution of this structure may be the ambipolar diffusion of electron and its dependence on bias power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

FIP BIAS EVOLUTION IN A DECAYING ACTIVE REGION

Solar coronal plasma composition is typically characterized by first ionization potential (FIP) bias. Using spectra obtained by Hinode’s EUV Imaging Spectrometer instrument, we present a series of large-scale, spatially resolved composition maps of active region (AR)11389. The composition maps show how FIP bias evolves within the decaying AR during the period 2012 January 4–6. Globally, FIP bias decreases throughout the AR. We analyzed areas of significant plasma composition changes within the decaying AR and found that small-scale evolution in the photospheric magnetic field is closely linked to the FIP bias evolution observed in the corona. During the AR’s decay phase, small bipoles emerging within supergranular cells reconnect with the pre-existing AR field, creating a pathway along which photospheric and coronal plasmas can mix. The mixing timescales are shorter than those of plasma enrichment processes. Eruptive activity also results in shifting the FIP bias closer to photospheric in the affected areas. Finally, the FIP bias still remains dominantly coronal only in a part of the AR’s high-flux density core. We conclude that in the decay phase of an AR’s lifetime, the FIP bias is becoming increasingly modulated by episodes of small-scale flux emergence, i.e., decreasing the AR’s overall FIP bias. Our results show that magnetic field evolution plays an important role in compositional changes during AR development, revealing a more complex relationship than expected from previous well-known Skylab results showing that FIP bias increases almost linearly with age in young ARs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Some assembly required: assembly bias in massive dark matter halos

Here, we study halo assembly bias for cluster-sized halos. Previous work has found little evidence for correlations between large-scale bias and halo mass assembly history for simulated cluster-sized halos, in contrast to the significant correlation found between bias and concentration for halos of this mass. This difference in behavior is surprising, given that both concentration and assembly history are closely related to the same properties of the linear-density peaks that collapse to form halos. Using publicly available simulations, we show that significant assembly bias is indeed found in the most massive halos with M ~ 10 15 M ⊙ , using essentially any definition of halo age. For lower halo masses M ~ 10 14 M ⊙ , no correlation is found between bias and the commonly used age indicator a 0.5 , the half-mass time. We show that this is a mere accident, and that significant assembly bias exists for other definitions of halo age, including those based on the time when the halo progenitor acquires some fraction f of the ultimate mass at z =0 . For halos with M vir ~ 10 14 M ⊙ , the sense of assembly bias changes sign at f =0.5 . We explore the origin of this behavior, and argue that it arises because standard definitions of halo mass in halo finders do not correspond to the collapsed, virialized mass that appears in the spherical collapse model used to predict large-scale clustering. Because bias depends strongly on halo mass, these errors in mass definition can masquerade as or even obscure the assembly bias that is physically present. Lastly, more physically motivated halo definitions using splashback should be free of this particular defect of standard halo finders.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Bias Correction in Urban Building Energy Modeling for Chicago Using Machine Learning

Urban-scale building energy modeling (UBEM) holds promise for optimizing energy usage across extensive geographic regions. However, there is a recognized bias between simulated energy consumption and actual measured data. This study, based on building data from Chicago, delved into bias correction techniques for enhancing the accuracy of UBEM energy consumption estimates. Initially, the AutoBEM simulation yielded a normalized mean bias error (NMBE) of 1.1% and 51% of Coefficient of the Variation of the Root Mean Square Error (CVRMSE) after outlier exclusion. To address this, three bias correction methods were deployed: Average Mean Bias Error based bias correction, Quantile mapping bias correction, and Machine learning-based bias correction using Linear Regression and Random Forest models. Post-correction results exhibited marked improvement. The NMBE values were diminished to 0 for Average MBE-based, 0.36 for Quantile Mapping, and 0 for Machine Learning-based corrections. Concurrently, the CVRMSE values registered reductions from an original 51 to 50.8 for Quantile Mapping, and 38.56 for Machine Learning-based corrections, pointing towards the effectiveness of specific bias correction methods in refining the precision of UBEM energy predictions. Such accurate estimations are paramount for informed energy planning and urban policy-making.

Chowdhury, Shovan↗
DOE OSTI2016

Moist Process Biases in Simulations of the Madden–Julian Oscillation Episodes Observed during the AMIE/DYNAMO Field Campaign

Two Madden–Julian oscillation (MJO) episodes observed during the 2011 Atmospheric Radiation Measurement Program MJO Investigation Experiment (AMIE)/DYNAMO field campaign are simulated using a regional model with various cumulus parameterizations, a regional cloud-permitting model, and a global variable-resolution model with a high-resolution region centered over the tropical Indian Ocean. Model biases in relationships relevant to existing instability theories of MJO are examined and their relative contributions to the overall model errors are quantified using a linear statistical model. The model simulations capture the observed approximately log-linear relationship between moisture saturation fraction and precipitation, but precipitation associated with the given saturation fraction is overestimated especially at low saturation fraction values. This bias is a major contributor to the excessive precipitation during the suppressed phase of MJO. After accounting for this bias using a linear statistical model, the spatial and temporal structures of the model-simulated MJO episodes are much improved, and what remains of the biases is strongly correlated with biases in saturation fraction. The excess precipitation bias during the suppressed phase of the MJO episodes is accompanied by excessive column-integrated radiative forcing and surface evaporation. A large portion of the bias in evaporation is related to biases in wind speed, which are correlated with those of precipitation. Furthermore, these findings suggest that the precipitation bias sustains itself at least partly by cloud radiative feedbacks and convection–surface wind interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Humidity Bias and Effect on Simulated Aerosol Optical Properties during the Ganges Valley Experiment

The radiosonde humidity profiles available during the Ganges Valley Experiment were compared to those simulated from the regional Weather Research and Forecasting (WRF) model coupled with a chemistry module (WRF -Chern) and the global reanalysis datasets. Large biases were revealed. On a monthly mean basis at Nainital, located in northern India, the WRFChern model simulates a large moist bias in the free troposphere (up to +20%) as well as a large dry bias in the boundary layer (up to -30%). While the overall pattern of the biases is similar, the magnitude of the biases varies from time to time and from one location to another. At Thiruvananthapuram, the magnitude of the dry bias is smaller, and in contrast to Nainital, the higher-resolution regional WRF -Chern model generates larger moist biases in the upper troposphere than the global reanalysis data. Furthermore, the humidity biases in the upper troposphere, while significant, have little impact on the model estimation of column aerosol optical depth (AOD). The frequent occurrences of the dry boundary-layer bias simulated by the large-scale models tend to lead to the underestimation of AOD. It is thus important to quantify the humidity vertical profiles for aerosol simulations over South Asia.

aerosol extinction↗
NASA NTRS2012

Cognitive Bias in the Verification and Validation of Space Flight Systems

Cognitive bias is generally recognized as playing a significant role in virtually all domains of human decision making. Insight into this role is informally built into many of the system engineering practices employed in the aerospace industry. The review process, for example, typically has features that help to counteract the effect of bias. This paper presents a discussion of how commonly recognized biases may affect the verification and validation process. Verifying and validating a system is arguably more challenging than development, both technically and cognitively. Whereas there may be a relatively limited number of options available for the design of a particular aspect of a system, there is a virtually unlimited number of potential verification scenarios that may be explored. The probability of any particular scenario occurring in operations is typically very difficult to estimate, which increases reliance on judgment that may be affected by bias. Implementing a verification activity often presents technical challenges that, if they can be overcome at all, often result in a departure from actual flight conditions (e.g., 1-g testing, simulation, time compression, artificial fault injection) that may raise additional questions about the meaningfulness of the results, and create opportunities for the introduction of additional biases. In addition to mitigating the biases it can introduce directly, the verification and validation process must also overcome the cumulative effect of biases introduced during all previous stages of development. A variety of cognitive biases will be described, with research results for illustration. A handful of case studies will be presented that show how cognitive bias may have affected the verification and validation process on recent JPL flight projects, identify areas of strength and weakness, and identify potential changes or additions to commonly used techniques that could provide a more robust verification and validation of future systems.

Larson, Steve↗
NASA NTRSDate not supplied

Cold-Point Tropopause Temperature Bias in Reanalyses Modulated By Equatorial Waves

In this reanalysis inter-comparison study, we compare the modeled Cold-point tropopause temperature (CPT from model level data) near the equator to that of multi-mission GNSS-RO within a preliminary time period of 2007-2011. The known reanalysis CPT temperature warm bias is studied relative to the phase of equatorial waves filtered from GNSS-RO at tropopause level. This uncovers a common denominator in the CPT temperature bias behavior in all reanalyses: - When equatorial waves are present, within their cold phase the reanalysis bias is increased by over 1K, i.e. >1K on top of the reanalysis average warm bias. - Within an equatorial wave’s warm phase, the opposite is observed, with the reanalysis CPT temperature bias even being reversed at higher equatorial wave amplitudes, i.e. the modeled CPT becoming too cold in these cases. - With no equatorial wave anomalies present, the reanalysis bias remains at the average reported in previous inter-comparisons that looked at zonal-mean CPT biases. Inertia-Gravity and Mixed Rossby-Gravity waves show this behavior most clearly, Kelvin waves show a similar modulation but with half of the magnitude, and equatorial Rossby wave modulation of CPT reanalysis bias is still apparent but with further decreased magnitude. This hints on a time-space scale-dependence, with medium-smaller-scale and faster equatorial waves influencing CPT reanalysis bias the most. For comparison, the large-scale and slow-moving MJO does not show any of the effects described above. Current work focuses on the data assimilation response of the reanalysis systems, again relative to the equatorial wave’s phases.

Tropopause↗
DOE OSTI2023

Summertime Near-Surface Temperature Biases Over the Central United States in Convection-Permitting Simulations

Convection-Permitting Model (CPM) simulations of the Central United States climate for the summer of 2011 are studied to understand the causes of warm biases in 2-m air temperature (T 2m ) and related underestimates of precipitation including that from mesoscale convective systems (MCSs). Based on 10 CPM simulations and 9 coarser-resolution model simulations, we quantify contributions from evaporative fraction (EF) and radiation to the T 2m bias with both types of models overestimating T 2m largely because they underestimate EF. The performance of CPMs in capturing MCS characteristics (frequency, rainfall, propagation) varies. The pre-summer precipitation bias has large correlation with mean summertime T 2m bias but the relationship between summertime MCS mean rainfall bias and T 2m bias is non-monotonic. Analysis of lifting condensation level deficit and convective available potential energy suggests that models with T 2m warm biases and low EF have too dry and stable boundary layers, inhibiting the formation of clouds, precipitation and MCSs. Among the CPMs with differing model formulations (e.g., transpiration, infiltration, cloud macrophysics and microphysics), evidence suggests that altering the land-surface model is more effective than altering the atmospheric model in reducing T 2m biases. In conclusion, these results demonstrate that land-atmosphere interactions play a very important role in determining the summertime climate of the Central United States.

2-m air temperature↗
DOE OSTI2022

Toroidal modeling of 3D perturbations generated by current filaments in scrape-off layer in tokamak with biased divertor targets

The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is employed to study the plasma response to the n = 2 (n is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and the associated neoclassical toroidal viscosity torque are also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin $\hat{R}_c$ diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

An Analysis of Gravity-Field Estimation Based on Intersatellite Dual-1-Way Biased Ranging

The GRACE (Gravity Recovery And Climate Experiment) mission is designed to make global, highly accurate measurements of the Earth's gravity field with high spatial resolution. Ancillary GPS occultation measurements are also to be carried out for atmospheric monitoring. In the dual-1-way biased ranging of this mission, the range between two satellites separated by 100 to 200 km in nearly polar, coplanar, circular orbits, is measured to very high precision, to within an additive constant, through the exchange of K- and Ka-band sinusoidal signals. Such biased ranging data, along with GPS L-band range and phase data, can be processed and fit over successive multiday intervals to obtain accurate estimates of the Earth's gravity field. This report approximately models and analyzes this process, from the generation of the RF signals at the two satellites through the extraction of the geopotential. The steps include generation of the transmitted signals, processing the received signals to extract high-rate baseband phase, carrying out a dual-1-way combination of baseband phase to extract high-rate biased range for each band, combining K- and Ka-band ranges to correct for the ionosphere effect, and processing the resulting high-rate biased range values to extract three types of reduced-rate observables: biased range, range rate and range acceleration. The version of dual-1-way biased ranging developed by this report improves upon previous versions in a number of ways: highly accurate satellite-timetag corrections derived from concurrent GPS data, better baseband phase extraction using highly digital processing, highly accurate USO-rate calibration derived from concurrent GPS data, an improved method for extracting high-rate biased range from baseband phase, improved filtering for extracting reduced- rate observables from high-rate biased range, and parallel extraction of three observable types.

SINUSOIDAL SIGNALS↗