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At least 145 records · Page 8

The Role of Local Heating in the 2015 Indian Heat Wave

India faced a major heat wave during the summer of 2015. Temperature anomalies peaked in the dry period before the onset of the summer monsoon, suggesting that local land-atmosphere feedbacks involving desiccated soils and vegetation might have played a role in driving the heat extreme. Upon examination of in situ data, reanalysis, satellite observations, and land surface models, we find that the heat wave included two distinct peaks: one in late May, and a second in early June. During the first peak we find that clear skies led to a positive net radiation anomaly at the surface, but there is no significant sensible heat flux anomaly within the core of the heat wave affected region. By the time of the second peak, however, soil moisture had dropped to anomalously low levels in the core heat wave region, net surface radiation was anomalously high, and a significant positive sensible heat flux anomaly developed. This led to a substantial local forcing on air temperature that contributed to the intensity of the event. The analysis indicates that the highly agricultural landscape of North and Central India can reinforce heat extremes under dry conditions.

Debjani Ghatak↗

El Nino-Southern Oscillation Correlated Aerosol Angstrom Exponent Anomaly Over the Tropical Pacific Discovered in Satellite Measurements

El Nino.Southern Oscillation (ENSO) is the dominant mode of interannual variability in the tropical atmosphere. ENSO could potentially impact local and global aerosol properties through atmospheric circulation anomalies and teleconnections. By analyzing aerosol properties, including aerosol optical depth (AOD) and Angstrom exponent (AE; often used as a qualitative indicator of aerosol particle size) from the Moderate Resolution Imaging Spectrometer, the Multiangle Imaging Spectroradiometer and the Sea ]viewing Wide Field ]of ]view Sensor for the period 2000.2011, we find a strong correlation between the AE data and the multivariate ENSO index (MEI) over the tropical Pacific. Over the western tropical Pacific (WTP), AE increases during El Nino events and decreases during La Nina events, while the opposite is true over the eastern tropical Pacific (ETP). The difference between AE anomalies in the WTP and ETP has a higher correlation coefficient (>0.7) with the MEI than the individual time series and could be considered another type of ENSO index. As no significant ENSO correlation is found in AOD over the same region, the change in AE (and hence aerosol size) is likely to be associated with aerosol composition changes due to anomalous meteorological conditions induced by the ENSO. Several physical parameters or mechanisms that might be responsible for the correlation are discussed. Preliminary analysis indicates surface wind anomaly might be the major contributor, as it reduces sea ]salt production and aerosol transport during El Nino events. Precipitation and cloud fraction are also found to be correlated with tropical Pacific AE. Possible mechanisms, including wet removal and cloud shielding effects, are considered. Variations in relative humidity, tropospheric ozone concentration, and ocean color during El Nino have been ruled out. Further investigation is needed to fully understand this AE ]ENSO covariability and the underlying physical processes responsible for it.

Li, Jing↗

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation Inc. that is designed to operate on live cables up to 1000 volts. One of the main conclusions of a previous effort was that cable reflectometry plots can be difficult for humans to analyze due to baseline noise, low or noisy anomaly response peaks, or large responses from cable ends. Detection of cable anomalies for many of these frequencies and test conditions was challenging for manual analysis. This presented an ideal opportunity for ML analysis to distinguish undamaged cable indications from anomalous cable indications. This research discusses application of machine learning (ML) to reflectometry cable test methods. The goal was to assess feasibility to distinguish undamaged cable reflectometry responses from damaged or anomalous cable reflectometry responses. The assessment considered the 3 instruments, multiple frequency bandwidths from each instrument, multiple cable anomalies and test conditions, and both supervised and unsupervised ML approaches. Although approaches and analysis methods were not identical or directly comparable, both outputs were encouraging. The unsupervised prediction weighted accuracy was assessed by instrument and by frequency. It performed better at high frequencies with the highest prediction accuracy of 0.84 for the higher frequency FDR, 0.79 for the 48-MHz LiveWire SSTDR, and 0.77 for 300-MHz PNNL SSTDR. The initial weighted accuracy average across all frequencies for using supervised ML was 0.56 to 0.68. The supervised analysis was repeated with noisier training data removed resulting in weighted accuracies of 0.69 to 0.87. These weighted accuracies are not directly comparable due to differences in the supervised and unsupervised analysis details but do indicate an encouraging trend. Even with limited and unbalanced data, strong prediction accuracies seem encouraging for further work including more data under a wider range of conditions.

42 ENGINEERING↗

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

Historically, cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation that is designed to operate on live cables up to 1000 volts and with a bandwidth of 48 MHz. Initial evaluation by the Pacific Northwest National Laboratory (PNNL) of the Live Wire system indicated that a broader bandwidth (BW) SSTDR may be better for many kinds of flaws. This led PNNL to develop an SSTDR laboratory instrument suitable for tests up to 500 MHz bandwidth. Testing on energized cables is also desirable for online monitoring systems so an inductive clamshell coupler was developed that allows energized cables to be tested up to at least 5 kV and likely higher voltage levels. Dielectric spectroscopy and tan delta testing plus various laboratory destructive tests were included in this data acquisition campaign directed to feed a machine learning (ML) study. With these kinds of developments, online energized cable tests may be possible with industrial adoption of such hardware advances but it will be completely impractical to have highly skilled data analysts continually examine these complex signals for indications of damage or compromised conditions. If online testing is to be implemented in new test hardware, it must be accompanied by software that can interpret the signals and alert plant operators of changing or degraded conditions. The thermally aged, shielded cable investigated here was separately treated for ML analysis. Visual analysis of electrical data showed generally increasing peaks where the cable entered and exited the oven. These peaks were not exactly aligned with expected locations, but these differences were attributed to velocity of propagation calibration errors. Only supervised ML was applied to the thermally aged data as this data was only available shortly before the committed publication date of this report. The supervised ML was structured to divide the 0 to 70-day responses as ‘normal’ from 0 to 35 days or ‘anomalous’ from 36 to 70 days, based on cable tensile elongation at break (EAB) insulation characterization. Using 80% of the data for training and 20% for testing, the supervised ML predicted normal versus anomalous was 70% accurate. Important conclusions include: • Accuracy to predict the presence of cable damage is improved from the 2023 effort by more training data. Weighted accuracies for comparisons among the instruments ranged from 67 to 89 % for unsupervised ML and 71 to 99% for supervised ML. • Based on the synthetic data tests, the unsupervised models are more generalizable to unseen anomalies. The Multi-Layer Perceptron classifier (MLP) model reported as high as 99.7% accuracy on the test data, but this dropped to 58.3% when tested on the synthetic data. In contrast, the unsupervised Pointwise model only achieved 89.7% accuracy on the experimental data but reported 78.3% accuracy on the synthetic data. • The best anomaly indicators are higher frequency (400 MHz BW) FDR data. Other tests may be interesting but for this study, this was the best predicter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Isostatic geoid anomalies on a sphere

Long-wavelength geoid anomalies due to lateral variations in the density or thickness of a thin layer in local isostatic equilibrium on the surface of a sphere depend sensitively on the assumed state of stress within the layer. A number of common intuitive definitions of local isostasy generally believed to be essentially identical are associated with quite different states of isostatic stress, and the corresponding theoretical geoid anomalies can vary by more than a factor of 2. This sensitivity of the theoretical anomaly to the exact definition of local isostasy constitutes an obstacle to any proposed program of interpreting or exploiting observed global isostatic geoid anomalies such as those associated with the aging of the oceanic lithosphere.

Dahlen, F. A.↗

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

Historically, cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages.

36 MATERIALS SCIENCE↗

Characterization of metal-polymer boundaries using Stoneley and Leaky waves

Optical and acoustooptical techniques for bonded surface inspection and interface wave detection are discussed. Interface wave propagation models based on viscous, elastic, and viscoelastic mechanical properties are reviewed. Gross boundary anomalies such as large defects and localized disbond regions were measured using conventional high frequency pulse echo and pitch catch ultratechniques. Bond durabilty is estimated by comparing detected wave attenuation versus frequency as a function of prebond surface preparation with the experimental limit obtained for perfect welded contact. Sensitivity of interface acoustic field periodicity to both residual and dc applied stress at the boundary surface is observed as well as hysteresis due to viscoelastic polymeric behavior as the applied stress is cycled.

Claus, R. O.↗

Differential spacecraft charging on the geostationary operational environmental satellites

Subsystems aboard the Geostationary Operational Environmental Satellites 4 and 5 showed instances of anomalous changes in state corresponding to false commands. Evidence linking the anomalous changes to geomagnetic activity, and presumably static discharges generated by spacecraft differential charging induced by substorm particle injection events is presented. The anomalies are shown to be correlated with individual substorms as monitored by stations of the North American Magnetometer Chain. The relative frequency of the anomalies is shown to be a function of geomagnetic activity. Finally a least squares fit to the time delay between substorm initiation and spacecraft anomaly as a function of spacecraft local time is shown to be consistent with injected electron populations with energy in the range 10 keV to 15 keV, in agreement with present understanding of the spacecraft charging mechanism. The spacecraft elements responsible for the differential charging were not satisfactorily identified. That question is currently under investigation.

Farthing, W. H.↗

Active modes of the Pacific ITCZ

ITCZ intensity across the Pacific for the 1975-1976 season is studied. Analysis of the data reveal: zonal bands of convective development; isolated patches of stronger convection; and several zonal bands which merge as tropical intraseasonal oscillations. The ITCZ intensity at 160 deg W is compared with the intensity averaged all the way across the Pacific. Composite outgoing longwave radiation anomaly maps for 22 days of local active ITCZ at 160 deg W, 26 days of zonally averaged active ITCZ, and 16 days of both local and zonal active ITCZ are presented and examined. It is noted that: systematic, yet different, patterns, movement, and temporal behavior correspond to local and zonally extensive convection; intensifying zonal convection moves southward; local convection occurs at two preferential latitudes; and local convection does not mean there is a generally active ITCZ.

Hayes, P. M.↗

Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

Modeling↗

Crosscutting Airborne Remote Sensing Technologies for Oil and Gas and Earth Science Applications

Airborne imaging spectroscopy has evolved dramatically since the 1980s as a robust remote sensing technique used to generate 2-dimensional maps of surface properties over large spatial areas. Traditional applications for passive airborne imaging spectroscopy include interrogation of surface composition, such as mapping of vegetation diversity and surface geological composition. Two recent applications are particularly relevant to the needs of both the oil and gas as well as government sectors: quantification of surficial hydrocarbon thickness in aquatic environments and mapping atmospheric greenhouse gas components. These techniques provide valuable capabilities for petroleum seepage in addition to detection and quantification of fugitive emissions. New empirical data that provides insight into the source strength of anthropogenic methane will be reviewed, with particular emphasis on the evolving constraints enabled by new methane remote sensing techniques. Contemporary studies attribute high-strength point sources as significantly contributing to the national methane inventory and underscore the need for high performance remote sensing technologies that provide quantitative leak detection. Imaging sensors that map spatial distributions of methane anomalies provide effective techniques to detect, localize, and quantify fugitive leaks. Airborne remote sensing instruments provide the unique combination of high spatial resolution (<1 m) and large coverage required to directly attribute methane emissions to individual emission sources. This capability cannot currently be achieved using spaceborne sensors. In this study, results from recent NASA remote sensing field experiments focused on point-source leak detection, will be highlighted. This includes existing quantitative capabilities for oil and methane using state-of-the-art airborne remote sensing instruments. While these capabilities are of interest to NASA for assessment of environmental impact and global climate change, industry similarly seeks to detect and localize leaks of both oil and methane across operating fields. In some cases, higher sensitivities desired for upstream and downstream applications can only be provided by new airborne remote sensing instruments tailored specifically for a given application. There exists a unique opportunity for alignment of efforts between commercial and government sectors to advance the next generation of instruments to provide more sensitive leak detection capabilities, including those for quantitative source strength determination.

hyperspectral↗

Inferred Sea Level Prediction in the NASA GMAO Seasonal Forecasting System

Reliable predictions of sea level anomalies on seasonal timescales with lead times of 1 to 9 months may have relevance to stakeholders – for example, in the advance deployment of resources for coastal flood mitigation. Routine prediction and analysis may also highlight physical processes associated with sea level change and modeling capabilities on seasonal and other timescales. These forecasts may represent interannual changes in the seasonal slope of the ocean surface, teleconnection effects such as the El Niño/Southern Oscillation phenomenon, and variations in seasonal hydrology including precipitation and coastal runoff. Coupled atmosphere/ocean models are routinely used in the seasonal prediction of temperature anomalies, precipitation anomalies, sea ice cover, and climate indices such as the Niño3.4 predictions under the North American Multi-Model Ensemble (NMME) protocol. Within the limits of their configuration, these complex Earth-system models have a potential for depicting regional changes in oceanic column properties, including the sea surface height. Seasonal prediction models generally have no representation of long-term mass contributions from melting land ice, or changes in vertical land motion; their output may be more specifically characterized as predictions of the ocean dynamic sea level. In practice however, the sea surface height prognostic variable is substantially compromised by the forecast model response to initial conditions. Imbalances between the initial, observed hydrologic cycle and the forecast model state produce abrupt adjustments in the model sea surface height. As a result, most seasonal prediction systems employ a constraint on the globally-averaged sea surface height that is applied at each time step. This essentially renders the prognostic sea surface height variable as unserviceable. Several approaches have previously been used to retrieve sea level information from seasonal forecasts beyond the use of the sea surface height variable. Here, we extend a method of relating other prognostic values, including ocean circulation and climate indices, to observed sea level variations. We use the merged altimetry record of the NASA MEaSUREs Gridded Sea Surface Height Anomalies data set and monthly revised local reference gauge observations from the National Oceanography Centre Permanent Service for Mean Sea Level (PSMSL) to evaluate derived prognostic variables from the NASA Global Modeling and Assimilation Office subseasonal-to-seasonal system version 2.1 (GMAO S2S v2.1). We focus on results for the midlatitudes with particular emphasis on US gauge locations. As shown in previous studies, prognostic ENSO-related indices in boreal winter are well correlated with gauge observations for the US west coast, but also for other locations in the southeastern US. Other forecast climate indices such as the North Atlantic Oscillation have relations to sea level that are limited both seasonally and spatially. As expected, surface atmospheric pressure (e.g., inverse barometer effect) is found to be particularly well correlated with observed sea level. We provide a characterization of forecast skill for seasonal sea level with this method.

Richard I Cullather↗

Anomaly-induced edge currents in hydrodynamics with parity anomaly

Here in this paper, we discuss relativistic hydrodynamics for a massless Dirac fermion in (2 + 1) dimensions, which has the parity anomaly—a global ’t Hooft anomaly between U(1) and parity symmetries. We investigate how hydrodynamics implements the party anomaly, particularly focusing on the transport phenomena at the boundary. Based on the parity anomaly matching and the second law of local thermodynamics, we find U(1) and entropy currents localized at the boundary, as well as the bulk anomalous current with vanishing divergence. These edge currents are similar to the ( 1 + 1)-dimensional chiral transports, but the coefficients are given by half of theirs. We also generalize our discussion to more general anomalies among multiple U(1) symmetries and single $\mathbb{Z}_2$ symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Recent Spatial and Temporal Anomalies and Trends of OLR as Observed by CERES and Computed Based on AIRS Retrievals

We show that a recent CERES-observed negative trend in OLR of approx.-0.1 W/sq m/yr averaged over the globe, for the time period of September 2002 through February 2010 used in this study, is found in the AIRS OLR data as well. Most importantly, even minute details (down to 1 x 1 Degree GCM-scale resolution) of spatial and temporal anomalies and trends of OLR as observed by CERES and computed based on AIRS-retrieved surface and atmospheric geophysical parameters over this time period are essentially the same. We see this correspondence even in the very large spatial variations of these trends with local values ranging from -2.6 W/sq m/yr to +3.0 W/sq m/yr in the tropics. This essentially perfect agreement of OLR anomalies and even local trends derived from observations by two different instruments, in totally independent and different manners, implies that both sets of results must be highly accurate; and indirectly validates the anomalies and trends of other AIRS derived products as well. These products show that global and regional anomalies and trends of OLR, water vapor and cloud cover over the last 7+ years are strongly influenced by El-Nino-La Nina cycles . We use the anomalies and trends of AIRS derived products to explain why the global OLR has a large negative trend over this time period; Global and tropical OLR began to decrease significantly at the onset of a strong La Nina in mid-2007. AIRS products show that cloudiness and mid-tropospheric water vapor began to increase in the tropics at roughly the same time, especially in the region 5degN - 20degS latitude extending eastward from 150degW to 30degE longitude, with a corresponding very large drop in OLR in this region. Late 2009 is characterized by a strong El-Nino, with a corresponding change in sign of observed tropical water vapor, cloud cover, and OLR anomalies. If one excludes the area 5degN - 20degS, 150degW - 30degE from the statistics, area mean OLR trends over the rest of the globe are substantially reduced over the time period under study.

Molnar, Gyula↗

Flash Drought as Captured by MERRA-2: Disentangling the Contributions of Precipitation Deficit and Excess Energy

Flash droughts uncharacteristically rapid dryings of the land system are naturally associated with extreme precipitation deficits. Such precipitation deficits, however, do not tell the whole story. Land surface drying can be exacerbated by anomalously high evapotranspiration (ET) rates driven, for example, by anomalously high temperatures (e.g., during heatwaves) and/or anomalously high incoming radiation (e.g., from reduced cloudiness). In this study the relative contributions of precipitation and ET anomalies to flash drought generation are quantified through the analysis of diagnostic fields contained within the MERRA-2 reanalysis product. Unique to the overall approach is the explicit treatment of soil moisture impacts on ET an ET anomaly that is negative relative to the local long-term climatological mean is still considered positive in terms of its contribution to a flash drought, if it is high for the concurrent value of soil moisture. Maps produced in the analysis show the fraction of flash drought production stemming specifically from ET anomalies and the degree to which these ET anomalies are related to temperature and radiation anomalies. ET is found to have a large impact, for example, on flash drought production in the east-central US and in parts of Russia known from past studies to be prone to heatwave-related drought.

Koster, Randal↗

Flash Drought as Captured by Reanalysis Data: Disentangling the Contributions of Precipitation Deficit and Excess Evapotranspiration

Flash droughts – uncharacteristically rapid dryings of the land system – are naturally associated with extreme precipitation deficits. Such precipitation deficits, however, do not tell the whole story, for land surface drying can be exacerbated by anomalously high evapotranspiration (ET) rates driven by anomalously high temperatures (e.g., during heatwaves), anomalously high incoming radiation (e.g., from reduced cloudiness), and other meteorological anomalies. In this study, the relative contributions of precipitation and ET anomalies to flash drought generation in the Northern Hemisphere are quantified through the analysis of diagnostic fields contained within the MERRA-2 reanalysis product. Unique to the approach is the explicit treatment of soil moisture impacts on ET through relationships diagnosed from the reanalysis data; under this treatment, an ET anomaly that is negative relative to the local long-term climatological mean is still considered positive in terms of its contribution to a flash drought if it is high for the concurrent value of soil moisture. Maps produced in the analysis show the fraction of flash drought production stemming specifically from ET anomalies and illustrate how ET anomalies for some droughts are related to temperature and radiation anomalies. While ET is found to have an important impact on flash drought production in the central US and in parts of Russia known from past studies to be prone to heatwave-related drought, and while this impact does appear stronger during the onset (first several days) of flash droughts, overall the contribution of ET to these droughts is small relative to the contribution of precipitation deficit.

R D Koster↗

Precise solution for a finite set of spherical coefficients from equiangular gridded data

An important goal of geodesy is to determine the anomalous potential and its derivatives outside of the earth. Representing the surface anomalies by a series of spherical harmonics is useful since it is then possible to do a term by term solution of Laplace's equation and upward continuation. The problem of finding such a spherical harmonic series for anomaly values given on an equiangular surface grid is addressed. (This is a first step toward the more complicated problem of finding a function such that locally averaged values fit a grid of mean anomalies.) Three approaches to this fitting problem are discussed and compared: the discrete Fourier technique, the discrete integral technique, and a new approach. The peculiar nature of the equiangular grid, with its increasing density of (noisy) data toward the poles, causes each method to exhibit a different type of difficulty. The new method is shown to be practical as well as precise since the numerical conditioning problems which appear can be successfully handled by such well-known techniques as a (simple) Kalman filter.

Zucker, Paul A.↗