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Development of Advanced Seed Laser Modules for Lidar and Spectroscopy Applications

We report on recent progress made in the development of highly compact, single mode, distributed feedback laser (DFB) seed laser modules for lidar and spectroscopy applications from space based platforms. One of the intended application of this technology is in the NASA's Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) mission. The DFB laser modules operating at 1571 nm and 1262 nm have advanced current and temperature drivers built into them. A combination of temperature and current tuning allows coarse and fine adjustment of the diode wavelengths.

Prasad, Narasimha S.↗

RACORO Continental Boundary Layer Cloud Investigations: 1. Case Study Development and Ensemble Large-Scale Forcings

Observation-based modeling case studies of continental boundary layer clouds have been developed to study cloudy boundary layers, aerosol influences upon them, and their representation in cloud- and global-scale models. Three 60 h case study periods span the temporal evolution of cumulus, stratiform, and drizzling boundary layer cloud systems, representing mixed and transitional states rather than idealized or canonical cases. Based on in situ measurements from the Routine AAF (Atmospheric Radiation Measurement (ARM) Aerial Facility) CLOWD (Clouds with Low Optical Water Depth) Optical Radiative Observations (RACORO) field campaign and remote sensing observations, the cases are designed with a modular configuration to simplify use in large-eddy simulations (LES) and single-column models. Aircraft measurements of aerosol number size distribution are fit to lognormal functions for concise representation in models. Values of the aerosol hygroscopicity parameter, kappa, are derived from observations to be approximately 0.10, which are lower than the 0.3 typical over continents and suggestive of a large aerosol organic fraction. Ensemble large-scale forcing data sets are derived from the ARM variational analysis, European Centre for Medium-Range Weather Forecasts, and a multiscale data assimilation system. The forcings are assessed through comparison of measured bulk atmospheric and cloud properties to those computed in "trial" large-eddy simulations, where more efficient run times are enabled through modest reductions in grid resolution and domain size compared to the full-sized LES grid. Simulations capture many of the general features observed, but the state-of-the-art forcings were limited at representing details of cloud onset, and tight gradients and high-resolution transients of importance. Methods for improving the initial conditions and forcings are discussed. The cases developed are available to the general modeling community for studying continental boundary clouds.

Boundary layers↗

Earth Science Technology Office (ESTO) New Observing Strategies (NOS) and NOS-Testbed (NOS-T)

With the advancement of space hardware technologies such as smaller spacecraft, component and instrument miniaturization and high performance space processors, and with the advancement of software technologies in artificial intelligence, big data analysis and autonomous decision making, Earth Science is looking at novel ways to observe phenomena that previously could not have been studied or would have been too expensive to study with traditional missions. In particular, the New Observing Strategies (NOS) component of the NASA Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST) Program aims at leveraging these novel technologies as well as low cost and easy access to space to acquire multi-temporal or simultaneous multi-angular, multi-locations, multi-resolution and multi-spectral observations that will provide better multi-source measurements and will build a more dynamic and comprehensive picture of Earth Science phenomena that need to be studied and analyzed. For applications such as water resources management, air quality monitoring, biodiversity studies or disaster management, NOS will integrate the use of small instruments, small spacecraft, constellations of spacecraft and networks of sensors to design new missions that will provide the necessary measurements to improve future forecast and science modeling systems.Measurement acquisition will therefore be approached as a system of systems rather than on a mission basis, and a system of this complexity should not be expected to work without full integration and experimental characterization. Although most of the individual technologies enabling to link and coordinate multi-source observations are more or less mature, a few technologies need to be developed and all of them need to be integrated and tested as a system. In order for this validation to occur, the AIST Program is developing the NOS Testbed that includes 3 main goals:1.Validate novel NOS technologies, independently and as a system2.Demonstrate novel distributed operations concepts3.Socialize new Distributed Spacecraft Mission (DSM) and SensorWeb (SW) technologies and concepts to the science community by significantly retiring the risk of integrating these new technologies.The NOS Testbed will consist of multiple sensing nodes, simulated or actual, representing space, air and/or ground measurements, that are interconnected by a communications fabric (infrastructure that permits nodes to transmit and receive data between one another and interact with each other). Each node will be supported by hardware capabilities required to perform nodes monitoring and command & control, as well as intelligent "onboard" computing. The nodes will work together in a collaborative manner to demonstrate optimal science capabilities. The testbed will enable to validate technologies such as inter-node communication models, techniques and protocols; inter-node coordination; real-time data fusion and understanding; planning; sensor re-targeting; etc. Additionally, the testbed will have the capability to interact with various mission design tools, OSSEs and one or several forecast models. More details about the NOS Testbed will be presented at the confererence.

Earth Science missions; Advanced information Syste↗

Lunar elemental analysis obtained from the Apollo gamma-ray and X-ray remote sensing experiment

Gamma-ray and X-ray spectrometers carried in the service modules of the Apollo 15 and Apollo 16 spacecraft were employed for compositional mapping of the lunar surface. The measurements involved the observation of the intensity and characteristic energy distribution of gamma rays and X-rays emitted from the lunar surface. A large-scale compositional map of over 10 percent of the lunar surface was obtained from an analysis of the observed spectra. The objective of the X-ray experiment was to measure the K spectral lines from Mg, Al, and Si. Spectra were obtained and the data were reduced to Al/Si and Mg/Si intensity ratios and ultimately to chemical ratios. Analyses of the results have indicated (1) that the Al/Si ratios are highest in the lunar highlands and considerably lower in the maria, and (2) that the Mg/Si concentrations generally show the opposite relationship. The objective of the gamma-ray experiment was to measure the natural and cosmic-ray-induced activity emission spectrum. At this time, the elemental abundances for Th, U, K, Fe, Ti, Si, and O have been determined over a number of major lunar regions. Regions of relatively high natural radioactivity were found in the Mare Imbrium and Oceanus Procellarum regions.

Trombka, J. I.↗

Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems

Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This paper proposes a blocktensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Herein, feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems and a 100- node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Adaptation and Response in Drylands (ARID): A Dryland Research Agenda and Campaign Strategy

Dryland ecosystems cover 41% of Earth’s land surfaces, account for 44% of cultivated lands and 60% of food sources, and make large contributions to the global water and carbon cycles. However, these ecosystems are experiencing unprecedented extremes including heatwaves, floods, and droughts as well as hotter temperatures and often declining water resource availability. These ecosystems are some of the most challenging to monitor given their high temporal variability with rapid response to their environment as well as vast spatial variability with intermixing of different plant species and life forms amongst bare soil coverage. The Adaptation and Response in Drylands (ARID) campaign was selected by National Aeronautics and Space Administration (NASA) as a scoping study to develop a research agenda for a dryland field campaign. Here, we detail our ARID science research agenda and implementation plan that were developed based on an extensive community engagement effort in over 160 events with over a thousand scientists, land managers, and Tribal communities between 2023 and 2024. The selected science themes cover drought and climate variability, ecosystem structure, function, and biodiversity, carbon cycle interannual variability and trends, and social ecological systems (land management and adaptation). We then detail our remote sensing, modeling, and field-based strategies to capture high temporal and high spatial resolution processes. Finally, our implementation strategy is presented which includes focus area selections in a core intensive western U.S. domain and distributed international domains. This strategy includes our overarching guiding principles of using multi-temporal airborne acquisitions and super sites as well as enhancing land management in co-development with end-user partners. While originally developed for NASA, our ARID report creates a blueprint for any future dryland field campaign, at any scale, that can be implemented widely for foundational and applied science objectives.

drylands↗

Genome-Wide Discovery of G-Quadruplexes in Wheat: Distribution and Putative Functional Roles

G-quadruplexes are nucleic acid secondary structures formed by a stack of square planar G-quartets. G-quadruplexes were implicated in many biological functions including telomere maintenance, replication, transcription, and translation, in many species including humans and plants. For wheat, however, though it is one of the world’s most important staple food, no G-quadruplex studies have been reported to date. Here, we computationally identify putative G4 structures (G4s) in wheat genome for the first time and compare its distribution across the genome against five other genomes (human, maize, Arabidopsis, rice, and sorghum). We identified close to 1 million G4 motifs with a density of 76 G4s/Mb across the whole genome and 93 G4s/Mb over genic regions. Remarkably, G4s were enriched around three regions, two located on the antisense and one on the sense strand at the following positions: 1) the transcription start site (TSS) (antisense), 2) the first coding domain sequence (CDS) (antisense), and 3) the start codon (sense). Functional enrichment analysis revealed that the gene models containing G4 motifs within these peaks were associated with specific gene ontology (GO) terms, such as developmental process, localization, and cellular component organization or biogenesis. We investigated genes encoding MADS-box transcription factors and showed examples of G4 motifs within critical regulatory regions in the VRN-1 genes in wheat. Furthermore, comparison with other plants showed that monocots share a similar distribution of G4s, but Arabidopsis shows a unique G4 distribution. Our study shows for the first time the prevalence and possible functional roles of G4s in wheat.

59 BASIC BIOLOGICAL SCIENCES↗

Remote Sensing of Clouds, Water Vapor, and Near-Surface Winds Under Various Aerosol Conditions During CAMP2Ex

The Cloud, Aerosol and Monsoon Processes Philippines Experiment (CAMP2Ex) field campaign took place from August – October 2019. CAMP2Ex science objectives include understanding aerosol-cloud interaction under various Meteorological conditions, and how these Meteorological phenomena affect aerosol distribution in the atmosphere. Numerous instruments were flown on the National Aeronautics and Space Administration (NASA) P-3 aircraft during 19 CAMP2Ex science flights, including the Advanced Microwave Precipitation Radiometer (AMPR) the Airborne Third Generation Precipitation Radar (APR-3), and the High Spectral Resolution Lidar 2 (HSRL2). Geophysical retrieval equations for cloud liquid water, columnar water vapor, and near-surface wind speed using AMPR brightness temperatures have been derived and tested using CAMP2Ex data. Water vapor and wind speed retrievals have been validated using in situ observations, such as dropsondes and shipborne instruments. This presentation will demonstrate these AMPR-based retrievals during CAMP2Ex, including discussions of retrieval uncertainties. Specific CAMP2Ex flights will be presented in greater detail, including inferences of other Meteorological phenomena in clear air and around precipitating and non-precipitating clouds, such as background wind speeds and potential identification of gust fronts. These analyses will be supplemented with APR-3 reflectivity and Doppler velocity data to infer microphysical processes occurring within and around selected clouds of interest. In cases where multiple remote-sensing measurements were obtained for the same cloud, a time-evolution analysis of these features may be performed. Throughout these analyses, HSRL2 data will be used to quantify aerosol properties beneath the P-3, and variations in the AMPR/APR-3 observations with respect to various aerosol conditions will be discussed.

Corey Amiot↗

RSP Data Status, Updates and Plans from the Team

•All radiance (L1C), aerosol and cloud (L2) products are in the archive. •Revised calibration performed at GSFC in July 2021 applied to reprocessing. •Clouds have smaller drops and higher optical depths (larger droplet number concentrations) in winter than in summer. Cloud top droplet size distributions tend to be narrow with roughly 80% having an effective variance of less than 0.07. This is relevant to how well bulk auto-conversion parameterizations are likely to work at cloud top (order of magnitude effects) and also to assumptions used in the remote sensing of droplet number (~ 10% effect). Real refractive index and effective radius retrievals are consistent with hygroscopic growth of aerosols Real refractive index and effective variance retrievals imply the presence of an insoluble fraction of aerosols Future work on clouds will look at differences in cloud top drizzle formation and auto-conversion rates between the different campaigns and at how well mixed phase clouds can be detected (if at all) from sensors such as VIIRS and PACE OCI.

Research Scanning Polarimeter↗

Recommendations for developing, documenting, and distributing data products derived from NEON data

The National Ecological Observatory Network (NEON) provides over 180 distinct data products from 81 sites (47 terrestrial and 34 freshwater aquatic sites) within the United States and Puerto Rico. These data products include both field and remote sensing data collected using standardized protocols and sampling schema, with centralized quality assurance and quality control (QA/QC) provided by NEON staff. Such breadth of data creates opportunities for the research community to extend basic and applied research while also extending the impact and reach of NEON data through the creation of derived data products—higher level data products derived by the user community from NEON data. Derived data products are curated, documented, reproducibly-generated datasets created by applying various processing steps to one or more lower level data products—including interpolation, extrapolation, integration, statistical analysis, modeling, or transformations. Derived data products directly benefit the research community and increase the impact of NEON data by broadening the size and diversity of the user base, decreasing the time and effort needed for working with NEON data, providing primary research foci through the development via the derivation process, and helping users address multidisciplinary questions. Creating derived data products also promotes personal career advancement to those involved through publications, citations, and future grant proposals. However, the creation of derived data products is a nontrivial task. Here we provide an overview of the process of creating derived data products while outlining the advantages, challenges, and major considerations.

54 ENVIRONMENTAL SCIENCES↗

Passive microwave remote sensing of rainfall with SSM/I: Algorithm development and implementation

A physically based algorithm sensitive to emission and scattering is used to estimate rainfall using the Special Sensor Microwave/Imager (SSM/I). The algorithm is derived from radiative transfer calculations through an atmospheric cloud model specifying vertical distributions of ice and liquid hydrometeors as a function of rain rate. The algorithm is structured in two parts: SSM/I brightness temperatures are screened to detect rainfall and are then used in rain-rate calculation. The screening process distinguishes between nonraining background conditions and emission and scattering associated with hydrometeors. Thermometric temperature and polarization thresholds determined from the radiative transfer calculations are used to detect rain, whereas the rain-rate calculation is based on a linear function fit to a linear combination of channels. Separate calculations for ocean and land account for different background conditions. The rain-rate calculation is constructed to respond to both emission and scattering, reduce extraneous atmospheric and surface effects, and to correct for beam filling. The resulting SSM/I rain-rate estimates are compared to three precipitation radars as well as to a dynamically simulated rainfall event. Global estimates from the SSM/I algorithm are also compared to continental and shipboard measurements over a 4-month period. The algorithm is found to accurately describe both localized instantaneous rainfall events and global monthly patterns over both land and ovean. Over land the 4-month mean difference between SSM/I and the Global Precipitation Climatology Center continental rain gauge database is less than 10%. Over the ocean, the mean difference between SSM/I and the Legates and Willmott global shipboard rain gauge climatology is less than 20%.

Ferriday, James G.↗

Integrating very-high-resolution imagery, Sentinel-2 time-series data, and machine learning to map shrub fractional abundance across arid and semi-arid ecosystems in China

Shrub fractional abundance (SFA), the proportion of shrub cover per unit area, serves as a critical indicator of environmental aridity and ecosystem health in arid and semi-arid regions, particularly across the Mongolian steppe. However, large-scale SFA mapping in Mongolian steppe ecosystems remains challenging due to the small crown size of shrubs, their sparse distribution, and spectral overlap with coexisting low vegetation (e.g., grasses and herbs), which hinders accurate detection using coarser-resolution satellite data or traditional field surveys. To address these challenges, we developed a two-step approach that integrates very-high-resolution (VHR) imagery, time-series Sentinel-2 data, and deep learning techniques. First, we generated high-accuracy benchmark maps of individual shrub crowns from 0.5 m VHR imagery by combining manual segmentation with a hybrid deep learning framework (Dino V2 and convolutional neural networks). Second, we used these shrub crown maps as training data to build an XGBoost model for predicting SFA from 20 m Sentinel-2 time-series data, leveraging phenological information to improve estimation. We validated our approach across 70 sites (1km 2 each) in the Inner Mongolia Autonomous Region, which is representative of Mongolian steppe ecosystems. From VHR imagery, we mapped 1.31 million shrub crowns with an accuracy of R 2 = 0.92. Scaling up with Sentinel-2 data yielded regional SFA maps with an R 2 = 0.60. Further SHAP (SHapley Additive exPlanations) analysis on the developed XGBoost model revealed that phenological metrics (particularly observations in early-May, mid-July, and late-September), which distinguish shrub phenology from that of other land cover types (e.g., grasses and bare soil), were the most influential predictors of SFA. Finally, our regional SFA maps uncovered unimodal relationships between shrub distribution and climate variables, peaking at mean annual minimum temperatures near 0 °C and annual precipitation around 200 mm. Collectively, these findings demonstrate how the integration of multi-source remote sensing and machine learning can overcome historical limitations in SFA mapping, enabling accurate, spatially continuous assessments across vast Inner-Mongolian steppe ecosystems. Our framework has the potential to be applied to other steppe ecosystems and dryland ecosystems across the Mongolian steppe and beyond, offering a foundation for improved monitoring and ecological impact assessments in the face of global climate changes.

Arid and semi-arid landscapes↗

Spectral Hardness of X- and Gamma-Ray Emissions From Lightning Stepped and Dart Leaders

During the 2022 New Mexico monsoon season, we deployed two X-ray scintillation detectors, coupled with a 180 MHz data acquisition system to detect X-rays from natural lightning at the Langmuir Lab mountain-top facility, located at 3.3 km above mean sea level. Data acquisition was triggered by an electric field antenna calibrated to pick up lightning within a few km of the X-ray detectors. We report the energies of over 240 individual photons, ranging between 13 keV and 3.8 MeV, as registered by the LaBr3(Ce) scintillation detector. These detections were associated with four lightning flashes. Particularly, four-stepped leaders and seven dart leaders produced energetic radiation. Importantly, the reported photon energies allowed us to confirm that the X-ray energy distribution of natural stepped and dart leaders follows a power-law distribution with an exponent ranging between 1.09 and 1.96, with stepped leaders having a harder spectrum. Characterization of the associated leaders and return strokes was done with four different electric field sensing antennas, which can measure a wide range of time scales, from the static storm field to the fast change associated with dart leaders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Isotope engineering for spin defects in van der Waals materials

Abstract Spin defects in van der Waals materials offer a promising platform for advancing quantum technologies. Here, we propose and demonstrate a powerful technique based on isotope engineering of host materials to significantly enhance the coherence properties of embedded spin defects. Focusing on the recently-discovered negatively charged boron vacancy center ($${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − ) in hexagonal boron nitride (hBN), we grow isotopically purified h 10 B 15 N crystals. Compared to$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − in hBN with the natural distribution of isotopes, we observe substantially narrower and less crowded$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − spin transitions as well as extended coherence timeT 2 and relaxation timeT 1 . For quantum sensing,$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − centers in our h 10 B 15 N samples exhibit a factor of 4 (2) enhancement in DC (AC) magnetic field sensitivity. For additional quantum resources, the individual addressability of the$${{{{{{{{\rm{V}}}}}}}}}_{{{{{{{{\rm{B}}}}}}}}}^{-}$$ V B − hyperfine levels enables the dynamical polarization and coherent control of the three nearest-neighbor 15 N nuclear spins. Our results demonstrate the power of isotope engineering for enhancing the properties of quantum spin defects in hBN, and can be readily extended to improving spin qubits in a broad family of van der Waals materials.

Science & Technology - Other Topics↗

Mapping the global distribution of C 4 vegetation using observations and optimality theory

Plants with the C 4 photosynthesis pathway typically respond to climate change differently from more common C 3 -type plants, due to their distinct anatomical and biochemical characteristics. These different responses are expected to drive changes in global C 4 and C 3 vegetation distributions. However, current C 4 vegetation distribution models may not predict this response as they do not capture multiple interacting factors and often lack observational constraints. Here, we used global observations of plant photosynthetic pathways, satellite remote sensing, and photosynthetic optimality theory to produce an observation-constrained global map of C 4 vegetation. We find that global C 4 vegetation coverage decreased from 17.7% to 17.1% of the land surface during 2001 to 2019. This was the net result of a reduction in C 4 natural grass cover due to elevated CO 2 favoring C 3 -type photosynthesis, and an increase in C 4 crop cover, mainly from corn (maize) expansion. Using an emergent constraint approach, we estimated that C 4 vegetation contributed 19.5% of global photosynthetic carbon assimilation, a value within the range of previous estimates (18–23%) but higher than the ensemble mean of dynamic global vegetation models (14 ± 13%; mean ± one standard deviation). Our study sheds insight on the critical and underappreciated role of C 4 plants in the contemporary global carbon cycle.

54 ENVIRONMENTAL SCIENCES↗

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

quantum error correction↗

Simulation of Plasma Emission in Magnetized Plasmas

The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

79 ASTRONOMY AND ASTROPHYSICS↗

Error in temperature measurements due to conduction along the sensors

When a sensor is embedded in a solid body to measure its internal temperature, any conduction to or from its sensing element may cause the indicated temperature to be different from the true temperature. This paper describes an analysis of the error caused by conduction when there is an arbitrary temperature distribution in the body along the sensor. The sensor is modeled as a cylindrical fin and the appropriate conduction equation is solved. The solution gives a correction for the error which depends on such parameters as, depth of immersion, thermocouple wire and insulation properties, contact between the sensor and the body, and temperature distribution in the body. The latter may not be known, but the measured temperature distribution can be used as a first approximation. The corrected value can then be used to obtain a better estimate of the error. The results show good agreement with experimental observations.

Singh, B. S.↗