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At least 127 records · Page 7

Alternatives to accuracy and bias metrics based on percentage errors for radiation belt modeling applications

This report reviews existing literature describing forecast accuracy metrics, concentrating on those based on relative errors and percentage errors. We then review how the most common of these metrics, the mean absolute percentage error (MAPE), has been applied in recent radiation belt modeling literature. Finally, we describe metrics based on the ratios of predicted to observed values (the accuracy ratio) that address the drawbacks inherent in using MAPE. Specifically, we define and recommend the median log accuracy ratio as a measure of bias and the median symmetric accuracy as a measure of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Measures of model performance based on the log accuracy ratio

Quantitative assessment of modeling and forecasting of continuous quantities uses a variety of approaches. We review existing literature describing metrics for forecast accuracy and bias, concentrating on those based on relative errors and percentage errors. Of these accuracy metrics, the mean absolute percentage error (MAPE) is one of the most common across many fields and has been widely applied in recent space science literature and we highlight the benefits and drawbacks of MAPE and proposed alternatives. We then introduce the log accuracy ratio, and derive from it two metrics: the median symmetric accuracy; and the symmetric signed percentage bias. Robust methods for estimating the spread of a multiplicative linear model using the log accuracy ratio are also presented. The developed metrics are shown to be easy to interpret, robust, and to mitigate the key drawbacks of their more widely-used counterparts based on relative errors and percentage errors. Their use is illustrated with radiation belt electron flux modeling examples.

54 ENVIRONMENTAL SCIENCES↗

Accuracy and Precision of Age Estimates Obtained from Three Calcified Structures for Known-Age Kokanee

Abstract Kokanee Oncorhynchus nerka growth is often density dependent; thus, proper management of kokanee populations necessitates an understanding of population dynamics using age structure data. To date, no calcified structures have been validated for kokanee. We compared the accuracy (i.e., the percentage of reconciled age estimates that matched the known ages of fish) and precision (i.e., the percentage of fish for which complete agreement was achieved on age estimates among all readers) of aging estimates for scales, sectioned otoliths, and sectioned pectoral fin rays from 455 known-age kokanee (ages 0–4) collected from five lentic waters in Idaho. Across all waters combined, mean weighted accuracy and precision were similar for scales (86% and 70%, respectively), fin rays (83% and 65%), and otoliths (82% and 65%), with no significant differences between structures. However, among water bodies, accuracy and precision of each calcified structure varied considerably. For example, scales were the most accurate and precise structure and otoliths were the least accurate and precise structure at one water body, while otoliths were the most accurate and precise structure and scales were the least accurate structure at two water bodies. Fin rays were the least precise structure at four of the five study waters, but were the least accurate structure for only one water body. Individual reader accuracy was most affected by fish age and water body, and older fish (age 3 and older) were consistently assigned incorrect ages regardless of the water body or the calcified structure. Taken collectively, all three structures produced satisfactory aging accuracy and precision for kokanee, but no structure was unequivocally best; at any individual water body, annual growth and local environmental conditions appeared to influence the readability of calcified structures.

Branigan, Philip R. (ORCID:0000000337990573)↗

Reader agreement and accuracy of ultrasound features for hepatic steatosis

Purpose: The purpose of the study is to assess the reader agreement and accuracy of eight ultrasound imaging features for classifying hepatic steatosis in adults with known or suspected hepatic steatosis. Methods: This was an IRB-approved, HIPAA-compliant prospective study of adult patients with known or suspected hepatic steatosis. All patients signed written informed consent. Ultrasound images (Siemens S3000, 6C1HD, and 4C1 transducers) were acquired by experienced sonographers following a standard protocol. Eight readers independently graded eight features and their overall impression of hepatic steatosis on ordinal scales using an electronic case report form. Duplicated images from the 6C1HD transducer were read twice to assess intra-reader agreement. Intra-reader, inter-transducer, and inter-reader agreement were assessed using intraclass correlation coefficients (ICC). Features with the highest intra-reader agreement were selected as predictors for dichotomized histological steatosis using Classification and Regression Tree (CART) analysis, and the accuracy of the decision rule was compared to the accuracy of the radiologists’ overall impression. Results: 45 patients (18 males, 27 females; mean age 56 ± 12 years) scanned from September 2015 to July 2016 were included. Mean intra-reader ICCs ranged from 0.430 to 0.777, inter-transducer ICCs ranged from 0.228 to 0.640, and inter-reader ICCs ranged from 0.014 to 0.561. The CART decision rule selected only large hepatic vein blurring and achieved similar accuracy to the overall impression (74% to 75% and 68% to 72%, respectively). Conclusions: Large hepatic vein blurring, liver–kidney contrast, and overall impression provided the highest reader agreement. Large hepatic vein blurring may provide the highest classification accuracy for dichotomized grading of hepatic steatosis.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Analyzing the post-contrast attenuation of the esophageal wall on routine contrast-enhanced MDCT examination can improve the diagnostic accuracy in response evaluation of the squamous cell esophageal carcinoma to neoadjuvant chemoradiotherapy in comparison with the esophageal wall thickness

Purpose: To evaluate the accuracy of the multidetector computed tomography (MDCT) in the response evaluation of the esophageal squamous cell carcinoma (ESCC) to neoadjuvant chemoradiotherapy (nCRT) by analyzing the thickness and post-contrast attenuation of the esophageal wall after the nCRT. Methods: Contrast-enhanced (CE)-MDCT examinations in portal venous phase of one hundred patients with locally advanced ESCC who received nCRT and underwent esophageal resection and histopathology assessment of tumor regression grade (TRG) were retrospectively analyzed by measuring the maximal thickness and mean density of the esophageal wall in the segment involved by tumor and visually searching for hyperdense foci within it. Diagnostic performance was evaluated using the ROC analysis. Results: Average attenuation of the esophageal wall had stronger diagnostic performance for predicting pathologic complete regression (pCR) (AUC = 0.994; p < 0.001) in relation to maximal esophageal wall thickness (AUC = 0.731; p < 0.001). Maximal esophageal wall thickness ≤ 9 mm and average attenuation of the esophageal wall ≤ 64 HU predicted pCR with the sensitivity, specificity, and overall accuracy of 62.5%, 77.9%, and 73%, and 96.9%, 98.5%, and 98%, respectively. Combination of both cutoff values enabled correct assessment of pCR with the 100% accuracy. Visual detection of the hyperdense focus within the esophageal wall predicted pCR with the sensitivity, specificity, and overall accuracy values of 100%, 94.1%, and 96%, respectively. Conclusion: Visual analysis and measurement of post-contrast attenuation of the esophageal wall after the nCRT can improve diagnostic accuracy of MDCT in the response evaluation of the ESCC to nCRT in comparison with measuring the esophageal wall thickness.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Accuracy, criteria, and clinical significance of visual assessment on diffusion-weighted imaging and apparent diffusion coefficient quantification for diagnosing acute appendicitis

Purpose: To assess the accuracy, criteria, and clinical significance of diffusion-weighted imaging (DWI) signal intensity and apparent diffusion coefficient (ADC) quantification for diagnosing acute appendicitis. Methods: Fifty-one patients with right lower abdominal pain [uncomplicated appendicitis (n = 25), complicated appendicitis (n = 10), and non-appendicitis (n = 16)] who underwent MR examination were enrolled in this retrospective study. Two radiologists independently measured appendiceal diameter and wall thickness. They assessed whether a wall defect, an abscess, extraluminal air, or an appendicolith was present on axial T2WI; evaluated intensity on DWI using a 5-point scale; and determined the ADC values of the appendix and peri-appendiceal tissue. Statistical analysis was performed to assess imaging findings for the diagnosis of appendicitis and complicated appendicitis. Cut-off values were determined using receiver operating characteristic analysis. Results: For diagnosing acute appendicitis, the accuracy improved from 78.4% using only T2WI to 86.3% using combined T2WI and DWI for reader 1 and from 82.4 to 86.3% for reader 2. For the appendix, the cut-off ADC values that diagnosed appendicitis were 1.41 × 10{sup −3} and 1.26 × 10{sup −3} mm{sup 2}/s with accuracies of 78.4% and 76.5%, respectively. For the peri-appendiceal tissue, these values of 1.03 × 10{sup −3} and 0.91 × 10{sup −3} mm{sup 2}/s differentiated between uncomplicated and complicated appendicitis with an accuracy of 97.1%. Conclusions: Combined DWI and T2WI provided high accuracy for diagnosing appendicitis. The inflamed appendix had lower ADC value than the normal appendix. The peri-appendiceal tissue presenting low ADC value was a notable finding of complicated appendicitis.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Evaluation of accuracy and convergence of numerical coupling approaches for poroelasticity benchmark problems

Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. Furthermore, this work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.

58 GEOSCIENCES↗

Time-Resolved Intrafraction Target Translations and Rotations During Stereotactic Liver Radiation Therapy: Implications for Marker-based Localization Accuracy

Purpose: Image guided liver stereotactic body radiation therapy (SBRT) often relies on implanted fiducial markers. The target localization accuracy decreases with increased marker-target distance. This may occur partly because of liver rotations. The aim of this study was to examine time-resolved translations and rotations of liver marker constellations and investigate if time-resolved intrafraction rotational corrections can improve localization accuracy in liver SBRT. Methods and Materials: Twenty-nine patients with 3 implanted markers received SBRT in 3 to 6 fractions. The time-resolved trajectory of each marker was estimated from the projections of 1 to 3 daily cone beam computed tomography scans and used to calculate the translation and rotation of the marker constellation. In all cone beam computed tomography projections, the time-resolved position of each marker was predicted from the position of another surrogate marker by assuming that the marker underwent either (1) the same translation as the surrogate marker; or (2) the same translation as the surrogate marker corrected by the rotation of the marker constellation. The localization accuracy was quantified as the root-mean-square error (RMSE) between the estimated and the actual marker position. For comparison, the RMSE was also calculated when the marker's position was estimated as its mean position for all the projections. Results: The mean translational and rotational range (2nd-98th percentile) was 2.0 mm/3.9° (right-left), 9.2 mm/2.9° (superior-inferior), 4.0 mm/4.0° (anterior-posterior), and 10.5 mm (3-dimensional). Rotational corrections decreased the mean 3-dimensional RMSE from 0.86 mm to 0.54 mm (P<.001) and halved the RMSE increase per millimeter increase in marker distance. Conclusions: Intrafraction rotations during liver SBRT reduce the accuracy of marker-guided target localization. Rotational correction can improve the localization accuracy with a factor of approximately 2 for large marker-target distances.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations

This study on overset meshes for incompressible-flow simulations is motivated by accurate prediction of wind farm aerodynamics involving large motions and deformations of components with complex geometry. Specifically, using first-order hyperbolic and elliptic equation proxies for the incompressible Navier-Stokes (NS) equations, we investigate the influence of information exchange between overset meshes on numerical performance where the underlying discretization is second-order accurate. The first aspect of information exchange surrounds interpolation of solution where we examine Lagrange and point-cloud-based interpolation for creating constraint equations between overset meshes. To maintain overall second-order accuracy, higher-order interpolation is required for elliptic problems, but linear interpolation is sufficient for hyperbolic problems in first-order form. Higher-order point-cloud-based interpolation provides a pathway to maintaining accuracy in unstructured meshes, but at higher complexity. The second aspect of information exchange focuses on comparing the approaches of overset single system (OSS) and overset Additive Schwarz (OAS) for coupling the linear systems of the overlapping meshes. While the former involves a single linear system, in the latter the discrete linear systems are solved separately, and solving the global system is accomplished through outer iterations and sequential information exchange in a Jacobi fashion. For the test cases studied, accuracy for hyperbolic problems is maintained by performing two outer iterations, whereas many outer iterations are required for elliptic systems. The order-of-accuracy studies explored here are critical for verifying the overset-mesh coupling algorithms used in engineering simulations. Accuracy of these simulations themselves is, however, quantified using engineering quantities of interest such as drag, power, etc. Consequently, we conclude with numerical experiments using NS equations for incompressible flows where we show that linear interpolation and few outer iterations are sufficient for achieving asymptotic convergence of engineering quantities of interest.

97 MATHEMATICS AND COMPUTING↗

Achieving Higher Order Accuracy in Space in Hydrodynamic Simulations of Self-Gravitating Gas

Modern astrophysical simulation codes employ a variety of numerical algorithms capable of achieving higher-order accuracy in both space and time. Albeit they succeed in achieving an effective higher spatial resolution and in suppressing the numerical damping of waves, to our knowledge, all current astrophysical simulations invoking self-gravity are limited to second-order accuracy in space. If we can devise an algorithm to evaluate self-gravity with a higher-order spatial accuracy, we can better the evaluation of the gravitational acceleration and gravitational energy release which dictate the evolution of many astrophysical systems. Herein, we present a numerical algorithm for self-gravitating hydrodynamics capable of achieving fourth-order accuracy for a given density distribution on a Cartesian uniform grid. First, we derive the cell-averaged gravitational potential at fourth-order accuracy from the cell-averaged density by solving the Poisson equation. Next, we obtain the cell average of the product of the density and gravitational acceleration, which differs from the cell-averaged density multiplied by the cell-averaged gravitational acceleration. We then show the verification of the algorithm by applying it to critical test problems: (1) maintaining equilibria of self-gravitating slabs, even upon advection, (2) evolving a polytropic sphere with a massive power-law envelope, and (3) conservation of specific entropy during the propagation of a sound wave.

79 ASTRONOMY AND ASTROPHYSICS↗

Accuracy of power spectra in dissipationless cosmological simulations

Abstract We exploit a suite of large N-body simulations (up to N = 40963) performed with abacus, of scale-free models with a range of spectral indices n, to better understand and quantify convergence of the matter power spectrum. Using self-similarity to identify converged regions, we show that the maximal wavenumber resolved at a given level of accuracy increases monotonically as a function of time. At 1 per cent level it starts at early times from a fraction of $k_\Lambda$, the Nyquist wavenumber of the initial grid, and reaches at most, if the force softening is sufficiently small, ${\sim}2{-}3 k_\Lambda$ at the very latest times we evolve to. At the $5{{\ \rm per\ cent}}$ level, accuracy extends up to wavenumbers of order $5k_\Lambda$ at late times. Expressed as a suitable function of the scale-factor, accuracy shows a very simple n-dependence, allowing a extrapolation to place conservative bounds on the accuracy of N-body simulations of non-scale-free models like LCDM. We note that deviations due to discretization in the converged range are not well modelled by shot noise, and subtracting it in fact degrades accuracy. Quantitatively our findings are broadly in line with the conservative assumptions about resolution adopted by recent studies using large cosmological simulations (e.g. Euclid Flagship) aiming to constrain the mildly non-linear regime. On the other hand, we remark that conclusions about small-scale clustering (e.g. concerning the validity of stable clustering) obtained using PS data at wavenumbers larger than a few $k_\Lambda$ may need revision in light of our convergence analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

Throughput-Oriented and Accuracy-Aware DNN Training with BFloat16 on GPU

Deep Neural Networks (DNNs) have transformed the field of artificial intelligence and achieved extraordinary success in many areas. The training of DNNs is commonly compute and memory-intensive, which has resulted in several optimizations in the training phase. Among them, reduced precision is a typical and widely used technique to accelerate DNN training and reduce memory requirements. However, applying a widely adopted reduced precision format such as Float16 to all involved operations in DNN training is not optimal as the use of Float16 in some operations can hurt model accuracy. Meanwhile, additional optimizations including loss scaling and autocast techniques can mitigate the accuracy loss but lead to inherent overhead and inadequate use of reduced precision. In this work, we leverage another reduced precision format, BFloat16, and introduce a throughput-oriented and accuracy-aware approach to maximize the performance potential of DNN training. Since the high throughput provided by BFloat16 format is accompanied by low precision of the floating-point representation, this approach achieves high throughput by using BFloat16 on all DNN operations and avoids the accuracy loss through a customized accuracy-aware normalization. Results show that our approach outperforms the state-of-the-art mixed-precision training by 1.21x on an NVIDIA A100 GPU.

Xie, Zhen↗

Chisel: reliability- and accuracy-aware optimization of approximate computational kernels

The accuracy of an approximate computation is the distance between the result that the computation produces and the corresponding fully accurate result. The reliability of the computation is the probability that it will produce an acceptably accurate result. Emerging approximate hardware platforms provide approximate operations that, in return for reduced energy consumption and/or increased performance, exhibit reduced reliability and/or accuracy. We present Chisel, a system for reliability- and accuracy-aware optimization of approximate computational kernels that run on approximate hardware platforms. Given a combined reliability and/or accuracy specification, Chisel automatically selects approximate kernel operations to synthesize an approximate computation that minimizes energy consumption while satisfying its reliability and accuracy specification. We evaluate Chisel on five applications from the image processing, scientific computing, and financial analysis domains. The experimental results show that our implemented optimization algorithm enables Chisel to optimize our set of benchmark kernels to obtain energy savings from 8.7% to 19.8% compared to the fully reliable kernel implementations while preserving important reliability guarantees.

97 MATHEMATICS AND COMPUTING↗

A refined assessment of nuclear data target accuracy requirements for ALFRED

The interest in target accuracy assessment has been recently renewed within the OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation with an update exercise, thanks to the invaluable initiative of Massimo Salvatores. This work, moving from evaluations on the main core integral parameters of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED), and the identification of the associated target accuracies needed for improving its design, approaches the retrieval of target accuracy requirements for nuclear data, as the inverse problem of uncertainty quantification. The preliminary results obtained in a previous work are here refined by explicitly taking into account the total contribution due to correlations among variables in the optimization constraint, while its various components are evaluated individually. Moreover, three different sets of cost parameters are considered to introduce a bias in the solution in order to take in due account the relative difficulties in the execution of new differential experiments as needed for achieving the proposed target accuracies. By this, the obtained results are deemed usefully informative, and proposed for the update of a High Priority List which identifies the isotopes-reaction couples of most interest for future refinement experiments, especially when integrated with further analogous information collected on other advanced nuclear systems. Among the cross-sections whose refinement contributes the most to the reduction of the multiplication factor, the fission of Pu{sup 239} was found, which needs to be fixed below 1% in the range of interest for ALFRED (2 keV-4 MeV). Another contribution for the amelioration of the multiplication factor calculation accuracy, is due to the capture channel of Pu{sup 239}, for which the initial high uncertainty (around 15%) can be significantly reduced resorting to easily practicable experiments. The same occurs for the inelastic of Pb{sup 207}, for which the initial uncertainty value of around 50% can be drastically reduced up to target values between 4% and 7%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

STTR Phase I: Low-Cost, High-Accuracy, Whole-Building Carbon Dioxide Monitoring for Demand Control Ventilation

This STTR Phase I project assessed the feasibility of a new CO 2 sensing system optimized for low-cost, high-accuracy, whole-building monitoring for use in demand control ventilation. The focus was on the development of a wireless networking platform and associated firmware to provide signal conditioning and conversion, fault- and disruptiontolerant networking, and multi-hop routing at building scales to avoid wiring costs. Early exploration of a bridge (or “gateway”) to direct digital control services was also explored. Results of the project contributed to an improved understanding of a new electrochemical sensor for monitoring indoor CO 2 concentrations, as well as the electronics and networking infrastructure required to deploy those sensors at building scales. New knowledge was acquired concerning the sensor’s accuracy, environmental response, and failure modes, and the acquisition electronics required to achieve accuracy over a wide range of CO 2 concentrations. The project demonstrated that the new sensor offers repeatable correspondence with commercial optical sensors, with supporting electronics that offer gain accuracy within 0.5%, and acquisition accuracy within 1.5% across three orders of magnitude variation in generated current. Considering production, installation, and maintenance costs, the technology presents a foundation for achieving whole-building CO 2 sensing at a price point below $0.066 / sq-ft – meeting economic feasibility criteria established by the Department of Energy. The technology developed under this award addresses obstacles on the critical path to enabling whole-building CO 2 sensing and demand control ventilation in commercial retrofits, small commercial buildings, residential complexes, and other highpotential structures that have been slow to adopt these technologies. It presents an opportunity to significantly reduce energy use throughout the United States.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Achieving Higher Order Accuracy in Space in Hydrodynamic Simulations of Self-Gravitating Gas

Modern astrophysical simulation codes employ a variety of numerical algorithms capable of achieving higher-order accuracy in both space and time. Albeit they succeed in achieving an effective higher spatial resolution and in suppressing the numerical damping of waves, to our knowledge, all current astrophysical simulations invoking self-gravity are limited to second-order accuracy in space. If we can devise an algorithm to evaluate self-gravity with a higher-order spatial accuracy, we can better the evaluation of the gravitational acceleration and gravitational energy release which dictate the evolution of many astrophysical systems. Herein, we present a numerical algorithm for self-gravitating hydrodynamics capable of achieving fourth order accuracy for a given density distribution on a Cartesian uniform grid. First, we derive the cell-averaged gravitational potential at fourth-order accuracy from the cell-averaged density by solving the Poisson equation. Next, we obtain the cell average of the product of the density and gravitational acceleration, which differs from the cell-averaged density multiplied by the cell-averaged gravitational acceleration. We then show the verification of the algorithm by applying it to critical test problems: (1) maintaining equilibria of self-gravitating slabs, even upon advection, (2) evolving a polytropic sphere with a massive power-law envelope, and (3) conservation of specific entropy during the propagation of a sound wave.

79 ASTRONOMY AND ASTROPHYSICS↗

Comments on the accuracy of Baker-Nunn observations

Many factors influence the accuracy with which the satellite positions may be derived from Baker-Nunn observations. Some of these factors are more important than others. In an accuracy study of satellite tracking methods there are invariably two distinct aspects to be investigated: the accuracy with which the satellite position can be referred to the reference system used - the stellar framework in the case of the optical observations, and the accuracy of the instant of observation. It is generally desirable to keep time as an independent variable so that any uncertainty in measuring the time of observation will be reflected in the positional accuracy.

Lambeck, K.↗

Derivation of clear-column temperature profiles with high vertical resolution and accuracy

It is noted that the optimum tradeoff between accuracy and resolution for current sounders leads to an rms accuracy of 2.5 K and a vertical resolution of about 5 km, while current numerical weather prediction models require temperature profiles with an accuracy of 1-1.5 K and a vertical resolution of about 2 km in the troposphere. The present paper shows that improvements in both the vertical resolution and accuracy require improvements in the informational content of the sounding systems and cannot be achieved by numerical means alone. Results are presented from a sounding system with narrow band channels to illustrate the improvements which can be achieved with future sounders. Finally, the results of several numerical simulations are discussed which show that clear column temperature profiles can be derived in the presence of clouds with an rms accuracy of 1.5 K and vertical resolution of 2 km in the troposphere.

Chahine, M. T.↗