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At least 757 records · Page 42

SU-F-T-273: Using a Diode Array to Explore the Weakness of TPS DoseCalculation Algorithm for VMAT and Sliding Window Techniques

Purpose: To identify the weakness of dose calculation algorithm in a treatment planning system for volumetric modulated arc therapy (VMAT) and sliding window (SW) techniques using a two-dimensional diode array. Methods: The VMAT quality assurance(QA) was implemented with a diode array using multiple partial arcs that divided from a VMAT plan; each partial arc has the same segments and the original monitor units. Arc angles were less than ± 30°. Multiple arcs delivered through consecutive and repetitive gantry operating clockwise and counterclockwise. The source-toaxis distance setup with the effective depths of 10 and 20 cm were used for a diode array. To figure out dose errors caused in delivery of VMAT fields, the numerous fields having the same segments with the VMAT field irradiated using different delivery techniques of static and step-and-shoot. The dose distributions of the SW technique were evaluated by creating split fields having fine moving steps of multi-leaf collimator leaves. Calculated doses using the adaptive convolution algorithm were analyzed with measured ones with distance-to-agreement and dose difference of 3 mm and 3%.. Results: While the beam delivery through static and step-and-shoot techniques showed the passing rate of 97 ± 2%, partial arc delivery of the VMAT fields brought out passing rate of 85%. However, when leaf motion was restricted less than 4.6 mm/°, passing rate was improved up to 95 ± 2%. Similar passing rate were obtained for both 10 and 20 cm effective depth setup. The calculated doses using the SW technique showed the dose difference over 7% at the final arrival point of moving leaves. Conclusion: Error components in dynamic delivery of modulated beams were distinguished by using the suggested QA method. This partial arc method can be used for routine VMAT QA. Improved SW calculation algorithm is required to provide accurate estimated doses.

60 APPLIED LIFE SCIENCES↗

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

assimilation↗

Improving Vertical Velocity Retrievals from Doppler Radar Observations of Convection Field Campaign Report

Our National Science Foundation (NSF)-supported project was designed to address two longstanding challenges in radar-, meso-scale-, and hydro-meteorology: (1) mitigating the effects of non-simultaneous data collection on radar data-based analysis products, and (2) improving estimates of the vertical velocity (w) field in dual-Doppler wind analyses. Errors associated with the non-simultaneous data collection introduce errors in all Doppler analyses, and impose a lower limit on the time and space scales that can be studied. For many investigations the w field is of prime meteorological importance, but it is the velocity component most difficult to accurately synthesize from dual-Doppler wind observations. Our original plan proposed for short field campaigns at the Atmospheric Radiation Measurement (ARM) user facility Southern Great Plains (SGP) Central Facility (CF) was to use multiple-Doppler radial wind data from the scanning ARM X-band radars to test and refine our multiple-Doppler wind analysis algorithms. An important part of our plan was the use of high-temporal-resolution w observations to verify the analyses. In our original plan, these data would be obtained from Doppler lidars, 915 MhZ profilers and Ka-band ARM Zenith Radar (KAZR) zenith-pointing radars at the CF and nearby ARM facilities in north-central Oklahoma. Using the data, we planned to test the utility of new spatially variable advection-correction/analysis procedures, the utility of the anelastic vertical vorticity equation as a constraint in variational multiple-Doppler wind analysis, and other Doppler wind analysis procedures. Idealized tests with numerically-simulated supercell data had suggested the vorticity constraint could help improve the vertical velocity field if the data were gathered with sufficiently high temporal resolution (e.g., volume scans completed in 30-60 sec), so we were interested in exploring the use of rapid-scan data from the X-band Scanning ARM Precipitation Radars (XSAPRs).

Southern Great Plains, convection, KAZR, XSAPR, ve↗

From plane waves to local Gaussians for the simulation of correlated periodic systems

Here, we present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TH-C-12A-08: New Compact 10 MV S-Band Linear Accelerator: 3D Finite-Element Design and Monte Carlo Dose Simulations

Purpose: To design a new compact S-band linac waveguide capable of producing a 10 MV x-ray beam, while maintaining the length (27.5 cm) of current 6 MV waveguides. This will allow higher x-ray energies to be used in our linac-MRI systems with the same footprint. Methods: Finite element software COMSOL Multiphysics was used to design an accelerator cavity matching one published in an experiment breakdown study, to ensure that our modeled cavities do not exceed the threshold electric fields published. This cavity was used as the basis for designing an accelerator waveguide, where each cavity of the full waveguide was tuned to resonate at 2.997 GHz by adjusting the cavity diameter. The RF field solution within the waveguide was calculated, and together with an electron-gun phase space generated using Opera3D/SCALA, were input into electron tracking software PARMELA to compute the electron phase space striking the x-ray target. This target phase space was then used in BEAM Monte Carlo simulations to generate percent depth doses curves for this new linac, which were then used to re-optimize the waveguide geometry. Results: The shunt impedance, Q-factor, and peak-to-mean electric field ratio were matched to those published for the breakdown study to within 0.1% error. After tuning the full waveguide, the peak surface fields are calculated to be 207 MV/m, 13% below the breakdown threshold, and a d-max depth of 2.42 cm, a D10/20 value of 1.59, compared to 2.45 cm and 1.59, respectively, for the simulated Varian 10 MV linac and brehmsstrahlung production efficiency 20% lower than a simulated Varian 10 MV linac. Conclusion: This work demonstrates the design of a functional 27.5 cm waveguide producing 10 MV photons with characteristics similar to a Varian 10 MV linac.

07 ISOTOPE AND RADIATION SOURCES↗

Sky-Scanning Sun-Tracking Airborne Radiometer (3STAR): Instrument Design, Flight Testing, and Tracking Performance

The Sky-Scanning, Sun-Tracking Airborne Radiometer (3STAR) adapts commercial radiometer technology developed for the ocean color research community to airborne measurement of spectrally resolved solar irradiance and sky radiance. These atmospheric observations are used to derive aerosol optical depth (AOD), supporting localized AOD inputs for atmospheric correction of satellite and airborne data over terrestrial and aquatic (including optically dark) targets. The ability to regionally “tune” atmospheric correction schemes with relevant spatial AOD supports constraining atmospheric correction of remote sensing reflectance. Very wide dynamic range has been achieved for multi-channel band-pass-filter-radiometers originally designed for deployment into the water column. By actively tracking and directly pointing to the Sun, the light attenuation by aerosol particles in the atmospheric column can be quantified. These measurements improve knowledge of atmospheric constituents and the atmospheric corrections required to improve remote sensing capabilities for interpreting reflectance measurements from the Earth surface. 3STAR incorporates a custom Sun-tracking/sky-scanning pointing head, a Sun-tracking camera, and a commercially available, cylindrical, 19-channel radiometer tube assembly. An accurate and responsive mount and tracking system has been developed and certified to NASA and Naval Air Systems Command (NAVAIR) airworthiness standards for deployment into the aircraft slipstream. Ground and flight testing indicate typical tracking errors of less than 0.1 degrees, well within the field of view of the radiometer as required to minimize measurement uncertainty from alignment error. Preliminary AOD measurements compare to within 0.013 with 15 measurements from an Aerosol Robotic Network (AERONET) Cimel instrument at 500 nm wavelength and low solar angle.

Atmosphere↗

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Uncertainty quantification for radiation measurements: Bottom-up error variance estimation using calibration information

One example of top-down uncertainty quantification (UQ) involves comparing two or more measurements on each of multiple items. One example of bottom-up UQ expresses a measurement result as a function of one or more input variables that have associated errors, such as a measured count rate, which individually (or collectively) can be evaluated for impact on the uncertainty in the resulting measured value. In practice, it is often found that top-down UQ exhibits larger error variances than bottom-up UQ because some error sources are present in the fielded assay methods used in top-down UQ that are not present (or not recognized) in the assay studies used in bottom-up UQ One would like better consistency between the two approaches in order to claim understanding of the measurement process. The purpose of this paper is to refine bottom-up uncertainty estimation by using calibration information so that if there are no unknown error sources, the refined bottom-up uncertainty estimate will agree with the top-down uncertainty estimate to within a specified tolerance. Then, in practice, if the top-down uncertainty estimate is larger than the refined bottom-up uncertainty estimate by more than the specified tolerance, there must be omitted sources of error beyond those predicted from calibration uncertainty. The paper develops a refined bottom-up uncertainty approach for four cases of simple linear calibration: (1) inverse regression with negligible error in predictors, (2) inverse regression with non negligible error in predictors, (3) classical regression followed by inversion with negligible error in predictors, and (4) classical regression followed by inversion with non-negligible errors in predictors. Our illustrations are of general interest, but are drawn from our experience with nuclear material assay by non-destructive assay. The main example we use is gamma spectroscopy that applies the enrichment meter principle. Previous papers that ignore error in predictors have shown a tendency for inverse regression to have lower error variance than classical regression followed by inversion. Our paper supports that tendency both with and without error in predictors. Furthermore, the paper shows that calibration parameter estimates using error in predictor methods perform worse than without using error in predictor methods in the case of inverse regression, but perform better than without using error in predictor methods in the case of classical regression followed by inversion. Both inverse and classical regression involve the ratio of dependent random variables; therefore, the assumed error distribution(s) will matter in parameter estimation and in uncertainty calculations. Mainly for that reason, calibration using a single predictor is distinct from simple regression, and it has not been thoroughly treated in the literature, nor in the ISO Guide to the Expression of Uncertainty in Measurements (GUM). This refined approach is based on simulation, because we illustrate that analytical approximations are not adequate when there are, for example, 10 or fewer calibration measurements, which is common in calibration applications, each consisting of measured responses from known quantities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The magnetic field of the earth - Performance considerations for space-based observing systems

Basic problems inherent in carrying out observations of the earth magnetic field from space are reviewed. It is shown that while useful observations of the core and crustal fields are possible at the peak of the solar cycle, the greatest useful data volume is obtained during solar minimum. During the last three solar cycles, the proportion of data with a planetary disturbance index of less than 2 at solar maximum was in the range 0.4-0.8 in comparison with solar minimum. It is found that current state of the art orbit determination techniques should eliminate orbit error as a problem in gravitational field measurements from space. The spatial resolution obtained for crustal field anomalies during the major satellite observation programs of the last 30 years are compared in a table. The relationship between observing altitude and the spatial resolution of magnetic field structures is discussed. Reference is made to data obtained using the Magsat, the Polar Orbiting Geophysical Observatory (POGO), and instruments on board the Space Shuttle.

Webster, W. J., Jr.↗

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We study a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and will be required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and a bias correction of forecast anomalies. In brief, the distortion is determined by minimizing the objective function by varying the displacement and bias correction fields. In the present project we use a global or hemispheric domain, and spherical harmonics to represent these fields. In this project we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically we study the forecast errors of the 500 hPa geopotential height field for forecasts of the short and medium range. The forecasts are those of the Goddard Earth Observing System data assimilation system. Results presented show that the methodology works, that a large part of the total error may be explained by a distortion limited to triangular truncation at wavenumber 10, and that the remaining residual error contains mostly small spatial scales.

Hoffman, Ross N.↗

Lateral charge transport from heavy-ion tracks in integrated circuit chips

A 256K DRAM has been used to study the lateral transport of charge (electron-hole pairs) induced by direct ionization from heavy-ion tracks in an IC. The qualitative charge transport has been simulated using a two-dimensional numerical code in cylindrical coordinates. The experimental bit-map data clearly show the manifestation of lateral charge transport in the creation of adjacent multiple-bit errors from a single heavy-ion track. The heavy-ion data further demonstrate the occurrence of multiple-bit errors from single ion tracks with sufficient stopping power. The qualitative numerical simulation results suggest that electric-field-funnel-aided (drift) collection accounts for single error generated by an ion passing through a charge-collecting junction, while multiple errors from a single ion track are due to lateral diffusion of ion-generated charge.

Zoutendyk, J. A.↗

TH-AB-202-02: Real-Time Verification and Error Detection for MLC Tracking Deliveries Using An Electronic Portal Imaging Device

Purpose: The added complexity of the real-time adaptive multi-leaf collimator (MLC) tracking increases the likelihood of undetected MLC delivery errors. In this work we develop and test a system for real-time delivery verification and error detection for MLC tracking radiotherapy using an electronic portal imaging device (EPID). Methods: The delivery verification system relies on acquisition and real-time analysis of transit EPID image frames acquired at 8.41 fps. In-house software was developed to extract the MLC positions from each image frame. Three comparison metrics were used to verify the MLC positions in real-time: (1) field size, (2) field location and, (3) field shape. The delivery verification system was tested for 8 VMAT MLC tracking deliveries (4 prostate and 4 lung) where real patient target motion was reproduced using a Hexamotion motion stage and a Calypso system. Sensitivity and detection delay was quantified for various types of MLC and system errors. Results: For both the prostate and lung test deliveries the MLC-defined field size was measured with an accuracy of 1.25 cm{sup 2} (1 SD). The field location was measured with an accuracy of 0.6 mm and 0.8 mm (1 SD) for lung and prostate respectively. Field location errors (i.e. tracking in wrong direction) with a magnitude of 3 mm were detected within 0.4 s of occurrence in the X direction and 0.8 s in the Y direction. Systematic MLC gap errors were detected as small as 3 mm. The method was not found to be sensitive to random MLC errors and individual MLC calibration errors up to 5 mm. Conclusion: EPID imaging may be used for independent real-time verification of MLC trajectories during MLC tracking deliveries. Thresholds have been determined for error detection and the system has been shown to be sensitive to a range of delivery errors.

60 APPLIED LIFE SCIENCES↗

Overview of the forthcoming AAPM TG-158 Report, 'Measurements and calculations of doses outside the treatment volume from External Beam Radiation Therapy' - Paper 85

The evolution of techniques and technology in radiotherapy has greatly improved our ability to deliver higher tumor doses while minimizing the dose to the adjacent organs at risk. However, this improved conformality has not removed the problem of doses to normal tissues outside the target volume. Whether these out-of-field doses arise from photons, electrons, protons or neutrons, there are unique challenges that many medical physicists may have limited knowledge about or experience with. With modern treatment planning systems, high dose regions and areas within the primary beam path are typically well described. However, their accuracy beyond a few centimeters outside the treatment field edge are usually poor. In these cases, alternate methods are required to assess the out-of-field dose. Such assessments require additional care to avoid potentially large errors associated with a variety of unique complications in performing dosimetry outside the treatment field. Furthermore, physicists will not always have an a priori estimate of the expected dose, and, as a result, large dosimetric errors are more easily missed. Low radiation doses outside the treatment volume are a concern because they can cause deleterious effects to the patient. The risk of late effects from the secondary radiation may be more evident today because of the success of cancer screening and modern therapies that have increased the number of cancer patients who survive and live long enough for the adverse radiation effects on healthy tissues to manifest. Simultaneously, radiotherapy procedures have become more complex, making the estimation of low out-of-field doses even more challenging. Over the past 30 years, numerous studies have been published detailing non-target doses from various radiotherapy treatments (for a detailed review see Xu et al. However, dosimetry data were obtained using a variety of measurement or computational techniques. An overview of dosimetry techniques for measuring low-level non-target doses is not available. Improved, or at least valid, dosimetry is important for several reasons. In clinical care (e.g. fetal dose estimates), large dose errors can lead to inappropriate or unnecessary treatment decisions, with potentially serious consequences to the patient. In a broader sense of somatic effects, more accurate dosimetry will improve patient risk assessment, understanding of dose responses, treatment planning, and design of the radiation delivery machines. Once reliable dosimetry data are available, it is then the clinician's responsibility to assess the risk vs. benefit of the radiotherapy treatment to make a sound and informed assessment of all possible treatment outcomes. (author)

61 RADIATION PROTECTION AND DOSIMETRY↗

High-precision method for determining the position of laser beam focal plane

The method of wavefront doubled-frequency spherical modulation for determining the laser beam waist position has been simulated and experimentally studied. The error in determining the focal plane position is less than 10{sup -5} D. The amplitude of the control doubled-frequency electric signal is experimentally found to correspond to 12% of the total radiation power. (laser beams)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Consideration for high accuracy radiation efficiency measurements for the Solar Power Satellite (SPS) subarrays

The transmit beam and radiation efficiency for 10 metersquare subarray panels were quantified. Measurement performance potential of far field elevated and ground reflection ranges and near field technique were evaluated. The state-of-the-art of critical components and/or unique facilities required was identified. Relative cost, complexity and performance tradeoffs were performed for techniques capable of achieving accuracy objectives. It is considered that because of the large electrical size of the SPS subarray panels and the requirement for high accuracy measurements, specialized measurement facilities are required. Most critical measurement error sources have been identified for both conventional far field and near field techniques. Although the adopted error budget requires advances in state-of-the-art of microwave instrumentation, the requirements appear feasible based on extrapolation from today's technology. Additional performance and cost tradeoffs need to be completed before the choice of the preferred measurement technique is finalized.

Kozakoff, D. J.↗

SU-F-T-190: Homogeneity Study of Proton and Heavy Ion Scanning Beams Based On Different Compositions of Spot Sizes (FWHM) and Grid Sizes

Purpose: Different particle scanning beam delivery systems have different delivery accuracies. This study was performed to determine, for our particle treatment system, an appropriate composition (n=FWHM/GS) of spot size(FWHM) and grid size (GS), which can provide homogenous delivered dose distributions for both proton and heavy ion scanning beam radiotherapy. Methods: We analyzed the delivery errors of our beam delivery system using log files from the treatment of 28 patients. We used a homemade program to simulate square fields for different n values with and without considering the delivery errors and analyzed the homogeneity. All spots were located on a rectilinear grid with equal spacing in the × and y directions. After that, we selected 7 energy levels for both proton and carbon ions. For each energy level, we made 6 square field plans with different n values (1, 1.5, 2, 2.5, 3, 3.5). Then we delivered those plans and used films to measure the homogeneity of each field. Results: For program simulation without delivery errors, when n≥1.1 the homogeneity can be within ±3%. For both proton and carbon program simulations with delivery errors and film measurements, the homogeneity can be within ±3% when n≥2.5. Conclusion: For our facility with system errors, the n≥2.5 is appropriate for maintaining homogeneity within ±3%.

60 APPLIED LIFE SCIENCES↗

Impact of Uncertainties and Errors in Converting NWS Radiosonde Hygristor Resistances to Relative Humidity

A set of 2,600 6-second, National Weather Service soundings from NASA's FIRE-II Cirrus field experiment are used to illustrate previously known errors and new potential errors in the VIZ and SDD ) brand relative humidity (RH) sensors and the MicroART processing software. The entire spectrum of RH is potentially affected by at least one of these errors. (These errors occur before being converted to dew point temperature.) Corrections to the errors are discussed. Examples are given of the effect that these errors and biases may have on numerical weather prediction and radiative transfer. The figure shows the OLR calculated for the corrected and uncorrected soundings using an 18-band radiative transfer code. The OLR differences are sufficiently large to warrant consideration when validating line-by-line radiation calculations that use radiosonde data to specify the atmospheric state, or when validating satellite retrievals. in addition, a comparison of observations of RH during FIRE-II derived from GOES satellite, raman lidar, MAPS analyses, NCAR CLASS sondes, and the NWS sondes reveals disagreement in the RH distribution and underlines our lack of an understanding of the climatology of water vapor.

Westphal, Douglas L.↗

Impact of Uncertainties and Errors in Converting NWS Radiosonde Hygristor Resistances to Relative Humidity

A set of 2,600 6-second, National Weather Service soundings from NASA's FIRE-II Cirrus field experiment are used to illustrate previously known errors and new potential errors in the VIZ and SDD brand relative humidity (RH) sensors and the MicroART processing software. The entire spectrum of RH is potentially affected by at least one of these errors. (These errors occur before being converted to dew point temperature.) Corrections to the errors are discussed. Examples are given of the effect that these errors and biases may have on numerical weather prediction and radiative transfer. The figure shows the OLR calculated for the corrected and uncorrected soundings using an 18-band radiative transfer code. The OLR differences are sufficiently large to warrant consideration when validating line-by-line radiation calculations that use radiosonde data to specify the atmospheric state, or when validating satellite retrievals. In addition, a comparison of observations of RE during FIRE-II derived from GOES satellite, raman lidar, MAPS analyses, NCAR CLASS sondes, and the NWS sondes reveals disagreement in the RH distribution and underlines our lack of an understanding of the climatology of water vapor.

Westphal, Douglas L.↗