Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “predictive mapping”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

The SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) Product

The Soil Moisture Active and Passive (SMAP) mission is being developed by NASA for launch in 2013 as one of four first-tier missions recommended by the U.S. National Research Council Committee on Earth Science and Applications from Space in 2007. The primary science objectives of SMAP are to enhance understanding of land surface controls on the water, energy and carbon cycles, and to determine their linkages. Moreover, the high resolution soil moisture mapping provided by SMAP has practical applications in weather and seasonal climate prediction, agriculture, human health, drought and flood decision support. In this paper we describe the assimilation of SMAP observations for the generation of the planned SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) product. The SMAP mission makes simultaneous active (radar) and passive (radiometer) measurements in the 1.26-1.43 GHz range (L-band) from a sun-synchronous low-earth orbit. Measurements will be obtained across a 1000 km wide swath using conical scanning at a constant incidence angle (40 deg). The radar resolution varies from 1-3 km over the outer 70% of the swath to about 30 km near the center of the swath. The radiometer resolution is 40 km across the entire swath. The radiometer measurements will allow high-accuracy but coarse resolution (40 km) measurements. The radar measurements will add significantly higher resolution information. The radar is however very sensitive to surface roughness and vegetation structure. The combination of the two measurements allows optimal blending of the advantages of each instrument. SMAP directly observes only surface soil moisture (in the top 5 cm of the soil column). Several of the key applications targeted by SMAP, however, require knowledge of root zone soil moisture (approximately top 1 m of the soil column), which is not directly measured by SMAP. The foremost objective of the SMAP L4_SM product is to fill this gap and provide estimates of root zone soil moisture that are informed by and consistent with SMAP observations. Such estimates are obtained by merging SMAP observations with estimates from a land surface model in a soil moisture data assimilation system. The land surface model component of the assimilation system is driven with observations-based surface meteorological forcing data, including precipitation, which is the most important driver for soil moisture. The model also encapsulates knowledge of key land surface processes, including the vertical transfer of soil moisture between the surface and root zone reservoirs. Finally, the model interpolates and extrapolates SMAP observations in time and in space. The L4_SM product thus provides a comprehensive and consistent picture of land surface hydrological conditions based on SMAP observations and complementary information from a variety of sources. The assimilation algorithm considers the respective uncertainties of each component and yields a product that is superior to satellite or model data alone. Error estimates for the L4_SM product are generated as a by-product of the data assimilation system.

Reichle, Rolf↗
NASA NTRS2012

Assimilation of Smos Observations to Generate a Prototype SMAP Level 4 Surface and Root-Zone Soil Moisture Product

The Soil Moisture Active and Passive (SMAP; [1]) mission is being implemented by NASA for launch in October 2014. The primary science objectives of SMAP are to enhance understanding of land surface controls on the water, energy and carbon cycles, and to determine their linkages. Moreover, the high-resolution soil moisture mapping provided by SMAP has practical applications in weather and seasonal climate prediction, agriculture, human health, drought and flood decision support. The Soil Moisture and Ocean Salinity (SMOS; [2]) mission was launched by ESA in November 2009 and has since been observing L-band (1.4 GHz) upwelling passive microwaves. In this paper we describe our use of SMOS brightness temperature observations to generate a prototype of the planned SMAP Level 4 Surface and Root-zone Soil Moisture (L4_SM) product [5].

Reichle, Rolf H.↗
NASA NTRS2013

Approach to Integrate Global-Sun Models of Magnetic Flux Emergence and Transport for Space Weather Studies

The Sun lies at the center of space weather and is the source of its variability. The primary input to coronal and solar wind models is the activity of the magnetic field in the solar photosphere. Recent advancements in solar observations and numerical simulations provide a basis for developing physics-based models for the dynamics of the magnetic field from the deep convection zone of the Sun to the corona with the goal of providing robust near real-time boundary conditions at the base of space weather forecast models. The goal is to develop new strategic capabilities that enable characterization and prediction of the magnetic field structure and flow dynamics of the Sun by assimilating data from helioseismology and magnetic field observations into physics-based realistic magnetohydrodynamics (MHD) simulations. The integration of first-principle modeling of solar magnetism and flow dynamics with real-time observational data via advanced data assimilation methods is a new, transformative step in space weather research and prediction. This approach will substantially enhance an existing model of magnetic flux distribution and transport developed by the Air Force Research Lab. The development plan is to use the Space Weather Modeling Framework (SWMF) to develop Coupled Models for Emerging flux Simulations (CMES) that couples three existing models: (1) an MHD formulation with the anelastic approximation to simulate the deep convection zone (FSAM code), (2) an MHD formulation with full compressible Navier-Stokes equations and a detailed description of radiative transfer and thermodynamics to simulate near-surface convection and the photosphere (Stagger code), and (3) an MHD formulation with full, compressible Navier-Stokes equations and an approximate description of radiative transfer and heating to simulate the corona (Module in BATS-R-US). CMES will enable simulations of the emergence of magnetic structures from the deep convection zone to the corona. Finally, a plan will be summarized on the development of a Flux Emergence Prediction Tool (FEPT) in which helioseismology-derived data and vector magnetic maps are assimilated into CMES that couples the dynamics of magnetic flux from the deep interior to the corona.

Mansour, Nagi N.↗
NASA NTRS2014

Amorphous and Crystalline H20 Ice at Rhea's Inktomi Crater

We present the analysis of Cassini spectral data from spectral mapping of Saturnian icy moons Dione and Rhea, to investigate possible effects of impact crater formation on the relative abundances of crystalline and amorphous water ice in the moons' ice crusts. Both moons display morphologically young ray craters as well as older craters. Possible changes in ice properties due to crater formation are conjectured to be more visible in younger craters, and as such Rhea's well imaged ray crater Inktomi is analysed, as are older craters for comparison. We used data from Cassini's Visual and Infrared Mapping Spectrometer (VIMS). For each pixel in the VIMS maps, spectral data were extracted in the near-infrared range (1.75 micrometers less than lambda less than 2.45 micrometers). Analysis was begun by fitting a single Gaussian to the peak in absorption at 2.0 micrometers, which was then subtracted from the data, leaving residuals with a minimum on either side of the original 2.0-micrometers band. The spectra of the individual spatial pixels were then clustered by the differences between these minima, which are sensitive to changes in both ice grain size and crystallinity. This yielded preliminary maps which approximated the physical characteristics of the landscape and were used to identify candidates for further analysis. Spectra were then clustered by the properties of the 1.5-micrometers band, to divide the map into regions based on inferred grain size. For each region, the predicted differences in minima from the Gaussian residuals, over a range of crystallinities, were calculated based on the found grain sizes. This model was used to find the crystallinity of each pixel via grain size and characteristics of the residual function. Preliminary results show a greater degree of crystallization of young crater interiors, particularly in Rhea's ray crater Inktomi, where ice showed crystalline ice abundances between 33 percent and 61 percent. These patterns in ice crystallization are possibly attributable to increased heat generated during crater formation.

Saturn Satellites↗
NASA NTRS2016

The NASA Severe Thunderstorm Observations and Regional Modeling (NASA STORM) Project

The NASA Severe Storm Thunderstorm Observations and Regional Modeling(NASA STORM) project enhanced NASA’s severe weather research capabilities, building upon existing Earth Science expertise at NASA Marshall Space Flight Center (MSFC). During this project, MSFC extended NASA’s ground-based lightning detection capacity to include a readily deployable lightning mapping array (LMA). NASA STORM also enabled NASA’s Short-term Prediction and Research Transition (SPoRT) to add convection allowing ensemble modeling to its portfolio of regional numerical weather prediction (NWP) capabilities. As a part of NASA STORM, MSFC developed new open-source capabilities for analyzing and displaying weather radar observations integrated from both research and operational networks. These accomplishments enabled by NASA STORM are a step towards enhancing NASA’s capabilities for studying severe weather and positions them for any future NASA related severe storm field campaigns.

modeling↗
NASA NTRSDate not supplied

Comparison of Boeing 777 Landing Gear Noise Simulations with Flight Test Data

Acoustic phased microphone array measurements of aircraft flyover noise acquired during the 2005 Quiet Technology Demonstrator II test were used to assess the accuracy of high-fidelity, full-scale simulations of landing gear noise produced by a large civilian aircraft. The simulations, conducted with the lattice Boltzmann solver PowerFLOW®, used a highly accurate digital model of a Boeing 777-300ER aircraft with the nose and main landing gear components replicating the full-scale geometries. The simulations were performed for aircraft parameters that matched those recorded during the flyover test conditions. For benchmarking purposes, several aircraft configurations were simulated: a) nose landing gear deployed with main landing gear and wing high-lift devices stowed, b) nose and main landing gear deployed with wing high-lift devices stowed and c) nose and main landing gear with wing high-lift devices deployed. To facilitate direct comparison with measured data, the simulated data sets were used to generate synthetic pressure records at the same array microphone locations as those used during the flight test. Broadly self-consistent beamforming techniques and procedures were used to process the synthetic pressure records and the measured data. Integration of select regions of the beamform maps containing the nose or main landing gear yielded good agreement between predicted and measured integrated far-field spectra for forward directivity angles where airframe noise is more prominent.

airframe noise↗
DOE OSTI2020

Method and system for routing based on a predicted connectivity quality

A system and method for routing based on a predicted connectivity quality is disclosed. The method includes receiving, by a controller, map information corresponding to a geographical area. The method also includes receiving, by the controller, wireless connectivity information corresponding to the geographical area. The method also includes generating output data of at least one route between a starting location and a destination location within the geographical area. The generating is based on the wireless connectivity information.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Evaluating switch lifetime in soft-switched single-stage differential-mode SST

The reliability of semiconductor switches in single-stage differential-mode solid-state transformers (DM-SSTs) has not been systematically evaluated under soft-switching operation and realistic grid conditions. This paper presents a switch-level reliability analysis for soft-switched and hard-switched DM-SST configurations by integrating converter-specific power loss modeling with empirical lifetime prediction. Analytical derivation of device current profiles specific to the DM-SST is used to characterize electrothermal stress, which is then mapped to lifetime using degradation models obtained from power cycling tests (PCTs). Applied to realistic SST load profiles and grid voltage variations, this approach provides a probabilistic prediction of switch lifetime for the DM-SST. Lifetime estimates for both SiC MOSFETs and Si IGBTs are presented, offering insight into device degradation under converter operating conditions. The results quantify the reliability benefits of soft switching in single-stage SSTs, highlighting how switching dynamics influence long-term switch degradation.

14 SOLAR ENERGY↗
DOE OSTI2020

Molecular dynamics simulations for glass transition temperature predictions of polyhydroxyalkanoate biopolymers

Polyhydroxyalkanoates (PHAs) represent an emerging class of biosynthetic and biodegradable polyesters that exhibit considerable potential to replace petroleum-based plastics towards a sustainable future. Despite the promise, general structure–property mappings within this class of polymers remain largely unexplored. An efficient exploration of this vast chemical space calls for the development and validation of predictive methods for accurate estimation of a diverse range of properties for PHA-based polymers. Towards this aim, we present and validate in this work the results of our molecular dynamics (MD) simulation based approach aimed at predicting glass transition temperatures (T g ) of PHA-based polymers. Since generally available and widely used polymer forcefields exhibit a relatively poor performance for T g predictions, we have developed a new forcefield by modifying the polymer consistent force field (PCFF) via refining a selected set of torsion potentials of the polymer backbone using accurate density functional theory (DFT) computations. After carefully assessing the dependence of critical simulation parameters, such as, polymer chain length, number of polymer chains, supercell size, and thermal quenching rate used in the simulation, the applicability and transferability of the modified PCFF (mPCFF) is demonstrated by directly comparing the computed T g predictions of various polymers with different chemistries, polymer side chain lengths and functional groups forming the polymer side chains against the respective experimentally measured values. Furthermore, the transport properties such as self-diffusion coefficient and viscosity are computationally determined and their well-known correlation with the target properties is demonstrated. Lastly, we have employed the developed approach to predict T g values for a number of yet-to-be-synthesized PHA-based polymers with a diverse set of functional groups in the polymer side chains. The results are further rationalized by correlating the predicted T g values with the inter-chain H-bond formation tendencies of the different side chain functional groups. This work represents an important first step towards computationally guided design of PHA-based functional polymers and opens up new directions for a systematic investigation of composition- and configuration-dependent structure–property relationships in more complex binary and ternary copolymer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material

We show although it is well-established that voids profoundly influence the initiation and reaction behaviors of heterogeneous energetic materials such as polymer-bonded explosives (PBX) and propellants, there has been little study of how void location in different constituents in the microstructures of such materials affect the macroscale behavior. Here, we use three-dimensional (3D) mesoscale simulations to study how void placement within the reactive grains versus the polymer binder influences the shock-to-detonation transition (SDT) in a polymer-bonded explosive. The material studied here has a microstructure comprised of 75% PETN (pentaerythritol tetranitrate) grains and 25% HTPB (hydroxyl-terminated polybutadiene) polymer binder by volume. Porosities up to 10% in the form of spherical voids distributed in both the grains and polymer are considered. An Arrhenius reactive burn relation is used to model the chemical kinetics of the PETN grains under shock loading, thereby resolving the heterogeneous detonation behavior of the PBX. The influence of void location on the shock initiation sensitivity of the material is quantitatively ranked by comparing the predicted run distance to detonation (RDD) for each sample. The analysis includes inherent quantification of uncertainties arising from the stochastic variations in the microstructure morphologies and void distributions by using statistically equivalent microstructure sample sets (SEMSS), leading to probabilistic formulations for the RDD as a function of shock pressure. The calculations reveal that the location of voids in the composite microstructure significantly affects the RDD. Specifically, voids exclusively within the grains cause the PBX to be more sensitive (having shorter RDD) than voids in the polymer binder. Unique probabilistic relationships are derived to map the probability of observing RDD for each void location material case, allowing for prediction of initiation behavior anywhere in the shock pressure – RDD space. These findings agree with trends reported in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Flexible allocation of energy storage in power grids

Methods and apparatus provide flexible allocation and regulation of scheduled energy transfers between energy storage devices (“batteries”) and a power grid. Piecewise mappings having at least one sloping segment enable gradual variations in scheduled energy transfers as cleared values of a medium of energy exchange deviate from predicted values of the medium of energy exchange. Thereby deviations from a battery's predicted energy transfer schedule can be reduced, and overall smoother operation of a power grid can be achieved. Two sloping linear segments can be separated by a dead band, a portion of the mapping in which the scheduled energy transfer amount is invariant. A dead zone can increase the likelihood of a battery meeting its predicted schedule.

Bhattarai, Bishnu P.↗
DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗
DOE OSTI2025

Damage modeling of power tower receiver tubes using the SRLIFE tool

Concentrating Solar Power (CSP) molten-salt central receivers are subject to high, transient incident flux during daily operation. The resulting creep-fatigue damage impacts the receiver’s reliability and restricts the permissible incident flux distribution for a given receiver. This paper aims to reduce CSP plants’ levelized cost of electricity by developing a methodology to predict lifetime and identifies the primary damage mechanism (creep vs fatigue) for any given fluid temperature and temperature gradient. Results are presented in the form of a damage map that serves as a valuable operation guide and design tool. Damage maps can be used to reduce maintenance costs by improving reliability and reduce receiver capital costs by better utilizing the receiver area. FEA simulation and damage modeling of tubes subject to asymmetrical flux conditions is performed in the open-source receiver design tool srlife. Parametric studies are performed over a range of inner tube temperatures and thermal gradients for A230, 316H, 740H, A282, A617, and 800H high temperature alloys. Damage maps are presented for each alloy. A parametric, FEA-based methodology is presented for comparison of fatigue-creep ratios and prediction of tube lifetime based on the critical thermal operating conditions. Fatigue is found to be negligible compared to creep for almost every case. Here, this finding suggests that fatigue effects associated with cloud events are insignificant compared to creep at these high temperature operating conditions. Additionally, lifetime predictions identify thermal conditions where small changes in operating conditions can result in large changes in predicted lifetime.

14 SOLAR ENERGY↗
DOE OSTI2025

Map-level baryonification: unified treatment of weak lensing two-point and higher-order statistics

Precision cosmology benefits from extracting maximal information from cosmic structures, motivating the use of higher-order statistics (HOS) at small spatial scales. However, predicting how baryonic processes modify matter statistics at these scales has been challenging. The baryonic correction model (BCM) addresses this by modifying dark-matter-only simulations to mimic baryonic effects, providing a flexible, simulation-based framework for predicting both two-point and HOS. We show that a 3-parameter version of the BCM can jointly fit weak lensing maps' two-point statistics, wavelet phase harmonics coefficients, scattering coefficients, and the third and fourth moments to within 2% accuracy across all scales ℓ < 2000 and tomographic bins for a DES-Y3-like redshift distribution ( z ≲ 2), using the FLAMINGO simulations. These results demonstrate the viability of BCM-assisted, simulation-based weak lensing inference of two-point and HOS, paving the way for robust cosmological constraints that fully exploit non-Gaussian information on small spatial scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗
NASA NTRS2011

Forest Biomass Mapping From Lidar and Radar Synergies

The use of lidar and radar instruments to measure forest structure attributes such as height and biomass at global scales is being considered for a future Earth Observation satellite mission, DESDynI (Deformation, Ecosystem Structure, and Dynamics of Ice). Large footprint lidar makes a direct measurement of the heights of scatterers in the illuminated footprint and can yield accurate information about the vertical profile of the canopy within lidar footprint samples. Synthetic Aperture Radar (SAR) is known to sense the canopy volume, especially at longer wavelengths and provides image data. Methods for biomass mapping by a combination of lidar sampling and radar mapping need to be developed. In this study, several issues in this respect were investigated using aircraft borne lidar and SAR data in Howland, Maine, USA. The stepwise regression selected the height indices rh50 and rh75 of the Laser Vegetation Imaging Sensor (LVIS) data for predicting field measured biomass with a R(exp 2) of 0.71 and RMSE of 31.33 Mg/ha. The above-ground biomass map generated from this regression model was considered to represent the true biomass of the area and used as a reference map since no better biomass map exists for the area. Random samples were taken from the biomass map and the correlation between the sampled biomass and co-located SAR signature was studied. The best models were used to extend the biomass from lidar samples into all forested areas in the study area, which mimics a procedure that could be used for the future DESDYnI Mission. It was found that depending on the data types used (quad-pol or dual-pol) the SAR data can predict the lidar biomass samples with R2 of 0.63-0.71, RMSE of 32.0-28.2 Mg/ha up to biomass levels of 200-250 Mg/ha. The mean biomass of the study area calculated from the biomass maps generated by lidar- SAR synergy 63 was within 10% of the reference biomass map derived from LVIS data. The results from this study are preliminary, but do show the potential of the combined use of lidar samples and radar imagery for forest biomass mapping. Various issues regarding lidar/radar data synergies for biomass mapping are discussed in the paper.

Sun, Guoqing↗
DOE OSTI2021

Accurate prediction of protein structures and interactions using a three-track neural network

DeepMind presented notably accurate predictions at the recent 14th Critical Assessment of Structure Prediction (CASP14) conference. We explored network architectures that incorporate related ideas and obtained the best performance with a three-track network in which information at the one-dimensional (1D) sequence level, the 2D distance map level, and the 3D coordinate level is successively transformed and integrated. The three-track network produces structure predictions with accuracies approaching those of DeepMind in CASP14, enables the rapid solution of challenging x-ray crystallography and cryo–electron microscopy structure modeling problems, and provides insights into the functions of proteins of currently unknown structure. The network also enables rapid generation of accurate protein-protein complex models from sequence information alone, short-circuiting traditional approaches that require modeling of individual subunits followed by docking. Here, we make the method available to the scientific community to speed biological research.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1976

The prediction of zenith range refraction from surface measurements of meteorological parameters

In the last two decades, increasingly sophisticated deep space missions have placed correspondingly stringent requirements on navigational accuracy. As part of the effort to increase navigational accuracy, and hence the quality of radiometric data, much effort has been expended in an attempt to understand and compute the tropospheric effect on range (and hence range rate) data. The general approach adopted has been that of computing a zenith range refraction, and then mapping this refraction to any arbitrary elevation angle via an empirically derived function of elevation. The prediction of zenith range refraction derived from surface measurements of meteorological parameters is presented. Refractivity is separated into wet (water vapor pressure) and dry (atmospheric pressure) components. The integration of dry refractivity is shown to be exact. Attempts to integrate wet refractivity directly prove ineffective; however, several empirical models developed by the author and other researchers at JPL are discussed. The best current wet refraction model is here considered to be a separate day/night model, which is proportional to surface water vapor pressure and inversely proportional to surface temperature. Methods are suggested that might improve the accuracy of the wet range refraction model.

Berman, A. L.↗