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All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Aerosol Source Plume Physical Characteristics from Space-based Multiangle Imaging

Models that assess aerosol effects on regional air quality and global climate parameterize aerosol sources in terms of amount, type, and injection height. The multiangle imaging spectroradiometer (MISR) aboard NASA's Terra satellite retrieves total column aerosol optical thickness (AOT), and aerosol type over cloud-free land and water. A stereo-matching algorithm automatically retrieves reflecting-layer altitude wherever clouds or aerosol plumes have discernable spatial contrast, with about 500-m accuracy, at 1.1-km horizontal resolution. Near-source biomass burning smoke, volcanic effluent, and desert dust plumes are observed routinely, providing information about aerosol amount, particle type, and injection height useful for modeling applications. Compared to background aerosols, the plumes sampled have higher AOT, contain particles having expected differences in Angstrom exponent, size, single-scattering albedo, and for volcanic plume and dust cloud cases, particle shape. As basic thermodynamics predicts, thin aerosol plumes lifted only by regional winds or less intense heat sources are confined to the boundary layer. However, when sources have sufficient buoyancy, the representative plumes studied tend to concentrate within discrete, high-elevation layers of local stability; the aerosol is not uniformly distributed up to a peak altitude, as is sometimes assumed in modeling. MISR-derived plume heights, along with meteorological profile data from other sources, make it possible to relate radiant energy flux observed by the moderate resolution imaging spectroradiometer (MODIS), also aboard the Terra spacecraft, to convective heat flux that plays a major role in buoyant plume dynamics. A MISR climatology of plume behavior based on these results is being developed.

aerosol plumes↗
NASA NTRS2019

Can OMPS and VIIRS Be Used as a Single Virtual Sensor for Aerosol Retrieval?

Satellite earth observation of aerosols using a single sensor have been done for more than three decades. The retrieved global distribution of column integrated aerosol optical depth (AOD) has been refined with higher accuracy and finer resolutions. However, the other aerosol properties, such as aerosol absorption and aerosol height, haven not been mapped as extensively using passive sensors. The detectors sensitive to these properties (UV-based sensors such as Aura-OMI) lack the adequate visible channels to tease out the absorption, height and loading contributions. In addition, their spatial resolution is prone to frequent cloud contamination impacting aerosol loading retrievals using only these spectral ranges. However, the deployment of the VIIRS and OMPS-NM sensors on the same Suomi NPP platform provides a first opportunity to carry out retrievals of aerosol single scattering albedo (SSA) and AOD with little cloud contamination using an expanded spectral range from the UV to the near-IR wavelengths. After collocated VIIRS pixel within the large OMPS footprint during the high resolution OMPS observing mode, we compared the radiance from OMPS and VIIRS to ensure the calibration from individual sensors are comparable. Then a look up table (LUT) was created for a smoke case over central Africa. The LUT is generated using 10 channels from 0.357 to 2.1 micron with 44 combinations of aerosol models and 4 different aerosol heights. With CALIOP and AERONET observation nearby, the possibility of using OMPS and VIIRS radiance as a single virtual sensor to simultaneously and consistently retrieve AOD, SSA, and aerosol height is explored.

Shi, Yingxi↗
NASA NTRS2023

Evaluating Greenland Surface-Mass-Balance and Firn-Densification Data Using ICESat-2 Altimetry

Surface-mass-balance (SMB) and firn-densification (FD) models are widely used in altimetry studies as a tool to separate atmospheric-driven from ice-dynamics-driven ice-sheet mass changes and to partition observed volume changes into ice-mass changes and firn-air-content changes. Until now, SMB models have been principally validated based on comparison with ice core and weather station data or comparison with widely separated flight radar-survey flight lines. Firn-densification models have been primarily validated based on their ability to match net densification over decades, as recorded in firn cores, and the short-term time-dependent component of densification has rarely been evaluated at all. The advent of systematic ice-sheet-wide repeated ice-surface-height measurements from ICESat-2 (the Ice Cloud, and land Elevation Satellite, 2) allows us to measure the net surface-height change of the Greenland ice sheet at quarterly resolution and compare the measured surface-height differences directly with those predicted by three FD–SMB models: MARv3.5.11 (Modèle Atmosphérique Régional version 3.5.11) and GSFCv1.1 and GSFCv1.2 (the Goddard Space Flight Center FD–SMB models version 1.1 and 1.2). By segregating the data by season and elevation, and based on the timing and magnitude of modelled processes in areas where we expect minimal ice-dynamics-driven height changes, we investigate the models' accuracy in predicting atmospherically driven height changes. We find that while all three models do well in predicting the large seasonal changes in the low-elevation parts of the ice sheet where melt rates are highest, two of the models (MARv3.5.11 and GSFCv1.1) systematically overpredict, by around a factor of 2, the magnitude of height changes in the high-elevation parts of the ice sheet, particularly those associated with melt events. This overprediction seems to be associated with the melt sensitivity of the models in the high-elevation part of the ice sheet. The third model, GSFCv1.2, which has an updated high-elevation melt parameterization, avoids this overprediction.

Benjamin E. Smith↗
NASA NTRS1979

Seasat visible and infrared radiometer

The visual and infrared radiometer (VIRR) system on Seasat is described, and methods used in the geophysical evaluation of digital data from this system are discussed. The main function of the radiometer system is to provide images of visual reflection and thermal infrared emission from ocean, coastal and atmospheric features to facilitate interpretation of data from other Seasat sensors; in addition, it is expected to provide some derived quantitative measurements of such factors as sea-surface temperature and cloud-top height. Some results of a statistical comparison of Seasat VIRR-derived sea-surface temperatures in a cloud-free region with a National Oceanic and Atmospheric Administration (NOAA) analysis based on surface measurements made in the same region are presented. The data sets were in agreement of plus or minus 1.7 deg K root-mean-square. The means of the two sets of temperatures were 293.9 deg K (VIRR) and 293.1 deg K (NOAA), and the standard deviations were 3.21 deg and 3.2 deg K, respectively.

Mcclain, E. P.↗
NASA NTRS1990

The 27-28 October 1986 FIRE IFO cirrus case study - Cloud parameter fields derived from satellite data

A cirrus parameter retrieval methodology and the results of its application over the cirrus Intensive Field Observation (IFO) area using data from the Geostationary Operational Environmental Satellite (GOES) taken during the FIRE cirrus case study days, October 27-28, 1986. An impirical cloud bidirectional reflectance model derived from another IFO analysis was combined with a theoretical ice crystal cloud albedo model to estimate visible cloud optical thickness, which was used to derive the cloud infrared emittance. Cloud altitude was adjusted based on the derived emittance and observed temperatures. The approach developed here produced a very reasonable picture of cirrus cloud fields. It was estimated that the cloud-top and cloud-center heights are derived with a precision of about 0.6 km, except in very broken cloud conditions. Cirrus cloud thicknesses were also estimated and it is found that the derived results are comparable to other case study observations.

Minnis, Patrick↗
NASA NTRS2009

The New Weather Radar for America's Space Program in Florida: A Temperature Profile Adaptive Scan Strategy

A new weather radar is being acquired for use in support of America s space program at Cape Canaveral Air Force Station, NASA Kennedy Space Center, and Patrick AFB on the east coast of central Florida. This new radar replaces the modified WSR-74C at Patrick AFB that has been in use since 1984. The new radar is a Radtec TDR 43-250, which has Doppler and dual polarization capability. A new fixed scan strategy was designed to best support the space program. The fixed scan strategy represents a complex compromise between many competing factors and relies on climatological heights of various temperatures that are important for improved lightning forecasting and evaluation of Lightning Launch Commit Criteria (LCC), which are the weather rules to avoid lightning strikes to in-flight rockets. The 0 C to -20 C layer is vital since most generation of electric charge occurs within it and so it is critical in evaluating Lightning LCC and in forecasting lightning. These are two of the most important duties of 45 WS. While the fixed scan strategy that covers most of the climatological variation of the 0 C to -20 C levels with high resolution ensures that these critical temperatures are well covered most of the time, it also means that on any particular day the radar is spending precious time scanning at angles covering less important heights. The goal of this project is to develop a user-friendly, Interactive Data Language (IDL) computer program that will automatically generate optimized radar scan strategies that adapt to user input of the temperature profile and other important parameters. By using only the required scan angles output by the temperature profile adaptive scan strategy program, faster update times for volume scans and/or collection of more samples per gate for better data quality is possible, while maintaining high resolution at the critical temperature levels. The temperature profile adaptive technique will also take into account earth curvature and refraction when geo-locating the radar beam (i.e., beam height and arc distance), including non-standard refraction based on the user-input temperature profile. In addition to temperature profile adaptivity, this paper will also summarize the other requirements for this scan strategy program such as detection of low-level boundaries, detection of anvil clouds, reducing the Cone Of Silence, and allowing for times when deep convective clouds will not occur. The adaptive technique will be carefully compared to and benchmarked against the new fixed scan strategy. Specific environmental scenarios in which the adaptive scan strategy is able to optimize and improve coverage and resolution at critical heights, scan time, and/or sample numbers relative to the fixed scan strategy will be presented.

Carey, L. D.↗
NASA NTRS2017

Coastal California's Fog as a Unique Habitable Niche: Design for Autonomous Sampling and Preliminary Aerobiological Characterization

Just as on the land or in the ocean, atmospheric regions may be more or less hospitable to life. The aerobiosphere, or collection of living things in Earth's atmosphere, is poorly understood due to the small number and ad hoc nature of samples studied. However, we know viable airborne microbes play important roles, such as providing cloud condensation nuclei. Knowing the distribution of such microorganisms and how their activity can alter water, carbon, and other geochemical cycles is key to developing criteria for planetary habitability, particularly for potential habitats with wet atmospheres but little stable surface water. Coastal California has regular, dense fog known to play a major transport role in the local ecosystem. In addition to the significant local (1 km) geographical variation in typical fog, previous studies have found that changes in height above surface of as little as a few meters can yield significant differences in typical concentrations, populations and residence times. No single current sampling platform (ground-based impactors, towers, balloons, aircraft) is capable of accessing all of these regions of interest.A novel passive fog and cloud water sampler, consisting of a lightweight passive impactor suspended from autonomous aerial vehicles (UAVs), is being developed to allow 4D point sampling within a single fog bank, allowing closer study of small-scale (100 m) system dynamics. Fog and cloud droplet water samples from low-altitude aircraft flights in nearby coastal waters were collected and assayed to estimate the required sample volumes, flight times, and sensitivity thresholds of the system under design.125 cloud water samples were collected from 16 flights of the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS) instrumented Twin Otter, equipped with a sampling tube collector, occurring between 18 July and 12 August 2016 below 1 km altitude off the central coast. The collector was flushed first with 70 ethanol, then with sterile DI water, between sampling regions. Collected volumes ranged from 100 L to 12 mL. All samples were diluted serially and plated on two different types of agar, nutrient-dense (PCA) and sparse (R-2A). Plates were incubated at room temperature and counted when colonies first appeared and again at 2 weeks.Preliminary results from seven flights are consistent with generally reported colony-forming unit (CFU) values for terrestrial fog water (e.g., [4]). The PCA assay ranged from 400 to 125,000 CFU/mL, R-2A from 700 to 130,000 CFU/mL. PCA and R-2A counts were not significantly different from each other at I^ plus or minus +/- 0.05, although observationally, the R2A plates had more pigmented colonies. CFU counts from the majority of flights were not different from each other in mean at the same level of significance, but about half differed in median, indicating differences in underlying distribution. These results validate the presence of viable microorganisms in coastal California fog at levels that should be easily detectable by our sampling system. The indicated distribution differences underscore the need for small-scale, long-term sampling surveys. Future planned work includes ion chromatography for limiting nutrients, ATP quantification, and qPCR for several microbial classes of interest.

Coastal↗
NASA NTRS2016

Effects of Polar Stratospheric Clouds in the Nimbus 7 LIMS Version 6 Data Set

The historic Limb Infrared Monitor of the Stratosphere (LIMS) measurements of 1978-1979 from the Nimbus 7 satellite were re-processed with Version 6 (V6) algorithms and archived in 2002. The V6 data set employs updated radiance registration methods, improved spectroscopic line parameters, and a common vertical resolution for all retrieved parameters. Retrieved profiles are spaced about every 1.6 of latitude along orbits and include the additional parameter of geopotential height. Profiles of O3 are sensitive to perturbations from emissions of polar stratospheric clouds (PSCs). This work presents results of implementing a first-order screening for effects of PSCs using simple algorithms based on vertical gradients of the O3 mixing ratio. Their occurrences are compared with the co-located, retrieved temperatures and related to the temperature thresholds needed for saturation of H2O and/or HNO3 vapor onto PSC particles. Observed daily locations where the major PSC screening criteria are satisfied are validated against PSCs observed with the Stratospheric Aerosol Monitor (SAM) II experiment also on Nimbus 7. Remnants of emissions from PSCs are characterized for O3 and HNO3 following the screening. PSCs may also impart a warm bias in the co-located LIMS temperatures, but by no more than 1-2K at the altitudes of where effects of PSCs are a maximum in the ozone; thus, no PSC screening was applied to the V6 temperatures. Minimum temperatures vary between 187 and 194K and often occur 1 to 2 km above where PSC effects are first identified in the ozone (most often between about 21 and 28 hPa). Those temperature-pressure values are consistent with conditions for the existence of nitric acid trihydrate (NAT) mixtures and to a lesser extent of super-cooled ternary solution (STS) droplets. A local, temporary uptake of HNO3 vapor of order 1-3 ppbv is indicated during mid-January for the 550K surface. Seven-month time series of the distributions of LIMS O3 and HNO3 are shown based on their gridded Level 3 data following the PSC screening. Zonal coefficients of both species are essentially free of effects from PSCs on the 550K surface, based on their average values along PV contours and in terms of equivalent latitude. Remnants of PSCs are still present in O3 on the 450K surface during mid- January. It is judged that the LIMS Level 3 data are of good quality for analyzing the larger-scale, stratospheric chemistry and transport processes during the Arctic winter of 1978- 1979.

Remsberg, Ellis↗
NASA NTRS2003

Satellite and Surface Data Synergy for Developing a 3D Cloud Structure and Properties Characterization Over the ARM SGP. Stage 1: Cloud Amounts, Optical Depths, and Cloud Heights Reconciliation

One of the primary Atmospheric Radiation Measurement (ARM) Program objectives is to obtain measurements applicable to the development of models for better understanding of radiative processes in the atmosphere. We address this goal by building a three-dimensional (3D) characterization of the cloud structure and properties over the ARM Southern Great Plains (SGP). We take the approach of juxtaposing the cloud properties as retrieved from independent satellite and ground-based retrievals, and looking at the statistics of the cloud field properties. Once these retrievals are well understood, they will be used to populate the 3D characterization database. As a first step we determine the relationship between surface fractional sky cover and satellite viewing angle dependent cloud fraction (CF). We elaborate on the agreement intercomparing optical depth (OD) datasets from satellite and ground using available retrieval algorithms with relation to the CF, cloud height, multi-layer cloud presence, and solar zenith angle (SZA). For the SGP Central Facility, where output from the active remote sensing cloud layer (ARSCL) valueadded product (VAP) is available, we study the uncertainty of satellite estimated cloud heights and evaluate the impact of this uncertainty for radiative studies.

Genkova, I.↗
NASA NTRS1981

A life history method for estimating convective rainfall

The remote sensing of rain amounts is of great interest for a great variety of operational applications, including hydrology, hydroelectricity and agriculture is discussed. The microwave radiometer represents the most obvious technique, however, poor spatial and temporal resolution, together with the problems associated with the estimation of effective rain layer height make visible and IR techniques more promising at the present time. Based on bivariate frequency distribution of brightness versus temperature, brightness enhancing or infrared technique alone may be inadequate to deduce details of convective activity. It is implied that better estimates of rainfall will come from visible and IR observations combined than from either used alone. The technique identifies clouds with high probability of rain as those which have large optical and presumably physical thickness as measured by the visible albedo in comparison with their height, determined by the intensity of the IR emission.

Martin, D. W.↗
NASA NTRS1992

Thermal disequilibrium at the top of volcanic clouds and its effect on estimates of the column height

Satellite images of large volcanic explosions reveal that the tops of volcanic eruptions columns are much cooler than the surrounding atmosphere. It is proposed that this effect occurs whenever a mixture of hot volcanic ash and entrained air ascends sufficiently high into a stably stratified atmosphere. Although the mixture is initially very hot, it expands and cools as the ambient pressure decreases. It is shown that cloud-top undercoolings in excess of 20 C may develop in clouds that penetrate the stratosphere, and it is predicted that, for a given cloud-top temperature, variations in the initial temperature of 100-200 C may correspond to variations in the column height of 5-10 km. It is deduced that the present practice of converting satellite-based measurements of the temperature at the top of volcanic eruptions columns to estimates of the column height will produce rather inaccurate results and should therefore be discontinued.

Woods, Andrew W.↗
NASA NTRS2014

Stereoscopic Retrieval of Smoke Plume Heights and Motion from Space-Based Multi-Angle Imaging, Using the MISR INteractive eXplorer(MINX)

Airborne particles desert dust, wildfire smoke, volcanic effluent, urban pollution affect Earth's climate as well as air quality and health. They are found in the atmosphere all over the planet, but vary immensely in amount and properties with season and location. Most aerosol particles are injected into the near-surface boundary layer, but some, especially wildfire smoke, desert dust and volcanic ash, can be injected higher into the atmosphere, where they can stay aloft longer, travel farther, produce larger climate effects, and possibly affect human and ecosystem health far downwind. So monitoring aerosol injection height globally can make important contributions to climate science and air quality studies. The Multi-angle Imaging Spectro-Radiometer (MISR) is a space borne instrument designed to study Earths clouds, aerosols, and surface. Since late February 2000 it has been retrieving aerosol particle amount and properties, as well as cloud height and wind data, globally, about once per week. The MINX visualization and analysis tool complements the operational MISR data products, enabling users to retrieve heights and winds locally for detailed studies of smoke plumes, at higher spatial resolution and with greater precision than the operational product and other space-based, passive remote sensing techniques. MINX software is being used to provide plume height statistics for climatological studies as well as to investigate the dynamics of individual plumes, and to provide parameterizations for climate modeling.

aerosols↗
NASA NTRS1993

Stratospheric Aerosol and Gas Experiment (SAGE 3)

The proposed SAGE III instrument would be the principal source of data for global changes of stratospheric aerosols, stratospheric water vapor, and ozone profiles, and a contributing source of data for upper tropospheric water vapor, aerosols, and clouds. The ability to obtain such data has been demonstrated by the predecessor instrument, SAGE II, but SAGE III will be substantially more capable, as discussed below. The capabilities for monitoring the profiles of atmospheric constituents have been verified in detail, including ground-based validations, for aerosol, ozone, and water vapor. Indeed, because of its self-calibrating characteristics, SAGE II was an essential component of the international ozone trend assessments, and SAGE II is now proving to be invaluable in tracking the aerosols from Mt. Pinatubo. Although SAGE profiles generally terminate at the height of the first tropospheric cloud layer, it has been found that the measurements extend down to 3 km altitude more than 40 percent of the time at most latitudes. Thus, useful information can also be obtained on upper tropospheric aerosols, water vapor, and ozone.

Mccormick, M. P.↗
NASA NTRS2006

Progress in the Development of Practical Remote Detection of Icing Conditions

The NASA Icing Remote Sensing System (NIRSS) has been under definition and development at NASA Glenn Research Center since 1997. The goal of this development activity is to produce and demonstrate the required sensing and data processing technologies required to accurately remotely detect and measure icing conditions aloft. As part of that effort NASA has teamed with NCAR to develop software to fuse data from multiple instruments into a single detected icing condition product. The multiple instrument approach utilizes a X-band vertical staring radar, a multifrequency microwave, and a lidar ceilometer. The radar data determine cloud boundaries, the radiometer determines the sub-freezing temperature heights and total liquid water content, and the ceilometer refines the lower cloud boundary. Data is post-processed with a LabVIEW program with a resultant supercooled liquid water profile and aircraft hazard depiction. Ground-based, remotely-sensed measurements and in-situ measurements from research aircraft were gathered during the international 2003-2004 Alliance Icing Research Study (AIRS II). Comparisons between the remote sensing system s fused icing product and the aircraft measurements are reviewed here. While there are areas where improvement can be made, the cases examined suggest that the fused sensor remote sensing technique appears to be a valid approach.

Reehorst, Andrew↗
NASA NTRS2014

Algorithm for Detection of Ground and Canopy Cover in Micropulse Photon-Counting Lidar Altimeter Data in Preparation for the ICESat-2 Mission

NASA's Ice, Cloud and Land Elevation Satellite-II (ICESat-2) mission is a decadal survey mission (2016 launch). The mission objectives are to measure land ice elevation, sea ice freeboard, and changes in these variables, as well as to collect measurements over vegetation to facilitate canopy height determination. Two innovative components will characterize the ICESat-2 lidar: 1) collection of elevation data by a multibeam system and 2) application of micropulse lidar (photon-counting) technology. A photon-counting altimeter yields clouds of discrete points, resulting from returns of individual photons, and hence new data analysis techniques are required for elevation determination and association of the returned points to reflectors of interest. The objective of this paper is to derive an algorithm that allows detection of ground under dense canopy and identification of ground and canopy levels in simulated ICESat-2 data, based on airborne observations with a Sigma Space micropulse lidar. The mathematical algorithm uses spatial statistical and discrete mathematical concepts, including radial basis functions, density measures, geometrical anisotropy, eigenvectors, and geostatistical classification parameters and hyperparameters. Validation shows that ground and canopy elevation, and hence canopy height, can be expected to be observable with high accuracy by ICESat-2 for all expected beam energies considered for instrument design (93.01%-99.57% correctly selected points for a beam with expected return of 0.93 mean signals per shot (msp), and 72.85%-98.68% for 0.48 msp). The algorithm derived here is generally applicable for elevation determination from photoncounting lidar altimeter data collected over forested areas, land ice, sea ice, and land surfaces, as well as for cloud detection.

Algorithms↗
NASA NTRS1976

Scattering in the atmosphere of Venus. I - Line profiles and curves of growth for isotropic scattering

Line profiles and curves of growth were computed for both reflected and transmitted radiation for typical lines in CO2 bands (in the photographic infrared) which occur in the spectrum of Venus. In the model, the pressure variation with altitude was considered, and the base of the cloud deck was set at the 2 bar level. The temperature was held constant at 250 K, and a Voigt profile was used for the line shape. It was also assumed that the scale height of the cloud particles was equal to the scale height of the gas. The calculations were made for four values of the scattering optical thickness (0.1, 1.0, and 100) using a continuum single-scattering albedo of 0.9975 (which gives a Bond albedo of 0.896 for a scattering optical thickness of 100, the value observed for Venus at these wavelengths). Curves of growth are also presented for reflected radiation which has been averaged over the visible disk for three values of the Venus phase angle (0, 86, and 166 deg).

Young, L. D. G.↗
NASA NTRS1984

Severe storm electricity

Successful ground truth support of U-2 overflights was been accomplished. Data have been reduced for 4 June 1984 and some of the results have been integrated into some of MSFC's efforts. Staccato lightning (multiply branched, single stroke flash with no continuing current) is prevalent within the rainfree region around the main storm updraft and this is believed to be important, i.e., staccato flashes might be an important indicator of severe storm electrification. Results from data analysis from two stations appear to indicate that charge center heights can be estimated from a combination of intercept data with data from the fixed laboratory at NSSL. An excellent data base has been provided for determining the sight errors and efficiency of NSSL's LLP system. Cloud structures, observable in a low radar reflectivity region and on a scale smaller than is currently resolved by radar, which appear to be related to electrical activity are studied.

Arnold, R. T.↗
NASA NTRS1990

Air-sea interaction during an extreme cold air outbreak from the eastern coast of the United States

An aircraft investigation of boundary layer mean and turbulent structure is reported, and the Lagrangian budgets of temperature and moisture in the subcloud layer following a streamline during an extreme cold air outbreak are evaluated. The maximum sea-air temperature difference was 23 K. Two aircraft were used: the NCAR Electra, which measured turbulent fluxes and investigated subcloud layer conditions, and the NASA Electra, which measured the height of cloud tops using lidar. A stratocumulus overcast was found from about 60 km offshore to the Gulf Stream core with cloud top rising downstream. East of the Gulf Stream cumulus congestus and snow showers were observed. Cloud base decreased downstream and numerous steam plumes filled the subcloud layer. Temperature cross sections show most warming, and moistening of the subcloud layer occurred before the Gulf Stream core. Windspeeds increased downstream and maxima were observed near cloud top (inversion) and in the subcloud layer. Lagrangian budgets showed most warming, and moistening of the layer between 70 m and about 100 m below mean cloud base was due to turbulent flux divergence.

Grossman, Robert L.↗