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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

A Fast Infrared Radiative Transfer Model for Overlapping Clouds

A fast infrared radiative transfer model (FIRTM2) appropriate for application to both single-layered and overlapping cloud situations is developed for simulating the outgoing infrared spectral radiance at the top of the atmosphere (TOA). In FIRTM2 a pre-computed library of cloud reflectance and transmittance values is employed to account for one or two cloud layers, whereas the background atmospheric optical thickness due to gaseous absorption can be computed from a clear-sky radiative transfer model. FIRTM2 is applicable to three atmospheric conditions: 1) clear-sky, 2) single-layered ice or water cloud, and 3) two simultaneous cloud layers in a column (e.g., ice cloud overlying water cloud). Moreover, FIRTM2 outputs the derivatives (i.e., Jacobians) of the TOA brightness temperature with respect to cloud optical thickness and effective particle size. Sensitivity analyses have been carried out to assess the performance of FIRTM2 for two spectral regions, namely the longwave (LW) band (587.3 - 1179.5/cm) and the short-to-medium wave (SMW) band (1180.1 - 2228.9/cm). The assessment is carried out in terms of brightness temperature differences (BTD) between FIRTM2 and the well-known discrete ordinates radiative transfer model (DISORT), henceforth referred to as BTD (F-D). The BTD (F-D) values for single-layered clouds are generally less than 0.8 K. For the case of two cloud layers (specifically ice cloud over water cloud), the BTD(F-D) values are also generally less than 0.8 K except for the SMW band for the case of a very high altitude (>15 km) cloud comprised of small ice particles. Note that for clear-sky atmospheres, FIRTM2 reduces to the clear-sky radiative transfer model that is incorporated into FIRTM2, and the errors in this case are essentially those of the clear-sky radiative transfer model.

Niu, Jianguo↗
NASA NTRS1977

Interstellar clouds and molecular hydrogen

Data obtained from the Copernicus Orbiting Astronomical Observatory, launched in 1972 and still obtaining information, are used in a discussion of the interstellar medium. The Copernicus instruments have facilitated direct estimates for the density and temperature of individual interstellar clouds, and improved the ability to determine where along the line of sight a cloud lies with respect to background stars. The physical characteristics of hydrogen molecules are considered, with attention to the formation and destruction of interstellar hydrogen. The differences between 'thin' clouds, in which molecular hydrogen is optically thin, and 'thick' clouds are examined. Several features of the interstellar medium are described.

Jura, M.↗
NASA NTRS2017

HST WFC3 Observations of Uranus' 2014 Storm Clouds and Comparison with VLT/SINFONI and IRTF/Spex Observations

In November 2014 Uranus was observed with the Wide Field Camera 3 (WFC3) instrument of the Hubble Space Telescope as part of the Hubble 2020: Outer Planet Atmospheres Legacy program, OPAL. OPAL annually maps Jupiter, Uranus and Neptune (and will also map Saturn from 2018) in several visible near- infrared wavelength filters. The Uranus 2014 OPAL observations were made on the 89th November at a time when a huge cloud complex, first observed by de Pater et al. (2015) and subsequently tracked by professional and amateur astronomers (Sayanagi et al., 2016), was present at 30-40deg N. We imaged the entire visible atmosphere, including the storm system, in seven filters spanning 467924 nm, capturing variations in the coloration of Uranus clouds and also vertical distribution due to wavelength dependent changes in Rayleigh scattering and methane absorption optical depth. Here we analyse these new HST observations with the NEMESIS radiative-transfer and retrieval code in multiple-scattering mode to determine the vertical cloud structure in and around the storm cloud system. The same storm system was also observed in the H-band (1.4-1.8 micrometers) with the SINFONI Integral Field Unit Spectrometer on the Very Large Telescope (VLT) on 31st October and 11th November, reported by Irwin et al. (2016, 10.1016j.icarus.2015.09.010). To constrain better the cloud particle sizes and scattering properties over a wide wavelength range we also conducted a limb-darkening analysis of the background cloud structure in the 30-40deg N latitude band by simultaneously fitting: a) these HSTOPAL observations at a range of zenith angles; b) the VLTSINFONI observations at a range of zenith angles; and c) IRTFSpeX observations of this latitude band made in 2009 at a single zenith angle of 23deg, spanning the wavelength range 0.8-1.8 micrometers (Irwin et al., 2015, 10.1016j.icarus.2014.12.020). We find that the HST observations, and the combined HSTVLTIRTF observations at all locations are well modelled with a three-component cloud comprised of: 1) a vertically thin, but optically thick deep tropospheric cloud at a pressure of approximately 2 bars; 2) a methane-ice cloud based at the methane-condensation level of approximately 1.23 bar, with variable vertical extent; and 3) a vertically extended tropospheric haze, also based at the methane-condensation level of 1.23 bar. We find that modelling both haze and tropospheric cloud with particles having an effective radius of approximately 0.1 micron provides a good fit the observations, although for the tropospheric cloud, particles with an effective radius as large as 1.0 micron provide a similarly good fit. We find that the particles in both the tropospheric cloud and haze are more scattering at short wave- lengths, giving them a blue color, but are more absorbing at longer wavelengths, especially for the tropospheric haze. We find that the spectra of the storm clouds are well modelled by localized thickening and vertical extension of the methane-ice cloud. For the particles in the storm clouds, which we assume to be composed of methane ice particles, we find that their mean radii must lie somewhere in the range 0. 1 1. 0 m. We find that the high clouds have low integrated opacity, and that streamers reminiscent of convective thunderstorm anvils are confined to levels deeper than 1 bar. These results argue against vigorous moist convective origins for the cloud features.

atmospheres↗
NASA NTRS2014

Remote Sensing of Cloud Top Height from SEVIRI: Analysis of Eleven Current Retrieval Algorithms

The role of clouds remains the largest uncertainty in climate projections. They influence solar and thermal radiative transfer and the earth's water cycle. Therefore, there is an urgent need for accurate cloud observations to validate climate models and to monitor climate change. Passive satellite imagers measuring radiation at visible to thermal infrared (IR) wavelengths provide a wealth of information on cloud properties. Among others, the cloud top height (CTH) - a crucial parameter to estimate the thermal cloud radiative forcing - can be retrieved. In this paper we investigate the skill of ten current retrieval algorithms to estimate the CTH using observations from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat Second Generation (MSG). In the first part we compare ten SEVIRI cloud top pressure (CTP) data sets with each other. The SEVIRI algorithms catch the latitudinal variation of the CTP in a similar way. The agreement is better in the extratropics than in the tropics. In the tropics multi-layer clouds and thin cirrus layers complicate the CTP retrieval, whereas a good agreement among the algorithms is found for trade wind cumulus, marine stratocumulus and the optically thick cores of the deep convective system. In the second part of the paper the SEVIRI retrievals are compared to CTH observations from the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) and Cloud Profiling Radar (CPR) instruments. It is important to note that the different measurement techniques cause differences in the retrieved CTH data. SEVIRI measures a radiatively effective CTH, while the CTH of the active instruments is derived from the return time of the emitted radar or lidar signal. Therefore, some systematic differences are expected. On average the CTHs detected by the SEVIRI algorithms are 1.0 to 2.5 kilometers lower than CALIOP observations, and the correlation coefficients between the SEVIRI and the CALIOP data sets range between 0.77 and 0.90. The average CTHs derived by the SEVIRI algorithms are closer to the CPR measurements than to CALIOP measurements. The biases between SEVIRI and CPR retrievals range from −0.8 kilometers to 0.6 kilometers. The correlation coefficients of CPR and SEVIRI observations vary between 0.82 and 0.89. To discuss the origin of the CTH deviation, we investigate three cloud categories: optically thin and thick single layer as well as multi-layer clouds. For optically thick clouds the correlation coefficients between the SEVIRI and the reference data sets are usually above 0.95. For optically thin single layer clouds the correlation coefficients are still above 0.92. For this cloud category the SEVIRI algorithms yield CTHs that are lower than CALIOP and similar to CPR observations. Most challenging are the multi-layer clouds, where the correlation coefficients are for most algorithms between 0.6 and 0.8. Finally, we evaluate the performance of the SEVIRI retrievals for boundary layer clouds. While the CTH retrieval for this cloud type is relatively accurate, there are still considerable differences between the algorithms. These are related to the uncertainties and limited vertical resolution of the assumed temperature profiles in combination with the presence of temperature inversions, which lead to ambiguities in the CTH retrieval. Alternative approaches for the CTH retrieval of low clouds are discussed.

Hamann, U.↗
NASA NTRS2016

First Transmitted Hyperspectral Light Measurements and Cloud Properties from Recent Field Campaign Sampling Clouds Under Biomass Burning Aerosol

We present a first view of data collected during a recent field campaign aimed at measuring biomass burning aerosol above clouds from airborne platforms. The NASA ObseRvations of CLouds above Aerosols and their intEractionS (ORACLES) field campaign recently concluded its first deployment sampling clouds and overlying aerosol layer from the airborne platform NASA P3. We present results from the Spectrometer for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR), in conjunction with the Solar Spectral Flux Radiometers (SSFR). During this deployment, 4STAR sampled transmitted solar light either via direct solar beam measurements and scattered light measurements, enabling the measurement of aerosol optical thickness and the retrieval of information on aerosol particles in addition to overlying cloud properties. We focus on the zenith-viewing scattered light measurements, which are used to retrieve cloud optical thickness, effective radius, and thermodynamic phase of clouds under a biomass burning layer. The biomass burning aerosol layer present above the clouds is the cause of potential bias in retrieved cloud optical depth and effective radius from satellites. We contrast the typical reflection based approach used by satellites to the transmission based approach used by 4STAR during ORACLES for retrieving cloud properties. It is suspected that these differing approaches will yield a change in retrieved properties since light transmitted through clouds is sensitive to a different cloud volume than reflected light at cloud top. We offer a preliminary view of the implications of these differences in sampling volumes to the calculation of cloud radiative effects (CRE).

airborne↗
NASA NTRS2019

Cloud Remote Sensing with EPIC/DSCOVR Observations: A Sensitivity Study with Radiative Transfer Simulations

The Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR) views nearly the whole sunlit face of the Earth with 10 spectral bands ranging from the UV to the near-infrared, including two oxygen absorbing bands centered at 764 nm (A-band) and 687.75 nm (B-band). Clouds are among the primary remote sensing targets using EPIC images because of their important impacts on the Earth’s radiation budget. In order to facilitate the EPIC cloud data product development, we have built a radiative transfer simulator featuring flexible cloud microphysical parameters, gas absorptions, and the instrument line shape functions for each EPIC band. The radiative transfer simulator is used to explore the sensitivity of EPIC observations on liquid-phase cloud microphysical parameters, including optical depth, geometric thickness, and cloud top height. We found that the ratios of the reflectances in the oxygen A and B bands to their respective continuum measurements can be used to increase the confidence level of cloud masking over scenes with sun-glint. In addition, the 388 nm band can be used to differentiate low and high clouds with the uncertainty of roughly 2–3 km. Combining this information with the oxygen absorption bands, the cloud geometric thickness can be obtained with the rough uncertainty of 3–4 km.

atmospheric and ocean optics↗
NASA NTRS1977

Evidence for weather on Neptune. II

Data obtained by Joyce et al., (1977) are interpreted as evidence for the formation of an optically-thin cloud high in the atmosphere of Neptune. About 10 months after the cloud's initial appearance and subsequent partial dissipation, the optical thickness of the cloud, averaged over the planet, had a value for tau in the vicinity of 1. The minimum effective radius indicated for the cloud particles is about 1 micron. The model which leads to this interpretation of the data is explained, and the calculations are presented. Implications of the model and also apparent similarities between Neptune's atmosphere and that of other planets are discussed.

Pilcher, C. B.↗
NASA NTRS1993

A numerical technique for the calculation of cloud optical extinction from lidar

A simple numerical algorithm which calculates optical extinction from cloud lidar data is presented. The method assumes a two-component atmosphere consisting of 'clear air' and cloud particulates. 'Clear air' may consist of either molecules only or a mix of molecules and atmospheric aerosols. For certain clouds, the method may be utilized to provide an estimate of the cloud-atmospheric parameter defined as the ratio of the cloud volume backscatter coefficient to the cloud extinction coefficient divided by the atmospheric volume backscatter coefficient at a given altitude. The cloud-atmospheric parameter may be estimated only from cloud data from which the optical thickness may reliably be used as a constraint on the numerical solution. This constraint provides the additional information necessary to obtain the cloud-atmospheric parameter. Conversely, the method may be applied to obtain cloud extinction and optical thickness from lidar cloud soundings if an estimate of the cloud-atmospheric parameter is available.

Alvarez, J. M.↗
NASA NTRS2009

Evaluation of the OMI Cloud Pressures Derived from Rotational Raman Scattering by Comparisons with other Satellite Data and Radiative Transfer Simulations

In this paper we examine differences between cloud pressures retrieved from the Ozone Monitoring Instrument (OMI) using the ultraviolet rotational Raman scattering (RRS) algorithm and those from the thermal infrared (IR) Aqua/MODIS. Several cloud data sets are currently being used in OMI trace gas retrieval algorithms including climatologies based on IR measurements and simultaneous cloud parameters derived from OMI. From a validation perspective, it is important to understand the OMI retrieved cloud parameters and how they differ with those derived from the IR. To this end, we perform radiative transfer calculations to simulate the effects of different geophysical conditions on the OMI RRS cloud pressure retrievals. We also quantify errors related to the use of the Mixed Lambert-Equivalent Reflectivity (MLER) concept as currently implemented of the OMI algorithms. Using properties from the Cloudsat radar and MODIS, we show that radiative transfer calculations support the following: (1) The MLER model is adequate for single-layer optically thick, geometrically thin clouds, but can produce significant errors in estimated cloud pressure for optically thin clouds. (2) In a two-layer cloud, the RRS algorithm may retrieve a cloud pressure that is either between the two cloud decks or even beneath the top of the lower cloud deck because of scattering between the cloud layers; the retrieved pressure depends upon the viewing geometry and the optical depth of the upper cloud deck. (3) Absorbing aerosol in and above a cloud can produce significant errors in the retrieved cloud pressure. (4) The retrieved RRS effective pressure for a deep convective cloud will be significantly higher than the physical cloud top pressure derived with thermal IR.

Vasilkov, Alexander↗
NASA NTRS2013

Cirrus Cloud Seeding has Potential to Cool Climate

Cirrus clouds, thin ice clouds in the upper troposphere, have a net warming effect on Earth s climate. Consequently, a reduction in cirrus cloud amount or optical thickness would cool the climate. Recent research indicates that by seeding cirrus clouds with particles that promote ice nucleation, their lifetimes and coverage could be reduced. We have tested this hypothesis in a global climate model with a state-of-the-art representation of cirrus clouds and find that cirrus cloud seeding has the potential to cancel the entire warming caused by human activity from pre-industrial times to present day. However, the desired effect is only obtained for seeding particle concentrations that lie within an optimal range. With lower than optimal particle concentrations, a seeding exercise would have no effect. Moreover, a higher than optimal concentration results in an over-seeding that could have the deleterious effect of prolonging cirrus lifetime and contributing to global warming.

Storelvmo, T.↗
NASA NTRS1992

SAGE II measurements of early Pinatubo aerosols

SAGE II satellite measurements of the Mt. Pinatubo eruption cloud in the stratosphere during June, July, and early August 1991 show that aerosols in the tropics reached as high as 29 km altitude with most of the cloud between 20 and 25 km. The most optically thick portions of the cloud covered latitudes from 10 deg S to 30 deg N during the early part of this period. By late July, high stratospheric optical depths were observed to at least 70 deg N, with the high values north of about 30 deg N from layers below 20 km. High pressure systems in both hemispheres were observed to be correlated with the movement of volcanic material at 21 km into the westerly jet stream at high southern latitudes and similarly to high northern latitudes at 16 km. By August, the entire Southern Hemisphere had experienced a 10-fold increase in optical depth relative to early July due to layers above 20 km. Initial mass calculations using SAGE II data place the aerosol produced from this eruption at 20 to 30 megatons, well above the 12 megatons produced by El Chichon.

Mccormick, M. P.↗
NASA NTRS1990

The 27-28 October 1986 FIRE IFO cirrus case study - Cloud optical properties determined by High Spectral Resolution Lidar

The High Spectral Resolution Lidar (HSRL) was operated from a roof-top site in Madison, Wisconsin. The transmitter configuration used to acquire the case study data produces about 50 mW of ouput power and achieved eye-safe, direct optical depth, and backscatter cross section measurements with 10 min averaging times. A new continuously pumped, injection seeded, frequency doubled Nd:YAG laser transmitter reduces time-averaging constraints by a factor of about 10, while improving the aerosol-molecular signal separation capabilities and wavelength stability of the instrument. The cirrus cloud backscatter-phase functions have been determined for the October 27-28, 1986 segment of the HSRL FIRE dataset. Features exhibiting backscatter cross sections ranging over four orders of magnitude have been observed within this 33 h period. During this period, cirrus clouds were observed with optical thickness ranging from 0.01 to 1.4. The altitude relationship between cloud top and bottom boundaries and the optical center of the cloud is influenced by the type of formation observed.

Grund, C. J.↗
NASA NTRS2013

Sensitivity of Downward Longwave Surface Radiation to Moisture and Cloud Changes in a High-elevation Region

Several studies have suggested enhanced rates of warming in high-elevation regions since the latter half of the twentieth century. One of the potential reasons why enhanced rates of warming might occur at high elevations is the nonlinear relationship between downward longwave radiation (DLR) and specific humidity (q). Using ground-based observations at a high-elevation site in southwestern Colorado and coincident satellite-borne cloud retrievals, the sensitivity of DLR to changes in q and cloud properties is examined and quantified using a neural network method. It is also used to explore how the sensitivity of DLR to q (dDLR/dq) is affected by cloud properties. When binned by season, dDLR/dq is maximum in winter and minimum in summer for both clear and cloudy skies. However, the cloudy-sky sensitivities are smaller, primarily because (1) for both clear and cloudy skies dDLR/dq is proportional to 1/q, for q>0.5 g/kg, and (2) the seasonal values of q are on average larger in the cloudy-sky cases than in clear-sky cases. For a given value of q, dDLR/dq is slightly reduced in the presence of clouds and this reduction increases as q increases. In addition, DLR is found to be more sensitive to changes in cloud fraction when cloud fraction is large. In the limit of overcast skies, DLR sensitivity to optical thickness decreases as clouds become more opaque. These results are based on only one high-elevation site, so the conclusions here need to be tested at other high-elevation locations.

cloud physics↗
NASA NTRS1999

Improving Pixel Level Cloud Optical Property Retrieval using Monte Carlo Simulations

The accurate pixel-by-pixel retrieval of cloud optical properties from space is influenced by radiative smoothing due to high order photon scattering and radiative roughening due to low order scattering events. Both are caused by cloud heterogeneity and the three-dimensional nature of radiative transfer and can be studied with the aid of computer simulations. We use Monte Carlo simulations on variable 1-D and 2-D model cloud fields to seek for dependencies of smoothing and roughening phenomena on single scattering albedo, solar zenith angle, and cloud characteristics. The results are discussed in the context of high resolution satellite (such as Landsat) retrieval applications. The current work extends the investigation on the inverse NIPA (Non-local Independent Pixel Approximation) as a tool for removing smoothing and improving retrievals of cloud optical depth. This is accomplished by: (1) Delineating the limits of NIPA applicability; (2) Exploring NIPA parameter dependences on cloud macrostructural features, such as mean cloud optical depth and geometrical thickness, degree of extinction and cloud top height variability. We also compare parameter values from empirical and theoretical considerations; (3) Examining the differences between applying NIPA on radiation quantities vs direct application on optical properties; (4) Studying the radiation budget importance of the NIPA corrections as a function of scale. Finally, we discuss fundamental adjustments that need to be considered for successful radiance inversion at non-conservative wavelengths and oblique Sun angles. These adjustments are necessary to remove roughening signatures which become more prominent with increasing absorption and solar zenith angle.

Oreopoulos, Lazaros↗
NASA NTRS1995

Transport of Volcanic Clouds Injected in the Tropics: Case Studies of El Chichon and Mt. Pinatubo

The eruptions of Mt. Pinatubo and El Chichon at nearly the same tropical latitude produced two of the largest volcanic clouds this century. Climatic effects of any volcanic eruption depend on spatial distribution of the volcanic cloud. We report the first global simulations which reproduce the markedly different inter-hemispheric transport observed for these clouds in the months immediately following each eruption. Differences in stratospheric mean easterly winds and unequal radiative heating of the clouds explain the different latitudinal transport. It is found that radiative heating of tropical clouds is insensitive to particle size for typical size ranges. Radiative energy balance of optically thick tropical volcanic clouds tends to position the clouds near 25 km altitude.

Young, R. E.↗
NASA NTRS2006

Potential Nighttime Contamination of CERES Clear-sky Field of View by Optically Thin Cirrus during the CRYSTAL-FACE Campaign

We investigate the outgoing broadband longwave (LW, 5 to approx. 200 microns) and window (WIN, 8 to approx. 12 microns) channel radiances at the top of atmosphere (TOA) under clear-sky conditions, using data acquired by the Cloud and the Earth s Radiant Energy System (CERES) and Moderate-Resolution Imaging Spectroradiometer (MODIS) instruments onboard the NASA Terra satellite platform. In this study, detailed analyses are performed on the CERES Single Scanner Footprint TOA/Surface Fluxes and Clouds product to understand the radiative effect of thin cirrus. The data are acquired over the Florida area during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers Florida Area Cirrus Experiment (CRYSTAL-FACE) field program. Of particular interest is the anisotropy associated with the radiation field. Measured CERES broadband radiances are compared to those obtained from rigorous radiative transfer simulations. Analysis of results from this comparison indicates that the simulated radiances tend to be larger than their measured counterparts, with differences ranging from 2.1% to 8.3% for the LW band and from 1.7% to 10.6% for the WIN band. The averaged difference in radiance is approximately 4% for both the LW and WIN channels. A potential cause for the differences could be the presence of thin cirrus (i.e., optically thin ice clouds with visible optical thicknesses smaller than approximately 0.3). The detection and quantitative analysis of these thin cirrus clouds are challenging even with sophisticated multispectral instruments. While large differences in radiance between the CERES observations and the theoretical calculations are found, the corresponding difference in the anisotropic factors is very small (0.2%). Furthermore, sensitivity studies show that the influence due to a 1 K bias of the surface temperature on the errors of the LW and WIN channel radiances is of the same order as that associated with a 2% bias of the surface emissivity. The LW and WIN errors associated with a 5% bias of water vapor amount in the lower atmosphere in conjunction with a 50% bias of water vapor amount in the upper atmosphere is similar to that of a 1 K bias of the vertical temperature profile. Even with the uncertainties considered for these various factors, the simulated LW and WIN radiances are still larger than the observed radiances if thin cirrus clouds are excluded.

Lee, Yong-Keun↗
NASA NTRS1989

Lidar validation of VAS cirrus cloud height determinations

The determination of cirrus cloud pressure altitude and IR attenuation using CO2 channel radiometric data from the VISSR (Visible and Infrared Spin Scan Radiometer) Atmospheric Sounder (VAS) on board the GOES geostationary satellite is discussed. The independent ground-based determination of cirrus cloud altitude, thickness, and optical properties obtained with the High Spectral Resolution Lidar (HSRL) is described. HSRL cirrus cloud measurements are compared to VAS CO2 cloud top height retrievals generated for the First International Satellite Cloud Climatology Project Regional Experiment cirrus intensive Field Observations, held in Wisconsin in October and November of 1986.

Grund, Christian J.↗
NASA NTRS1984

X-ray nebular models. II - Constant pressure clouds

Models are presented for the ionization and temperature structure of X-ray illuminated gas clouds under the assumption that the clouds' pressure is fixed. Models are considered which have a variety of different combinations of X-ray source spectrum and cloud pressure, characteristic of galactic X-ray sources and interstellar gas. It is shown that optically thick constant pressure clouds obey scaling laws for their ionized column densities which are analogous to the scaling behavior of constant density models. The results of constant pressure models are contrasted with constant density model results, and it is shown that the constant pressure assumption leads to enhanced thermal instability effects and also causes important differences in the line spectra emergent from X-ray illuminated clouds. Observable consequences for X-ray illuminated interstellar clouds are discussed.

Kallman, T. R.↗