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At least 577 records · Page 32

Application of High-Dimensional Fuzzy K-Means Cluster Analysis to CALIOP/CALIPSO Version 4.1 Cloud-Aerosol Discrimination

This study applies fuzzy k-means (FKM) cluster analyses to a subset of the parameters reported in the CALIPSO lidar level 2 data products in order to classify the layers detected as either clouds or aerosols. The results obtained are used to assess the reliability of the cloud–aerosol discrimination (CAD) scores reported in the version 4.1 release of the CALIPSO data products. FKM is an unsupervised learning algorithm, whereas the CALIPSO operational CAD algorithm (COCA) takes a highly supervised approach. Despite these substantial computational and architectural differences, our statistical analyses show that the FKM classifications agree with the COCA classifications for more than 94 % of the cases in the troposphere. This high degree of similarity is achieved because the lidar-measured signatures of the majority of the clouds and the aerosols are naturally distinct, and hence objective methods can independently and effectively separate the two classes in most cases. Classification differences most often occur in complex scenes (e.g., evaporating water cloud filaments embedded in dense aerosol) or when observing diffuse features that occur only intermittently (e.g., volcanic ash in the tropical tropopause layer). The two methods examined in this study establish overall classification correctness boundaries due to their differing algorithm uncertainties. In addition to comparing the outputs from the two algorithms, analysis of sampling, data training, performance measurements, fuzzy linear discriminants, defuzzification, error propagation, and key parameters in feature type discrimination with the FKM method are further discussed in order to better understand the utility and limits of the application of clustering algorithms to space lidar measurements. In general, we find that both FKM and COCA classification uncertainties are only minimally affected by noise in the CALIPSO measurements, though both algorithms can be challenged by especially complex scenes containing mixtures of discrete layer types. Our analysis results show that attenuated backscatter and color ratio are the driving factors that separate water clouds from aerosols; backscatter intensity, depolarization, and mid-layer altitude are most useful in discriminating between aerosols and ice clouds; and the joint distribution of backscatter intensity and depolarization ratio is critically important for distinguishing ice clouds from water clouds.

Zeng, Shan↗

Comparison Between GOES-12 Overshooting-Top Detections, WSR-88D Radar Reflectivity, and Severe Storm Reports

Studies have found that convective storms with overshooting-top (OT) signatures in weather satellite imagery are often associated with hazardous weather, such as heavy rainfall, tornadoes, damaging winds, and large hail. An objective satellite-based OT detection product has been developed using 11-micrometer infrared window (IRW) channel brightness temperatures (BTs) for the upcoming R series of the Geostationary Operational Environmental Satellite (GOES-R) Advanced Baseline Imager. In this study, this method is applied to GOES-12 IRW data and the OT detections are compared with radar data, severe storm reports, and severe weather warnings over the eastern United States. The goals of this study are to 1) improve forecaster understanding of satellite OT signatures relative to commonly available radar products, 2) assess OT detection product accuracy, and 3) evaluate the utility of an OT detection product for diagnosing hazardous convective storms. The coevolution of radar-derived products and satellite OT signatures indicates that an OT often corresponds with the highest radar echo top and reflectivity maximum aloft. Validation of OT detections relative to composite reflectivity indicates an algorithm false-alarm ratio of 16%, with OTs within the coldest IRW BT range (less than 200 K) being the most accurate. A significant IRW BT minimum typically present with an OT is more often associated with heavy precipitation than a region with a spatially uniform BT. Severe weather was often associated with OT detections during the warm season (April September) and over the southern United States. The severe weather to OT relationship increased by 15% when GOES operated in rapid-scan mode, showing the importance of high temporal resolution for observing and detecting rapidly evolving cloud-top features. Comparison of the earliest OT detection associated with a severe weather report showed that 75% of the cases occur before severe weather and that 42% of collocated severe weather reports had either an OT detected before a severe weather warning or no warning issued at all. The relationships between satellite OT signatures, severe weather, and heavy rainfall shown in this paper suggest that 1) when an OT is detected, the particular storm is likely producing heavy rainfall and/or possibly severe weather; 2) an objective OT detection product can be used to increase situational awareness and forecaster confidence that a given storm is severe; and 3) this product may be particularly useful in regions with insufficient radar coverage.

Dworak, Richard↗

Arctic Clouds Infrared Imaging Field Campaign Report

The Infrared Cloud Imager (ICI), a passive thermal imaging system, was deployed at the North Slope of Alaska site in Barrow, Alaska, from July 2012 to July 2014 for measuring spatial-temporal cloud statistics. Thermal imaging of the sky from the ground provides high radiometric contrast during night and polar winter when visible sensors and downward-viewing thermal sensors experience low contrast. In addition to demonstrating successful operation in the Arctic for an extended period and providing data for Arctic cloud studies, a primary objective of this deployment was to validate novel instrument calibration algorithms that will allow more compact ICI instruments to be deployed without the added expense, weight, size, and operational difficulty of a large-aperture onboard blackbody calibration source. This objective was successfully completed with a comparison of the two-year data set calibrated with and without the onboard blackbody. The two different calibration methods produced daily-average cloud amount data sets with correlation coefficient = 0.99, mean difference = 0.0029 (i.e., 0.29% cloudiness), and a difference standard deviation = 0.054. Finally, the ICI instrument generally detected more thin clouds than reported by other ARM cloud products available as of late 2015.

54 ENVIRONMENTAL SCIENCES↗

LOW-METALLICITY YOUNG CLUSTERS IN THE OUTER GALAXY. I. Sh 2-207

To study star formation in low-metallicity environments ([M/H] ∼ −1 dex), we obtained deep near-infrared (NIR) images of Sh 2-207 (S207), which is an H ii region in the outer Galaxy with a spectroscopically determined metallicity of [O/H] ≃ −0.8 dex. We identified a young cluster in the western region of S207 with a limiting magnitude of K{sub S} = 19.0 mag (10σ) that corresponds to a mass detection limit of ≲0.1 M{sub ⊙} and enables the comparison of star-forming properties under low metallicity with those of the solar neighborhood. From the fitting of the K-band luminosity function (KLF), the age and distance of the S207 cluster are estimated at 2–3 Myr and ∼4 kpc, respectively. The estimated age is consistent with the suggestion of small extinctions of stars in the cluster (A{sub V} ∼ 3 mag) and the non-detection of molecular clouds. The reasonably good fit between the observed KLF and the model KLF suggests that the underlying initial mass function (IMF) of the cluster down to the detection limit is not significantly different from the typical IMFs in the solar metallicity. From the fraction of stars with NIR excesses, a low disk fraction (<10%) in the cluster with a relatively young age is suggested, as we had previously proposed.

79 ASTRONOMY AND ASTROPHYSICS↗

Interstellar Isomers: The Importance of Bonding Energy Differences

We present strong detections of methyl cyanide (CH3CN), vinyl cyanide (CH2CHCN), ethyl cyanide (CH3CH2CN) and cyanodiacetylene (HC4CN) molecules with the Green Bank Telescope (GBT) toward the Sgr B2(N) molecular cloud. Attempts to detect the corresponding isocyanide isomers were only successful in the case of methyl isocyanide (CH3NC) for its J(sub K) = 1(sub 0) - 0(sub 0) transition, which is the first interstellar report of this line. To determine the spatial distribution of CH3NC, we used archival Berkeley-Illinois-Maryland Association (BIMA) array data for the J(sub K) = 1(sub 0) - 0(sub 0) transitions but no emission was detected. From ab initio calculations, the bonding energy difference between the cyanide and isocyanide molecules is greater than 8500 per centimeter (greater than 12,000 K). Thus, cyanides are the more stable isomers and would likely be formed more preferentially over their isocyanide counterparts. That we detect CH3NC emission with a single antenna (Gaussian beamsize(omega(sub B))=1723 arcsec(sup 2)) but not with an interferometer (omega(sub b)=192 arcsec(sup 2)), strongly suggests that CH3NC has a widespread spatial distribution toward the Sgr B2(N) region. Other investigators have shown that CH3CN is present both in the LMH hot core of Sgr B2(N) and in the surrounding medium, while we have shown that CH3NC appears to be deficient in the LMH hot core. Thus, largescale, non-thermal processes in the surrounding medium may account for the conversion of CH3CN to CH3NC while the LMH hot core, which is dominated by thermal processes, does not produce a significant amount of CH3NC. Ice analog experiments by other investigators have shown that radiation bombardment of CH3CN can produce CH3NC, thus supporting our observations. We conclude that isomers separated by such large bonding energy differences are distributed in different interstellar environments, making the evaluation of column density ratios between such isomers irrelevant unless it can be independently shown that these species are co-spatial.

Remijan, Anthony J.↗

Utilizing the MODIS 1.38 micrometer Channel for Cirrus Cloud Optical Thickness Retrievals: Algorithm and Retrieval Uncertainties

The cloud products from the Moderate Resolution Imaging Spectroradiometers (MODIS) on Terra and Aqua have been widely used within the atmospheric research community. The retrieval algorithms, however, oftentimes have difficulty detecting and retrieving thin cirrus, due to sensitivities to surface reflectance. Conversely, the 1.38 micron channel, located within a strong water vapor absorption band, is quite useful for detecting thin cirrus clouds since the signal from the surface can be blocked or substantially attenuated by the absorption of atmospheric water vapor below cirrus. This channel, however, suffers from nonnegligible attenuation due to the water vapor located above and within the cloud layer. Here we provide details of a new technique pairing the 1.38 micron and 1.24 micron channels to estimate the above/in-cloud water vapor attenuation and to subsequently retrieve thin cirrus optical thickness (tau) from attenuation-corrected 1.38 p.m reflectance measurements. In selected oceanic cases, this approach is found to increase cirrus retrievals by up to 38% over MOD06. For these cases, baseline 1.38 micron retrieval uncertainties are estimated to be between 15 and 20% for moderately thick cirrus (tau > 1), with the largest error source being the unknown cloud effective particle radius, which is not retrieved with the described technique. Uncertainties increase to around 90% for the thinnest clouds (tau < 0.5) where instrument and surface uncertainties dominate.

Meyer, Kerry↗

DOE ASR Final Report on “Use of ARM Observations to Investigate the Role of Tropical Radiative Processes and Cloud Radiative Effects in Climate Simulations”

The overall objective of this ASR funded project is to investigate the role of cloud radiative effects, especially those associated with tropical thin cirrus clouds in the tropical tropopause layer, by analyzing the ARM observations combined with numerical models. In particular, we have processed and analyzed the observations from the Raman lidar at the ARM SGP and TWP sites. In the tenure of the project (8/15/2013 – 8/14/2016 and with a no-cost extension to 8/14/2017), we have been concentrating on (i) developing an automated feature detection scheme of clouds and aerosols for the ARM Raman lidar; (ii) developing an automated retrieval of cloud and aerosol extinctions for the ARM Raman lidar; (iii) investigating cloud radiative effects based on the observations on the simulated temperatures in the tropical tropopause layer using a radiative-convective model; and (iv) examining the effect of changes of atmospheric composition on the tropical lower-stratospheric temperatures. In addition, we have examined the biases in the CALIPSO-inferred aerosol direct radiative effects using ground-based Raman lidars at the ARM SGP and TWP sites, and estimated the impact of lidar detection sensitivity on assessing global aerosol direct radiative effects. We have also investigated the diurnal cycle of clouds and precipitation at the ARM site using the cloud radar observations along with simulations from the multiscale modeling framework. The main results of our research efforts are reported in the six referred journal publications that acknowledge the DOE Grant DE-SC0010557.

47 OTHER INSTRUMENTATION↗

On the Retrieval and Analysis of Multilevel Clouds

An accurate satellite retrieval of cloud properties depends upon the detection and analysis of multilayered, overlapping cloud systems that surface observations show to be common. Multiple cloud layers are often found, for instance, in frontal situations, where cirrus overlays boundary layer convective cloud or low-to mid-level stratus cloud. Surface observers (Hahan et al., 1982) indicate that over ocean in the Northern Hemisphere between 30 deg. N and 60 deg. N, 51 percent of observations are of multilevel clouds. A satellite analysis by Coakley (1983) over the Pacific Ocean finds that more than 50 percent of 500 (250 sq km) frames exhibit evidence of multilayered cloud systems. The questions addressed in this study are the following: What error is introduced when inferring the cloud pressure from a Field-Of-View (FOV) that contains some arbitrary amount of transparent cloud overlaying a lower-level black cloud, such as stratus, by making the assumption that there is only a single cloud layer in the FOV, and what may be done to improve the cloud retrieval? The CO2 slicing methods (e.g. McCleese and Wilson, 1976; Smith and Platt, 1978; Chahine, 1974) have been shown to provide accurate means of inferring cirrus cloud altitude from passive infrared radiance measurements. The CO2 techniques have been applied to radiometric data from several instruments, notably the High Resolution Infrared Radiometric Sounder (HIRS/2, hereafter referred to as HIRS), the VISSR Atmospheric Sounder (VAS) (e.g., Menzel et al., 1983; Wylie and Menzel, 1989), and most recently to the High Resolution Interferometer Sounder (HIS) (Smith and Frey, 1990). The methods take advantage of the fact that infrared CO2 sounding channels spaced closely in wavenumber each have varying opacity to CO2, thereby causing each channel to be sensitive to a different level in the atmosphere. The techniques have been shown to be effective for single-layered, nonblack, mid- to high-level clouds such as cirrus, but are generally applied operationally to any given cloud occurrence. The CO2 slicing algorithms are most accurate for clouds than occur in a single, well-defined layer, or for multi-layered cloud cases in which the uppermost cloud layer is nearly black. Significant cloud height retrieval errors may ensue if the HIRS Field-Of-View (FOV) is cotaminated with low cloud. McCleese and Wilson (1976) have shown that the retrieved cloud height for the case of multiple cloud layers is a weighted average of the cloud heights actually present. The weight is approximately proportional to the product of the cloud heigt and the effective cloud amount. The effect of their result is that the uppermost cloud layer dominates the cloud pressure retrieval. Beyond stating that the higher cloud dominates the cloud pressure retrieval, there is no quantitative information to provide a way of estimating the errors in cloud pressure retrieval one should expect for certain common multilevel cloud situations or any suggestions on how to reduce the errors. In this paper we estimate the magnitude of the errors and use a simple algorithm to reduce the errors in optically thin cloud height retrival.

Baum, Bryan A.↗

A Unified Satellite-Observation Polar Stratospheric Cloud (PSC) Database for Long-Term Climate-Change Studies

This report summarizes the project team's activity and accomplishments during the period 12 February, 1999 - 12 February, 2000. The primary objective of this project was to create and test a generic algorithm for detecting polar stratospheric clouds (PSC), an algorithm that would permit creation of a unified, long term PSC database from a variety of solar occultation instruments that measure aerosol extinction near 1000 nm The second objective was to make a database of PSC observations and certain relevant related datasets. In this report we describe the algorithm, the data we are making available, and user access options. The remainder of this document provides the details of the algorithm and the database offering.

Fromm, Michael↗

Chemical Complexity Induced by Efficient Ice Evaporation in the Barnard 5 Molecular Cloud

Cold gas-phase water has recently been detected in a cold dark cloud, Barnard 5 located in the Perseus complex, by targeting methanol peaks as signposts for ice mantle evaporation. Observed morphology and abundances of methanol and water are consistent with a transient non-thermal evaporation process only affecting the outermost ice mantle layers, possibly triggering a more complex chemistry. Here we present the detection of the complex organic molecules (COMs) acetaldehyde (CH3CHO) and methyl formate (CH3OCHO), as well as formic acid (HCOOH) and ketene (CH2CO), and the tentative detection of di-methyl ether (CH3OCH3) towards the ''methanol hotspot'' of Barnard 5 located between two dense cores using the single dish OSO 20 m, IRAM 30 m, and NRO 45 m telescopes. The high energy cis-conformer of formic acid is detected, suggesting that formic acid is mostly formed at the surface of interstellar grains and then evaporated. The detection of multiple transitions for each species allows us to constrain their abundances through LTE and non-LTE methods. All the considered COMs show similar abundances between approx. 1 and approx. 10% relative to methanol depending on the assumed excitation temperature. The non-detection of glycolaldehyde, an isomer of methyl formate, with a [glycolaldehyde]/[methyl formate] abundance ratio lower than 6%, favours gas phase formation pathways triggered by methanol evaporation. According to their excitation temperatures derived in massive hot cores, formic acid, ketene, and acetaldehyde have been designated as ''lukewarm'' COMs whereas methyl formate and di-methyl ether were defined as ''warm'' species. Comparison with previous observations of other types of sources confirms that lukewarm and warm COMs show similar abundances in low-density cold gas whereas the warm COMs tend to be more abundant than the lukewarm species in warm protostellar cores. This abundance evolution suggests either that warm COMs are indeed mostly formed in protostellar environments and/or that lukewarm COMs are efficiently depleted by increased hydrogenation efficiency around protostars.

ISM: molecules↗

Chemical Complexity Induced by Efficient Ice Evaporation in the Barnard 5 Molecular Cloud

Cold gas-phase water has recently been detected in a cold dark cloud, Barnard 5 located in the Perseus complex, by targeting methanol peaks as signposts for ice mantle evaporation. Observed morphology and abundances of methanol and water are consistent with a transient non-thermal evaporation process only affecting the outermost ice mantle layers, possibly triggering a more complex chemistry. Here we present the detection of the complex organic molecules (COMs) acetaldehyde (CH3CHO) and methyl formate (CH3OCHO), as well as formic acid (HCOOH) and ketene (CH2CO), and the tentative detection of di-methyl ether (CH3OCH3) towards the ‘methanol hotspot’ of Barnard 5 located between two dense cores using the single dish OSO 20m, IRAM 30m, and NRO 45m telescopes. The high energy cis- conformer of formic acid is detected, suggesting that formic acid is mostly formed at the surface of interstellar grains and then evaporated. The detection of multiple transitions for each species allows us to constrain their abundances through LTE and non-LTE methods. All the considered COMs show similar abundances between ∼ 1 and ∼ 10 % relative to methanol depending on the assumed excitation temperature. The non-detection of glycolaldehyde, an isomer of methyl formate, with a [glycolaldehyde]/[methyl formate] abundance ratio lower than 6 %, favours gas phase formation pathways triggered by methanol evaporation. According to their excitation temperatures derived in massive hot cores, formic acid, ketene, and acetaldehyde have been designated as ‘lukewarm’ COMs whereas methyl formate and di-methyl ether were defined as ‘warm’ species. Comparison with previous observations of other types of sources confirms that lukewarm and warm COMs show similar abundances in low-density cold gas whereas the warm COMs tend to be more abundant than the lukewarm species in warm protostellar cores. This abundance evolution suggests either that warm COMs are indeed mostly formed in protostellar environments and/or that lukewarm COMs are efficiently depleted by increased hydrogenation efficiency around protostars.

astrochemistry – ISM: abundances – ISM: clouds – I↗

DETECTION OF EXTREMELY BROAD WATER EMISSION FROM THE MOLECULAR CLOUD INTERACTING SUPERNOVA REMNANT G349.7+0.2

We performed Herschel HIFI, PACS, and SPIRE observations toward the molecular cloud interacting supernova remnant G349.7+0.2. An extremely broad emission line was detected at 557 GHz from the ground state transition 1{sub 10}-1{sub 01} of ortho-water. This water line can be separated into three velocity components with widths of 144, 27, and 4 km s{sup −1}. The 144 km s{sup −1} component is the broadest water line detected to date in the literature. This extremely broad line width shows the importance of probing shock dynamics. PACS observations revealed three additional ortho-water lines, as well as numerous high-J carbon monoxide (CO) lines. No para-water lines were detected. The extremely broad water line is indicative of a high velocity shock, which is supported by the observed CO rotational diagram that was reproduced with a J-shock model with a density of 10{sup 4} cm{sup −3} and a shock velocity of 80 km s{sup −1}. Two far-infrared fine-structure lines, [O i] at 145 μm and [C ii] line at 157 μm, are also consistent with the high velocity J-shock model. The extremely broad water line could be simply from short-lived molecules that have not been destroyed in high velocity J-shocks; however, it may be from more complicated geometry such as high-velocity water bullets or a shell expanding in high velocity. We estimate the CO and H{sub 2}O densities, column densities, and temperatures by comparison with RADEX and detailed shock models.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of the KSC-ER Cloud-to-Ground Lightning Surveillance System (CGLSS) and the U.S. National Lightning Detection Network(TradeMark)(NLDN)

The NASA Kennedy Space Center (KSC) and Air Force Eastern Range (ER) use data from two cloud-to-ground lightning detection networks, CGLSS and NLDN, during ground and launch operations at the KSC-ER. For these applications, it is very important to understand the location accuracy and detection efficiency of each network near the KSC-ER. If a cloud-to-ground (CG) lightning strike is missed or mis-located by even a small amount, the result could have significant safety implications, require expensive retests, or create unnecessary delays or scrubs in launches. Therefore, it is important to understand the performance of each lightning detection system in considerable detail. To evaluate recent upgrades in the CGLSS sensors in 2000 and the entire NLDN in 2002- 2003, we have compared. measurements provided by these independent networks in the summers of 2005 and 2006. Our analyses have focused on the fraction of first strokes reported individually and in-common by each network (flash detection efficiency), the spatial separation between the strike points reported by both networks (relative location accuracy), and the values of the estimated peak current, Ip, reported by each network. The results within 100 km of the KSC-ER show that the networks produce very similar values of Ip (except for a small scaling difference) and that the relative location accuracy is consistent with model estimates that give median values of 200-300m for the CGLSS and 600-700m for the NLDN in the region of the KSC-ER. Because of differences in the network geometries and sensor gains, the NLDN does not report 10-20% of the flashes that have a low Ip (2 kA < |Ip| < 16 kA), both networks report 99 % of the flashes that have intermediate values of Ip (16< |Ip| < 50 kA), and the CGLSS fails to report 20-30% of the high-current events (|Ip| >=0 kA).

Ward, Jennifer G.↗

Using OMI Observations to Measure Aerosol Absorption of Biomass Burning Aerosols Above Clouds

The presence of absorbing aerosol layers above clouds is unambiguously detected by the TOMS/OMI UV Aerosol Index (AI) that uses satellite observations at two near-UV channels. A sensitivity study using radiative transfer calculations shows that the AI signal of resulting from the presence of aerosols above clouds is mainly driven by the aerosol absorption optical depth and the optical depth of the underlying cloud. Based on these results, an inversion algorithm has been developed to retrieve the aerosol optical depth (AOD) of aerosol layers above clouds. In this presentation we will discuss the sensitivity analysis, describe the retrieval approach, and present results of applications of the retrieval method to OMI observations over the South Atlantic Ocean. Preliminary error analyses, to be discussed, indicate that the AOD can be underestimated (up to -30%) or overestimated (up to 60%) depending on algorithmic assumptions.

Torres, Omar↗

An Open, Cloud-Based Platform for Whole-Building Fault Detection and Diagnostics

Small commercial buildings in the U.S. waste an estimated 300 Trillion BTU (approximately $6 billion in energy costs) annually due to faults, but lack cost-effective automated fault detection and diagnosis (AFDD) tools. NREL and GE Global Research are partnering to develop hybrid AFDD algorithms tailored to the unique needs of small commercial buildings (</=10,000 sq. ft.). The approach combines physics-based energy modeling tools with state-of-the-art machine learning algorithms to enable diagnostics using modeled input data. NREL, in partnership with Purdue University, has adapted DOE's physics-based modeling software EnergyPlus and OpenStudio to simulate common building faults. Cloud-based implementations of these physics-based models were used to generate data for multiple climate zones. The data were then used to train machine learning algorithms, such as those available in GE's Predix platform, to detect and diagnose building faults. Key features of the system including the automated, cloud-implementation of EnergyPlus, genetic algorithms for automated model feature selection, multiclass detection and diagnosis models, and anomaly detection algorithms will be presented.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Detection of CO emission from massive molecular clouds in the inner disk of M31

Faint emission in the CO(1-0) and CO(2-1) spectral lines at mm wavelengths has been discovered from dark dust clouds in the inner disk of M31. These dust clouds are located in regions of the galaxy where there is little evidence of star-forming activity. The CO emission from these clouds is resolved, and comes from roughly the same area covered by the dust clouds. The line profile widths and cloud sizes imply cloud masses typical for giant molecular clouds (GMCs) in the Galaxy, but the observed surface brightnesses are only a few tenths of a K, and the typical CO(1-0) luminosities are a factor of about 10 smaller than those of Galactic GMCs of the same size and velocity line width. The CO(2-1)/CO(1-0) line ratios are very low, suggesting subthermal excitation, and precluding use of this ratio alone to determine the kinetic temperature. However, there are indications that the kinetic temperatures are significantly lower than the values of 10-30 K typical for Galactic GMCs, and may be close to the 2.7 K cosmic background.

Allen, Ronald J.↗