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DOE OSTI2016

On the controls of daytime precipitation in the Amazonian dry season

The Amazon plays an important role in the global energy and hydrological budgets. The precipitation during the dry season (June–September) plays a critical role in maintaining the extent of the rain forest. The deployment of the first Atmospheric Radiation Measurement (ARM) Mobile Facility (AMF-1) in the context of the Green Ocean Amazon (GOAmazon) field campaign at Manacapuru, Brazil, provided comprehensive measurements of surface, cloud, precipitation, radiation, and thermodynamic properties for two complete dry seasons (2014 and 2015). The precipitation events occurring during the nighttime were associated with propagating storm systems (nonlocal effects), while the daytime precipitation events were primarily a result of local land–atmosphere interactions. During the two dry seasons, precipitation was recorded at the surface on 106 days (43%) from 158 rain events with 82 daytime precipitation events occurring on 64 days (60.37%). Detailed comparisons between the diurnal cycles of surface and profile properties between days with and without daytime precipitation suggested the increased moisture at low and midlevels to be responsible for lowering the lifting condensation level, reducing convective inhibition and entrainment, and thus triggering the transition from shallow to deep convection. Although the monthly accumulated rainfall decreased during the progression of the dry season, the contribution of daytime precipitation to it increased, suggesting the decrease to be mainly due to reduction in propagating squall lines. Lastly, the control of daytime precipitation during the dry season on large-scale moisture advection above the boundary layer and the total rainfall on propagating squall lines suggests that coarse-resolution models should be able to accurately simulate the dry season precipitation over the Amazon basin.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Scaling Optimal Allocation of Cloud Resources Using Lagrange Relaxation

The rapid growth of Cloud Computing (CC) has increased the variety of computing resources, storage, and communication services that pose significant new challenges for the efficient use of cloud resources. The cost-efficient allocation of cloud resources has become a decisive premise for the adoption of CC services. The cost-efficient selection and scheduling of these resources to meet the demands of a scientific workflow is a challenging problem that is exacerbated by the inclusion of multiple CC providers. In this paper, we present a novel strategy for the cost-efficient selection of CC resources using Lagrange relaxation. Our approach is based on preselection of resources and demand decomposition to create a series of smaller sub-problems, which allow the estimation of the best cost-structures and selection of CC service providers for a subset of the time period of the planning horizon. Decomposition of the demand is achieved through the boundary analysis of a continuous relaxation of the problem. Using the metrics defined in terms of the cost and time of completion, we demonstrate excellent performance in relation to optimal solutions. Our method reduced the computational time from hours to seconds for a representative 36-month problem and provided high-quality solutions (< 0.05% relative error). Given the importance of selecting resources and scheduling complex scientific workflows, we believe that this novel strategy will be beneficial for many researchers and users of cloud computing resources.

De La Torre, Luis↗

DOE OSTI2021

Low-Level Mesoscale and Cloud-Scale Interactions Promoting Deep Convection Initiation

Data from scanning radars, radiosondes, and vertical profilers deployed during three field campaigns are analyzed to study interactions between cloud-scale updrafts associated with initiating deep moist convection and the surrounding environment. Three cases are analyzed in which the radar networks permitted dual-Doppler wind retrievals in clear air preceding and during the onset of surface precipitation. These observations capture the evolution of (i) the mesoscale and boundary layer flow, and (ii) low-level updrafts associated with deep moist convection initiation (CI) events yielding sustained or short-lived precipitating storms. The elimination of convective inhibition did not distinguish between sustained and unsustained CI events, though the vertical distribution of convective available potential energy may have played a role. The clearest signal differentiating the initiation of sustained versus unsustained precipitating deep convection was the depth of the low-level horizontal wind convergence associated with the mesoscale flow feature triggering CI, a sharp surface wind shift boundary, or orographic upslope flow. The depth of the boundary layer relative to the height of the LFC failed to be a consistent indicator of CI potential. Widths of the earliest detectable low-level updrafts associated with sustained precipitating deep convection were ~3–5 km, larger than updrafts associated with surrounding boundary layer turbulence (~1–3 km wide). It is hypothesized that updrafts of this larger size are important for initiating cells to survive the destructive effects of buoyancy dilution via entrainment.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Turbulent properties from Doppler lidar

Permanent and mobile facilities deployed by the ARM program cover a wide range of climatic regions, with a suite of active remote-sensing of cloud and aerosol profiles complemented by comprehensive in-situ measurements of the chemical, physical and optical properties of aerosol measured at the surface. To be able to fully exploit these datasets requires an understanding of the transport from the surface and within the atmosphere, especially within the planetary boundary layer. This requires a method of identifying when the surface and atmosphere are dynamically-linked. Determining the state of the boundary layer, and defining a well-mixed boundary-layer, is therefore suitably described in terms of mixing; here, we will assume that mixing essentially means turbulent mixing. This necessitates accurate measurements of the winds and turbulent mixing in the atmosphere. Doppler lidar is an excellent tool for observing turbulent properties, and ARM has deployed commercially available Doppler lidars at many of the fixed and mobile facilities. Doppler lidars have been shown to provide accurate retrievals of wind and turbulent properties within the boundary layer , however, robust characterization and calculation of the Doppler lidar measurement uncertainties is required before deriving higher level data products.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

The characteristics of atmospheric boundary layer height over the Arctic Ocean during MOSAiC

The important roles that the atmospheric boundary layer (ABL) plays in the central Arctic climate system have been recognized, but the atmospheric boundary layer height (ABLH), defined as the layer of continuous turbulence adjacent to the surface, has rarely been investigated. Using a year-round radiosonde dataset during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition, we improve a Richardson-number-based algorithm that takes cloud effects into consideration and subsequently analyze the characteristics and variability of the ABLH over the Arctic Ocean. The results reveal that the annual cycle is clearly characterized by a distinct peak in May and two respective minima in January and July. This annual variation in the ABLH is primarily controlled by the evolution of the ABL thermal structure. Temperature inversions in the winter and summer are intensified by seasonal radiative cooling and warm-air advection with the surface temperature constrained by melting, respectively, leading to the low ABLH at these times. Meteorological and turbulence variables also play a significant role in ABLH variation, including the near-surface potential temperature gradient, friction velocity, and turbulent kinetic energy (TKE) dissipation rate. In addition, the MOSAiC ABLH is more suppressed than the ABLH during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment in the summer, which indicates that there is large variability in the Arctic ABL structure during the summer melting season.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

Evaluation of ERTS imagery for spectral geological mapping in diverse terranes of New York State

The author has identified the following significant results. Preliminary visual examination of film positives of thirty ERTS-1 scenes obtained over New York State and adjacent areas indicates the following: (1) sixty percent of the imagery has a cloud cover of 70-100 percent, twenty-five percent has a cloud cover of 0-30 percent, and the remainder has a cover of 40-65 percent; (2) on the useable imagery, the spectral lines which may turn out to be geologically-linked totals as follows: spectral linears, 5200 km; broadly curved lines (spectral curvilinears), 700 km; major forest boundaries, 3100 km; areas with spectral geological fabric, 3100 sgkm. In the central and northwest Adirondacks, known lineaments and faults were subtracted from the spectral linears leaving a residue which totals 160 km in the central Adirondacks and 230 km in the northwest Adirondacks. It must be emphasized that these are spectral linears which have not yet been checked out against any ground truth except geological.

Isachsen, Y. W.↗

NASA NTRS1981

Two-stream Maxwellian kinetic theory of cloud droplet growth by condensation

A new growth rate formula (NGRF) is developed for the rate of growth of cloud droplets by condensation. The theory used is a modification of the Lees-Shankar theory in which the two-stream Maxwellian distribution function of Lees is used in Maxwell's method of moments to determine the transport of water vapor to and heat away from the droplet. Boundary conditions at the droplet are the usual conditions set in terms of accommodation coefficients, and the solution passes smoothly into diffusion flow in the far region. Comparisons are given between NGRF and the conventional formula showing close agreement (approximately 0.1%) for large radii with significant difference (approximately 5%) for small radii (not greater than 1 micron). Growth times for haze droplets in a Laktionov chamber are computed.

Robinson, N. F.↗

NASA NTRS2007

Impacts of Urbanization in the Coastal Tropical City of San Juan, Puerto Rico

Urban sprawl in tropical locations is rapidly accelerating and it is more evident in islands where a large percentage of the population resides along the coasts. This paper focuses on the analysis of the impacts of land use and land cover for urbanization in the tropical coastal city of San Juan, in the Caribbean island of Puerto Rico. A mesoscale numerical model, the Regional Atmospheric Modeling System (RAMS), is used to study the impacts of land use for urbanization in the environment including specific characteristics of the urban heat island in the San Juan Metropolitan Area (SJMA), one of the most noticeable urban cores of the Caribbean. The research also makes use of the observations obtained during the airborne San Juan Atlas Mission. Surface and rawinsonde data from the mission are used to validate the atmospheric model yielding satisfactory results. Airborne high resolution remote sensing data are used to update the model's surface characteristics in order to obtain a more accurate and detailed configuration of the SJMA and perform a climate impact analysis based on land cover/land use (LCLU) changes. The impact analysis showed that the presence of the urban landscape of San Juan has an impact reflected in higher air temperatures over the area occupied by the city, with positive values of up to 2.5 C, for the simulations that have specified urban LCLU indexes in the model's bottom boundary. One interesting result of the impact analysis was the finding of a precipitation disturbance shown as a difference in total accumulated rainfall between the present urban landscape and with a potential natural vegetation, apparently induced by the presence of the urban area. Results indicate that the urban enhanced cloud formation and precipitation development occur mainly downwind of the city, including the accumulated precipitation. This spatial pattern can be explained by the presence of a larger urbanized area in the southwest sector of the city, and of the approaching northeasterly trade winds. No significant impacts were found in the sea breeze patterns of the city.

Comarazamy, Daniel E.↗

NASA NTRS2012

A Review of Low Frequency Electromagnetic Wave Phenomena Related to Tropospheric-Ionospheric Coupling Mechanisms

Investigation of coupling mechanisms between the troposphere and the ionosphere requires a multidisciplinary approach involving several branches of atmospheric sciences, from meteorology, atmospheric chemistry, and fulminology to aeronomy, plasma physics, and space weather. In this work, we review low frequency electromagnetic wave propagation in the Earth-ionosphere cavity from a troposphere-ionosphere coupling perspective. We discuss electromagnetic wave generation, propagation, and resonance phenomena, considering atmospheric, ionospheric and magnetospheric sources, from lightning and transient luminous events at low altitude to Alfven waves and particle precipitation related to solar and magnetospheric processes. We review in situ ionospheric processes as well as surface and space weather phenomena that drive troposphere-ionosphere dynamics. Effects of aerosols, water vapor distribution, thermodynamic parameters, and cloud charge separation and electrification processes on atmospheric electricity and electromagnetic waves are reviewed. We also briefly revisit ionospheric irregularities such as spread-F and explosive spread-F, sporadic-E, traveling ionospheric disturbances, Trimpi effect, and hiss and plasma turbulence. Regarding the role of the lower boundary of the cavity, we review transient surface phenomena, including seismic activity, earthquakes, volcanic processes and dust electrification. The role of surface and atmospheric gravity waves in ionospheric dynamics is also briefly addressed. We summarize analytical and numerical tools and techniques to model low frequency electromagnetic wave propagation and solving inverse problems and summarize in a final section a few challenging subjects that are important for a better understanding of tropospheric-ionospheric coupling mechanisms.

Simoes, Fernando↗

DOE OSTI2018

Background Free‐Tropospheric Ice Nucleating Particle Concentrations at Mixed‐Phase Cloud Conditions

Abstract Clouds containing ice are vital for precipitation formation and are important in determining the Earth's radiative budget. However, primary formation of ice in clouds is not fully understood. In the presence of ice nucleating particles (INPs), the phase change to ice is promoted, but identification and quantification of INPs in a natural environment remains challenging because of their low numbers. In this paper, we quantify INP number concentrations in the free troposphere (FT) as measured at the High Altitude Research Station Jungfraujoch (JFJ), during the winter, spring, and summer of the years 2014–2017. INPs were measured at conditions relevant for mixed‐phase cloud formation at T = 241/242 K. To date, this is the longest timeline of semiregular measurements akin to online INP monitoring at this site and sampling conditions. We find that INP concentrations in the background FT are on average capped at 10/stdL (liter of air at standard conditions [ T = 273 K and p = 1013 hPa]) with an interquartile range of 0.4–9.6/stdL, as compared to measurements during times when other air mass origins (e.g., Sahara or marine boundary layer) prevailed. Elevated concentrations were measured in the field campaigns of 2016, which might be due to enhanced influence from Saharan dust and marine boundary layer air arriving at the JFJ. The upper limit of INP concentrations in the background FT is supported by measurements performed at similar conditions, but at different locations in the FT, where we find INP concentrations to be below 13/stdL most of the time.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2014

Introducing Multisensor Satellite Radiance-Based Evaluation for Regional Earth System Modeling

Earth System modeling has become more complex, and its evaluation using satellite data has also become more difficult due to model and data diversity. Therefore, the fundamental methodology of using satellite direct measurements with instrumental simulators should be addressed especially for modeling community members lacking a solid background of radiative transfer and scattering theory. This manuscript introduces principles of multisatellite, multisensor radiance-based evaluation methods for a fully coupled regional Earth System model: NASA-Unified Weather Research and Forecasting (NU-WRF) model. We use a NU-WRF case study simulation over West Africa as an example of evaluating aerosol-cloud-precipitation-land processes with various satellite observations. NU-WRF-simulated geophysical parameters are converted to the satellite-observable raw radiance and backscatter under nearly consistent physics assumptions via the multisensor satellite simulator, the Goddard Satellite Data Simulator Unit. We present varied examples of simple yet robust methods that characterize forecast errors and model physics biases through the spatial and statistical interpretation of various satellite raw signals: infrared brightness temperature (Tb) for surface skin temperature and cloud top temperature, microwave Tb for precipitation ice and surface flooding, and radar and lidar backscatter for aerosol-cloud profiling simultaneously. Because raw satellite signals integrate many sources of geophysical information, we demonstrate user-defined thresholds and a simple statistical process to facilitate evaluations, including the infrared-microwave-based cloud types and lidar/radar-based profile classifications.

Planetary Boundary Layer↗

DOE OSTI2022

Charge carrier motion and effect of fixed oxide charge in a microstructured silicon radiation detector

Signal formation in a microstructured semiconductor neutron detector is more complex than in planar diode geometry. Three-dimensional microstructures are laterally smaller than the ionization cloud length, and the electric fields may be weak enough to exhibit plasma time effects. This work is the first detailed treatment of charge carrier motion in these complex semiconductor devices to replicate the time profile and signal magnitude. Simulations were performed using COMSOL Multiphysics to investigate various parameters that affect the propagation of the charge cloud. It was observed that the size of the simulated three-dimensional structure had an impact on the induced current pulse, indicating the importance of simulation geometry optimization to accurately simulate charge cloud expansion. COMSOL Multiphysics was used to replicate accurate charge creation profiles using energy deposition information imported from radiation transport codes. A detailed simulation methodology is presented to benchmark preamplifier event pulses along with complexities in modeling the charge carrier motion along the etched microstructured trenches with Si–SiO 2 boundary conditions, including fixed oxide charge and interface trapping.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1998

Upper tropospheric water vapor: A field campaign of two Raman lidars, Airborne hygrometers, and Radiosondes

Water vapor in the atmosphere plays an important role in radiative transfer and the process of radiative balance so critical for understanding global change. It is the principal ingredient in cloud formation, one of the most difficult atmospheric processes to model, and the most variable component of the Earth-atmosphere albedo. And as a free molecule, it is the most active infrared absorber and emitter, thus, the most important greenhouse gas. The radiative impact of water vapor is important at all levels of the atmosphere. Even though moisture decreases by several orders-of-magnitude from the Earth's surface to the tropopause, recent research has shown that, from a radiative standpoint, a small percentage change in water vapor at any level is nearly equivalent. Therefore accurate and precise measurements of this important atmospheric constituent are needed at all levels to evaluate the full radiative impact. The need for improved measurements in the upper troposphere is particularly important because of the generally hostile (very dry and cold) conditions encountered. Because of the importance of water vapor to the understanding of radiative transfer, the Department of Energy's Atmospheric Radiation Measurements (ARM) program initiated a series of measurement campaigns at the Cloud And Radiation Testbed (CART) site in Oklahoma, especially focused on atmospheric water vapor. Three water vapor intensive observation period (water vapor IOP) campaigns were planned. Two of the water vapor IOP campaigns have been completed: the first IOP was held during the fall of 1996 with a focus on boundary layer water vapor measurements, and the second was conducted during the fall of 1997 with a focus on both boundary layer moisture e and moisture in the upper troposphere. This paper presents a review of the intercomparisons of water vapor measurements in the upper troposphere aquired during the second water vapor IOP. Data to be presented include water vapor measurements ements from: two Raman Lidars, the NASA Goddard Scanning Raman Lidar (SRL) and the CART Raman Lidar (CARL), a number of Vaisala radiosondes launched during the IOP campaign, and a dew point hygrometer flown on the University of North Dakota Cessna Citation Aircraft.

Melfi, S. Harvey↗

NASA NTRS2007

A Numerical Study of the Urban Heat Island in the Coastal Tropical City of San Juan, Puerto Rico: Model Validation and Impacts of LCLU Changes

Urban sprawls in tropical locations are rapidly accelerating and it is more evident in islands where a large percentage of the population resides along the coasts. This paper focuses on the analysis of the impacts of land use and land cover for urbanization in the tropical coastal city of San Juan, in the tropical island of Puerto Rico. A mesoscale numerical model, the Regional Atmospheric Modeling System (RAMS), is used to study specific characteristics and patterns of the urban heat island in the San Juan Metropolitan Area (SJMA), the most noticeable urban core of the Caribbean. The research present in this paper makes use of the observations obtained during the airborne San Juan Atlas Mission in two ways. First, surface and rawinsonde data are used to validate the atmospheric model yielding satisfactory results. Second, airborne remote sensing information is used to update the model's surface characteristics to obtain a detailed configuration of the SJMA in order to perform the LCLU changes impact analysis. This analysis showed that the presence of San Juan has an impact reflected in higher air temperatures over the area occupied by the city, with positive values of up to 2.5 C, for the simulations that have specified urban LCLU indexes in the bottom boundary. One interesting result of the impact analysis was the finding of a precipitation disturbance shown as a difference in total accumulated rainfall between simulation with the city and with a potential natural vegetation induced by the presence of the urban area. Model results indicate that the urban-induced cloud formation and precipitation development occur mainly downwind of the city, including the accumulated precipitation. This spatial pattern can be explained by the presence of a-larger urbanized area in the southwest sector of the city, and of the approaching northeasterly trade winds.

Comarazamy, Daniel E.↗

NASA NTRS2007

Impacts of Urbanization in the Coastal Tropical City of San Juan, Puerto Rico

Urban sprawl in tropical locations is rapidly accelerating and it is more evident in islands where a large percentage of the population resides along the coasts. This paper focuses on the analysis of the impacts of land use and land cover for urbanization in the tropical coastal city of San Juan, in the Caribbean island of Puerto Rico. A mesoscale numerical model, the Regional Atmospheric Modeling System (RAMS), is used to study the impacts of land use for urbanization in the environment including specific characteristics of the urban heat island in the San Juan Metropolitan Area (SJMA), one of the most noticeable urban cores of the Caribbean. The research also makes use of the observations obtained during the airborne San Juan Atlas Mission. Surface and raw insonde data from the mission are used to validate the atmospheric model yielding satisfactory results. Airborne high resolution remote sensing data are used to update the model's surface characteristics in order to obtain a more accurate and detailed configuration of the SJMA and perform a climate impact analysis based on land cover/land use (LCLU) changes. The impact analysis showed that the presence of the urban landscape of San Juan has an impact reflected in higher air temperatures over the area occupied by the city, with positive values of up to 2.5 degrees C, for the simulations that have specified urban LCLU indexes in the model's bottom boundary. One interesting result of the impact analysis was the finding of a precipitation disturbance shown as a difference in total accumulated rainfall between the present urban landscape and with a potential natural vegetation, apparently induced by the presence of the urban area. Results indicate that the urban-enhanced cloud formation and precipitation development occur mainly downwind of the city, including the accumulated precipitation. This spatial pattern can be explained by the presence of a larger urbanized area in the southwest sector of the city, and of the approaching northeasterly trade winds.

Comarazamy, Daniel E.↗

DOE OSTI2026

The Spatial and Temporal Variability of the Clear Convective Boundary Layer at the ARM SGP Supersite

The convective boundary layer (CBL), also known as the mixing layer, constitutes the critical lower segment of the atmosphere that significantly influences daily human activities. The growing demand for precise weather forecasts is driven by the requirements of agriculture, transportation, and routine societal functions. Here, to enhance understanding of the CBL, this study investigates the spatiotemporal variability in the CBL and its controlling factors using four-year Doppler lidar, surface flux, and profiling measurements at five ARM Southern Great Plains sites within a 100 km radius. This investigation utilizes data collected exclusively under clear-sky conditions or scattered low-cloud conditions. Results reveal significant spatial differences in CBL evolutions. Daily mixing layer heights (MLHs) vary up to 1 km (30% of the mean) in late afternoon. There is a clear east–west contrast: western sites (C1, E32, E37) exhibit higher summer MLH (1.9–2.1 km) and vertical velocity variances (1.0–1.2 m 2 s −2 ) than eastern sites (1.6–1.8 km), reversing in winter. Temporally, the MLH peaks at 70% of the sunrise–sunset interval, the lagging heat flux (HF) peaks at 50%; and the seasonal MLH maxima lag the HF by approximately one month, influenced by nighttime PBL (planetary boundary layer) properties. The HF and lower tropospheric stability are the main factors of influence for the CBL, but site-specific dependencies highlight the critical roles of local factors, underscoring the need for including them in CBL modeling.

ARM SGP site↗

DOE OSTI2025

Biomass burning aerosol radiative effects in the Southeast Atlantic depend strongly on meteorological forcing method

Biomass burning aerosols (BBAs) from African fires may strongly impact Earth’s radiation budget in the southeast Atlantic (SEA), but the sign and magnitude of the overall radiative effect (RE) remain uncertain. Aerosol–climate models are needed to separately quantify direct, indirect, and semi-direct REs. Here, we evaluate improved simulations with the UK Met Office's Unified Model and explore REs resulting from various methods used to match observed meteorology (nudging or running forecasts reinitialized at different frequencies). REs are calculated as differences in radiative fluxes between simulations with and without smoke emissions and with and without aerosol absorption. All model setups agree on net warming for the SEA dominated by the direct effect. Simulated smoke, clouds, and the direct effect agree better with observations than previous studies using the same model, though biases in aerosol extinction and liquid water path remain. Changes in cloud droplet number concentration due to BBA self-lofting influence how cleanly we can separate cloud effects into semi-direct and indirect effects. Total RE, which remains unaffected, ranges from +3.0 to +7.9 W m −2 . The 4.9 W m −2 spread arises mainly from simulated semi-direct effects. Forecasts three days long or less probably do not allow time for plausible differences in boundary layer properties due to semi-direct effects to accumulate. Free running simulations with and without smoke accumulate differences in meteorology that are likely spurious “butterfly effects”. We recommend future research quantifying BBA REs over weeks to months to use meteorological forcing techniques that allow aerosol absorption to affect the boundary layer.

Giuffrida, Eric [Carnegie Mellon University, Pitts↗

NASA NTRS1974

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays in a certain sense the role of the thermodynamic potential for compressible adiabatic flow. The stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and temperature to be generalized velocities. In the fluid context, the definition of proper-time differentiation involves the fluid velocity expressed in terms of three particle identity parameters. The pressure function is then converted into a functional which is the Lagrangian density of the variational principle. Being also a minimum principle, the variational principle provides a means for comparing the relative stability of different flows. For boundary conditions with a high degree of symmetry, as in the case of a uniformly expanding spherical gas box, the most stable flow is a rectilinear flow for which the world-trajectory of each particle is a straight line. Since the behavior of the interior of a freely expanding cosmic cloud may be expected to be similar to that of the fluid in the spherical box of gas, this suggests that the cosmic principle is a consequence of the laws of thermodynamics, rather than just an ad hoc postulate.

Schmid, L. A.↗