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At least 937 records · Page 52

Role of Longwave Cloud-Radiation Feedback in the Simulation of the Madden-Julian Oscillation

The role of the cloud-radiation interaction in the simulation of the Madden-Julian oscillation (MJO) is investigated. A special focus is on the enhancement of column-integrated diabatic heating due to the greenhouse effects of clouds and moisture in the region of anomalous convection. The degree of this enhancement, the greenhouse enhancement factor (GEF), is measured at different precipitation anomaly regimes as the negative ratio of anomalous outgoing longwave radiation to anomalous precipitation. Observations show that the GEF varies significantly with precipitation anomaly and with the MJO cycle. The greenhouse enhancement is greater in weak precipitation anomaly regimes and its effectiveness decreases monotonically with increasing precipitation anomaly. The GEF also amplifies locally when convection is strengthened in association with the MJO, especially in the weak precipitation anomaly regime (less than 5 mm day(exp -1)). A robust statistical relationship is found among CMIP5 climate model simulations between the GEF and the MJO simulation fidelity. Models that simulate a stronger MJO also simulate a greater GEF, especially in the weak precipitation anomaly regime (less than 5 mm day(exp -1)). Models with a greater GEF in the strong precipitation anomaly regime (greater than 30 mm day(-1)) represent a slightly slower MJO propagation speed. Many models that lack the MJO underestimate the GEF in general and in particular in the weak precipitation anomaly regime. The results herein highlight that the cloud-radiation interaction is a crucial process for climate models to correctly represent the MJO.

Clouds↗

TPSAS-NF1676L-19256-DND

The NASA/GEWEX (Global Energy and Water Exchanges project) Surface Radiation Budget (SRB) project produces longwave and shortwave radiative fluxes for the surface and top-of-atmosphere (TOA) (see, Stackhouse et al., 2011, GEWEX News). The primary inputs of cloud and meteorology data have been undergoing improvements in quality and spatial and temporal resolution. In anticipation of the release of these data, the SRB longwave flux algorithm has been updated both to accommodate these data and to improve the algorithm used in deriving radiative fluxes. Changes in the inputs and algorithm are as follows: - Synchronized algorithm with version used by NASA CERES (Rose et al. 2006). - Atmospheric aerosols were added. - Beta version of ISCCP H cloud properties used. - Beta version of ISCCP nnHIRS temperature and humidity used. - Option of using a newly derived beta Princeton land surface temperature and diurnal Seaflux sea surface temperature as surface skin temperature added - Updated ozone profile with GISS ozone and MEaSUREs GOZCARDS. - Updated maps of surface topography, vegetation type, and snow/ice by ISCCP. The beta GLW v4 IP has enhanced the output fluxes by adding pristine-sky (no clouds or aerosols) fluxes. The new version also computes fluxes at selected atmospheric levels (including the tropopause) rather than just at the surface and TOA. The purpose of this study is to explore the effect of the above changes on the surface and top-of-atmosphere fluxes. These fluxes are compared to the previous version (release 3.1). We show preliminary results for the mid-seasonal months of 2007.

J Colleen Mikovitz↗

Sensitivity Study for Forecasting Variables of WRF-Solar Using a Tangent Linear Approach

Integrating solar generation in recent years has highlighted the need for improved accuracy in predicting solar power. Confidence in solar power forecasting can be achieved by designing an ensemble that provides reliable probabilistic information for solar radiation with reduced uncertainty and error. Ideally, ensemble members are created through the optimized perturbation of the initial conditions in numerical weather prediction (NWP) models. Tangent linear models are capable of efficiently investigating the sensitivity of solar radiation to model input parameters because they do not require individual perturbation of each variable. This sensitivity study using tangent linear models provide us the capability to identify the right variables to perturb in an ensemble prediction system. In this study, we developed tangent linear models for WRF-Solar modules that directly impact the computation of solar radiation and the simulation of cloud formation and dissipation including the Fast All-sky Model for Solar Applications (FARMS), the Noah land surface model (LSM), the Thompson microphysics, the Mello-Yamada-Nakanishi-Niino (MYNN) boundary layer parameterization, and the Deng scheme for a shallow-convection parameterization. A sensitivity analysis was conducted under various scenarios based on satellite observations and model simulations from the National Solar Radiation Data Base (NSRDB) and WRF-Solar, respectively. Critical forecasting variables that are highly sensitive to the forecasting of global horizontal irradiance (GHI), direct normal irradiance (DNI), cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes were determined using the relevant WRF-Solar module. This study will be used as a guidance on future research leading to high-quality probabilistic solar forecasting. In this presentation, we discuss the validation of tangent linear approach for WRF-Solar modules and illustrate how the sensitivity results are valuable in the improvement of probabilistic solar prediction.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Towards Lightweight Data Integration Using Multi-Workflow Provenance and Data Observability

Modern large-scale scientific discovery requires multidisciplinary collaboration across diverse computing facilities, including High Performance Computing (HPC) machines and the Edge-to-Cloud continuum. Integrated data analysis plays a crucial role in scientific discovery, especially in the current AI era, by enabling Responsible AI development, FAIR, Reproducibility, and User Steering. However, the heterogeneous nature of science poses challenges such as dealing with multiple supporting tools, cross-facility environments, and efficient HPC execution. Building on data observability, adapter system design, and provenance, we propose MIDA: an approach for lightweight runtime Multi-workflow Integrated Data Analysis. MIDA defines data observability strategies and adaptability methods for various parallel systems and machine learning tools. With observability, it intercepts the dataflows in the background without requiring instrumentation while integrating domain, provenance, and telemetry data at runtime into a unified database ready for user steering queries. We conduct experiments showing end-to-end multi-workflow analysis integrating data from Dask and MLFlow in a real distributed deep learning use case for materials science that runs on multiple environments with up to 276 GPUs in parallel. We show near-zero overhead running up to 100,000 tasks on 1,680 CPU cores on the Summit supercomputer.

Santos Souza, Renan↗

North Atlantic Aerosol Radiative Impacts Based on Satellite Measurements and Aerosol Intensive Properties from TARFOX and ACE-2

We estimate the impact of North Atlantic aerosols on the net shortwave flux at the tropopause by combining maps of satellite-derived aerosol optical depth (AOD) with model aerosol properties. We exclude African dust, primarily by restricting latitudes to 25-60 N. Aerosol properties were determined via column closure analyses in two recent experiments, TARFOX and ACE 2. The analyses use in situ measurements of aerosol composition and air- and ship-borne sunphotometer measurements of AOD spectra. The resulting aerosol model yields computed flux sensitivities (dFlux/dAOD) that agree with measurements by airborne flux radiometers in TARFOX. It has a midvisible single-scattering albedo of 0.9, which is in the range obtained from in situ measurements of aerosol scattering and absorption in both TARFOX and ACE 2. Combining seasonal maps of AVHRR-derived midvisible AOD with the aerosol model yields maps of 24-hour average net radiative flux changes at the tropopause. For cloud-free conditions, results range from -9 W/sq m near the eastern US coastline in the summer to -1 W/sq m in the mid-Atlantic during winter; the regional annual average is -3.5 W/sq m. Using a non- absorbing aerosol model increases these values by about 30%. We estimate the effect of clouds using ISCCP cloud-fraction maps. Because ISCCP midlatitude North Atlantic cloud fractions are relatively large, they greatly reduce the computed aerosol-induced flux changes. For example, the regional annual average decreases from -3.5 W/sq m to -0.8 W/sq m. We compare results to previous model calculations for a variety of aerosol types.

Russell, Philip B.↗

North Atlantic Aerosol Radiative Effects Based on Satellite Measurements and Aerosol Intensive Properties from TARFOX and ACE-2

We estimate the impact of North Atlantic aerosols on the net shortwave flux at the tropopause by combining maps of satellite-derived aerosol optical depth (AOD) with model aerosol properties. We exclude African dust, primarily by restricting latitudes to 25-60 N. Aerosol properties were determined via column closure analyses in two recent experiments, TARFOX and ACE 2. The analyses use in situ measurements of aerosol composition and air- and ship-borne sunphotometer measurements of AOD spectra. The resulting aerosol model yields computed flux sensitivities (dFlux/dAOD) that agree with measurements by airborne flux radiometers in TARFOX. It has a midvisible single-scattering albedo of 0.9, which is in the range obtained from in situ measurements of aerosol scattering and absorption in both TARFOX and ACE 2. Combining seasonal maps of AVHRR-derived midvisible AOD with the aerosol model yields maps of 24-hour average net radiative flux changes at the tropopause. For cloud-free conditions, results range from -9 W/sq m near the eastern US coastline in the summer to -1 W/sq m in the mid-Atlantic during winter; the regional annual average is -3.5 W/sq m. Using a non- absorbing aerosol model increases these values by about 30%. We estimate the effect of clouds using ISCCP cloud-fraction maps. Because ISCCP midlatitude North Atlantic cloud fractions are relatively large, they greatly reduce the computed aerosol-induced flux changes. For example, the regional annual average decreases from -3.5 W/sq m to -0.8 W/sq m. We compare results to previous model calculations for a variety of aerosol types.

Bergstrom, Robert W.↗

Surface Irradiances of Edition 4.0 Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Data Product

The algorithm to produce the Clouds and the Earth’s Radiant Energy System (CERES) Edition 4.0 (Ed4) Energy Balanced and Filled (EBAF)-surface data product is explained. The algorithm forces computed topof- atmosphere (TOA) irradiances to match with Ed4 EBAF-TOA irradiances by adjusting surface, cloud, and atmospheric properties. Surface irradiances are subsequently adjusted using radiative kernels. The adjustment process is composed of two parts: bias correction and Lagrange multiplier. The bias in temperature and specific humidity between 200 and 500 hPa used for the irradiance computation is corrected based on observations by Atmospheric Infrared Sounder (AIRS). Similarly, the bias in the cloud fraction is corrected based on observations by Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and CloudSat. Remaining errors in surface, cloud, and atmospheric properties are corrected in the Lagrange multiplier process. Ed4 global annual mean (January 2005 through December 2014) surface net shortwave (SW) and longwave (LW) irradiances increase by 1.3Wm22 and decrease by 0.2Wm22, respectively, compared to EBAF Edition 2.8 (Ed2.8) counterparts (the previous version), resulting in an increase in net SW 1LWsurface irradiance of 1.1Wm22. The uncertainty in surface irradiances over ocean, land, and polar regions at various spatial scales are estimated. The uncertainties in all-sky global annual mean upward and downward shortwave irradiance are 3 and 4Wm22, respectively, and the uncertainties in upward and downward longwave irradiance are 3 and 6Wm22, respectively. With an assumption of all errors being independent, the uncertainty in the global annual mean surface LW 1 SW net irradiance is 8Wm22.

Kato, Seiji↗

Dependable classical-quantum computing systems engineering

Increasing evidence suggests quantum computing (QC) complements traditional High-Performance Computing (HPC) by leveraging its unique capabilities, leading to the emergence of a new, hybrid paradigm, QHPC. However, this integration introduces new challenges, with dependability–defined by reproducibility, resiliency, and security and privacy–emerging as a central concern for building trustworthy systems that provide an advantage to the users. This paper proposes a framework for dependable QHPC system design, organized around these three pillars. We identify integration challenges, anticipate roadblocks, and highlight productive synergies across QC, HPC, cloud platforms, and network security. Drawing from both classical computing principles and quantum-specific insights, we present a roadmap for co-design that supports robust hybrid architectures. Our approach offers concrete metrics for assessing dependability, provides design guidance for engineers working at the QC-HPC interface, and surfaces new engineering questions around complexity, scale, and fault tolerance. Ultimately, designing for dependability is key to realizing practical, scalable QHPC systems and accelerating the broader quantum ecosystem capable of translating quantum promises into actual application delivery.

HPC↗

Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures

The last decade has seen tremendous growth in cloud dynamical and microphysical models that are able to simulate storms and storm systems with very high spatial resolution, typically of the order of a few kilometers. The fairly realistic distributions of cloud and hydrometeor properties that these models generate has in turn led to a renewed interest in the three-dimensional microwave radiative transfer modeling needed to understand the effect of cloud and rainfall inhomogeneities upon microwave observations. Monte Carlo methods, and particularly backwards Monte Carlo methods have shown themselves to be very desirable due to the quick convergence of the solutions. Unfortunately, backwards Monte Carlo methods are not well suited to treat polarized radiation. This study reviews the existing Monte Carlo methods and presents a new polarized Monte Carlo radiative transfer code. The code is based on a forward scheme but uses aliasing techniques to keep the computational requirements equivalent to the backwards solution. Radiative transfer computations have been performed using a microphysical-dynamical cloud model and the results are presented together with the algorithm description.

Kummerow, Christian↗

Modelling of IR emission of interstellar clouds. I - Emission of isolated clouds and dust abundance variations

A model for the IR emission and extinction properties of small dust particles is used here to compute the IR emissions in the IRAS photometric bands for a set of isolated, spherical, and nonhomogeneous clouds heated by the local interstellar radiation field. It is predicted that the IR limb brightening (LB) in the IRAS photometric bands caused by selective absorption of UV photons of different energies in the cloud generally happens for central extinctions over 4 mag at 12 microns and greater than 10 mag at 100 microns and intermediate extinctions for the other IRAS bands. The surface brightness in the four IRAS bands is limited to about 0.4, 0.6, 3, and 10 MJy/sr at 12, 25, 60, and 100 microns respectively when no strong density discontinuity is present at the cloud edge.

Bernard, J. P.↗

ProvLight: Efficient Workflow Provenance Capture on the Edge-to-Cloud Continuum

Modern scientific workflows require hybrid infrastructures combining numerous decentralized resources on the IoT/Edge interconnected to Cloud/HPC systems (aka the Computing Continuum) to enable their optimized execution. Understanding and optimizing the performance of such complex Edge-to-Cloud workflows is challenging. Capturing the provenance of key performance indicators, with their related data and processes, may assist in understanding and optimizing workflow executions. However, the capture overhead can be prohibitive, particularly in resource-constrained devices, such as the ones on the IoT/Edge.To address this challenge, based on a performance analysis of existing systems, we propose ProvLight, a tool to enable efficient provenance capture on the IoT/Edge. We leverage simplified data models, data compression and grouping, and lightweight transmission protocols to reduce overheads. We further integrate ProvLight into the E2Clab framework to enable workflow provenance capture across the Edge-to-Cloud Continuum. This integration makes E2Clab a promising platform for the performance optimization of applications through reproducible experiments.We validate ProvLight at a large scale with synthetic workloads on 64 real-life IoT/Edge devices in the FIT IoT LAB testbed. Evaluations show that ProvLight outperforms state-of-the-art systems like ProvLake and DfAnalyzer in resource-constrained devices. ProvLight is 26—37x faster to capture and transmit provenance data; uses 5—7x less CPU; 2x less memory; transmits 2x less data; and consumes 2—2.5x less energy. ProvLight [1] and E2Clab [2] are available as open-source tools.

Rosendo, Daniel↗

Scattering Properties and Brightness Temperatures Associated with Solid Precipitation

In the past few years, early solid precipitation detection and retrieval algorithms have been developed and shown to be applicable for snowing clouds and blizzards. NOAA has an operational snow versus rain classifier based on AMSU-B observations. Solid precipitation retrieval algorithms reported in the literature over the past two years include those that rely on neural nets, statistics, or physical relationships. All of the algorithms require the use of millimeter-wave radiometer observations. The millimeter-wave frequencies are especially sensitive to the scattering and emission properties of frozen particles due to the ice particle refractive index. Passive radiometric channels respond to both the integrated particle mass throughout the volume and field of view, and to the amount, location, and size distribution of the frozen (and liquid) particles with the sensitivity varying for different frequencies and hydrometeor types. This investigation probes the sensitivity of scattering and absorption coefficients, and hence computed brightness temperatures, resulting from variations in solid precipitation cloud profiles. The first study compares the single scattering, absorption, and asymmetry parameters associated with snow particles in clouds. Several methodologies are used to convert the physical characteristics (e.g., shape, size distributions, ice-air-water ratios) of ice particles to electromagnetic properties (e.g., absorption, scattering, and asymmetry factors). These methodologies include: conversion to solid ice particles, homogeneous dielectric mixing, or discrete dipole approximation. Changes in the conversion methodology can produce computed brightness temperature differences greater than 50 Kelvin.

Skofronick-Jackson, Gail M.↗

Quantum computation of silicon electronic band structure

Development of quantum architectures during the last decade has inspired hybrid classical–quantum algorithms in physics and quantum chemistry that promise simulations of fermionic systems beyond the capability of modern classical computers, even before the era of quantum computing fully arrives. Strong research efforts have been recently made to obtain minimal depth quantum circuits which could accurately represent chemical systems. Here, we show that unprecedented methods used in quantum chemistry, designed to simulate molecules on quantum processors, can be extended to calculate properties of periodic solids. In particular, we present minimal depth circuits implementing the variational quantum eigensolver algorithm and successfully use it to compute the band structure of silicon on a quantum machine for the first time. We are convinced that the presented quantum experiments performed on cloud-based platforms will stimulate more intense studies towards scalable electronic structure computation of advanced quantum materials.

36 MATERIALS SCIENCE↗

Clouds and Earth Radiant Energy System (CERES), a Review: Past, Present and Future

The Clouds and Earth Radiant Energy System (CERES) project s objectives are to measure the reflected solar radiance (shortwave) and Earth-emitted (longwave) radiances and from these measurements to compute the shortwave and longwave radiation fluxes at the top of the atmosphere (TOA) and the surface and radiation divergence within the atmosphere. The fluxes at TOA are to be retrieved to an accuracy of 2%. Improved bidirectional reflectance distribution functions (BRDFs) have been developed to compute the fluxes at TOA from the measured radiances with errors reduced from ERBE by a factor of two or more. Instruments aboard the Terra and Aqua spacecraft provide sampling at four local times. In order to further reduce temporal sampling errors, data are used from the geostationary meteorological satellites to account for changes of scenes between observations by the CERES radiometers. A validation protocol including in-flight calibrations and comparisons of measurements has reduced the instrument errors to less than 1%. The data are processed through three editions. The first edition provides a timely flow of data to investigators and the third edition provides data products as accurate as possible with resources available. A suite of cloud properties retrieved from the MODerate-resolution Imaging Spectroradiometer (MODIS) by the CERES team is used to identify the cloud properties for each pixel in order to select the BRDF for each pixel so as to compute radiation fluxes from radiances. Also, the cloud information is used to compute radiation at the surface and through the atmosphere and to facilitate study of the relationship between clouds and the radiation budget. The data products from CERES include, in addition to the reflected solar radiation and Earth emitted radiation fluxes at TOA, the upward and downward shortwave and longwave radiation fluxes at the surface and at various levels in the atmosphere. Also at the surface the photosynthetically active radiation and ultraviolet radiation (total, UVA and UVB) are computed. The CERES instruments aboard the Terra and Aqua spacecraft have served well past their design life times. A CERES instrument has been integrated onto the NPP platform and is ready for launch in 2011. Another CERES instrument is being built for launch in 2014, and plans are being made for a series of follow-on missions.

Smith, G. L.↗

Automated Tracking of Shallow Maritime Clouds on Geostationary Imagery to Extract Lifecycle Characteristics

Shallow moist convection is ubiquitous throughout the tropics and represents a key player in boundary layer processes. Satellites have provided many statistics on shallow clouds, such as size, structure, and geographical coverage, from static views of recurring cloud fields. But determining why certain cloud features appear and persist for different periods requires a time-evolving view of their behaviors. Geostationary satellites provide a unique opportunity to follow the time evolution of individual convective features, given their enhanced spatial and temporal sampling. A cloud-tracking tool was developed to identify properties of cloud lifecycle from the NASA Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP2EX) field campaign of 2019. The mission conducted intensive sampling of shallow cumulus in the West Pacific Ocean, in tandem with Rapid Scan imagery from the Advanced Himawari Imager (AHI) on the Japan Meteorological Agency’s (JMA) Himawari-8 satellite. Shallow cumulus was segmented according to thresholds in 0.5-km visible reflectance and with blurring techniques. Despite being limited to daytime hours, the segmentations yielded the best resolution possible for capturing cloud initiation and decay. The tracking procedure is based on a computer vision package that includes Kalman filters for motion prediction, object overlap search, and the Hungarian (or Kuhn-Munkres) matching algorithm for track designation. AHI radiances available within the tracked cloud boundaries are assembled to form individual spectral histories. The resulting catalog provides thousands of cloud histories for domains measuring only a few degrees in latitude and longitude. We present an overview of the cloud-tracking tool, strategies to identify development stages from cloud tracks, and preliminary results that document cumulus lifecycle properties from satellite. The application of AHI 0.5-km reflectance has both strengths and limitations when attempting to track lifecycles of the smallest resolvable clouds. We show that by aggregating cloud tracks from a few case studies of CAMP2EX, we can discern differences in cloud lifetime and development according to ensembles selected from areas of interest. The results demonstrate an ability to quantify lifetimes and assess rates of change in cloud characteristics that are likely controlled by the surrounding environment and meteorology.

Cloud Tracking↗

3D Cloud Masking Across A Broad Swath Using Multi-Angle Polarimetry and Deep Learning

Understanding the 3-dimensional structure of clouds is of crucial importance to modeling our changing climate. Active sensors, such as radar and lidar, provide accurate vertical cloud profiles, but are mostly restricted to along-track sampling. Passive sensors can capture a wide swath, but struggle to see beneath cloud tops. In essence, both types of products are restricted to two dimensions: as a cross-section in the active case, and an image in the passive case. However, multi-angle sensor configurations contain implicit information about 3D structure, due to parallax and atmospheric path differences. Extracting that implicit information can be challenging, requiring computationally expensive radiative transfer techniques. Machine learning, as an alternative, may be able to capture some of the complexity of a full 3D radiative transfer solution with significantly less computational expense. In this work, we make three contributions towards understanding 3D cloud structure from multi-angle polarimetry. First, we introduce a large-scale, publicly available dataset that fuses existing cloud products into a format more amenable to machine learning. This dataset treats multi-angle polarimetry as an input, and radar-based vertical cloud profiles as an output. Second, we describe and evaluate strong baseline machine learning models based that predict these profiles from the passive imagery. Notably, these models are trained only on center-swath labels, but can predict cloud profiles over the entire passive imagery swath. Third, we leverage the information-theoretic nature of machine learning to draw conclusions about the relative utility of various sensor configurations, including spectral channels, viewing angles, and polarimetry. These findings have implications for Earth-observing missions such as NASA’s Plankton, Aerosol, Cloud-ocean Ecosystem (PACE) and Atmosphere Observing System (AOS) missions, as well as in informing future applications of computer vision to atmospheric remote sensing.

clouds↗

Workflows Community Summit 2022: A Roadmap Revolution

Scientific workflows have become integral tools in broad scientific computing use cases. Science discovery is increasingly dependent on workflows to orchestrate large and complex scientific experiments that range from the execution of a cloud-based data preprocessing pipeline to multi-facility instrument-to-edge-to-HPC computational workflows. Given the changing landscape of scientific computing (often referred to as a computing continuum) and the evolving needs of emerging scientific applications, it is paramount that the development of novel scientific workflows and system functionalities seek to increase the efficiency, resilience, and pervasiveness of existing systems and applications. Specifically, the proliferation of machine learning/artificial intelligence (ML/AI) workflows, need for processing large-scale datasets produced by instruments at the edge, intensification of near real-time data processing, support for long-term experiment campaigns, and emergence of quantum computing as an adjunct to HPC, have significantly changed the functional and operational requirements of workflow systems. Workflow systems now need to, for example, support data streams from the edge-to-cloud-to-HPC, enable the management of many small-sized files, allow data reduction while ensuring high accuracy, orchestrate distributed services (workflows, instruments, data movement, provenance, publication, etc.) across computing and user facilities, among others. Further, to accelerate science, it is also necessary that these systems implement specifications/standards and APIs for seamless (horizontal and vertical) integration between systems and applications, as well as enable the publication of workflows and their associated products according to the FAIR principles.

97 MATHEMATICS AND COMPUTING↗

Criteria for fragmentation in a collapsing rotating cloud

The isothermal collapse of a rotating protostar with pressure and self-gravity is calculated by a hydrodynamic computer code that treats three space dimensions. A number of initial conditions are tested to determine the conditions under which a cloud is unstable to fragmentation. It is shown that fragmentation does not proceed to a significant extent during the first free-fall time, but that in most cases fragmentation has occurred by 1.5 to 2 times the initial free-fall time. The extent to which the density in the fragments is enhanced over that in their surroundings on this time scale depends on the initial ratio of thermal to gravitational energy, but is only weakly dependent on the type and amplitude of the perturbation and on the initial rotational energy.

Bodenheimer, P.↗