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At least 163 records · Page 9

Load‐Balancing Intense Physics Calculations to Embed Regionalized High‐Resolution Cloud Resolving Models in the E3SM and CESM Climate Models

Abstract We design a new strategy to load‐balance high‐intensity sub‐grid atmospheric physics calculations restricted to a small fraction of a global climate simulation's domain. We show why the current parallel load balancing infrastructure of Community Earth System Model (CESM) and Energy Exascale Earth Model (E3SM) cannot efficiently handle this scenario at large core counts. As an example, we study an unusual configuration of the E3SM Multiscale Modeling Framework (MMF) that embeds a binary mixture of two separate cloud‐resolving model grid structures that is attractive for low cloud feedback studies. Less than a third of the planet uses high‐resolution (MMF‐HR; sub‐km horizontal grid spacing) relative to standard low‐resolution (MMF‐LR) cloud superparameterization elsewhere. To enable MMF runs with Multi‐Domain cloud resolving models (CRMs), our load balancing theory predicts the most efficient computational scale as a function of the high‐intensity work's relative overhead and its fractional coverage. The scheme successfully maximizes model throughput and minimizes model cost relative to precursor infrastructure, effectively by devoting the vast majority of the processor pool to operate on the few high‐intensity (and rate‐limiting) high‐resolution (HR) grid columns. Two examples prove the concept, showing that minor artifacts can be introduced near the HR/low‐resolution CRM grid transition boundary on idealized aquaplanets, but are minimal in operationally relevant real‐geography settings. As intended, within the high (low) resolution area, our Multi‐Domain CRM simulations exhibit cloud fraction and shortwave reflection convergent to standard baseline tests that use globally homogenous MMF‐LR and MMF‐HR. We suggest this approach can open up a range of creative multi‐resolution climate experiments without requiring unduly large allocations of computational resources.

54 ENVIRONMENTAL SCIENCES↗

H2 cooling, dissociation, and infrared emission in shocked molecular clouds

Models are presented of interstellar shocks in molecular clouds over ranges of ambient molecular density from 1000 to 10 million per cu cm and shock velocity from 6 to 14 km/s. Estimates of H2-H2 collisional-excitation rates are used to derive the H2 radiative cooling rates from vibrational-rotational quadrupole transitions as a function of n(H2) and temperature. The emissivities integrated through the shock of the strongest infrared lines in the v = 1-0, 2-0, and 2-1 bands of H2. The effectiveness of H2 dissociative cooling is considered for the highest-velocity shocks. The H2 line intensities from such shocks are compared with those produced by the 'competitive' mechanism of UV pumping for two likely driving mechanisms of shocks - wind-driven shells and expanding H II regions.

Shull, J. M.↗

Simulation of mesoscale convective response

Results are reported from a transfer of thermodynamic and dynamic data downscale from a two-dimensional mesoscale model to a two-dimensional cloud model and a subsequent examination of the differential convective response of the cloud model to a mesoscale structure. The mesoscale model included a high resolution PBL formulation, with convective forces expressed in a profile of exchange coefficients over the height of the PBL and the magnitude of the surface heat flux. Account was also taken of forcing by long- and short-wave radiation, surface forcing by the surface energy budget, the terrain shape, and possible wave reflection at the top boundary. The slab-symmetric cloud model possessed subgrid-scale features, five types of moisture terms, and a subroutine for accretion processes. The mesoscale environment was observed to have a significant impact on convective response, i.e., the vertical velocity and the cloud water. Various factors which were not included in the study and which must be considered are discussed.

Mcnider, R. T.↗

Cloud model-based simulations of satellite microwave data and their application to an SSM/I rain algorithm

Satellite microwave observations of convective rain systems are simulated using a three-dimensional cloud model and a microwave radiative-transfer model. The simulated data sets are then used as a basis to derive rain estimation algorithms which are tested on actual satellite data. A tropical simulation is discussed, and the algorithms are applied to SSM/I data.

Adler, Robert F.↗

A Convective Vorticity Vector Associated With Tropical Convection: A 2D Cloud-Resolving Modeling Study

Although dry/moist potential vorticity is a useful physical quantity for meteorological analysis, it cannot be applied to the analysis of 2D simulations. A convective vorticity vector (CVV) is introduced in this study to analyze 2D cloud-resolving simulation data associated with 2D tropical convection. The cloud model is forced by the vertical velocity, zonal wind, horizontal advection, and sea surface temperature obtained from the TOGA COARE, and is integrated for a selected 10-day period. The CVV has zonal and vertical components in the 2D x-z frame. Analysis of zonally-averaged and mass-integrated quantities shows that the correlation coefficient between the vertical component of the CVV and the sum of the cloud hydrometeor mixing ratios is 0.81, whereas the correlation coefficient between the zonal component and the sum of the mixing ratios is only 0.18. This indicates that the vertical component of the CVV is closely associated with tropical convection. The tendency equation for the vertical component of the CVV is derived and the zonally-averaged and mass-integrated tendency budgets are analyzed. The tendency of the vertical component of the CVV is determined by the interaction between the vorticity and the zonal gradient of cloud heating. The results demonstrate that the vertical component of the CVV is a cloud-linked parameter and can be used to study tropical convection.

Gao, Shou-Ting↗

Evaluating Clouds in Long-Term Cloud-Resolving Model Simulations with Observational Data

Two 20-day, continental midlatitude cases are simulated with a three-dimensional (3D) cloud-resolving model (CRM) and compared to Atmospheric Radiation Measurement (ARM) data. This evaluation of long-term cloud-resolving model simulations focuses on the evaluation of clouds and surface fluxes. All numerical experiments, as compared to observations, simulate surface precipitation well but over-predict clouds, especially in the upper troposphere. The sensitivity of cloud properties to dimensionality and other factors is studied to isolate the origins of the over prediction of clouds. Due to the difference in buoyancy damping between 2D and 3D models, surface precipitation fluctuates rapidly with time, and spurious dehumidification occurs near the tropopause in the 2D CRM. Surface fluxes from a land data assimilation system are compared with ARM observations. They are used in place of the ARM surface fluxes to test the sensitivity of simulated clouds to surface fluxes. Summertime simulations show that surface fluxes from the assimilation system bring about a better simulation of diurnal cloud variation in the lower troposphere.

Zeng, Xiping↗

Multi-Layer Arctic Mixed-Phase Clouds Simulated by a Cloud-Resolving Model: Comparison with ARM Observations and Sensitivity Experiments

A cloud-resolving model (CRM) is used to simulate the multiple-layer mixed-phase stratiform (MPS) clouds that occurred during a three-and-a-half day subperiod of the Department of Energy-Atmospheric Radiation Measurement Program s Mixed-Phase Arctic Cloud Experiment (M-PACE). The CRM is implemented with an advanced two-moment microphysics scheme, a state-of-the-art radiative transfer scheme, and a complicated third-order turbulence closure. Concurrent meteorological, aerosol, and ice nucleus measurements are used to initialize the CRM. The CRM is prescribed by time-varying large-scale advective tendencies of temperature and moisture and surface turbulent fluxes of sensible and latent heat. The CRM reproduces the occurrences of the single- and double-layer MPS clouds as revealed by the M-PACE observations. However, the simulated first cloud layer is lower and the second cloud layer thicker compared to observations. The magnitude of the simulated liquid water path agrees with that observed, but its temporal variation is more pronounced than that observed. As in an earlier study of single-layer cloud, the CRM also captures the major characteristics in the vertical distributions and temporal variations of liquid water content (LWC), total ice water content (IWC), droplet number concentration and ice crystal number concentration (nis) as suggested by the aircraft observations. However, the simulated mean values differ significantly from the observed. The magnitude of nis is especially underestimated by one order of magnitude. Sensitivity experiments suggest that the lower cloud layer is closely related to the surface fluxes of sensible and latent heat; the upper cloud layer is probably initialized by the large-scale advective cooling/moistening and maintained through the strong longwave (LW) radiative cooling near the cloud top which enhances the dynamical circulation; artificially turning off all ice-phase microphysical processes results in an increase in LWP by a factor of 3 due to interactions between the excessive LW radiative cooling and extra cloud water; heating caused by phase change of hydrometeors could affect the LWC and cloud top height by partially canceling out the LW radiative cooling. It is further shown that the resolved dynamical circulation appears to contribute more greatly to the evolution of the MPS cloud layers than the parameterized subgrid-scale circulation.

Luo, Yali↗

Cloud-Feedback Model Intercomparison Project: Tier 2 Simulations (Final Report)

The University of Miami (Subcontractor)’s Research Scientist James Benedict (with oversight by PI Amy Clement) was tasked with producing global climate model simulations as part of the Cloud-Feedback Model Intercomparison Project (CFMIP) Tier 2 protocol, managing the output of these simulations, providing assistance (as requested) to staff at Lawrence Livermore National Lab (LLNL) regarding model output and setup, and meeting with LLNL scientists and team members to coordinate work on the project. The simulations represent an important contribution to the CFMIP data repository and will advance understanding of a wide range of critical cloud, circulation, and precipitation responses to climate change. The Subcontractor completed all proposed simulations, formatted the model output to be compliant with CFMIP protocols, and published the model data to the CFMIP repository. When requested, the Subcontractor provided assistance to LLNL for model output and configuration queries. Benedict and/or Clement also met in person or virtually 1-2 times per year with project scientists to coordinate work and review results.

54 ENVIRONMENTAL SCIENCES↗

CO2 Condensation Models for Mars

During the polar night in both hemispheres of Mars, regions of low thermal emission, frequently referred to as "cold spots", have been observed by Mariner 9, Viking and Mars Global Surveyor (MGS) spacecraft. These cold spots vary in time and appear to be associated with topographic features suggesting that they are the result of a spectral-emission effect due to surface accumulation of fine-grained frost or snow. Presented here are simulations of the Martian polar night using the NASA Ames General Circulation Cloud Model. This cloud model incorporates all the microphysical processes of carbon dioxide cloud formation, including nucleation, condensation and sedimentation and is coupled to a surface frost scheme that includes both direct surface condensation and precipitation. Using this cloud model we simulate the Mars polar nights and compare model results to observations from the Thermal Emission Spectrometer (TES) and the Mars Orbiter Laser Altimeter (MOLA). Model predictions of "cold spots" compare well with TES observations of low emissivity regions, both spatially and as a function of season. The model predicted frequency of CO2 cloud formation also agrees well with MOLA observations of polar night cloud echoes. Together the simulations and observations in the North indicate a distinct shift in atmospheric state centered about Ls 270 which we believe may be associated with the strength of the polar vortex.

Colaprete, A.↗

Earth System Model Aerosol–Cloud Diagnostics (ESMAC Diags) package, version 2: assessing aerosols, clouds, and aerosol–cloud interactions via field campaign and long-term observations

Abstract. Poor representations of aerosols, clouds, and aerosol–cloud interactions (ACIs) in Earth system models (ESMs) have long been the largest uncertainties in predicting global climate change. Huge efforts have been made to improve the representation of these processes in ESMs, and the key to these efforts is the evaluation of ESM simulations with observations. Most well-established ESM diagnostics packages focus on the climatological features; however, they lack process-level understanding and representations of aerosols, clouds, and ACIs. In this study, we developed the Earth System Model Aerosol–Cloud Diagnostics (ESMAC Diags) package to facilitate the routine evaluation of aerosols, clouds, and ACIs simulated the Energy Exascale Earth System Model (E3SM) from the US Department of Energy (DOE). This paper documents its version 2 functionality (ESMAC Diags v2), which has substantial updates compared with version 1 (Tang et al., 2022a). The simulated aerosol and cloud properties have been extensively compared with in situ and remote-sensing measurements from aircraft, ship, surface, and satellite platforms in ESMAC Diags v2. It currently includes six field campaigns and two permanent sites covering four geographical regions: the eastern North Atlantic, the central US, the northeastern Pacific, and the Southern Ocean. These regions produce frequent liquid- or mixed-phase clouds, with extensive measurements available from the DOE Atmospheric Radiation Measurement user facility and other agencies. ESMAC Diags v2 generates various types of single-variable and multivariable diagnostics, including percentiles, histograms, joint histograms, and heatmaps, to evaluate the model representation of aerosols, clouds, and ACIs. Select examples highlighting the capabilities of ESMAC Diags are shown using E3SM version 2 (E3SMv2). In general, E3SMv2 can reasonably reproduce many observed aerosol and cloud properties, with biases in some variables such as aerosol particle and cloud droplet sizes and number concentrations. The coupling of aerosol and cloud number concentrations may be too strong in E3SMv2, possibly indicating a bias in processes that control aerosol activation. Furthermore, the liquid water path response to a perturbed cloud droplet number concentration behaves differently in E3SMv2 and observations, which warrants further study to improve the cloud microphysics parameterizations in E3SMv2.

54 ENVIRONMENTAL SCIENCES↗

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Tao, W.-K.↗

Cloud Resolving Modeling

One of the most promising methods to test the representation of cloud processes used in climate models is to use observations together with cloud-resolving models (CRMs). CRMs use more sophisticated and realistic representations of cloud microphysical processes, and they can reasonably well resolve the time evolution, structure, and life cycles of clouds and cloud systems (with sizes ranging from about 2-200 km). CRMs also allow for explicit interaction between clouds, outgoing longwave (cooling) and incoming solar (heating) radiation, and ocean and land surface processes. Observations are required to initialize CRMs and to validate their results. This paper provides a brief discussion and review of the main characteristics of CRMs as well as some of their major applications. These include the use of CRMs to improve our understanding of: (1) convective organization, (2) cloud temperature and water vapor budgets, and convective momentum transport, (3) diurnal variation of precipitation processes, (4) radiative-convective quasi-equilibrium states, (5) cloud-chemistry interaction, (6) aerosol-precipitation interaction, and (7) improving moist processes in large-scale models. In addition, current and future developments and applications of CRMs will be presented.

Tao, Wei-Kuo↗

Simulation of Shallow Cumuli and Their Transition to Deep Convective Clouds by Cloud-resolving Models with Different Third-order Turbulence Closures

The abilities of cloud-resolving models (CRMs) with the double-Gaussian based and the single-Gaussian based third-order closures (TOCs) to simulate the shallow cumuli and their transition to deep convective clouds are compared in this study. The single-Gaussian based TOC is fully prognostic (FP), while the double-Gaussian based TOC is partially prognostic (PP). The latter only predicts three important third-order moments while the former predicts all the thirdorder moments. A shallow cumulus case is simulated by single-column versions of the FP and PP TOC models. The PP TOC improves the simulation of shallow cumulus greatly over the FP TOC by producing more realistic cloud structures. Large differences between the FP and PP TOC simulations appear in the cloud layer of the second- and third-order moments, which are related mainly to the underestimate of the cloud height in the FP TOC simulation. Sensitivity experiments and analysis of probability density functions (PDFs) used in the TOCs show that both the turbulence-scale condensation and higher-order moments are important to realistic simulations of the boundary-layer shallow cumuli. A shallow to deep convective cloud transition case is also simulated by the 2-D versions of the FP and PP TOC models. Both CRMs can capture the transition from the shallow cumuli to deep convective clouds. The PP simulations produce more and deeper shallow cumuli than the FP simulations, but the FP simulations produce larger and wider convective clouds than the PP simulations. The temporal evolutions of cloud and precipitation are closely related to the turbulent transport, the cold pool and the cloud-scale circulation. The large amount of turbulent mixing associated with the shallow cumuli slows down the increase of the convective available potential energy and inhibits the early transition to deep convective clouds in the PP simulation. When the deep convective clouds fully develop and the precipitation is produced, the cold pools produced by the evaporation of the precipitation are not favorable to the formation of shallow cumuli.

Cheng, Anning↗

Cloud model-based simulation of spaceborne radar observations

Simulations of observations from potential spaceborne radars are made based on storm structure generated from the three-dimensional (3D) Goddard cumulus ensemble model simulation of an intense overland convective system. Five frequencies of 3, 10, 14, 35, and 95 GHz are discussed, but the Tropical Rainfall Measuring Mission precipitation radar sensor frequency (14 GHz) is the focus of this study. Radar reflectives and their attenuation in various atmospheric conditions are studied in this simulation. With the attenuation from cloud and precipitation in the estimation of reflectivity factor (dBZ), the reflectivities in the lower atmosphere in the convective cores are significantly reduced. With spatial resolution of 4 km X 4 km, attenuation at 14 GHz may cause as large as a 20-dBZ difference between the simulated measurements of the peak, Z(sub mp) and near-surface reflectivity, Z(sub ms) in the most intense convective region. The Z(sub mp) occurs at various altitudes depending on the hydrometeor concentrations and their vertical distribution. Despite the significant attenuation in the intense cores, the presence of the rain maximum is easily detected by using information of Z(sub mp). In the stratiform region, the attenuation is quite limited (usually less than 5 dBZ), and the reduction of reflectivity is mostly related to the actual vertical structure of cloud distribution. Since Z(sub ms) suffers severe attenuation and tends to underestimate surface rainfall intensity in convective regions. Z(sub mp) can be more representative for rainfall retrieval in the lower atmosphere in these regions. In the stratiform region where attenuation is negligible, however, Z(sub mp) tends to overestimate surface rainfall and Z(sub ms) is more appropriate for rainfall retrieval. A hybrid technique using a weight between the two rain intensities is tested and found potentially usefull for future applications. The estimated surface rain-rate map based on this hybrid approach captures many of the details of the cloud model rain field but still slightly underestimates the rain-rate maximum.

Yeh, H.-Y. M.↗

One-dimensional cloud fluid model for propagating star formation

The aim of this project was to study the propagation of star formation (SF) with a self-consistent deterministic model for the interstellar gas. The questions of under what conditions does star formation propagate in this model and what are the mechanisms of the propagation are explored. Here, researchers used the deterministic Oort-type cloud fluid model of Scalo and Struck-Marcell (1984, also see the review of Struck-Marcell, Scalo and Appleton 1987). This cloud fluid approach includes simple models for the effects of cloud collisional coalescence or disruption, collisional energy dissipation, and cloud disruption and acceleration as the result of young star winds, HII regions and supernovae. An extensive one-zone parameter study is presented in Struck-Marcell and Scalo (1987). To answer the questions above, researchers carried out one-dimensional calculations for an annulus within a galactic disk, like the so-called solar neighborhood of the galactic chemical evolution. In the calculations the left-hand boundary is set equal to the right hand boundary. The calculation is obviously idealized; however, it is computationally convenient to study the first order effects of propagating star formation. The annulus was treated as if it were at rest, i.e., in the local rotating frame. This assumption may remove some interesting effects of a supersonic gas flow, but was necessary to maintain a numerical stability in the annulus. The results on the one-dimensional propagation of SF in the Oort cloud fluid model follow: (1) SF is propagated by means of hydrodynamic waves, which can be generated by external forces or by the pressure generated by local bursts. SF is not effectively propagated via diffusion or variation in cloud interaction rates without corresponding density and velocity changes. (2) The propagation and long-range effects of SF depend on how close the gas density is to the critical threshold value, i.e., on the susceptibility of the medium.

Titus, Timothy N.↗

Sensitivity of a Cloud-Resolving Model to the Bulk and Explicit Bin Microphysical Schemes

A cloud-resolving model is used to study sensitivities of two different microphysical schemes, one is the traditional bulk type, and the other is an explicit bin scheme, in simulating a mid-latitude squall line case (PRE-STORM, June 10-1 1,1985). Simulations using different microphysical schemes are compared with each other and also with the observations. Both the bulk and bin models reproduce the general features during the developing and mature stage of the system. Furthermore, the observations and the well-proven bulk scheme simulation serve as validations for the newly incorporated bin scheme. However, it is also shown that the bulk and bin simulations have distinct differences, most notably in the stratiform region of the squall line system. Weak convective cells exist in the stratiform region in the bulk simulation, but not in the bin simulation. These weak convective cells in the stratiform region simulated in the bulk scheme model are remnants of the stronger convections previously at the leading edge of the system, sustained by horizontal vorticity generated by its own cool pool near the surface. The bin simulation, on the other hand, has a horizontally homogeneous stratiform cloud structure, which agrees better with the observations. Examinations of the downdraft core strength, the potential temperature perturbation, and the evaporative cooling rate show that the differences between the bulk and bin models are due mainly to the stronger low-level evaporative cooling in the convective zone simulated in the bulk microphysical scheme, which is unrealistic because of the assumptions made in raindrop size distribution. Further sensitivity tests that reduce the evaporation rate in bulk scheme artificially produce more upright convective core and less weak cores in stratiform region. However, they produce weaker upper level outflow and consequently less stratiform rain area. The addition of a more realistic raindrop breakup scheme in the bin scheme results more realistic radar reflectivity and stronger surface rainfall. Despite the increase of the rain evaporation and strengthening of the near surface cool pool, bin scheme with rain breakup shows homogeneous stratiform rain. These sensitivity tests prove the robustness of the bin microphysical scheme and the difficulty of tuning the limited parameters in the bulk microphysical scheme to realistically reproduce detail structures in a mid-latitude squall line case study.

Li, Xiao-Wen↗

Model calculations for diffuse molecular clouds

A steady state isobaric cloud model is developed. The pressure, thermal, electrical, and chemical balance equations are solved simultaneously with a simple one dimensional approximation to the equation of radiative transfer appropriate to diffuse clouds. Cooling is mainly by CII fine structure transitions, and a variety of heating mechanisms are considered. Particular attention is given to the abundance variation of H2. Inhomogeneous density distributions are obtained because of the attenuation of the interstellar UV field and the conversion from atomic to molecular hyrodgen. The effects of changing the model parameters are described and the applicability of the model to OAO-3 observations is discussed. Good qualitative agreement with the fractional H2 abundance determinations has been obtained. The observed kinetic temperatures near 80 K can also be achieved by grain photoelectron heating. The problem of the electron density is solved taking special account of the various hydrogen ions as well as heavier ones.

Glassgold, A. E.↗

Multiscale Cloud System Modeling

The central theme of this paper is to describe how cloud system resolving models (CRMs) of grid spacing approximately 1 km have been applied to various important problems in atmospheric science across a wide range of spatial and temporal scales and how these applications relate to other modeling approaches. A long-standing problem concerns the representation of organized precipitating convective cloud systems in weather and climate models. Since CRMs resolve the mesoscale to large scales of motion (i.e., 10 km to global) they explicitly address the cloud system problem. By explicitly representing organized convection, CRMs bypass restrictive assumptions associated with convective parameterization such as the scale gap between cumulus and large-scale motion. Dynamical models provide insight into the physical mechanisms involved with scale interaction and convective organization. Multiscale CRMs simulate convective cloud systems in computational domains up to global and have been applied in place of contemporary convective parameterizations in global models. Multiscale CRMs pose a new challenge for model validation, which is met in an integrated approach involving CRMs, operational prediction systems, observational measurements, and dynamical models in a new international project: the Year of Tropical Convection, which has an emphasis on organized tropical convection and its global effects.

Tao, Wei-Kuo↗