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At least 487 records · Page 27

Effects of Uncertainty in TRMM Precipitation Radar Path Integrated Attenuation on Interannual Variations of Tropical Oceanic Rainfall

Considerable uncertainty surrounds the issue of whether precipitation over the tropical oceans (30 deg N/S) systematically changes with interannual sea-surface temperature (SST) anomalies that accompany El Nino (warm) and La Nina (cold) events. Time series of rainfall estimates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) over the tropical oceans show marked differences with estimates from two TRMM Microwave Imager (TMI) passive microwave algorithms. We show that path-integrated attenuation derived from the effects of precipitation on the radar return from the ocean surface exhibits interannual variability that agrees closely with the TMI time series. Our analysis of discrepancies between the PR rainfall and attenuation suggests that uncertainty in the assumed drop size distribution and associated attenuation/reflectivity/rainfall relationships inherent in single-frequency radar methods is a serious issue for studies of interannual variability.

Robertson, Franklin R.↗

Tropical Ocean Global Atmosphere (TOGA) Meteorological and Oceanographic Data Sets for 1985 and 1986

The Tropical Ocean Global Atmosphere (TOGA) Program is a component of the World Meteorological Organization (WMO)/International Council of Scientific Unions (ICSU) World Climate Research Program (WCRP). One of the objectives of TOGA, which began in 1985, is to determine the limits of predictability of monthly mean sea surface temperature variations in tropical regions. The TOGA program created a raison d'etre for an explosive growth of the tropical ocean observing system and a substantial improvement in numerical simulations from atmospheric and oceanic general circulation models. Institutions located throughout the world are involved in the TOGA-distributed active data archive system. The diverse TOGA data sets for 1985 and 1986, including results from general circulation models, are included on a CD-ROM. Variables on the CD-ROM are barometric pressure, surface air temperature, dewpoint temperature Cartesian components of surface wind, surface sensible and latent heat fluxes,Cartesian components of surface wind stress and of an index of surface wind stress, sea level, sea surface temperature, and depth profiles of temperature and current in the upper ocean. Some data sets are global in extent, some are regional and cover portions of an ocean basin. Data on the CD-ROM can be extracted with an Apple Macintosh or an IBM PC.

Halpern, D.↗

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↗

Warm Rain Processes Over the Tropical Oceans and Implications on Climate Change

In this talk, we will first show results from TRMM regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to a larger portion of the increase. The abundant rainout of warm precipitation at middle to low levels causes a reduction of high cloud cover due to the depletion of water available for ice-phase rain production. As a result, more isolated, but more intense penetrative convection develops. Results also show that increased autoconversion reduces the convective adjustment time scale tends, implying a faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbance on daily to weekly time scales. The causes of the sensitivity of the dynamical regimes to the microphysics parameterization in the GCM will be discussed.

Lau, William K. M.↗

Warm Rain Processes Over the Tropical Oceans and Implications on Climate Change: Results from TRMM and GOES GCM

In this talk, we will first show results from TRMM data regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to a larger portion of the increase. The abundant rainout of warm precipitation causes a reduction of low and middle cloud amount due to rainout, and reduced high clouds due to less water vapor available for ice-phase convection. However, clod radiation feedback caused by the increased rainfall efficiency, leads to differential vertical heating/cooling producing a more unstable atmosphere, allowing, more intense, but isolated penetrative convection, with contracted anvils to develop. Results also show that increased autoconversion reduces the convective adjustment time scale, resulting in faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbances on daily to weekly time scales. The crucial link of precipitation microphysical processes to climate change including the effects of aerosols will be discussed.

Lau, William K. M.↗

Warm Rain Processes over the Tropical Oceans and Implications on Climate Change: Results from TRMM and GEOS GCM

In this talk, we will first show results from TRMM data regarding the characteristics of warm rains over the tropical oceans, and the dependence of rate of warm rain production on sea surface temperature. Results lead to the hypothesis that warm rain production efficiency, i.e., autoconversion, may be increased in a warm climate. We use the GEOS-II GCM to test this hypothesis. Our modeling results show that in a climate with increased rate of autoconversion, the total rain amount is increased, with warm rain contributing to larger portion of the increase. The abundant rainout of warm precipitation causes a reduction of low and middle cloud amount due to rainout, and reduced high clouds due to less water vapor available for ice-phase convection. However, clod radiation feedback caused by the increased rainfall efficiency, leads to differential vertical heating/cooling producing a more unstable atmosphere, allowing, more intense, but isolated penetrative convection, with contracted anvils to develop. Results also show that increased autoconversion reduces the convective adjustment time scale, resulting in faster recycling of atmospheric water. Most interestingly, the increased low level heating associated with warm rain leads to more energetic Madden and Julian oscillations in the tropics, with well-defined eastward propagation. While reducing the autoconversion leads to an abundant mix of westward and eastward tropical disturbances on daily to weekly time scales. The crucial link of precipitation microphysical processes to climate change including the effects of aerosols will be discussed.

Lau, William K. M.↗

New Insights on Tropical Ozone from SHADOZ (Southern Hemisphere Additional Ozonesondes) Profiles

The SHADOZ (Southern Hemisphere Additional Ozonesondes) ozone sounding network was initiated in 1998 to improve the coverage of tropical in-situ ozone measurements for satellite validation, algorithm development and related process studies. Over 2000 soundings have been archived at the website, , for 12 stations: Ascension Island; Nairobi and Malindi, Kenya; Irene, South Africa; Reunion Island, Watukosek, Java; Fiji; Tahiti; American Samoa; San Cristobal, Galapagos; Natal, Brazil; Paramaribo, Surinam. Key results from SHADOZ will be described from among the following: 1) By using ECC sondes with similar procedures, 5-10% accuracy and precision (1-sigma) of the sonde total ozone measurement was achieved; 2) Week-to-week variability in tropospheric ozone is so great that statistics are frequently not Gaussian; most stations vary up to a factor of 3 in tropospheric column over the course of a year; 3) Longitudinal variability in tropospheric ozone profiles is a consistent feature, with a 10-15 DU column-integrated difference between Atlantic and Pacific sites; this causes a "zonal wave-one" feature in total ozone. 4) The ozone record from Paramaribo, Surinam (6N, 55W) is a marked contrast to southern tropical ozone because Surinam is often north of the Intertropical Convergence Zone; 5) Indian Ocean region pollution may contribute up to half of the excess ozone observed in the south tropical Atlantic paradox in the December-January-February period of the year.

Thompson, Anne M.↗

[Summary of Research on Relationship Between Core Convective Structure and Intensity Change in Tropical Cyclones]

The downshear reformation of Tropical Storm Gabrielle (2001) was investigated using radar reflectivity and lightning data that were nearly continuous in time, as well as frequent aircraft reconnaissance flights. Initially the storm was a marginal tropical storm in an environment with strong 850-200 hPa vertical wind shear of 12-13 meters per second and an approaching upper tropospheric trough. Both the observed outflow and an adiabatic balance model calculation showed that the radial-vertical circulation increased with time as the trough approached. Convection was highly asymmetric, with almost all radar return located in one quadrant left of downshear in the storm. Reconnaissance data show that an intense mesovortex formed downshear of the original center. This vortex was located just south of, rather than within, a strong downshear left lightning outbreak, consistent with tilting of the horizontal vorticity associated with the vertical wind shear. The downshear mesovortex contained a 972 hPa minimum central pressure, 20 hPa lower than minimum pressure in the original vortex just three hours earlier. The mesovortex became the new center of the storm, but weakened somewhat prior to landfall. It is argued that dry air carried around the storm from the region of upshear subsidence, as well as the direct effects of the shear, prevented the reformed vortex from continuing to intensify. Despite the subsequent weakening of the reformed center, it reached land with greater intensity than the original center. It is argued that this intensification process was set into motion by the vertical wind shear in the presence of an environment with upward motion forced by the upper tropospheric trough. In addition, the new center formed much closer to the coast and made landfall much earlier than predicted. Such vertical shear-induced intensity and track fluctuations are important to understand, especially in storms approaching the coast. The structures of the highly sheared tropical storm Chantal During CAMEX-4 is also discussed.

Source record↗

GCM Simulations of the Tropical Hydrogen Distribution Observed by Mars Odyssey

The age and nature of the tropical hydrogen deposits on Mars remain uncertain. Competing theories suggest that the deposits are composed of either ancient, hydrated minerals or recently emplaced water ice. We use the GFDL Mars GCM with a fully coupled atmosphere-regolith water cycle to explore which of these hypotheses is best supported by model results. Such a conclusion can be drawn from the resultant trends in subsurface ice evolution during various obliquity and polar cap conditions. Our results suggest that the tropical hydrogen distribution is best explained by recent emplacement of ice through either exposure of the south polar ice cap or by burial of tropical surface ice from the most recent high obliquity excursions.

Mischna, M. A.↗

Interannual Rainfall Variability in the Tropical Atlantic Region

Rainfall variability on seasonal and interannual-to-interdecadal time scales in the tropical Atlantic is quantified using a 25-year (1979-2003) monthly rainfall dataset from the Global Precipitation Climatology Project (GPCP). The ITCZ measured by monthly rainfall between 15-37.5 deg W attains its peak as moving to the northernmost latitude (4-10 deg N) during July-September in which the most total rainfall is observed in the tropical Atlantic basin (17.5 deg S-22.5 deg N, 15 deg-37.5 deg W); the ITCZ becomes weakest during January-February with the least total rainfall as it moves to the south. In contrast, rainfall variability on interannual to interdecadal time scales shows a quite different seasonal preference. The most intense interannual variability occurs during March-May when the ITCZ tends to be near the equator and becomes weaker. Significant, negative correlations between the ITCZ strength and latitude anomalies are observed during boreal spring and early summer. The ITCZ strength and total rainfall amount in the tropical Atlantic basin are significantly modulated by the Pacific El Nino and the Atlantic equatorial mode (or Atlantic Nino) particularly during boreal spring and summer; whereas the impact of the Atlantic interhemispheric mode is considerably weaker. Regarding the anomalous latitudes of the ITCZ, the influence can come from both local, i.e., the Atlantic interhemispheric and equatorial modes, and remote forcings, i. e., El Nino; however, a direct impact of El Nino on the latitudes of the ITCZ can only be found during April-July, not in winter and early spring in which the warmest SST anomalies are usually observed in the equatorial Pacific.

Gu, Guojun↗

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.↗

Interannual and Seasonal Variability of the Tropopause Layer over the Tropical Americas

This study explores the thermodynamic and convective characteristics of the Tropical Tropopause Layer (TTL) over the Tropical Americas using multi-platform measurements collected during the last five years. This region is chosen for the following reasons: (i) it becomes the second most dominant source of air to the TTL, (ii) it exhibits the largest seasonal increase in percent contribution to stratospheric moisture, (iii) it has the warmest tropical tropopause temperatures, and (iv) it can be influenced by midlatitude and subtropical air masses that are transported equatorward by the upper-level circulation associated with the North American Monsoon. We examine the interannual and seasonal variability of water vapor, ozone, and temperature using aircraft data collected aboard the WB-57, satellite data from the Aura-MLS and Aqua-AIRS instruments, and GPS radio occultation measurements from the CHAMP satellite. We also examine the vertical extent and frequency of convection in the region using data from TRMM. In addition, we perform seasonal trajectory calculations to elucidate the origin and fate of air masses found in our region of interest.

Pittman, Jasna V.↗

Spectroscopic Detection of COClF in the Tropical and Mid-Latitude Lower Stratosphere

We report retrievals of COClF (carbonyl chlorofluoride) based on atmospheric chemistry experiment (ACE) solar occultation spectra recorded at tropical and mid-latitudes during 2004-2005. The COClF molecule is a temporary reservoir of both chlorine and fluorine and has not been measured previously by remote sensing. A maximum COClF mixing ratio of 99.7+/-48.0 pptv (10(exp -12) per unit volume, 1 sigma) is measured at 28km for tropical and subtropical occultations (latitudes below 20deg in both hemispheres) with lower mixing ratios at both higher and lower altitudes. Northern hemisphere mid-latitude mixing ratios (30-50degN) resulted in an average profile with a peak mixing ratio of 51.7+/-32.1 pptv, 1 sigma, at 27 km, also decreasing above and below that altitude. We compare the measured average profiles with the one reported set of in situ lower stratospheric mid-latitude measurements from 1986 and 1987, a previous two-dimensional (2-D) model calculation for 1987 and 1993, and a 2-D-model prediction for 2004. The measured average tropical profile is in close agreement with the model prediction; the northern mid-latitude profile is also consistent, although the peak in the measured profile occurs at a higher altitude (2.5-4.5km offset) than in the model prediction. Seasonal average 2-D-model predictions of the COClF stratospheric distribution for 2004 are also reported.

Rinsland, Curtis P.↗

The Effect of Environmental Conditions on Tropical Deep Convective Systems Observed from the TRMM Satellite

This study uses measurements of radiation and cloud properties taken between January and August 1998 by three Tropical Rainfall Measuring Mission (TRMM) instruments, the Clouds and the Earth's Radiant Energy System (CERES) scanner, the TRMM Microwave Imager (TMI), and the Visible and InfraRed Scanner (VIRS), to evaluate the variations of tropical deep convective systems (DCS) with sea surface temperature (SST) and precipitation. This study finds that DCS precipitation efficiency increases with SST at a rate of approx. 2%/K. Despite increasing rainfall efficiency, the cloud areal coverage rises with SST at a rate of about 7%/K in the warm tropical seas. There, the boundary layer moisture supply for deep convection and the moisture transported to the upper troposphere for cirrus-anvil cloud formation increase by approx. 6.3%/K and approx. 4.0%/K, respectively. The changes in cloud formation efficiency, along with the increased transport of moisture available for cloud formation, likely contribute to the large rate of increasing DCS areal coverage. Although no direct observations are available, the increase of cloud formation efficiency with rising SST is deduced indirectly from measurements of changes in the ratio of DCS ice water path and boundary layer water vapor amount with SST. Besides the cloud areal coverage, DCS cluster effective sizes also increase with precipitation. Furthermore, other cloud properties, such as cloud total water and ice water paths, increase with SST. These changes in DCS properties will produce a negative radiative feedback for the earth's climate system due to strong reflection of shortwave radiation by the DCS. These results significantly differ from some previous hypothesized dehydration scenarios for warmer climates, and have great potential in testing current cloud-system resolving models and convective parameterizations of general circulation models.

Lin, Bing↗

Dominance of ENSO-Like Variability in Controlling Tropical Ocean Surface Energy Fluxes in the Satellite Era

Ocean surface turbulent and radiative fluxes are critical links in the climate system since they mediate energy exchange between the two fluid systems (ocean and atmosphere) whose combined heat transport determines the basic character of Earth's climate. Moreover, interannual to decadal climate variability depends crucially on the nature of these exchange processes. For example, addressing the question of the degree to which the global hydrologic cycle is changing depends on our ability to observe and model these fluxes accurately. In this work we investigate the interannual to decadal variation of fluxes over the global tropics, especially the tropical oceans. Recent versions of satellite-derived fresh water flux estimates as well as some reanalyses (e.g. products from Remote Sensing Systems, the Woods Hole Oceanographic Institute, and Global Precipitation Climatology Project) suggest that increases in evaporation and precipitation over the past 20 years exceed those expected on the basis of climate model projected responses to greenhouse gas forcing. At the same time, it is well known that E1 Nino / Southern Oscillation behavior in the Pacific exhibits significant variability at scales longer than interannual. We examine here the degree to which surface fluxes attending these interannual to decadal fluctuations are related to ENSO. We examine consistency between these data sets and explore relationships between SST variations, flux changes and modulation of tropical Walker and Hadley circulations.

Robertson, F. R.↗

Tropical Cyclones Feed More Heavy Rain in a Warmer Climate

The possible linkage of tropical cyclones (TC) to global warming is a hotly debated scientific topic, with immense societal impacts. Most of the debate has been focused on the issue of uncertainty in the use of non-research quality data for long-term trend analyses, especially with regard to TC intensity provided by TC forecasting centers. On the other hand, it is well known that TCs are associated with heavy rain during the processes of genesis and intensification, and that there are growing evidences that rainfall characteristics (not total rainfall) are most likely to be affected by global warming. Yet, satellite rainfall data have not been exploited in any recent studies of linkage between tropical cyclones (TC) and global warming. This is mostly due to the large uncertainties associated with detection of long-term trend in satellite rainfall estimates over the ocean. This problem, as we demonstrate in this paper, can be alleviated by examining rainfall distribution, rather than rainfall total. This paper is the first to use research-quality, satellite-derived rainfall from TRMM and GPCP over the tropical oceans to estimate shift in rainfall distribution during the TC season, and its relationships with TCs, and sea surface temperature (SST) in the two major ocean basins, the northern Atlantic and the northern Pacific for 1979-2005. From the rainfall distribution, we derive the TC contributions to rainfall in various extreme rainfall categories as a function to time. Our results show a definitive trend indicating that TCs are contributing increasingly to heavier rain events, i.e., intense TC's are more frequent in the last 27 years. The TC contribution to top 5% heavy rain has nearly doubled in the last two decades in the North Atlantic, and has increased by about 10% in the North Pacific. The different rate of increase in TC contribution to heavy rain may be related to the different rates of different rate of expansion of the warm pool (SST >2S0 C) area in the two oceans.

Lau, K.-M.↗

Saharan Air and Atlantic Tropical Cyclone Suppression From a Global Modeling Perspective

During summer 2006, the NASA African Monsoon Multidisciplinary Analysis (NAMMA) organized a field campaign in Africa called Special Observation Period (SOP-3), in which scientists in the field were involved in a number of surface network and aircraft measurements. One of the scientific goals of the campaign was to understand the nature and causes for tropical cyclogenesis originating out of African Easterly Waves (AEWs, westward propagating atmospheric disturbances sometimes associated with precursors of hurricanes), and the role that the Saharan Air Layer (SAL, a hot and dry air layer advecting large amounts of dust) can play in the formation or suppression of tropical cyclones. During the NAMMA campaign a high-resolution global model, the NASA GEOS-5, was operationally run by the NASA Global Modeling and Assimilation Office (GMAO) in support to the mission. The daily GEOS-5 forecasts were found to be very useful by decision-making scientists in the field as an aid to discriminate between developing and non-developing AEWs and plan the flight tracks. In the post-event analyses which were performed mostly by the Goddard Laboratory for Atmospheres, two events were highlighted: a non-developing AEW which appeared to have been suppressed by Saharan air, compared to a developing AEW which was the precursor of hurricane Helene. Both events were successfully predicted by the GEOS-5 during the real-time forecasts provided in support to the mission. In this work it is found that very steep moisture gradients and a strong thermal dipole, with relatively warm air in the mid-troposphere and cool air below, are associated with SAL in both the GEOS-5 forecasts and the NCEP analyses, even at -great distance- from the Sahara. The presence of these unusual thermodynamic features over the Atlantic Ocean, at several thousands of kilometers from the African coastline, is suggestive that SAL mixing is very minimal and that the model's capability of retaining the different properties of air masses during transport are important to represent effectively the role of dry air intrusions in the tropical circulation.

Reale, O.↗

Atlantic Tropical Cyclogenetic Processes during SOP-3 NAMMA in the GEOS-5 Global Data Assimilation and Forecast System

This article investigates the role of the Saharan Air Layer (SAL) in tropical cyclogenetic processes associated with a non-developing and a developing African easterly wave observed during the Special Observation Period (SOP-3) phase of the 2006 NASA African Monsoon Multidisciplinary Analyses (NAMMA). The two waves are chosen because both interact heavily with Saharan air. A global data assimilation and forecast system, the NASA GEOS-5, is being run to produce a set of high-quality global analyses, inclusive of all observations used operationally but with denser satellite information. In particular, following previous works by the same Authors, the quality-controlled data from the Atmospheric Infrared Sounder (AIRS) used to produce these analyses have a better coverage than the one adopted by operational centers. From these improved analyses, two sets of 31 5-day high resolution forecasts, at horizontal resolutions of both half and quarter degrees, are produced. Results show that very steep moisture gradients are associated with the SAL in forecasts and analyses even at great distance from the Sahara. In addition, a thermal dipole (warm above, cool below) is present in the non-developing case. Moderate Resolution Imaging Spectroradiometer (MODIS) show that aerosol optical thickness is higher in the non-developing case. Altogether, results suggest that radiative effect of dust may play some role in producing a thermal structure less favorable to cyclogenesis. Results also indicate that only global horizontal resolutions on the order of 20-30 kilometers can capture the large-scale transport and the fine thermal structure of the SAL, inclusive of the sharp moisture gradients, reproducing the effect of tropical cyclone suppression which has been hypothesized by previous authors from observational and regional modeling perspectives. These effects cannot be fully represented at lower resolutions. Global resolution of a quarter of a degree is a minimum critical threshold to investigate Atlantic tropical cyclogenesis from a global modeling perspective.

Reale, Oreste↗