A "dimensional reduction" ("DR") method is introduced for analyzing lightning field changes (Delta Es) whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight (x, y, z, Q, x', y', z', Q') to just four (x, y, z, Q). The four unknowns (x, y, z, Q) are found by performing a numerical minimization of a chi-square function. At each step of the minimization, an overdetermined fixed matrix (OFM) method is used to immediately retrieve the best "residual source" (x', y', z', Q'), given the values of (x, y, z, Q). In this way, all eight parameters (x, y, z, Q, x', y', z', Q') are found, yet a numerical search of only four parameters (x, y, z, Q) is required. The DR method has been used to analyze lightning-caused Delta Es derived from multiple ground-based electric field measurements at the NASA Kennedy Space Center (KSC) and U.S. Air Force Eastern Range (ER). The accuracy of the DR method has been assessed by comparing retrievals with data provided by the lightning detection and ranging (LDAR) system at the KSC-ER, and from least squares error estimation theory, and the method is shown to be a useful "stand alone" charge retrieval tool. Since more than one charge distribution describes a finite set of Delta Es (i.e., solutions are nonunique), and since there can be appreciable differences in the physical characteristics of these solutions, not all DR solutions are physically acceptable. Hence, an alternative and more accurate method of analysis is introduced that uses LDAR data to constrain the geometry of the charge solutions, thereby removing physically unacceptable retrievals. The charge solutions derived from this method are shown to compare well with independent satellite- and ground-based observations of lightning in several Florida storms.

A taxonomy of tropical convective and stratiform vertical structures is constructed through cluster analysis of 3 yr of Tropical Rainfall Measuring Mission (TRMM) "warm-season" (surface temperature greater than 10 degrees C) precipitation radar (PR) vertical profiles, their surface rainfall, and associated radar-based classifiers (convective/stratiform and brightband existence). Twenty-five archetypal profile types are identified, including nine convective types, eight stratiform types, two mixed types, and six anvil/fragment types (nonprecipitating anvils and sheared deep convective profiles). These profile types are then hierarchically clustered into 10 similar families, which can be further combined, providing an objective and physical reduction of the highly multivariate PR data space that retains vertical structure information. The taxonomy allows for description of any storm or local convective spectrum by the profile types or families. The analysis provides a quasi-independent corroboration of the TRMM 2A23 convective/stratiform classification. The global frequency of occurrence and contribution to rainfall for the profile types are presented, demonstrating primary rainfall contribution by midlevel glaciated convection (27%) and similar depth decaying/stratiform stages (28%-31%). Profiles of these types exhibit similar 37- and 85-GHz passive microwave brightness temperatures but differ greatly in their frequency of occurrence and mean rain rates, underscoring the importance to passive microwave rain retrieval of convective/stratiform discrimination by other means, such as polarization or texture techniques, or incorporation of lightning observations. Close correspondence is found between deep convective profile frequency and annualized lightning production, and pixel-level lightning occurrence likelihood directly tracks the estimated mean ice water path within profile types.

The observed reduction in cloud-to-ground lightning in the near-equatorial zone is examined from the perspective of the width of the main negative charge region. Thermodynamic observations of cloud base height also show a climatological minimum value in the near-equatorial region. The association of low cloud bases with both narrow updrafts and narrow charging zones may impede the bridging of the large air gap to ground, and thereby suppress cloud-to-ground lightning activity. This width dependence may be more important than the ∼ 10% variation in height of the freezing level in encouraging flashes to ground.

During its first three years, the Tropical Rainfall Measuring Mission (TRMM) satellite observed nearly six million precipitation features. The population of precipitation features is sorted by lightning flash rate, minimum brightness temperature, maximum radar reflectivity, areal extent, and volumetric rainfall. For each of these characteristics, essentially describing the convective intensity or the size of the features, the population is broken into categories consisting of the top 0.001%, top 0.01%, top 0.1%, top 1%, top 2.4%, and remaining 97.6%. The set of "weakest/smallest" features composes 97.6% of the population because that fraction does not have detected lightning, with a minimum detectable flash rate of 0.7 flashes (fl) min(-1). The greatest observed flash rate is 1351 fl min(-1); the lowest brightness temperatures are 42 K (85 GHz) and 69 K (37 GHz). The largest precipitation feature covers 335000 km(2), and the greatest rainfall from an individual precipitation feature exceeds 2 X 10(12) kg h(-1) of water. There is considerable overlap between the greatest storms according to different measures of convective intensity. The largest storms are mostly independent of the most intense storms. The set of storms producing the most rainfall is a convolution of the largest and the most intense storms.This analysis is a composite of the global Tropics and subtropics. Significant variability is known to exist between locations, seasons, and meteorological regimes. Such variability will be examined in Part II. In Part I, only a crude land-ocean separation is made. The known differences in bulk lightning flash rates over land and ocean result from at least two differences in the precipitation feature population: the frequency of occurrence of intense storms and the magnitude of those intense storms that do occur. Even when restricted to storms with the same brightness temperature, same size, or same radar reflectivity aloft, the storms over water are considerably less likely to produce lightning than are comparable storms over land.

Two approaches are used to characterize how accurately the north Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., anomalous VHF noise sources) are neglected. The detailed spatial distributions of retrieval errors are provided. Even though the two methods are independent of one another, they nevertheless provide remarkably similar results. However, altitude error estimates derived from the two methods differ (the Monte Carlo result being taken as more accurate). Additionally, this study clarifies the mathematical retrieval process. In particular, the mathematical difference between the first-guess linear solution and the Marquardt-iterated solution is rigorously established thereby explaining why Marquardt iterations improve upon the linear solution.

The Optical Transient Detector (OTD) is a space‐based instrument specifically designed to detect and locate lightning discharges as it orbits the Earth. This instrument is a scientific payload on the MicroLab‐1 satellite that was launched into a 70° inclination low Earth orbit in April 1995. Given the orbital trajectory of the satellite, most regions of the Earth are observed by the OTD instrument more than 400 times during a 1 year period, and the average duration of each observation is 2 min. The OTD instrument optically detects lightning flashes that occur within its 1300 × 1300 km2 field of view during both day and night conditions. A statistical examination of OTD lightning data reveals that nearly 1.4 billion flashes occur annually over the entire Earth. This annual flash count translates to an average of 44 ± 5 lightning flashes (intracloud and cloud‐to‐ground combined) occurring around the globe every second, which is well below the traditional estimate of 100 fl s−1 that was derived in 1925 from world thunder day records. The range of uncertainty for the OTD global totals represents primarily the uncertainty (and variability) in the flash detection efficiency of the instrument. The OTD measurements have been used to construct lightning climatology maps that demonstrate the geographical and seasonal distribution of lightning activity for the globe. An analysis of this annual lightning distribution confirms that lightning occurs mainly over land areas, with an average land/ocean ratio of ∼10:1. The Congo basin, which stands out year‐round, shows a peak mean annual flash density of 80 fl km−2 yr−1 in Rwanda, and includes an area of over 3 million km2 exhibiting flash densities greater than 30 fl km−2 yr−1 (the flash density of central Florida). Lightning is predominant in the northern Atlantic and western Pacific Ocean basins year‐round where instability is produced from cold air passing over warm ocean water. Lightning is less frequent in the eastern tropical Pacific and Indian Ocean basins where the air mass is warmer. A dominant Northern Hemisphere summer peak occurs in the annual cycle, and evidence is found for a tropically driven semiannual cycle.

It is widely held that identifiable 'convective regimes' exist in nature, although precise definitions of these are elusive. Examples include land / Ocean distinctions, break / monsoon beahvior, seasonal differences in the Amazon (SON vs DJF), etc. These regimes are often described by differences in the realized local convective spectra, and measured by various metrics of convective intensity, depth, areal coverage and rainfall amount. Objective regime identification may be valuable in several ways: regimes may serve as natural 'branch points' in satellite retrieval algorithms or data assimilation efforts; one example might be objective identification of regions that 'should' share a similar 2-R relationship. Similarly, objectively defined regimes may provide guidance on optimal siting of ground validation efforts. Objectively defined regimes could also serve as natural (rather than arbitrary geographic) domain 'controls' in studies of convective response to environmental forcing. Quantification of convective vertical structure has traditionally involved parametric study of prescribed quantities thought to be important to convective dynamics: maximum radar reflectivity, cloud top height, 30-35 dBZ echo top height, rain rate, etc. Individually, these parameters are somewhat deficient as their interpretation is often nonunique (the same metric value may signify different physics in different storm realizations). Individual metrics also fail to capture the coherence and interrelationships between vertical levels available in full 3-D radar datasets. An alternative approach is discovery of natural partitions of vertical structure in a globally representative dataset, or 'archetypal' reflectivity profiles. In this study, this is accomplished through cluster analysis of a very large sample (0[107) of TRMM-PR reflectivity columns. Once achieved, the rainconditional and unconditional 'mix' of archetypal profile types in a given location and/or season provides a description of the local convective spectrum which retains vertical structure information. A further cluster analysis of these 'mixes' can identify recurrent convective spectra. These are a first step towards objective identification of convective regimes, and towards answering the question: 'What are the most convectively similar locations in the world?'

During September - October 2001, the East Pacific Investigation of Climate Processes in the Coupled Ocean Atmosphere System (EPIC-2001) intertropical convergence zone (ITCZ) field campaign focused on studies of deep convection in the warm-pool region of the eastern Pacific. This study combines C-band Doppler radar, sounding, and surface heat flux data collected aboard the R/V Ronald H. Brown during EPIC to describe the kinematic and thermodynamic states of the ITCZ environment, together with tendencies in convective structure, lightning, rainfall, and surface heat fluxes as a function of 3-5-day easterly wave phase.Three easterly waves were observed at the location of the R/V Brown during EPIC-2001. Wind and thermodynamic data reveal that the wave trough axes exhibited positively correlated u and v winds, a slight westward phase tilt with height, and relatively strong ( weak) northeasterly tropospheric shear following the trough ( ridge) axis. Temperature and humidity perturbations exhibited mid- to upper-level cooling ( warming) and drying ( moistening) in the northerly ( trough and southerly) phase. At low levels, warming ( cooling) and moistening ( drying) occurred in the northerly ( southerly) phase.Composited radar, sounding, lightning, and surface heat flux observations suggest the following systematic behavior as a function of wave phase: zero to one-quarter wavelength ahead of ( behind) the wave trough in northerly ( southerly) flow, larger ( smaller) convective available potential energy ( CAPE), lower ( higher) convective inhibition (CIN), weaker ( stronger) tropospheric shear, larger ( smaller) convective rain fractions, higher ( lower) conditional mean rain rates, higher ( lower) lightning flash densities, and more ( less) robust convective vertical structure occurred. Latent and sensible heat fluxes reached a minimum in the northerly phase and then increased through the trough, reaching a peak during the ridge phase ( leading the peak in CAPE). Larger areas of light convective and stratiform rain and slightly larger (10%) area-averaged rain rates occurred in the vicinity of, and just behind, the trough axes in southerly and ridge flow. Importantly, the transition in convective structure observed across the trougth axis when considered with the relatively small change in area mean rain rates suggests the presence of a transition in the vertical structure of diabatic heating across the easterly waves examined. The inferred transition in heating structure is supported by radar-diagnosed divergence profiles that exhibit convective ( stratiform) characteristics ahead of ( behind) the trough.

Satellite observations of lightning flash rate are merged with proximal surface station thermodynamic observations toward understanding the response of the global circuit to temperature. These comparisons support an important role for cloud base height in regulating the transfer of Convective Available Potential Energy (CAPE) to updraft kinetic energy in thunderstorms. This role for cloud base height gives preference to dry bulb temperature over wet bulb temperature as the lightning-regulating temperature in regions characterized by moist convection. INTRODUCTION The global electrical circuit has long been recognized as a natural global integrator of electrified weather [Whipple, 1929]. In this study, “global circuit” is construed to include both the traditional ‘DC’ global circuit as well as the Schumann resonances (SR) in the ELF range. The growing interest in global warming in the 1990’s spurred ideas linking the global circuit with global temperature and the accumulation of a large body of supporting empirical evidence [Williams, 1992, 1994, 1999; Price, 1993; Fullekrug and Fraser-Smith, 1998; Reeve and Toumi, 1999; Markson and Price, 1999; Moore and Idone, 1999; Markson, 2003]. More recently, connections between SR and upper tropospheric water vapor have been investigated [Price, 2000]. The linkage between the global circuit and temperature/water vapor is complicated by two incompletely understood phenomena that resist analytical treatment: tropospheric convection and charge separation in electrified clouds. This study is concerned with a re-examination of the physical linkage between temperature and the global circuit, based primarily on new observations linking thermodynamics and lightning activity at the cloud scale. Perhaps the most important variable linking temperature and the global circuit response is the vertical air motion. Numerous field experiments [Williams et al., 1992; Rutledge et al., 1992] underscore the sensitive relationship between updraft speed and lightning activity, and recent model results [Baker et al., 1999] indicate lightning flash rate is proportional to the forth power of vertical velocity. At the outset it should be emphasized that vertical air motions are caused by temperature gradients, not by temperature, but one expects these quantities to be correlated. One idealization in which such a correlation is absent is the moist neutral troposphere [Xu and Emanuel, 1989], but numerous subsequent observations [Williams and Renno, 1993] cast doubt on this condition. In assessing vertical air motion in moist convection, appeal is often made to the thermodynamic quantity Convective Available Potential Energy (CAPE). The initial hypothesis [Williams, 1992, 1994] linking the global circuit with temperature invoked a temperature-dependent CAPE [Williams and Renno, 1993], but in which the temperature variable was wet bulb potential temperature, θw. This hypothesis is based on tightly correlated relationships between CAPE and θw throughout the tropics in the present climate. Two problems have been identified that weaken the CAPE-based hypothesis. The first is that CAPE over warm tropical oceans is of comparable magnitude as over the land [Williams and Renno, 1993; Lucas et al., 1996], yet the lightning activity differs by more than an order of magnitude [Williams and Stanfill, 2002]. At the same time, the mean maximum θw values over land exceed those over the ocean by 1-2C, equivalent to 1000-2000 joules/kg in CAPE, if CAPE-θw correlations are considered [Williams and Renno, 1993]. This is indirect evidence that the air temperature over land (ocean) has already adjusted to the surface conditions over land (ocean). The second problem is an older one: parcel theory, on which any evaluation of CAPE is based, is flawed by the very nature of turbulent convection: mixing is highly prevalent. The maximum air speeds predicted on the basis of CAPE and parcel theory are substantially greater than observations, in all but the largest supercells [Williams and Stanfill, 2002]. If parcel theory is unreliable, then any hypothesis based on it for which vertical velocity is a key variable may also be unreliable. The two problems cited above led Williams and Stanfill [2002] to consider ways in which differences in updraft speed between land and ocean could be achieved with essentially the same CAPE. They re-examined the idea [Lucas et. al., 1994] that both the width of boundary layer thermals and the width of the ensuing moist convection scale with cloud base height (CBH). The working hypothesis then holds that oceanic convection with typical 500 meter CBH’s will exhibit narrower updrafts, smaller convective ‘bubbles’, and smaller conversion efficiency of CAPE to updraft kinetic energy. Continental convection with CBH’s 2-5 times larger will exhibit stronger updrafts on this basis. CBH is a quantity extractable from thermodynamics [Betts, 1997; Bradbury, 2000], and is proportional to the dew point depression, T-Td, where T is the dry bulb temperature and Td is the dew point temperature of surface air. CBH is a quantity not considered in the evaluation of CAPE, and therefore of no importance in the initial hypothesis linking the global circuit with temperature. The availability of simultaneous values of CBH and lightning flash rate provides an opportunity to test this alternative idea for temperature control of lightning activity. This study is concerned with such a test. METHODOLOGY Unlike previous studies linking lightning activity with temperature on a global basis, this study seeks to relate lightning flash rate and thermodynamic quantities pertaining to the same storm, for many storms. This goal is achieved through comparisons of satellite observations of lightning flash rate and surface thermodynamic observations of the air ingested by the same thunderstorms. Lightning flash rate for thunderstorms throughout the latitude range 35 S to 35 N are recorded with the Lightning Imaging Sensor (LIS) on board the NASA TRMM (Tropical Rainfall Measuring Mission) satellite. This flash rate is representative of the observation periods (of the order of 80 sec) typically afforded by the satellite’s low earth orbit. Flash rates are determinable in day and night conditions, but in this study, the daytime storms were targeted. Routine surface observations of T, Td, and pressure recorded at intervals varying from 1 to 3 to 6 hours at stations worldwide were obtained as a global data set from NCAR as the Surface ADP File. Stations were selected on the basis of their proximity in space and time to those thunderstorms documented by the LIS. Only stations within 50 km of the thunderstorm of interest were queried for thermodynamic information. Maximum values of temperature, CBH and θw were then extracted from the raw station data. For storms in close proximity to stations it was fairly typical to see the values of all these quantities rising prior to the storm, and then dropping fairly abruptly at the time of the storm. Connected satellite (flash rate) and ground station (T, CBH, θw ) scenarios were identified for the entire period January-June, 2000. RESULTS Figure 1 shows the results of thunderstorm flash rate (flashes/min) versus thunderstorm cloud base height (meters) for all thunderstorms within 50 km of a corresponding ground station. The data were grouped in 100-meter intervals of CBH with standard deviations about the mean flash rates also included. Despite considerable scatter, the results show a quasi-exponential increase of mean flash rate with CBH and an order-ofmagnitude increase from the 500 m typical of tropical oceanic convection to the 3000 m typical of strongly continental convection. (Note however that while the full range of 50

The relationship between cloud height and lightning activity is examined using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. Coincident data from the precipitation radar (PR) and Lightning Imaging Sensor aboard the TRMM satellite are used to examine whether lightning flash rate is proportional to the fifth power of cloud top height. This study is unique in that (1) the relationship between instantaneous rather than maximum storm height and flash rate is obtained and (2) relatively unbiased full data sets for different locations and seasons over the globe are used. The relationship between thunderstorm height and flash rate is nonlinear with large variance. The overall trend shows that flash rate increases exponentially with storm height. Some tall thunderstorms do not have large flash rates, but the reverse situation never occurs. The fifth power dependency that is derived from scaling laws is not inconsistent with, but not necessarily required by, the observed data.

Range dependencies in total (intracloud and cloud to ground) lightning observed by the Kennedy Space Center Lightning Detection and Ranging (LDAR) network are established through cross comparison with other lightning sensors. Using total lightning observed from space by the Lightning Imaging Sensor (LIS), LDAR flash detection efficiency is shown to remain above 90% out to 90–100 km range, and to be below 25% at 200 km range. LDAR VHF source location error distributions are also determined as a function of range and are found to be asymmetric with standard deviation increasing roughly as r2. Range normalization schemes for total VHF source density are tested and shown to yield significant improvements in correlation with National Lightning Detection Network (NLDN) ground flash density at hourly, daily, monthly, and climatological timescales (up to 50% over uncorrected source densities using an exponential‐in‐range correction factor with 40–50 km e‐folding scale).

Four years of observations from the NASA Optical Transient Detector and Global Atmospherics National Lightning Detection Network are combined to determine the geographic distribution of the climatological intracloud-cloud-to-ground (CG) lightning ratio, termed Z, over the continental United States. The value of Z over this region is 2.64-2.94, with a standard deviation of 1.1-1.3 and anomalies as low as 1.0 or less over the Rocky and Appalachian Mountains and as high as 8-9 in the central-upper Great Plains. There is some indication that Z covaries with ground elevation, although the relationship is nonunique. Little evidence is found to support a latitudinal covariance. The dynamic range of local variability is comparable to the range of values cited by previous studies for latitudinal variation from the deep Tropics to midlatitudes. Local high Z anomalies in the Great Plains are coincident with anomalies in the climatological percentage of positive CG occurrence, as well as in the occurrence of large positive CGs characteristic of organized or severe storms. This suggests that storm type, morphology, and level of organization may dominate over environmental cofactors in the local determination of this ratio.

An analytic framework is developed in which to analyze climatological VHF (66 MHz) radiation measurements taken by the Kennedy Space Center Lightning Detection and Ranging (LDAR) network. A 19 month noise‐filtered sample of LDAR observations is examined using this framework. It is found that the climatological impulsive VHF source density as observed by LDAR falls off ∼10 dB every 71 km of ground range away from the network centroid (a 31 km e‐folding scale). The underlying vertical distribution of impulsive VHF sources is approximately normally distributed with a mean altitude of 9 km and a standard deviation of 2.7 km; this implies that the loss of below‐horizon sources has a negligible effect on column‐integrated source densities within a 200 km ground range. At medium to far ranges, location errors are primarily radial and have a slightly asymmetric distribution whose standard deviation increases as r2. Error moments estimated from observed lightning are significantly higher than those from aircraft‐based signal generator or analytic estimates. LDAR bulk flash detection efficiency is predicted to be above 90% to 94–113 km range from the network centroid and to fall below 10% at ranges greater than 200–240 km.

3‐dimensional lightning mapping observations obtained in central Oklahoma by the New Mexico Tech Lightning Mapping Array (LMA) have been compared with optical observations of the discharges from space obtained by NASA's Lightning Imaging Sensor (LIS). Excellent spatial and temporal correlations were obtained between the two sets of observations. All lightning discharges seen by LIS were mapped by the LMA. Most of the detected optical events were associated with lightning channels that extended into the upper part of the storm. Cloud‐to‐ground discharges that were confined to mid‐ and lower‐altitudes were less well detected than intracloud discharges, and tended to be detected late in the discharge. Intracloud discharges were readily detected by LIS as soon as they extended into the upper part of the storm, and often extensively illuminated the cloud at the end or part way through the discharge. The extensive illumination was impulsive in nature and was also seen at the end of some cloud‐to‐ground discharges.

NOx (NO and NO2) and ozone were measured on 98 flights during August to November 1997 in the framework of the projects Pollution From Aircraft Emissions in the North Atlantic Flight Corridor (POLINAT 2) and Subsonic Assessment Ozone and Nitrogen Oxide Experiment (SONEX). The fully automated measurement system Nitrogen Oxides and Ozone Along Air Routes (NOXAR) was permanently installed aboard an inservice Swissair B‐747 airliner operating in the North Atlantic Flight Corridor. Below the tropopause, predominantly over the U.S. east coast, the patchy occurrence of NOx enhancements up to 3000 parts per trillion by volume (pptv) was observed frequently and led to a lognormal probability density function of NOx. These plumes extend over several hundred kilometers. In three case studies the origin of such plumes was investigated using back trajectories, satellite infrared images, and lightning observations from the U.S. National Lightning Detection Network (NLDN) and the Optical Transient Detector (OTD) satellite instrument. In the case of frontal activity above the continental United States, the location of NOx plumes was explained with maps of convective influence. In another case, NOx seems to have been produced by lightning in a marine thunderstorm over the eastern Atlantic. Lightning activity triggered over the warm Gulf Stream is found to be an important source for the regional upper tropospheric NOx budget, at least for the time period considered. With a method that we call “lightning tracing” we show for the first time that (in some cases) the number of lightning flashes, accumulated along back trajectories, was proportional to the NOx concentrations observed several hundred kilometers downwind of the anvil outflows. We suggest that mixing processes in convective clouds reduce the initially highly heterogeneous NOx field rapidly, but that following this phase, the structure of large‐scale plumes remains stable over relatively long periods of time (as they decay).

Observations from the National Aeronautics and Space Administration Optical Transient Detector (OTD) and Tropical Rainfall Measuring Mission (TRMM)-based Lightning Imaging Sensor (LIS) are analyzed for variability between land and ocean, various geographic regions, and different (objectively defined) convective "regimes.'' The bulk of the order-of-magnitude differences between land and ocean regional flash rates are accounted for by differences in storm spacing (density) and/or frequency of occurrence, rather than differences in storm instantaneous flash rates, which only vary by a factor of 2 on average. Regional variability in cell density and cell flash rates closely tracks differences in 85-GHz microwave brightness temperatures. Monotonic relationships are found with the gross moist stability of the tropical atmosphere, a large-scale "adjusted state'' parameter. This result strongly suggests that it will be possible, using TRMM observations, to objectively test numerical or theoretical predictions of how mesoscale convective organization interacts with the larger-scale environment. Further parameters are suggested for a complete objective definition of tropical convective regimes.