1. Introduction
Over the tropical ocean, convective storm cells transport surface air to the upper troposphere in the upward leg of the planetary-scale Hadley circulation (Riehl and Malkus 1958; Riehl and Simpson 1979). These convective cells are observed to have only modest updrafts in the low and midtroposphere (Zipser and LeMone 1980; Jorgensen and LeMone 1989; Lucas et al. 1994; Wei et al. 1998). The modest updrafts make it seem difficult for oceanic cells to transport significant mass from surface to upper troposphere.
In an attempt to resolve the apparent paradox of slow updrafts with the clear requirement for mass transport to the upper troposphere, Zipser (2003) proposes that oceanic updrafts accelerate above the midtroposphere because of the release of latent heat of fusion. Fierro et al. (2009) see this mechanism at work in an aircraft and modeling study of a tall oceanic cell. In contrast, the present study examines a large number of such cells, observed by the Tropical Rainfall Measuring Mission (TRMM) satellite, and seeks evidence of this mechanism.
This study examines the tallest convective cells over the tropical ocean to determine if they have unusually fast updrafts or if they form in unusual environments. Satellite surveys suggest that precipitation at 17 km (56 000 feet) is especially rare over ocean (Liu and Zipser 2005, Fig. 1a; Liu et al. 2007, Figs. 8a, 9a). In contrast, cloud tops are observed 17 km high almost equally often over ocean and land (Casey et al. 2007, Fig. 1a; Dessler et al. 2006, Fig. 2).
The TRMM satellite observes a sufficient number of cells with 17-km-tall precipitation that the influence of continents can be minimized by analyzing only the cells that are at least 1000 km away from continents (Petersen and Rutledge 2001). Land differs from ocean in a number of ways that might increase the relative vigor of continental convection (Lucas and Zipser 1996), a subject of ongoing research. Unlike the ocean, the surface roughness of land varies greatly from place to place, which can encourage low-level convergence (Van Den Heever and Cotton 2007, p. 828). The sun warms land in the afternoon, which increases convective instability (Michaud 1996, p. 1211). Various natural and manmade objects emit condensation nuclei over land, which may increase the mass of liquid hydrometeors lifted to the freezing level (Khain et al. 2005).
The study begins by developing quality control techniques to distinguish the rare 17-km-tall cells from equally rare instrument anomalies (section 2). Next, sections 3 and 4 examine observations of 17-km-tall cells and make inferences about updraft speed and related microphysics. Last, section 5 discusses several issues raised by the results of this study.
2. Data and method
a. Satellite instruments
The TRMM satellite provides a unique platform for studying individual convective cells because it observes them, near simultaneously, with radar, passive microwave, infrared, and lightning sensors (Kummerow et al. 1998). The TRMM precipitation radar (PR) measures the three-dimensional structure of storms, but with lower resolution than radars on research aircraft (Hood et al. 2006, section 2). When compared to aircraft, the TRMM satellite has the advantage of providing a fairly uniform coverage of the tropics and of observing literally millions of storms (Zipser et al. 2006) during more than a decade of continuous operation.
The TRMM precipitation radar measures reflectivity profiles with a 250-m vertical resolution, 5-km horizontal resolution, and approximately 5-km horizontal spacing between profile centers (Kozu et al. 2001). The 5-km horizontal resolution suggests a nominal 20 km2 horizontal cross-sectional area for an individual reflectivity profile (πr 2 ≈ 20 km2). At the center of the TRMM radar’s data swath, the profile is vertical and the center point of the profile’s highest observation has a 19.75-km altitude most of the time. At the edge of the swath, profiles are tilted 17° from vertical and the highest observation has 18.8-km altitude most of the time [Kelley 2008, Eq. (3.4)]. In place of “profile”, the term “ray,” “angle bin,” or “line of sight” is sometimes used.
The TRMM Microwave Imager (TMI) is a passive microwave radiometer that measures 37-and 85-GHz radiation, among other frequencies. TMI’s conical scan intersects the earth’s ellipsoid at a fixed 53° angle from vertical (Kummerow et al. 1998). To first order, 85-GHz radiation is emitted by the earth’s surface and by liquid hydrometeors. TMI sees the 85-GHz radiation that is not scattered out of the line of sight by the intervening layer of ice hydrometeors in the upper portion of a convective storm cell (Olson et al. 2001). The situation at 37 GHz is similar except that ice scattering plays a smaller role and that the larger footprint is more likely to have a considerable amount of signal come from the horizontal region outside of the convective cell.
The TRMM Visible and Infrared Scanner (VIRS) measures 11-μm infrared brightness temperature with better than ±1-K accuracy and 2-km resolution (Lyu and Barnes 2003). The 11-μm temperature corresponds to the air temperature, on average, 1 km below the visible cloud top (Sherwood et al. 2004, Fig. 1).
The TRMM Lightning Imaging Sensor (LIS) has a 75% to 90% detection efficiency for intracloud and cloud-to-ground lightning during LIS’s typical observation time of ∼83 s for a given point on the ocean’s surface (Christian 2000; Boccippio et al. 2000, p. 2232). Because of its brief observation time, LIS has difficulty reliably measuring flash rates under two flashes per minute.
Figure 1 indicates, in a simplified way, how the TRMM instruments provide information about various parts of a tall convective cell. The figure shows clouds observed by VIRS and precipitation inside them observed by the TRMM radar. As suggested by the diagram, the measurements of the various instruments come from different altitudes within the cloud. As described in the next section, this study identifies tall cells using the height of the precipitation region inside of them, not the height of their cloud top.
b. Definition of tall convective cell
Ice precipitation consists of ice particles that are large enough to require an updraft to maintain or increase their altitude. In contrast, ice particles too small to rapidly fall out of the cloud generally define the outer boundary of the cloud above the freezing level. Even cloud ice has a nonzero fall speed, so the boundary between cloud ice and precipitation ice is somewhat arbitrary. Houze (1993, pp. 91, 94) and Matrosov (1999), for example, define the smallest precipitation ice to be 0.3 mm in diameter or to have a 0.3 m s−1 fall speed. Cloud ice may include individual crystals, ice that was rimed by accreting supercooled liquid water, or aggregates of several crystals (Houze 1993, p. 85). Below the freezing level, the analogous boundary between cloud droplets and raindrops is often considered to be a ∼0.1-mm diameter (Houze 1993, p. 75), which corresponds to approximately a 0.3–0.8 m s−1 fall speed (Gunn and Kinzer 1949, Table 1; Beard and Pruppacher 1969).
This study uses a 20-dBZ radar reflectivity threshold to define the top of the region within the convective cell that contains precipitation-sized ice. The same 20-dBZ threshold is used in previous studies of convection (Liu and Zipser 2005; Geerts and Dejene 2005; Kelley 2008). A 20-dBZ threshold can safely be used on the entire TRMM dataset. Kozu et al. (2001) find that the TRMM radar’s sensitivity was 16–18 dBZ prior to the August 2001 orbit boost, and others find that the sensitivity was 17.2–19.2 dBZ after the boost (Shimizu et al. 2003; Takahashi and Iguchi 2004b).
In the context of this paper, a tall cell is defined as a collection of adjacent radar reflectivity profiles, each of them containing a 20-dBZ radar reflectivity signal at least 17 km above the earth’s ellipsoid. The ellipsoid is within 50 m of the ocean surface in most locations (Seeber 1993, p. 454). For convenience, the text refers to these cells as “17 km tall” cells, although the 20-dBZ height of the sample of oceanic cells in this study ranges from 17 km to ∼18.4 km.
The number of these cells that lift ice into the stratosphere depends where one places the lower boundary of the tropical stratosphere. By convention, the climatological lower boundary of the tropical stratosphere may be marked by the 380-K potential temperature level. Holton et al. (1995) place the 380-K level at ∼15-km altitude, while Fueglistaler et al. (2009) place the 380-K level at ∼17-km altitude. As shown in Fig. 1, Alcala and Dessler (2002) define 14 to 18 km as the climatological location of the tropical tropopause layer with the stratosphere beginning just above that layer. Fueglistaler et al. (2009) place the lower boundary of the tropical stratosphere at 18.5 km.
c. Quality-control procedures
From 1998 to 2007, the TRMM precipitation radar observed 3212 reflectivity profiles over the ocean that contain a 20-dBZ radar reflectivity signal at least 17 km above the earth’s ellipsoid. The height calculation takes into account the tilt of the profile relative to the earth’s ellipsoid (Kelley 2008, section 3.2). These 3212 profiles are labeled “convective rain certain” by the TRMM 2A25 algorithm and have a zero value for the TRMM 1B21 system noise warning flag (JAXA 2005). Only ∼21% of these profiles (681 out of 3212 profiles) are “open ocean” profiles; that is, they occur at least 1000 km from continents. This 21% of the profiles is retained for further analysis.
Of the radar profiles far from continents, 11% of them are rejected (75 out of 681 profiles) because TMI or VIRS collected no data or because LIS observed the region near the radar profile for less than 60 s. It is important to exclude radar profiles that are contaminated with nonmeteorological signals. After we apply the two groups of criteria described in the following paragraphs, only 48% of the profiles remain (325 out of 681 profiles).
The first group of criteria detects radio interference from manmade devices transmitting at the TRMM radar’s 13.8-GHz frequency (JAXA 2005, p. 21). To search for radio interference, the median dBZ value is calculated every 2 km along the profile from 10-km altitude to the altitude of the tallest 20-dBZ signal. If all of these 2-km medians differ by ≤1 dB, then the profile is rejected for being so nearly constant with respect to altitude that no meteorological process could have produced it. If ≥40 dBZ is observed in the top altitude bin or ≥70 dBZ is observed at any altitude, then the profile is rejected. If the system noise estimated by the TRMM 1B21 algorithm is above −109.75 dBm, then the profile is rejected (Takahashi and Iguchi 2004a, Fig. 8).
A second group of criteria detects the rare but anticipated random fluctuation of the noise level inside the TRMM radar (JAXA 2005, p. 21). If half or more of the bins between the 10-km altitude and the maximum 20-dBZ height contain reflectivities weaker than 20 dBZ, then the profile is rejected. If more than one of the three bins have <20 dBZ immediately beneath the bin with the highest altitude 20-dBZ signal, then the profile is rejected. If the profile’s 25-dBZ height is less than 10 km, then the profile is rejected.
TMI and VIRS provide evidence that each of the 325 radar profiles just selected do contain a significant meteorological event. All 325 radar profiles have an 11-μm cloud-top temperature and an 85-GHz polarization corrected brightness temperature (PCT) under 200 K. Cecil et al. (2002) define PCT at 85 and 37 GHz.
The observed annual frequency of 17-km-tall oceanic profiles appears to be slightly greater after the August 2001 boost in the TRMM satellite’s orbit than before the boost. During 1998 to 2000, the TRMM radar annually observed 9 to 20 oceanic profiles that were 17 km tall. During 2002 to 2007, the TRMM radar annually observed 12 to 27 oceanic profiles that were 17 km tall. It is unclear if this difference is natural variability or if it is related to the orbit boost. The performance of the TRMM radar has been validated following the orbit boost (Shimizu et al. 2003; Takahashi and Iguchi 2004b).
One variation in the observed frequency of 17-km-tall oceanic profiles does appear to be instrument related. The TRMM radar observes more such profiles near the edge of the radar swath than near the swath center. More specifically, if one takes five lines of sight at one edge or the other edge of the precipitation radar’s swath (lines of sight 1–5 or 44–49), then those five lines of sight will contain a 17-km-tall oceanic profile approximately twice as often as the five lines of sight at the center of the swath (lines of sight 22–26). Kozu (1989, Fig. 3) suggests that the lower portion of a TRMM radar’s cylindrical data volume would drop approximately 0.25 km lower when the profile were tilted 17° off vertical compared with a vertical profile. Next, combine this geometric idea with a meteorological idea: the frequency with which a 20-dBZ radar reflectivity is observed increases approximately exponentially when altitude is decreased. A 0.25-km decrease in altitude corresponds to roughly a factor of two increase in frequency (Cecil et al. 2002, Fig. 3b fourth panel).
d. Grouping profiles into convective cells
As stated in section 2b, this study defines a tall cell as a set of adjacent radar reflectivity profiles that each contains a 20-dBZ signal at least 17 km tall. The 325 radar reflectivity profiles identified in the previous section can be grouped into 174 such “tall cells.”
This study finds that most tall cells contain only one or two TRMM reflectivity profiles with a 20-dBZ signal 17 km high. Table 1 lists the 25th to 75th percentile range of horizontal area as 20 to 40 km2, using a multiple of the nominal 20-km2 horizontal area of a TRMM radar profile (column e, row 9). Only 7% of the tall cells are “wide” (13 out of 174), defined in this study as cells that contain five or more adjacent reflectivity profiles with a 20-dBZ signal 17 km high.
The actual horizontal cross section of a storm cell’s ice column is likely to differ somewhat from the nominal area reported in Table 1 because of hydrometeor variations on a scale too small for the TRMM radar to resolve. The actual area may be greater or less than the observed area. For the sake of argument, a 20-dBZ signal might exist over a 30-km2 area but only one of the 20-km2 radar profiles would detect a 20-dBZ signal. On the other hand, a 23-dBZ signal might exist over a 10-km2 area, for example, and be reported as a profile with 20-dBZ signal over the profile’s nominal 20-km2 area.
Having located 17-km-tall oceanic cells, the next step is to calculate each cell’s observed properties. The maximum 20-dBZ height and 40-dBZ height of a cell are easy to identify as the maximum occurring in any of the radar reflectivity profiles that make up the cell.
Before determining the exact method for calculating other properties of a tall cell, several cells were examined using diagrams similar to Fig. 2a. The radar-observed 17-km-tall ice precipitation signal (red) is placed at the center of Fig. 2a. Near to the radar observation is the region where TMI observes significant ice scattering; that is, the low 85- and 37-GHz temperatures (green and violet). Also within a 15-km radius (gray line) is an LIS-observed lightning flash (yellow) and a VIRS-observed very cold cloud top (dark blue). The cell in Fig. 2, as is true for many tall cells, occurred inside of a mesoscale convective system (MCS) that is several hundred kilometers across (white regions in Figs. 2b–d). This MCS contains several active convective cells (dark red regions in Figs. 2b–e). As shown by the arrows in the lower right of Fig. 2a, National Oceanic and Atmospheric Administration’s (NOAA) National Centers for Environmental Prediction (NCEP) 6-hourly reanalysis suggests that the lower- to midtropospheric wind (925–500 hPa) is blowing toward the west northwest while the upper-level outflow (300–200 hPa) is blowing toward the southwest.
Diagrams such as Fig. 2 show that the extreme observations of the various TRMM instruments generally occur within 15-km horizontally of the 17-km-tall radar signal. Because of the different tilts of the various TRMM instruments (Kummerow et al. 1998; Hong et al. 2000), the tall cell observations made by the different instruments do not line up perfectly. The horizontal fields of view overlap the most when multi-instrument comparisons are made somewhere in the upper troposphere because the upper troposphere contains the ice being observed. For this reason, the comparisons in this paper between TMI, VIRS, and the TRMM radar are made at an 8-km altitude.
3. The frequency and location of 17-km-tall oceanic cells
a. Observed frequency and location
This section reports the observed frequency of 17-km-tall oceanic cells as a function of geographic location, time of day, season, and mesoscale setting. In terms of geography, the TRMM radar observes most 17-km-tall cells in the west Pacific warm pool (Figs. 3 and 4a). The geographic location also roughly corresponds to locations where the temperature at 17-km altitude is frequently cold (Fig. 4b), as calculated in section 4d. Figure 4b suggests a steep drop in the tropopause height between 20° and 25° of latitude from the equator (Hoinka 1999, Fig. 1). TRMM observes few 17-km-tall cells farther than 20° from the equator.
With respect to warm ocean and cool 17-km temperature, Fig. 4 shows that the Atlantic Ocean is less favorable for 17-km-tall cells than is the west Pacific warm pool. Perhaps for this reason, the 17-km-tall cells that do form in the Atlantic have favorable mesoscale settings: mesoscale convective systems or cyclonic systems (Figs. 3a,b). TRMM does not observe any “isolated” 17-km-tall cells in the Atlantic (Fig. 3c), although TRMM does observe such cells in the west Pacific warm pool. In this context, “isolated” means that a cell forms outside of an MCS or cyclonic system.
Geographic exceptions do occur, such as the 17-km-tall cell shown in Fig. 2. In Fig. 3b, this same cell can be seen just south of the equator and a little more than 1000 km west of the west coast of South America. This cell formed during the El Niño of early 1998, when the ocean temperature was warmer than usual for this region (29.8°C at the time of the TRMM overflight based on the weekly Reynolds sea surface temperature). In other respects, this geographically unusual cell is comparable to other 17-km-tall oceanic cells.
The 174 oceanic cells that are 17 km tall and far from continents exhibit the diurnal variation that one would expect over ocean (Liu and Zipser 2008, Fig. 3b). There are slightly more 17-km-tall cells in early morning than in early afternoon: 38% of cells occur from 2000 to 0400 local time (LT) and 26% of cells occur from 0900 to 1700 LT. In this paper, the universal time in the TRMM archive is converted to a local time by adding an offset equal to the convective cell’s longitude divided by 15°E longitude per hour.
The seasonal variation in the occurrence of 17-km-tall oceanic cells is also what one would expect. In the Northern Hemisphere, 78% of the cells occur in July through December, bracketing the early fall when the ocean’s surface is warmest. In the Southern Hemisphere, 81% of the cells occur in January through June, which is six months offset from the Northern Hemisphere. For the Sahel region of Africa discussed later, 97% of the cells occur in April through September.
One would expect tall oceanic convection to occur within an MCS or tropical cyclone (Rossow and Pearl 2007). A full 43% of the TRMM-observed 17-km-tall oceanic cells (74 out of 174) occur both inside of an MCS as defined by Nesbitt et al. (2000, p. 4091) and outside of any tropical depression, tropical storm, or tropical cyclone (Table 1). To make this determination, this study obtains worldwide coverage by combining best-track data from the National Hurricane Center and the Joint Typhoon Warning Center.
The TRMM satellite observes tall cells within 500 km of the center of various cyclonic systems including tropical depressions (9% or 15 cells), tropical storms (12% or 20 cells), category 1 tropical cyclones (5% or 8 cells), and category 2 or 3 tropical cyclones (1 cell each). In 1998–2007, TRMM observed no 17-km-tall cell near a category 4 or 5 tropical cyclone. Because only tropical cyclones of category 2 and stronger tend to have well-defined eyewalls (Velden et al. 2006, Figs. 3, 4; Dvorak 1975, Figs. 2, 3), TRMM almost never observes a 17-km-tall cell in a tropical cyclone eyewall. Some of the cyclonic systems that contain 17-km-tall cells also meet Nesbitt et al.’s (2000) criteria for MCSs. For the sake of clarity, cells in cyclonic systems are included only in the cyclonic category of Table 1 and are excluded from the MCS category of Table 1.
While cells closer than 1000 km to continents are excluded from the statistics in this study, Fig. 4a does show the locations of cells that are only 100–1000 km away from continents. There are almost 3 times as many of these coastal 17-km-tall cells as there are 17-km-tall cells far from continents: 490 coastal cells are 100–1000 km away from continents, while the previously cited 174 open-ocean cells are at least 1000 km offshore. The coastal cells are clustered east of India and Asia, and to a lesser extent, in the Gulf of Mexico and west of equatorial Africa.
b. Frequency of occurrence
Because of limited sampling, the TRMM radar sees only a fraction of the 17-km-tall cells that occur in nature. The true frequency of occurrence over the open ocean is likely to be much greater than the observed 174 cells in 10 years.
To estimate the frequency of occurrence, one must first assume an average duration for the 17-km-tall signal of an individual cell. This assumption is necessary because the TRMM satellite cannot measure duration: the satellite flies over a particular cell only once before the cell dissipates. After estimating the frequency of occurrence, the estimate can easily be adjusted for different assumed durations because frequency varies inversely with average duration of an individual cell.
If the assumed duration of an individual cell’s 17-km-tall signal were changed from 5 min to 1 h, then frequency of occurrence would drop from 41 to 3 cells per day. The change from 41 to 3 cells per day is obtained by holding constant the total duration of the 17-km-tall signal while changing the average duration of an individual cell. A one-hour duration for an individual cell’s 17-km-tall signal would suggest some sort of plume of buoyant air flowing across the level of neutral buoyancy (Emanuel 1994, chapter 2; Houze 1993, section 7.3.2). A plume of such long duration at such high altitude is difficult to imagine. As a point of reference, an hour is close to the overall duration of a convective cell of more modest height and longer than the ∼20 min active phase of a typical convective cell over land (Houze 1993, Fig. 8.2).
In contrast, sticking to the original 5-min duration would suggest that the 17-km-tall signal might be due to a few buoyant “bubbles” overshooting their level of neutral buoyancy (Malkus and Ronne 1954). To a first approximation, an air parcel that overshoots and returns to its neutral level has undergone half of a gravity-driven oscillation (Lane et al. 2001, p. 1250). Hence, the process would occur in half of the Brunt–Väisälä period of approximately 4–5 min in the upper troposphere (Lane and Reeder 2001, p. 2428; Wallace and Hobbs 2006, p. 89).
The Kwajalein ground radar provides further evidence that the typical duration of a 17-km-high precipitation signal is closer to 5 min than to 1 h. Kwajalein Atoll is at the edge of the west Pacific warm pool as indicated on Fig. 4a with the dot labeled “KWAJ.” The Weather Surveillance Radar-1988 Doppler (WSR-88D) ground radar at Kwajalein Atoll (8.7°N, 167.7°E) may be the only weather radar over open ocean with a well-calibrated multiyear archive of observations. Marks et al. (2009) and Silberstein et al. (2008) calibrate Kwajalein radar reflectivity, but they do not search for 17-km-tall cells. Even after their careful calibration, it remains difficult to definitively identify 17-km-tall cells because of the ground radar’s coarse vertical resolution. In an initial pass through the Kwajalein 2000 to 2004 archive, this study tentatively locates 43 convective cells that have a 20-dBZ signal at least 17 km high. Of these cells, 90% maintain a 20-dBZ signal ≥17 km high for just one radar volume scan; that is, for approximately 5 to 10 min.
4. Properties of 17-km-tall cells
a. TRMM-observed properties
This section describes the observed properties of 17-km-tall oceanic cells, compares these cells to oceanic convection in general, and last, tries to infer properties of 17-km-tall cells that the TRMM satellite cannot directly observe. Table 1 lists some properties that the TRMM satellite does observe. The ranges in the table state the 25th and 75th percentiles.
Table 1 breaks the overall population of 17-km-tall oceanic cells into three categories based on their mesoscale setting. The categories are cells that form inside of cyclonic systems (tropical cyclones, storms, or depressions), cells that form inside of mesoscale convective systems, and “isolated” cells whose mesoscale systems are too weak to be classified as a cyclonic system or MCS. The properties of the three categories are described in columns a, b, and c of Table 1. In many respects, the cells in these three categories have similar properties even though different dynamics are at work in their mesoscale setting. In particular, the three categories of cells have similar ranges of cloud-top height, maximum height reached by precipitation-sized ice, lightning flash rates, and horizontal area of the 17-km-tall precipitation region inside of each cell (Table 1, rows 8, 2, 6, and 9).
The most striking difference in the three categories of 17-km-tall cells may be the number of “wide” cells in each category. In cyclonic systems, a full 22% of 17-km-tall cells are wide. In this study, “wide” means that a cell contains at least five adjacent radar profiles with a 17-km-tall 20-dBZ signal. Wide cells are most frequent in cyclonic systems, less frequent in MCSs, and never observed outside of MCSs and cyclonic systems. One explanation for this pattern might be that the locations that are conducive to MCSs and cyclonic systems are already favorable for wide 17-km-tall cells. An alternative explanation is that cyclones and MCSs transform their environment into being conducive for wide 17-km-tall cells.
The 17-km-tall oceanic cells can be put into context by comparing them with the general population of oceanic storms. To do this, Table 2 is constructed from approximately 8.9 million features in the TRMM precipitation feature database that are at least 1000 km away from continents, that are within 35° of the equator, and that occurred between 1998 and 2007. These features range from entire mesoscale systems to small isolated storms that cover only an 80-km2 area of the ocean’s surface (Nesbitt et al. 2000, p. 4091). Table 2 states the extreme values that the precipitation features exhibit with the probability stated in the table’s top row.
Table 2 shows that both the 20-dBZ height and cloud-top height of a 17-km-tall cell are rare to an approximately equally degree. Among oceanic features, a 20-dBZ height of 17 km has a probability between 10−4 and 10−5, which is equivalent to a frequency of 1 in 104 to 105 features (row 1). The extremely cold cloud tops of 17-km-tall cells (176–180 K) also occur in about 1 out of 104.5 oceanic features (row 6). These cloud tops are cold, but not record holders (Ebert and Holland 1992).
Table 2 also shows that the least unusual property of 17-km-tall oceanic cells is the height of the 40-dBZ signal, which is typically only 5.0 to 6.8 km. Row 2 of Table 2 shows that about 0.1%–1% of precipitation features over the tropical ocean have a 40-dBZ height similar to the 40-dBZ height of the much rarer 17-km-tall oceanic cells. The 40-dBZ height loosely correlates with the updraft speed in the midtroposphere (Zipser et al. 2006). The rather low 40-dBZ height is the first piece of evidence that 17-km-tall cells have relatively modest updraft speeds in midtroposphere, a topic discussed further in sections 4b and 4c. This conclusion leaves open the possibility that 17-km-tall cells might have stronger updrafts prior to achieving a 17 km height. On the basis of aircraft radar observations, Heymsfield et al. (2010, section 2c) suggest that the strongest updrafts occur prior to a tall cell achieving its radar-observed maximum height.
Some properties of 17-km-tall cells cannot be directly observed by the TRMM satellite, but it is possible to infer some information about these properties from TRMM observations. In particular, the total mass of ice precipitation at various altitudes remains somewhat mysterious because the TRMM satellite does not measure the distribution of hydrometeor size, density, or phase. Nonetheless, it is reasonable to expect a combination of snow, graupel, supercooled raindrops, frozen raindrops, cloud droplets, and cloud ice just above the freezing level in tall oceanic cells (Kingsmill et al. 2004, Fig. 9; Black et al. 2003). McFarquhar and Black (2004, Fig. 7b) describe graupel as generally 2–4-mm diameter aggregates of lightly rimed ice particles with low density in the neighborhood of 0.2 g cm−3. While graupel is likely in oceanic cells, hail is unlikely (McCumber et al. 1991; Li et al. 2008, p. 2703). Hail is solid ice at least 5 mm in diameter (Glickman 2000). The authors know of no report from research aircraft of hail in convective cells far from land, and there are extremely few reports of hail at sea level from ship or remote island (e.g., Takahashi 1987; Young 1927, p. 147; Frisby and Sansom 1967, p. 342).
When lightning is observed, one can be more confident that a 17-km-tall cell contains a mixture of graupel and small ice particles. Such a mix of ice hydrometeors, in the presence of supercooled liquid cloud water and an updraft, is consistent with the widely accepted noninductive ice–ice collision process of cloud electrification that leads to lightning (Zipser and Lutz 1994; Rakov and Uman 2003, pp. 85–88; Simpson et al. 1998, p. 30). The TRMM LIS observes at least one lightning flash in 48% of the 17-km-tall oceanic cells. Cells without any LIS-observed lightning flashes may have no lightning, or alternatively, may have flash rates that are too low for LIS to detect.
A second unsolved mystery is the rainfall rate at the ocean surface under these 17-km-tall cells (Table 3). The surface rain estimates of the TRMM radar and TMI differ because the two instruments have different horizontal resolution and different responses to hydrometeors of various sizes (Masunaga et al. 2002, p. 850). Furthermore, separate algorithms are used to estimate surface rain for TMI over land and over ocean. All of these factors may contribute to the systematic difference in surface rain rate of 17-km-tall cells: on average the radar estimate is triple TMI’s over ocean and half of TMI’s over the Sahel region of Africa, a region discussed in section 4c.
In 17-km-tall cells, estimating surface rain is difficult because intervening hydrometeors attenuate 65%–99% of the TRMM radar’s signal. The two-way attenuation near the ocean’s surface is 3.5–19.5 dBZ according to the TRMM 2A25 algorithm. The green dots in Fig. 5a indicate that, below the freezing level, ≥90% of the signal is attenuated in most 17-km-tall oceanic cells.
Rows 12 through 16 of Table 3 show that 17-km-tall oceanic cells are “off the charts” relative to some published ranges of brightness temperature and of indices used to estimate surface rainfall rate from passive microwave observations (Liu and Curry 1998, Fig. 1; Bennartz and Petty 2001, Fig. 12; Dinku and Anagnostou 2005; Ferraro and Marks 1995, Fig. 1b; Berg et al. 2002, Fig. 6).
b. Lower bound of oceanic cells’ updraft speed
The introduction of this paper states that updraft speed is one of the poorly understood properties of 17-km-tall cells. This section and the following one will try to extract information about updraft speed from TRMM observations.
Various TRMM observations suggest a 10 m s−1 lower bound for the midtropospheric updraft speed based on evidence presented in this section. This paper only attempts to establish a lower bound for the peak updraft speed, not the mean updraft speed over a 1-km2 horizontal area or even over the nominal cross-sectional area of a TRMM precipitation radar profile (20 km2). Detailed characterization of the horizontal and vertical extent of the updraft is simply not possible using only TRMM observations.
A 10 m s−1 lower bound for the midtropospheric peak updraft is reasonable even though Black et al. (1996, Fig. 5a) finds that ∼1% of hurricane eyewall updrafts exceed just 8 m s−1 along 0.75 km of an aircraft’s flight path. More recently, Heymsfield et al. (2010, Figs. 6d and 7) observe several convective cells with 10 m s−1 updrafts near 5-km altitude increasing to a maximum of 15–25 m s−1 at 9–14-km altitude. These convective cells were both over ocean and outside of tropical cyclones. Anderson et al. (2005, Fig. 1) observe 10 m s−1 updrafts approximately 5 km across with peak updrafts of 15 m s−1 near Kwajalein Atoll in the west Pacific. Fierro et al. (2009, Fig. 6b) simulate ∼10 m s−1 updrafts near 5-km altitude increasing to ∼20 m s−1 around 11-km altitude in oceanic convection that reaches 15.5-km altitude. Section 2 of Fierro et al. (2009) shows that they obtain these updraft thresholds with a mesoscale model that uses inputs from a bulk microphysical model. This microphysical model includes 12 species of cloud ice and precipitation-sized ice.
In the half of 17-km-tall cells observed with lightning (Table 1, row 7), it is reasonable to suppose a ≥10 m s−1 peak updraft in midtroposphere based on the reasoning of Zipser and Lutz (1994). Furthermore, there is evidence for graupel in the TRMM observations, and graupel requires approximately a ≥10 m s−1 updraft to form. Just above the freezing level, the TRMM radar observes a radar reflectivity of 40–45 dBZ in most 17-km-tall oceanic cells (Fig. 5a), which could be due to graupel or to large raindrops recently lifted above the freezing level. While 2–4-mm-diameter graupel has only a 2–6 m s−1 fall speed (McFarquhar and Black 2004, Fig. 4a), simulations of oceanic convection that contain graupel exhibit ≥10 m s−1 updrafts (Fierro et al. 2008, pp. 370–371).
In fact, if TRMM observations imply graupel, then they also suggest updrafts fast enough to lift raindrops above the freezing level because such raindrops are commonly observed graupel embryos (Kingsmill et al. 2004, p. 1615). To lift raindrops, updrafts must be a few meters per second faster than the 4–8 m s−1 fall speed that 1–3-mm-diameter raindrops exhibit near the freezing level (Doviak and Zrnic 1993, p. 217; Zipser and Lutz 1994, p. 1758).
Were a significant number of raindrops and cloud droplets to freeze, then sufficient latent heat of fusion would be released to potentially increase upper-tropospheric updraft speed. Zipser (2003) proposes that vigorous oceanic cells may transport up to 4 g kg−1 of cloud water and liquid precipitation above the freezing level, causing approximately 12 m s−1 of updraft acceleration between mid- and upper troposphere. Aircraft have observed 3.5 to 4 g kg−1 ice hydrometeor mixing ratios near the −10°C level in oceanic convection (Li et al. 2008, Fig. 8b). In addition, Zipser (2003) and Fierro et al. (2009) point out that an additional boost in upper-tropospheric updraft speed occurs because of parcels shifting from the water to the ice adiabat.
TRMM observations suggest that somewhat less than the 4 g kg−1 of liquid condensate proposed by Zipser (2003) are present in the 17-km-tall oceanic cells. Even with <4 g kg−1, sufficient latent heat of fusion would be released to cause an updraft boost unless other factors, such as water loading, cancel it out. Lucas et al. (1994, p. 3190), Emanuel (1994, pp. 467–468), and Cotton and Anthes (1989, p. 135) discuss water loading in convective cells.
The radar-based ice mixing ratio remains under 4 g kg−1 in 17-km-tall oceanic cells, even if one takes into account the ∼0.2 g kg−1 of cloud ice estimated by TMI (Fig. 5i). In addition, the TMI estimate for precipitation-sized ice is ∼1.5 g kg−1 (Fig. 5g), which is close to the radar-based estimate under the assumption of graupel. The TRMM radar and TMI do estimate a similar precipitation ice mixing ratio, but both are potentially in error by a factor of two (100% error: L’Ecuyer and Stephens 2002, Fig. 4; 30% error: Grecu et al. 2004, p. 574).
For 17-km-tall oceanic cells, this study puts a 10 m s−1 lower bound on midtropospheric updrafts. This study can neither confirm nor contradict the possibility that 17-km-tall cells experience acceleration that turns ∼10 m s−1 midtropospheric updrafts into the 15–25 m s−1 upper-tropospheric updrafts observed over ocean by Heymsfield et al. (2010). Even if the upper tropospheric updraft were 20 m s−1 in a 17-km-tall oceanic cell, this updraft would still be less vigorous than the ≥30 m s−1 updrafts that are occasionally observed in continental cells (Heymsfield et al. 2010; Bluestein et al. 1988).
c. Relative updraft speed of oceanic and African cells
The previous section attempted to estimate the absolute speed of updrafts in 17-km-tall oceanic cells and the result was a lower bound to the updraft speed. To look for additional information, this section estimates the relative updraft speed of 17-km-tall oceanic cells and the vigorous updrafts known to exist over land.
TRMM observations establish that 17-km-tall oceanic cells have weaker updrafts than do equally tall cells in a region of Africa known for convection with vigorous updrafts (Geerts and Dejene 2005, pp. 904, 912; Zipser et al. 2006, p. 1063). Specifically, this study looks for tall cells in the semidesert Sahel (Warner 2004, Fig. 3.13) in western Africa. For the purposes of this study, the Sahel is defined as 10°–15°N and 5°E–15°W. The properties of 17-km-tall cells in the Sahel for 1998 to 2007 are summarized in column f of Table 1.
Plentiful lightning and a tall 40-dBZ height are associated with vigorous updrafts (Zipser et al. 2006). Oceanic 17-km-tall cells have, on average, an order of magnitude less lightning than do cells of comparable height over Africa (Table 1). The average 40-dBZ height of oceanic 17-km-tall cells is 6.6 km lower than the average 40-dBZ height of 17-km-tall cells over Africa. Although it does not affect the results of this paper, the TRMM 40-dBZ height may be in error by ±1 km because of inaccuracies of the attenuation correction in the version 6 TRMM 2A25 algorithm (J. Kwiatkowski and T. Iguchi 2009, personal communication).
Unlike lightning and the 40-dBZ height, two other properties proposed by Zipser et al. (2006) appear to be more ambiguous with respect to inferring updraft differences between 17-km-tall oceanic cells and 17-km-tall African cells. These properties are the 85- and 37-GHz polarization corrected brightness temperatures. At 85 GHz in particular, the oceanic and African 17-km-tall cells have overlapping 25th to 75th percentile ranges (row 4 of Table 1). The difference between the vertically and horizontally polarized 85-GHz brightness temperature is near zero (row 8 of Table 3), as one would expect in just moderately strong convective storms [Olson et al. 2001, Eq. (8)]. The surprise is that the polarization difference is slightly negative in most 17-km-tall oceanic cells, a subject to be discussed in section 5.
Going beyond the measures proposed in Zipser et al. (2006), the precipitation ice mixing ratio in Fig. 5f might also provides evidence that the updrafts speeds of tall cells over Africa are likely to be faster than those over ocean. If one assumes that the African cells are predominantly graupel, then the African cell’s mixing ratio would exceed 4 g kg−1, which would indicate the release of a significant amount of latent heat of fusion. Alternatively, some African cells might contain a mix of hail and graupel, which could reduce the mixing ratio below 4 g kg−1 while still suggesting rapid updrafts. As a rule of thumb, hail requires midtropospheric updrafts in excess of 20 m s−1 in order to form (Knight and Knight 2001, p. 237).
These updraft results answer a question posed in the introduction. Specifically, it appears that oceanic cells reach 17 km not because of especially rapid updrafts, but instead because the environment in which the cells form is favorable for modest updrafts to reach extreme heights. The next section explores what can be learned about the large-scale environment of TRMM-observed convective cells using the NCEP reanalysis.
d. Comparison with the NCEP reanalysis
The NCEP reanalysis is a historical run of a global model that assimilates decades of observations (Kalnay et al. 1996; Kistler et al. 2001). Ideally, a reanalysis permits observations in data-rich regions to determine the simulated storms and air masses that flow, a few days downstream, to data-sparse regions such as the open ocean. For the temperature profile and other aspects of the large-scale environment that spawns a 17-km-tall oceanic cell, the NCEP reanalysis or a similar product may be the closest available thing to an observation, albeit of uncertain accuracy. Although exact error estimates are unavailable, it is reasonable to expect ∼3-K errors in the NCEP reanalysis surface and tropopause temperatures over the Pacific warm pool where most 17-km-tall cells form (Pawson and Fiorino 1998, Fig. 3; Ma et al. 2008, p. 6). The results presented below are not invalidated by errors of this magnitude.
Since the upper -tropospheric lapse rate is favorable at the location of 17-km-tall cells, one might wonder about other locations. The potential temperature at 17-km altitude can give a sense for how often a location is favorable for 17-km-tall cells to form. More specifically, this study uses Bolton (1980) to calculate the pseudoadiabatic equivalent potential temperature θe from the NCEP reanalysis at all locations in the tropics. Excluding other factors, the more frequently that the upper-tropospheric θe is cold, the more frequently that conditions are favorable for 17-km-tall cells to form. The basic idea is that a rising air parcel can continue its buoyant upward acceleration if it remains warmer than the background. The 380-K threshold that is used to define “cold” in Fig. 4b is chosen because it is a typical value at 17-km altitude in regions, such as the west Pacific, where the upper troposphere is colder than the global average.
While the NCEP upper-tropospheric θe has considerable geographic variability, NCEP temperature profiles vary too little on time scales of 6 h for the NCEP reanalysis to reliably measure a 6-hourly change in θe. The 6-h period prior to a 17-km tall oceanic cell has nearly the same NCEP temperature profile as does the period that contains the cell. The 25th to 75th percentile range of the 6-h surface temperature change is −0.5 to +0.8 K, and at 17-km altitude, the 6-h temperature change is −2.5 to +0.4 K.
The absolute value of the NCEP upper-tropospheric θe may, at first glance, seem to be impossibly warm for 17-km-tall cells to form by the buoyant ascent of air parcels. To quantify this situation, the 25th to 75th percentile range of NCEP θe is calculated at the locations and times where TRMM observes a 17-km-tall oceanic cell. Just above the ocean surface, θe is 353–359 K, and θe is somewhat cooler (343–349 K) near the top of the boundary layer; that is, at 0.75-km altitude (925 hPa). Both of these near-surface θe ranges are much cooler than the 377–385-K θe that the NCEP profiles have at the typical 17.2–17.5-km altitude at which the TRMM radar observes ice precipitation in the 17-km-tall cells studied in this paper.
It is a fallacy; however, that updrafts are restricted to altitudes at which θe is cooler than at cloud base. Liu and Zipser (2005, Fig. 1c) estimate that, over the ocean, air parcels occasionally overshoot by more than 3 km the level of neutral buoyancy implied in the NCEP reanalysis. Furthermore, the level of neutral buoyancy could be higher than the altitude where the surface θe equals NCEP′s upper-tropospheric θe. Latent heat of fusion can increase a parcel’s θe by as much as 7 K (Fierro et al. 2009, Fig. 8a; see also Zipser 2003).
The ambiguity between overshooting and earlier background modification is highlighted by the VIRS infrared observations. The middle 50% of 17-km-tall oceanic cells have an infrared cloud-top temperature of 176–180 K, which is 10–14 K colder than the 16.4–16.9-km-high NCEP lapse-rate tropopause at the time and locations of the 17-km-tall oceanic cells. Figure 6a suggests that the cloud tops are also about 10–14 K colder than the coldest point in the NCEP temperature profile. While cloud-top height is not observed directly, the observed 10–14-K temperature deficit suggests that the cloud tops (the red oval in Fig. 6a) are about 1.0 to 1.4 km higher than the NCEP lapse-rate and cold-point tropopause.
If we assume that the NCEP upper troposphere does not have an unreported systematic bias of 10–14 K, then two alternative explanations stand out. Either the rising air parcels overshoot the NCEP profile, cooling at the dry-adiabatic lapse rate of ∼10 K km−1, or it is the local background profile that has been lifted and cooled approximately dry-adiabatically relative to the NCEP profile. Halverson et al. (2006, Fig. 11) observe a ∼1-km tropopause elevation, which could imply a tropopause cooling of 10 K if it were lifted adiabatically. The simulation of Mullendore et al. (2005, Fig. 5) shows the ambiguity between background modification and parcel overshooting in the neighborhood of a convective cell. This section has shown that the NCEP reanalysis sheds some light on how 17-km-tall cells might form, but ambiguity remains.
5. Discussion
This study raises several questions relating to tropopause overshooting, the 85-GHz polarization, and troposphere-to-stratosphere water transport. First, there are several options for explaining the rather striking mismatch between the height of cloud tops inferred from infrared observations and the level of neutral buoyancy inferred from the NCEP reanalysis. Two of the options are that cloud tops overshoot their neutral level with considerably stronger updrafts than suggested in section 4 or the tropopause is locally lifted, permitting a rather weak updraft to reach observed heights. Until targeted observations are obtained, a challenging prospect, it is unlikely that we can distinguish which of these alternatives is closer to the truth.
A second question is how to explain the subtle but systematic polarization that TMI observes at 85 GHz (Fig. 7a) where near zero polarization may be expected [Olson et al. 2001, Eq. (8)] because ice inside of convective cells is randomly oriented or roughly spherical (Heymsfield and Fulton 1994, p. 2584). Polarization is defined as the vertical minus the horizontal polarized brightness temperature.
TMI observes polarization differences of ±5 K at points A and B of Fig. 7. These convective cells may be electrified (Fig. 7b), which would be consistent with fairly large ice or supercooled raindrops lifted above the freezing level (Fig. 7e) and updrafts that lift smaller ice much higher (Figs. 7c,d). Points A and B are different only in that the cells at point B have lightning flashes every 3–5 s (Fig. 7b). A lightning flash can temporarily remove a portion of the electric field, and it may take tens of seconds for the electric field to recharge (Caylor and Chandrasekar 1996, p. 849).
One might speculate that, for the convective cells at point A, an electric field vertically orients their ice crystals, a process suggested by the radiative transfer simulation of Prigent et al. (2005). Vertically oriented ice could contribute to the observed negative polarization at point A. Furthermore, if lightning canceled the electric field for the convective cells at point B, then any vertically tilted ice would relax to its aerodynamic horizontal orientation (Hendry and McCormick 1976; Caylor and Chandrasekar 1996). Horizontally oriented ice could contribute to the observed positive polarization at point B.
A difficulty with the above speculation is that cloud ice smaller than 0.2 mm across is small enough and asymmetric enough to be easily tilted by a cloud’s electric field (Saunders and Rimmer 1999, p. 342; Shao and Krehbiel 1996, plate 1), but it is too small to scatter an appreciable amount of the upwelling 85-GHz radiation (Prigent et al. 2005, Fig. 2; Jiang and Zipser 2006, p. 1097; Cecil et al. 2002, p. 774). Graupel is large enough to scatter 85-GHz radiation, but most graupel is nearly spherical (Heymsfield and Fulton 1994, pp. 2593–2594) and would be too large for anything except a very strong electric field to deflect it from its aerodynamic orientation.
Alternatively, a positive 85-GHz polarization might be due to a hole in the cloud cover because the ocean surface is vertically polarized by 20 K or more (Olson et al. 2001, p. 1581). A negative polarization might be due to oblate raindrops because they emit horizontally polarized radiation (Czekala et al. 2001). This paper only mentions a few of the possible explanations for the observed polarization and points to the need for further investigation.
The third question is if 17-km-tall oceanic cells can increase the stratosphere’s humidity (Dessler et al. 2007; James et al. 2008). Such an increase might be possible if the lower stratosphere were initially unsaturated (Fueglistaler et al. 2009, Fig. 8b), if overshooting cloud tops contain hydrometeors that were small enough to evaporate before falling out of the stratosphere (Stohl et al. 2003, p. 9; James et al. 2003, p. 7), and if the overshooting air has a chance to mix with stratospheric air before negative buoyancy returns it to the troposphere. Based on this second consideration, cloud ice ejected into the stratosphere is more likely to increase stratospheric humidity than is precipitation-sized ice (Nielsen et al. 2007, pp. 691–692; Khaykin et al. 2009, p. 2276). While the TRMM radar sees only precipitation ice, not cloud ice, statistics from TRMM observations can contribute to a rough estimate of the cloud ice mass entering the stratosphere.
On the other hand, the 17-km-tall cells studied in this paper, those at least 1000 km from continents, are only 2%–6% of the global total number of 17-km-tall cells, based on the TRMM precipitation feature database. Furthermore, section 4 suggests that, on average, continental cells are more vigorous and transport more ice per cell than do oceanic cells.
6. Conclusions
TRMM observations suggest that the tallest convective cells over the tropical ocean do have slower updrafts than the vigorous updrafts known to exist in the summertime convective cells of the Sahel region of Africa. Relative updraft speed is inferred from the oceanic cells having a 7-km lower 40-dBZ height and an order of magnitude less lightning.
Neither the absolute updraft speed nor an upper bound to the updraft speed can be estimated from TRMM observations. However, a lower bound of 10 m s−1 is suggested by TRMM observations for the midtropospheric peak updraft speed of 17-km-tall cells over ocean. This lower bound comes from TRMM observations that suggest the presence of graupel and supercooled raindrops in the first kilometer or two above the freezing level.
Despite the relatively modest updraft speed in midtroposphere, oceanic cells can definitely lift precipitation-sized ice to a 17-km-altitude, based on 20-dBZ radar reflectivity observed by the TRMM satellite radar. Care is taken to distinguish these rare events from equally rare nonmeteorological signals.
It remains somewhat mysterious how these oceanic cells can reach such extreme heights. Several factors may contribute to the extreme heights being achieved, although the relative importance of these factors is unclear from the available data. At the locations that these cells form, the tropopause is high (16–17 km) and the ocean is warm (≥29°C). TRMM observes considerable ice in these cells, suggesting that liquid hydrometeors are lifted until they freeze, releasing latent heat of fusion to accelerate the updrafts in the mid- to upper troposphere. Favorable dynamics in a cell’s mesoscale setting may also contribute to the cell’s ability to reach high altitude despite negative factors such as water loading from the lifted hydrometeors. More specifically, most 17-km-tall oceanic cells occur inside of mesoscale convective systems, tropical storms, or tropical depressions.
In the Pacific warm pool, where most 17-km-tall cells form, a favorable lapse rate makes it easier for a modest updraft to overshoot its level of neutral buoyancy. The NCEP reanalysis suggests that the background profile through which a 17-km-tall cell rises has a lapse rate that averages near 50% of the saturated-adiabatic lapse rate in the upper 2 km of a 17-km-tall cell. Overshooting or tropopause lifting of 1–2 km appears necessary based on TRMM radar and infrared observations combined with the NCEP reanalysis temperature profile and equivalent potential temperature. More precision would either require detailed modeling that is beyond the scope of this paper or would require temperature profiles that are more precise in space and time than the NCEP reanalysis.
While the TRMM precipitation radar observes only 174 of the 17-km-tall oceanic cells in 10 years, such cells are likely to occur much more frequently than this because the TRMM radar, on average, observes a specific location in the tropics approximately once every three days. Even allowing for error in the extrapolation, 17-km-tall oceanic cells are likely to occur more often than once per day, on average, over warm seas more than 1000 km from continents.
Acknowledgments
Various ideas in this paper were discussed with James Beall, Daniel Cecil, Jeffery Halverson, Menas Kafatos, Genevieve Demos Kelley, John Kwiatkowski, Chuntao Liu, David Marks, Bill Olson, and Dave Silberstein. NASA and the Japan Aerospace Exploration Agency (JAXA) provided TRMM satellite and ground radar data. The Global Hydrology Resource Center at the University of Alabama provided TRMM LIS and Reynolds sea surface temperature data. The TRMM precipitation feature database was provided by Steve Nesbitt, Chuntao Liu, and Ramesh Kakar under the NASA precipitation measurement missions. For this study, the NASA Goddard Library performed an exhaustive literature search for reports of hail over the tropical ocean. The authors thank two anonymous reviewers for suggestions that improved the organization of the paper.
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