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    Idealized latent heating profiles for different types of precipitating cloud (after Schumacher et al. 2007).

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    Approximate locations of the field campaigns.

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    (a) Mean (solid) and mean +1 std dev (dashed), and (b) the first (solid) and second (dashed) EOF (thin) and REOF (thick) modes of Q1 from TOGA COARE.

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    Time series of Q1 (K day−1) from TOGA COARE. (a) Original data based on sounding observations and (b) data reconstructed using the first two REOF modes.

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    Phase diagram defined in terms of the PCs of the first two REOF modes of the TOGA COARE Q1 time series. Each point corresponds to a single profile. The white circle marks the one standard deviation of the amplitude defined as (PC12 + PC2)1/2. Phase identifications are given in the corners.

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    Composites of Q1 using original TOGA COARE data (circles), reconstructed from the two REOF leading modes and time mean (solid lines), the first REOF mode (dashed), and the second REOF mode (dotted) for the eight phases (marked in the upper right corners) defined in Fig. 5. The occurrence probability of each phase is given atop each panel.

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    PDF of phase angle change (Δθ) derived from Fig. 5. The bin width corresponds to the eight phases in Fig. 5.

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    Composite time evolution of TOGA COARE Q1 based on the most probable phase transition in Table 2 using (a) the original Q1 data, (b) the first two leading REOF modes and the time mean, (c) the first REOF mode, and (d) the second REOF mode. The position of each phase is scaled by the probability of a heating profile to remain in the same phase in two consecutive times.

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    (a) Mean (solid) and mean plus one standard deviation (dashed), and (b) the first (solid) and second (dashed) EOF (thin) and REOF (thick) modes of Q1 from all eight field campaigns combined.

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    As in Fig. 5, but the first two REOF modes were derived from Q1 time series of the eight field campaigns combined and the eight phases were consolidated into four.

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    Composites of Q1 using original data (circles), reconstructed from the two REOF leading modes and time mean (solid lines), the first REOF mode (dashed), and the second REOF mode (dotted) for the four phases (marked in the upper right corners) defined in Fig. 9 for all data combined. The occurrence probability of each phase is given atop each panel.

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    Probability (%) of 4-phase transition of Q1 from all (a) 6-hourly and (b) daily sounding data combined. In each cell, the upper number is the probability of the preceding phase being followed by the succeeding phase; the lower number is the probability for the succeeding phase being preceded by the preceding phase. Highest probabilities of “moving to” a different phase (unshaded cells) are bolded; highest probabilities of “moving from” a different phase (unshaded cells) are underlined. The column for succeeding phase A is repeated once. Arrows mark the directions of the most probable phase transitions.

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    As in Fig. 7, but for (a) 6-hourly and (b) daily combined Q1 data. The bin width corresponds to any equally divided four phases.

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    Schematic diagram summarizing the fractional contributions by idealized building-block profiles to each composite heating profile in the most probable structural evolution.

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    (left) Meridional-vertical circulation, (right) zonal-vertical circulation, and (center) their corresponding vertical profiles of moisture convergence (kg kg−1 day−1) forced by heating profiles (colors, K day−1) of the composites of phases A, B, and C in Fig. 11. Vertical motions are amplified by a factor of 50. See text for other details.

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    Zonal-vertical circulations averaged over 5°S–5°N forced by (top) composite heating profiles (solid lines in Fig. 11), same as phases A, B, and C in the right column of Fig. 15, and by idealized (second row) stratiform heating, (third row) deep convective heating, and (bottom) shallow convection/congestus heating shown in Fig. 1 for phases (left) A, (middle) B, and (right) C. The heating amplitudes (colors, K day−1) for the three idealized profiles are scaled to their fractional contributions to the composites (Fig. 14). Vertical motions are amplified by a factor of 50.

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    Probability distribution function of maximum heating levels based on all 6-hourly Q1 data.

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Bi-modal Structure and Variability of Large-Scale Diabatic Heating in the Tropics

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  • 1 RSMAS, University of Miami, Miami, Florida
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Abstract

Tropical diabatic heating profiles estimated using sounding data from eight field campaigns were diagnosed to document their common and prevailing structure and variability that are relevant to the large-scale circulation. The first two modes of a rotated empirical orthogonal function analysis—one deep, one shallow—explain 85% of the total variance of all data combined. These two modes were used to describe the heating evolution, which led to three composited heating profiles that are considered as prevailing large-scale heating structures. They are, respectively, shallow, bottom heavy (peak near 700 hPa); deep, middle heavy (peak near 400 hPa); and stratiform-like, top heavy (heating peak near 400 hPa and cooling peak near 700 hPa). The amplitudes and occurrence frequencies of the shallow, bottom-heavy heating profiles are comparable to those of the stratiform-like, top-heavy ones. The sequence of the most probable heating evolution is deep tropospheric cooling to bottom-heavy heating, to middle heavy heating, to stratiform-like heating, then back to deep tropospheric cooling. This heating transition appears to occur on different time scales. Each of the prevailing heating structures is interpreted as being composed of particular fractional populations of various types of precipitating cloud systems, which are viewed as the building blocks for the mean. A linear balanced model forced by the three prevailing heating profiles produces rich vertical structures in the circulation with multiple overturning cells, whose corresponding moisture convergence and surface wind fields are very sensitive to the heating structures.

Corresponding author address: Chidong Zhang, MPO/RSMAS, 4600 Richenbacker Causeway, Miami, FL 33149. Email: czhang@rsmas.miami.edu

Abstract

Tropical diabatic heating profiles estimated using sounding data from eight field campaigns were diagnosed to document their common and prevailing structure and variability that are relevant to the large-scale circulation. The first two modes of a rotated empirical orthogonal function analysis—one deep, one shallow—explain 85% of the total variance of all data combined. These two modes were used to describe the heating evolution, which led to three composited heating profiles that are considered as prevailing large-scale heating structures. They are, respectively, shallow, bottom heavy (peak near 700 hPa); deep, middle heavy (peak near 400 hPa); and stratiform-like, top heavy (heating peak near 400 hPa and cooling peak near 700 hPa). The amplitudes and occurrence frequencies of the shallow, bottom-heavy heating profiles are comparable to those of the stratiform-like, top-heavy ones. The sequence of the most probable heating evolution is deep tropospheric cooling to bottom-heavy heating, to middle heavy heating, to stratiform-like heating, then back to deep tropospheric cooling. This heating transition appears to occur on different time scales. Each of the prevailing heating structures is interpreted as being composed of particular fractional populations of various types of precipitating cloud systems, which are viewed as the building blocks for the mean. A linear balanced model forced by the three prevailing heating profiles produces rich vertical structures in the circulation with multiple overturning cells, whose corresponding moisture convergence and surface wind fields are very sensitive to the heating structures.

Corresponding author address: Chidong Zhang, MPO/RSMAS, 4600 Richenbacker Causeway, Miami, FL 33149. Email: czhang@rsmas.miami.edu

1. Introduction

Tropical convective systems affect the large-scale circulation most effectively through diabatic heating due largely to latent heat release and, to a lesser degree, radiative effects. Here, “large-scale” refers to scales associated with synoptic disturbances and waves, the intraseasonal oscillation, and seasonally and interannually varying planetary-scale zonal (Walker) and meridional overturning circulations. Understanding vertical structures and evolution of diabatic heating is central to the study of the large-scale circulation in the tropics and its interaction with moist convection. Previous studies on the role of heating profiles in the large-scale circulation used either observed heating profiles of mesoscale convective systems (e.g., Mapes and Houze 1995; Schumacher et al. 2004) or idealized profiles for large-scale diabatic heating (e.g., Geisler 1981; Hartmann et al. 1984; Wu et al. 2000). Our knowledge of large-scale heating structures and variability directly from in situ observations has been limited to specific locations and times. In this study, based on in situ observations from various locations, we discuss the prevailing vertical structures and variability of diabatic heating that are common in different climate regimes of the tropics and relevant to the tropical large-scale circulation. Such diabatic heating can be considered as averaged over areas (103–105 km2) embedding a variety of mesoscale convective systems, equivalent to a grid box in a coarse-resolution global climate model.

Many efforts have been made to estimate, describe, simulate, and understand tropical diabatic heating. Diabatic heating has been estimated from in situ observations mainly through two methods.1 One is calculating the residual of the energy budget using atmospheric sounding data. The result is commonly known as the “apparent heat source” (Q1) following Yanai et al. (1973):
i1520-0469-66-12-3621-e1
where t is time, p pressure, s = cpT + gz the dry static energy, QR the atmospheric radiative heating, QL the latent heat source, ω the vertical velocity, and sω′ the vertical eddy transport of sensible heat. Overbars and primes denote respectively the average over a sounding array and subgrid-scale deviations from the average. The latent heat source can be expressed as
i1520-0469-66-12-3621-e2
where Lυ and Lf are latent heat of vaporization and fusion and c, e, d, s, f, and m are rates of condensation, evaporation, deposition, sublimation, freezing, and melting, respectively. In (1), the first line illustrates how Q1 can be estimated from sounding observations by calculating the terms on the right-hand side. This can be done using a line integral method (e.g., Yanai et al. 1973), a gridded method (Ciesielski et al. 2003), or a variational method (Zhang and Lin 1997) over a polygonal (minimally triangle) sounding array. Hereafter, these methods will be referred to as “sounding based.” Issues regarding the pros and cons of these methods and possible differences in their outcomes are discussed in Zhang et al. (2001). The second line of (1) and (2) give the physical interpretation of Q1. Normally, ∂()/∂p is small, except at the melting level and near the tropopause (Mapes 2001; Shie et al. 2003). So in general Q1 is very close to total diabatic heating.
The other method, described in detail by Houze (1982, 1989), is based on our knowledge of the structure and microphysics of tropical mesoscale convective systems (MCSs). It directly estimates each term in the second line of (1) in a slightly different form, which explicitly expresses contributions from convective and stratiform precipitation:
i1520-0469-66-12-3621-e3
where σcloud, σc, and σs are fractional coverage respectively by total, precipitating convective, and precipitating stratiform clouds; Qrc is net radiative heating in cloud; and p, s, ω, c, e, m, Lυ, and Lf are the same as in (2), with subscripts cu, cd, mu, and md indicating respectively convective updrafts and downdrafts, mesoscale updrafts, and downdrafts in the stratiform region. In the last term, subscript i refers to the various subdivisions of the cloud area and c to the convective precipitation region. At the center of this method is a conceptual model of MCSs that, based mainly on radar observations, describes structures of mesoscale flows and microphysical properties in a typical tropical MCS and their evolution through its life cycle (see Figs. 1 and 2 in Houze 1989). For this reason, this method will hereafter be referred to as “radar based.”

A common essential element in both methods is the vertical profile of ω. Because temperature in the tropics changes little horizontally in the tropics, mean profiles of ω dictate the vertical structure of Q1. In the sounding-based method, ω is calculated from horizontal wind divergence and its accuracy is sensitive to data quality. The radar-based method uses conceptualized vertical profiles of ω based on wind measurements by rawinsondes, aircraft, Doppler radars, and wind profilers. Three idealized heating profiles have been proposed (Fig. 1) using conceptualized vertical profiles of ω for stratiform, deep convective, and shallow convective clouds. Strongly detraining cumulus congestus is not separated from shallow convective cloud here. Both may contribute significantly to tropical total rainfall and both share similar heating profiles except detrainment cooling near the cloud top for cumulus congestus (Schumacher et al. 2007).

Diabatic heating profiles estimated using the two methods sometimes match very well, especially for the top-heavy profile with its heating peak in the upper troposphere (400–300 hPa) and cooling in the lower troposphere due to evaporation of stratiform rain (e.g., Reed and Recker 1971; Johnson and Young 1983). They can, however, differ substantially for two reasons. First, sounding-based Q1 includes radiative and latent heating, whereas radar-based Q1 includes primarily latent heating. Second, the domain coverage of radar data is often smaller than a sounding array. When MCSs are the dominant convective systems in a sounding array, the sounding-based heating profile should be similar to that of the radar-based estimate for MCSs. When the sounding array is occupied by a variety of convective clouds (both precipitating and nonprecipitating), there is no reason to expect same results from the two methods. An example of their discrepancy is heating profiles estimated using soundings from the tropical Atlantic, which often show heating peaks at a much lower level than expected from that of an idealized MCS (e.g., Nitta 1977; Song and Frank 1983; Frank and McBride 1989).

The large-scale circulation responds to heating profiles averaged over time and space. The idealized heating profiles shown in Fig. 1 associated with particular types of precipitating clouds are embedded in the averaging time and space and serve as “building blocks” for constructing averaged heating profiles (Mapes et al. 2006). In a linear system, the large-scale response to an averaged heating profile is a superposition of all responses to individual convective systems—namely, the building blocks (Mapes and Houze 1995). Understanding responses to individual convective systems provides insights into their roles in the large-scale dynamics. On the other hand, studies that focus on the role of a specific heating profile—for example, the top-heavy stratiform heating (Hartmann et al. 1984; Mapes and Houze 1995; Schumacher et al. 2004) or cloud radiative heating (Bergman and Hendon 2000)—in the tropical large-scale circulation are incomplete. Potential roles of other types of heating structures, such as bottom-heavy heating profiles, in the large-scale circulation also need to be explored (Wu 2003).

The following issues are addressed in this study: What are the prevailing vertical structures of tropical diabatic heating that the large-scale circulation directly responds to and that must be correctly reproduced by global climate models? How do they vary in time? How are they composed by building blocks of various precipitating cloud types? How sensitive is the large-scale circulation to different prevailing vertical structures of tropical diabatic heating?

These issues are addressed by using sounding-based diabatic heating data (Q1) from eight field campaigns. They are traditionally viewed as the ground truth for validating numerical model simulations and calibrating satellite retrievals, despite errors and uncertainties in observational sources (e.g., Ciesielski et al. 2003; Mapes et al. 2003) and estimate methods (Zhang et al. 2001). Their main shortcoming is the limitation in spatial and temporal coverage. When sounding-based heating profiles are compared with profiles based on satellite retrievals (Tao et al. 2001; Shige et al. 2004) and global reanalyses (Sardeshmukh 1993), intriguing information emerges, which is reported in detail by Hagos et al. (2010) and will be briefly discussed later in this study.

We will demonstrate that observed large-scale sounding-based diabatic heating in the tropics possesses a variety of vertical structures, including bottom- and middle-heavy profiles as well as top-heavy, stratiform-like profiles. Here we define bottom-, middle-, and top-heavy profiles based on where the majority of heating occurs (lower, mid, and upper troposphere) as well as the level of the heating peak. When cooling occurs in the lower troposphere in a top-heavy sounding-based heating profile, we refer it as stratiform-like because even though it resembles a heating profile of purely stratiform precipitation, it is a mean including heating/cooling due to other types of precipitating and nonprecipitating clouds. We also use “deep” to describe a profile with substantial heating throughout most of the troposphere, as opposed to “shallow” where heating is confined to either the upper or lower troposphere.

To objectively identify prevailing vertical structures of diabatic heating, we adapted a rotated empirical orthogonal function (REOF) analysis. Its first two leading modes explain 85% of the total variance of all Q1 data combined. These two REOF modes are used to reconstruct the main features in the total (as opposed to anomalous) heating profiles and their variability—hence “bi-modal” in the title of this article.

The data and method are described in section 2. Results from one particular sounding dataset are first presented in section 3 to demonstrate the utility of our method. Section 4 presents generalized results obtained by the same analysis procedure applied to all sounding data combined. Dynamical implications of prevailing heating structures derived from section 4 are illustrated in section 5 using a linear balanced model. A summary and discussions are given in section 6.

2. Data and method

The Q1 time series estimated from radiosonde observations of eight field campaigns2 (Table 1) were acquired from various sources. Their approximate locations are marked in Fig. 2. All data represent averages over areas of roughly 103–105 km2 and are relevant to the large-scale circulation. These datasets were collected from all three tropical oceans and near or over four continents. They are in a variety of environments, including open oceans with only small or no islands [the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE), the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), the Kwajalein Experiment (KWAJEX), and the Mirai Indian Ocean Cruise for the Study of the MJO Convection Onset (MISMO)], coastal and monsoon regions [the North American Monsoon Experiment (NAME), the South China Sea Monsoon Experiment (SCSMEX), and the Tropical Warm Pool–International Cloud Experiment (TWP-ICE)], and continental rain forest [the Large-Scale Biosphere–Atmosphere Experiment in Amazonia (LBA)]. Topographic effects can be strong in some locations (NAME, LBA). Atmospheric phenomena that influence the structure and variability of Q1 at these locations are quite diverse. They include synoptic-scale waves, tropical intraseasonal oscillation (TOGA COARE, KWAJEX, SCSMEX, NAME, LBA, MISMO), sea/land breezes (NAME, TWP-ICE), monsoon circulation (TOGA COARE, SCSMEX, NAME), and perhaps extratropical perturbations (LBA). Common in all locations are mesoscale convective systems, such as squall lines, and the diurnal cycle. Even though these data came from different sources and have been derived using different methods, we treat them as results of our best efforts of estimating Q1 from sounding observations. This collection of data, however, does not cover all tropical climate regimes, and they are biased toward oceanic regions, with only one dataset (LBA) representing a continental region. Data from semiarid land such as the Sahel, flat forest such as central Africa, and nondeep convective regions such as the southeastern Pacific, for example, are missing. These and other limits of the data should be kept in mind when their results are interpreted.

The time interval of all Q1 data is 6 h and the vertical levels are from 1000 to 100 hPa with a 25-hPa increment. All data are single time series. The TOGA COARE data were for the Intensive Flux Array (IFA). The GATE data are gridded (1° × 1°). An average over a 3° × 3° domain covering the B-scale ship array (Fig. 1 in Song and Frank 1983) was used in this study.

The dominant variability in a given Q1 time series can be identified using the empirical orthogonal function (EOF) or principal component analysis (PCA) (Frank and McBride 1989; Fraedrich et al. 1997). An example of EOF analysis applied to the TOGA COARE Q1 time series is shown in Fig. 3. The eigenvector of the first EOF mode is deep (thin solid line in Fig. 3b). It explains a large fractional variance (79.4%). The structure of the second EOF mode (thin dashed line in Fig. 3b) is baroclinic and the sign switches near the melting level. It explains a smaller fractional variance (11.2%). These two leading EOF modes may resemble some of the idealized heating profiles shown in Fig. 1; however, they represent different cloud systems averaged over the domain of the sounding array. It is possible that their physical interpretations are compromised by the orthogonality constraint of the EOF method. Physically meaningful modes may not be orthogonal to each other. Cases in point are the radar-based heating profiles shown in Fig. 1 that are associated with individual types of precipitating systems.

An alternative method is the rotated EOF (REOF). In this method, the orthogonality constraint to eigenvectors is replaced by other requirement, often based on a simple structure principle (Thurstone 1947). The main advantage of an REOF method over the EOF method is a possibly better physical interpretation of the leading modes. However, when the orthogonality constraint is replaced by other criteria, the uniqueness of the resulting modes might be lost.3 Alexander et al. (1993) and Lin and Arakawa (2000) applied this method to Q1 combined with an apparent moisture sink (Q2) and associated each of the leading modes with a distinct physical process. Lin and Arakawa (2000) systematically compared REOF to EOF in diagnosing diabatic heating profiles and demonstrated the advantage of REOF.

We applied a varimax REOF method (Kaiser 1958; Wilks 2006) to the TOGA COARE Q1 data. This method replaces the spatial orthogonality requirement with one that maximizes the variance of squared eigenvectors such that the shapes of the rotated eigenvectors become the simplest they can be. Twelve eigenvectors were retained for the rotation. The rotation is performed such that the new eigenvectors are not orthogonal but the new principal components (PCs) are uncorrelated. The first REOF mode (thick solid line in Fig. 3b) is almost identical to the first EOF mode (thin solid line). The second REOF mode resembles the second EOF mode in the lower troposphere, but its amplitudes at the upper levels are reduced to near zero (thick dashed line). Its shape is thus simpler than that of the second EOF mode. Tung et al. (1999) combined Q1 and Q2 from TOGA COARE in a REOF analysis and their first two modes for Q1 are similar to what we have here. Many of our results based on the REOF and EOF analyses are similar. The first two modes from both EOF and REOF are clearly separated from the rest according to the North et al. (1982) criterion. They explain nearly 90% of the total variance of TOGA COARE Q1 (90.6% for EOF and 86.7% for REOF), with the third mode contributing a much smaller fractional variance (5.1% for EOF, 1.5% for REOF). We will present our results based on REOF only for the benefit of their clearer interpretations.

3. Results of TOGA COARE data

We first demonstrate the utility of our method using the TOGA COARE data. Then in the next section we will extend the analysis to all sounding data combined to generalize the results. The mean profile of TOGA COARE Q1 exhibits a deep (almost through the troposphere), middle-heavy (peak near the 450-hPa level) structure (solid line in Fig. 3a), as shown by Lin and Johnson (1996). The shape of this mean profile resembles that of deep convective heating in Fig. 1, except its level of maximum heating is higher, roughly at the same peak level of the stratiform heating profile in Fig. 1. There is little or no low-level cooling in this mean profile and it heating occupies almost the entire troposphere; hence it is “middle heavy” and deep.

a. Prevailing structures

The gross characteristics of Q1, including its prevailing structures and their variability, can be adequately described using the first two REOF modes. This is clearly demonstrated first in Fig. 4, where the original time series of Q1 from TOGA COARE is compared to the reconstruction using the first two REOF modes as
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where t and p are time and pressure, respectively; Q1(p) is the time mean of Q1; En(p) and Pn(t) are the eigenvector and PC of REOF mode n. The reconstructed time series (Fig. 4b) captures all identifiable features of the original one (Fig. 4a) except for high-frequency variability above the 200-hPa level.

The REOF PCs are orthogonal to each other, even though the eigenvectors are not. This allows a phase diagram to be constructed using the PCs of the two leading modes (Fig. 5). Here, the term “phase” is broadly applied and could be replaced by other words such as “regime” or “stage.” Eight phases are defined. Composite Q1 profiles can be made for each phase using original Q1 data and reconstructions of the first two REOF modes following (4). They are almost identical (Fig. 6, solid lines and circles).

The composites are total (including the time mean), not anomalous, profiles and represent averages in both time (within each phase) and space (over the TOGA COARE IFA sounding array). They are therefore large-scale and need not resemble the idealized heating profiles shown in Fig. 1. If they do, it indicates the dominance of a particular type of cloud system. The composite Q1 in phases 1 and 8 exhibits a deep, middle-heavy structure without much cooling, very similar to the mean profile seen in Fig. 3. The composite of Q1 in phases 2 and 3 is bottom heavy, with peaks at 500 and 700 hPa, respectively, and more heating in the lower than upper troposphere. It is reasonable to speculate that shallow precipitating clouds dominate these two phases. Weak heating in the lower troposphere and weak cooling aloft in phase 4 resemble very much the idealized heating profile associated with strongly detraining congestus (Schumacher et al. 2007). Phase 5 represents deep tropospheric cooling presumably due to longwave radiation in both clear and nonprecipitating cloudy sky. Finally, composite Q1 in phases 6 and 7 is similar to the idealized top-heavy stratiform heating profile, with upper-level heating and lower-level cooling.

The composite profiles are based on eight empirically constructed phases coming from a REOF analysis without any attempt to fit them to an existing preconception of heating profiles. In this sense, they are objectively derived. We propose that these eight composite Q1 profiles are representative of the large-scale heating structure. It remains to be seen whether a better set of composite Q1 representing prevailing large-scale heating profiles can be derived by a less empirical, more physical method.

The occurrence frequencies of the eight phases, estimated from the number of soundings in each phase, are given atop the heating profiles in Fig. 6. Phase 5 is the most frequent one. Even in an active convective location such as the TOGA COARE IFA, the absence of precipitating clouds is still the most common situation. In contrast, phase 8 is the least frequent one. It is of particular interest that phase 3, the bottom-heavy profile, is about as frequent as those of phase 6 and 7, the top-heavy, stratiform-like heating profiles. Their amplitudes are also comparable. These suggest that prevailing large-scale diabatic heating during TOGA COARE consists of a variety of vertical structures including bottom-heavy as well as top-heavy profiles.

b. Structural evolution

The phase transitions of Q1 can be described as the probabilities of a particular phase being followed and preceded by other phases. Such phase transition probability is listed in Table 2.4 An upper number in a cell should be compared to other upper numbers in the same row, which are the probabilities of the next (succeeding) phases following the phase given at the left of the row. For example, once in phase 1, the highest probability in the upper line of the row for preceding phase 1 is 41.7% (bold) for succeeding phase 8. This means phase 8 is the most probable phase following phase 1. The lower number in each cell should be compared to the other lower numbers in the same column, which are the probabilities of the previous phases preceding the phase given at the top of the column. For example, once in phase 1, the highest probability in the second line of the column for succeeding phase 1 is 33.3% (bold and underlined) for preceding phase 2. This means phase 2 is the most probable phase proceeding phase 1. In most cases, a profile would most likely remain in the same phase (highest probabilities in italic). In terms of phase transitions, we are more interested in different phases that follow or proceed. The two examples given above suggest a sequence of phase transition 2–1–8. The same logics would lead a clear pattern of 8–7–6–5–4–3–2–1–8 … . in Table 2 based on the most probable preceding phases (bold and underlined numbers). A similar pattern can almost be identified also from the most probable succeeding phases (bold), except for (preceding) phases 4 and 5. Another highly probable phase transition sequence is 2–3–4–5–6.

The sequence of phase transition suggested by Table 2 indicates either a clockwise (phases 8–7–6–5–4–3–2–1–8) or counterclockwise (phases 2–3–4–5–6) rotation in time in the phase diagram of Fig. 5. However, the phase definition in Fig. 5 is somewhat arbitrary. To see which direction dominates the evolution of heating profiles without the arbitrarily defined phases, a phase angle θ = tan−1(PC1/PC2) can be used instead. Each phase in Fig. 5 corresponds to a range of θ (e.g., 135° ≤ θ < 180° for phase 7). If changes in amplitude are ignored for a moment, changes in the vertical structure can be simply represented by changes in θ (i.e., Δθ) independent of any phase definition. For example, if two consecutive points in time have the same θ, their vertical structures are the same, albeit with different amplitudes. A positive change in θθ > 0) means a clockwise rotation in Fig. 5 and vice versa. A probability distribution function (PDF) of Δθ in Fig. 7 (see footnote 4) shows that for transition between neighboring phases (|Δθ| < 45°) positive Δθ obviously dominates negative Δθ. This supports the phase transition in the direction of 8–7–6–5–4–3–2–1 suggested in Table 2, even though other sequences in the opposite direction (2–3–4–5–6) can also be identified from the table.

The evolution of heating profiles following the most probable sequence of phase transition (8–7–6–5–4–3–2–1) suggested by Table 2 and Fig. 7 can be visualized in a composite profiles in the same sequence. The relative time that a phase persists can be scaled by the probability of a profile to remain in the same phase in two consecutive times. Choosing phase 3 to start the sequence, we show such composite evolutions of Q1 profiles in Fig. 8 using (i) the original Q1 data, (ii) reconstructed Q1 profiles based on the first two REOF modes and the mean, and (iii) the first and (iv) the second REOF modes, respectively. The evolutions of Q1 based on the original and reconstructed data are practically identical. They both portray a gradual development from shallow, bottom-heavy heating (phases 3 and 2) to deep, middle-heavy profiles (phases 1 and 8), and then to top-heavy stratiform-like heating accompanied by low-level cooling (phases 7 and 6). This is followed by a deepening of low-level cooling through the entire troposphere (phase 5). The last stage of this phase evolution (phase 4) is upper-level cooling and low-level heating, however weak, resembling the idealized heating profile due to detraining congestus cloud (Schumacher et al. 2007).

The roles of the first two REOF modes in the Q1 evolution are clearly demonstrated in Fig. 8. The first mode determines the general timing of precipitating (tropospheric heating) versus nonprecipitating (cooling) periods. It alone, however, does not yield any evolution in the vertical structure. That needs the second mode. With its heating/cooling confined to the lower troposphere, the second mode, when combined with the first mode and the mean profile, determines when the bottom-, middle-, and top-heavy heating profiles occur. These distinct roles of the first two REOF modes in the evolution of the Q1 structure are much simpler than those of the EOF leading modes, whose second mode projects heating/cooling variability in both the upper and lower troposphere. This gives REOF an advantage over EOF analysis. At this stage the leading REOF modes serve as convenient and objective tools to explore Q1 structures and their evolution. It has yet to be determined whether they have any clear physical identities (see discussion in section 6).

As discussed previously, shallow, bottom-heavy heating (phases 3 and 4) is as frequent as top-heavy, stratiform-like heating (phases 7 and 6), and they have comparable magnitudes. This is consistent with the observation that the contribution of shallow convection to total rainfall is significant in the tropics (e.g., Short and Nakamura 2000). Therefore, they should be treated as equally important to the tropical large-scale circulation. The deep, middle-heavy heating profiles (phases 1 and 8) are the strongest even though they are less frequent than the bottom- and top-heavy profiles. Possible differential roles of the various heating profiles in the large-scale circulation will be discussed in section 5.

Derived from the 6-hourly data, the transition sequence takes at least two days to complete through all eight phases. Observations have revealed both quasi-two-day waves (Takayabu et al. 1996) and mesoscale convective systems that took more than 24 h to develop and decay (Chen et al. 1996) in the TOGA COARE period. But all convective systems may not go through the entire phase transition shown in Fig. 8. The phase transition sequence only illustrates the most probable tendency of structural evolution in large-scale diabatic heating.

4. Results of all Q1 data

We now examine whether the descriptions of the structure and evolution of TOGA COARE Q1 would also apply to Q1 time series derived from other tropical regions.

a. Applicability of the REOF approach

We first repeated the REOF analysis for each of the other sounding datasets listed in Table 1. Despite differences in the mean profiles, all, with the exception of the GATE data, yielded results similar to the TOGA COARE data: The two leading REOF modes, one deep, one shallow, explain 62%–96% of variance for each of the datasets (Table 3).

For the GATE data, its first mode is very similar to those of the others, but its second mode is unique, with its amplitude remaining very small throughout most of the troposphere and becoming large only near the tropopause (not shown). It may result from a peculiar heating/cooling near the tropopause in the GATE Q1 data. The third mode of GATE Q1 data resembles the second, shallow mode for all other Q1 data. When the REOF analysis is performed for the GATE Q1 data without the top levels (e.g., for 1000–200 hPa), the first two leading modes become the same as for the other data. This result reconfirms that even with such peculiar heating behavior,5 the shallow, bottom-heavy mode is still resolved as a leading REOF mode, and this mode together with the first deep, middle-heavy mode explains roughly 80% of the total variance of GATE Q1.

Next, all data were treated as sparse sampling of the total population of tropical diabatic heating and were combined into one set. The same REOF analysis used in section 3 was applied to the combined data. The leading modes (Fig. 9) are very similar to those for the TOGA COARE data and other individual datasets: one is deep and one shallow, and they explain nearly 85% of the total variance of all data combined and 65%–98% of variance for individual subsets (Table 4).

b. Data comparisons

One advantage of using the single pair of leading modes to describe the structure and evolution of Q1 is that different Q1 time series can be compared quantitatively on the same ground. The fractional variance associated with the first, deep mode listed in Table 4 indicates the strength of deep convective and stratiform heating (see section 5a). It is highest for TWP-ICE (83.1%) and KWAJEX (80.8%) and lowest for NAME (45.2%) and LBA (46.7%). The fractional variance of the second, shallow mode also varies substantially among the different datasets. The highest values are for LBA (33.9%) and GATE (25.7%) and the lowest for SCSMEX (8.2%) and TWP-ICE (8.7%). Also listed in Table 4 is the ratio between the fractional variance of shallow and deep heating (right column), indicating the relative abundance of shallow versus deep precipitating clouds. Shallow convection is known to be more abundant during GATE, with its mean heating peak at a lower level than in other tropical regions (e.g., Song and Frank 1983). The strong existence of shallow heating in LBA is probably associated with the early stages of the diurnal cycle (Pereira and Rutledge 2006). TWP-ICE and SCSMEX share some commonalities because both were over ocean adjacent to land with strong influences from monsoons or land/sea breezes.

c. Composite structural evolution

The main effort of this study is to seek commonality among all Q1 datasets rather than unique features in each of them. The phase diagram based on the REOF PCs for the combined data is plotted in Fig. 10 the same way as in Fig. 5. For simplicity and conciseness, the eight phases in Fig. 5 were consolidated into four, whose composite Q1 profiles provide a summary of prevailing heating structures in the tropics (Fig. 11). Composite Q1 profiles using the original data (circles) are very well reproduced by reconstructions using the two REOF leading modes plus the mean (solid lines). Phase A (combining phases 2 and 3) represents a shallow heating profile with its peaks near 700 hPa (cf. Figs. 6 and 11). This profile will be referred to as the bottom-heavy heating (BH) profile. Phase B (combining phases 1 and 8) represents a deep, middle-heavy heating (MH) profile with its peak near 450 hPa. The heating profile of phase C (combining phases 6 and 7) is top heavy (TH, heating only in the upper troposphere) and stratiform-like (cooling in the lower troposphere). In phase D (combining phases 4 and 5), deep tropospheric radiative cooling (RC) dominates at the presence of scattered fair weather cumulus and weakly precipitating cumulus congestus. The occurrence probabilities of each phase are given atop the composite profiles in Fig. 11. Again, bottom-heavy profiles (phase A) tend to occur as frequently as top-heavy ones (phase C) with comparable amplitudes, suggesting they should be treated equally. Indeed, shallow convection that produces “warm rain” is common in the tropics, even in deep convective regions (Liu and Zipser 2009).

Probabilities of phase transitions among the four phases can be calculated (Fig. 12a) as previously for the eight phases (Table 2). Again, while remaining in the same phase is the most probable scenario (shaded cells), it is the phase transition (i.e., changing from one phase to another) that interests us. Starting from preceding phase A, the largest probability for phase transition (upper numbers in unshaded cells) is 17.4% for succeeding phase B (bold). This indicates that phase A is more likely to be followed by phase B than by the other two phases. Comparing the lower numbers in the same column for succeeding phase A, the largest probability for phase transition (unshaded cells) is 22.2% for preceding phase D (underscored). This means phase A is more likely to come from phase D than from the other phases. Similarly, most probably phase B is followed by phase C and preceded by phase A, phase C is followed and preceded both by phase D, and phase D is preceded by phase C and followed by both phases C and A.

These most probable phase transitions are marked in Fig. 12a by arrows. An arrow pointing toward the right (left) indicates a clockwise (counterclockwise) rotation in the phase diagram of Fig. 10. There are uncertainties in the direction of the phase transition between phases C and D. The definition of the four phases is as arbitrary as that of the eight phases in Fig. 5. To seek an indication of the direction of the phase transition independent of any phase definition, the PDF of changes in the phase angle was calculated and plotted in Fig. 13a as for Fig. 7, except that the Δθ bin width was chosen to correspond to four rather than eight phases. In this case, positive Δθ also dominates negative ones for |Δθ| < 90°, indicating the transition in the direction of A–B–C–D is favored, even though phase transition D–C is also of high probability.

The exact same analysis procedures were also applied to daily Q1 data to see if the previous results depend sensitively on the time scales implied in the data interval. Most of its results were almost identical to those based on the 6-hourly data. The probability of phase transition is listed in Fig. 12b and the PDF of Δθ shown in Fig. 13b. Now there is no uncertainty in the direction of phase transition as seen in the 6-hourly data. The phase transition of D–A–B–C–D unambiguously emerges. The phase transition of D–C (radiative cooling to top-heavy heating profiles) appears to be highly probable in the 6-hourly data, perhaps because of the traverse of fast-moving stratiform precipitating systems (such as squall lines) across the sounding arrays.

5. Dynamical implications

The three composite heating profiles in phases A, B, and C derived in the previous section raise two questions: 1) What are the compositions of these profile in terms of the different building blocks (Fig. 1) associated with particular types of precipitating clouds? 2) What are the differential large-scale dynamical responses to the three heating profiles? In this section, we provide brief discussions of these two questions to motivate later more thorough investigations.

a. Cloud-type composition

The composite heating profiles in Fig. 11, or any profiles averaged on a certain period and/or area, are composed of profiles associated with individual types of precipitating cloud (examples are shown in Fig. 1). Understanding the cloud-type composition of mean heating profiles in their evolution may provide insights into scale-interaction problems. Here, we take a simple approach by considering statistical relationships between the set of idealized profiles associated with the three cloud types in Fig. 1 and the mean heating profiles in each of the phases in Fig. 11, excluding the contribution of fair weather cumulus and cloud radiative effects.

The idealized profiles associated with the three cloud types are taken as the fundamental building blocks that constitute composite diabatic heating in Fig. 11, averaged over a large-scale area and/or period. A linear combination of the three idealized profiles to best fit a particular composite profile is selected as representing the cloud-type composition of the composite. Two independent criteria for the best fit, maximum correlation, and minimum root-mean-square (rms) difference between the composites and their fits yielded the same results. The correlation coefficients are all larger than 0.98. The normalized rms differences, defined as rms divided by the norm of each composite profile, are all smaller than 0.023 (i.e., the rms differences <2.3% of the total heating/cooling amount). Figure 14 summarizes the results. Phase A (bottom-heavy heating) is dominated equally by deep convection, which contributes 45% to the composite heating, and by shallow convection/congestus (40%); stratiform heating contributes a distant 15%. The bottom-heavy profile in phase A has considerably large amplitudes in the midtroposphere than the building block profile of shallow convection/congestus (Fig. 1), which comes from the contribution by deep convection. In phase B (middle-heavy heating), the fractional contribution of deep convection remains about the same as in phase A (43%). In contrast, that of stratiform heating increases substantially (37%) from phase A and that of shallow convection/congestus is reduced by half (20%). The stratiform contribution becomes dominant (56%) for phase C, as expected, while the contribution from deep convection continues to decrease slightly (38%) and that of shallow convection/congestus now becomes negligible (6%).

Combining the information of mesoscale contributions to each phase and the most probable phase transition, Fig. 14 illustrates the decreasing role of deep convection and increasing role of stratiform precipitation through the transition. This connects our knowledge of convective development in the tropics (e.g., Houze 1989, 1997) to the variability of large-scale heating profiles. This empirical approach was adapted only to make two points. First, any large-scale mean heating profile is composed of a variety of building block profiles associated with different cloud types and should not be interpreted as representing the heating profile of any single precipitating cloud type, however similar the two might be. Second, the structural evolution in large-scale diabatic heating is a consequence of changes in fractional abundance of the building block profiles. These changes are presumably modulated by the large-scale circulation (Mapes et al. 2006). The precise contributions by different cloud types to a mean heating profile will have to be quantified by more sophisticated approaches using ground radar or high-resolution satellite data.

b. Response of large-scale circulation

Previous studies have emphasized on the role of stratiform, top-heavy heating in the large-scale circulation (Hartmann et al. 1984; Mapes and Houze 1995; Schumacher et al. 2004). The composite profiles in Fig. 11 clearly indicate that there are other types of heating profiles that should also be considered along with the stratiform, top-heavy heating profile. Here we compare the large-scale responses to the three composite heating profiles in the three phases (A, B, and C) in Fig. 11 that represent the prevailing large-scale heating structures (bottom, middle, and top heavy).

For this, a simple linear balanced model was used. It is a three-dimensional dynamical system for hydrostatic, steady-state perturbations in a stratified atmosphere on an equatorial β plane, driven by diabatic heating and constrained by friction (Hagos and Cook 2005; Moura and Shukla 1981):
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i1520-0469-66-12-3621-e5c
i1520-0469-66-12-3621-e5d
where u, υ, and ω are the x, y, and p components of velocity; ϕ is the geopotential height; and ε, Sp = (T/θ)(∂θ/∂p), and Q1 are the friction coefficient, stability parameter, and the total diabatic heating, respectively. All variables are nondimensionalized by their respective typical values for the tropical large-scale environment. For given Q1, ε, and Sp, the complete solution, provided in the appendix of Hagos and Cook (2005), was used to estimate moisture convergence, − · (rV), where r is the mixing ratio and V the horizontal wind vector. In the calculation, ε = 0.1, corresponding to a 10-day frictional time scale. Profiles of globally averaged Sp and r from the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) were used. The only representation of the planetary boundary layer in the model is implicitly in these profiles.

The three composite Q1 profiles in phases A, B, and C in Fig. 11 are considered to be the main constituents of the time mean Q1 profile shown in Fig. 9. Figure 15 shows the meridional-vertical wind vector on the left, and zonal-vertical wind vectors on the right, and their associated moisture convergence forced by the mean and three composite Q1 profiles in the center. In the meridional-vertical case, the heating is zonally constant and centered at the equator with a Gaussian distribution in latitude (shown by colors) whose half-width is 5°. In the zonal-vertical case, the heating is centered at the equator and a reference longitude (0°) with a Gaussian distribution of a 5° half-width in both latitude and longitude. The wind vectors are averages over 15°S–15°N in the zonal-vertical case. The moisture convergence profiles are averages over a 10° distance symmetric in the directions of the Gaussian distributions. They are almost the same for the meridional and zonal cases.

The gross features of the meridional and zonal overturning circulations forced by the mean profile are very similar except for the zonal asymmetry in the zonal case. The stronger circulation to the west than the east of the heating in the absence of zonal mean wind (Rosenlof et al. 1986) signals the dominance of the Rossby wave component over the Kelvin wave component. Both meridional and zonal circulations exhibit a clear double-cell structure. There are maximum inflows toward the heating center and maximum moisture convergence near the surface and the 550-hPa level, with a single outflow in the upper troposphere. Associated with this double-cell circulation structure is a profile of moisture convergence that shows a primary maximum near the surface and a secondary maximum at the same level of the midlevel inflow. The midlevel inflow and convergence are at roughly similar levels as the mesoscale midlevel inflow associated with stratiform precipitating clouds (e.g., Kingsmill and Houze 1999). Using a simple deep and top-heavy heating profile, Mapes (2001) produced a similar double cell structure of the circulation in association with a gravity wave mode. Here, it is produced without any transient variability.

The model was then forced by the three composites of phases A, B, and C to examine the cause of the double cell structure. The strong midlevel inflow and the upper-level outflow are primarily forced by the middle-heavy heating of phase B (third row from the top in Fig. 15), whereas the surface inflow is mainly due to the bottom-heavy heating of phase A (second row in Fig. 15). The top-heavy, stratiform-like heating of phase C also generates a midlevel inflow and upper-level outflow as does the middle-heavy heating of phase B, but its low-level cooling forces near-surface outflow and divergence (bottom row in Fig. 15).

To illustrate the linear role of each building block heating profile associated with different precipitating cloud types, we used the three idealized heating profiles shown in Fig. 1 to force the zonal circulation. The relative amplitudes of the three idealized heating profiles were determined by their fractional contributions to the prevailing heating of each phase listed in Fig. 14. Stratiform, deep convective, and shallow convective/congestus heating play their respective roles similarly in all three phases. Because of its upper-level heating and lower-level cooling, stratiform heating generates a dual-cell circulation pattern with a single midlevel inflow (convergence) and two outflows (divergence) in the upper troposphere and near the surface, respectively (second row from top in Fig. 16). In contrast, deep convective heating generates a deep single-cell circulation pattern with its inflow in the lower troposphere and outflow in the upper troposphere (third row in Fig. 16). The circulation pattern forced by shallow convective/congestus heating is similar to that by deep convective heating, except it is confined to the lower troposphere (bottom row in Fig. 16).

6. Summary and discussion

A rotated EOF (REOF) analysis was applied to tropical diabatic heating (Q1) data derived from in situ soundings collected from eight field campaigns. The two leading modes—one deep, one shallow—in combination explain 85% of the variance in all Q1 data combined. These two modes were used to describe the main features in Q1 profiles and their variability directly relevant to the large-scale circulation. The two leading modes serve as a common framework to compare heating profiles from different locations and to consolidate their similarities. The central concept of this study is that regardless of its shape, a mean (in either space or time or both) heating profile relevant to the large-scale circulation must be interpreted as an aggregate of heating due to a variety of individual cloud types. This has led to the following main results:

  • (i) Based on the two leading REOF modes, three prevailing large-scale diabatic heating profiles were composited: top-heavy, stratiform-like heating (heating peak near 400 hPa and cooling peak near 700 hPa); bottom-heavy heating (peak near 700 hPa); and middle-heavy heating (peak near 400 hPa). The strengths and the occurrence frequencies of the top-heavy, stratiform-like and bottom-heavy heating profiles are comparable. The middle-heavy heating is much stronger but less frequent than the other two.
  • (ii) The most probable structural evolution of the prevailing large-scale heating profiles takes the sequence of bottom-, middle- and top-heavy, preceded and followed by deep tropospheric cooling. This structural evolution appears to exist on different time scales.
  • (iii) In a simple linear balanced model, the mean heating, its three prevailing composites, and their building blocks of idealized precipitating cloud types produced multiple overturning cells in the large-scale zonal and meridional circulations. The model demonstrated large sensitivities of moisture convergence and surface wind to the vertical structure of diabatic heating.

The structures of the two dominant REOF modes—namely, one shallow and bottom heavy, one deep and middle heavy—are not unique to Q1 estimated from sounding observations. They have been found in Q1 estimated from satellite retrievals and global reanalyses (Hagos et al. 2010). Their vertical structures are similar in the entire tropics among different estimates, despite very different profiles of the means. The spatial independence of empirical leading modes has also been found by Lin and Arakawa (2000) in sounding-based Q1 data and by Yuan and Hartmann (2008) in vertical motion profiles from a global reanalysis. The ubiquity of the two leading modes in tropical diabatic heating profiles is intriguing. It is unclear, however, what physical significance it may have. It may suggest fundamental mechanisms for the structure and variability of tropical diabatic heating that are independent of climate regimes and can be captured using different data and methods. The melting level inversion (Johnson et al. 1996) comes to mind. This midtropospheric inversion, however weak, separates cloud microphysical processes that involve with ice (cold rain) from those that do not (warm rain). These two types of precipitation processes are perhaps instrumental to the bimodal probability distributions in the echo top of precipitating cloud (Short and Nakamura 2000) and levels of maximum diabatic heating (Fig. 17), with one peak above the melting level and the other below. It has yet to be determined as whether and how our “bi-modal” definition in terms of empirical decomposition of heating profiles is related to the classic definition of “bimodal” in terms of two peaks in the probability distribution functions of the echo top and maximum heating level.

Our results also indicate that if there are three types of cloud populations in the tropics (Johnson et al. 1999), their heating profiles aggregate into three large-scale prevailing heating profiles that can be sufficiently represented by two REOF modes. Instead of associating these two modes or the three prevailing composite heating profiles with any particular types of precipitating clouds, we view them as consequences of different fractional contributions from various cloud types, including stratiform cloud, deep convection, shallow convection/congestus, and even nonprecipitating clouds.

Previous studies on the role of diabatic heating in the tropical large-scale circulation have often emphasized the importance of top-heavy stratiform heating (e.g., Hartmann et al. 1984; Mapes and Houze 1995; Schumacher et al. 2004). The results from this study suggest that the shallow, bottom-heavy heating also has to be included to produce complete patterns of the responding circulation because of its comparable strengths and occurrence frequencies. Missing the bottom-heavy heating would undesirably compromise the strength of responding low-level and surface wind. It has been proposed that the sensitivity of low-level moisture convergence to the shallow heating profile is central to the tropical intraseasonal oscillation (Wu 2003). This has been supported by recent modeling studies (Zhang and Mu 2005; Li et al. 2009). The large sensitivity of surface wind to the vertical structure of diabatic heating, also demonstrated for mesoscale systems (Mapes and Houze 1995), suggests the potential importance of the structure of diabatic heating to air–sea interaction. If so, the possible important role of surface evaporation in the tropical intraseasonal oscillation (e.g., Sobel et al. 2009) can be satisfactorily investigated by numerical models only if they adequately reproduce bottom-heavy diabatic heating.

The Q1 profiles and their structural evolution (tropospheric cooling–bottom-heavy heating–middle-heavy heating–top-heavy heating–tropospheric cooling) based on the two leading REOF modes were statistically derived without any preconception of their dynamical association. Interestingly, they are consistent with structural evolutions of tropical convection for several types of large-scale waves (see a review of Kiladis et al. 2008). The similar structural evolutions on two time scales (based on 6-hourly and daily data) provide supporting evidence for the concept of convective “self-similarity.” This concept asserts similar evolution in vertical structures of convective systems on different scales (e.g., Straub and Kiladis 2003; Kiladis et al. 2005; Mapes et al. 2006; Haertel et al. 2008), which has served as foundation for new modeling approaches (e.g., Majda 2007; Khouider and Majda 2008).

The tropical atmosphere has been theoretically described in terms of two vertical modes (Mapes 2000; Haertel and Kiladis 2004; Peters and Bretherton 2006; Kuang 2008). Heating profiles represented by these two modes are similar to the two EOF leading modes in Fig. 3 (also see Fig. 8 in Haertel and Kiladis 2004). Whether these modes can be appropriately interpreted as exclusively associated with stratiform and deep convective heating, respectively, depends on the scale involved. For large scales, they must be interpreted as aggregates of different types of precipitating clouds. Khouider and Majda (2008) considered three modes whose combinations represent heating due to various types of convection. In our linear model, the two-cell structure in the vertical overturning circulation forced by the observed mean heating (top row in Fig. 15) breaks into more complicated multicell structures corresponding to the prevailing composite heating profiles. The results from this study echo the concern raised by Wu et al. (2000) on the applicability of a single-mode model to the tropical large-scale atmosphere.

The meridional multicell circulation induced by the prevailing heating profiles have been observed from in situ observations (e.g., Zhang et al. 2004, 2006; Zuidema et al. 2006) and global reanalyses (Trenberth et al. 2000; Zhang et al. 2008) and have been simulated by theoretical and numerical models (Nolan et al. 2007). The multicell structure in the zonal circulation has yet to be confirmed by observations. Of particular interest is the shallow overturning circulations that are confined to the lower troposphere produced by the bottom-heavy heating of phase A and the shallow convection/congestus building block heating profile (Fig. 16). Nolan et al. (2007) showed that in the presence of a strong gradient in surface pressure provided by the gradient in sea surface temperature (SST), such a shallow circulation exists only in the absence of interactive deep convection. Here we have shown that the needed gradient in surface pressure can be provided also by atmospheric bottom-heavy diabatic heating without any SST gradient.

In conclusion, the diagnostic tool based on the two leading REOF modes allows us to document and compare the structure and evolution of tropical large-scale diabatic heating and to explore their roles in the large-scale circulation in a simple, objective, and uniform framework. Even though we are still facing uncertainties in estimating tropical diabatic heating (Hagos et al. 2010), our results demonstrate how much information can be mined from this quantity to advance our understanding of the tropical large-scale dynamics. We therefore appeal to all modelers to archive tropical diabatic heating time series as standard output for model diagnostics and validation.

Acknowledgments

This study would be impossible without the collegial and unselfish help from many in our efforts of collecting the Q1 data. Some directly handed over their data; others made suggestions, even though all did not lead to success. For this, we are grateful to Paul Ciesielski, Steve Esbensen, Richard Johnson, Masaki Katsumata, Yasu-Masa Kodama, Steve Kruger, Wei-Kuo Tao, Wen-wen Tung, Xiaoqing Wu, Michio Yanai, Xiping Zeng, and Minghua Zhang. The authors would also like to thank Robert Houze and Eric Maloney for their comments on preliminary results of this study, Brian Mapes for his detailed comments on a draft of this manuscript, and Shoichi Shige, Courtney Schumacher, and an anonymous reviewer for their specific and constructive comments on the submitted manuscript, which all led to substantial improvement of this article. This research was support by a NASA TRMM/PMM project, Award NNX07AD41G.

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  • Zhang, M. H., , and J. L. Lin, 1997: Constrained variational analysis of sounding data based on column-integrated budgets of mass, heat, moisture, and momentum: Approach and application to ARM measurements. J. Atmos. Sci., 54 , 15031524.

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  • Zhang, M. H., , J. L. Lin, , R. T. Cederwall, , J. J. Yio, , and S. C. Xie, 2001: Objective analysis of ARM IOP data: Method and sensitivity. Mon. Wea. Rev., 129 , 295311.

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  • Zuidema, P., , B. Mapes, , J. Lin, , C. Fairall, , and G. Wick, 2006: The interaction of clouds and dry air in the eastern tropical Pacific. J. Climate, 19 , 45314544.

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Fig. 1.
Fig. 1.

Idealized latent heating profiles for different types of precipitating cloud (after Schumacher et al. 2007).

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 2.
Fig. 2.

Approximate locations of the field campaigns.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 3.
Fig. 3.

(a) Mean (solid) and mean +1 std dev (dashed), and (b) the first (solid) and second (dashed) EOF (thin) and REOF (thick) modes of Q1 from TOGA COARE.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 4.
Fig. 4.

Time series of Q1 (K day−1) from TOGA COARE. (a) Original data based on sounding observations and (b) data reconstructed using the first two REOF modes.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 5.
Fig. 5.

Phase diagram defined in terms of the PCs of the first two REOF modes of the TOGA COARE Q1 time series. Each point corresponds to a single profile. The white circle marks the one standard deviation of the amplitude defined as (PC12 + PC2)1/2. Phase identifications are given in the corners.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 6.
Fig. 6.

Composites of Q1 using original TOGA COARE data (circles), reconstructed from the two REOF leading modes and time mean (solid lines), the first REOF mode (dashed), and the second REOF mode (dotted) for the eight phases (marked in the upper right corners) defined in Fig. 5. The occurrence probability of each phase is given atop each panel.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 7.
Fig. 7.

PDF of phase angle change (Δθ) derived from Fig. 5. The bin width corresponds to the eight phases in Fig. 5.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 8.
Fig. 8.

Composite time evolution of TOGA COARE Q1 based on the most probable phase transition in Table 2 using (a) the original Q1 data, (b) the first two leading REOF modes and the time mean, (c) the first REOF mode, and (d) the second REOF mode. The position of each phase is scaled by the probability of a heating profile to remain in the same phase in two consecutive times.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 9.
Fig. 9.

(a) Mean (solid) and mean plus one standard deviation (dashed), and (b) the first (solid) and second (dashed) EOF (thin) and REOF (thick) modes of Q1 from all eight field campaigns combined.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 10.
Fig. 10.

As in Fig. 5, but the first two REOF modes were derived from Q1 time series of the eight field campaigns combined and the eight phases were consolidated into four.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 11.
Fig. 11.

Composites of Q1 using original data (circles), reconstructed from the two REOF leading modes and time mean (solid lines), the first REOF mode (dashed), and the second REOF mode (dotted) for the four phases (marked in the upper right corners) defined in Fig. 9 for all data combined. The occurrence probability of each phase is given atop each panel.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 12.
Fig. 12.

Probability (%) of 4-phase transition of Q1 from all (a) 6-hourly and (b) daily sounding data combined. In each cell, the upper number is the probability of the preceding phase being followed by the succeeding phase; the lower number is the probability for the succeeding phase being preceded by the preceding phase. Highest probabilities of “moving to” a different phase (unshaded cells) are bolded; highest probabilities of “moving from” a different phase (unshaded cells) are underlined. The column for succeeding phase A is repeated once. Arrows mark the directions of the most probable phase transitions.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 13.
Fig. 13.

As in Fig. 7, but for (a) 6-hourly and (b) daily combined Q1 data. The bin width corresponds to any equally divided four phases.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 14.
Fig. 14.

Schematic diagram summarizing the fractional contributions by idealized building-block profiles to each composite heating profile in the most probable structural evolution.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 15.
Fig. 15.

(left) Meridional-vertical circulation, (right) zonal-vertical circulation, and (center) their corresponding vertical profiles of moisture convergence (kg kg−1 day−1) forced by heating profiles (colors, K day−1) of the composites of phases A, B, and C in Fig. 11. Vertical motions are amplified by a factor of 50. See text for other details.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 16.
Fig. 16.

Zonal-vertical circulations averaged over 5°S–5°N forced by (top) composite heating profiles (solid lines in Fig. 11), same as phases A, B, and C in the right column of Fig. 15, and by idealized (second row) stratiform heating, (third row) deep convective heating, and (bottom) shallow convection/congestus heating shown in Fig. 1 for phases (left) A, (middle) B, and (right) C. The heating amplitudes (colors, K day−1) for the three idealized profiles are scaled to their fractional contributions to the composites (Fig. 14). Vertical motions are amplified by a factor of 50.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Fig. 17.
Fig. 17.

Probability distribution function of maximum heating levels based on all 6-hourly Q1 data.

Citation: Journal of the Atmospheric Sciences 66, 12; 10.1175/2009JAS3089.1

Table 1.

List of the field campaigns from which sounding-based Q1 time series were used in this study.

Table 1.
Table 2.

Probability (%) of transition for Q1 from TOGA COARE. In each cell, the upper number is for the preceding phase being followed by the succeeding phase; the lower number is for the succeeding phase being preceded by the preceding phase. Bold fonts highlight highest phase-change probabilities in a row (upper numbers); bold and underlined fonts highlight highest phase-change probabilities in a column (lower numbers). Probabilities of remaining in the same phase are in italic. Phase 1 is repeated once.

Table 2.
Table 3.

Fractional variance explained by the leading modes of EOF and REOF for sounding-based Q1 from eight field campaigns. A mode with a mid-heavy profile is indicated by bolded font and that with a bottom-heavy profile is italic.

Table 3.
Table 4.

Fractional variance (%) of Q1 of each sounding dataset and their combination (Total) explained by the two leading REOF modes and their ratios derived from all Q1 combined.

Table 4.

1

A method that estimates divergence rather than heating profiles using aircraft Doppler radar data (Mapes and Houze 1995) is also relevant here.

2

There are other Q1 data that have been used previously in the literature but are not available to us: Marshall Island (Yanai et al. 1973), the Barbados Oceanographic and Meteorological Experiment (BOMEX; Nitta and Esbensen 1974), AMEX (Holland et al. 1986), MONEX (Johnson and Young 1983), and others. An effort of restoring all in situ sounding observations in the past into modern digital forms would be an invaluable contribution to research.

3

Unique REOF modes exist with respect to specific given criteria.

4

To reduce the uncertainties in phase transitions due to small variations in the PCs, only points in Fig. 5 whose amplitudes are greater than one standard deviation were used.

5

This might be the consequence of errors in vertical velocity of the GATE data in the Q1 estimate being amplified by large static stability near the tropopause or simply of poor data quality.

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