1. Introduction
Tropical deep convection is known to vary on a broad range of space and time scales. While a portion of this variability can be characterized as noise (Wheeler and Kiladis 1999, hereafter WK99), there are also coherent wavelike disturbances that can often be tracked for days or even weeks, implying a certain level of deterministic predictability (e.g., Waliser et al. 2003; Mapes et al. 2008). Such disturbances are of practical interest owing to their strong influence on sensible weather in both the tropics and midlatitudes via Rossby wave teleconnections (e.g., Schreck et al. 2011; Jones et al. 2011; Roundy and Gribble-Verhagen 2010, and references therein). Thus, it is essential to have a clear understanding of how tropical convection is organized in space and time, as well as the mechanisms responsible for producing such organization.
Fourier transform methods have proven useful for assessing the role of large-scale waves in organizing tropical convection (Hayashi 1974). A relevant example is the study by WK99, who documented the space–time spectrum of many years of satellite-observed outgoing longwave radiation (OLR), a proxy for convective activity. Similar to previous work by Takayabu (1994), the spectrum was found to exhibit characteristics of red noise, but with enhanced power along the dispersion curves of several different equatorial wave modes, including Kelvin, equatorial Rossby (ER), mixed Rossby–gravity (MRG), and inertia–gravity waves. Remarkably, all of these convectively coupled equatorial waves (CCEWs) were found to have equivalent depths in the range 12–50 m, much shallower than the peak projection response to deep convective heating (e.g., Fulton and Schubert 1985). Enhanced power was also seen in association with the planetary-scale Madden–Julian oscillation (MJO). However, unlike CCEWs, signals of the MJO could not be matched to any linear wave mode, implying that the dynamics of the MJO involves more than just convection coupling to linear shallow water waves (Hendon and Wheeler 2008).
Despite the considerable advances made through Fourier decomposition, as outlined above, there are at least two drawbacks to the approach. The first relates to difficulties in identifying and tracking specific wave events. To illustrate, Fig. 1 compares the space–time evolution of raw satellite brightness temperature Tb data against spectrally filtered data, intended to isolate eastward-moving Kelvin wave signals with phase speeds in the range 10–20 m s−1 [see Kiladis et al. (2009) for details about the filter]. In Fig. 1a, the raw disturbance (gray shading) is localized in space and time and shows no evidence of eastward propagation. That is, the raw data show no evidence of a Kelvin-like wave as the filtered data implies (black contours). Similarly, Fig. 1b is an example of a compact disturbance propagating eastward at about 5 m s−1, whereas the filtered data indicates the presence of a faster-moving Kelvin wave. This type of mismatch occurs because the filtered data contains signals due to a broad range of propagating and nonpropagating disturbances, in addition to signals associated with actual Kelvin wave disturbances propagating eastward at 10–20 m s−1. Another drawback to the spectral approach is that disturbances that are relatively compact in physical space tend to appear relatively diffuse in spectral space, as power is spread over a relatively broad range of frequencies and zonal wavenumbers. This spreading of power makes it difficult to isolate the signals of relatively compact disturbances, such as mesoscale squall lines and gravity waves, especially when these signals are superimposed on a red-noise background. In contrast to Fourier methods, wavelet transforms have the advantage of allowing one to localize a specific signal in time and/or space (Yano et al. 2001a,b; Kikuchi and Wang 2010). While filtering using wavelets is potentially a superior strategy for spectral decomposition, it has some of the same limitations as traditional Fourier decomposition due to the unknown nature of the background variability.
Time–longitude sections of raw CLAUS Tb data (shading) during (a) September and (b) June 1987 averaged from 7.5°S to 7.5°N, overlaid with Kelvin-filtered Tb (black contours). The dashed contour in (b) is at 245 K.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
An alternative strategy for studying the organization of tropical convection is through an object-based approach (e.g., Williams and Houze 1987; Mapes and Houze 1993; Machado and Rossow 1993; Machado et al. 1998). In terms of satellite Tb data, this approach involves detecting contiguous regions where Tb is below a given threshold, indicating a coherent region of convective activity. The morphology of these convective regions (or objects) is then analyzed in terms of their location, lifespan, and trajectory. Generally speaking, convective objects in past studies have sizes and durations comparable to a single mesoscale convective system (MCS) or “cloud cluster,” although objects can occasionally be much larger [e.g., the rare “superclusters” of Mapes and Houze (1993)]. In addition to Tb data, several recent studies have used satellite estimates of rainfall, which is a more direct proxy for convective activity than Tb (Siqueira et al. 2005; Skok et al. 2009). However, because of data availability or computing limitations, most of these object-based studies have tended to focus on only a portion of the globe, for time periods spanning just a single season or at most a few years. Moreover, the method used to track individual objects through time has been rather arbitrary, typically involving some spatial overlap criterion between successive time stamps. Finally, little attention has been given to how the properties of convective objects depend on the underlying threshold used to define them; Tb thresholds that have been considered in the literature include 215 (“deep convection”; Fu et al. 1990), 225 (“cold cloud index”; Nakazawa 1988), 233 (Arnaud et al. 1992), and 253 K (Machado and Rossow 1993).
A major limitation of object-based approaches is that propagating disturbances do not necessarily have a well-defined boundary. The boundaries are determined by both the choice of threshold and the specific data resolution such that objects merge with one another with decreasing space/time resolution, as well as with increasing Tb (or decreasing precipitation rate). As a result, this type of method tend to be less successful in detecting synoptic- to planetary-scale convective disturbances because their convective signal are typically less contiguous in space and time. Regardless of these sensitivities, an object approach applied to tropical convection data can only, and at best, identify the convectively active phase of propagating disturbances such as CCEWs and the MJO.
The major goal of the present study is to investigate the relationship between scales and propagation characteristics of synoptic- to planetary-scale waves such as CCEWs and the MJO, and the smaller-scale organization embedded within them such as mesoscale squall lines and gravity waves. This is achieved via a combination of object and spectral approaches that is designed to circumvent some of the limitations of each techniques described above. Whether systematic relationships across these scales are essential to properly representing tropical variability is an open question, and the MJO is a clear example of inconsistencies among theories and models. On the one hand, some of the basic features of the MJO (e.g., slow eastward phase speed and quadrupole vortex structure) have been well described using a simple model (Majda and Stechmann 2009). This model includes only effects of low-level moisture anomalies and subplanetary-scale convective wave activity (i.e., no distinction is made between modes of synoptic/mesoscale variability), implying that the particular phases and scales of smaller-scale disturbances are not essential to simulating the evolution of the MJO. On the other hand, studies by Lin et al. (2006, 2008) have suggested that poor simulation of the MJO and CCEWs by many global circulation models (GCMs) is due to the poor treatment of systematic interactions of tropical convection across scales in these models.
The above example motivates the broader question of whether successful simulation and prediction of tropical low-frequency variability depends critically on properly resolving higher-frequency modes of variability. In the present study, we take a first step toward addressing this question by focusing on the scales of organized tropical convection identified as objects versus those seen as peaks in global space–time spectra, along with the relationships between them. Specifically, this paper describes an object-based analysis of 20 yr of high-resolution satellite Tb data (0.5° in space; 3 hourly in time). The analysis involves the detection of contiguous cloud regions (CCRs) in the three-dimensional space of latitude, longitude, and time where Tb falls below a threshold. Ultimately, the questions we aim to address are the following: (i) How do CCRs scales and propagation characteristics change with Tb thresholds? (ii) What is the relationship between the scales and propagation characteristics of CCRs and CCEWs? Section 2 describes the data and methods, as well as a technique for distinguishing between zonally propagating and nonpropagating CCRs. Section 3 then presents a global analysis of zonally propagating CCRs, including their sensitivity to Tb threshold. To investigate the relationship between CCEWs and CCRs, we introduce in section 4 a data reconstruction method based on the CCRs identified in section 3. Comparison between space–time spectral characteristics of individual CCRs and the reconstructed data highlights the role of modulation across scales in tropical convection organization. In the final section, we summarize and discuss our main results.
2. Data and methods
a. Identifying CCRs
The primary data come from the Cloud Archive User Services (CLAUS) dataset, which consists of 23 yr (July 1983–June 2006) of satellite Tb estimates archived every 3 h, on a globally uniform grid with 0.5° spacing (Hodges et al. 2000). We identify CCRs in the latitude–longitude–time domain for a range of different thresholds Tb0 (discussed further below) and the algorithm used to detect CCRs is described in appendix A. Because our interest is on relatively large CCRs that develop in the tropics, we require that CCRs last more than 12 h, span more than 10 longitude grid points (approximately 550 km), and fall within 15°S–15°N. The method is applied to CLAUS data to produce a dataset of an average of 20 000 CCRs for each threshold that are stored for later statistical processing.
b. Distinguishing between propagating and nonpropagating CCRs
While a number of CCRs can be described as amorphous blobs, many others show clear evidence of propagation, typically in the zonal direction, as illustrated by the example in Fig. 2. To determine whether a CCR is zonally propagating or not, as well as its speed of propagation, we developed an algorithm based on the Radon transform [for a review of Radon transform and applications, see Deans (1983)]. As discussed further in appendix B, the algorithm involves optimizing the fit of a given phase line in the longitude–time plane to a CCR’s meridionally averaged Tb field. This process is used to estimate the zonal propagation speed c of each CCR [similar to the method used in Dias and Pauluis (2011)], as well as the “goodness” of the phase speed fit. Following the criteria detailed in appendix B, only CCRs that meet our goodness-of-fit criterion and that have c in the range 1.5–60 m s−1 are classified as zonally propagating; the remaining CCRs, including those whose goodness of fit is below a certain tolerance level, are classified as nonpropagating. The statistics shown in the next section are not sensitive to this speed cutoff. One caveat to this approach is that any CCR whose propagation speed changes substantially during the course of its lifetime will likely be classified as nonpropagating, owing to a poor goodness of fit.
Example of an eastward CCR propagating along the western Pacific at a speed of about 19 m s−1.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
c. Threshold choices
As already mentioned, one of the primary goals of this study is to understand how the statistical properties of CCRs depend on the choice of threshold Tb0 used to define them. To come up with an appropriate range of thresholds to explore, we computed the probability density function (PDF) of CLAUS Tb data for latitudes in the range 15°S–15°N. The results are shown in Fig. 3, together with some previous threshold choices that have been adopted in the literature. Note that the PDF is highly negatively skewed and that the 257-K threshold (15th percentile) is still on the tail of the distribution. Here, CCRs were identified independently for Tb0 ranging from the first to the 15th percentile of the distribution (210–257 K), using one-percentile increments. This range of thresholds (later denoted T1–T15) encompasses the 215-K deep convection index of Fu et al. (1990), as well as the 225-K cold cloud index of Nakazawa (1988).
PDF of CLAUS Tb from 15°S to 15°N. The solid lines correspond to the range of tested thresholds, and the dashed lines to thresholds that have been used in previous studies.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
3. CCR scales and propagation characteristics
a. General properties
As might be expected, CCR numbers are found to depend strongly on the choice of threshold. Figure 4a shows a sharp increase in numbers between T1 and T4, followed by a more gradual decrease between T6 and T15. This behavior is not too surprising because at very low thresholds, a larger number of CCRs are rejected because they are smaller than the minimum size we retain. At the same time, objects merge with one another at warmer thresholds, decreasing the number of objects with increasing thresholds. Therefore the total number of CCRs is controlled by these two competing effects. In addition, at warmer thresholds CCRs tend to be larger in size and thus are more commonly rejected because of the criterion that their starting and end points fall within 15°S–15°N. The net effect is that the typical sizes of CCRs that are retained in our analysis are more or less independent of threshold by an order of magnitude. This near size invariance is illustrated in Fig. 5, which shows that CCRs most commonly have zonal widths of around 400 km and lifespans of 1 day, regardless of threshold. The fact that most CCRs have zonal widths between 200 and 1000 km implies that they are essentially meso-alpha-scale objects. The reason why CCRs most commonly have 1-day lifespans is presumably related to the diurnal cycle of convection over land. While the typical zonal width may be related to the data spatial resolution, the mean width is not too sensitive to spatial resolution (more details are given in appendix C).
CCR sensitivity to temperature threshold. The x axis corresponds to the percentiles of Tb, as shown in Fig. 3. (a) The total number of CCRs. (b) The ratio between propagating to nonpropagating CCRs (solid) and between westward and eastward CCRs (dashed).
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
(a) The histogram of the mean zonal width (km) CCRs as a function of threshold. (b) As in (a), but for the lifespan (days). The histograms at each threshold are normalized to area 1. The stair plots correspond to the mean histogram over all thresholds, and the white symbols show the mean at each threshold.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
Considering the distinction between propagating and nonpropagating CCRs, the solid curve in Fig. 4b shows that the former invariably outnumber the latter, especially at low thresholds where the difference is on the order of 100%. Although the exact ratio of propagating to nonpropagating CCRs depends on the choice of propagation criterion, the decay shown in Fig. 4b is robust to slight changes in the cutoff parameter described in appendix B. Meanwhile, the dashed curve in Fig. 4b shows that the number of westward-moving CCRs always exceeds the number of eastward-moving CCRs, especially at warmer thresholds where the difference is once again on the order of 100%. This bias toward westward propagation is consistent with recent observations and modeling work by Tulich and Kiladis (2012) showing that convectively coupled inertia–gravity waves in the tropics favor westward propagation, apparently because of the effects of vertical shear of the background flow.
b. Phase speed histograms
Focusing on the set of propagating CCRs, Fig. 6 shows how the histogram of phase speed depends on threshold. For ease of comparison, the histogram at each threshold has been normalized to area 1 and the bin size is 2 m s−1. The circles show that the peak phase speed of westward-moving CCRs is around 15 m s−1, regardless of threshold, whereas eastward-moving CCRs have a peak speed of around 15 m s−1 for thresholds in the range T10–T15, decreasing to 11 m s−1 for thresholds less than T10. Because of the highly skewed shape of the histograms, these peaks tend to be 6–8 m s−1 slower than the corresponding averaged speeds, as illustrated by the asterisks. The values of these mean speeds are comparable to the observed speeds of convectively coupled Kelvin and inertia–gravity waves (Straub and Kiladis 2002; Haertel and Kiladis 2004; Tulich and Kiladis 2012). Also, the phase speed PDF is robust both to slight changes in data resolution, and to the choice of dataset as is further detailed in appendix C.
Zonal phase speed (m s−1) distribution as a function of threshold, as in Fig. 5. The white asterisks (circles) correspond to the mean (peak) westward and eastward phase speed at each threshold.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
To assess the sensitivity of the phase speed histograms to lifespan, CCRs were split into four subsets: (i) <2, (ii) 2–3, (iii) 3–4, and (iv) >4 days. The results of this separation are shown in Fig. 7. As might be expected, CCRs lasting less than 2 days (which represent a majority of the distribution) exhibit phase speed characteristics very similar to those of the total population just mentioned. On the other hand, longer-lived CCRs show a clear tendency toward slower mean phase speeds, especially when considering the very lowest thresholds. The reduction in phase speed is most dramatic for CCRs lasting longer than 4 days, in which case both the mean westward and eastward speeds are seen to decrease from around 15–20 m s−1 to around 9 m s−1 as threshold decreases from T8 to T1. Averaging over all thresholds, the solid curves in Figs. 7c and 7d show that westward-moving CCRs with lifespans greater than 3 days exhibit a clear bimodal speed distribution with distinct peaks at around 5 and 15 m s−1. As already noted, the latter speed is comparable to the speed of westward inertia–gravity (WIG) waves, whereas the former speed is close to the speed of ER waves, easterly waves, and tropical storms.
As in Fig. 6, but the data are split according to CCR lifespan.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
The analyses shown here raise a number of questions on the CCRs dynamical characteristics, the physical mechanisms involved on their onset and propagation, and their relationship to the background flow. Because the focus of the present work is on the relationship between CCRs and CCEWs, an extended analysis of CCRs’ geographic and seasonal variability, along with composites of their dynamical fields, will be published elsewhere. Also, to simplify the presentation, all analyses presented in the next sections are shown for four thresholds: the 2nd (T2; 216 K), 4th (T4; 227 K), 8th (T8; 241 K), and 12th (T12; 251 K) percentiles.
c. Spectral properties of CCRs
Because they are compact objects, space–time spectra of individual CCRs will have power that is spread across both frequency and wavenumber. Nevertheless, peaks in phase speed seen in Fig. 6 can also be seen by computing the mean of all individual CCR spectra. To show this, we first average the Tb of each CCR over its latitude range. Next, we embed the CCR at the center of a 108-day and full-longitude window and set the surrounding values to zero, and then compute its space–time spectrum as in WK99 (including tapering in time and space). These spectra are then averaged for all identified CCRs for a given threshold. For example, Fig. 8a shows the average wavenumber–frequency diagram over all propagating CCRs at T4, and Fig. 8b is a similar plot for T8. The black lines correspond to phase speeds of 10, 15, 20, and 25 m s−1. We show frequencies ranging from 
CCR wavenumber–frequency diagrams. (a),(b) The base-10 logarithm of the mean over all CCRs space–time spectra at T4 and T8, respectively. (c),(d) As in (a),(b), but only the nonpropagating CCRs are included. (e) The power in (a) divided by (c), after normalization to variance one. (f) As in (e), but using the power in (b) divided by (d). The black lines correspond to phase speeds of 10, 15, 20, and 25 m s−1.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
d. CCRs sensitivity to data resolution
As discussed in the introduction, CCR boundaries, and therefore overall size, are sensitive to data resolution. In particular, by smoothing the data in space and time, objects become larger. To illustrate this point, CCRs are also identified in space–time-filtered CLAUS data where we retain a relatively small range of wavenumbers, and periods longer than 1.25 days. In Fig. 9, black lines correspond to a filter where planetary wavenumbers less than 20 are included, and gray dashed lines to the case where planetary wavenumbers less than 30 are included, in both cases at T4 (relative to the filtered Tb). The eastward speed peak between 15–20 m s−1 is consistent with Kelvin waves whereas the westward peak is more spread out, but still within the range of speeds of westward-moving inertia–gravity waves. Figure 9 also shows that objects tend to be larger in zonal width and last longer when fewer wavenumbers are included. Although the fact that these objects are roughly at synoptic scales is by construction, it is interesting that they propagate at speeds typical of CCEWs. Further analysis is necessary in order to assess whether these objects actually correspond to CCEWs identified via spectral filtering. For instance, composites on dynamical variables based on particular subsets of these objects can reveal further details of their horizontal and vertical structure. While the possibility of identifying CCEWs as objects using filtered data certainly merits further investigation, a thorough analysis is beyond the scope of the present study.
Statistics of propagating CCRs identified on filtered data: (a) zonal phase speed (m s−1), (b) mean zonal width (km), and (c) lifespan (days).
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
Importantly, both statistics of CCRs identified in raw data and their spectral properties suggest that these objects are at smaller scales than CCEWs. Moreover, visual analyses of global time–longitude plots of tropical cloudiness data suggests that CCRs are embedded in larger-scale wave envelopes (e.g., Kiladis et al. 2009). However, it is difficult to infer or quantify details of this modulation from simple visual inspection. For instance, it would be of interest to know to what extent coherent zonally propagating CCRs are the dominant features embedded within larger-scale waves such as MJO, or whether there is a particular kind of CCR (e.g., propagating versus nonpropagating, or eastward versus westward propagating) associated with large-scale waves such as ER waves, Kelvin waves, or the MJO. In the next section, we introduce a methodology to further investigate and quantify the relationships between scales and propagation characteristics of CCRs and synoptic- to planetary-scale waves.
4. CCRs and large-scale modulation
As mentioned in the introduction, there are a number of possible reasons that the object approach presented here emphasizes the mesoscale to at most synoptic scale, even when using warmer thresholds to detect cloudy regions. The most obvious reason is that, as already mentioned, large-scale waves behave more like wave envelopes made of sequences of smaller-scale waves, so that these envelopes are not necessarily contiguous in Tb. To identify relationships between space–time scales of organized tropical convection, we introduce an object-based method of data reconstruction.
a. Data reconstruction
The goal of the data reconstruction process is to assess the contribution of CCRs to the total space–time variability of tropical cloudiness. Stated differently, our objective is to relate the scales of organized tropical convection detected as objects to the typical scales seen in the space–time spectrum of tropical convection. Once we obtained a set of CCRs for each threshold, the objects are positioned in their physical location in latitude–longitude–time space by assigning a constant temperature inside the space–time region occupied by the CCR and a different constant temperature outside the CCR. Specifically, we assign the threshold temperature inside the CCRs and a flat temperature above the warmest threshold everywhere else. The next step of the data reconstruction process is to overlap CCRs from all choices of threshold, retaining the lowest temperature where they intersect. Note that we can choose up to which threshold we want to include. For example, a reconstruction for up to p = 4 means that all CCRs up to the 4th percentile have been used, and this dataset is denoted object data T4 (similarly for T2, T8, and T12). The data reconstruction process is illustrated in Fig. 10, where raw brightness temperature averaged from 15°S to 15°N is displayed in Fig. 10a and the corresponding object data T8 in Fig. 10b. In this process the use of a higher threshold results in a dataset that will be closer to the original, although we will never exactly reproduce the raw data because all CCRs that are not within 15°S–15°N, that last for less than 12 h, and that extend less than 10° longitude have been excluded.
Example of the data reconstruction process in the latitude–time space from May 1987. (a) Raw Tb averaged from 15°S to 15°N. (b) Reconstruction where all objects below T8 are retained. Scale is shown in K.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
The differences between raw and object data are further illustrated by comparing the global space–time power spectrum of the object data with that of the raw data below the same threshold. The thresholded raw dataset is obtained by using all of the data below a given threshold and replacing the rest of the domain with a constant value. These datasets are denoted raw data T2, T4, T8, and T12 depending on the threshold used. The space–time spectrum is computed following a slightly modified version of the technique introduced by Hayashi (1974) and modified by WK99. We first split the data into segments of 108 days, overlapping by 20 days. Next, for each segment we compute the longitude–time power spectrum at each latitude from 15°S to 15°N. Then, we average over all segments and latitudes and normalize the power spectrum over the entire space–time domain to a variance of one.
Figures 11a and 11b show the normalized power spectra of the object data for T4 and T8, respectively (T2 is similar to T4, and T12 is similar to T8). To focus on synoptic to planetary scales, we show only planetary wavenumbers k ≤ 30 and frequencies 
Space–time power spectrum of (a) object data T4, (b) object data T8, (c) raw data T4, and (d) raw data T8. Gray shading corresponds to the base-10 logarithm of the power spectrum. White contours highlight regions where the ratio between the power spectrum and the estimated background exceeds 10% (thick lines) and 30% (thin lines). The dispersion curves are shown only for the first symmetric shallow water modes for three gravity wave speeds: 10, 15, and 20 m s−1. (e),(f) Shading shows the ratio between the object and raw power spectra at T4 and T8, respectively.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
b. Randomized data
As previously mentioned, a reasonable interpretation for the differences between the CCR spectral peaks shown in Fig. 8 and the object-data global power spectra (Figs. 11a,b) is that the smaller-scale CCRs are embedded in larger-scale wave envelopes that in turn dominate the global space–time power spectrum. To further investigate the role of large-scale organization, we randomize envelopes of zonally propagating CCRs by altering the data reconstruction in the following way. Instead of positioning each CCR at their original location, it is placed at a random location. For example, say the centroid of a particular CCR is at (xj, yj, tj), representing latitude, longitude, and time, respectively. We then draw a new centroid 
As in Fig. 10, but the objects are placed at random locations. The plus signs represent the centroid location of the original objects.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
As in Fig. 11b, but for the random data T8.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
c. Testing CCRs modulation
An interesting question related to the link between CCRs and CCEWs is whether these large-scale wave envelopes are sensitive to the particular morphology of CCRs, or whether all that matters is the CCR location in time and space. A simple first test is to reconstruct two object datasets, one with only the propagating CCRs, and the other with only the nonpropagating CCRs. Although there is some sensitivity to the specific cutoff parameters we use (see appendix A), we find that the propagating object-data power spectrum tend to show more distinct peaks along WIG, ER, and Kelvin wave curves whereas peaks associated with MRG waves are more coherent for the nonpropagating object-data power spectrum. However, this type of analysis has the limitation that modulation is sensitive to the total number and size of CCRs used in the reconstruction, which depends on our propagation cutoff criteria.
A perhaps more objective way to look into the role of different types of CCRs is to preserve their original locations. In this particular reconstruction, we replace each CCR by a random CCR at the same threshold, and of similar scale in space and lifetime. In this way, we do not alter the CCRs distribution in time and space very much. Specifically, starting with object 1, we first create a set of objects of width and duration within 10% of the width and duration of object 1. Then one of these objects is chosen at random and placed at the centroid corresponding to object 1, and this process is repeated for all objects. When compared to the example shown in Fig. 10, this process corresponds to placing these “similar” objects at the original centroids shown with black symbols. The power spectrum of this particular data reconstruction is shown in Fig. 14 for T8 (the other thresholds are similar). Once more, the power spectrum has no coherent peaks along CCEWs, except for a westward bias with some power above the background along the WIG dispersion curve, likely due to the fact that, because of their smaller scale, some WIGs may be identified as objects. Interestingly, the spectral signal associated with the MJO is more spread out but can still be seen.
As in Fig. 13, but original CCR locations are preserved; however, each CCR is replaced by a random CCR of similar scale.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
We tested many variations of the reconstruction where we preserve the locations of the CCRs, including one where we substitute the original CCR by a CCR of not only similar scale, but also similar phase speed. This last dataset also does not show significant spectral peaks along CCEWs. Naturally, at the limit of very small-scale CCRs, substitution by CCRs of same scale should preserve modulation at larger scales. However, CCRs identified here are mesoscale objects; thus, our results imply a tight link between mesoscale organization and synoptic-scale waves. Thus, the randomization tests described here suggest the possibility of a two-way feedback: (i) synoptic-scale organization is sensitive to the morphology, location, and time of occurrence of CCRs, and (ii) CCRs are sensitive to the environment of the large-scale waves.
d. An empirical object-based background power spectrum
Further evidence that large-scale waves are most frequently observed as a sequence of CCRs, and much less frequently as a single object is shown in Fig. 15, which displays the ratio between power spectrum of the object data T8 and the mean power spectra over many realizations of the randomizing process at T8. Specifically, we repeat the random positioning step many times and compute the average of the power spectrum over all realizations, and then use the resulting spectrum to normalize the object-data spectrum. Peaks associated with ER waves, the MJO, and Kelvin waves are the most evident, and they are in close agreement with the standard normalized spectrum of WK99. A noticeable difference is that peaks associated with WIGs are fairly weak, suggesting once more that those waves are most frequently detected as individual CCRs. In fact, the WIG peak at lower thresholds is stronger and the Kelvin and ER peaks are weaker (not shown). Interestingly, we do not observe peaks around convectively coupled eastward inertio-gravity (EIG) wave dispersion curves. Even at lower thresholds (T2 and T4), the MJO signal is the only eastward peak above the background. Because the CCR phase speed PDF has a distinct eastward peak at lower thresholds, these results suggest that eastward, relative cold CCRs with speeds around 11 m s−1 are likely embedded in larger-scale waves such as the MJO convective envelope.
Ratio between object data T8 and mean over many realizations of the randomizing process at T8.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
Recall that to highlight CCEWs’ spectral peaks we reproduced the normalization of the power spectrum by an estimated background following the method used by WK99. Although less practical and computationally more expensive, the reconstruction and randomizing method proposed here provides an alternative, and arguably more physically based way of revealing planetary- and synoptic-scale spectral peaks associated with CCEWs. “Physically based” here simply means that the derivation is predicated on the premise that CCEWs are wave envelopes that are comprised of smaller-scale organized convective activity. A natural follow-up on the empirical derivation of the background is to create a dataset with minimal time–longitude propagating-like structures that either arise from the actual propagation of CCRs or are due to modulation. This background can be obtained by repeating the randomizing procedure many times where we substitute propagating by nonpropagating CCRs. While the method proposed here seems more physical than, for instance, smoothing the raw spectra, we find that the background spectrum derived in this way is very sensitive to both the choice of CCRs that are included in the process and to the threshold. For instance, using a fairly strict cutoff for selecting nonpropagating CCRs and at T8, the normalized spectrum is above 10% of the background in a region much more symmetric and spread in frequency and wavenumber. With a less strict cutoff, the normalized spectra are more similar to the cases where we include the propagating CCRs (Fig. 15). Another issue is that by using a stricter cutoff, more CCRs have to be repeated in order to match the total variance of the background spectrum with the reconstructed spectrum; thus, the procedure becomes much less physically justified. Importantly, even using an empirical background that has only nonpropagating CCRs, we do not observe spectral peaks at the typical scale of propagating CCRs. This result reinforces that CCEWs with equivalent depths in the range 12–50 m, along with the MJO, dominate synoptic- to planetary-scale tropical convection organization.
5. Discussion and conclusions
A critical step toward understanding the physical mechanisms of the multiscale interactions between deep convection and atmospheric circulation involves diagnostic analysis. To this end, we present an object-based method for identifying zonally propagating cloudy regions in space and time. In contrast to time–space spectral peaks seen in tropical cloudiness data, but similarly to previous object-based studies, the structures we isolate are primarily at mesoscales. For example, at thresholds ranging from 210 to 257 K, most of the objects last from 1 to 2 days, and their mean longitudinal width is about 400 km. There are always more westward- than eastward-propagating structures, and the PDF of phase speeds is clearly bimodal, with a peak around 15 m s−1 westward and another at around 11 m s−1 eastward. Phase speeds are also sensitive to lifetime. In particular, there is a third westward peak at 5 m s−1 among CCRs that last more than 3 days. These results are robust to slight changes in data resolution and are consistent with objects found using TRMM data. Importantly, within the range of tested thresholds, most CCRs are mesoscale objects and only rarely synoptic or planetary scales.
To investigate the role of synoptic- to planetary-scale modulation in organizing tropical convection, we introduced a data reconstruction method using CCRs identified over a wide range of thresholds. Comparison between global space–time spectra of the object-based reconstructed data versus raw data (Fig. 11) reveals remarkable similarities, with the global power spectrum of the reconstructed data having peaks typical of CCEWs and the MJO, even though CCRs are at much smaller scales. The prominent role of synoptic- to planetary-scale modulation of CCRs is further emphasized through a CCR disarrangement process. Experiments that were tested include randomly repositioning CCRs and swapping CCRs with objects of similar space–time scales while preserving their original locations. Because all these tests resulted in a disarray of spectral power peaks associated with CCEWs, they suggest a two-way relationship between large-scale waves and mesoscale convective events. While CCRs are likely sensitive to the large-scale wave environment, it is also likely that CCEWs are themselves dependent on the morphology of CCRs embedded within them, and the nature of their coherence.
A caveat of the WK99 normalization method is that the statistical significance of the spectral peaks standing above the background depends on the precise method of smoothing in frequency and zonal wavenumber of the raw power spectrum. Although there is no theoretical consensus for what the background spectrum should be, there have been attempts to derive more physically based background power spectra (Cho et al. 2004; Masunaga et al. 2006; Hendon and Wheeler 2008). These studies have shown that peaks along CCEW theoretical dispersion curves are robust to the normalization method. The reconstruction and randomizing method proposed here leads to a novel pathway for producing an empirical background power spectrum that also reveals synoptic- to planetary-scale waves. In particular, the background power spectrum used in Fig. 15 corresponds to an average of the space–time power spectra of many realizations of the randomizing process in physical space, and peaks associated with CCEW dispersion curves are still evident. Interestingly, the fact that the signal associated with WIGs is much weaker in comparison to the standard normalized power spectrum, along with the fact that WIGs are smaller structures, implies that these waves are often identified as objects. This leads to the conclusion that their signal is weak in the normalized spectrum because they are included in the estimated background.
Though westward CCR speeds peak at 15 m s−1, and our results suggest that at least some of these relatively fast westward objects can be interpreted as WIGs, this interpretation does not apply to eastward-propagating CCRs. For example, EIG wave spectral signals are weak or absent using the standard or the empirical normalized power spectrum. In fact, the dominant eastward spectral peaks are the MJO at all thresholds, along with Kelvin waves at warmer thresholds. The MJO is too slow, while Kelvin waves are too fast in comparison to the eastward 11 m s−1 peak in CCRs. Thus, unlike the westward CCRs, our results imply that most eastward CCRs are embedded in larger-scale wave envelopes. We plan on further analysis of CCRs associated with particular CCEWs and the MJO, which will be undertaken through a combination of the spectral filtering and object-based approaches. This analysis will include composites of fields using in situ observations along with reanalysis data to characterize the dynamic and thermodynamic structure of different types of CCRs. Some relevant issues include whether the vertical structure of CCRs is related to their horizontal scale or phase speed (e.g., are relatively slow phase speeds associated with shallower vertical modes?) and the background flow associated with different types of CCRs.
The method presented here can be applied to other datasets and can be used to test models in a straightforward and objective manner. Given the critical gaps remaining for a full understanding of how tropical convection is organized, the methodology developed here provides a highly practical tool to characterize the means in which mesoscale structures propagate and interact with each other and with synoptic- to planetary-scale waves.
Acknowledgments
We thank S. Leroux, M. Wheeler, J.-I. Yano, and Z. Kuang for their careful and thoughtful suggestions that greatly improved this paper. J. Dias acknowledges the support by CIRES Visiting Fellowship and NRC Research Associate fellowship. S. Tulich acknowledges the support by NSF Grant ATM-0806553.
APPENDIX A
Adjacency Criterion
APPENDIX B
CCR Propagation Criteria
The Radon transform (RT; Deans 1983) is used to classify CCRs as either zonally propagating or nonpropagating. This method involves projecting data along phase lines at each angle from 0° to 180° in the longitude–time plane (Yang et al. 2007, and references therein). In the idealized context of a simple plane wave, variance will tend to be largest when phase lines are oriented perpendicular to the crests and troughs of the wave. Thus, the angle perpendicular to this direction will give the wave propagation speed in the longitude–time plane. There are a number of ways to determine the goodness of the phase speed fit. In the present work, a CCR is classified as zonally propagating if there is a single peak in variance corresponding to a phase speed between 1.5 and 60 m s−1, eastward or westward, and this peak exceeds the mean variance plus 1.5 standard deviations (std dev). Figure B1 illustrates the method showing a time–longitude map of a CCR (Fig. B1a) and the corresponding variance of the projected data (Fig. B1b). In this particular case, variance peaks at 166°, corresponding to a westward phase speed of 19.5 m s−1. For all CCRs classified as zonally propagating, phase speed is determined by the peak in variance. To assess the sensitivity of the method to the particular cutoff choice of 1.5 std dev, we tested the method for 1.25 and 1.75 std dev. Unless stated otherwise, our results are robust within this range of parameters. To better characterize the morphology of CCRs, all comparative analyses of propagating versus nonpropagating CCRs in section 4 are done using a stricter cutoff. For propagation we use 1.75 std dev above the mean, and for nonpropagation the peak in the Radon variance has to be below the mean plus 1.25 std dev. Once again, our results are robust to slight changes in these cutoff parameters.
(a) Time–longitude section of a zonally propagating CCR and (b) the variance along lines of the projected CCR Tb.
Citation: Journal of the Atmospheric Sciences 69, 8; 10.1175/JAS-D-11-0293.1
APPENDIX C
CCR Sensitivity to Data and Dataset
To test CCRs’ sensitivity to data resolution and to the particular choice of dataset, we tested our CCR detection algorithm on CLAUS data at ⅓°, and also on 0.25° 3B-42 Tropical Rainfall Measuring Mission (TRMM) data, both for 2 yr. We found that CCRs obtained using CLAUS data at ⅓° are very similar to that using 0.5° in terms of size and phase speed. In particular, while CCR size increases with decreasing resolution, this scaling is sublinear. In general TRMM data has many more missing values than CLAUS data. These missing values were interpolated in time before applying the object identification algorithm. Also, for a more accurate comparison to CLAUS data, we regridded TRMM to 0.5° spatial resolution. We identified objects at thresholds ranging from the 86th to 98th percentile of all data where the precipitation rate is larger than zero. Comparing CCRs obtained in the same 2-yr period, the TRMM phase speed PDF (not shown) has the same westward and eastward peaks, and a similar decay away from the peaks. Consistent with objects identified in CLAUS data, the peaks are not very sensitive to the threshold used. Moreover, after including only objects that last for more than 3 days, we also observe the slow westward peak at 5 m s−1 seen in Fig. 7.
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