The mean climate state at any location is the aggregate effect of day-to-day variations. For rainfall, in particular, this long-term average is contributed by discrete weather systems. In the mid- to high-latitude regions, there exists a consensus among the research community and the operational meteorological agencies of what constitutes a synoptic-scale weather system. They include surface features, such as fronts and cyclones , and some mid- to upper-tropospheric flow objects, like potential vorticity (PV) cutoffs and streamers and warm conveyor belts WCBs; see also. Meanwhile, besides tropical cyclones (TCs) and tropical lows or depressions, there is no consensus on how to define analogous rain-bearing tropical weather systems.

A key challenge is the range of spatial scales on which one may define tropical weather systems. One approach is to focus on thunderstorms and the associated mesoscale convective systems MCSs; see e.g., using object tracking. Alternatively, a complementary view applies spectral analysis to decompose tropical motions into large-scale wave-like disturbances, such as the Madden–Julian oscillation MJO; and equatorial waves . The MCS point of view examines weather from an object-based perspective and deals with tangible weather elements, like rainfall and clouds, but less with the underlying dynamics. For example, around a single TC, there are sometimes multiple clusters of MCS “objects”, even though they are most likely all under the dynamical influence of the TC. On the other hand, the equatorial wave perspective highlights the dynamics responsible for the rainfall, but views them from an Eulerian point of view. A case of twin cyclonic vortices symmetric about the equator, for example, may be seen through equatorial wave theory as part of the westward propagating n=1 equatorial Rossby (ER) wave see e.g.,, but the trajectories of the two cyclones may diverge, or one may outlive the other, and this cannot be fully explained by equatorial wave theory.

The two examples above motivate the current study to explore a new approach of describing dynamical disturbances in the tropics that is more analogous to that used for the mid-latitudes. Conceptually, the approach is to fill the gap between the planetary-scale waves in the “background” and the smaller-scale MCSs with the synoptic-scale tropical weather systems. Here, we introduce an approach that combines the spectral and object tracking perspectives. Recently, used a scale analysis of the governing equations to identify seven distinct types of tropical motions. They applied a theoretical framework, developed by a number of authors over the past two decades (reviewed in Sect. ), in which disturbances are distinguished by the role played by moisture in their dynamics. The theory implies that slow-moving disturbances have the strongest coupling to moisture, and they are known as moisture modes. At the other end of the spectrum, disturbances that move rapidly behave like inertio-gravity waves. Motivated by this work, we separate convectively coupled dynamical systems other than TCs into three categories based on their phase speed: slow systems are described as moisture modes, fast systems as inertio-gravity (IG) waves, and those in between, which we call mixed systems. Using this framework, we aim to answer the following questions.

What is the observed relative importance of moisture and temperature perturbations in moisture modes, mixed systems, and IG waves?

The ability to decompose tropical weather into discrete systems has some useful and beneficial applications. For example, model forecasts of a particular type of weather system could be used in combination with the statistics of such weather systems to forecast the likelihood of an extreme event. showed that such a conditional forecasting method can lead to improved skill for rainfall extremes occurring over the Maritime continent. Another application would be to investigate the changes in tropical rainfall in a warming climate. As emphasised in previous studies e.g.,, changes in tropical precipitation under global warming are not as simple as the Clausius-Clapeyron scaling of 7 % increase per 1 K of warming. The weather system framework could allow such changes to be separated into changes in frequency of different system types and changes in their respective contribution to rainfall, as has been done in the extratropics e.g.,, helping to elucidate the key physical mechanisms at play.

In the next section, we summarise the theoretical framework underlying our separation of tropical weather systems; the moisture mode-to-gravity wave spectrum. In Sect. , we explain our methodology of defining weather system types. Section presents the main characteristics of each type of tropical weather system. We explore how these systems affect the occurrences of extreme rainfall events by investigating the rainfall characteristics associated with each of them in Sect. . Lastly, we present the summary and discuss the results in Sect. .

Here we introduce the theoretical framework of tropical motions existing on a spectrum between fast inertio-gravity waves and slow moisture modes, each with contrasting propagation and maintenance mechanisms. We begin with the study of that sought to explain the complementary control of convective inhibition and lower-tropospheric moisture on convection. They developed an idealised atmospheric model with two distinct unstable modes. The first mode governs the precipitation by modulating the column saturation fraction (i.e., the ratio between column specific humidity and column saturation specific humidity), which they referred to as a moisture mode. The second mode controls convection by altering the convective inhibition just above the boundary layer, and this buoyancy-modulating system was identified as a convectively coupled gravity wave. While buoyancy itself is also affected by moisture anomalies, moisture modes are distinct in that they are present even under weak temperature gradient WTG; e.g., conditions, with no large-scale buoyancy anomalies. These two distinct modes were also found to move at different speeds, with the moisture mode propagating slower than the convectively coupled gravity wave.

Moisture modes themselves were first described in a modelling study by . By applying the WTG approximation and adding a prognostic moisture equation to their shallow water model of the tropics, they discovered a mode that owes its existence to horizontal moisture advection. This mode is related to the background horizontal moisture gradient in a manner similar to how the barotropic Rossby wave is related to the background potential vorticity gradient. Later studies suggest that some of the well-known forms of tropical intraseasonal variability, such as the MJO e.g.,, which does not appear in any dry atmosphere models, and the ER wave e.g.,, whose observed propagation characteristics are slightly different from what the dry theory suggests, may be moisture modes. The main characteristic of a moisture mode is that it has strong moisture perturbations throughout the lower free troposphere, creating an environment that is supportive of deep convection . Due to their slow propagation, moisture modes are also characterised by WTG balance, as their timescale is long enough to allow the temperature anomalies from latent heat release in deep convection to be smoothed out by gravity waves see e.g.,. This implies that the moisture perturbations associated with moisture modes are more important for their dynamics than the temperature or buoyancy perturbations.

Compared to moisture modes, convectively coupled IG waves have been known far longer, as they appear in the solutions of the “dry” shallow water model of equatorial waves in . In the atmosphere, disturbances such as the syntoptic-scale 2 d waves appearing over the Western Pacific in Austral Summer have been identified as IG waves e.g.,. With gravity acting as their main restoring force, IG waves induce significant density or buoyancy variations as they propagate, and these buoyancy anomalies reduce the static stability of the tropospheric column . This can lower the convective inhibition above the boundary layer, making the environment more suitable for deep convection. In short, temperature or buoyancy variations are thought to dominate the coupling of IG waves to convection, while moisture variations are thought to dominate this coupling for moisture modes.

The main distinction in the thermodynamics between moisture modes and IG waves can be summarised as a single parameter , 1Nmode≡CpT′Lq′≃s′Lq′, where CpT is enthalpy, Lq is latent energy, T is temperature, q is specific humidity, s is dry static energy (DSE; s=CpT+gz), z is geopotential height, and the constants L=2.5×106 J kg⁻¹, Cp=1005 J kg⁻¹ K⁻¹, and g=9.81 m s⁻² refer to latent heat of vaporisation, specific heat of dry air at constant pressure, and gravitational acceleration, respectively. The prime (^′) denotes the magnitude of a perturbation associated with a given weather system. The approximation CpT′≃s′ is based on the assumption that the perturbation in DSE is dominated by that in enthalpy, rather than by that in geopotential. The approximate form of Eq. () is more useful because the numerator and denominator now add up to the moist static energy (MSE; h=s+Lq) perturbation. The value of Nmode represents the relative size of moisture and temperature anomalies within a given disturbance. As such, we expect moisture modes to have a small value of Nmode because their moisture perturbations are large, while an IG wave would be expected to have a large value of Nmode because it has a large temperature perturbation, which is tightly related to its DSE perturbation.

and further find that Nmode is a fundamental parameter governing the dynamics of the tropical atmosphere, and that it may be related to the phase speed of a propagating tropical weather system. Specifically, performed a comprehensive scaling of the governing equations to show that Nmode could be written as Nmode≡max⁡Frτ2,Bu-11α^1-α^,Frτ≡cpc,Bu≡LdLy2, where Frτ is the Froude number, Bu is the Burger number, α^=∂Lq/∂p∂s/∂p-1 is the ratio between vertical gradient of latent energy and vertical gradient of DSE, also known as the scale, cp is the phase speed of the system, c is the dry gravity wave speed, Ly is the meridional length scale of the system, Ld=c/f is the Rossby radius of deformation, and f is the planetary vorticity. In the tropics, where f is reasonably small, and for synoptic-scale systems, whose Ly∼1000 km, Bu tends to be large. Therefore, here we assume that Frτ2>Bu-1, which implies a direct relationship between Nmode and the phase speed of a disturbance: 2Nmode≈cpc21α^1-α^. In Appendix , we sketch a derivation of a slightly different version of Eq. () following . The assumption that Frτ2>Bu-1 may breakdown, however, for systems occurring near the subtropical edge regions, where f can no longer be considered small, or for systems with Ly≫1000 km, since Bu-1 becomes larger than Frτ2. The extent to which this approximation yields meaningful results is discussed further in Sect. .

Combined with Eq. (), the relation in Eq. () tells us that systems with slow propagation will have a small value of Nmode and more dominant moisture perturbations, while fast-moving systems will have a large value of Nmode and more significant temperature perturbations, consistent with what was found in . Moreover, because cp is a continuous quantity, this means that Nmode is also continuous, and it implies that moisture modes and convectively coupled gravity waves are not a dichotomy of types of tropical weather system, but rather there exists a spectrum of types of system with moisture modes and IG waves at the opposing ends: a moisture mode-to-gravity wave spectrum. Another implication of this is that a system with a moderate propagating speed will have characteristics that are a mixture of those of a moisture mode and an IG wave: a mixed system. An illustration of this spectrum of systems is shown in Fig. .

As noted by , systems with similar thermodynamics (i.e., similar Nmode values) can have different dynamical structures or balances. For example, a moisture mode can exist with a convergent-type low-level dynamics under semigeostrophic balance or with a rotational vortex-like structure under nonlinear balance. argued that convergent-type moisture modes are more likely near the equator, while rotational-type moisture modes are more likely off the equator. As with moisture modes, mixed systems may also be separated into equatorial convergent-type and off-equatorial rotational-type. Outside of this moisture mode-to-gravity wave spectrum, identified two other special weather systems in the tropics (cf. Fig. 5 in ), tropical cyclones (TCs), which satisfy gradient wind balance, and moist quasi-geostrophic (QG) systems, which have phase speeds in the range of mixed systems, but have small Rossby numbers and satisfy QG balance, and are typically strongly extratropically influenced. For simplicity, in this paper we limit the scope to focus only on moisture modes, mixed systems, and IG waves, as well as some comparisons to TCs. We find it worth investigating how the separation of the convectively coupled large-scale motion signals in the tropics based on this framework, rather than on the traditional equatorial wave dispersion relations, can help us understand further the complex interactions between large-scale dynamics and moist convective processes.

In this section, we will present the spatial distribution and general characteristics, both thermodynamic and dynamic, of the tropical weather systems defined in the moisture mode-to-gravity wave spectrum framework.

Figure shows that moisture modes mainly occur along the edges of the deep tropics, around 15° N/S. These regions coincide with the climatological location of the moist margin see e.g.,, where the background horizontal moisture gradient is large. This is thought to be one of the supportive environmental conditions for the maintenance and growth of moisture modes . On the other hand, mixed systems and IG waves are more confined along the intertropical convergence zone (ITCZ), especially over the Pacific and Atlantic, and over some land regions, such as equatorial Africa. We also notice that there are some occurrences of mixed systems, and, to a lesser extent, IG waves, along the northern and southern boundaries of the domain (i.e., 30° N/S). These are likely to be the imprints of extratropical frontal bands and other systems moving with similar propagating speeds: the moist QG systems.

Seasonal variations in track density are consistent with the known seasonal cycle of precipitation in the tropics. For example, along the eastern Pacific during the March–May period, we can see two zonal bands where mixed systems and IG waves mainly occur (Fig. f, g), and these bands are also observed in precipitation the double ITCZ; see e.g.,. Therefore, from the weather system perspective, we posit that moisture modes might be the building blocks of the South Pacific convergence zone (SPCZ), while mixed systems and IG waves might be the building blocks of the ITCZ.

We associate rainfall with a weather system if it falls within a 1000 km radius of the system centre at any time during its lifetime (see Fig. ). This method is chosen to also account for rainfall in the vicinity of the systems but outside of their OLR object boundaries. According to this attribution method, the four tropical weather systems studied here, including TCs, are found to be associated altogether with about 60 % of total rainfall received within the global deep tropics (20° S–20° N; Fig. ). Individual influences of moisture modes and mixed systems are each associated with almost 20 % of total rainfall. Meanwhile, IG waves and TCs individually contribute much less to rainfall in this region, only up to 5 % each, due partly to their less frequent and less widespread occurrences compared to moisture modes and mixed systems (Fig. ). Besides these individual contributions from the four systems, the “compound” influences of more than one type of system (i.e., occurring at the same location and at the same time) are also significant, about 10 % of total rainfall (not shown), making the “sum” term in Fig. a greater than 50 %. If we only consider heavy rainfall as in Fig. b, defined as rainfall above an accumulation of 30 mm 3h-1, the total contribution from the four systems investigated here increases to almost 80 %, leaving only around 20 %–25 % of unexplained high rainfall events. This indicates that the weather systems defined in this study account for the vast majority of heavy and impactful rain events in the tropics.

To further investigate the potential impacts of these weather systems on tropical rainfall, we assess the general characteristics of rainfall associated with each of these systems. In the equatorial region, mean rainfall intensity around the centres of moisture modes, mixed systems, and IG waves at their time of maximum OLR activity can reach 2 mm h⁻¹, with mixed systems having the highest median and upper quartile of the distribution (Fig. a). In the off-equatorial regions, both in the northern and southern hemispheres, all systems except TCs have considerably lower values of their associated mean rainfall intensity (Fig. b, c). In these regions, moisture modes have larger mean precipitation compared to mixed systems and IG waves, but still rank below TCs. We also compare the systems by the areal maximum of rainfall intensity around their centres (Fig. d–f). Equatorial moisture modes and mixed systems have very similar distributions of core maximum rainfall intensity, unlike their core averaged distributions in Fig. a. This could possibly mean that the mesoscale structure of rainfall around the centre of equatorial mixed systems is more widespread, whereas that around equatorial moisture modes is more “patchy”.

The fact that the systems we identify have characteristics of high rainfall intensity as described above means that their occurrences increase the chance of extreme rainfall intensity events (see Sect.  for the definition of an extreme event). This is shown in Fig. , which shows the likelihood change of an extreme event at a given location relative to a system's centre at the time of maximum OLR activity. In the equatorial region, extreme rainfall intensity events become 5.12 and 5.85 times more likely around the vicinity of moisture modes and mixed systems, respectively, whereas IG waves have a smaller but still significant impact of about a 300 % increase in extreme probability (Fig. a, d, g). This is in line with the previous results in Fig. , where mixed systems are associated with higher mean rainfall intensity than the other equatorial systems. Off the equator, however, moisture modes have a larger increase in extreme likelihood of up to 650 % around their centre (Fig. b–c), followed by mixed systems and IG waves. Note also that the region of influence (i.e., the spatial scale of the green shaded region) is larger for IG waves than for moisture modes because faster-moving systems travel further within the 3 h compositing period.

The extreme probability change analysis in Fig. , albeit indicating how strongly each type of system can modulate extreme rainfall occurrences, may not tell us the whole story of how impactful each system is to extreme rainfall in the tropics. For example, Fig. j, k show that TCs are associated with a much larger change in the likelihood of extreme events compared to the off-equatorial moisture modes (Fig. b, c). However, from Fig. , we know that the occurrence of TCs is much lower and less widespread than that of moisture modes in the off-equatorial regions. By also taking into account this frequency factor, in Fig. we show that moisture modes are, in fact, associated with more extreme rainfall intensity events along the edges of the deep tropics. About 45 %–75 % of extreme rainfall intensity events in the 15–20° N/S region can be associated with moisture modes (we use the same attribution method as illustrated in Fig. ). This number is about as large as that of extreme events associated with TCs in the TC-prone regions, such as the Philippines and off the west coast of Central America (Fig. g). In fact, in some regions that are commonly associated with TC occurrences like the Caribbean and the Bay of Bengal, moisture modes contribute a higher percentage of extreme rainfall events than TCs. This should give us some sense of how impactful the off-equatorial moisture mode is in terms of extreme 3-hourly rainfall events despite being only associated with only around 20 % of the region's total rainfall (Fig. b). For the equatorial region, the extreme events are more associated with mixed systems (Fig. c) and, to a much lesser extent, IG waves (Fig. e), as expected from the previous analyses. In the equatorial region, particularly along the Pacific ITCZ, high intensity rainfall events are disproportionately associated with mixed systems – these systems contribute almost half of the extreme rainfall (Fig. c), but only 30 % of the total rainfall (Fig. d).

In this study, we divide the synoptic-to-planetary-scale convectively coupled systems in the tropics, other than TCs, into three categories based on their phase speed. The slow-moving systems are dominated by strong moisture perturbations and are called moisture modes. The fast-moving systems have weaker moisture anomalies but significant temperature perturbations, reminiscent of IG waves. The third category comprises systems with moderate propagating speed that have mixed characteristics of the other two, which we refer to as mixed systems. We employ this classification to define object-based weather systems in the tropics in a similar sense to those in the mid-latitudes. We find that moisture modes tend to occur along the edges of the deep tropics, confirming the hypothesis that a strong horizontal moisture gradient, as found along the climatological moist margin e.g.,, is fundamental to their growth and propagation . On the other hand, mixed systems and IG waves are more commonly found closer to the equator, mostly along the ITCZ and especially over the Western Pacific warm pool. There are also some mixed system occurrences along the subtropical edges (i.e., 30° N/S), and these are likely to be the imprints of the moist QG system, which may be considered to be a mixed system with a small Rossby number and strong influences from the extratropics .

Analyses of the thermodynamic perturbation profiles show that the magnitude of moisture perturbations decreases from moisture modes to IG waves. However, the magnitude of temperature perturbations, here represented by the low-level DSE anomaly, does not seem to change with phase speed. Our results here support those of and that the ratio of DSE to latent energy perturbation magnitudes (i.e., Nmode) increases from the slow-moving moisture mode to the fast-moving IG wave, as slower moving systems have a longer time scale allowing them to reach the WTG condition. We also find that this is mainly due to the changes in latent energy alone rather than in both moisture and DSE anomalies, consistent with . However, in contrast to and , we do not find that Nmode≫1 for IG waves, or even Nmode∼1 for mixed systems, indicating that some of the scaling values they used might be unrealistic. Rather, we find ratios closer to those found in , which are, expressed in g kg⁻¹:K units, about 1.6:1 for IG waves and 2:1 for mixed systems. In other words, the moisture perturbation does not become negligible in the faster-moving systems, but the relative importance of moisture and temperature does change with phase speed.

We also test the hypothesis that systems with similar thermodynamics (i.e., similar values of Nmode) can occur under different types of dynamical configuration or balance. Here we find that moisture modes in the equatorial region (10° S–10° N) have convergent-type dynamics, where the convectively active region is marked by the confluence of anomalous winds. Off the equator (10–20° N/S), the dynamics of moisture modes are more rotational, with the anomalous winds almost perfectly balancing the pressure perturbation field. A notable characteristic of the off-equatorial moisture mode is that its convectively active region is not collocated with its low-pressure centre as in TCs, but is shifted to over the poleward flow of the low-level vortex. This provides observational support for these slow-moving systems being energised by the moisture-vortex instability discussed in and . Further evidence of this mechanism is found by focusing on the northern Indian ocean region in Boreal Summer. In this region, the moisture gradient is reversed, and this is associated with a shift of the ascent region of moisture modes to the western side of the disturbance, in line with the predictions of MVI theory. This signifies that the characteristics of moisture modes in particular, and perhaps the other tropical weather systems in general, are influenced by the underlying background state see also e.g.,. It is therefore worth exploring in future research how these characteristics might change under the changing background state due to warming. For example, some studies e.g., indicate that the subtropical Western Pacific has a higher column water vapour trend than the equatorial Western Pacific. It remains an open question how this projected weakening of the meridional moisture gradient over the warm pool might change the frequency of occurrence as well as the characteristics of moisture modes over the region.

The distinction between equatorial and off-equatorial dynamics is also seen in mixed systems, but becomes less discernible in IG waves. For both equatorial and off-equatorial systems, we find that the proximity to nonlinear balance e.g., decreases with phase speeds; faster-moving systems tend to be more unbalanced than slower-moving systems, consistent with the theory of . We therefore conclude that, as in the thermodynamics, there is also a dynamical spectrum from the balanced moisture modes to the unbalanced IG waves.

Connecting back to our main motivation laid out in the Introduction, we argue that our study here is an attempt to define a set of synoptic-scale weather systems in the tropics analogous to those in the extratropics. As in the extratropics, continuous atmospheric waves are the “background” dynamics of the weather. For example, a typical Rossby wave train in the midlatitudes can give rise to several pairs of high- and low-pressure systems. These highs and lows are the extratropical “weather systems”, not the Rossby wave itself. These synoptic-scale systems are the bridge between the planetary-scale background dynamics and the smaller-scale tangible weather occurrences, such as thunderstorms and wind gusts. Applying this idea to the tropics, we posit that equatorial waves, including the MJO, are the dynamics occurring in the “background”, and they can spawn synoptic-scale weather systems investigated in this study. For instance, ER waves are characterised by sets of gyres, and, among these, the cyclonic gyres may be identified as moisture mode “objects”, or may amplify and become TCs e.g.,. Furthermore, as different types of waves commonly co-occur, our methods here implicitly take into account the interactions among different waves in the same phase speed category, which are argued to have similar thermodynamic characteristics, when we do the spectral filtering. In this way, a detected synoptic “object” may be a manifestation of those interactions in the background, rather than representing only a single type of wave.

The characteristics of the weather systems we define, including their dominant dynamical balances, phase relations between vertical and horizontal motion, and thermodynamic structure are broadly consistent with the prototype weather systems described in based on a theoretical scaling of the governing equations. This suggests that the moisture mode-to-gravity wave spectrum provides a useful framework for separating tropical systems by their dynamics.

Another aspect of the three types of weather system that we study here is their impacts on tropical rainfall, especially on rainfall events that are considered extreme. The synoptic weather systems defined here (including TCs) are associated with almost 60 % of total rainfall received in the deep tropics and mainly with events with high rainfall accumulation. Moisture modes are particularly important for precipitation in the off-equatorial regions, where they are associated with 45 %–75 % of extreme 3-hourly rainfall events, almost as much as TCs in TC-prone regions. On the other hand, mixed systems and, to a lesser extent, IG waves are more important for precipitation in the equatorial regions, especially along the Pacific ITCZ. These results provide a new insight on the relationship between atmospheric phenomena and precipitation in the tropics. Past studies usually only attributed most of the tropical mean and extreme precipitation to MCSs and TCs see e.g.,. Here, we aim to define weather systems on synoptic scales similar to the scales of TCs, and we therefore do not consider MCSs directly. Rather, we present the attribution of rainfall to the three systems comprising the moisture mode-to-gravity wave spectrum.

Finally, we note some caveats of the weather system identification we present. By decomposing based on phase speed, we may “split” a robust signal of a coherent object just because it moves with speed close to the phase speed threshold we prescribe in our methods. Furthermore, we decompose objects by zonal phase speed, and objects with substantial meridional phase speed may be misrepresented as having lower phase speed. Additionally, our fundamental assumption that phase speed is a proxy for thermodynamics also has some limitations. As mentioned in Sect. , Eq. () comes from a reasonable assumption that Frτ2>Bu-1 for typical synoptic-scale systems near the equator. This approximation becomes less valid for systems occurring farther from the equator, as illustrated in the following example. A moisture mode system with Lx, Ly∼1000 km occurring at 10° latitude will have a Burger number of about Bu≈150, and therefore Frτ2 will always be greater than Bu-1 for this slow-moving category (cp≲9 m s⁻¹). However, if the same system occurs at 25° latitude, its Burger number will be Bu≈26, and Frτ2 will no longer be greater than Bu-1. We attempt to avoid these systems for which the approximation in Eq. () is invalid by only including systems whose centroids are not beyond 20° latitude in the off-equatorial moisture mode composites, but even then systems with Ly≳1200 km will have Frτ2≲Bu-1 and Nmode≳10-0.5. Therefore, our results on off-equatorial moisture modes should be treated and interpreted more carefully, as they are likely to be “contaminated” by systems technically belonging to the mixed system category.

While the theory hypothesises that systems with similar Nmode have similar thermodynamics, observational studies have shown that eastward- and westward-propagating disturbances with similar phase speed can have different vertical profiles and phase tilts e.g.,. Since our compositing technique combines both eastward- and westward-propagating disturbances, it can hide such phase tilts or other asymmetries associated with the direction of phase propagation. However, separating the eastward- and westward-propagating signals (see Supplement) does not change the general conclusions described above.

Another caveat of this study is that we use OLR to represent convective signals. Even though OLR has long been used, and is still widely used, to study large-scale convectively coupled signals in the tropics, it is not objectively the best variable to use, as some large stratiform-cloud covered areas may also be captured as strong OLR activity. The 3-hourly time resolution of the ISCCP dataset we use is also a limitation, and may not be sufficient to capture the fastest-moving IG wave signals. In addition to these, we also recognise that the removal of diurnal cycle excludes the most important rainfall-related processes over coastal areas and islands. Moreover, this could also underestimate the activity of IG wave, as some previous studies e.g., suggest that this fast-moving system is tightly connected to diurnal convective activity. Nevertheless, we believe that this study provides an important step towards a coherent description of synoptic weather in the tropics from a more object-based weather system perspective. This study is also the first one to apply the theoretical framework of a moisture mode-to-gravity wave spectrum towards this goal. Future research could use this framework to assist extreme weather forecasting, help understand tropical rainfall changes in a warmer climate, and contribute to our understanding of the complex relation between large-scale dynamics and convection in the tropics.