1. Introduction
The Indian monsoon exhibits pronounced variation at subseasonal time scale in the form of active and break phases in rainfall during the boreal summer (e.g., Krishnamurthy and Kinter 2003). The Western Ghats and central India experience high rainfall during the active phase whereas much of India receives low or almost no rainfall during the break phase (Krishnamurthy and Shukla 2000). Convective activity starts in the equatorial Indian Ocean and propagates northward (Sikka and Gadgil 1980) to establish the active phase of rainfall over the Indian subcontinent. The active phase is followed by a similar movement of suppressed convection when the break phase occurs. The active–break cycle is now understood to involve intraseasonal oscillations (ISOs) of convection in the monsoon region (e.g., Krishnamurthy and Shukla 2007, 2008). While several studies (e.g., Yasunari 1979; Lau and Chan 1986) have identified the period of the intraseasonal variability to be in the range of 10–90 days, more detailed space–time analyses (Krishnamurthy and Shukla 2007, 2008) have shown that the leading monsoon intraseasonal oscillation (MISO) is nonlinear with a broadband spectrum centered at 45 days. The convection and rainfall anomalies of the leading MISO spatially extend from the Indian subcontinent to the western Pacific, and propagate in northeastward direction. The Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972) has some similarities with the leading MISO but with predominantly eastward propagation in the equatorial Indian and Pacific Oceans and is stronger during the boreal winter.
The leading MISO is also observed in three-dimensional circulation over the monsoon region (Krishnamurthy and Achuthavarier 2012). A cyclonic circulation in the low-level horizontal wind propagates from the Indian Ocean to the Indian subcontinent while strengthening the mean southwesterly monsoon flow. The peak active phase of the oscillation consists of two connected cyclonic flows over India and the western Pacific. The second half of the oscillation, during which the break phase occurs over India, consists of anticyclonic flows that weaken the mean monsoon flow. The oscillatory feature extends up to the upper level where the horizontal winds are of opposite direction. The vertical velocity is consistent with the horizontal winds at lower and upper levels. Deep regional Hadley circulation moves northward, bringing the ascending (descending) branch over India during the active (break) phase. Additionally, a regional Walker circulation propagates eastward over the equatorial Indian Ocean.
The space–time structures of precipitation, convection, and circulation in the leading MISO are somewhat better understood. In the tropics, the diabatic heating is the main source of energy that drives the atmospheric circulation, which in turn influences the diabatic heating through atmospheric instabilities. The tropical region receives two-thirds of the global rainfall (Tao et al. 2006), and the associated latent heat forms the dominant part of the diabatic heating. The large-scale tropical circulation is found to be significantly influenced by the vertical distribution of the latent heat (e.g., Lau and Peng 1987; Emanuel et al. 1994; Schumacher et al. 2004). The coupling between the vertical structure of convective heating and circulation plays an important role in determining the structure, evolution, and time scale of tropical intraseasonal oscillations (Sui and Lau 1989; Yanai et al. 2000; Wang 2005).
Despite the progress made in monsoon simulation by coupled models, most of the models in phase 5 of the Coupled Model Intercomparison Project (CMIP5) were not able to properly simulate the intraseasonal variability (Sperber et al. 2013). The problems are related to life cycle, northeastward propagation, and the spatial extent of the MISO. The role of diabatic heating is important in generating proper air–sea interaction and sea surface temperature (SST) required for northeastward propagation of convection (Achuthavarier and Krishnamurthy 2011). A study with cloud-resolving models showed that, in addition to coupled models, a realistic representation of convection is necessary for better simulation of MISO (Krishnamurthy et al. 2014). Therefore, a better understanding of the space–time structure of the diabatic heating is required for improved simulation and prediction of the monsoon at intraseasonal time scale.
While some studies have described the three-dimensional structure of the diabatic heating in MJO during the boreal winter (Jiang et al. 2009, 2011; Ling and Zhang 2011), a complete description of the diabatic heating in the boreal summer MISO is lacking. Wong et al. (2011) have estimated apparent heat sources and water vapor sinks using remote sensing retrieval and evaluated them in the context of MISO. They found that the northward propagations of the heat sources and water vapor sinks are consistent with the propagation of precipitation. They also indicate a moisture–convection feedback in MISO. A recent study (Chattopadhyay et al. 2013) discussed the monsoon diabatic heating, but the description is limited to the structure over the Indian subcontinent during the active phase only using prefiltered data.
Recently, the diabatic heating in the tropical intraseasonal variability, both for MISO and MJO, has received significant attention. One of the observations by the recent field campaign for Dynamics of the Madden–Julian Oscillation (DYNAMO) included the vertical profile of heating in the Indian Ocean. The simulation of the three-dimensional structure of the diabatic heating in the tropics is also one of the foci of the recently conducted model intercomparison project under the Global Atmospheric System Studies (GASS). In view of these recent activities, there is a need for a clear description of the three-dimensional diabatic heating at intraseasonal time scales both for model validation and for further understanding of the dynamics of the MISO and MJO. The objective of the present study is to provide the space–time structure of the three-dimensional diabatic heating in MISO over the Indo-Pacific region. The study will focus on providing the horizontal and vertical structure of the diabatic heating associated with MISO and the properties of eastward and northward propagations from the Indian Ocean to the Pacific Ocean. The discussion will cover both the active and break phases during the leading MISO. Since the atmospheric response can arise from remote forcing of the heating, the spatial extent of the diabatic heating in MISO will be determined by considering the entire Indian monsoon region and the tropical Indian and Pacific Oceans. The relation of the diabatic heating MISO with other fields such as moisture, precipitation, and temperature will be investigated in order to provide possible mechanism responsible for the propagation of MISO. The leading MISO in three-dimensional diabatic heating is extracted by a data-adaptive method called the multichannel singular spectrum analysis (MSSA) without prefiltering. This method has been firmly established to extract the ISO without being contaminated by other modes by several earlier studies (Krishnamurthy and Shukla 2007, 2008; Krishnamurthy and Achuthavarier 2012).
The data and the method of analysis are described in section 2. Section 3 discusses the mean monsoon diabatic heating and the leading MISO. The horizontal structure and the vertical structure of the MISO in diabatic heating are described in sections 4 and 5, respectively. Section 6 provides a summary and discussion.
2. Data and method
a. Data
To calculate the diabatic heating using Eq. (1), the required data were obtained from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis (ERA-Interim; Dee et al. 2011). The zonal velocity u, meridional velocity υ, ω, and T on T255 horizontal grid (~0.703° resolution) and at 37 vertical levels between 1000 and 1 hPa were obtained at 6-hourly interval. The variables with overbars are the daily averages in Eq. (1), while primed variables are the deviations of 6-hourly values from daily averages. A dataset of daily mean diabatic heating with the horizontal and vertical resolutions of the ERA-Interim was created for the period 1979–2011 for this study. Daily mean specific humidity from ERA-Interim at all pressure levels has also been used. Daily means of precipitation, on a 0.25° × 0.25° horizontal grid, from version 7 of the Tropical Rainfall Measuring Mission (TRMM) 3B42 product for the period 1998–2011 (Huffman et al. 2007) are also used.
b. Method of analysis
The main method of analysis used in this study is the MSSA, which can extract nonlinear oscillations and persistent modes (Ghil et al. 2002). The MSSA is equivalent to extended empirical orthogonal function analysis but differs in the choice of key parameters and interpretation (Ghil et al. 2002). Previous studies (Krishnamurthy and Shukla 2007, 2008; Krishnamurthy and Achuthavarier 2012) have successfully used MSSA to extract monsoon intraseasonal oscillations in rainfall, outgoing longwave radiation (OLR), and circulation. A given time series of data at L grid points (or channels) and N discrete times is supplemented by M lagged copies, and a lagged covariance matrix 
3. Mean and leading MISO in diabatic heating
a. Mean and standard deviation
Before discussing the intraseasonal oscillation, a brief description of the mean and standard deviation of the diabatic heating is useful. The climatological mean of mass-weighted vertical average of the diabatic heating for June–September (JJAS) is shown in Fig. 1a to examine the horizontal structure. The heating (positive values) occurs mainly to the north of 10°S, extending from the Arabian Sea to the west coast of the Americas. The strongest heating (>1.8 K day−1) is over most of the monsoon region (west coast of India, Bay of Bengal, and central and northeastern India), the warm pool region in the western Pacific, and the intertropical convergence zone (ITCZ) in the Pacific. Since latent heat is a major part of the diabatic heating in the tropics, the JJAS climatological mean of precipitation from TRMM data is shown in Fig. 1b for comparison. The spatial structure of the precipitation has good correspondence with that of the diabatic heating, with intense precipitation zones coinciding with regions of strong heating. In Fig. 1c, the standard deviation of the daily anomalies of the diabatic heating for JJAS is presented. The spatial structure of the standard deviation is somewhat similar to that of the climatological mean (Fig. 1a) with higher values over the Indian monsoon region and the warm pool and ITCZ in the Pacific. The standard deviation of the daily precipitation for JJAS (Fig. 1d) also has a similar structure with larger values in the regions where stronger heating activity occurs.
JJAS climatological mean of (a) vertically averaged diabatic heating (K day−1) and (b) precipitation (mm day−1). Standard deviation of daily anomalies of (c) vertical averaged diabatic heating (K day−1) and (d) precipitation (mm day−1) during JJAS.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The vertical structures of the mean and standard deviation of the diabatic heating are shown in Fig. 2 averaged over different longitudinal and latitudinal belts. The spatial averages were computed after calculating the mean and standard deviation at each grid point. In the equatorial belt of 10°S–10°N, the mean heating (Fig. 2a) and standard deviation (Fig. 2b) show large values in 60°E–180° with two centers of maximum. Strong heating occurs in the 600–350-hPa layer in the Indian Ocean while it is deeper in the western Pacific. A somewhat similar pattern is also seen in both the mean and standard deviation of heating (Figs. 2c,d) in the northern latitude belt of 10°–30°N but with some differences. The two centers of strong heating are closer and extend from 70°E to 160°W. The heating over the Indian subcontinent and its adjoining oceanic region is much stronger and covers a deep layer from 1000 to 300 hPa while it is a bit shallower in the western Pacific. In the longitudinal belt of 65°–95°E, the region north of 10°S shows heating while there is mostly cooling to the south except for the lowest layer (Fig. 2e). The maximum heating occurs in the 600–400-hPa layer between 5° and 20°N and in the 1000–500-hPa layer just to the south of 30°N. The standard deviation in this longitudinal belt (Fig. 2f) also has a similar vertical structure with magnitude proportional to the strength of the mean value. The heating and cooling structure in the longitudinal belt 120°–150°E over the western Pacific (Fig. 2g) is similar to that of the Indian monsoon region (Fig. 2e) but with stronger heating extending from the equator to 20°N in the 600–300-hPa layer and in the lowest layer to the south of the equator. The corresponding standard deviation (Fig. 2h) is higher in the middle layer to the north of the equator.
Vertical cross section of JJAS climatological mean of diabatic heating (K day−1) averaged over (a) 10°S–10°N, (c) 10°–30°N, (e) 65°–95°E, and (g) 120°–150°E. Vertical cross section of standard deviation of daily anomalies of diabatic heating (K day−1) during JJAS averaged over (b) 10°S–10°N, (d) 10°–30°N, (f) 65°–95°E, and (h) 120°–150°E. The y axis is pressure in hectopascals.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
b. Leading MISO
The leading intraseasonal oscillation over the monsoon region was extracted by MSSA of daily anomalies of diabatic heating at 37 vertical levels between 1000 hPa and 1 hPa in the domain 35°S–35°N, 40°E–70°W. There is considerable variation in the magnitude of the diabatic heating in the vertical. The diabatic heating anomalies are therefore normalized at each level separately in order to make sure that the variance explained by the MSSA modes is not dominated by any particular vertical level. At each vertical level, the normalization constant is taken as the root-mean-square of the anomalies at all the grid points for the entire time period. Before the MSSA procedure is applied, the anomaly at each grid point is divided by the normalization constant of the corresponding vertical level. Later, the MSSA eigenvectors are multiplied by the corresponding normalization constants.
The MSSA of the diabatic heating was carried out for JJAS of the period 1979–2011 using lags of 0–60 days at 1-day intervals. Each resulting eigenmode has an ST-EOF that consists of 61 three-dimensional (i.e., at 37 vertical levels) lagged patterns and an ST-PC. The MSSA eigenmodes can be trends, persisting patterns, or oscillations depending on what they represent. An oscillation appears as a pair of eigenmodes with nearly equal eigenvalues while their ST-PCs are in phase quadrature (Ghil et al. 2002). The eigenmodes are arranged in the descending order of the eigenvalues. Since the objective of this study is to describe the leading MISO in the diabatic heating, the first pair of oscillatory eigenmodes will be identified. An examination of the ST-EOFs and ST-PCs showed that first three eigenmodes are seasonally persisting modes with interannual variability and without intraseasonal variation. The first three eigenmodes are related, respectively, to El Niño–Southern Oscillation (ENSO), the trend, and the Indian Ocean dipole (IOD). Since the domain used in this study consists of the entire tropical Pacific and Indian Oceans, it is not surprising that the ENSO and IOD modes have emerged as leading modes. The eigenmodes 4 and 5, however, emerge as the leading oscillatory pair with intraseasonal variability and satisfy all the criteria to be oscillatory (see Ghil et al. 2002). The power spectra of PC4 and PC5 (Fig. 3) overlap, and show broadband structure with a peak at 45 days. This pair is a nonlinear oscillation with variability close to 45 days but not periodic as evidenced by the broadband structure of the spectra. This oscillation is similar to the leading ISO found in precipitation and OLR in earlier studies (Krishnamurthy and Shukla 2007, 2008). The oscillatory pair represented by eigenmodes 4 and 5, therefore, will be identified as the leading MISO in diabatic heating. For brevity, this oscillation will be referred to as only MISO in the rest of the paper.
Power spectra of PC4 (red) and PC5 (blue) of the MSSA eigenmodes.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The existence of MISO in the three-dimensional diabatic heating over the Indo-Pacific region was also confirmed by performing MSSA in different domains. One of the domains considered is 25°S–35°N, 40°–160°E, which is exactly the same as that used by Krishnamurthy and Achuthavarier (2012) and very close to the domain used by Krishnamurthy and Shukla (2008). In this case, the first eigenmode is trend while eigenmodes 2 and 3 emerge as MISO, similar to the results by Krishnamurthy and Achuthavarier (2012) and to that of Krishnamurthy and Shukla (2008) except for the trend. The seasonally persisting modes are represented by lower-order eigenmodes. A further analysis was performed by applying MSSA on vertically averaged diabatic heating over both the smaller and larger domains. In each case, a pair of oscillatory eigenmodes emerged as MISO, but in different order for the two domains. The MISO of the vertically averaged diabatic heating is the same as the vertical average of the MISO found in the three-dimensional diabatic heating.
Further analysis of MISO will be carried out by constructing the RCs of eigenmodes 4 and 5 by combining the corresponding ST-EOFs and ST-PCs [see Ghil et al. (2002) for the procedure]. Since the RCs are additive, the RCs of eigenmodes 4 and 5 are added to obtain the complete RC of MISO. The RC has the same spatial dimensions (including the 37 vertical levels) and temporal length as the raw anomalies of the diabatic heating. This RC is the MISO component filtered out of the raw anomalies.
4. Horizontal structure of MISO
The analysis of MISO is performed by examining the composites of various fields based on the phases of a complete cycle of the oscillation. The amplitude A(t) and the phase angle θ(t) of the nonlinear oscillation, as time t varies, were determined by following the procedure used by Moron et al. (1998). The phase angle θ, which was determined for each day of the period of analysis, varies from 0 to 2π in a cycle, although not in a strictly periodic manner. For the most part of the analysis, a complete cycle of the oscillation is divided into eight phase intervals, denoted by k = 1, 2, …, 8, such that (k − 1)π/4 ≤ θ ≤ kπ/4. The phase composites of any field are constructed by averaging the particular field over all values of θ in each phase interval for the entire period of the analysis. In this section, the horizontal structure of the MISO of the diabatic heating and its relation to other fields are discussed using the phase composites.
a. MISO diabatic heating
The general horizontal structure of MISO is studied by computing the vertical average of daily RC of MISO diabatic heating. The mass-weighted vertical averaging is done over the column extending from surface pressure to 1 hPa. The phase composites of the vertically averaged RC of MISO diabatic heating for eight equal phase intervals, each of length π/4 in a cycle of 0–2π, are shown in Fig. 4. The average period of the phase composite cycle is 45 days. Phase 1 shows a tilted (northwest–southeast) band of cooling anomalies extending from the Arabian Sea to the equatorial western Pacific and covering the Indian subcontinent while weak heating anomalies appear over the equatorial Indian Ocean. The negative anomalies move northward in phases 2–4 with high amplitude in phase 2. The cooling decreases considerably in phase 4 and disappears over most of India. The heating anomalies start to intensify over the equatorial Indian Ocean in phase 2, and expand and propagate eastward over the Maritime Continent in phase 3. The northward propagation of the heating anomalies is clearly evident in phase 4 when they reach the Indian subcontinent. In phase 5, the heating anomalies are organized in a tilted pattern with higher amplitude over central India, the west coast of India, the Bay of Bengal, and the western Pacific. The rain shadow region in southern India has very low amplitude. Subsequently, in phases 6–8, the heating anomalies move farther northward and diminish over the western Pacific. The patterns in phases 5–8 are almost exactly the same as those in phases 1–4, respectively, but with opposite sign. The heating and cooling anomalies with significant amplitude in the MISO cycle are confined to the region 15°S–30°N, 60°E–180°. The MISO cycle of diabatic heating is similar to the leading ISO in OLR (Krishnamurthy and Shukla 2008).
Phase composites of vertically averaged daily RC of diabatic heating (K day−1) of MISO for eight phase intervals of the oscillation. The phase interval k is marked at the top-right corner of each panel. The phase intervals are (k − 1)π/4 ≤ θ < kπ/4 with k = 1, 2, …, 8. The stippled region indicates composites above 5% significance level.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The propagation of the diabatic heating is demonstrated through Hovmöller diagrams of the RC of MISO. Using the phase angle as time, the phase composites of the RC are constructed in intervals of π/12 for better resolution. To examine the eastward propagation, the phase composites of RC averaged over 10°S–10°N and 10°–30°N are plotted as longitude–phase cross sections in Figs. 5a and 5b, respectively. In the equatorial belt (Fig. 5a), the diabatic heating shows an almost standing pattern in 70°–100°E and eastward propagation in 100°–160°E. The standing pattern in the Indian Ocean represents the expansion of the diabatic heating with very slight eastward movement in that region. The northern region (Fig. 5b) shows generally standing pattern and no clear eastward propagation anywhere. The northward propagation of the diabatic heating is shown in the latitude–phase cross sections of the MISO RC averaged over 65°–95°E and 120°–150°E, respectively, in Figs. 5c and 5d. In both the Indian monsoon region (Fig. 5c) and the western Pacific (Fig. 5d), the diabatic heating propagates northward in the region 5°S–25°N. There is a phase difference between the two regions, consistent with the eastward propagation and the tilted structure of the heating pattern seen in Fig. 4.
Longitude–phase cross section of the vertically averaged RC of diabatic heating (K day−1) averaged over (a) 10°S–10°N and (b) 10°–30°N and latitude–phase cross section of the vertically averaged RC of diabatic heating averaged over (c) 65°–95°E and (d) 120°–150°E for a complete cycle of MISO.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The horizontal structures of the MISO diabatic heating at three individual vertical levels (850, 650, and 400 hPa) are shown in Fig. 6. The vertically averaged diabatic heating in Fig. 4 showed that the heating anomalies develop and reach peak values during phases 2–5 while phases 1 and 6–8 show the same half-cycle with anomalies of opposite sign. It is sufficient to show the half-cycle of phases 2–5 in MISO, as in Fig. 6. The heating and cooling anomalies at all the three vertical levels (Fig. 6) show northeastward propagation with different intensities. The spatial structure of the anomalies is similar in all the levels. Although the structure of MISO is discernable at 850 hPa (Fig. 6a), the heating anomalies are weak. At 650 hPa, the amplitude of the anomalies (Fig. 6b) is comparable to that of the vertical averaged anomalies (Fig. 4). The heating and cooling anomalies are much stronger at 400 hPa (Fig. 6c) and cover wider longitudinal and latitudinal extents. The amplitude at 400 hPa is 1.5 times that of the vertically averaged anomalies.
Phase composites of daily RC of diabatic heating (K day−1) at (a) 850, (b) 650, and (c) 400 hPa for a half cycle (phases 2–5) of MISO. The phase interval is marked at the top-right corner of each panel. The stippled region indicates composites above 5% significance level.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
b. Relation with other fields
The relation of the MISO diabatic heating with precipitation, specific humidity, and circulation is examined here. The phase composites of the daily raw anomalies of these fields based on the phases of the diabatic heating MISO were constructed. The phase composites of TRMM precipitation for phases 2–5 (half-cycle of MISO) are shown in Fig. 7a. The spatial structures of the precipitation composites have good resemblance to those of the diabatic heating RC in Figs. 4 and 6. The strong negative anomalies of precipitation in phases 2 and 3 (Fig. 7a) correspond to the break phase in the monsoon over the Indian subcontinent. These anomalies extend from the Arabian Sea to the western Pacific, and are in correspondence with the cooling anomalies in the diabatic heating (Fig. 4). The positive anomalies of precipitation develop in the equatorial Indian Ocean in phase 2 and expand and intensify during phases 3 and 4 while propagating northward. A tilted band of intense precipitation is formed in phase 5, establishing the active phase of the monsoon over India. This sequence is similar to the northward propagation of the positive anomalies in the diabatic heating (Figs. 4 and 6). The moisture content associated with MISO is shown by the phase composites of vertically averaged specific humidity in Fig. 7b. The positive and negative anomalies of specific humidity also have spatial structure and propagation properties similar to those of precipitation (Fig. 7a) and diabatic heating (Figs. 4 and 6). Generally, the precipitation and specific humidity seem to be in phase with the diabatic heating. A similar northward propagating signal in the water vapor sink has been reported by Wong et al. (2011).
Phase composites of daily anomalies of (a) precipitation (mm day−1) and (b) vertically averaged specific humidity (g kg−1) for a half cycle (phases 2–5) of MISO. The phase interval is marked at the top-right corner of each panel. The stippled region indicates composites above 5% significance level.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The relation with the circulation is determined through the phase composites of daily anomalies of horizontal wind (u, υ) at 850 hPa (Fig. 8a) and pressure vertical velocity (ω) at 500 hPa (Fig. 8b). These composites are also constructed on the basis of the phases of the diabatic heating MISO, and shown for phase intervals 2–5 in Fig. 8. For convenience, −ω is plotted in Fig. 8b so that positive (negative) anomalies represent ascending (descending) motion. Phase 2 consists of a cyclonic circulation centered in the equatorial Indian Ocean and an anticyclonic flow in the western Pacific at 850 hPa (Fig. 8a). Strong easterlies from the western Pacific stretch over the Indian subcontinent and oppose the mean monsoon circulation. There is strong descending motion at 500 hPa (Fig. 8b) corresponding to the low-level easterlies and ascending motion in the equatorial Indian Ocean. The circulation is consistent with the precipitation pattern (Fig. 7a) and diabatic heating (Figs. 4 and 6) in phase 2. The entire system moves northward in phases 3–5. The easterlies at 850 hPa move over to northern India while strong southwesterlies appear over the Arabian Sea and the Indian subcontinent and strengthen the mean monsoon in phase 5 (Fig. 8a). At the same time, a tilted band of strong ascending motion at 500 hPa is established from the Arabian Sea to the western Pacific (Fig. 8b). The patterns of low-level horizontal wind and the midlevel vertical velocity are dynamically consistent with the precipitation patterns and diabatic heating in the MISO cycle.
Phase composites of daily anomalies of (a) horizontal wind (m s−1) at 850 hPa as streamlines and (b) pressure vertical velocity −ω (10−2 Pa s−1) at 500 hPa for a half cycle (phases 2–5) of MISO. The phase interval is marked at the top-right corner of each panel.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
5. Vertical structure of MISO
In this section, the vertical structures of the diabatic heating in MISO and related fields such as specific humidity and temperature are discussed. For this purpose, the vertical cross sections of the phase composites of the relevant fields based on the phases of the diabatic heating MISO are examined. The vertical cross sections are shown for different longitudinal and latitudinal belts.
a. MISO diabatic heating
The phase composites of the daily RC of diabatic heating in MISO are averaged over 10°S–10°N and 10°–30°N and plotted in Figs. 9a and 9b, respectively. These phase composites are the same as those in Figs. 4 and 6, but now illustrated as longitude–pressure cross sections. Figure 9 also includes the phase composites of TRMM precipitation averaged over the respective latitudinal belts.
Vertical cross section of the phase composite of daily RC of diabatic heating (K day−1) averaged over (a) 10°S–10°N and (b) 10°–30°N for a complete cycle of MISO. The phase composite of precipitation (mm day−1) averaged over the same latitudes is also plotted (green curve). Pressure (hPa) is marked on the left-hand side of the y axis, while the scale for precipitation is on the right-hand side. The phase interval is marked at the top-right corner of each panel. The stippled region indicates composites above 5% significance level.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
In the equatorial belt (Fig. 9a), the heating (positive) anomalies develop over the central Indian Ocean in phase 2 and expand eastward during phases 3 and 4. Maximum heating occurs at about 450 hPa and shows a very slight eastward movement. In phase 4, the heating anomalies cover a wider longitudinal extent with deeper heating in the western Pacific. The heating over the Indian Ocean diminishes almost completely in phase 5 while the rest of the heating anomalies over the Pacific propagate eastward and diminish near the date line in phase 7. A similar sequence of negative (cooling) anomalies takes place during phases 1–3 and 6–8. The positive (negative) anomalies of precipitation are in concert with the evolution of the heating (cooling) anomalies (Fig. 9a). The maximum (minimum) in the precipitation has good correspondence with the maximum (minimum) in the diabatic heating both in intensity and spatial extent.
There is a difference of about two phase intervals between the northern belt (Fig. 9b) and the equatorial belt (Fig. 9a) in the phase composites, which accounts for the northward propagation of the diabatic heating in MISO. Weak positive anomalies appear over India in phase 4 in the northern belt (Fig. 9b). The heating intensifies and expands eastward up to the western Pacific during phases 5 and 6. In phase 7, the heating attains maximum value in the western Pacific but becomes less intense over India and the Bay of Bengal. The heating anomalies diminish over the western Pacific in phase 8 before disappearing completely in phase 1. The same sequence is repeated with negative (cooling) anomalies from phase 8 to 4. In the northern belt, the heating expands eastward and does not reveal any eastward propagation, consistent with the Hovmöller diagram shown in Fig. 5b. The anomalies are deeper and extend from near surface to about 300 hPa with maximum value around 450 hPa. The precipitation composite in each phase matches with the variation of the diabatic heating in sign, intensity, and spatial extent. The eastward propagation extends up to the date line in the equatorial belt whereas it extends to 150°E in the northern belt.
The latitude–pressure cross sections of the phase composites of the RC of MISO diabatic heating are described next. The averages of RC over 65°–95°E and 120°–150°E are presented in Figs. 10a and 10b, respectively. Here also, the phase composites of TRMM precipitation averaged over the respective longitudinal belts are plotted.
As in Fig. 9, but for averages over (a) 65°–95°E and (b) 120°–150°E.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
In the Indian monsoon belt (65°–95°E), the heating (positive) anomalies appear in the equatorial Indian Ocean in phase 1 and becomes intense in phase 2 (Fig. 10a). There is expansion and northward propagation of the heating anomalies during phases 3 and 4. The northward movement continues in phases 5–7 where the heating is more compact meridionally. The heating anomalies extend from 800 to 300 hPa with maximum around 450 hPa. The clear northward propagation from the equator to 25°N during phases 2–7 confirms the finding in the Hovmöller diagram in Fig. 5c. The same sequence with cooling (negative) anomalies occurs during phases 1–3 and 5–8. In all the phases, the positive (negative) anomalies of precipitation are in good agreement with the heating (cooling) anomalies in intensity and location.
As seen earlier in Fig. 9a, the heating anomalies propagate eastward from the Indian Ocean and reach the western Pacific along the equatorial belt. Because of this, the heating anomalies first appear in phase 3 in the western Pacific belt (120°–150°E) (Fig. 10b), showing a phase difference with the Indian monsoon belt (Fig. 10a). The heating anomalies become stronger and steadily propagate northward from the equator to 20°N from phase 4 to 7 and diminish in phase 8 (Fig. 10b). The northward propagation is consistent with the Hovmöller diagram in Fig. 5d. The heating anomalies are deeper in the western Pacific also with a maximum around 450 hPa. The anomalies in the western Pacific are more intense than those in the Indian monsoon region. Again, the cooling (negative) anomalies go through a similar sequence from phase 7 through 4. Here also, the precipitation composite shows very good correspondence with the diabatic heating.
b. Relation with specific humidity and temperature
The relation between the diabatic heating and the specific humidity in MISO is examined through the phase composites of the raw anomalies of the specific humidity at 37 vertical levels. The specific humidity composites averaged over 10°S–10°N are presented as longitude–pressure cross sections in Fig. 11a for a half cycle of MISO. Here, only the half cycle of phases 2–5 is shown because the heating anomalies develop in the 10°S–10°N belt during these phases, as seen in Fig. 9a. The other half cycle consists of the same patterns with anomalies of opposite sign. The phase composites of precipitation averaged over the same latitudes are also included in Fig. 11a. The positive anomalies of specific humidity appear in the Indian Ocean in phase 2, expand, and propagate eastward from phase 3 to 5 (Fig. 11a). The spatial extent and the propagation of the wet anomalies have good correspondence with those of the heating anomalies (Fig. 9a). Similar agreement is also seen with the precipitation anomalies. The maximum values in the specific humidity occur near 600 hPa in the Indian Ocean and near 800 hPa in the western Pacific (Fig. 11a). In phases 3 and 4, the deep heating and maximum precipitation in the Indian Ocean (Fig. 9a) are consistent with deep enhanced moisture in the same region (Fig. 11a). Ahead of this, the shallow or weak heating in the western Pacific (Fig. 9a) coincides with shallow wet anomalies confined to the lower layer (Fig. 11a), indicating a possible preconditioning process. The phase relation between the heating and moisture will be discussed later.
Vertical cross section of the phase composite of daily anomalies of specific humidity (g kg−1) averaged over (a) 10°S–10°N and (b) 10°–30°N for a half cycle of MISO. (c),(d) The corresponding cross sections of temperature (K) are also shown. The phase composite of precipitation (mm day−1) averaged over the same latitudes is also plotted (green curve). Pressure (hPa) is marked on the left-hand side of the y axis, while the scale for precipitation is on the right-hand side. The phase interval is marked at the top-right corner of each panel.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The composites of specific humidity averaged over 10°–30°N, which includes the Indian subcontinent, are presented as longitude–pressure cross sections in Fig. 11b. In this half cycle of MISO, phases 4–7 are included since they correspond to the development of the heating anomalies in the northern belt (Fig. 9b). Positive (moist) anomalies appear in the lowest layer in phase 4 and intensify and cover the troposphere up to 400 hPa in phase 5 (Fig. 11b). While the intensity of the moist anomalies reduces over the Indian subcontinent in phases 6 and 7, weaker moist anomalies expand eastward up to the date line below 500 hPa. The moist anomalies do not reveal eastward propagation. The moisture patterns are consistent with the heating and precipitation patterns (Fig. 9b).
The corresponding vertical cross sections of the temperature anomalies are shown in Figs. 11c and 11d for averages over 10°S–10°N and 10°–30°N, respectively. The patterns of temperature anomalies are not as clear as the specific humidity patterns. In the equatorial belt, the temperature is cooler in the Indian Ocean (Fig. 11c) where there is deeper heating (Fig. 9a) and deeper moisture content (Fig. 11a). We speculate that this could be due to latent cooling. The western Pacific region has a cooler temperature in phases 2 and 3, and becomes warmer in phases 4 and 5. This indicates eastward propagation of warm anomalies that deepen by phase 5. In the northern belt (Fig. 11d), the temperature is cooler in phases 4 and 5 and warmer in phases 6 and 7 throughout the region. As in the case of diabatic heating, there is no clear eastward propagation. In both the equatorial and northern belts, there is generally a difference in the temperature between the lower and upper layers.
The northward propagation of the moisture is clearly demonstrated in the latitude–pressure cross section of the phase composites of the specific humidity anomalies averaged over 65°–95°E (Fig. 12a) and 120°–150°E (Fig. 12b). In both the regions, the moisture anomalies are deeper and extend from 900 to 400 hPa. In both the Indian monsoon region and the western Pacific, the positive peaks in precipitation coincide with maxima in specific humidity. The moist anomalies propagate from the equator to 25°N during phases 2–5 in the Indian monsoon region and during phases 4–7 in the western Pacific. The phase difference between the two regions is due to the eastward propagation along the equator. Another notable feature in Figs. 12a and 12b is the larger meridional extent of moisture anomalies compared to that of the heating anomalies (Figs. 10a,b). The moisture anomalies extend farther to the north in each phase compared to heating anomalies, indicating a possible preconditioning process, similar to the observation in the boreal winter MJO (Benedict and Randall 2007). The possibility of moisture preconditioning in the northward propagation of MISO is also discussed by Wong et al. (2011).
As in Fig. 11, but for averages over (a),(c) 65°–95°E and (b),(d) 120°–150°E.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The vertical cross sections of the phase composites of temperature anomalies averaged over 65°–95°E and 120°–150°E are shown in Figs. 12c and 12d, respectively. Here, there is some structure in the evolution of the temperature composites although not as clearly as for the specific humidity. In the Indian monsoon region (Fig. 12c), the negative anomalies in phase 2 move northward in phases 3–5, followed by positive anomalies to the south. Vertically, the upper layers have higher value compared to the lower layers. In the western Pacific region (Fig. 12d), the positive anomalies move northward from the equator during phases 4–7. The upper layers are warmer than the lower layers. The precipitation anomalies do not show any particular correspondence with the temperature profiles. Different physical processes may be contributing for the appearance of cold anomalies in the Indian Ocean region and warm anomalies in the western Pacific. A more detailed analysis of the radiation and heat budgets and the advection of thermodynamic variables may be needed to better understand the temperature profiles.
To obtain a better picture of the phase relations among the various variables, four horizontal boxes—10°S–10°N, 65°–95°E; 10°–30°N, 65°–95°E; 10°S–10°N, 120°–150°E; and 10°–30°N, 120°–150°E, denoted as regions A, B, C and D, respectively—are considered. The phase composites of diabatic heating, specific humidity, temperature at 37 levels, and TRMM precipitation are area-averaged over the four regions. For better resolution, the phase composites were constructed in 24 phase intervals, each of length π/12, in MISO. The phase–pressure plots of MISO RC of diabatic heating and specific humidity anomalies averaged over the four regions are presented in Fig. 13. The averages of precipitation are also included in Fig. 13. In all the regions, positive (negative) moisture anomalies lead the positive (negative) heating anomalies by a phase angle of about π/6–π/4 or about 4–6 days. The precipitation varies in tune with the diabatic in regions A and B (Indian monsoon region) but leads in C and D (western Pacific). The maximum and minimum values in moisture anomalies are found in the lower layers while those in the heating anomalies are around 500 hPa. Both the heating and moisture anomalies show a slanting structure in the vertical in region C, possible because of the oceanic region and the land regions of the Maritime Continent. A similar set of area-averaged plots of the temperature is shown in Fig. 14. The diabatic heating and precipitation averages in Fig. 14 are the same as those in Fig. 13. The vertical profile of temperature consists of anomalies of the same sign over almost the entire vertical column but with stronger anomalies in the upper layers except in region C, which shows slanting structure. Figure 14 clearly shows the oscillatory feature of the vertical columns of the temperature at the MISO period. The phase relation between the temperature and heating anomalies varies considerably from one region to another.
Phase–pressure cross sections of the phase composite of daily anomalies of specific humidity (g kg−1) area-averaged over (a) 10°S–10°N, 65°–95°E; (b) 10°–30°N, 65°–95°E; (c) 10°S–10°N, 120°–150°E; and (d) 10°–30°N, 120°–150°E, for a complete cycle of MISO (shaded). The corresponding cross sections of the RC of the diabatic heating (K day−1) are plotted as contour lines (black). The phase composite of precipitation (mm day−1) averaged over the same areas is also plotted (green curve). Pressure (hPa) is marked on the left-hand side of the y axis, while the scale for precipitation is on the right-hand side. The x axis is labeled with the phase angle for one cycle.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
As in Fig. 13, but for temperature (K, shaded). The plots of diabatic heating and precipitation are the same as in Fig. 13.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
The phase relations among the four variables are shown in a more convenient manner in Fig. 15 by using the vertically averaged values of diabatic heating RC, specific humidity, and temperature anomalies. These are further area averaged (horizontally) over the regions A–D, similar to the plots in Figs. 13 and 14. The area averages of precipitation are also included in Fig. 15. In regions A and B, the diabatic heating and precipitation vary in phase, while the specific humidity leads them. However, the temperature is of opposite phase in region A but leads all other fields in B. The precipitation, specific humidity, and temperature vary in phase in C and D but lead the diabatic heating. Generally, the moisture anomalies lead the diabatic heating anomalies, and may be playing a role in the propagation of MISO.
Phase composite of daily RC of the diabatic heating (K day−1, red) area-averaged over (a) 10°S–10°N, 65°–95°E; (b) 10°–30°N, 65°–95°E; (c) 10°S–10°N, 120°–150°E; and (d) 10°–30°N, 120°–150°E, for a complete cycle of MISO. The corresponding area averages of the daily anomalies of specific humidity (g kg−1, purple), temperature (K, blue), and precipitation (mm day−1, green) are also plotted. Diabatic heating, specific humidity, and temperature are also vertically averaged. The x axis is labeled with the phase angle for one cycle. The scale for diabatic heating, specific humidity, and temperature is on the left-hand side of the y axis, while the scale for precipitation is on the right-hand side.
Citation: Journal of Climate 28, 6; 10.1175/JCLI-D-14-00280.1
6. Summary and discussion
This study has described the space–time structure of the leading intraseasonal oscillation in diabatic heating over the Indian monsoon region during the boreal summer. The three-dimensional diabatic heating data used in this study were constructed by the residual method of the thermodynamic equation using ERA-Interim data at a daily time scale. The leading MISO was extracted by applying MSSA on daily anomalies of diabatic heating at 37 vertical levels over the Indo-Pacific region for the period 1979–2011. The diabatic heating MISO is nonlinear with a broad spectral peak centered at 45 days. This study is complementary to the description of the diabatic heating in the boreal winter MJO by some recent studies (e.g., Jiang et al. 2011) and brings out distinguishing features, such as the northward propagation, during the boreal summer. The intraseasonal oscillations in precipitation and circulation over the monsoon region are known (e.g., Krishnamurthy and Shukla 2007; Krishnamurthy and Achuthavarier 2012). While only very few studies have attempted to describe the diabatic heating in MISO (Wong et al. 2011; Chattopadhyay et al. 2013), there is a need for better understanding of the main driver of the monsoon circulation (i.e., the diabatic heating) at intraseasonal time scales over the Indo-Pacific region. This study fulfils such a need by describing the horizontal and vertical structures of the diabatic heating MISO.
The mean and standard deviation of the diabatic heating during the boreal summer show large values over India and the adjoining oceanic regions. The horizontal structure of the mean heating has good resemblance to that of the precipitation, indicating the important role of latent heat. The vertical structure of the mean heating indicates maximum values at about 450 hPa and deep heating in several parts of the region. The leading intraseasonal oscillation in the diabatic heating exhibits many features observed in the MISOs of precipitation, OLR, and circulation. The period (45 days) of the diabatic heating is the same as that in precipitation and OLR. In MISO, the heating or cooling anomalies develop in the equatorial Indian Ocean and propagate northeastward, forming a long tilted band that extends from the Indian subcontinent to the western Pacific. The horizontal structure and the propagation of the heating (cooling) anomalies have close resemblance to those of positive (negative) anomalies of precipitation, and account for the active (break) phase of the monsoon over India. Similarly, the heating (cooling) anomalies strengthen (weaken) the low-level mean monsoon circulation and correspond to the ascending (descending) motion.
The vertical structure of the diabatic heating MISO indicates columns of heating or cooling anomalies extending from 800 to 300 hPa with maximum values around 450 hPa. Along the equatorial region, the heating anomalies expand and propagate eastward from the Indian Ocean to the western Pacific. However, no eastward propagation is observed over the Indian subcontinent and to its east. Northward propagation of heating and cooling anomalies is clearly evident both in the Indian monsoon region and the western Pacific, and takes place from 10°S to 30°N. The vertical structure also shows close correspondence between the heating (cooling) anomalies and positive (negative) anomalies in precipitation.
The vertical structure of the specific humidity corresponding to MISO exhibits the same propagation properties as the diabatic heating. The vertical structure of the moisture anomalies is similar to that of the diabatic heating but the maxima occur at lower layers. The wet (dry) anomalies have correspondence with the heating (cooling) anomalies but with a phase difference. The moisture anomalies lead the heating anomalies by about 4–6 days. This feature may indicate a preconditioning process that plays a role in the northward propagation of the diabatic heating and convection, similar to the mechanism suggested for the eastward propagation of MJO (Benedict and Randall 2007) and for northward propagation (Wong et al. 2011). The vertical structure of the temperature also shows the oscillatory features associated with MISO as well as the northward propagation. However, the phase difference between the diabatic heating and temperature varies considerably from region to region.
While this study has provided a description of the MISO in diabatic heating, the relation with other fields needs to be better understood with further studies. The relation with the temperature needs more detailed analysis of the radiation and heating budget and the advection of various variables. Such an analysis may provide a better understanding of the mechanism involved in the northward and eastward propagation. Model experiments with prescribed oscillatory diabatic heating profiles will also be useful in providing insights into the response to the diabatic heating at intraseasonal time scale.
Acknowledgments
This work was supported by National Science Foundation (Grants ATM-0830062 and ATM-0830068), National Oceanic and Atmospheric Administration (Grant A09OAR4310058), and National Aeronautics and Space Administration (Grant NNX09AN50G). This work formed a part of the Ph.D. thesis of Abheera Hazra at George Mason University.
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