Diagnosing Ocean Feedbacks to the BSISO: SST‐Modulated Surface Fluxes and the Moist Static Energy Budget

The oceanic feedback to the atmospheric boreal summer intraseasonal oscillation (BSISO) is examined by diagnosing the sea surface temperature (SST) modification of surface fluxes and moist static energy on intraseasonal scales. SST variability affects intraseasonal surface latent heat (LH) and sensible heat (SH) fluxes, through its influence on air‐sea moisture and temperature gradients (∆q and ∆T, respectively). According to bulk formula decomposition, LH is mainly determined by wind‐driven flux perturbations, while SH is more sensitive to thermodynamic flux perturbations. SST fluctuations tend to increase the thermodynamic flux perturbations over active BSISO regions, but this is largely offset by the wind‐driven flux perturbations. Enhanced surface fluxes induced by intraseasonal SST anomalies are located ahead (north) of the convective center over both the Indian Ocean and the western Pacific, favoring BSISO northward propagation. Analysis of budgets of column‐integrated moist static energy (⟨m⟩) and its time rate of change (∂⟨m⟩/∂t) shows that SST‐modulated surface fluxes can influence the development and propagation of the BSISO, respectively. LH and SH variability induced by intraseasonal SSTs maintain 1–2% of ⟨m⟩ day−1 over the equatorial western Indian Ocean, Arabian Sea, and Bay of Bengal but damp about 1% of ⟨m⟩ day−1 over the western North Pacific. The contribution of intraseasonal SST variability to ∂⟨m⟩/∂t can reach 12–20% over active BSISO regions. These results suggest that SST variability is conducive, but perhaps not essential, for the propagation of convection during the BSISO life cycle.


Introduction
The intraseasonal oscillation (ISO) is one of the dominant modes of variability in the tropics. It has significant seasonality in frequency (Hartmann et al., 1992), intensity (Madden, 1986), and propagation (Wang & Rui, 1990). The ISO during boreal winter, also known as the Madden-Julian Oscillation (MJO), is characterized by planetary-scale convective anomalies, with continuous eastward propagation from the western Indian Ocean to the central and eastern Pacific (Madden & Julian, 1971, 1972. The ISO during boreal summer (BSISO) has a more complex structure than the MJO, due to its intense interaction with the Asian summer monsoon (Krishnamurti & Subrahmanyam, 1982;Yasunari, 1979). It exhibits multiple propagation pathways: east and north in the Indian monsoon region (Gadgil & Srinivasan, 1990;Hartmann & Michelsen, 1989;Murakami & Nakazawa, 1985) and northwest over the western North Pacific (Chen & Murakami, 1988;Lau & Chan, 1986;Murakami, 1980). Northward propagation is the most prominent feature of the BSISO. As the BSISO propagates north from the equator into monsoon areas, its activity substantially affects monsoon rainfall (Webster et al., 1998;Wu & Wang, 2001;Zhou & Chan, 2005), tropical cyclones (Hartmann & Maloney, 2001;Straub & Kiladis, 2003), and the occurrence of extreme events (Hsu et al., 2017;Li et al., 2015;Ren et al., 2013;Sun et al., 2016).
Internal atmospheric dynamics are essential to the initiation, development, and propagation of the BSISO (Bellon & Sobel, 2008;Hsu & Weng, 2001;Kawamura et al., 1996;Lawrence & Webster, 2002;Wang & Rui, 1990;Wang & Xie, 1997). Using an intermediate-complexity model, Wang and Xie (1997) suggested the BSISO may originate from Rossby waves, in which the background sea surface temperature (SST) and moisture distribution led to the emanation of Rossby waves from the equatorial Kelvin-Rossby wave packet. Meridionally asymmetric structures of vorticity and moisture with respect to BSISO convection are found in observations and model simulations, which may play an essential role in its northward propagation (Ajayamohan et al., 2011;Bellon & Sobel, 2008;Jiang et al., 2004;Kawamura et al., 1996). The model results in Wang and Xie (1996) and Xie and Wang (1996) indicate that the interaction between the strong vertical shear of the summer mean flow and equatorial Rossby waves coupled free-atmospheric baroclinic and barotropic modes, which generated barotropic vorticity north of convection (Lawrence & Webster, 2002). Besides the vertical wind shear mechanism, Jiang et al. (2004) also examined the moisture-convection feedback mechanism using reanalysis and an atmospheric general circulation model (AGCM). They showed that both the anomalous moisture advection induced by the mean meridional wind and the mean moisture advection induced by the anomalous meridional wind could contribute to BSISO northward propagation. Due to mean state differences, the mechanisms for BSISO propagation in the Indian Ocean may differ from those in the western Pacific (Chou & Hsueh, 2010;DeMott et al., 2013). High-frequency variability can also feed back upscale to the development and propagation of the large-scale ISO circulation through atmospheric eddy momentum, heat, and moisture transports (Biello & Majda, 2005;Gao et al., 2018;Maloney, 2009;Wang & Liu, 2011;Zhou & Li, 2010).
Air-sea interaction may also contribute to BSISO northward propagation (Kemball-Cook & Wang, 2001;Krishnamurti et al., 1988;Roxy & Tanimoto, 2012;Waliser & Graham, 1993). Warm (cold) SST anomalies are observed ahead of (behind) the BSISO convective center, associated with increased (decreased) shortwave radiative heating (SW) and reduced (enhanced) evaporation related to the anomalous BSISO convection (Hendon & Glick, 1997;Webster, 1983;Woolnough et al., 2000). While the possibility for the feedback of oceanic anomalies to BSISO convection has been discussed often, only a small handful of studies have hypothesized physical mechanisms for this feedback. SST anomalies and their gradients may induce anomalous boundary layer convergence (Lindzen & Nigam, 1987) and destabilize the atmosphere ahead of convection on intraseasonal scales (Hsu & Li, 2012). The anomalous SST can also affect the atmospheric ISO convection by modifying surface fluxes (DeMott et al., 2016;Wang et al., 2018). DeMott et al. (2016) analyzed the effect of intraseasonal SST variability on the MJO by computing surface flux component terms using daily mean and 61-day running mean SST. In the framework of the moist static energy (MSE) budget, the difference between "full SST" and "smoothed SST" flux projections onto column-integrated MSE (hmi) and its time rate of change (∂hmi/∂t) reveals the SST effect on the MJO hmi budget. Intraseasonal SST variability maintains 1-2% of daily equatorial hmi anomalies but damps 1-2% of daily subtropical hmi anomalies. The SST effect can offset roughly 10% of the equatorial hmi loss induced by the vertical advection of hmi (10-20% of hmi day À1 ). SST fluctuations also promote MJO eastward propagation, with a contribution of up to 10% of ∂hmi/∂t across the Warm Pool. Recently, Wang et al. (2018) showed that warm SST anomalies to the north of convection tend to increase surface turbulent fluxes by amplifying the air-sea temperature and moisture gradients over the western North Pacific, which promotes BSISO northward propagation by preconditioning the boundary layer for convection.
The role of air-sea coupling in the northward propagation of BSISO has been revealed by modeling studies (Fu et al., 2003;Fu & Wang, 2004;Klingaman et al., 2008;Lin et al., 2011;Rajendran & Kitoh, 2006;Seo et al., 2007). Kemball-Cook et al. (2002) found that the simulated BSISO was more realistic in a coupled general circulation model than in its counterpart AGCM. Fu et al. (2007) showed that the prediction skill of BSISO-related rainfall over the Asian-western Pacific region was about 17 days in the ECHAM4 AGCM, while it extended to about 24 days when the AGCM was coupled to an intermediate-complexity ocean model. Compared to daily coupling frequency, coupled general circulation models with subdaily coupling frequency show improved fidelity for the BSISO (Hu et al., 2015;Klingaman et al., 2008;Woolnough et al., 2007). In contrast, Neena et al. (2017) showed that the skill for BSISO eastward and northward propagation in an AGCM can be as good as, or even better than, that simulated by the coupled version of the same model. This disagreement among modeling studies indicates the role of air-sea interaction in the BSISO has not been fully understood, especially the oceanic feedback to the atmosphere. We address this gap by assessing the effect of SST fluctuations on the BSISO in reanalysis data, which is an important tool for improving our understanding of the climate system.
The importance of MSE in MJO initiation (Peters & Neelin, 2006;Raymond, 2000;Sobel et al., 2014) and propagation (Andersen & Kuang, 2012;Kemball-Cook & Weare, 2001;Maloney, 2009) has been addressed by interrogating reanalyses and numerical experiments. A buildup of MSE occurs before MJO deep convection, and it is discharged during and after the MJO convective and stratiform stages: the so-called recharge-discharge mechanism for MJO dynamics (Andersen & Kuang, 2012;Bladé & Hartmann, 1993;Johnson et al., 1999;Kiladis et al., 2005). Despite the growing wealth of studies on the MSE budget of the MJO, only a few studies have examined the BSISO MSE budget (e.g., Ajayamohan et al., 2011). This paper investigates oceanic feedbacks to the atmospheric BSISO convection in the context of the MSE budget using two modern reanalyses. We extend the air-sea interaction analysis framework of DeMott et al. (2016) from the boreal winter (November-April) MJO to the boreal summer (May-October) ISO. We further extend DeMott et al. (2016) by considering interbasin differences in the strength of the SST feedback to the BSISO between the Indian and Pacific Oceans, which is critical given the complex structure of the BSISO as it propagates north and east. The paper is organized as follows. The data and diagnostic methods are described in section 2. Section 3 shows the modification of surface flux variability by intraseasonal SSTs. Quantitative contributions of MSE budget terms and SST-rectified surface fluxes to hmi and ∂hmi/∂t are shown in section 4. Discussion and summary are given in section 5.

Data
We diagnose the oceanic feedback to atmospheric BSISO convection by using two reanalyses: the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERAI) at a resolution of 1.5°× 1. 5°(Dee et al. 2011), and the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective Analysis for Research and Applications v2 (MERRA) at a resolution of 1°× 1° (Rienecker et al., 2011). The daily-mean variables from each data set include the following: precipitation, 850-hPa wind speed, longwave radiative heating (LW), SW, surface variables associated with latent heat (LH) and sensible heat (SH) fluxes, and the three-dimensional variables related to MSE and the MSE budget. As the SST boundary condition for ERAI has been prescribed from satellite analyses corrected by buoy observation since 1986 (Reynolds et al., 2002), we use data from 1986 to 2016.

Surface Flux Decomposition
SST fluctuations exert an impact on the atmosphere, and thus on BSISO activity, through variations in surface fluxes. The surface bulk formulae are adopted to calculate the SST contribution to the intraseasonal LH and SH. LH and SH can be computed as follows (Weare et al., 1981): where ρ is near-surface air density; L v denotes the latent heat of condensation; C e and C h are the constant transfer coefficients for moisture and heat, respectively; C p is the heat capacity of dry air; Δq and ΔT are the specific humidity and temperature differences between the sea surface and the near-surface atmosphere (2 m above the surface), respectively; and |V| is the wind speed at 10 m above the surface. To estimate the relative importance of wind and moisture (heat) fluctuations to LH (SH) variability, the intraseasonal anomalies of LH (SH) are decomposed into three parts: where the overbar represents the low-frequency (>100 days) background and a prime represents the intraseasonal (20-to 100-day filtered) variability. To distinguish our computed fluxes from the values in the reanalyses themselves (e.g., LH and SH), we write our fluxes as LH * and SH * , respectively. In (3) and (4) ) flux perturbations. The scaling coefficient of ρL v C e (ρC p C h ) is determined by regressing the sum of these three flux perturbations onto the total LH (SH) at each grid point. Next, (3) and (4) are recalculated using the SST field without the intraseasonal component (referred to as "noISO SST") in (1) and (2). The difference between LH * (SH * ) calculated based on the full and noISO SST can reveal the role of intraseasonal SST variability in LH * (SH * ). To avoid confusion, LH * and SH * derived from the full SST are denoted LH Ã SST and SH Ã SST , while values derived from the noISO SST are denoted LH Ã SST noISO and SH Ã SST noISO . Our definition of intraseasonal SST (20-to 100-day filtered) differs from that by DeMott et al. (2016), in which the authors used the departure from 61-day running mean. The choice of definition makes little difference to our results and no difference to our conclusions. We adopt the 20-to 100-day filtered SST to unify the definition of the intraseasonal scale throughout the study.

The MSE Budget
As in many studies (Kiranmayi & Maloney, 2011;Maloney, 2009) and shown in section 3, the temporal evolution of MSE is highly consistent with that of rainfall; thus, MSE can also be treated as a proxy for convection. The SST effect on BSISO convection can be diagnosed through MSE budget analysis following Neelin and Held (1987). The column-integrated MSE (hmi) is defined as where T is temperature, g is gravitational acceleration, Z is geopotential height, and q is specific humidity. Angled brackets denote a mass-weighted vertical integral from 1,000 to 100 hPa. To understand specific processes responsible for MSE temporal variability, the budget for the time rate of change of MSE (∂hmi/∂t) is adopted, which can be written as where V is the horizontal wind vector, ∇ is the horizontal gradient operator, ω is the vertical pressure velocity, and p is pressure. The first two terms on the right-hand side in equation (6) are the horizontal and vertical advection of hmi. The column-integrated LW and SW (i.e., hLWi and hSWi) are calculated as the differences of net fluxes between the top of the atmosphere and the surface. Figure 1 shows the seasonal mean hmi and 850-hPa wind, and the standard deviations of 20-to 100-day filtered hmi and ∂hmi/∂t. The pattern of mean hmi is similar to that of summer mean SST (Figure 2e), and the maximum mean hmi is located over South Asia (80°E-120°E, 10°N-25°N). Influenced by the Asian summer monsoon, the low-level circulation is dominated by strong southwesterlies over the Indian Ocean and southeasterlies over the western Pacific. The distributions of intraseasonal variability of hmi and ∂hmi/∂t resemble each other, with maxima off the equator in the Northern Hemisphere.

Modification of LH and SH Variability by Intraseasonal SST
As the results from the ERAI and MERRA data sets are highly similar, to save space, we show most of our results for ERAI only. Before diagnosing the SST effect on surface turbulent fluxes (LH and SH), the daily SST skewness during boreal summer is analyzed ( Figure 3). Significant positive SST skewness appears over the western Indian Ocean, southern Arabian Sea, and Bay of Bengal, which implies that the amplitude of warm SST anomalies is larger than that of the cold SST anomalies. Negative SST skewness is observed over the South China Sea and Philippine Sea; skewness is weak over the equatorial western Pacific. Strong positive (negative) SST is a consequence of large (small) net surface heat fluxes (Q net ) due to enhanced (reduced) SW and calm (strong) winds that decrease (increase) surface turbulent fluxes and ocean vertical mixing. These processes lead to a shoaling (deepening) of the mixed layer depth, which can enhance (weaken) the SST response to the anomalous ISO convection (Duvel et al., 2004;Duvel & Vialard, 2007;Roxy et al., 2013). A stronger oceanic feedback may exist over the western Indian Ocean, Arabian Sea, and Bay of Bengal, as warm SST anomalies may destabilize the atmosphere.

Contribution of Intraseasonal SST to LH and SH Variability
Next, the SST effect on LH and SH is investigated using the bulk formulae calculated from the full and noISO SST (section 2.2). LH Ã SST is highly consistent with LH (Figures 4a and 4b), which gives us confidence for further diagnosis. The left-column panels in Figure 4 show the standard deviations of intraseasonally filtered  Figure 4f) is stronger than that of the saturated specific humidity at the SST (q Ã SST ; Figure 4g), highlighting the importance of q air over q Ã SST for LH Ã SST . The pattern The same as (a)-(h), except the panels show the difference between the values shown in (a)-(h) and the standard deviations of the corresponding variable calculated using SST without the intraseasonal component ("noISO" SST). LH = latent heat; SST = sea surface temperature; ERAI = European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis.

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Journal of Geophysical Research: Atmospheres variability. However, the SST effect on each of the three flux components is positive. This suggests that the component terms offset each other. The reduced LH * is largely due to the enhanced Δq The Δq 0 V j j with full SST is broadly 1-4 W/m 2 larger than Δq 0 V j j with noISO SST, and exceeds 4 W/m 2 over the active BSISO regions.
The same approach is applied to SH ( Figure 5). As for LH, σ SH Ã SST À Á highly resembles σ(SH). The pattern of σ SH Ã SST À Á is mainly determined by ΔT (Figures 5b and 5h). This is consistent with the result of DeMott et al.

Role of SST Fluctuations in BSISO Northward Propagation
In this section, the SST effect on BSISO northward propagation is investigated through lead-lag composites. The composites of variables are constructed with respect to two reference domains that represent the two major regions of BSISO activity: the eastern Indian Ocean (75°E-85°E, 0°-10°N) and the western Pacific (140°E-150°E, 0°-10°N). Figure 6 shows the lag regression coefficients of hmi and its tendency terms onto the intraseasonal precipitation during the BSISO life cycle (lag ±25 days) over the Indian Ocean. The 20-to 100-day filtered (75°E-85°E) averaged variables are regressed onto the 20-to 100-day filtered (75°E-85°E, 0°-10°N) averaged rainfall, as a function of latitude, to reveal the northward propagating features associated with the BSISO. Note that in DeMott et al. (2016), unfiltered variables are regressed onto filtered rainfall. We examined both methods and found that the choice makes little qualitative difference to the results, which implies that intraseasonal component of the unfiltered variable has the strongest linear relationship to the filtered rainfall, relative to other components of the unfiltered variable. The convection displays an apparent northward propagation, with a speed of about 1.8 m/s. At lag 0, intraseasonal convection reaches its maximum. The structure of hmi is highly in phase with the intraseasonal rainfall, with enhanced (reduced) hmi within the active (suppressed) BSISO region (Figure 6a). Intense moistening occurs approximately 1 week prior to the convection maximum ( Figure 6f). Following Andersen & Kuang, (2012), we assume that components that are in phase with hmi affect the convection maintenance, while processes that are in phase with ∂hmi/∂t are related to the propagation of BSISO convection. Figures 6b-6e and 6g-6j show the results for MSE tendency terms on the right-hand side of equation (6). We note that the sum of these terms is smaller than ∂hmi/∂t, with about 30-40% underestimation. This suggests the MSE budget is not closed in these reanalyses; some processes are missing or miscalculated. Further, the propagation speed of the sum of terms is somewhat slower than that of ∂hmi/∂t, with maxima slightly shifting toward the strongest convection. These residuals are related to the deficiencies of precipitation in the atmospheric models on which the reanalyses depend (Adames & Wallace, 2015;Mapes & Bacmeister, 2012). Despite these residuals, the MSE budget equation provides a useful tool to evaluate the contribution of each process to ∂hmi/ ∂t. hmi is dissipated by the vertical and horizontal advection of hmi (Àhω · ∂m/∂pi and Àh|V| · ∇mi; Figures 6b-c), as they exhibit positive (negative) values over suppressed (active) convection. However, Àhω · ∂m/∂pi and Àh|V| · ∇mi maximize over the suppressed convection center and ahead (north) of the active convection center, respectively. Thus, ∂hmi/∂t is largely supported by Àh|V| · ∇mi, particularly by the zonal advection of hmi (Àhu · ∂m/∂xi). The meridional advection of hmi (Àhv · ∂m/∂yi) only increases ∂hmi/∂t for equatorial convection (Figures 6c-6e). Column-integrated LW (hLWi) is the primary contributor to hmi (Figure 6g), with a secondary contribution from LH (Figure 6h), although the maximum LH lags the convective center slightly. SH and hSWi also support hmi but with weaker amplitude (Figures 6i and 6j).
Intraseasonal SST can feed back to BSISO convection by modifying LH and SH. Figure 7 shows the SST effects on LH * (left panels) and SH * (right panels) over the eastern Indian Ocean. The second-order term is small and neglected here. As expected, the wind-driven flux perturbation of LH Ã SST (Δq V j j 0 , red) is much larger than the thermodynamic term of LH Ã SST (Δq

Journal of Geophysical Research: Atmospheres
When the intraseasonal SST is removed, Δq 0 V j jis reduced and shifts toward longer leads (dashed blue). As a consequence, compared to the component LH * using the noISO SST (LH Ã SST noISO , dashed magenta), the maximum LH * using the full SST (LH Ã SST ) shifts toward the convective center (+1 day), 1 day earlier than the maximum LH Ã SST noISO (+2 days). The right panel in Figure 7 shows the SST effect on SH * . SH Ã SST is more sensitive than LH Ã SST to SST. ΔT V j j 0 and ΔT 0 V j j both maintain convection, with about 2 days' phase difference. Without the intraseasonal SST, there are significant phase changes in ΔT 0 V j j, from 1 day ahead of convection to 1 day behind. Correspondingly, SH Ã SST is located at the convective center, while SH Ã SST noISO lags convection. We next analyze the role of flux perturbations and intraseasonal SST in the northward propagation of BSISO convection. The phase relationships between the convection and wind-driven, thermodynamic, and second-order flux perturbations over the Indian Ocean are shown in Figures 8a-8c. Positive wind-driven flux perturbations appear at and south of the convective center throughout the BSISO life cycle, which is consistent with Figures 7a and 7c. This indicates that wind-driven flux perturbations support BSISO convection but are not favorable for northward propagation. The enhanced wind-driven flux south of the convective center is due to the stronger wind speeds from the BSISO-related southwesterly anomalies superimposed on the background southwesterly monsoon flow. In contrast, the thermodynamic flux perturbations (Figure 8b) maximize~10 days before the strongest convection. They reduce the degree to which the wind-driven flux perturbations slow BSISO propagation. Off the equator, it is slightly shifted toward the convective center, supporting the convection. Second-order flux perturbations (Figure 8c) are smaller than the other two perturbations; their spatial structure resembles noise. The sum of these three terms is the component total flux (Figure 8d), which is highly similar to the winddriven flux term (Figure 8a). The difference between the surface component total fluxes calculated from the full and noISO SST (Figures 8d-8f) reveals the role of intraseasonal SST in the surface fluxes associated with the BSISO. It is obvious that the surface fluxes from intraseasonal SSTs maximize about 10 days before convection. The "SST effect" on surface fluxes is approximately 1 W/m 2 , which

Journal of Geophysical Research: Atmospheres
represents about 20-25% of the total fluxes. Off the equator, the positive anomalies are larger than the negative anomalies. This may be associated with the substantial positive SST skewness over the Bay of Bengal (Figure 3). The SST effect promotes more evaporation and boundary layer heating north of convection, which is conductive to BSISO northward propagation over the Indian Ocean.
The phase relationships between the convection and surface flux perturbations over the western Pacific are shown in Figure 9. The 140°E-150°E averaged variables are regressed onto the (140°E-150°E, 0°-10°N) averaged intraseasonal rainfall. The convection over the western Pacific also exhibits significant northward propagation, with a faster speed than over the Indian Ocean. For equatorial convection, the maximum wind-driven flux perturbation lags~4 days behind the strongest convection. As the convection moves northward, the flux anomaly shifts toward the convective center and even slightly leads convection (Figure 9a). The thermodynamic flux perturbation (Figure 9b) is positive ahead of convection over the equatorial western Pacific. Off the equator, it is out of phase with convection. The structure of the second-order term (Figure 9c) resembles that of the thermodynamic flux perturbation: It leads convection within 15°N of the equator. It is interesting that the SST effect on surface fluxes over the western Pacific is still positive at negative lags and negative at positive lags, promoting northward propagation. However, in more detail, a positive SST effect appears across the suppressed convection region, while the SST effect over the Indian Ocean is nearly in quadrature with the convection. The

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Journal of Geophysical Research: Atmospheres SST effect on convection over the western Pacific may differ from that over the Indian Ocean, despite it contributing to northward propagation in both basins. Besides, the SST effect is weaker in the western Pacific than in the Indian Ocean (Figures 8f and 9f), which might be a consequence of weak SST skewness over the equatorial western Pacific and strong negative SST skewness over the off-equatorial western Pacific (Figure 3), or because of the different phasing between q air and q Ã SST in the two basins (Hendon & Glick, 1997). As a whole, intraseasonal SST favors the northward propagation of convection over both the Indian Ocean and western Pacific. Besides BSISO northward propagation, we also analyzed the SST effect on the eastward and westward propagating BSISO modes in the Indian Ocean and western Pacific, respectively. Results for the SST effect on zonal propagation in the Indian Ocean are largely similar to those in DeMott et al. (2016) for the boreal winter MJO. In the western Pacific, the SST effect on zonal propagation is similar to that in the Indian Ocean, except that in the western Pacific the BSISO propagation is mostly westward rather than eastward and has a faster phase speed. Maximum surface fluxes induced by intraseasonal SST significantly leads convection as well, suggesting that SST fluctuations are important for BSISO propagation (figures not shown).
Next, we examine why the role of the wind-driven flux perturbation varies during different stages in the BSISO life cycle over the western Pacific, while it always slows the convection over the Indian Ocean. Figure 10 illustrates the regression coefficients of hmi (shading) and 850-hPa winds (vectors) at various lags onto intraseasonal rainfall (contours) in the Indian Ocean and west Pacific. The temporal and spatial distribution of hmi moves coherently with rainfall throughout the BSISO life cycle. Equatorial

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Journal of Geophysical Research: Atmospheres convection induces a southerly anomaly to its south and a northeasterly anomaly to its north (Figures 10b, 10c, 10g, and 10h). Thus, there are stronger winds south of convection over both the Indian Ocean and the western Pacific, from the combination of southerly wind anomalies with the mean state winds (southwesterly over the Indian Ocean and southeasterly over the western Pacific; Figure 1a). When the convection moves off the equator, an anomalous cyclone appears northwest of the convection (Figures 10d, 10e, 10i, and 10j) as part of the Rossby wave response to BSISO heating (Gill, 1980) and/or the interaction between the anomalous vertical motion and background vertical shear (Jiang et al., 2004). This anomalous cyclone produces larger wind-driven flux perturbations to the south (north) of convection over the eastern Indian Ocean (western Pacific), when coupled with the background southwesterly (southeasterly).

Quantitative Contributions of MSE Budget Terms and SST Variability to BSISO
In this section, we aim to calculate the quantitative contributions of each moistening process (P), including SST variability, to the maintenance and propagation of BSISO convection by regressing each process onto intraseasonal hmi and ∂hmi/∂t (R(hmi, P), R(∂hmi/∂t, P)). Following DeMott et al. (2016), the fractional contribution of a given process to hmi, F hmi (P), is derived by converting R(hmi, P) to units of % hmi day À1 . Similarly, the fractional contribution of a given process to ∂hmi/∂t, F ∂hmi/∂t (P), is derived by converting R(∂hmi/∂t, P) to units of % ∂hmi/∂t: The geographic distributions of F hmi (P) and F ∂hmi/∂t (P) illustrate the contribution of a given process to the maintenance/damping and generation/destruction of hmi (i.e., the development and propagation of convection). Figure 11 shows the fractional contributions of the MSE budget terms to the intraseasonal hmi (Figures 11a-11h) and ∂hmi/∂t (Figures 11i-11p). Obviously, <LW> is the most important contributor to intraseasonal hmi (Figure 11a). It supports the convection symmetrically about the equator, maximizing on the equator. The distribution of F hmi (LH) (Figure 11f) is similar to that of intraseasonal precipitation ( Figure 2f) and maintains convection over the active BSISO regions. Maintenance of hmi also comes from SH over the tropical regions and <SW> over all areas (Figures 11g and 11h). hmi is destroyed by Àhω · ∂m/∂pi over the entire Warm Pool and by Àh|V| · ∇mi over the tropical oceans (Figures 11b and  11c). In contrast, the advection of hmi contributes most to ∂hmi/∂t, particularly Àh|V| · ∇mi, which contributes more than 70% of ∂hmi/∂t. The distribution of F ∂hmi/∂t (LH) (Figure 11n) is negative over the equatorial and northern Indian Ocean and positive over the northern Philippine Sea. This is consistent with Figures 8d  and 9d, as LH Ã SST always lags BSISO convection in the Indian Ocean, while LH Ã SST transitions from lagging convection to leading convection when the BSISO moves north over the western Pacific. It is interesting that SH contributes not only to the maintenance but also to the generation of hmi over most active BSISO regions (Figures 11g and 11o), although the contributions are not as large as those for LH. SH may be important in the development and propagation of BSISO convection.
Over the ocean, the horizontal advection of hmi (Àh|V| · ∇mi) dominates ∂hmi/∂t. F ∂hmi/∂t (Àh|V| · ∇mi) is larger over the Indian Ocean (80%) than over the western Pacific (>60%), which may be related to the position of Asian summer monsoon trough over the western Pacific. Àh|V| · ∇mi is mainly controlled by the zonal advection of hmi (Àhu · ∂m/∂xi). This differs from the study of Jiang et al. (2004), which only emphasized the importance of meridional moisture advection for the northward propagation (Chou & Hsueh, 2010;DeMott et al., 2013). It may be attributed to the background southerly flow in the eastern Indian Ocean, where northward propagation is most obvious. Our results verify that the meridional advection of hmi dominates the horizonal advection of hmi over the Bay of Bengal (Figure 11). The zonal advection of hmi also contributes to the propagation, but with weaker amplitude. F ∂hmi/∂t (Àhu · ∂m/∂xi) is larger than F ∂hmi/∂t (Àhv · ∂m/∂yi) over the equatorial Indian Ocean and western Pacific. However, Àhv · ∂m/∂yi is more important to ∂hmi/∂t over the Bay of Bengal, South China Sea, and coastal East Asia. Particularly, over the South China Sea, Àhv · ∂m/∂yi contributes most to ∂hmi/∂t, while Àhu · ∂m/∂xi tends to decrease ∂hmi/∂t. We further decompose Àhu · ∂m/∂xi and Àhv · ∂m/∂yi to show that over the Indian Ocean, the advection of mean hmi by perturbation zonal wind (À u 0 ·∂m=∂x h i ) is the largest source for Àhu · ∂m/∂xi. The strong anomalous easterlies north of the convection import the background zonal gradient of hmi to the northeast of BSISO convection, as the maximum climatological hmi is located over South Asia (Figures 1 and 10). Over the Bay of Bengal, the advection of anomalous hmi by the mean meridional wind (À v·∂m 0 =∂y h i ) is the largest of the horizonal hmi advection terms. The southerlies become much stronger over the Bay of Bengal (Figure 1a), which transport the enhanced hmi near the convective center to the north ( Figure 10). À v·∂m 0 =∂y h ialso enhances northward propagation over the South China Sea and western Pacific, as revealed by Wang et al. (2018), in which they reported the importance of the anomalous moisture by mean meridional wind (À v·∂q 0 =∂y h i ) to the northward propagation of convection. The anomalous hmi advection by the anomalous zonal wind (Àu 0 · ∂m 0 /∂x) is negative over the South China Sea, largely inhibiting propagation.
The fractional contributions of flux perturbations associated with LH to hmi are shown in Figures 12a-12e can support convection not only over the active BSISO regions but also over the southern Indian Ocean and the equatorial and eastern Pacific (Figures 12a-12c). In contrast, Δq 0 V j j damps Figure 11. Regression coefficients of 20-to 100-day filtered moist static energy budget terms onto 20-to 100-day filtered 〈m〉: (a) 〈LW〉, (b) À〈ω · ∂m/∂p〉, (c) À〈|V| · ∇m〉, (d) À〈u · ∂m/∂x〉, (e) À〈v · ∂m/∂y〉, (f) LH, (g) SH, and (h) 〈SW〉. (i-p) The same as (a)-(h), except for the variables regressed onto ∂〈m〉/∂t. The stippled areas are not statistically significant at the 5% level. LW = longwave radiative heating; LH = latent heat; SH = sensible heat; SW = shortwave radiative heating; ERAI = European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis. V j j, are observed over the far western Indian Ocean, Arabian Sea, and Bay of Bengal. Over the far western Indian Ocean, SST variability strengthens hmi anomalies during the BSISO initiation, contributing about 1.5% of hmi day À1 . We also examined the contributions of flux perturbations to ∂hmi/∂t (figure not shown). Wind-driven flux perturbations inhibit propagation over the Asian summer monsoon regions, except for a small region over the Philippine Sea, as the perturbations always lag the convection (Figures 8 and 9). Thermodynamic flux perturbations contribute to propagation across the active BSISO region. Figure 13 shows the total effect of intraseasonal SST variability on hmi and ∂hmi/∂t through modifying LH * and SH * , using ERAI and MERRA. They are obtained by subtracting F m The strong resemblance between these two reanalyses suggests that the intraseasonal SST effects on hmi and ∂hmi/∂t are robust. The SST-modulated LH * accounts for more than 12% of ∂hmi/∂t. The contribution of SST variability to F hmi (SH * ) and F ∂hmi/∂t (SH * ) (Figures 13b, 13e, 13h, and 13k) is about 20-25% of those for F hmi (LH * ) and F ∂hmi/∂t (LH * ) (Figures 13a, 13d, 13g, and 13j), with very similar geographic distributions. They result in a stronger SST effect on hmi and ∂hmi/∂t. The SST contributions to F hmi (LH * + SH * ) show large values over the equatorial western and central Indian Ocean, northern Arabian Sea, and Bay of Bengal, with contributions  intraseasonal rainfall over the Indian Ocean and western Pacific, respectively. Obviously, SST-modulated flux anomalies (shading in Figure 15) are coherent with the SST anomalies (shading in Figure 14) over the Indian Ocean (left panels) and western Pacific (right panels). Over the Indian Ocean, warm SST and enhanced fluxes always appear to the northeast of the convective center, conductive to propagation from the equatorial west/central Indian Ocean to the Bay of Bengal. Positive intraseasonal SST and flux anomalies lead the convection. Particularly, when convective anomalies are over the equatorial central Indian Ocean and Bay of Bengal at À5 and +10 days (Figures 14b and 14e and Figures 15b and 15e), respectively, warm SST and enhanced fluxes appear over the convective center. This suggests the intraseasonal SST can support convection over the equatorial central Indian Ocean and Bay of Bengal, where the SST effect on hmi shows large positive values (Figures 13c and 13f). Over the western Pacific, at negative lags (À10 and À5 days; Figures 14f and 14g and Figures 15f and 15g), positive SST and flux Journal of Geophysical Research: Atmospheres anomalies show near-quadrature phase relationships with convection. However, as the convection further develops and moves off the equator, descending motion (suppressed convection) ahead of the active convection becomes very weak or even absent (Figures 14h-14j and 15h-15j). At lag +0, the intraseasonal SST is out of phase with convection (Figures 14h and 15h). At +5 and +10 days, positive SST and SSTinduced flux anomalies lead 180°ahead of the convection (Figures 14i-14j and 15i-15j). There are weak and negative SST and flux anomalies over the convective region. Thus, the intraseasonal SST tends to damp the BSISO convection over the western Pacific, particularly over the off-equatorial regions where the SST effect on hmi is negative (Figures 13c and 13f).  maximum LH slightly lags MJO convection; thus, it can maintain hmi but cannot contribute to ∂hmi/∂t. In winter, SH supports convection over the active MJO region but only contributes to ∂hmi/∂t over the Indian Ocean, unlike in boreal summer, when it supports convection and contributes to ∂hmi/∂t across the active BSISO region. hmi ahead (east) of MJO convection is opposed by Δq V j j 0 and supported by Δq 0 V j j; these two terms strongly offset each other. MJO and BSISO hmi is primarily maintained by hLWi and reduced by the vertical and horizontal advection of hmi. The oceanic feedbacks to the MJO and BSISO are remarkably similar over the Indian Ocean. SST anomalies support convection during initiation over the western Indian Ocean. Intraseasonal SST fluctuations ahead of convection favor MJO and BSISO propagation, with contributions larger than 10% and 12% of ∂hmi/∂t, respectively. Results for boreal summer ISO are generally consistent with those for boreal winter MJO, which may be due to strong association between BSISO and MJO (Lawrence & Webster, 2002). Unlike DeMott et al. (2016), we find a strong difference in SST feedbacks over the Indian Ocean and western Pacific, associated with differences in the boreal summer background state in these basins. As a result of the interaction between anomalous wind speed and background wind speed, wind-driven flux perturbations and horizonal advection of hmi play different roles in BSISO convection in these basins. What is more, while the intraseasonal SST contributes to the convection northward propagation over both basins, it supports hmi over the Indian Ocean but damps hmi over the western Pacific. This is related to the different phase relationships between convection and intraseasonal SST, as well as between convection and SST-modulated flux anomalies.

Discussion and Summary
Although the SST effects on hmi and ∂hmi/∂t from ERAI and MERRA are similar, issues in both products may affect the robustness of our results. The root mean square difference of daily ERAI and MERRA LH (SH) from buoy observations is approximately 20-40 W/m 2 (4-5 W/m 2 ) over the Asian summer monsoon region, despite ERAI and MERRA assimilating some buoy data (10-m wind, 2-m air temperature, and 2-m relative humidity; Bentamy et al., 2017). Dry biases in near-surface specific humidity are strongly correlated with the positive LH biases (Brunke et al., 2011;Praveen Kumar et al., 2012;Sanchez-Franks et al., 2018). Sanchez-Franks et al. (2018) also show that cold biases in SST, relative to buoy data, appear in both ERAI and MERRA; they attribute these biases to the common use of the Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) foundation SST product (Donlon et al., 2012). Therefore, our "SST effect" may be slightly underestimated. Wang et al. (2018) found that the intraseasonal SST anomalies could induce boundary layer moisture convergence and increase surface turbulent flux anomalies, which tend to heat and moisten the boundary layer, favoring the northward propagation of BSISO. Based on our diagnostics, intraseasonal SST variability contributes up to 20% to the propagation of convection (∂hmi/∂t). Although the SST effect enhances propagation, the intraseasonal SST variability alone could not drive propagation; most of the "work" of propagation is accomplished by the atmospheric circulation. The BSISO circulation also exerts a strong control on the pattern of intraseasonal SST (Hendon & Glick, 1997;Woolnough et al., 2000), such that air-sea feedbacks to the BSISO are themselves coupled to the circulation. Thus, the internal atmospheric dynamics are essential to the northward propagation of BSISO convection, with the assistance of oceanic feedbacks.

Summary
The effect of intraseasonal SST on boreal summer ISO activity is examined through reanalysis diagnostics within an MSE framework. The patterns of intraseasonal column-integrated MSE (hmi) and its time rate of change (∂hmi/∂t) resemble each other, with maxima off the equator in the Northern Hemisphere. Summer mean hmi maximizes over South Asia. Influenced by the Asian summer monsoon, the low-level circulation is dominated by strong southwesterlies over the Indian Ocean and southeasterlies over the western Pacific. The precipitation shows significant intraseasonal variability over the Asian summer monsoon regions. Enhanced intraseasonal SST appears over the Warm Pool region and northern Pacific, with stronger variability in the Indian Ocean than in the western Pacific associated with mixed-layer depth differences. Significant positive SST skewness is observed over the southern Arabian Sea and Bay of Bengal, while negative skewness exists over the Philippine Sea.
Based on bulk formula decomposition, LH and SH are divided into three parts: the wind-driven, thermodynamic, and second-order flux perturbations. While LH is mainly determined by the wind-driven flux perturbations, SH is more sensitive to the thermodynamic flux perturbations. The wind-driven and 10.1029/2018JD029303 Journal of Geophysical Research: Atmospheres thermodynamic flux perturbations associated with LH tend to offset each other, while for SH these two terms support convection. Over the Indian Ocean and equatorial western Pacific, the wind-driven flux perturbation slightly lags convection, while the maximum thermodynamic flux perturbation leads convection. This suggests the thermodynamic perturbation reduces the degree to which the wind-driven perturbation slows BSISO propagation. The SST effect on surface fluxes enhances variability ahead of the convection over both the Indian Ocean and the western Pacific, favoring northward propagation.
To quantitatively investigate the contribution of intraseasonal SST to the atmospheric BSISO convection, we compute budgets of hmi and ∂hmi/∂t. Column-integrated LW is the primary contributor to hmi. hmi is destroyed by the vertical export over the Warm Pool region and horizonal advection over the equatorial oceans. In contrast, the horizonal advection of hmi is the most important driver of ∂hmi/∂t, with zonal advection contributing across almost the entire active BSISO region, accompanied by meridional advection contributing over the Bay of Bengal and South China Sea. During most of the BSISO life cycle, LH supports intraseasonal hmi but not ∂hmi/∂t, as the maximum LH slightly lags convection. It is interesting that SH supports not only the maintenance but also the generation of hmi, though the amplitude is small. SSTmodulated surface fluxes account for~2% of hmi day À1 over the far western Indian Ocean, northern Arabian Sea, and Bay of Bengal, while they damp hmi over the western Pacific. This is associated with different phase relationships between convection and SST anomalies over these regions. Intraseasonal SST plays a more important role in ∂hmi/∂t, with a contribution of more than 12%. Intraseasonal SST variability enhances the propagation of BSISO convection across the active BSISO region.
In this study, the oceanic feedback to BSISO convection is diagnosed using the reanalysis through the SST influence on surface fluxes. SST fluctuations may affect the BSISO through other dynamic or thermal processes, such as boundary layer convergence induced by SST gradients. Previous modeling studies also found subdaily SST variability can influence the simulated BSISO (Hu et al., 2015;Klingaman et al., 2011) due to the intense SST diurnal cycle over the Asian summer monsoon region. Each of these processes may play an important role in the BSISO MSE budgets (especially ∂hmi/∂t), and each fundamentally relies on SH. Although SH variability is small compared to LH, it may play an important role in processes that contribute to BSISO propagation. It is necessary to consider LH and SH separately when assessing intraseasonal coupled feedbacks. These feedbacks should be examined using reanalysis data sets across the BSISO region and throughout the BSISO life cycle. Comprehensive understanding of ocean feedbacks to the BSISO using reanalysis is a key tool to investigate the ocean coupling in model simulations and then help improve the accuracy of BSISO simulations. Future work should apply these methods to assess the influence of ocean coupling on the BSISO in current model simulations.