A Cold Lid on a Warm Ocean: Indian Ocean Surface Rain Layers and Their Feedbacks to the Atmosphere

Ocean surface rain layers (RLs) form when relatively colder, fresher, less dense rain water stably stratifies the upper ocean. RLs cool sea surface temperature (SST) by confining surface evaporative cooling to a thin near‐surface layer, and generate sharp SST gradients between the cool RL and the surrounding ocean. In this study, ocean‐atmosphere coupled simulations of the November 2011 Madden‐Julian Oscillation (MJO) event are conducted with and without RLs to evaluate two pathways for RLs to influence the atmosphere. The first, termed the “SST gradient effect,” arises from the hydrostatic adjustment of the boundary layer to RL‐enhanced SST gradients. The second, termed the “SST effect,” arises from RL‐induced SST reductions impeding the development of deep atmospheric convection. RLs are found to sharpen SST gradients throughout the MJO suppressed and suppressed‐to‐enhanced convection transition phases, but their effect on convection is only detected during the MJO suppressed phase when RL‐induced SST gradients enhance low‐level convergence/divergence and broaden the atmospheric vertical velocity probability distribution below 5 km. The SST effect is more evident than the SST gradient effect during the MJO transition phase, as RLs reduce domain average SST by 0.03 K and narrow vertical velocity distribution, thus delaying onset of deep convection. A delayed SST effect is also identified, wherein frequent RLs during the MJO transition phase isolate accumulated subsurface ocean heat from the atmosphere. The arrival of strong winds at the onset of the MJO active phase erodes RLs and releases subsurface ocean heat to the atmosphere, supporting the development of deep convection.


Introduction
The Madden-Julian Oscillation (MJO) is an eastward propagating, planetary scale convective disturbance that circumnavigates the global tropics on time scales of 30-60 days (Madden & Julian, 1971).MJO influence on tropical climate ranges from intraseasonal time scales, where it is the dominant mode of tropical variability, to interannual time scales, where it influences the onset and evolution of El Niño Southern Oscillation events (e.g., McPhaden et al., 1988).In addition to it's impact on tropical climate, diabatic heating anomalies from MJO convection perturb circulations in the extratropics and represent an important source of extratropical atmospheric predictability on subseasonal time scales (Hoskins & Karoly, 1981;Weickmann, 1983;Vitart, 2017;Tseng et al., 2019;Wang et al., 2020;Stan et al., 2022).
Abstract Ocean surface rain layers (RLs) form when relatively colder, fresher, less dense rain water stably stratifies the upper ocean.RLs cool sea surface temperature (SST) by confining surface evaporative cooling to a thin near-surface layer, and generate sharp SST gradients between the cool RL and the surrounding ocean.In this study, ocean-atmosphere coupled simulations of the November 2011 Madden-Julian Oscillation (MJO) event are conducted with and without RLs to evaluate two pathways for RLs to influence the atmosphere.The first, termed the "SST gradient effect," arises from the hydrostatic adjustment of the boundary layer to RL-enhanced SST gradients.The second, termed the "SST effect," arises from RL-induced SST reductions impeding the development of deep atmospheric convection.RLs are found to sharpen SST gradients throughout the MJO suppressed and suppressed-to-enhanced convection transition phases, but their effect on convection is only detected during the MJO suppressed phase when RL-induced SST gradients enhance low-level convergence/divergence and broaden the atmospheric vertical velocity probability distribution below 5 km.The SST effect is more evident than the SST gradient effect during the MJO transition phase, as RLs reduce domain average SST by 0.03 K and narrow vertical velocity distribution, thus delaying onset of deep convection.A delayed SST effect is also identified, wherein frequent RLs during the MJO transition phase isolate accumulated subsurface ocean heat from the atmosphere.The arrival of strong winds at the onset of the MJO active phase erodes RLs and releases subsurface ocean heat to the atmosphere, supporting the development of deep convection.
Plain Language Summary Rain water is less dense than near-surface ocean water.For this reason, rain water can float on the ocean surface following rain events and form a "rain layer" in the upper ocean.Rain layers that form in the tropical Indian Ocean reduce sea surface temperature (SST) and shield the subsurface ocean below the rain layer from the atmosphere, thus altering heat exchange between the ocean and atmosphere.In this study, we conduct model experiments over the tropical Indian Ocean to investigate rain layer feedbacks to the atmosphere.We identify two potential rain layer feedback mechanisms, one in which rain-enhancement of SST gradients contributes to the formation of clouds and precipitation in the atmosphere, and a second in which rain-driven SST reduction suppresses the development of clouds and precipitation.Our results indicate that rain-driven SST reduction is the dominant immediate feedback, as clouds and precipitation are reduced in the presence of rain layers.A delayed rain layer feedback is also identified, wherein rain layers insulate subsurface ocean heat from the atmosphere.When rain layers are destroyed by wind-driven mixing, the stored ocean heat is released to the atmosphere, and supports the development of clouds and precipitation.SHACKELFORD ET AL.Over the Indian and western Pacific Oceans, the MJO manifests as coupled regions of enhanced and suppressed cloudiness, referred to as the MJO active and suppressed phases, respectively.From the Eulerian perspective of the central Indian Ocean, an MJO event starts with the suppressed phase, characterized by large-scale subsidence, calm winds, shallow convection, light rainfall, and high outgoing longwave radiation (OLR) (Johnson et al., 1999).As the disturbance propagates eastward, MJO suppressed conditions are gradually replaced with MJO active conditions, characterized by large-scale rising motion, increased winds, deep convection, heavy rainfall, and reduced OLR.Because of the slow propagation speed (∼4-5 m s −1 ) and large-scale nature of the MJO, the transition from convectively suppressed to convectively enhanced regimes occurs gradually over the course of several days.For this reason, it's helpful to define an intermediate MJO phase that describes the characteristics distinct to this transition period, referred to as the "transition" phase by the atmospheric science community (e.g., Ruppert & Johnson, 2016).The MJO transition phase is characterized by an increase in cumulus congestus clouds and increasing rainfall relative to the suppressed phase, but without the strong westerly winds and deep convection evident during the active phase (Johnson et al., 1999;Moum et al., 2014;Thompson et al., 2019).
During the MJO transition phase, the vertical structure of ocean mixing is distinctly different from that observed during either the MJO suppressed or active phases (Pujiana et al., 2018;Thompson et al., 2019).The oceanography community refers to this period as the "disturbed" phase.For reasons that will become evident later in study, we hereafter refer to the MJO transition phase as the disturbed phase, since the emphasis of this study is the ocean's influence on the MJO.
Increased rainfall during the MJO disturbed phase deposits relatively colder, fresher, and less dense rain water on the ocean surface.Because wind speeds remain low to moderate during the disturbed phase, the less dense rain water frequently acts to stably stratify the upper ocean, forming near-surface rain layers (RLs; e.g.Asher et al., 2014;Drushka et al., 2016;Reverdin et al., 2012;Shackelford et al., 2022;Thompson et al., 2019;Wijesekera et al., 1999).Unlike DWLs, which are stabilized by a temperature gradient, RLs are stabilized by a salinity gradi ent and are more resistant to destruction via nocturnal convection (Thompson et al., 2019).While DWLs and RLs can occur during all MJO phases, and can be present simultaneously, DWLs are most frequent during the MJO suppressed phase and RLs are most frequent during the MJO disturbed phase (Shackelford et al., 2022;Thompson et al., 2019).During the MJO active phase, the stabilizing buoyancy flux from surface heat and freshwater inputs is typically insufficient to withstand mixing by strong surface winds (Moum et al., 2014;Shackelford et al., 2022;Thompson et al., 2019).Thus, the ocean frequently becomes well-mixed to the thermocline with a diurnally uniform SST during this period.
Ocean turbulent heat fluxes feed back to MJO convection through SST variability that is largely driven by MJO forcing and regulated by ocean stable layers.Anomalous high SST in DWLs during the suppressed phase enhances turbulent heat fluxes and reduces convective inhibition.This effect initiates convection and facilitates column moistening that "preconditions" the free troposphere to deep convection prior to the active MJO (Ruppert Jr. & Johnson, 2016).Additionally, increased SSTs ahead of MJO convection may support propagation and maintenance of MJO convection by enhancing surface fluxes and frictional moisture convergence (Wang & Rui, 1990a;de Szoeke et al., 2015;DeMott et al., 2016;Zhang & Anderson, 2003;Hudson & Maloney, 2022).SST gradient-induced moisture convergence may also play a role in recharging moist static energy prior to the active MJO (de Szoeke & Maloney, 2020).
The importance of ocean feedbacks to MJO convection is evidenced by improved representation of the MJO in coupled versus uncoupled model simulations (e.g., DeMott et al., 2015DeMott et al., , 2019;;Kemball-Cook et al., 2002;Woolnough et al., 2000Woolnough et al., , 2007;;Zhang et al., 2006).In coupled simulations, high vertical resolution in the upper ocean and frequent ocean-atmosphere coupling further improve MJO representation, with the improvement in both cases attributed to better resolving the SST diurnal cycle (Bernie et al., 2005;Woolnough et al., 2007;Zhao & Nasuno, 2020).

10.1029/2023JD039272
3 of 22 While ocean feedback to the MJO via DWLs is well documented (Bellenger et al., 2010;de Szoeke et al., 2021;Ruppert Jr. & Johnson, 2016;Woolnough et al., 2000Woolnough et al., , 2007)), the feedbacks associated with near-surface RLs to MJO convection are less explored.Regular observation of RLs has been limited by the coarse vertical resolution and infrequent sampling of buoys and Argo floats.Thus, most observations of RLs have been collected with ship-based measurements (Asher et al., 2014;Drushka et al., 2019;Iyer & Drushka, 2021;Thompson et al., 2019) and drifters equipped to profile the near-surface ocean (Reverdin et al., 2012), hindering observational analysis of RL feedbacks to the atmosphere.
Because of observational constraints, RL characteristics as a function of meteorological surface forcing and ocean background state are often described using idealized, single-column model experiments (Drushka et al., 2016;Iyer & Drushka, 2021).However, the idealized, 1D nature of these ocean simulations provide limited information on RL behavior under realistic surface forcing and on RL feedbacks to the atmosphere.Shackelford et al. (2022) studied RL formation under realistic atmospheric conditions by forcing a 2D array of 1D ocean column models using output from a convection-permitting simulation of the November 2011 DYNAMO event.Their findings are consistent with in situ observations of RLs analyzed by Thompson et al. (2019), and corroborate the results of previous model experiments (Pei et al., 2018) that RLs reduce local SST through the surface input of cold rain and sustain and enhance SST reductions through a stable salinity stratification that confines wind-driven evaporative cooling to the near-surface RL.Shackelford et al. (2022) also demonstrated the role of RLs in enhancing small-scale SST gradients that induce pressure perturbations in the atmospheric boundary layer and potentially excite atmospheric convection (Back & Bretherton, 2009;Li & Carbone, 2012;Lindzen & Nigam, 1987).Additionally, Pei et al. (2018) demonstrated that RLs may produce a slight subsurface ocean heating effect below the RL base.We hypothesize that this presents another potential mechanism for RLs to influence the atmosphere, in which statically stable RLs isolate the subsurface ocean from the atmosphere until wind mixing erodes RLs and exposes the atmosphere to previously shielded subsurface warm water.The incomplete understanding of RL feedbacks to the atmosphere motivates the following questions.
1. What is the relative importance of RL generated SST gradients and RL-induced SST reduction in RL feedbacks to the atmosphere? 2. How does the frequent separation of the subsurface ocean and the atmosphere by RLs during the MJO disturbed phase feed back to MJO convection?
This study utilizes a regional coupled ocean-atmosphere model to investigate the nature of RL feedbacks to the atmosphere.Section 2 provides details on the model and our simulations.Feedbacks to the atmosphere by SST gradients and reduced SST in RLs are analyzed in Section 3, with an overall focus on how these effects vary as a function of MJO phase.We discuss the significance of these results in Section 4 before presenting a concise summary and final conclusions in Section 5.

Methods
A description of the Scripps-KAUST Regionally Integrated Prediction System (SKRIPS) is provided in Section 2.1.SKRIPS simulations used to evaluate RL feedbacks to the atmosphere are outlined in Section 2.2.

SKRIPS Model
The Scripps-KAUST Regionally Integrated Prediction System (SKRIPS) is a regional ocean-atmosphere coupled model developed in a collaborative effort between Scripps Institute of Oceanography and the King Abdullah University of Science and Technology (Sun et al., 2019).SKRIPS is comprised of an atmospheric solver, the Weather Research and Forecasting model (WRF; Skamarock et al., 2019), an ocean solver, the MITgcm (Marshall et al., 1997), and a coupler, the Earth Systems Modeling Framework (ESMF) coupled driver (Hill et al., 2004).The ESMF component is a two-way coupler that receives near-surface atmospheric variables (10-m u-and v-wind components, 2-m temperature and specific humidity, turbulent and radiative heat fluxes) and ocean surface conditions (SST and ocean surface velocity) that are then used to update the MITgcm surface forcing and WRF lower boundary conditions, respectively (Sun et al., 2019).Surface turbulent heat fluxes are computed by WRF using the COARE bulk flux algorithm (Fairall et al., 1996(Fairall et al., , 2003) ) and then passed to MITgcm by the coupler.SKRIPS output has been previously validated against atmosphere and ocean observations and reanalysis products in 30-day simulations of extreme heat events in the Red Sea region (Sun et al., 2019), and in 14-day hindcasts of atmospheric river events over the Pacific Ocean (Sun et al., 2021). 10.1029/2023JD039272 4 of 22 SKRIPS currently cannot account for the temperature of rain that falls onto the ocean surface, so rain temperature is effectively the same as that of the SST.In reality, the temperature of rain is more typically that of the near-surface wetbulb air temperature, which can be several °C cooler than the SST (Gosnell et al., 1995).The warm bias of rain temperature in SKRIPS could potentially over-stabilize the upper ocean and exaggerate the effects of RL feedbacks to the atmosphere.We compared near-surface temperature and salinity stratification in our SKRIPS simulation to that in a simulation of a 1D ocean mixing model with rain temperature set to the wetbulb temperature (Shackelford et al., 2022).The differences in temperature stratification between SKRIPS and the 1D model are small, and rain-driven changes to salinity stratification are much greater than rain-driven changes to temperature stratification in both SKRIPS and the 1D model.This is consistent with the findings of Thompson et al. (2019), which showed that positive buoyancy induced by rain freshening is an order of magnitude larger than negative buoyancy induced by rain cooling, and thus, warm rain temperature does not negatively influence the results of our study.

Model Experiments
We investigate RL feedbacks to the atmosphere by running a 29-day SKRIPS simulation over the tropical Indian Ocean from November 1-30, 2011.This time period and location coincides with the November 2011 MJO event that was observed and studied during the Dynamics of the Madden-Julian Oscillation field campaign (DYNAMO; Yoneyama et al., 2013) The model is configured for a 10° by 10° domain centered on 75°E and 2.5°S (Figure 1), with 2 km horizontal grid spacing in both the ocean and atmosphere.The 2 km horizontal grid spacing supports a convection-permitting WRF simulation.At convection-permitting scales (1-4 km), horizontal grid-spacing begins to approach the size of individual convective elements, "permitting" the removal of convective parameterizations from model simulations (Lucas-Picher et al., 2021).The fine-scale horizontal grid spacing of these simulations provides a detailed depiction of both atmospheric convection and the upper ocean temperature and salinity response to rainfall, both of which are critical in evaluating RL influence on the atmosphere.
Vertically, MITgcm is initialized on a stretched grid of 78 levels to a depth of 69.1 m, with 10 cm grid-spacing in the upper 2 m of the ocean and a telescoping vertical grid below 2 m.The MITgcm time step is 60 s and sub-grid scale horizontal mixing is parameterized using nonlinear Smagorinsky viscosities, while sub-grid scale vertical mixing is parameterized using the K-profile parameterization (Large et al., 1994).WRF is initialized with 35 vertical sigma levels and a model top of 50 hPa.A summary of WRF parameterizations can be found in Table 1.Initial and boundary conditions are provided by ERA-5 for the atmosphere (Hersbach et al., 2020) and Hybrid Coordinate Ocean Model (HYCOM; Chassignet et al., 2007) reanalyzes for the ocean, with lateral boundary forcing applied to both every 3 hr.WRF-MITgcm coupling frequency is set to 60 s, at which point WRF lower boundary forcing and MITgcm surface forcing are updated and applied.
To investigate the impact of RLs on the atmosphere, we conduct a second simulation over this domain with an identical model setup except that precipitation flux passed from WRF to MITgcm by the ESMF coupler is set to 0.0 at every time step.Therefore, in this second simulation, precipitation generated by WRF is prevented from falling on the ocean surface.We refer to the control experiment as RL and this second simulation as no-RL.

RL Feedbacks to the Atmosphere
Here, we investigate two pathways in which RLs have the potential to influence the atmosphere.The first is the "SST gradient effect," wherein RL-induced SST gradients induce locally enhanced boundary layer convergence and divergence patterns that can regulate convective initiation (Li & Carbone, 2012, Section 3.1).The second, the more general "SST effect," describes both the direct effect of local SST reduction within RLs on atmospheric convection, and the delayed effect RL static stability may have on SST, and turbulent heat fluxes, by isolating the subsurface ocean from the atmosphere (Section 3.2).

The SST Gradient Effect
The SST gradient effect refers to the hydrostatic adjustment of the marine boundary layer to SST gradients that force pressure-induced wind accelerations and drive patterns of low-level convergence and divergence (Back & Bretherton, 2009;Li & Carbone, 2012;Lindzen & Nigam, 1987).While SST gradients that exist on large spatial scales (≥100 km) and long time scales (≥1 day) are accepted as a frequent precursor to atmospheric convection, the transient nature and smaller-scale of rain-induced SST gradients have presented challenges in evaluating their impact on the atmosphere.We expect RLs to sharpen SST gradients in the RL simulation compared to the no-RL simulation during the MJO suppressed and disturbed phases.In the atmosphere, locally enhanced boundary layer convergence from RL-induced SST gradients could lead to convective initiation, in a manner similar to that shown by Li and Carbone (2012) for SST gradients on 25 km scales.An increase in the frequency of strong vertical updrafts in the RL simulation during MJO suppressed and disturbed phases would be indicative of the RL-SST gradient-convergence-convection feedback.
Li and Carbone (2012) showed theoretically that, for the West Pacific warm pool, the time derivative of surface wind divergence is proportional to the Laplacian of the SST field (∇ 2 SST).Hence, we compute ∇ 2 SST for both RL and no-RL at each grid cell to evaluate the role of RLs in generating and enhancing spatial SST gradients.∇ 2 SST is computed with adjacent grid cells using a 5-point stencil, and ∇ 2 SST distribution for the two simulations composited by MJO phase can be seen in Figure 2. To quantify differences in the two distributions, we take the median of the absolute value of ∇ 2 SST as an approximation of the width parameter of the underlying distribution, which reveals roughly a factor of two increase in the ∇ 2 SST width parameter for RL (0.029) compared to no-RL (0.014) over the entire simulation.The factor of two increase in ∇ 2 SST width parameter is consistent with findings of similarly constrained experiments conducted in an ocean environment with 1-dimensional dynamics (Shackelford et al., 2022).RL enhancement of SST gradients is most pronounced during the disturbed MJO, when ∇ 2 SST width parameter is nearly tripled in RL (0.048) compared to no-RL (0.017), while SST gradients in both simulations were greatly reduced during the active phase with RL and no-RL ∇ 2 SST width parameters less Longwave radiation Rapid radiative transfer model for GCMs (Iacono et al., 2008) Shortwave radiation Rapid Radiative Transfer Model for GCMs (Iacono et al., 2008) Microphysics scheme Morrison 2-moment (Morrison et al., 2005) PBL scheme Mellor-Yamada-Nakanishi-Niino (Nakanishi & Niino, 2009) Surface layer Revised MM5 scheme (Jiménez et 2).Comparisons of RL and no-RL ∇ 2 SST distributions in the form of a Kolmogorov-Smirnov test indicates that differences between the two distributions are significant at a 95% confidence threshold across all three MJO phases (not shown).
RL feedback to the atmosphere through the SST gradient effect is evaluated by viewing the temporal coincidence between enhanced SST gradients and enhanced low-level convergence and divergence.Figure 3 displays time series of (from top to bottom): ∇ 2 SST spatial variance for RL and no-RL, 10 m divergence spatial variance for RL and no-RL, and percent change in 10 m divergence variance.Time series of ∇ 2 SST variance for RL and no-RL corroborate the findings of Figure 2 that RLs broaden the distribution of ∇ 2 SST during the MJO suppressed and disturbed phases.The suppressed phase also features a 4 day period (11/05-11/09) in which 10 m divergence variance is roughly 5%-10% larger in RL than no-RL (Figure 3), and total accumulated rainfall is 6.2% higher in RL than no-RL (not shown).We revisit the coincident increase in rainfall and low-level divergence variance in the discussion section.This period coincides with increased ∇ 2 SST variance in RL, consistent with our understanding that SST gradients can enhance boundary layer convergence and excite atmospheric convection.
Figure 2 demonstrates that SST gradients are largest in RL during the disturbed phase, and differences in ∇ 2 SST variance between RL and no-RL are also most evident during the disturbed phase (Figure 3).However, 10 m divergence variance is reduced in RL relative to no-RL during the disturbed phase, suggesting that RL-induced SST gradients may only influence the atmosphere during the suppressed phase.We attribute the contrasting feedback of SST gradients between the suppressed and disturbed phases to changes in free tropospheric forcing between these two periods.In the suppressed phase, free troposphere forcing on the atmospheric boundary layer (e.g., latent heating above the trade wind inversion, downward momentum mixing, entrainment) is weak, thus, the influence of SST gradients on surface wind convergence/divergence is detectable.In the disturbed phase, free troposphere forcing on the atmospheric boundary layer is enhanced and free troposphere contributions to surface convergence/divergence overwhelm boundary layer contributions to surface convergence/divergence.SST gradients in the active phase are small in both simulations, and therefore not expected to feed back to the atmosphere (Figure 2).The influence of RL-driven SST gradients on horizontal organization of convection was evaluated using the organizational index (I org ), but results from this analysis were inconclusive (not shown).

The SST Effect
The SST effect refers to two distinct mechanisms in which RLs have the potential to influence the atmosphere by modifying SST.The direct SST effect results from RLs reducing SST locally through a stable salinity stratification that shoals ocean mixed-layer depth and confines evaporative cooling to a thin, near-surface layer.We expect the direct SST effect to be most pronounced during the MJO disturbed phase when RLs are frequently present and may hinder the development of atmospheric convection by reducing SST.The delayed SST effect arises from statically stable RLs isolating the subsurface ocean from the atmosphere.This separation of the subsurface ocean and atmosphere confines air-sea interaction to a near-surface cool layer, and limits exchange between the atmosphere and subsurface ocean heat in the presence of RLs.We expect the delayed SST effect to amplify MJO convection when surface winds are sufficiently strong to erode the RL and expose warm subsurface water to the atmosphere.

RL Influence on SST and the Surface Energy Budget
To evaluate the SST effect, it is useful to begin by viewing upper ocean stability in the RL simulation as a function of MJO state.Figure 4   The MJO suppressed phase is characterized by infrequent rainfall, low winds, and high amounts of solar radiation impinging upon the ocean surface (Figure 4).Upper ocean stability is dominated by a diurnal cycle in   2  and   2  + , driven by daytime stabilization through DWLs and nocturnal convection mixing upper ocean heat downward and deepening the ocean mixed layer.Sparse precipitation during the suppressed phase results in a generally well-mixed upper ocean with respect to   2  , but low wind speeds enable the upper ocean to become readily stabilized during occasional periods of enhanced rainfall (e.g., 11/04, 11/13).
The MJO disturbed phase features increasing rainfall, decreasing downwelling solar radiation, and gradually increasing wind speeds (Figure 4).This corresponds to an upper ocean that is frequently stably stratified near the surface with respect to ), which allows the instability in the temperature stratification to persist within the overall statically stable column.While DWLs are present during the disturbed phase, their amplitude and frequency are reduced.The MJO active phase is signified by a rapid increase in wind speeds followed by two large pulses of rainfall on November 26 and 28 (Figure 4).The convective envelope of the November 2011 MJO event consisted of two convectively coupled Kelvin waves, resulting in the double pulses in wind speed and rain rate in Figure 4 during the MJO active phase (Moum et al., 2014(Moum et al., , 2016)).While a brief relaxation in wind speed between the two pulses on November 27th allowed for transient, weak stabilization in both   2  and   2  , wind bursts at the leading edge of the two Kelvin waves induced turbulent mixing in the upper ocean that inhibited the formation of near-surface stable layers.
To quantify the effect of RLs on SST and their feedback to the atmosphere over the MJO lifecycle, we return to comparisons between RL and no-RL simulations.Figure 5 displays time series of domain mean values for rain rate, wind speed, sea surface salinity (SSS), SST, SST difference (SST RL -SST no−RL ), and net surface heat flux difference (Q net;RL -Q net;no−RL ).Note that Q net > 0 represents heat flux into the ocean, while Q net < 0 represents heat flux into the atmosphere.While wind speed and moisture flux convergence (and hence rainfall) are constrained by boundary forcing and therefore appear similar in the two simulations, differences in SSS, SST, and Q net are more evident.Since differences in SSS between the two simulations are expected, we focus on differences in domain mean SST and Q net between RL and no-RL.
The SST difference time series reveals two clear signals as a function of MJO phase.First, lower domain average SST in RL relative to no-RL during the MJO disturbed phase (−0.029K), and second, higher domain average SST in RL relative to no-RL during the MJO active phase (+0.022K).Reduced SSTs with RLs develop during the disturbed phase despite +3.29 W m −2 more domain averaged ocean heating in RL than in no-RL (Figure 5).The disturbed phase SST reduction in RL is the result of frequent RL presence concentrating evaporative cooling in thin, near surface RLs (Shackelford et al., 2022).The physical explanation for higher SSTs in RL during the MJO active phase, however, is not consistent with surface forcing, as the mean net surface heat flux is reduced in  RL compared to no-RL (−0.45 W m −2 ).SST difference between RL and no-RL during the MJO disturbed phase is on the same order of magnitude as the standard error of domain mean SST, but standard error is larger than SST difference for all three MJO phases (not shown).We suspect this is more reflective of the relatively small effective sample size provided by a single MJO event, rather than the significance of SST differences between RL and no-RL.Additionally, SST differences of ∼0.03 K represent approximately 10%-15% of the SST range throughout composite MJO events (0.2-0.3 K; DeMott et al., 2016), indicating that RL-induced SST changes modulate MJO SST range by 10%-15%.
To better understand how RLs affect the net surface energy budget, we further investigate how each component of Q net changes between RL and no-RL simulations for each MJO phase.Table 2 displays the RL simulation mean value (   ), RL minus no-RL absolute change (Δ), and RL minus no-RL percent change (%Δ) of rain rate, SST, Q net , net surface shortwave heat flux (SW net ), net surface longwave heat flux(LW net ), latent heat flux (LHF), sensible heat flux (SHF), and cold cloud fraction (CCF; defined as the fractional area where OLR < 115 W m −2 ) as a function of MJO phase.During the MJO suppressed and disturbed phases, differences in SW net , LW net , LHF, and SHF between RL and no-RL are all positive, indicating that all Q net components enhance ocean heating and/or reduce ocean cooling in RL.However, SW net changes are the dominant effect, accounting for 66% and 59% of total Q net changes during the suppressed and disturbed phases, respectively.RL shoaling of the ocean mixed-layer depth allows approximately 50% (1 W m −2 ) of the additional SW net in RL to penetrate below the mixed-layer (Paulson & Simpson, 1977) and heat the subsurface ocean.We attribute the increase in SW net with RLs to the 2.05% and 3.38% reductions in CCF during suppressed and disturbed conditions that allow more downward solar radiation to reach the surface in RL than in no-RL.RL minus no-RL changes to all Q net component terms are roughly 1 W m −2 (1%) or less (Δ and %Δ columns in Table 1) during suppressed and disturbed conditions.Changes to Q net itself, however, are larger, with an additional 1.25 W m −2 (+1.93%) ocean surface warming during suppressed conditions, and an additional 3.29 W m −2 (+21.7%)ocean surface warming during disturbed conditions.The implications of these RL-induced changes to Q net are discussed further in Section 4.
Changes to CCF and Q net with RLs during active conditions are opposite to those observed during the suppressed and disturbed conditions.In the active phase, CCF increases 3.05% and Q net decreases by 0.45 W m 2 (0.69%).In contrast to suppressed and disturbed conditions, however, the decrease in Q net is dominated by the combined changes in LHF and SHF, indicating greater ocean cooling in RL than in no-RL.Interestingly, active phase SW net is larger in RL than in no-RL, despite the greater CCF in RL.We speculate that this could be the result of changes to convective organization with RLs, but more work is needed to understand this aspect of RL feedbacks to the atmosphere.

RL Influence on Ocean Heat Content
Here, we present additional evidence that RL effects extend beyond the ocean surface.Particularly, they also regulate ocean heat content and the development of convection throughout the MJO lifecycle.
Figure 6 displays a vertical profile of domain mean ocean temperature and salinity difference between RL and no-RL.RL signatures can first be identified as instances of lower near-surface ocean temperature and salinity in RL during the MJO suppressed phase.During the MJO disturbed phase, these signatures increase in magnitude and frequency, reflecting the increasing presence of RLs as the MJO transitions from a convectively suppressed to convectively active state.Since RLs inhibit vertical mixing of surface waters with those of the deeper ocean (Reverdin et al., 2012;Shackelford et al., 2022;Thompson et al., 2019), cooling by surface evaporation in RL remains trapped near the ocean surface.Meanwhile, the reduced vertical mixing below the RL combined with the additional ∼1 W m −2 shortwave radiation that penetrates below the RL base amplify subsurface warming to a depth of about 40 m relative to the no-RL simulation.Offline calculations (not shown) indicate that enhanced SW net penetrating below the RL base in RL accounts for 43% of the enhanced ocean heating between 2 and 40 m, while reduced vertical mixing below the RL base accounts for the other 57%.Below 40 m, the ocean is relatively cooler in RL with little salinity change, as the reduction of vertical mixing by RLs limits the vertical extent of downward mixing of heat and freshwater.The subsurface ocean near 40 m is thus stabilized, which reduces the entrainment of colder ocean water below 40 m in RL and further helps confine heat to the 2-40 m layer.This sequence represents a classic example of barrier layer formation by surface freshening (Cronin & McPhaden, 2002;McPhaden et al., 1988;Sprintall & Tomczak, 1992;You, 1998).
With the arrival of the MJO active phase, RLs are eroded and subsurface ocean heat previously trapped beneath the surface during the disturbed phase is mixed to the ocean surface, raising SST in RL relative to no-RL.Thus, the accumulation of subsurface heat in RL during the disturbed phase, and it's later release to the ocean surface during the active phase, presents a delayed pathway for the SST effect to feed back to MJO convection.
We quantify changes in subsurface ocean heat content (OHC) between RL and no-RL by computing OHC from 0 to 70 m for both simulations.Figure 7 shows a time series of OHC from 0 to 70 m for RL (top), OHC change at each time step for RL (δOHC; middle), and difference in OHC change between RL and no-RL (ΔδOHC; bottom).The evolution of OHC in the RL simulation (Figure 7, top) shows that the gain, maintenance, and loss of OHC is distinct across the three MJO phases.OHC increases monotonically during the suppressed phase, increases at a slower rate during the disturbed phase, then decreases during the active phase with the onset of strong winds.The difference in OHC change between RL and no-RL (ΔδOHC) also reveals a systematic regulation of ocean heat uptake by RLs across the three MJO phases.For the later half of the suppressed phase and the duration of the disturbed phase (11/10-11/24), ΔδOHC is positive.This indicates that RLs allow the ocean to store more heat in RL than no-RL during this period by isolating the subsurface ocean from the effects of surface cooling.As the MJO transitions to the active phase, ΔδOHC begins to decrease and become negative as a portion of the excess stored ocean heat in RL during the suppressed and disturbed phases is lost to the atmosphere through enhanced surface fluxes (Table 2).The large increase in ΔδOHC on 11/03-11/04 (Figure 7) is associated with a short-lived, isolated convective disturbance in the northern region of the domain and is not associated with the large-scale envelope of MJO convection.
The physical mechanism for increased subsurface OHC in RL relative to no-RL becomes evident upon inspection of domain mean ocean stability profiles.Figure 8   the bottom of the uppermost stable layer (e.g., mixed-layer depth).We define an ocean layer as "stable" when   2  + > 0.0001.During the MJO suppressed phase, upper ocean stability exhibits a strong diurnal cycle in both RL and no-RL, as DWLs shoal the ocean mixed-layer during the day and nocturnal convection deepens the ocean mixed-layer overnight.However, occasional RLs during the suppressed phase reduce the frequency and duration of nocturnal convection in RL, which allows for subsurface OHC to accumulate in RL relative to no-RL.As the MJO transitions from suppressed to disturbed conditions, this effect becomes more apparent, when more frequent RLs stabilize the upper ocean and confine the ocean mixed-layer depth to <∼4 m in RL.Because RLs are so  (Thompson et al., 2019).This allows for the accumulation of subsurface ocean heat in RL relative to during the MJO suppressed and disturbed phases.With the arrival of the MJO active phase, the upper ocean is generally well-mixed by wind in both RL and no-RL, with some transient stabilization present during the lull between the two Kelvin waves (Figure 8).

RL Feedbacks to MJO Convection
To this point, it remains unclear if RL-induced changes to SST and OHC influence the structure and organization of convection.Qualitative comparisons of domain mean rain rate time series between RL and no-RL are inconclusive (Figure 5) and total accumulated rainfall in the two simulations is similar (∼1% less total rainfall in RL).To expand our investigation of RL feedbacks to convection over the MJO lifecycle, we evaluate select atmospheric variables as a function of both MJO phase and rain rate.Figure 9 shows, for the RL simulation and each MJO phase, from top row to bottom row: rain rate frequency, fractional contribution to total rainfall by rain rate, and mean OLR as a function of rain rate.Very light rain rates (R < 0.01 mm hr −1 ) dominate the rain rate frequency 10.1029/2023JD039272 15 of 22 distribution during the MJO suppressed phase, but the distribution peak shifts toward higher rain rates (0.01 mm hr −1 < R < 1 mm hr −1 ) during the MJO disturbed and active phases.Fractional contribution to total rainfall by rain rate (Figure 9, middle row) varies little with MJO phase, although intermediate rain rates (1-10 mm hr −1 ) make a relatively larger contribution to total rainfall during the MJO active phase, while heavy rain rates ( > 10 mm hr −1 ) make a relatively smaller contribution.Mean OLR binned by rain rate decreases as rain rate increases for all MJO phases, with the lowest mean OLR values occurring during the MJO active phase.
We compute changes in rain rate frequency, fractional contribution to total rainfall by rain rate, and mean OLR by rain rate between RL and no-RL to asses the role of the SST effect in regulating convection across MJO phase.Figure 10 shows the same distributions as Figure 9, but as percent change per rain rate bin between RL and no-RL.For the same rain rate bins, cloud top temperatures in RL are higher than those in no-RL during the MJO suppressed and disturbed phases, while cloud top temperatures are lower in RL during the MJO active phase.This suggests that for the same rain rate, clouds in RL are shallower than no-RL during MJO suppressed and disturbed phases, and deeper during the MJO active phase.Figure 10 also shows that there is less rainfall in RL during the suppressed and disturbed phases and more rainfall in RL during the active phase.Furthermore, the underlying gradients generated by RL cool patches enhance boundary layer convergence over the RL-adjacent higher SST regions and facilitate the initiation of convection; and second, via the SST effect, wherein SST reductions within RLs reduced the buoyancy of plumes rising from the boundary layer, thereby limiting the vertical development of convection.
RLs and their associated SST gradients begin to form during the MJO suppressed phase, but are most prevalent during the MJO ocean disturbed phase, which corresponds to the atmospheric convection suppressed-to-deep transition phase.If the SST gradient mechanism is important for atmospheric convection, it would be reflected in more frequent and more vigorous convection in the RL simulation, as measured by an increase in cold cloud fraction (CCF) and a broadening of the distribution of vertical velocity (w) throughout the troposphere.Instead, RLs are associated with a decrease in CCF during MJO suppressed and disturbed phases (Table 2), and a narrowing of the w distribution for all heights during the MJO disturbed phase (Figure 11).The strongest evidence for the SST gradient effect is seen during the MJO suppressed phase in the broader w distribution with RLs below 5 km (Figure 11).We conclude that, while the SST gradient effect appears to invigorate shallow convection during the MJO suppressed phase when free tropospheric forcing is weak, it does not appear to enhance convection during the MJO disturbed/transition phase when free tropospheric forcing is enhanced.
The RL-affected direct SST effect, wherein cool RLs reduce SST and the vigor of atmospheric convection, appears to be the more important RL feedback pathway for convection, but this mechanism proved to involve unanticipated nuances of how the ocean regulates atmospheric convection.The lower SST (Figures 5 and 6; Table 2), reduced CCF (Table 2), and narrower w distribution (Figure 11) in RL during the MJO disturbed phase are all consistent with the direct SST effect.As previously noted in Shackelford et al., 2022, the stably stratified upper ocean in RLs reduces vertical mixing below the RL, subsequently leading to a warmer subsurface ocean in RL than in no-RL during the MJO disturbed phase (Figure 6).However, the disturbed phase also features a 22% increase in net surface heating in RL compared to no-RL (Table 2).Roughly half of this increase comes from increased net surface shortwave radiation into the ocean in RL (Table 2).We attribute the increase in net surface shortwave heating in RL to the reduction in CCF that allows more incoming solar radiation to reach the ocean surface.RL shoaling of the ocean mixed-layer depth allows the increased surface shortwave radiation to penetrate below the RL base and heat the subsurface ocean, while RL interruption of the diurnal cycle of nocturnal convection insulates subsurface heat from surface evaporative cooling (Figure 8).In essence, RLs cool the ocean surface while simultaneously warming the subsurface ocean (Figure 12).RLs thus act as a "cool lid" on the ocean surface that prevents the atmosphere from accessing subsurface ocean heat.
The direct weakening of convection by RLs and the associated subsurface ocean warming sets up the delayed SST effect.This mechanism is activated by the onset of westerly wind bursts that erode RLs and expose subsurface ocean heat content to the atmosphere that was previously shielded by disturbed phase RLs.The transfer of greater ocean heat content in RL to the atmosphere is reflected in greater CCF (Table 2) and a broader w distribution (Figure 11) in RL compared to no-RL during the MJO active phase.Through this feedback mechanism, RLs lead to more vigorous convection during the MJO active phase.
Our findings are relevant for understanding processes that regulate MJO periodicity and intensity.It is clear that RLs in our experiments delay the onset of deep convection, but then help maintain its intensity once developed.The delay in the onset of deep convection could slow the development of the east-of-convection atmospheric Kelvin wave response to heating and its associated low-level convergence that regulates MJO eastward propagation (Chen & Wang, 2020;Wang & Rui, 1990b;Wang & Xie, 1998), thus reducing MJO propagation speed compared to that of convectively coupled Kelvin waves (Roundy, 2020;Roundy & Frank, 2004;Wheeler & Kiladis, 1999).
Results of our study may also be relevant for understanding some common biases in MJO simulation with global coupled models.Most models tend to overestimate MJO eastward propagation speed and underestimate MJO intensity (Ahn et al., 2017;Ahn et al., 2020;Wang et al., 2018).Vertical resolution of the upper ocean in these models is typically 0(10 m) (Danabasoglu et al., 2020;Klingaman et al., 2011), which is not sufficient to capture the vertical salinity gradients formed by RLs.Hence, rainfall in these models is not likely to stratify the upper ocean, thus inhibiting the RL-induced surface cooling during the MJO disturbed/transition phase.These models, therefore, will not capture the RL-reduced SST during the MJO disturbed/transition phase, nor the subsequent reduction in CCF, increase in ocean surface shortwave heating, reduction in subsurface ocean vertical mixing, and enhancement of subsurface ocean heat.The lack of these RL-induced processes is consistent with a reduced MJO periodicity (i.e., more rapid eastward propagation) and reduced MJO intensity.
Improved MJO representation in coupled simulations with high resolution vertical grid-spacing in the upper ocean is typically attributed to better resolving the diurnal cycle in SST (Klingaman et al., 2011;Woolnough et al., 2007).We speculate that, in addition to resolving SST diurnal cycle and DWLs, resolving RL-induced SST changes may also be responsible for improved MJO simulation in these cases.Recent efforts to parameterize the effects of RLs on SST (Bellenger et al., 2016;Witte et al., 2023) may mitigate the need for fine ocean vertical resolution, and thus improve MJO simulation when these parameterizations are incorporated into coupled models.We speculate that refinements to ocean vertical resolution or adoption of RL parameterizations in coupled forecast models could also lead to improved forecasts of MJO teleconnections, as part of the challenge of these forecasts lies in correctly simulating the MJO itself (e.g., Wang et al., 2020).
RLs may also interact with other forms of convective organization.Previous studies have noted that ocean coupling may delay or inhibit convective aggregation (Coppin & Bony, 2018;Holloway et al., 2017;Wing et al., 2017), and some studies attribute this delay to SST gradients inducing low-level circulation patterns that oppose patterns favoring convective aggregation (Hogenegger & Stevens, 2016).Additionally, RL enhancement of SSTs during the MJO active phase is qualitatively consistent with similar experiments investigating the influence of salinity stratification on tropical cyclone (TC) intensity.For example, Balaguru et al. (2022) found that salinity stratification in a RL-type simulation led to weaker SST reductions beneath the TC compared to a no-RL-type simulation, and thus promoted TC intensification.Future work could focus on RL influence on convective organization, as well as the generality of RL formation and feedbacks in regions of more complex ocean dynamics and air-sea interactions, such as the Maritime Continent.

Conclusions and Summary
We used a regional coupled atmosphere-ocean model to demonstrate that ocean surface RLs influence the evolution of atmospheric convection over the Indian Ocean associated with the MJO.We conducted two model simulations to evaluate RL feedbacks to the atmosphere and MJO convection: one in which rainfall freshens and cools the ocean surface (RL), and a second in which rain freshening and cooling of the ocean surface is disabled The SST gradient effect refers to the hydrostatic adjustment of the atmospheric boundary layer to small-scale, rain-induced SST gradients, which has the potential to induce patterns of low-level convergence that excite atmospheric convection.Rain-induced SST gradients are most prominent during the MJO disturbed phase, as evidenced by a factor of four increase in the ∇ 2 SST width parameter in RL compared to no-RL.However, the disturbed phase features reduced 10 m divergence variance and a narrower distribution of vertical velocity (w) throughout the atmospheric column in RL compared to no-RL.The SST gradient effect is only detected during the MJO suppressed phase, when enhanced SST gradients with RLs coincide with increased low-level divergence variance and a broadened distribution of w below 5 km.
The SST effect refers to both the direct influence of RL-driven SST reductions on atmospheric convection, and the delayed influence that RL-induced upper ocean stabilization exerts on SST.The direct SST effect is readily apparent during the MJO disturbed phase, when RLs are frequently present and reduce domain mean SST by 0.03 K in RL compared to no-RL, leading to reduced cold cloud fraction (−3%) and a narrowing of the w distribution throughout the column.Concurrent with reduced SST in RL during the disturbed phase is a 0.15%-0.20%increase in upper ocean heat content (0-40 m) in RL relative to no-RL.Accumulated subsurface ocean heat in RL is isolated from the atmosphere by statically stable RLs until the arrival of westerly wind bursts at the onset of the MJO active phase erodes RLs and releases subsurface heat to the ocean surface, raising domain average SST by 0.02 K in RL compared to no-RL during the active phase.Higher SST in RL leads to increased CCF (+3%) and broader w distribution throughout the column relative to no-RL, thus presenting a delayed pathway in which RLs support the development of deep convection during the MJO active phase.

Figure 1 .
Figure 1.CMORPH daily average rainfall (mm) for November 2011.The 10° by 10° model domain is outlined in red and the inner model domain used for computing ocean stability profiles in Figure 4 is outlined in orange.

Figure 2 .
Figure 2. Top: distribution of sea surface temperature (SST) Laplacian for rain layer (RL) (purple) and no-RL (orange), composited column-wise by Madden-Julian Oscillation (MJO) phase.Bottom: change in SST Laplacian frequency (RL−no-RL), composited column-wise by MJO phase.Note that while difference in the MJO active phase RL and no-RL distributions appear quite large, both distributions are narrowly peaked around 0 and large SST gradients in both simulations are uncommon during MJO active phase.

Figure 4 .
Figure 4. Time series of mean values for rain layer simulation over 1° by 1° subdomain of: rain rate (mm hr −1 ), wind speed (m s −1 ), downwelling shortwave radiation at ocean surface (W m −2 ), the temperature component of the buoyancy frequency for the upper ∼4 m of the ocean (s −1 ), the salinity component of the buoyancy frequency for the upper ∼4 m of the ocean (s −1 ), total buoyancy frequency for the upper ∼4 m of the ocean (s −1 ).1° by 1° subdomain is centered within larger overall domain.Vertical lines separate Madden-Julian Oscillation phase.The N 2 color scale is consistent across   2  ,

Figure 6 .
Figure 6.Top: Time series of domain mean vertical ocean temperature profile difference between rain layer (RL) and no-RL (T RL − T no−RL ).Bottom: Time series of domain mean vertical ocean salinity profile difference between RL and no-RL (S RL − S no−RL ).Vertical lines separate Madden-Julian Oscillation phase, and the black contour in the lower panel represents the zero-difference line.

Figure 7 .
Figure 7. Top: time series of ocean heat content (OHC) and 24-hr running mean OHC for the entire ocean column (0-70 m) for the rain layer (RL) simulation.Middle: time series of 2-day running mean OHC change for each time step for the RL simulation (δOHC), displayed in units of W m −2 .Bottom: time series of 2-day running mean δOHC difference between RL and no-RL (ΔδOHC).The values in the bottom two panels represent mean values in δOHC and ΔδOHC for each Madden-Julian Oscillation phase.

Figure 8 .
Figure 8.Time series of domain mean   2  ,   2  , and   2  + for rain layer (RL) (top), and for no-RL (bottom).The solid lines marks the top of the uppermost stable layer, while the dashed line marks the bottom of the uppermost stable layer (e.g., mixed-layer depth).Note the depth intervals on the y-axis are displayed as a telescoping vertical grid.

Figure 9 .
Figure 9. From top row to bottom row: rain rate frequency, contribution to rainfall total by bin, and outgoing longwave radiation, all binned by rain rate and composited column-wise by Madden-Julian Oscillation phase.

Figure 10 .
Figure 10.Same as for Figure 9, but as percent change between rain layer (RL) and no-RL.

Figure 12 .
Figure 12.Schematic illustration of the time evolution of ocean stability and rain layer feedbacks to the Madden-Julian Oscillation (MJO) during the November 2011 MJO event from a Eulerian viewpoint.MJO phase is denoted by the colorbar and time moves from left to right.While the November 2011 MJO event is shown here, the physical mechanisms also broadly apply to the MJO in general.
+ , reflecting the nearly constant presence of RLs during the disturbed phase.Note that for RLs in both the MJO suppressed and disturbed phases, salinity stabilization ( ). 1° by 1° subdomain is centered within larger overall domain.Vertical lines separate Madden-Julian Oscillation phase.The N 2 color scale is consistent across 2  + (see colorbar in   2  time series).

Table 2
Mean Value in Rain Layer (RL) Simulation ( Rain Rate (R), Sea Surface Temperature, Net Surface Heat Flux (Q net ), Net Surface Shortwave Heat Flux (SW net ), Net Surface Longwave Heat Flux (LW net ), Latent Heat Flux, Sensible Heat Flux, and Fraction of Domain Occupied by Cold Cloud Tops (CCF; OLR <115 W m −2 ) ), Absolute Change Between RL and no-RL Simulation (Δ; RL−no-RL), and Percent Change Between RL and no-RL (%Δ;  RL−no-RL RL) as a Function of Madden-Julian Oscillation Phase for (Top to Bottom): shows time series of domain mean  + for the two simulations, with solid black lines marking the top of the uppermost ocean stable layer and dashed lines marking