Mean State Biases and Interannual Variability Affect Perceived Sensitivities of the Madden‐Julian Oscillation to Air‐Sea Coupling

Atmosphere‐ocean feedbacks often improve the Madden‐Julian oscillation (MJO) in climate models, but these improvements are balanced by mean state biases that can degrade the MJO through changing the basic state on which the MJO operates. The Super‐Parameterized Community Atmospheric Model (SPCAM3) produces perhaps the best representation of the MJO among contemporary models, which improves further in a coupled configuration (SPCCSM3) despite considerable mean state biases in tropical sea surface temperatures and rainfall. We implement an atmosphere‐ocean‐mixed‐layer configuration of SPCAM3 (SPCAM3‐KPP) and use a flux‐correction technique to isolate the effects of coupling and mean state biases on the MJO. When constrained to the observed ocean mean state, air‐sea coupling does not substantially alter the MJO in SPCAM3, in contrast to previous studies. When constrained to the SPCCSM ocean mean state, SPCAM3‐KPP fails to produce an MJO, in stark contrast to the strong MJO in SPCCSM3. Further KPP simulations demonstrate that the MJO in SPCCSM3 arises from an overly strong sensitivity to El Niño–Southern Oscillation events. Our results show that simulated interannual variability and coupled‐model mean state biases affect the perceived response of the MJO to coupling. This is particularly concerning in the context of internal variability in coupled models, as many previous MJO sensitivity studies in coupled models used relatively short (20‐ to 50‐year) simulations that undersample interannual‐decadal variability. Diagnosing the effects of coupling on the MJO requires simulations that carefully control for mean state biases and interannual variability.


Introduction
The Madden-Julian oscillation (MJO; Madden & Julian, 1971) is a quasiperiodic (30-to 70-day), eastward propagating (≈5 m/s) mode of variability in the tropical climate system. Convective anomalies associated with the MJO are a key cause of rainfall variability throughout the tropics, including in the major monsoon regions (e.g., Lawrence & Webster, 2002;Lorenz & Hartmann, 2006;Wheeler et al., 2009). The associated circulation anomalies project strongly onto Zonal Wavenumber 1. At low levels, anomalous westerly winds are associated with the "active" (enhanced convection) phase of the MJO, while easterly anomalies are For more than 20 years, evaluations of climate-length simulations of general circulation models (GCMs) have concluded that GCMs struggle to represent the period, amplitude, and propagation speed of the MJO, as well as its effects on local and global circulation (e.g., Ahn et al., 2017;Hung et al., 2013;Jiang et al., 2015;Lin et al., 2008;Slingo et al., 1996;Zhang et al., 2006). Improvements to GCM representations of the MJO have come mainly from revising the subgrid-scale treatment of convection, particularly to increase the sensitivity of convection to free-tropospheric relative humidity (e.g., Hannah & Maloney, 2011;Hirons et al., 2013;Klingaman & Woolnough, 2014a). This reduces the erroneous tendency of convective parameterizations to produce excessive precipitation in anomalously dry regions, which leads to more intense MJO suppressed phases and stronger intraseasonal variability (ISV). These convective physics changes can degrade the simulated mean state, however, resulting in a tension between the simulated fidelity of ISV and the background climate (e.g., Benedict & Maloney, 2013;Johnson et al., 2015;Kim et al., 2011).
GCMs in which the conventional convective parameterization is disabled or replaced often produce an improved MJO. The parameterization is typically disabled only in sub-10-km resolution global or regional experiments (e.g., Holloway et al., 2013;Miyakawa et al., 2014). At coarser resolutions, so-called "superparameterized" (SP) GCMs replace inside each GCM grid box the parameterization with a two-dimensional cloud-resolving model that computes convective and radiative heating and moistening tendencies (Khairoutdinov et al., 2005). The SP configuration of the National Center for Atmospheric Research Community Atmospheric Model (SPCAM3) produces a coherent, eastward propagating MJO (Benedict & Randall, 2009), which improves with air-sea coupling in the Super Parameterized Community Climate System Model (SPCCSM3; Benedict & Randall, 2011;DeMott et al., 2014;Stan et al., 2010). SPCAM3 and SPCCSM3 were two of the highest-fidelity GCMs for the MJO in a comparison of 20-year climate simulations from more than two dozen models . DeMott et al. (2014) demonstrated that SPCAM consistently produced a stronger and more realistic MJO than the standard (non-SP) CAM, even when both models were driven by the same prescribed, interannually varying sea surface temperatures (SSTs) from SPCCSM3. We analyze the same SPCCSM3 simulation in this manuscript.
Air-sea coupling in GCMs often also improves the MJO (DeMott et al., 2015, and references therein), although these improvements are usually secondary to those from modified convective physics (e.g., Klingaman & Woolnough, 2014b). In particular, well-resolved air-sea interactions-subdaily (typically 3 hr) air-sea exchanges and a fine (typically 1 m) oceanic vertical resolution-are required to capture the intraseasonal thermodynamic oceanic response to atmospheric forcing. Coarser spatial or temporal resolutions fail to simulate the peak diurnal SST warming and mixed-layer shoaling during the MJO suppressed phase, which rectifies onto intraseasonal scales (e.g., Bernie et al., 2005Bernie et al., , 2008Klingaman et al., 2011;Tseng et al., 2015). While the oceanic dynamical response to MJO forcing may be important for the development of subsequent MJO events that have no obvious atmospheric precursors (Webber et al., 2010(Webber et al., , 2012, GCM experiments (e.g., Klingaman & Woolnough, 2014b;Tseng et al., 2015) and observational analysis (Halkides et al., 2015;Lau & Sui, 1997) show that most intraseasonal tropical SST variability can be recovered through thermodynamic air-sea interactions alone, particularly for regions more than ±3 • latitude from the equator. Recent comparisons of coupled (CGCM) and uncoupled (AGCM) configurations of four models, in which the CGCMs and AGCMs had identical SST climatologies, demonstrated coupling improved the MJO through enhanced mean meridional moisture gradients near the equator and strengthened convective moistening at high rain rates during the MJO active phase, helping to support equatorial convection and maintain column instability (DeMott et al., 2019). DeMott et al. (2019) included the same SPCCSM3 simulation that we analyze here.
In coupled GCMs with dynamical oceans, incorporating air-sea interactions inevitably leads to biases in the coupled mean state, such as cold SST biases in regions of excessive rainfall and associated strong turbulent fluxes into the atmosphere. These biases can degrade the simulated MJO by altering the background circulation and moisture fields to inhibit MJO propagation (e.g., Warm Pool easterlies rather than westerlies, cold 10.1029/2019MS001799 SST biases that limit convection and evaporation, reversals of mean zonal and meridional moisture gradients; Kim et al., 2017;Sperber et al., 2005;Zhang et al., 2006). Removing or damping these biases through flux corrections improves the MJO, demonstrating the strong control that the mean state exerts on subseasonal variability Seo et al., 2007). Klingaman and Woolnough (2014b) found that cold tropical mean SST biases in the coupled Met Office Unified Model (MetUM) were associated with a poor MJO. The SST biases also influenced the perceived effect of air-sea interactions: Air-sea coupling appeared to have no impact on the MJO under the CGCM ocean mean state, but coupling improved the MJO when the ocean mean state biases were reduced through prescribed flux corrections.
It is not clear why in some GCMs (e.g., SPCCSM3) the apparent benefits of air-sea coupling for the MJO outweigh the degradations, while in other models (e.g., MetUM) the degradations outweigh the benefits. For SPCCSM3 in particular, no study has separated the effects of mean state errors and intraseasonal air-sea feedbacks to the MJO, to address whether the MJO in SPCCSM3 benefits from some aspect of the background state that is sensitive to coupling. For the intraseasonal MJO, the background state includes not only the time-mean climate but also coupled modes of interannual variability, including the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), that influence tropical atmospheric and oceanic circulations. During El Niño, warm SSTs in the central Pacific encourage the MJO to propagate farther east (e.g., Tam & Lau, 2005;Woolnough et al., 2000); MJO events are also more frequent (e.g., Jones et al., 2004) and shorter-lived (Pohl & Matthews, 2007). Positive IOD events are linked to stronger MJO activity in the western Indian Ocean but limited propagation from the Indian Ocean to the Maritime Continent; negative IOD years show increased MJO activity in the eastern Indian Ocean (e.g., Wilson et al., 2013). Few studies have examined the effect on the MJO of CGCM biases in ENSO and IOD activity or of biases in teleconnections from these interannual modes to the MJO. Changes in these modes and their teleconnections represent another, potentially important, mechanism for air-sea coupling to influence the MJO. Further, previous studies of the SPCCSM3 MJO have identified the role of air-sea coupling MJO only under the biased SPCCSM3 mean state, by running "replay" experiments in which the SPCAM is forced by SPCCSM SSTs (DeMott et al., 2014). A more accurate assessment of the effects of coupling would compare coupled and atmosphere-only simulations under an SST mean state that is closer to observations, as recommended in DeMott et al. (2015).
We address the mechanisms by which coupling improves the MJO in SPCCSM3, using a set of experiments with a coupled atmosphere-ocean-mixed-layer configuration of SPCAM, in which the ocean mean state can be constrained to a target climatology. We employ this configuration to systematically isolate the effects of coupling on the MJO through (a) intraseasonal air-sea feedbacks, (b) mean state errors, and (c) ENSO activity. We describe this configuration, our experiments, and analysis techniques in section 2; identify the effects of coupling on the simulated MJO in section 3; discuss the implications of our results for future modeling studies of the role of coupling in the MJO in section 4; and summarize our key conclusions in section 5.

Models
We analyze simulations with three model configurations based on SPCAM, Version 3 (SPCAM3; DeMott et al., 2007;Khairoutdinov et al., 2005Khairoutdinov et al., , 2008: (a) an AGCM configuration (SPCAM3), in which SSTs and sea ice are prescribed as lower-boundary conditions; and two CGCM configurations in which SPCAM3 is coupled to (b) the Parallel Ocean Program (POP; Danbasoglu et al., 2006;Smith & Gent, 2004) three-dimensional ocean, which includes ocean dynamics (SPCCSM3; Stan et al., 2010) and (c) the Multi-Column configuration of the one-dimensional K Profile Parameterization boundary layer ocean model (MC-KPP; Large et al., 1994). We call (c) "SPCAM3-KPP" hereafter. In all simulations, we use T42L30 resolution: a triangular truncation at Wavenumber 42 in the horizontal (equivalent to ≈300 km at the equator) and 30 points in the vertical. The embedded cloud-resolving model in SPCAM3 is two-dimensional, with thirty-two 4-km-wide columns. In SPCCSM3, POP has a 10-m-thick top layer and exchanges SSTs and surface fluxes with SPCAM3 once per day. We focus the remainder of our discussion on SPCAM3-KPP, as the other configurations are documented in the studies above.
SPCAM3-KPP follows the design of the Global Ocean Mixed Layer coupled configuration of the Met Office Unified Model (MetUM-GOML; Hirons et al., 2015), in which one instance of KPP is placed under each atmospheric grid point. KPP uses a 1,000-m vertical domain, through which 100 points are unequally spaced, such that the vertical resolution is finest (≈1 m) near the surface, degrading to a constant 25 m through the lowest ≈700 m of ocean. Because KPP lacks ocean dynamics, SPCAM3-KPP must be constrained to a target ocean climatology. We use this capability extensively, including constraining SPCAM3-KPP to a multiannual climatology of alternating ENSO states, described below. The constraints are applied via corrections to ocean temperature and salinity, made at all vertical grid points in each coupled column and at each time step. These corrections are computed from a simulation in which SPCAM3-KPP is relaxed toward the target climatology with a timescale of 15 days. In all cases, the length of this "tendency simulation" is 10 times the length of the target climatology (e.g., 10 years for an annual climatology and 30 years for a 3-year climatology) to obtain a robust estimate of the required corrections. We store the temperature and salinity relaxation tendencies from this simulation, and then we compute a daily climatology of corrections of the same length as the target ocean climatology; the climatology is also smoothed with a 31-day running mean, to remove high-frequency variability. This mean seasonal cycle of corrections is applied as a periodic (in time) forcing in a second, "free simulation" that can be integrated effectively infinitely. The free simulation has no relaxation, which avoids damping variability. Hirons et al. (2015) and Peatman and Klingaman (2018) demonstrated that multidecadal free simulations using this correction method had very small SST biases against the target ocean climatology. The corrections represent the effect of the mean ocean dynamics in SPCAM3-KPP and counteract coupled-model drift from errors in atmospheric surface fluxes.
Unlike MetUM-GOML, in which MetUM and MC-KPP exchange fields via a flux coupler, in SPCAM3-KPP the KPP ocean is implemented as a subroutine within SPCAM3. KPP uses the same time step as SPCAM3 (15 min), although this is purely for ease of coupling the models, not for computational stability; SPCAM3 and KPP exchange coupled fields each time step. Since SPCAM3-KPP lacks a sea ice model, SPCAM3 and KPP are not coupled at "ice-covered" grid points, which are points where the sea ice concentration is ≥0.3 for ≥30 days/year for ≥3 years in the 1980-2009 data set from the Atmospheric Model Intercomparison Project (AMIP) component of the Coupled model Intercomparison Project Phase 5 (Taylor et al., 2012), which is derived from Hurrell et al. (2008). Zero ice cover is assumed at all coupled grid points, including those in which the AMIP data set contains ice cover below the threshold above. There is no coupling over inland basins, such as the Great Lakes, or over the Red Sea. At uncoupled points, climatological sea ice from the AMIP data set and SSTs from the target ocean climatology are prescribed. A five-grid point blending between modeled and prescribed SSTs is imposed at all boundaries between coupled and uncoupled regions, with linearly decreasing weight given to the modeled SSTs further away from the coupled region.

Simulations
We refer to all simulations using first the letters "SPA" for SPCAM3 with prescribed SST, "SPC" for SPCCSM3, and "SPK" for a SPCAM3-KPP. For SPCAM3 and SPCAM3-KPP, we then use a code to identify the SST boundary condition (for SPCAM3) or the target ocean mean state (for SPCAM3-KPP); these are explained below. Table 1 summarizes the experiments.
We analyze data from 20-year SPCAM3 and SPCCSM3 simulations provided to the "Vertical structure and physical processes of the MJO" model evaluation project , specifically the 20-year climate component . SPCAM3 (hereafter "SPA-AMIP") was forced with prescribed weekly SSTs and sea ice concentrations from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation V2 data set (Reynolds et al., 2002). The SPCCSM3 simulation ("SPC") is the same as in Stan et al. (2010).
For SPCAM3-KPP, we perform a 50-year simulation ("SPK-OBS") with KPP constrained to the 1980-2009 climatology from the Met Office (UKMO) ocean analysis (Smith & Murphey, 2007). To isolate the effects of intraseasonal air-sea feedbacks on the MJO in SPK-OBS, we extract the daily SSTs from SPK-OBS, smooth them with a 31-day running mean to remove high-frequency variability and prescribe those SSTs in a 50-year SPCAM3 simulation ("SPA-KOBS"). High-frequency variability is removed following the analysis of Pegion and Kirtman (2008) 2015), which found that high-frequency SSTs erroneously improved the simulated MJO due to an incorrect in-phase relationship between SSTs, surface fluxes, and rainfall. To isolate the effect of SPCCSM3 mean state SST errors on the MJO, we perform a 50-year SPCAM3-KPP simulation with MC-KPP constrained to the mean ocean state from SPC ("SPK-SPC"). To analyze the effects of intraseasonal air-sea feedbacks under the SPCCSM3 mean state, we extract the daily SSTs from SPK-SPC, smooth them with a 31-day running mean and prescribe them to SPCAM3 ("SPA-KSPC"). For each 50-year SPCAM3-KPP simulation, we first perform a 10-year simulation with relaxation, to compute the required climatological temperature and salinity corrections (section 2.1).
To isolate the role of the SPCCSM3 ENSO for the MJO (section 3.4), we partition SPC into three categories, based on terciles of the November-April (NDJFMA) mean Niño 3.4 SST index (SST anomalies averaged 5 • S to 5 • N, 180 • -240 • E; Figure 1). As there are only 19 November-April periods in the 20-year SPC simulation, we select the warmest six periods as "El Niño," the coldest six periods as "La Niña," and the remaining seven periods as "neutral." Mean seasonal cycles of ocean temperature and salinity are computed for each state, using May-April data to limit mixing ENSO phases. A 3-year composite ENSO cycle is formed by concatenating the 1-year climatologies for neutral, El Niño, and La Niña conditions, in that order. We perform a 30-year SPCAM3-KPP simulation with relaxation to this 3-year composite, to compute the mean 3-year cycle of temperature and salinity corrections necessary to maintain a target "mean state" of the repeating 3-year SPCCSM3 composite ENSO cycle. We then perform a 61-year SPCAM3-KPP simulation imposing those corrections ("SPK-ENSO") to obtain 20 complete 3-year cycles of May-April data. To test the sensitivity of the interannually varying ENSO signal on the MJO, we also perform a 50-year SPCAM3-KPP simulations constrained to a climatology of each phase of the SPC ENSO composite: El Niño (SPK-EN), La Niña (SPK-LN), and neutral (SPK-NN).

Methods
MJO propagation is evaluated through the standard technique of lag regressions of outgoing longwave radiation (OLR), which has first been filtered to an intraseasonal window (20-80 days, using a Lanczos filter with 181 weights) and latitude-averaged 10 • S to 10 • N. We use data for extended boreal winter, NDJFMA, because the MJO is most active during that period. We use regressions against a base point at 100 • E, approximately the eastern boundary of the Indian Ocean, to focus on propagation from the Indian Ocean through the Maritime Continent to the West Pacific. This is a strict test of models, which often fail to propagate the MJO beyond the Indian Ocean (e.g., Jiang et al., 2015). We compare MJO propagation and strength in simulations and observations with three metrics. For propagation fidelity, we use the average pattern correlation of the observed and simulated regression maps at 100 • E and 150 • E, masking the longitudes within 15 • of the base point. This tests MJO propagation through the Indian Ocean to the West Pacific . Masking the region near the base point avoids high correlations in simulations that produce a standing oscillation (Wang et al., 2017;DeMott et al., 2019). For propagation speed, we use the average of the time between the maximum regressions at 70 • E and 100 • E and between 100 • E and 130 • E. For strength, we use the standard deviation of 20-to 80-day filtered OLR in the box 10 • S to 10 • N, 90-100 • E. Metrics for all simulations and observations can be found in Table 2. Note. See the text for further details on the methods. Note that some data sets are analyzed for only one ENSO phase, which is noted in parentheses after the data set name. The pattern correlation of NOAA is 1.0 by definition.
To diagnose the influence of time-varying SSTs on the MJO in a CGCM, we employ the diagnostic framework of DeMott et al. (2016). In that study, the authors used a moist static energy (MSE) approach to understand the effect of variable SSTs on intraseasonal tropical convection. Using European Centre for Medium-range Weather Forecasts Interim reanalysis data (ERA-Interim), the authors decomposed the vertically integrated MSE budget (⟨m⟩) and its time rate of change ( ⟨m⟩ t ) to determine the contributions from the latent (LH) and sensible (SH) fluxes. Reynolds decomposition was employed to separate the thermodynamic (SST-driven) and dynamic (wind-driven) components of the fluxes. The contributions of ISV in SST were computed by recalculating LH and SH from 61-day smoothed SSTs, then projecting the full and smoothed fluxes onto ⟨m⟩ and ⟨m⟩ t ; the difference between these projections is the effect of SST ISV. Including the ISV in SST led to increased equatorial moistening and reduced off-equatorial moistening, favoring equatorial convection that would project strongly onto Kelvin wave modes.

Data Sets
Apart from the SST, sea ice and ocean temperature and salinity data sets mentioned above, we employ satellite-derived OLR data from NOAA Cooperative Institute for Research in Environmental Sciences data set for 1979-2013, available daily on a 2.5 • × 2.5 • grid. We use the same ERA-Interim reanalysis data as DeMott et al. (2016DeMott et al. ( ) (1986DeMott et al. ( -2013 to compute the "SST effect" on LH and SH. Observed SST data for 1979-2013 are taken from the NOAA OI data set discussed above (Reynolds et al., 2002).   SPC produces considerable cold SST biases throughout most of the tropics, both in NDJFMA (Figure 3a) and in the annual-mean (not shown). We compute biases against SSTs from the UKMO ocean analysis, as this is the climatology to which SPK-OBS is constrained and we wish to cleanly compare biases between SPC and SPK-OBS. SPC SST biases reach ≈-2.2 K west of the observed Pacific cold tongue region, the West Pacific warm pool, the Arabian Sea, and near the Maritime Continent. The pattern resembles an extended Pacific cold tongue. It weakens the zonal gradient of SST between the Indian Ocean and the Maritime Continent and enhances the zonal gradient between the Maritime Continent and central Pacific. The structure and magnitudes of the SST biases are remarkably similar to those from the MetUM "GA3-NEMO" simulation in Klingaman and Woolnough (2014b) (Figure 3b), which strongly damped the amplitude of the MetUM MJO. We return to the similarity between these mean states in section 4. SPC slightly underestimates ISV in equatorial SSTs (Figure 4c) relative to ERA-Interim (Figure 4a), with the greatest biases in the eastern equatorial Indian Ocean and northwest of Australia. ISV in precipitation is substantially overestimated, particularly in the western equatorial Indian Ocean, near the Maritime Continent, and in the South Pacific Convergence Zone (Figure 4d).

Air-Sea Coupling Under the Observed Ocean Mean State
First, we explore the tropical mean state and ISV in SPK-OBS, beginning with mean SST biases (Figure 3c) to establish that the temperature and salinity corrections effectively constrain SPCAM3-KPP to the target climatology, here from the UKMO ocean analysis. SST biases are smaller than ±0.5 K nearly everywhere and often smaller than from ERA-Interim (Figure 4a), with higher ISV in the Seychelles thermocline ridge in the western Indian Ocean, in the shallow seas between the Maritime Continent and Australia and across the equatorial Indian Ocean. Tropical SST ISV is improved over SPC (Figure 4c) throughout the domain, particularly near the Maritime Continent, in the western equatorial Indian Ocean and in the subtropics. This supports many past studies that have shown that SST ISV improves in CGCMs with high vertical resolution (≈1 m) and subdaily coupling frequency (e.g., Bernie et al., 2008;Klingaman et al., 2011;Tseng et al., 2015) and that most SST ISV is thermodynamically driven, particularly away from the equator (e.g., Halkides et al., 2015;Lau & Sui, 1997). Relative to ERA-Interim (Figure 4b), SPK-OBS overestimates ISV in tropical precipitation, especially south of the equator in the Indian Ocean and in the South Pacific Convergence Zone (Figure 4d). Mean precipitation is also overestimated in these regions (not shown). (Figure 2c), although the phase speed is faster than in NOAA ( Figure 2a) and SPC (Figure 2b). On average, the SPK-OBS MJO does not propagate as far into the West Pacific as in NOAA, but the extent of propagation is similar to SPC. These results suggest that the smaller SST biases and larger ISV in tropical SSTs in SPK-OBS relative to SPC do not materially alter the MJO.

10.1029/2019MS001799
To diagnose the effect of intraseasonal (periods <61 days) SSTs on the MJO MSE budget, we compute the "SST effect" diagnostic for LH and SH (combined; section 2.3). In ERA-Interim, intraseasonal SSTs maintain ⟨m⟩ on the equator and discourage off-equatorial ⟨m⟩ (Figure 5a); intraseasonal SSTs also support ⟨m⟩ t (equivalent to MJO propagation) in the eastern equatorial Indian Ocean and the West Pacific (Figure 5b; DeMott et al. (2016)). SPC displays a broadly similar pattern of SST effect for ⟨m⟩, with intraseasonal SSTs maintaining ⟨m⟩ in the equatorial Indian Ocean (Figure 5c). The effect of intraseasonal SSTs on ⟨m⟩ t is generally weaker in the equatorial Indian Ocean in SPC than in ERA-Interim, although the effect is still positive (Figure 5d). Intraseasonal SSTs also influence the LH and SH contribution to ⟨m⟩ in SPK-OBS (Figure 5e), although the effect does not extend as far into the eastern Indian Ocean as in SPC. When combined with the relatively small contribution to ⟨m⟩ t in the same region (Figure 5f), this may explain the somewhat weaker MJO propagation from the Indian Ocean to the Maritime Continent in SPK-OBS (Figure 2c). Indeed, SST ISV in SPK-OBS is small along the western coast of Sumatra, perhaps due to the lack in KPP of either wind-driven upwelling or warm-water advection by anomalous ocean currents in response to low-level anomalous easterly winds. SPK-OBS shows an increased subtropical SST effect relative to SPC, where the effect in SPC is too weak relative to ERA-Interim. This may be due to the increased SST ISV in SPK-OBS compared to SPC (Figure 4), which in turn may be associated with the increased oceanic vertical resolution or subdaily air-sea coupling in SPK-OBS. These diagnostics confirm that intraseasonal SSTs play a similar role in the MJO ⟨m⟩ budget in SPK-OBS as in SPC and that both simulations resemble the effect diagnosed from ERA-Interim.
The cleanest test of the effect of air-sea coupling in SPK-OBS is through comparison with the SPA-KOBS "replay" SPCAM3 simulation, in which the SPK-OBS 31-day smoothed SSTs are prescribed (e.g., DeMott et al., 2014;Klingaman & Woolnough, 2014b;DeMott et al., 2015). MJO propagation in SPA-KOBS is weaker than SPK-OBS, particularly from the Indian Ocean to the Maritime Continent, although the pattern correlation with NOAA is similar (Figure 2d). The MJO phase speed is slower in SPA-KOBS than SPK-OBS, bringing the speed closer to NOAA. Eastward propagation is still clearly evident, however, which confirms previous studies that found a robust MJO in SPCAM3 AMIP-type experiments (e.g., Khairoutdinov et al., 2008;DeMott et al., 2014). Smoothing the prescribed SSTs strongly damps ISV of SST in SPA-KOBS to less than half that in SPK-OBS (Figure 4g). This reduction is particularly severe in the eastern equatorial Indian Ocean, which may cause weak MJO propagation from the Indian Ocean to the Maritime Continent. Despite this reduction in SST ISV, SPA-KOBS produces slightly stronger precipitation ISV than SPK-OBS (Figure 4h), likely due to the tendency for AGCMs to generate excessive convection over warm intraseasonal SSTs relative to CGCMs, since the former lack negative local feedbacks through surface fluxes and SSTs (e.g., Pegion & Kirtman, 2008;DeMott et al., 2015;Hirons et al., 2018). These diagnostics suggest only modest effects of air-sea coupling on the MJO in SPCAM3 under a near-observed SST mean state, improving (increasing) MJO amplitude but degrading (quickening) propagation speed.

Air-Sea Coupling Under the SPC Ocean Mean State
Next, we consider the effect of changing from the UKMO analysis ocean mean state to the ocean mean state from SPC, by comparing SPK-SPC and SPK-OBS. It is important to highlight the differences between SPK-SPC and SPC: While the two have similar mean SSTs, SPC contains modes of coupled ocean-atmosphere variability (e.g., ENSO and IOD) that the MC-KPP ocean in SPK-SPC cannot represent; MC-KPP has finer vertical resolution than the POP ocean in SPC (1 and 10 m in the top layer, respectively) and a higher coupling frequency (15 min and 24 hr, respectively). The minimal differences between SPK-SPC and SPC in mean SST (Figure 6a) and precipitation and 850-hPa wind (Figure 6b) demonstrate the effectiveness of the SPCAM3-KPP correction technique.
Despite these small mean state differences, SPK-SPC lacks a propagating MJO (Figure 2e), in stark contrast to the strong and coherent MJO in SPC (Figure 2b) and SPK-OBS (Figure 2c). The cold tropical mean SST biases in SPC (Figure 3a) apparently suppress the MJO in SPK-SPC, in line with Klingaman and Woolnough (2014b) for MetUM, as well as with , Sperber (2004), Zhang et al. (2006), and others. Using the SPC ocean mean state reduces SST ISV in SPK-SPC (Figure 4i) relative to SPK-OBS (Figure 4e), as expected for cooler mean SSTs. Precipitation ISV is also smaller in SPK-SPC (Figure 4j), with considerably lower variance in the equatorial Indian Ocean and the Maritime Continent. Yet the ISVs in precipitation and SST in SPK-SPC are broadly similar to those in SPC (Figures 4b and 4c), so it is unlikely that these reductions in variance can explain the degraded MJO in SPK-SPC. SPA-KSPC, an SPCAM3 simulation driven by 31-day smoothed SST from SPK-SPC, also fails to produce a propagating MJO (Figure 2f), which confirms that air-sea interactions are not responsible for the lack of an MJO in SPK-SPC. Diagnostics of the "SST effect" on the MJO ⟨m⟩ budget are similar for SPK-SPC (Figures 5g and 5h) and SPC (Figures 5c and 5d). The contribution of intraseasonal SSTs through LH and SH to ⟨m⟩ remains positive in the equatorial Indian Ocean, as does the contribution to ⟨m⟩ t ; the contribution to ⟨m⟩ is also negative in the off-equatorial regions, in agreement with ERA-Interim and SPC. Using the SPC mean state reduces the contribution to ⟨m⟩ t in the equatorial Indian Ocean in SPK-SPC relative to SPK-OBS (Figure 5f), but as the contribution in SPK-SPC is similar to SPC it is unlikely to account for the degraded MJO. These diagnostics show that intraseasonal SSTs, and thus air-sea coupling, support MJO convection in SPK-SPC, which suggests intraseasonal SSTs alone are insufficient to produce an MJO in SPCAM3-KPP.

The Effect of ENSO
The results of section 3.3 imply that the MJO in SPC arises from some characteristic of SPCCSM3 that is missing in SPCAM3-KPP. Having shown that the mean state, ISV and effect of time-varying SSTs are similar in the two experiments, we investigate the effects of ENSO. While SPCAM3-KPP can produce weak, thermodynamically driven SST variability in the ENSO region (not shown), this variability is much smaller than in SPC (Figure 1); this variability in SPCAM3-KPP lacks the period and the phase locking to the seasonal cycle of the ENSO in observations or SPC.
First, we condition MJO propagation on ENSO phase in SPC and observations (Figure 7). We separate SPC by ENSO phase as in section 2.2. For observations , we apply the same method to separate observed NDJFMA Niño 3.4 SST anomalies into terciles. The influence of ENSO phase on MJO propagation in SPC is striking: MJO propagation beyond the Maritime Continent (130 • E) occurs only in El Niño years (Figure 7a  weakens under La Niña (Figure 7f). Propagation from the Indian Ocean to the Maritime Continent is similar regardless of ENSO phase, unlike in SPC. Previous studies have shown similar results (e.g., Hendon et al., 1999;Gushchina & Dewitte, 2012;Tam & Lau, 2005;Woolnough et al., 2000). The major differences between SPC and observations are (a) a lack of propagation to the Pacific in neutral years in SPC and (b) weaker propagation in SPC through the Indian Ocean in neutral and La Niña years.
We hypothesize that the weakened propagation in neutral and La Niña years in SPC, relative to El Niño years, is associated with the cold tropical SST biases in SPC (Figure 3a). Composite SST anomalies in SPC by ENSO phase show that the SPC El Niño SST anomaly (Figure 8a) is similar in structure and magnitude to the equatorial Pacific mean cold bias. Thus, El Niño in SPC effectively reduces the model's mean state error, which may allow the MJO to propagate further into the Pacific by altering the zonal gradient of SST across the Warm Pool. Neutral years have nearly zero SST anomaly ( Figure 8c) and so retain the mean state bias, while La Niña years resemble an intensified mean state bias (Figure 8e).
To test the hypothesis that stronger propagation in El Niño years causes the improved MJO propagation in SPC, we assess MJO propagation in SPK-ENSO. In SPK-ENSO, MC-KPP is forced to reproduce the composite SPC 3-year ENSO cycle, which progresses neutral El Niño-La Niña (section 2.2). An advantage of SPCAM3-KPP is that this 3-year cycle can be reproduced effectively indefinitely, giving a large sample size of 20 El Niño periods (NDJFMA), 20 neutral periods, and 20 La Niña periods (Figure 9), determined by applying the same tercile-based classification as for SPC. SPK-ENSO reproduces the target climatology well, although the La Niña events are slightly weaker than the target event. As a result, the average SPK-ENSO El Niño event is stronger than the La Niña event. SPK-ENSO successfully reproduces the ENSO composite SST anomalies from SPC (Figures 8b, 8d, and 8f). The correction technique is less successful at constraining East Pacific SST, likely due to the substantial role for upwelling there, which cannot be captured by MC-KPP.
Prescribing the 3-year composite ENSO cycle in SPK-ENSO also recovers the ENSO-driven anomalies in precipitation and 850-hPa winds in SPC ( Figure 10). El Niño is associated with increased precipitation and westerly anomalies over the equatorial Pacific, while reduced precipitation and easterly anomalies prevail across the Maritime Continent and eastern Indian Ocean (Figures 10a and 10b). La Niña shows roughly the opposite pattern (Figures 10e and 10f). SPK-ENSO produces lower precipitation and slight easterly anomalies over the Maritime Continent relative to SPC in all ENSO phases, a factor which may be important for MJO propagation and to which we will return in section 4. This difference is most

Journal of Advances in Modeling Earth Systems
10.1029/2019MS001799 Figure 10. As in Figure 8 but for composites by ENSO phase of (shading) precipitation (mm/day) and (vectors) 850-hPa wind (m/s). Note that as in Figure 8, the SPK-ENSO anomalies are computed relative to the SPC climatology. apparent in SPK-ENSO neutral composite ( Figure 10d); it may be related to the cold SST bias west of the Maritime Continent in SPK-ENSO, relative to SPC (Figure 8d). We emphasize that while the MC-KPP corrections produce oceanic and atmospheric mean states that are very similar to the target climatology, small (but potentially important) differences remain.
The 3-year ENSO cycle in SPK-ENSO reproduces most of the MJO propagation behavior from SPC (Figures 11a and 11b). Overall propagation in SPK-ENSO is considerably improved over SPK-SPC ( Figure 2e). As the only difference between these simulations is the composite ENSO cycle from SPC, ENSO variability is clearly essential to MJO propagation in SPC. As in SPC, when MJO propagation in SPK-ENSO is composited by ENSO phase, propagation through the Maritime Continent is strong only under El Niño (Figure 11c) with weaker or absent propagation in neutral and La Niña years. For any ENSO phase, or for all years, propagation in SPK-ENSO is somewhat weaker than for the same conditions in SPC. We hypothesize that this is due to the slightly colder SSTs in the eastern Indian Ocean in SPK-ENSO, alongside reduced precipitation and anomalous easterly lower-tropospheric winds near the Maritime Continent, or to associated differences in column water vapor during ENSO phases (Demott et al., 2018). For an active MJO in the Indian Ocean, such anomalies are consistent with reduced horizontal moisture advection from the east, a factor several studies have concluded is key for robust eastward MJO propagation in models (e.g., DeMott et al., 2014;Kim et al., 2017). While the strong MJO in El Niño years may support the El Niño event itself in SPC (e.g., through westerly wind bursts and oceanic Kelvin waves), it is unlikely that the SPC MJO triggers El Niño events, as the MJO is weak in non-El Niño conditions. Further, this mechanism cannot operate in SPK-ENSO, as MC-KPP lacks ocean dynamics.
While SPK-ENSO reproduces most of the behavior of SPC in each ENSO phase, as well as in all years, none of the ENSO-phase composites in SPK or SPC resemble the standing oscillation in SPK-SPC (Figure 2 e). Even in La Niña years, when ENSO increases the SPC mean state biases in the Pacific, SPK and SPC still show some eastward propagation. One hypothesis is that the transient response of the MJO to cycling between ENSO states differs from the steady-state response to a given ENSO state. For example, a decaying El Niño event may influence the oceanic and atmospheric state as the next La Niña event develops in the same year.
To test this, we analyze the three 50-year SPCAM3-KPP simulations in which the ocean is constrained to the mean state of each SPC ENSO phase: SPK-EN, SPK-LN, and SPK-NN (Table 1). SPK-EN shows a strong, eastward propagating MJO (Figure 12 b), which propagates faster and further east than the MJO in all years of SPK-ENSO (Figure 12 a), but not as far east as the MJO in El Niño years of SPK-ENSO (Figure 11 c).  (Figure 11 e). These results suggest that the standing oscillation in SPK-SPC arises from the steady-state response to the biases in the SPC mean ocean state. ENSO variability mitigates this response, allowing MJO propagation from the Indian Ocean to the Maritime Continent in La Niña and neutral years, potentially through lagged effects of preceding El Niño events.
These results strongly suggest that the robust MJO propagation in SPC arises from neither air-sea interactions on intraseasonal timescales, which only slightly improve MJO propagation under either the observed or SPC SST mean state or from any feature of the SPC mean state, which strongly degrades the MJO. Rather, the SPC MJO arises from the response to ENSO variability, particularly the warm Pacific SST anomalies in El Niño years that effectively cancel the SPC cold SST bias.

Discussion
Our results highlight that tropical systematic errors and coupled modes of interannual variability (e.g., ENSOa and IOD) can alter the perceived effects of air-sea interactions on the MJO. Many studies of air-sea feedbacks to the MJO in models have compared a CGCM to its AGCM counterpart, forced by either observed, AMIP-type SSTs or by SSTs from the CGCM (e.g., DeMott et al., 2014DeMott et al., , 2019Liess et al., 2004;Rajendran & Kitoh, 2006;Zhang et al., 2006). As highlighted previously (DeMott et al., 2015;Klingaman & Woolnough, 2014a), comparing CGCM and AMIP-type AGCM simulations conflates the effects of mean state biases and air-sea feedbacks. Our study suggests that these comparisons are also flawed because they do not account for changes in interannual variability between the CGCM and AGCM, either in the phenomena themselves (e.g., CGCM biases in the representation of ENSO or the IOD) or in their teleconnections to the MJO (e.g., an overly strong MJO response to ENSO, as in SPC).
Perhaps more importantly, our results demonstrate that so-called "replay" simulations-comparisons against AGCM simulations with prescribed, interannually varying CGCM SSTs-are also problematic, because they do not cleanly isolate the effects of air-sea feedbacks within the MJO from the effects of air-sea coupling on other processes, such as the response to ENSO. For example, DeMott et al. (2014) concluded that air-sea feedbacks improved MJO propagation in SPCCSM3, based on differences between SPCCSM3 and "replay" SPCAM3 simulations with temporally smoothed SPCCSM3 SSTs. Our SPCAM3-KPP simulations reveal that the strong MJO in SPCCSM3 arises from a strong response to ENSO variability, complicated by strong mean state SST errors in the equatorial Pacific. Air-sea interactions play a secondary role, under either the SPCCSM3 or observed ocean states. We note that we did not analyze the "replay" SPCAM3 simulation with SPCCSM3 SSTs from DeMott et al. (2014). Those studies concluded that air-sea interactions improved, but were not essential to, the representation of the MJO in SPCCSM3, which supports the results here about the secondary effect of coupling. The replay SPCAM3 simulation includes the SPCCSM3 ENSO variability, but DeMott et al. (2014) did not analyze the role of coupling as a function of ENSO phase, only in the simulation as a whole. Understanding how ENSO alters air-sea interactions within the MJO, and how consequent changes in MJO structure and amplitude feed back to ENSO activity, remain active areas of future research.
Further, many CGCM-based studies of the MJO evaluate a simulation only a few decades long, perhaps 50 years at most. If the CGCM MJO responds strongly to ENSO, as it does in SPCCSM3, then the diagnosed MJO fidelity is sensitive to chaotic internal coupled variability in the CGCM. For example, one 30-year simulation of a given CGCM might contain more El Niños than La Niñas, while another might contain more La Niñas than El Niños; one simulation might exhibit excessive ENSO variance, while another shows little; one simulation might produce more central Pacific ENSO events, while another produces more eastern Pacific events. An even more important issue for model development is that a given physics perturbation, or resolution change, might systematically or randomly alter internal variability to amplify or degrade the MJO, leading to erroneous conclusions about the influence of that physical process or resolution change on the MJO. Similar issues have been recognized for climate projections, leading to the creation of large ensembles to more robustly sample natural variability (Kay et al., 2015).
These issues also affect comparisons of the role of air-sea interactions in the MJO among models, as models will differ considerably in their representations of ENSO and its teleconnections, due to differences in formulations as well as in internal variability (e.g., Bellenger et al., 2014;Langenbrunner & Neelin, 2013). We motivated our study by identifying that although MetUM and SPCCSM3 suffered from similar systematic SST errors, SPCCSM3 produced a strong MJO, while MetUM did not. We initially assumed that air-sea feedbacks to the MJO must be stronger in SPCCSM3 or that some aspect of the SPCCSM3 mean state must enhance the MJO. In light of our results, it is possible that the distinction between SPCCSM3 and MetUM lies not in simulated MJO physics, but in the response of the simulated MJO to ENSO: MetUM may have a lower ENSO variance, or the response of the background state to El Niño may favor MJO propagation in SPCCSM3 more than in MetUM. Given the same ENSO variability as SPCCSM3, MetUM might produce a strong MJO. These results particularly affect the conclusions of CGCM-AGCM intercomparison studies, where the CGCM includes a dynamical ocean capable of simulating ENSO (e.g., DeMott et al., 2019;Rajendran & Kitoh, 2006;Zhang et al., 2006). Relatedly, we note that our analysis based on only one GCM, which produces a strong MJO, excessive intraseasonal variance in rainfall, and high ENSO variance, and which uses an unconventional treatment of convection. We anticipate further studies with other GCMs in a similar atmosphere-ocean-mixed-layer coupled framework, to confirm these results.
The interpretation of our simulations is complicated by slight variations in the basic state between experiments. SPK-SPC and SPK-ENSO are systematically drier near the Maritime Continent relative to SPC (Figure 10), associated with a slight cold SST bias (Figure 8). These differences may be sufficient to reduce

Journal of Advances in Modeling Earth Systems
10.1029/2019MS001799 the zonal moisture gradient across the Indian Ocean and inhibit propagation across the Maritime Continent (e.g., Gonzalez & Jiang, 2017;Kim et al., 2017). We cannot rule out the influence of these errors on the poor MJO propagation in SPK-SPC relative to SPC or the slightly weaker MJO propagation in SPK-ENSO relative to SPC. However, we note that SPK-ENSO produces a strong MJO in spite of these biases; comparing SPK-SPC and SPK-ENSO, both affected by these biases, clearly shows that include the SPC ENSO cycle dramatically improves the MJO.
We recommend that future model studies of air-sea interactions in the MJO control for the effects on the background state of not only model systematic errors but also interannual variability. The atmosphere-ocean-mixed-layer framework presented here is an effective way to control for these factors, but other methods include restoring the ocean state to an observed climatology with flux corrections-with a relaxation timescale suitably long so as not to damp ISV-or subsampling only a certain phase of variability (e.g., ENSO neutral) in a simulation. Isolating the role of air-sea interactions on intraseasonal scales remains challenging, but the systematic isolation of mean state biases and interannual variability presented here shows a path to more tightly constraining the problem.

Conclusions
The MJO is often poorly simulated in climate models, which limits our understanding of its basic physics and creates uncertainty in regional projections of climate change, since the MJO is a major cause of extreme weather globally. Including air-sea interactions in models frequently improves the MJO (DeMott et al., 2015, and references therein), but the aspects of the MJO that improve (e.g., propagation speed, amplitude, and period) and the degree of improvement vary among models. It remains unclear whether air-sea feedbacks are important to the real-world MJO, in part because model sensitivity experiments have not identified a consistent mechanism by which air-sea coupled processes influence intraseasonal tropical convection. Model intercomparison efforts are hampered by intermodel variability in the simulated basic state, elements of which influence MJO propagation (e.g., Crueger et al., 2013;Klingaman & Woolnough, 2014b). SPCCSM3 produces one of the best representations of the MJO among contemporary models , including relative to its counterpart atmosphere-only model, SPCAM3 (e.g., DeMott et al., 2014;Stan et al., 2010). However, SPCCSM3 exhibits similar systematic errors to other coupled models, including MetUM, in which those biases strongly degraded the MJO (Klingaman & Woolnough, 2014b). Previous studies with SPCCSM3 assessed the role of air-sea interactions under only this biased mean state, and did not consider the effects of interannual variability (e.g., ENSO) on the background state for the MJO.
To more thoroughly investigate the mechanisms underlying the realistic representation of the MJO in SPCCSM3, we systematically isolated the effects of (a) intraseasonal air-sea coupled feedbacks, (b) mean state SST errors, and (c) ENSO on the simulated MJO. We accomplished this through a new model configuration, SPCAM3-KPP, in which SPCAM3 is coupled to many columns of a one-dimensional ocean model, similar to Hirons et al. (2015) for MetUM. SPCAM3-KPP can be easily constrained to a target state, which in this study includes the observed mean annual cycle, the SPCCSM3 mean annual cycle, and a repeating 3-year composite ENSO cycle from SPCCSM3. The lack of a direct simulation of ENSO and IOD in SPCAM3-KPP limits the potentially complicating effects of these modes on our analysis of the MJO.
Under the observed ocean mean state, SPCAM3-KPP produces a coherent, eastward propagating MJO. A "replay" SPCAM3 simulation-with prescribed, interannually varying SSTs from SPCAM3-KPP-shows a slightly weaker, but still strong MJO, suggesting that intraseasonal air-sea feedbacks are not essential to MJO propagation in SPCAM3-KPP under the observed ocean mean state. Under the SPCCSM3 ocean mean state, SPCAM3-KPP fails to produce an MJO, in stark contrast to SPCCSM3 itself. Again, air-sea feedbacks make little difference to simulated ISV. When the SPCCSM3 ENSO cycle is imposed, on top of the SPCCSM3 ocean mean state, SPCAM3-KPP generates an MJO highly similar to that in SPCCSM3, suggesting high ENSO variance is associated with the strong SPCCSM3 MJO, in spite of its systematic errors. Further analysis shows that SPCCSM3, and SPCAM3-KPP with the imposed SPCCM3 ENSO cycle, displays a strong MJO only in El Niño years, when anomalously warm equatorial Pacific SSTs counteract the cold systematic SST biases. In neutral and La Niña years, SPCCSM3 produces little MJO activity, in contrast to observations.