The role of air–sea coupling in the simulation of the Madden–Julian oscillation in the Hadley Centre model

The role of air–sea coupling in the simulation of the Madden–Julian oscillation (MJO) is explored using two configurations of the Hadley Centre atmospheric model (AGCM), GA3.0, which differ only in F, a parameter controlling convective entrainment and detrainment. Increasing F considerably improves deficient MJO‐like variability in the Indian and Pacific Oceans, but variability in and propagation through the Maritime Continent remains weak.


The Madden-Julian oscillation
The Madden-Julian oscillation (MJO: Madden and Julian, 1971) is the leading mode of subseasonal (30-60 day) tropical variability. The active MJO phase comprises a broad envelope of enhanced convection and precipitation, focused near the Equator, that often initiates in the Indian Ocean before propagating east through the Maritime Continent and into the Pacific. Suppressed convective conditions, slack westerly winds and strong insolation precede and follow the active phase. The MJO influences regional

Air-sea coupling and the simulation of the MJO
The MJO is strongly coupled to variability in air-sea fluxes and hence to variability in upper-ocean temperatures. Seasurface temperature (SST) anomalies associated with subseasonal tropical convection have been observed during field campaigns (e.g. Anderson et al., 1998;Bhat et al., 2001) and in satellite observations (Woolnough et al., 2000;Vecchi and Harrison, 2002;Klingaman et al., 2008b). These SST anomalies, largely forced by the atmosphere (Jones et al., 1998;Waliser et al., 2004), exhibit a near-quadrature phase relationship with outgoing longwave radiation (OLR): warm (cold) SSTs precede enhanced (suppressed) convection by 7-10 days (Fu et al., 2003). Over nearly 20 years, intercomparisons have repeatedly demonstrated that general circulation models (GCMs) struggle to capture the observed intensity, propagation speed, horizontal and vertical structure and teleconnections of tropical subseasonal variability (Slingo et al., 1996;Lin et al., 2006;Sperber and Annamalai, 2008;Kim et al., 2009). Such intercomparisons have not identified a unifying characteristic among models that simulate the MJO well, nor a common failing among those that perform poorly. Many sensitivity studies have been conducted with one or several GCMs, focusing on horizontal resolution Jia et al., 2008), vertical resolution (Inness et al., 2001), the parametrization of deep convection (Zhu et al., 2009;Benedict and Maloney, 2013), the accuracy of the tropical mean state , the temporal resolution of prescribed SSTs (Kim et al., 2008) and the presence and representation of air-sea coupling (Kemball-Cook et al., 2002;Kim et al., 2010). The results of these studies often conflict: similar changes applied to different GCMs produce opposite-signed impacts.
In particular, there is contention over the effect of coupling on the simulation of subseasonal convection. Sperber (2004) and Sperber et al. (2005) found that coupling improved the MJO in the National Center for Atmospheric Research Community Climate System Model (CCSM) and the Max Planck GCM (ECHAM4), respectively, although CCSM in particular still underestimated MJO amplitude considerably. More recently, Crueger et al. (2013) used many configurations of ECHAM6 to demonstrate that coupling enhanced MJO amplitude, though again all configurations displayed less subseasonal power than observed. In the Hadley Centre GCM (HadAM3),  concluded that coupling improved MJO intensity and propagation; this was confirmed by Bernie et al. (2008) using a very high-resolution three-dimensional ocean model and by Klingaman et al. (2011) using a mixed-layer ocean for the boreal-summer MJO. A succession of hindcast studies found that coupling increased predictive skill for the MJO to a greater or lesser extent (Fu et al., 2007;Woolnough et al., 2007;Kim et al., 2010). Yet Hendon (2000) found a degradation in MJO variability when the Geophysical Fluid Dynamics Laboratory (GFDL) GCM was coupled to a mixed-layer ocean. In contrast to studies showing an improved MJO with coupling, the GFDL atmospheric GCM (AGCM) overestimated rather than underestimated subseasonal variability. Likewise,  found no improvement in the MJO with coupling in ECHAM4 when compared with an AGCM integration driven by the coupled-model SSTs. In aqua-planet simulations with a slab ocean, Grabowski (2006) demonstrated that interactive SSTs inhibited convective organization due to negative feedback between the SST anomalies and the strength of convection. Using a coupled linear inverse model, Newman et al. (2009) showed that air-sea interactions had little or no effect on simulated atmospheric subseasonal variability; coupled processes influenced the evolution of the atmosphere mainly on interannual time-scales.
Many of the sensitivity studies that concluded that coupling improved the MJO were performed with AGCMs that displayed weak subseasonal variability in organized, large-scale tropical variability. For example, HadAM3 had very little MJO-like activity when driven by monthly mean observed SSTs (Klingaman et al., 2008a). In observations, however, the MJO is known to be a predominantly atmospheric mode of variability; AGCMs with parametrized (Benedict and Maloney, 2013) and superparametrized or explicit convection (Khairoutdinov et al., 2005) can capture the MJO. The sudden appearance of MJO-like variability in a coupled GCM (CGCM), where none exists the counterpart AGCM, raises the issue of whether coupled models are simulating the MJO by the correct (i.e. real-world) physical mechanisms. One hypothesis is that coupling introduces highfrequency SST variability that acts as a kind of 'crutch' for an AGCM, producing SST anomalies that can feed back on convection and encourage some degree of organization and propagation. Studies in which subseasonal tropical variability has been dramatically increased by prescribing daily or weekly observed SSTs in AGCMs, instead of monthly means, lend support to this hypothesis (Reicher and Roads, 2005;Kim et al., 2008;Klingaman et al., 2008a). The role of air-sea interactions in a CGCM in which the AGCM simulates adequate subseasonal variability requires further investigation.
The mean-state biases that inevitably result from air-sea coupling further complicate the analysis of the impact of coupling on the MJO. By comparing a standard coupled simulation of the Hadley Centre model (HadCM3) with one with heat-flux corrections,  found that mean-state errors in HadCM3 prevented the propagation of the MJO into the Pacific. Several studies have attempted to quantify the impact of mean-state errors by prescribing climatological or otherwise temporally degraded CGCM SSTs in the AGCM (e.g. Fu and Wang, 2004), but this neglects the effect of mean-state errors on air-sea interactions (i.e. the role of coupling may depend on the mean state). Many investigations of the sensitivity of the simulated MJO to coupling have not estimated the impact of mean-state biases.

The purpose of the present study
The influence of air-sea interactions in the representation of the MJO in GCMs remains an open question, particularly because many AGCMs used to explore this sensitivity display poor subseasonal variability in tropical convection. The authors have recently improved the simulation of MJO-like variability in the Hadley Centre model, HadGEM3 (Walters et al., 2011), by using hindcasts to explore the sensitivity of the simulated MJO to various physical parameters (Klingaman and Woolnough, 2013). Increasing by 50% the rates of entrainment ( ) and mixing detrainment (δ m ) for diagnosed deep and mid-level convection improved hindcast predictive skill, for this limited set of events, from 12 to 22 days. Klingaman and Woolnough (2013) briefly analyzed a 20 year simulation with the modified HadGEM3, finding that MJO activity approached observations, whereas a control simulation produced only half of the observed activity. MJO propagation also improved, but remained deficient relative to observations, particularly through the Maritime Continent.
This provides a rare opportunity to explore the effects of air-sea coupling on the representation of the MJO in highly similar configurations of a model that differ substantially in their levels of tropical subseasonal variability. We analyze these effects by conducting atmosphere-only and coupled simulations at default and higher and δ m . We employ the coupling strategy of Klingaman et al. (2011), using many columns of a boundary-layer ocean model, with climatological heat corrections to maintain a similar mean state to the corresponding atmosphere-only integrations. This increases the likelihood that differences in MJO activity between coupled and uncoupled simulations are due to air-sea interactions rather than mean-state biases. We also demonstrate the effects on the MJO of mean-state SST errors from the fully coupled HadGEM3 (i.e. with a three-dimensional ocean GCM) by conducting atmosphere-only and coupled simulations using the SSTs from the fully coupled model. Section 2 describes the HadGEM3 configurations used in this study, the details of the coupling, the experiments performed and the datasets and analysis methods employed. Section 3 explores how the impact of air-sea interactions changes depending on the level of subseasonal variability in the AGCM. In section 4, we analyze the impact on MJO propagation of the K-profile parametrization (KPP) mean SSTs and coupling in the Maritime Continent and West Pacific, motivated by the results in section 3. Section 5 demonstrates a technique for separating the effect of coupling on the MJO in a fully coupled model into (i) the direct role of air-sea interactions and (ii) the role of mean-state errors. We discuss the results of this study in section 6 and summarize them in section 7.

HadGEM3 Global Atmosphere 3.0
All experiments use the HadGEM3 Global Atmosphere 3.0 (GA3.0: Arribas et al., 2011;Walters et al., 2011) AGCM. The horizontal resolution is 1.875 • longitude × 1.25 • latitude with 85 points in the vertical -50 of which are in the tropical troposphere (18 km) -and a rigid lid at 85 km. HadGEM3 is under development, but GA3.0 is a fixed scientific configuration of the model. Klingaman and Woolnough (2013) used a slightly older configuration, GA2.0, to explore the role of increased entrainment and detrainment rates on the simulated MJO. There are only slight differences in MJO activity between GA2.0 and GA3.0; the effect of increasing and δ m is also similar (see section 3.1). Walters et al. (2011) describes the differences between GA2.0 and GA3.0.
Of particular consequence to this study are the formulations of and δ m in the modified Gregory and Rowntree (1990) convection scheme in GA3.0. Entrainment for diagnosed deep and mid-level convection is parametrized at each vertical gridpoint (z) as where F is a scaling factor, p and ρ are pressure and density, g is gravity and p * is surface pressure. We increase by increasing F, which also increases δ m for deep convection: where R is relative humidity. The parcel is forced to detrain completely at the level of neutral buoyancy (i.e. there is no 'overshooting'). Further details can be found in Stratton et al. (2009), Derbyshire et al. (2011 and Walters et al. (2011).

Coupling to the KPP model
We couple GA3.0 to many columns of the KPP boundary-layer ocean model (Large et al., 1994) via the Ocean-Atmosphere-Sea Ice-Soil (OASIS: Valcke et al., 2003) coupler, version 3. We refer to this model as GA3.0-KPP. The coupling strategy is identical to that for HadKPP in Klingaman et al. (2011), but with updated versions of the AGCM and OASIS. As KPP simulates only vertical mixing, depth-varying temperature corrections are used to constrain the monthly mean ocean temperature profile towards a reference climatology. This climatology is taken from either observations or a fully coupled version of HadGEM3 (see section 2.3). The corrections are computed as in Klingaman et al. (2011): for each GA3.0-KPP integration, the surface fluxes from each of the first ten years of the corresponding GA3.0 integration are used to drive a one-year KPP integration. At the end of each month, the KPP integration is paused; the profile of corrections required to remove the monthly mean temperature bias is computed; the profile is then imposed in a second integration for that month, before continuing to the next month. The climatological, monthly mean corrections are computed from the ten years of KPP integrations and imposed in GA3.0-KPP. In the forced KPP and GA3.0-KPP simulations, salinity is relaxed to the climatological, monthly mean profile with a 90-day timescale. This damps seasonal-time-scale salinity variability but, as our focus is subseasonal variability, this damping is not expected to affect our results.
By constraining ocean temperature and salinity, GA3.0-KPP produces small SST biases and hence a similar mean state to the corresponding GA3.0 simulations (see section 3.2). This limits the possibility that differences in MJO behaviour between GA3.0 and GA3.0-KPP simulations are due to changes in the mean state. Section 4.1 tests the role of the climatological GA3.0-KPP SSTs in MJO propagation.  Table 1 summarizes the experiments, which are all 20 years long.

Experiments
A set of four experiments are conducted using GA3.0 and GA3.0-KPP with default and higher F: A-CTL-OBS, K WP -CTL-OBS, A-ENT-OBS and K WP -ENT-OBS. In A-CTL-OBS and A-ENT-OBS, SSTs and sea ice are prescribed from a monthly mean climatology  of the Met Office ocean analysis (Smith and Murphy, 2007). In K WP -CTL-OBS and K WP -ENT-OBS, KPP is constrained to the temperature and salinity profiles from that climatology within the coupled region (Table 1). Outside that region, the Smith and Murphy (2007) climatological SSTs and sea ice are prescribed; a five-point linear blending is applied at the boundaries to reduce SST gradients.
Two sensitivity tests are performed to understand the results of K WP -ENT-OBS: a GA3.0 integration with prescribed K WP -ENT-OBS climatological SSTs (A-ENT-K WP ) and a GA3.0-KPP integration with the eastern coupling boundary at the western edge of the Maritime Continent (K IO -ENT-OBS). The role of coupledmodel mean-state biases is investigated with the climatology of a 30-year integration of GA3.0 coupled to the Nucleus for European Modelling of the Ocean (NEMO) model (GA3.0-NEMO), the standard ocean model for HadGEM3. The A-CTL-NEMO and K WP -CTL-NEMO experiments are as in A-CTL-OBS and K WP -CTL-OBS, but replace the Met Office ocean climatology with the NEMO climatology; section 5.1 contains further information on these experiments and the motivation behind them.

Methods and data
In simulations and observations, MJO activity is assessed through the Real-time Multivariate MJO (RMM) indices of Wheeler and Hendon (2004). RMM indices are computed from model data using the method outlined there, except that no regression on ENSO is removed; there is no ENSO in any integration due to the use of climatological SSTs. We project model anomalies on to the observed RMM empirical orthogonal functions (EOFs). The observed RMM indices for 1975-2011 are taken from Matt Wheeler's website (http://www.cawcr.gov.au/staff/mwheeler/ maproom/RMM).
As in Klingaman and Woolnough (2013), we diagnose MJO 'activity' as the fraction of days in which the RMM amplitude is ≥ 1 ('strong MJO'), for all RMM phases and for each phase separately, as shown in Figure 1. That study demonstrated that this measure was strongly linked to other diagnostics of tropical Table 1. A summary of the experiments analyzed in this study, including the label used in the text, the value of the F parameter controlling entrainment and mixing detrainment, the domain in which the atmosphere is coupled to KPP, if any, and the SST boundary condition used outside the coupling region. All experiments are 20 years long.  the daily frequency of strong activity (amplitude ≥ 1) in each phase, relative to all days in the integration, using the colour scale to the left of (d). For each phase, the decimal fractions are probabilities that, on the day following strong activity in that phase, the MJO transitions to the next (anticlockwise) phase ('Next') or moves into the unit circle ('Decay', i.e. an amplitude less than one). The frequency of weak MJO activity is given inside the unit circle. The values next to the arrows crossing the unit circle show the relative probabilities of MJO genesis in each phase.
subseasonal variability, such as wavenumber-frequency power spectra, and was a useful 'one-look' measure of MJO activity in a GCM. Phase composites are constructed by taking the average of a quantity over all days with amplitude ≥ 1 in that phase. These composites are computed using anomalies from a daily climatology. We also remove the mean of the previous 120 days before each day in each phase composite to isolate intra-seasonal signals, as in Wheeler and Hendon (2004).
To assess zonal propagation, we compute lag regressions of latitude-averaged (10 • N-10 • S), 20-100 day bandpass-filtered OLR using base points in the central Indian Ocean (70 • E) and the western (100 • E) and eastern (130 • E) edges of the Maritime Continent. The latter two points are selected to focus on propagation through the Maritime Continent. This diagnostic is recommended by the CLIVAR MJO Task Force (Kim et al., 2009).
OLR data are taken from the National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR) dataset for 1979-2012 on a 2.5 • ×2.5 • horizontal grid. Rainfall data come from the Tropical Rainfall Measuring Mission (TRMM: Kummerow et al., 1998) 3B42 product, version 6, for 1998-2012 on a 0.25 • ×0.25 • grid. SST data are obtained from the blended TRMM Microwave Imager (TMI: Wentz, 2000) and Advanced Microwave Scanning Radiometer (AMSRE) product from Remote Sensing Systems for 1998-2012, on the TRMM grid. Daily mean, pressurelevel specific-humidity data are taken from the European Centre for Medium-range Weather Forecasts Interim reanalysis (ERA-Interim: Uppala et al., 2005) for 1989-2008. Rainfall, SSTs and specific humidity are interpolated to the GA3.0 grid, using an area-weighted method.

Atmosphere-only simulations
In observations, 61% of days have a strong MJO in any phase (Figure 1(a)). By contrast, 41% of days in A-CTL-OBS have a strong MJO (Figure 1(b)). This percentage is higher than that (34%) for the 20 year GA2.0 control integration in Klingaman and Woolnough (2013), suggesting the MJO is slightly stronger in GA3.0. Still, A-CTL-OBS produces only 65% of the observed MJO activity by this measure. Lag composites of strong MJO activity show that A-CTL-OBS is often unable to maintain a strong MJO beyond three days (Figure 2), as the composites quickly decay into the unit circle with little propagation. In observations, the composites remain outside the unit circle for 8-10 days. In A-CTL-OBS, the probability of a strong MJO event 'decaying' into the unit circle on the next day is 50-100% greater than observed in all phases (compare Figure 1(a) and (b)). The probability of decay was separated into 'death' -in which the RMM index remains <1 for 10 days or more -and 'illness' -10 days or less (not shown); in observations and all simulations, illness (death) accounted for about two-thirds (one-third) of decay. Illness indicates an intermittent MJO, while death can be used to separate events. Phase composites of TRMM rainfall anomalies show the canonical eastward movement of heavy rainfall from the Indian Ocean (Figure 3(a)) to the Maritime Continent (Figure 3(b)) and the West Pacific (Figure 3(c)), with negative anomalies to the west and east. (For brevity, we focus on RMM phases 2, 4 and 6 throughout the study.) A-CTL-OBS displays much less spatial coherence and weaker anomalies in all phases (Figure 3(d)-(f)), with the strongest (weakest) anomalies off (on) the Equator, whereas the observations typically have maxima on the Equator. Weak equatorial variability in convection is a known bias in Hadley Centre models (Yang et al., 2009). This is particularly evident in phase 2: there is no suppressed convection in the West Pacific and a meridional split in the active phase across the Indian Ocean.
To examine eastward propagation, we compute lag regressions of latitude-averaged ( As in Klingaman and Woolnough (2013) for GA2.0, using 1.5F (1) raises MJO activity in A-ENT-OBS (58.6%; Figure 1(c)) to near-observed levels (61.1%; Figure 1(a)). The distribution of activity around the phase space is skewed towards the Indian Ocean and West Pacific phases (2, 3, 6 and 7), with relatively less activity near the Maritime Continent and in the Western Hemisphere (4, 5, 8 and 1). A-ENT-OBS favours variability in Wheeler and Hendon (2004) EOF1 -the anticorrelation between the Indian Ocean and West Pacific -over EOF2, which describes intraseasonal variability over the Maritime Continent.
Lag composites in RMM space demonstrate longer lifetimes for strong MJO events in most phases in A-ENT-OBS over A-CTL-OBS ( Figure 2). Events in the Indian Ocean, in particular, propagate further through phase space before decaying into the unit circle. The mean RMM amplitude in each phase (blue circles) increases substantially in A-ENT-OBS. The origin in phase space, equivalent to no projection on to either Wheeler and Hendon (2004) EOF, remains a strong attractor even in A-ENT-OBS. RMM phase composites of rainfall anomalies show an increase in magnitude, with increased equatorial rainfall variability compared to A-CTL-OBS (Figure 3(g)-(i)). The anomalies are more spatially coherent, particularly in the Indian Ocean in phase 2 (Figure 3(g)). Substantial biases remain, including an erroneous extension of positive (negative) rainfall anomalies in phase 2 (phase 6) from the Indian Ocean into the West Pacific, where the observations show negative (positive) anomalies. While the observations show enhanced rainfall extending northwest from the Maritime Continent to India in phase 4 (Figure 3(b)), no such extension exists in A-ENT-OBS (Figure 3(h)).
Although MJO propagation improves in A-ENT-OBS (Figure 4(g)-(i)) relative to A-CTL-OBS, it remains deficient. In particular, active (suppressed) convection in the Indian Ocean (Figure 4(g)) fails to move coherently across the Maritime Continent. Similarly, the active phases over the Maritime Continent (Figure 4(h)) are not strongly connected to convection propagating from the Indian Ocean or to the West Pacific, as in observations (Figure 4(b)). Combined with the too-strong (tooweak) variability in RMM1 (RMM2), this suggests that instead of a coherent, propagating MJO, A-ENT-OBS produces a standing oscillation between the Indian Ocean and West Pacific that projects on to the Wheeler and Hendon (2004) EOFs.

Air-sea coupling at standard entrainment
Comparing K WP -CTL-OBS and A-CTL-OBS reveals the impact of air-sea coupling at default F, when GA3.0 has a poor MJO. Coupling to KPP produces changes in tropical rainfall and SST that are generally less than 1 mm day −1 and 0.2 K, respectively, but locally up to 2 mm day −1 and 0.5 K ( Figure 5). The warm SSTs and increased rainfall around the Maritime Continent may influence MJO propagation; we test the effects of the mean SST change in section 4.1. K WP -CTL-OBS (Figure 1(d)) has more frequent MJO activity (55% of days) than A-CTL-OBS (Figure 1(b)). This is somewhat lower than observed (61%) and A-ENT-OBS (59%), but indicates that coupling to KPP improves intraseasonal variability at default F. The lifetimes of K WP -CTL-OBS composite MJO events are longer than in A-CTL-OBS in all phases, particularly those in the Indian Ocean and Maritime Continent (Figure 2). Amplitude and propagation are weaker than in A-ENT-OBS, however. Klingaman et al. (2011) found that coupling to KPP made similar improvements to boreal-summer MJO amplitude and lifetimes in HadAM3, which also demonstrated poor subseasonal variability in atmosphere-only integrations.
Phase composites of K WP -CTL-OBS rainfall anomalies (Figure 3 Air-sea coupling has been found to improve the phase relationship between anomalies in SST and convection (Woolnough et al., 2001;Fu and Wang, 2004;Rajendran and Kitoh, 2006). A-CTL-OBS and A-ENT-OBS have coincident, positive correlations between OLR and SST anomalies, while K WP -CTL-OBS and K WP -ENT-OBS show a near-quadrature relationship with warm (cold) SSTs leading negative (positive) OLR anomalies by seven days (not shown), somewhat shorter than the observed lead of ten days (Vecchi and Harrison, 2002). To examine the spatial structure of MJO SST anomalies, phase composites were constructed as for rainfall ( Figure 6). For TMI/AMSRE SSTs, much of the Indian Ocean and Maritime Continent is  anomalously warm during phase 2 (Figure 6(a)), except for near the Equator where the strongest TRMM rainfall anomalies occur (Figure 3(a)). The warm anomalies are weaker in K WP -CTL-OBS ( Figure 6(d)), consistent with the smaller rainfall anomalies (Figure 3(j)) and suggesting weaker-than-observed surface forcing. Phases 4 and 6 (Figure 6(e) and (f)) also show much weaker anomalies than observed (Figure 6(b) and (c)). When GA3.0 has poor subseasonal variability (i.e. A-CTL-OBS), coupling improves MJO amplitude, propagation and spatial structure. None of these characteristics reaches observed levels: MJO activity is too low, propagation is limited to the Indian Ocean and the structure is still zonally elongated on the Equator. Air-sea feedback may act to amplify and organize the MJO in AGCMs with weak subseasonal variability in tropical convection.

Air-sea coupling at higher entrainment
Comparing K WP -ENT-OBS and A-ENT-OBS demonstrates the role of coupling at 1.5F, when GA3.0 has improved tropical subseasonal variability. The differences in mean precipitation and SST between K WP -ENT-OBS and A-ENT-OBS (not shown) are similar to those in Figure 5. K WP -ENT-OBS has similar total MJO activity (60.6%: Figure 1(e)) to A-ENT-OBS (58.6%: Figure 1(c)). This contrasts with section 3.2, in which coupling increased MJO activity at default F. The distribution of activity in K WP -ENT-OBS is more equitable than in A-ENT-OBS: activity increases in the Maritime Continent (phases 4 and 5) and the Western Hemisphere (phases 8 and 1) and decreases in the Indian Ocean (2 and 3) and West Pacific (6 and 7). This improves the biases in A-ENT-OBS (section 3.1), bringing the frequency of each phase closer to observations (Figure 1(a)). K WP -ENT-OBS has longer MJO lifetimes in nearly all phases than A-ENT-OBS ( Figure 2). In particular, the phase 2 composite in K WP -ENT-OBS propagates much further outside the unit circle, reaching the boundary with phase 4, as in observations. Improved propagation across the Maritime Continent is also apparent from regressions of 20-100 day filtered OLR (Figure 4(m)-(o)). Using a base point in the Indian Ocean (70 • E), K WP -ENT-OBS displays coherent eastward movement through the Maritime Continent with approximately the observed phase speed (Figure 4(m)). OLR anomalies over the Maritime Continent lag those over the Indian Ocean and lead those in the West Pacific (Figure 4(n)). Regression coefficients are slightly smaller than in observations, indicating weaker coherent intraseasonal OLR variability, but propagation improves over A-ENT-OBS (Figure 4(g)-(i)).
Coupling also improves the spatial coherence of MJO-related precipitation. Phase 2 anomalies in K WP -ENT-OBS (Figure 3(m)) are more strongly focused in the Indian Ocean than in A-ENT-OBS (Figure 3(g)). The zonally elongated anomalies in A-ENT-OBS are less apparent in K WP -ENT-OBS, although weak positive anomalies still exist east of the Maritime Continent. Similar improvements can be seen in phases 4 (compare Figure 3(n) and(h)) and 6 (compare Figure 3(o) and (i)). In phase 4, the spatial pattern in K WP -ENT-OBS is closer to TRMM (Figure 3(b)), with a clear westward tilt with latitude away from the Equator. K WP -ENT-OBS displays stronger and more coherent rainfall anomalies than K WP -CTL-OBS (Figure 3(j)-(l)). Associated with these are more intense SST anomalies (Figure 6(g)-(i)), particularly near the Maritime Continent, where MJO propagation shows the greatest improvement. The magnitude of the K WP -ENT-OBS anomalies agrees with TMI/AMSRE (Figure 3(a)-(c)), with a similar spatial pattern. K WP -ENT-OBS produces SST anomalies in the western Indian Ocean of the opposite sign to TMI/AMSRE, which may be due to the too-short phase lag between convection and SST (see section 3.2). When GA3.0 has a reasonable level of MJO activity, then, air-sea coupling does not further increase MJO amplitude or frequency of occurrence -as when the model has poor subseasonal variability -but instead improves the organization and propagation of convection.
To analyze the effect of coupling on the vertical structure of the MJO in the 1.5F simulations, we use phase composites of latitudeaveraged (15 • S-15 • N) specific humidity anomalies from the model and ERA-Interim (Figure 7). Although reanalysis humidity is influenced by the convective parametrization of the model used to produce the reanalysis, large-scale moisture variations should be reasonably well-constrained by observations. In phase 2, ERA-Interim shows deep moisture anomalies in the eastern Indian Ocean near 90 • E and a westward tilt with height; there are shallow positive anomalies across the Maritime Continent, with mid-and upper-level dry anomalies extending to the West Pacific (Figure 7(a)). A-ENT-OBS has weaker anomalies, little zonal tilt with height and a pronounced peak in moisture anomalies near the freezing level (Figure 7(d)). The positive anomalies over the Maritime Continent are too deep, consistent with the zonal elongation of equatorial rainfall anomalies (Figure 3(g)), suggesting convection still deepens too quickly in this region even at 1.5F. By contrast, K WP -ENT-OBS (Figure 7(g)) shows moisture anomalies that are more concentrated in the Indian Ocean, with the strongest anomalies extending throughout the lower and mid troposphere, rather than the narrow, mid-level peak in A-ENT-OBS. K WP -ENT-OBS also has a stronger westward tilt with height, although the positive anomalies over the Maritime Continent are still deeper than in ERA-Interim. The mid-and upper-level dry anomalies in K WP -ENT-OBS suggest that air-sea coupling improves the persistence of suppressed conditions east of the active phase. The cold SST anomalies in the West Pacific in phase 2 in K WP -ENT-OBS (Figure 6(g)), presumably from the previous active phase, may enhance the suppressed phase and delay the onset of deep convection. We note that all GA3.0 and GA3.0-KPP integrations show stronger boundary-layer specific-humidity anomalies than ERA-Interim. This is particularly evident in Figure 7(g), for example. This may indicate that convection in GA3.0 is overly sensitive to boundary-layer humidity, rather than free tropospheric humidity. The behaviour does not seem to be caused by increasing F, as A-CTL-OBS and K WP -CTL-OBS (not shown) also display strong boundary-layer anomalies. Further analysis of these features is outside the scope of this study; however, they warrant investigation.

The effect of the KPP-coupled mean state
Section 3.3 suggested that, when GA3.0 has reasonable tropical subseasonal variability, the key effect of coupling is to aid eastward propagation. Despite constraining KPP to climatological SSTs, the mean state of K WP -ENT-OBS differs from A-ENT-OBS, with more precipitation and warmer SSTs in the Maritime Continent (not shown, but similar to Figure 5). To test whether the mean SST changes caused the improved propagation, we prescribe the K WP -ENT-OBS climatological SSTs in A-ENT-K WP (section 2.3). A-ENT-K WP produces a similar distribution of MJO activity in RMM phase space (not shown) to A-ENT-OBS (Figure 1(c)), with an amplitude ≥ 1 on 61.3% of days and relatively lower activity in the Maritime Continent phases. Lag composites of strong events show similar or worse propagation to A-ENT-OBS in all phases (Figure 8(a) and (b)). A-ENT-K WP demonstrates limited eastward propagation in intraseasonal OLR (Figure 9(a)-(c)), particularly from the Indian Ocean through the Maritime Continent. Propagation is more similar to A-ENT-OBS (Figure 4(g)-(i)) than K WP -ENT-OBS (Figure 4(m)-(o)). This experiment confirms that the improved propagation in K WP -ENT-OBS is not due to the effect of coupling on the mean seasonal cycle of tropical SST. The changes in mean precipitation between these experiments are discussed in section 6.

Coupling in the Maritime Continent and West Pacific
Using K IO -ENT-OBS, we examine the sensitivity of the MJO in K WP -ENT-OBS to coupling in the Maritime Continent and the West Pacific by placing the eastern coupling boundary at 100 • E (Table 1).
K IO -ENT-OBS has a similar level of MJO activity (61.0%) and distribution in phase space to A-ENT-OBS (Figure 1(c)): the Indian Ocean and West Pacific (Maritime Continent and Western Hemisphere) phases occur relatively more (less) frequently (not shown). Lag composites of strong MJO activity (Figure 8(a) and (b)) show that coupling only in the Indian Ocean reverses the improvements in MJO lifetime and propagation from K WP -ENT-OBS (Figure 2(e)). The composites for strong Indian Ocean (phases 2 and 3) MJO events decay more quickly in K IO -ENT-OBS and fail to extend as far into phase 4 as in K WP -ENT-OBS or observations (Figure 2), indicating that the Maritime Continent is a stronger barrier when coupling only in the Indian Ocean.
The lack of propagation in K IO -ENT-OBS can also be seen in lag regressions of OLR (Figure 9(d)-(f)). Whereas K WP -ENT-OBS showed smooth propagation from the Indian Ocean to the West Pacific (Figure 4(m)), K IO -ENT-OBS displays propagation only to the 100 • E coupling boundary (Figure 9(d)). Using a base point at 100 • E (Figure 9(e)) shows some propagation from the Indian Ocean, but it is much weaker than in observations and   K WP -ENT-OBS (Figure 4(b) and (n)) and there is no propagation to the West Pacific. The structures of moisture anomalies associated with the MJO also degrade in K IO -ENT-OBS. In the phase 2 and phase 4 composites (Figure 7(j) and (k)), positive moisture anomalies terminate sharply near 100 • E at most heights. This weakens the westward tilt with height seen in K WP -ENT-OBS (Figure 7(g)-(i)) and ERA-Interim (Figure 7(a)-(c)). There is only a very weak extension of low-level anomalies from the Indian Ocean to the Maritime Continent in K IO -ENT-OBS in phase 2 and of upperlevel anomalies from the Maritime Continent to the Indian Ocean in phase 4, compared with K WP -ENT-OBS or reanalysis. The dry anomalies in phase 6 (Figure 7(l)) also decline at the coupling boundary and are weaker than K WP -ENT-OBS and ERA-Interim. In all aspects, the simulated tropical subseasonal variability in K IO -ENT-OBS resembles A-ENT-OBS more strongly than K WP -ENT-OBS.
A-ENT-K WP and K IO -ENT-OBS demonstrate that the key improvement from coupling at 1.5F -propagation through the Maritime Continent -relies upon the realistic simulation of air-sea interactions in the Maritime Continent and West Pacific. Coupling in the Indian Ocean alone is insufficient to produce a realistic MJO in GA3.0.

Motivation
In section 3.2, coupling at default F (K WP -CTL-OBS) enhanced the amplitude and propagation of subseasonal tropical convection compared with A-CTL-OBS. The UK Met Office Hadley Centre performed a similar experiment to K WP -CTL-OBS, but with GA3.0 coupled to NEMO (GA3.0-NEMO; section 2.3). Unlike KPP, NEMO includes horizontal ocean dynamics and does not use temperature or salinity corrections. Following Bernie et al. (2005Bernie et al. ( , 2008, Klingaman et al. (2011) and others, and as GA3.0-KPP, GA3.0-NEMO employs a 1 m near-surface ocean vertical resolution and a three-hourly coupling frequency, to improve intraseasonal SST variability. The simulated MJO in GA3.0-NEMO is slightly weaker (36.4% of days with amplitude ≥ 1) than in A-CTL-OBS (40.6%), particularly in the Maritime Continent and Western Hemisphere phases (not shown). There are also no improvements to the propagation or lifetime of composite MJO events (Figure 8(c) and (d)) relative to A-CTL-OBS (Figure 2(a) and (b)). This appears to contradict our result that well-resolved air-sea interactions improve the amplitude and propagation of subseasonal convection in GA3.0 at default F. Coupling to KPP and using climatological heat corrections (section 2.2) results in limited mean SST differences ( Figure 5) that do not affect the MJO substantially (section 4.1). GA3.0-NEMO, as with many fully coupled models, produces a considerably different mean state to its atmosphere-only counterpart (A-CTL-OBS; Figure 10). GA3.0-NEMO has colder SSTs throughout the Tropics than the Smith and Murphy (2007) SSTs prescribed in A-CTL-OBS and A-ENT-OBS; the difference approaches 1.5 K in the eastern Indian Ocean and the central equatorial Pacific.
To understand the extent to which these mean-state differences influence the representation of the MJO in GA3.0-NEMO and hence the diagnosed response of the MJO to coupling, we perform two experiments: A-CTL-NEMO and K WP -CTL-NEMO (section 2.3; Table 1). These experiments allow the differences between A-CTL-OBS and GA3.0-NEMO to be decomposed into (i) the presence of air-sea coupling, absent substantial changes in the mean state (comparing K WP -CTL-NEMO and A-CTL-NEMO), and (ii) the change in the mean state (A-CTL-NEMO versus A-CTL-OBS or K WP -CTL-NEMO versus K WP -CTL-OBS). While (ii) is caused by coupling, it can be thought of as a side effect of simulating air-sea interactions; (i) quantifies the direct impact of air-sea feedback.

Results
A-CTL-NEMO (33.4%; not shown) has considerably less MJO activity than A-CTL-OBS (40.6%) and somewhat less than GA3.0-NEMO (36.4%), confirming that mean-state biases degrade the MJO in GA3.0-NEMO. MJO activity in A-CTL-NEMO is most severely reduced in the eastern Indian Ocean and Maritime Continent (phases 3 and 4; not shown), the region of coldest SST errors in GA3.0-NEMO (Figure 10(a)). In these phases, the MJO 'decay' probability is 18% (i.e. an MJO event in phase 4 has an 18% chance of decaying into the unit circle on the next day), almost twice that in observations (9.9%, Figure 1(a)), suggesting that MJO events rarely pass from the Indian Ocean to the West Pacific. This is confirmed by RMM lag composites (Figure 8(c) and (d)), which are strongly attracted to the origin in phase space, and by lag regressions of OLR, which show no discernible propagation (Figure 9(g)-(i)). K WP -CTL-NEMO has improved subseasonal variability over A-CTL-NEMO, even though KPP is constrained to the same mean SSTs as prescribed in A-CTL-NEMO. MJO activity increases by about one third from A-CTL-NEMO (33.4%) to K WP -CTL-NEMO (43.2%), similar to the fractional increase from A-CTL-OBS (40.6%) to K WP -CTL-OBS (55.3%). K WP -CTL-NEMO displays some anticlockwise movement in the RMM lag composites (Figure 8(c) and (d)) and weak eastward propagation of OLR anomalies (Figure 9(j)-(l)). K WP -CTL-NEMO does not simulate a realistic MJO, but by all diagnostics it is an improvement over A-CTL-NEMO. In many phases, K WP -CTL-NEMO is also an improvement over GA3.0-NEMO; the reasons for this are unclear. The MJO in K WP -CTL-NEMO remains weaker than that in K WP -CTL-OBS, however, again demonstrating the degradation from the GA3.0-NEMO mean state. Coupling can improve MJO-like variability even when the mean state strongly suppresses it.

Discussion
As in Klingaman and Woolnough (2013), increasing F improves the representation of tropical subseasonal variability in HadGEM3. While that study examined the MJO in a 20-year 1.5F simulation only cursorily, here we have demonstrated that 1.5F primarily increases MJO amplitude, with limited improvements in propagation. The lack of variability in RMM2 in A-ENT-OBS, combined with the decay in RMM amplitude in the lag composites near the Maritime Continent (Figure 2), makes it difficult to reject the hypothesis that subseasonal variability in A-ENT-OBS consists primarily of an anticorrelation between the Indian Ocean and the West Pacific. Such variability would project on to RMM1, but does not resemble the real-world MJO. This emphasizes the need for a range of diagnostics, such as the RMM indices, lag composites and phase composites of several fields, when assessing a model representation of the MJO. Nevertheless, A-ENT-OBS has improved subseasonal variability over A-CTL-OBS.
The comparisons of KPP-coupled and atmosphere-only integrations at default F (A-CTL-OBS and K WP -CTL-OBS) and 1.5F (A-ENT-OBS andK WP -ENT-OBS) strongly suggest that the role of air-sea coupling depends upon the level of subseasonal variability simulated by the AGCM. In K WP -CTL-OBS, as in many previous works (Sperber, 2004;Crueger et al., 2013), adding air-sea interactions to an AGCM with poor intraseasonal variability somewhat improves amplitude and propagation. Even in K WP -CTL-NEMO, when the MJO was strongly suppressed by the GA3.0-NEMO mean state, adding coupling resulted in a modest increase in MJO amplitude and some eastward propagation. Interpreted on their own, as we and others have often done, these results would suggest that coupling is required to bring the level of simulated intraseasonal convection closer to observations.
Yet when the amplitude, if not the spatial distribution, of subseasonal variability in the AGCM approaches observations, as in A-ENT-OBS, coupling has no effect on MJO intensity or frequency (Figure 1). There is nothing to prevent a further increase in MJO activity in K WP -ENT-OBS beyond the observed level or that in A-ENT-OBS; several models have been shown to have 'hyperactive' MJOs (e.g. Hendon, 2000). Rather, K WP -ENT-OBS indicates that when an AGCM is able to simulate strong intraseasonal variability, air-sea coupling no longer provides a positive feedback on that intensity. We obtained these results even when using a 1 m near-surface ocean vertical resolution and sub-daily coupling, generating intraseasonal SST anomalies of comparable magnitude to observations (Figure 6), which past studies showed amplified subseasonal convective activity (Woolnough et al., 2007;Bernie et al., 2008). This supports the hypothesis, presented in section 1.2, that, in AGCMs with poor intraseasonal variability in tropical convection, introducing coupling provides some high-frequency SST anomalies that feed back and amplify what little subseasonal convection exists in the AGCM. It is known that AGCMs respond to prescribed highfrequency SSTs with additional MJO-like activity (Kim et al., 2008;Klingaman et al., 2008a), so it is plausible to construct a similar argument for coupled models. Amplifying those SST anomalies by refining ocean vertical resolution and including the diurnal cycle of air-sea interactions would intensify that effect (Klingaman et al., 2011). It is possible, therefore, that, in AGCMs with poor subseasonal variability, coupling acts as a 'crutch' that amplifies intraseasonal convective anomalies. The mechanism by which this crutch operates requires further studies, the most productive of which may be a systematic set of experiments with several GCMs.
Our K WP -ENT-OBS, A-ENT-K WP and K IO -ENT-OBS experiments indicate that air-sea interactions still have a substantial role in MJO propagation and maintenance, even when the AGCM generates intense, spatially coherent subseasonal convection. The improved MJO propagation in K WP -ENT-OBS over A-ENT-OBS results in a more equitable distribution of activity around phase space, since fewer events decay near the Maritime Continent. A-ENT-K WP demonstrated that this improvement was not due to the relatively small mean SST differences from coupling to KPP. Since we prescribed only the mean seasonal cycle of SST from K WP -ENT-OBS in A-ENT-K WP , it remains possible that the interannual SST variability in K WP -ENT-OBS is somehow responsible for the improved MJO propagation. Further, there are differences in mean precipitation between A-ENT-K WP and K WP -ENT-OBS (not shown), which may be caused by the lack of either interannual SST variability or air-sea coupling in A-ENT-K WP , or some combination of the two. The Maritime Continent (tropical Northwest Pacific) is wetter (drier) in K WP -ENT-OBS by approximately 2 mm day −1 in the annual mean; both changes reduce model biases relative to TRMM. Increased moisture in the Maritime Continent may influence MJO propagation in K WP -ENT-OBS. The results of A-ENT-K WP dismiss only the climatological SST differences between K WP -ENT-OBS and A-ENT-OBS.
K IO -ENT-OBS indicates that MJO propagation in GA3.0 requires well-resolved air-sea interactions in the Maritime Continent and West Pacific. This agrees with Weng and Yu (2010), who found that eastward propagation terminated sharply at the coupling boundary when coupling only in the Indian Ocean. Other studies have found coupling in the Indian Ocean to be more important, but many of these have focused on northward propagation during boreal summer (e.g. Lin et al., 2011;Achuthavarier and Krishnamurthy, 2011). One hypothesis for the influence of coupling on propagation, which is by no means novel, is that air-sea interactions cool SSTs under and to the west of active convection, in the former location from reduced surface fluxes and in the latter from increased winddriven mixing. At the same time, SSTs east of the convection warm from increased insolation and reduced evaporation. This anomalous SST distribution would stabilize the atmosphere near the enhanced convection while maintaining instability to the east, 'enticing' propagation. SST phase composites from K WP -ENT-OBS support, but cannot confirm, this hypothesis ( Figure 6). With no SST anomalies in the Maritime Continent or West Pacific, K IO -ENT-OBS is unable to propagate the MJO out of the Indian Ocean; coupling in the Indian Ocean alone has no effect on either MJO propagation or amplitude in GA3.0.
By coupling with KPP and using climatological heat corrections, we have separated the impacts on the MJO from air-sea interactions as far as possible from those from changes in the tropical mean state. This is an important separation, as mean-state errors may influence not only the level of subseasonal convective variability but also the simulation of air-sea exchanges themselves, for instance by altering mean low-level wind direction  or air-sea temperature gradients. This framework has allowed us to test the sensitivity of the MJO in the fully coupled model, GA3.0-NEMO, to the mean-state biases in that model. Analyzing only A-CTL-OBS and GA3.0-NEMO would have led us to conclude that air-sea coupling has no effect on, or even worsens, the MJO. K WP -CTL-NEMO and A-CTL-NEMO demonstrate that the direct effect of air-sea interactions is actually to improve the amplitude and propagation of subseasonal convection, albeit modestly and from a very low baseline, but that the GA3.0-NEMO mean state substantially suppresses intraseasonal variability. Many previous sensitivity studies on the role of coupling in the MJO have not separated these effects, or have attempted to do so by prescribing coupledmodel SSTs in an AGCM integration. The latter experiment, while somewhat useful, does not consider the the influence of mean-state errors within the coupled framework. These can be assessed here by comparing K WP -CTL-OBS and K WP -CTL-NEMO, which conclusively show that mean-state biases in GA3.0-NEMO weaken an already low level of variability. Further, prescribing SSTs in an AGCM imposes an erroneous lower boundary condition, since AGCMs generally fail to simulate the near-quadrature phase relationship between SSTs and convection (Fu and Wang, 2004). Future experiments exploring the sensitivity of the simulated MJO to air-sea coupling should distinguish the 'direct' impact of coupling -exchanges between the atmosphere and ocean -from the 'indirect' impact -changes to the mean state of the model.

Summary and conclusions
To summarize the simulated MJO in our experiments, we compute the Sperber and Kim (2012) 'simplified MJO metrics', based on projecting maps of model 20-100 day bandpass-filtered OLR on to the first two EOFs of observed OLR (with the same filtering applied). Lag correlations of the resulting principal component (PC) time series are then computed; the metrics are the maximum positive correlation and the lag at which it occurs (Figure 11(a)). Proximity to observations, which have a correlation of 0.69 at a lag of 11 days, indicates strong eastward propagation with observed phase speed. The standard deviations of the PCs measure MJO amplitude (Figure 11(b)). We also compute the east-west power ratio metric (Kim et al., 2009): the sum of eastward spectral power in wavenumbers 1-3 and periods of 30-80 days divided by the sum of westward power at the same wavenumbers and periods (Figure 11(c)).
We conducted atmosphere-only and coupled experiments to explore the roles of air-sea interactions on the intensity and propagation of the MJO in two configurations of the Hadley Centre model (GA3.0). The configurations differ by a single parameter, F, which controls the rates of entrainment and mixing detrainment for diagnosed deep and mid-level convection. Klingaman and Woolnough (2013) found that increasing F by 50% (1.5F) increased MJO activity in hindcasts and a 20 year simulation. Motivated by those results, we have analyzed how the level of subseasonal convective variability in an atmospheric GCM alters the impact of air-sea interactions on that variability. Initially, we performed four 20 year GA3.0 integrations (Table 1): two atmosphere-only, one at default F (A-CTL-OBS) and one with 1.5F (A-ENT-OBS); and two coupled to many columns of the KPP boundary-layer ocean in the tropical Indo-Pacific (30 • S-30 • N, 20 • -200 • E), as in Klingaman et al. (2011), one at default F (K WP -CTL-OBS) and one with 1.5F (K WP -ENT-OBS). Climatological temperature corrections in KPP maintained similar mean states in coupled and uncoupled experiments (Figure 5), while producing near-observed levels of subseasonal SST variability ( Figure 6).
As in Klingaman and Woolnough (2013), A-ENT-OBS (Figure 1(c)) produced a stronger MJO than A-CTL-OBS (Figure 1(b)), bringing GA3.0 closer to observations (Figure 1(a)). Propagation remained deficient in A-ENT-OBS, particularly through the Maritime Continent (Figure 2). A-ENT-OBS produced most of its variability in (Wheeler and Hendon, 2004) RMM1, an anticorrection between the Indian Ocean and the West Pacific, with relatively less in RMM2, which is centred over the Maritime Continent. The lack of consistent propagation led us to conclude that, while A-ENT-OBS was a substantial improvement over A-CTL-OBS, it did not fully capture the MJO. The Sperber and Kim (2012) and east-west power ratio metrics confirm that A-ENT-OBS (unfilled square) has a stronger MJO than A-CTL-OBS (unfilled star) with improved propagation, although propagation remains deficient (Figure 11).
The MJO in K WP -CTL-OBS (Figure 1(d)) was also stronger than A-CTL-OBS, with some eastward propagation (Figure 2), confirming previous studies (Sperber, 2004;Rajendran and Kitoh, 2006) that found that air-sea coupling improved the MJO in AGCMs with deficient subseasonal variability. Amplitude and propagation remained weaker than observed (Figure 11, filled star). At 1.5F, coupling (K WP -ENT-OBS) did not affect overall MJO activity (compare Figure 1(c) and (e)), but considerably improved propagation (Figure 4). This is confirmed by the Sperber and Kim (2012) propagation metric (Figure 11(a), compare unfilled and filled squares) and the east-west power ratio (Figure 11(c)), with little change in the amplitude metric ( Figure 11(b)).
The results of an AGCM integration with climatological K WP -ENT-OBS SSTs, A-ENT-K WP , demonstrated that the small mean SST changes from coupling to KPP were not responsible for the improved MJO propagation in K WP -ENT-OBS (section 4.1). Our experiment design cannot dismiss the roles of interannual SST variability or changes in climatological precipitation in MJO propagation, however, so it remains possible that subseasonal air-sea interactions are not the sole cause of the improved MJO in K WP -ENT-OBS (section 6). A sensitivity experiment with coupling only in the Indian Ocean, K IO -ENT-OBS, produced an MJO more similar to A-ENT-OBS than K WP -ENT-OBS (Figure 8(a) and (b)), confirming that air-sea interactions in the Maritime Continent and West Pacific are critical for improved propagation in K WP -ENT-OBS.
The differing impacts of coupling in K WP -CTL-OBS and K WP -ENT-OBS suggest that, for AGCMs with poor tropical subseasonal variability, coupling may provide a 'crutch' that artificially enhances variability in convection via feedback from high-frequency SST anomalies. Since the MJO is primarily an atmospheric mode of variability, A-ENT-OBS provides a better approximation of real-world subseasonal variability than A-CTL-OBS. Based on our experiments, the likely role of coupling in MJO events is to maintain convective anomalies and promote propagation, as in K WP -ENT-OBS, rather than to increase intensity.
A final set of atmosphere-only (A-CTL-NEMO) and KPPcoupled (K WP -CTL-NEMO) integrations demonstrated the ability of the GA3.0-KPP framework to separate cleanly two effects of air-sea interactions in a fully coupled model, GA3.0-NEMO, on simulated subseasonal variability: the inclusion of air-sea exchanges -the 'direct impact' of coupling -and coupled-model mean-state biases -the 'indirect impact'. Comparing GA3.0-NEMO and A-CTL-OBS showed no improvement in MJO activity from coupling, in contrast to comparison of K WP -CTL-OBS and A-CTL-OBS (Figure 11). A-CTL-NEMO and K WP -CTL-NEMO revealed that the small change in activity in GA3.0-NEMO was the result of two larger but offsetting impacts: an increase from the direct impact (comparing K WP -CTL-NEMO and A-CTL-NEMO), but a degradation due to the indirect impact (comparing K WP -CTL-NEMO and K WP -CTL-OBS or A-CTL-NEMO and A-CTL-OBS). If the impacts of coupling are not separated, then changes (or the lack thereof) in intraseasonal variability between AGCM and coupled simulations may be incorrectly attributed to the inclusion of air-sea interactions, when they may be partially or entirely due to mean-state biases.
The mechanisms by which coupling improved the amplitude and propagation of subseasonal convection in K WP -CTL-OBS and the propagation of convection in K WP -ENT-OBS remain unclear. Further experiments, carefully designed to distinguish between the direct and indirect impacts of coupling and using a range of models, are necessary to understand these mechanisms.