We do not attempt to provide a comprehensive or balanced review of MJO theory. This is beyond our intended scope, and several recent reviews cover the ground well [Wang, 2005; Zhang, 2005; Waliser, 2006]. Instead we focus on theories in which variations in surface enthalpy fluxes figure prominently.
 Approximately simultaneously, Emanuel  and Neelin et al.  proposed that air-sea interaction could destabilize a moist Kelvin wave, leading to intraseasonal variability in the tropics. The arguments involved linear analysis of idealized moist models in which the temperature structure is assumed to be represented by a first baroclinic mode, and convection is controlled by quasi-equilibrium principles. Essentially, convection acts in these systems to eliminate some local measure of stability of the column to deep convection. The atmosphere is adjusted by convection towards a reference value of the stability measure [e.g., convective available potential energy (CAPE)], which for present purposes may be assumed zero. The dynamics of such models is discussed in more detail in a number of reviews [e.g., Emanuel et al., 1994; Neelin, 1997, Stevens et al., 1997; Smith, 1997; Arakawa, 2004; Emanuel, 2007]. Neelin et al.  also performed numerical simulations with a general circulation model (GCM).
 We refer to models of the type discussed by Emanuel et al.  as “‘quasi-equilibrium’ (QE) models”. In its most general sense, the term QE refers to a broader category, including all models in which the convection is assumed close to statistical equilibrium with its forcings. Traditional QE models incorporate additional assumptions, in particular that of a pure first baroclinic mode vertical structure, which can be relaxed without relaxing the assumption of QE per se. In models assuming a first baroclinic mode structure as well as QE, the interaction of deep convection with large-scale dynamics alone does not generate unstable large-scale modes. In the simplest such models convection is assumed to respond instantaneously to large-scale forcing (which can come from large-scale dynamics, radiation, or surface fluxes) so as to remove all local instability completely; Emanuel et al.  called this “strict quasi-equilibrium”. In this case, the interaction of convection and large-scale dynamics reduces the effective stratification and thus the phase speed of convectively coupled gravity and Kelvin waves, but does not stabilize or destabilize them (in the sense of linear instability of a dynamical mode, as opposed to the local instability which causes convection). If instead the convection is assumed to relax the CAPE (or other measure of column instability) towards its reference value with a finite timescale, then the interaction damps disturbances, a phenomenon known as “moist convective damping”. Disturbances in these models cannot become linearly unstable through the interaction of convection with large-scale dynamics alone, but only through feedbacks involving processes which can act as sources of moist static energy (or moist entropy) to the column. The two most important such processes are surface turbulent fluxes and radiative cooling.
 The requirement for moist static energy sources to be involved in any linear instability is an interesting feature of first baroclinic mode quasi-equilibrium models. In extratropical atmospheric dynamics it has proved extremely useful to separate dry adiabatic dynamical mechanisms [e.g., Hoskins et al., 1985] from those in which “diabatic” processes (defined for a dry working fluid with phase changes of water considered external), which break the conservation of potential temperature and potential vorticity, are fundamentally involved. It is clear that dry adiabatic dynamics are inadequate to describe many important aspects of the tropical atmospheric circulation and its variability, but the relative importance of moist adiabatic dynamics — as opposed to dynamics in which moist diabatic processes (those which break the conservation of moist static energy and moist entropy) are critical — remains unresolved. The analogy to extratropical dynamics, and the overall centrality of quasi-conserved variables in all of physics, suggests that it is fruitful to ascertain the relative importance of moist adiabatic and diabatic processes to intraseasonal variability. This is a separate and more fundamental question than that regarding the validity of first baroclinic mode QE models, since the latter make a number of additional restrictive assumptions. Nonetheless those models provide a useful starting point for discussion since they make a clear prediction on the relevance of diabatic processes, as well as being both relatively tractable and based on principles that are at root physically reasonable (convection acts to eliminate instability) even though some of their simplifying assumptions may be too strong for some purposes.
 In the models of Emanuel  and Neelin et al. , Kelvin waves are destabilized by the interaction of a convectively coupled wave with surface flux perturbations induced by the wave's surface wind perturbations. This interaction was called “wind-evaporation feedback” by Neelin et al.  and “wind-induced surface heat exchange (WISHE)” by Emanuel . For an eastward moving Kelvin wave in a westward mean flow, a positive surface wind speed anomaly occurs a quarter wavelength ahead of the location where the positive precipitation and vertical velocity anomalies would be in the absence of surface flux anomalies, but in phase with the temperature anomaly. Under the strict quasi-equilibrium assumption, the convection responds immediately to surface flux anomalies, so the surface flux anomaly causes the heating anomaly to shift eastward, putting it partly in phase with the temperature anomaly and destabilizing the wave.
 Key features of this linear theory for intraseasonal variability are that the waves must occur in an easterly mean surface flow, that the winds under the convective phase of the disturbance are easterly, and that the intraseasonal disturbances are Kelvin waves. All of these features have been shown to be inconsistent with observations. It was immediately recognized that the strongest MJO events occur in regions of mean westerlies [Wang, 1988; Emanuel, 1988; Neelin, 1988]. It was then shown that the active phases, featuring enhanced precipitation, occur in surface westerlies [e.g., Kiladis et al., 1994; Zhang and McPhaden, 2000]. Wheeler and Kiladis  then showed that “convectively coupled” Kelvin waves do exist, but that their spectral signatures are quite distinct from that of the MJO, indicating that the two are different phenomena. These observations showed that the linear models of Emanuel  and Neelin et al.  are, in their specifics, incorrect as explanations of the MJO.
 The observations are not, however, inconsistent with the general notion that surface flux anomalies may be important to the dynamics of the MJO, but only with the specific linear models proposed by Emanuel  and Neelin et al. . If the disturbance is something other than a linear Kelvin wave, the requirements for mean easterly flow and net easterly flow in regions of active convection no longer apply. Some studies with nonlinear models have identified such “nonlinear WISHE” as being important in simulated MJO-like disturbances [Raymond, 2001; Maloney and Sobel, 2004]. In general, there is not a simple or straightforward relationship between the formulation of a given model (whether a full-physics GCM or an idealized model) and the importance of surface flux feedbacks. For example, while WISHE was first proposed in first baroclinic mode quasi-equilibrium linear models, there is no a priori reason it cannot occur in models with more complex vertical structure, different physical parameterizations, and full nonlinearity. Whether WISHE or cloud-radiative feedbacks are active in any particular model is often most easily determined by disabling these mechanisms and examining the resulting changes in the model solution at intraseasonal timescales.
 A misperception that sometimes arises is that the enhancement of precipitation by surface fluxes in a model in which WISHE is active operates directly through the moisture budget — that is, that a perturbation in surface latent heat flux results in an equal perturbation in rainfall, simply because the extra water vapor put into the atmosphere by the extra flux precipitates out locally. If this were the case, the observation that precipitation anomalies in the MJO (as in many other tropical circulations) tend to greatly exceed surface evaporation anomalies would seem to contradict WISHE. This is incorrect. A positive surface flux anomaly in QE models enhances precipitation through its effect on buoyancy, not through simple local moisture recycling, and in those models (as in observations) it is generally true that the lion's share of anomalous precipitation results from moisture convergence. The moisture budget by itself is not particularly useful in discriminating between different theories for the dynamics of the MJO.
 In the two decades since the publication of Emanuel  and Neelin et al. , much more work has been done with idealized moist models which aim to explain either the MJO, other aspects of tropical intraseasonal variability (such as the northward-propagating mode found in northern hemisphere summer, discussed further below), or other parts of the convectively coupled wave spectrum. These studies have broadened and deepened our understanding of the spectrum of possible mechanisms that can occur in large-scale geophysical flows with embedded deep convection. In the case of the MJO, however, none of them has been broadly accepted as providing a satisfactory explanation of the essential mechanisms [Zhang, 2005;Wang, 2005; Waliser, 2006].
 A number of recent studies have developed idealized models which incorporate effects not included in earlier studies. Many of these include a second baroclinic mode in addition to the first [Mapes, 2000; Majda and Shefter, 2001a; Khouider and Majda, 2006a, b; Kuang, 2008], and some include non-equilibrium effects in their convective closures. These additional effects can under some circumstances render disturbances linearly unstable purely through the interaction of convection with large-scale dynamics, without feedbacks via surface enthalpy fluxes. Other recent studies focus on the role of upscale energy transfer from synoptic- or mesoscales to the planetary-scale intraseasonal disturbances [Biello and Majda, 2005, 2006; Biello et al., 2007]. As with previous studies, these continue to broaden and deepen our understanding of potentially relevant mechanisms, but have not yet led to a coalescence of agreement on their centrality to observed intraseasonal variability.
 The lack of broad agreement on the mechanism of the MJO does not necessarily indicate that previous studies are not correct to some degree. It may instead reflect the fact that a number of very different models predict the occurrence of intraseasonal oscillations which are comparable in the degree to which they resemble the observed ones, so that distinguishing between them is difficult; or that simulated intraseasonal oscillations (in models at all levels of complexity) are very sensitive to the representation of deep convection, a difficult and controversial problem from many perspectives. Regardless, this lack of agreement is a fact, and its existence at this point should lead us to consider whether there is something we can do beyond what we have been doing to resolve it. Further development of idealized models is surely warranted, and may yet lead to a breakthrough which will be broadly recognized as one. We argue that it is also worth treating the assessment of available theoretical ideas against available evidence as an important problem in its own right, and spending more effort on it than we, the community of researchers interested in this problem, have done. The motivation for doing this increases further as new modeling and observational resources become available. We emphasize this problem here preferentially over more detailed discussion of recent theoretical developments, interesting and promising as those may be.
2.2. Northern Summer Intraseasonal Variability
 In northern summer, intraseasonal variability modulates the Asian and western Pacific monsoons. Spectra of atmospheric variability exhibit two significant peaks in the intraseasonal range: one at 10-20 days and one at 30-60 days [Goswami, 2005]. The 10-20-day mode is characterized by convective disturbances which propagate from the western Pacific warm pool and the maritime continent towards the northern Bay of Bengal and South Asia. These disturbances have been associated with equatorial Rossby waves deviated northward by the mean monsoon flow [Chatterjee and Goswami, 2004]. The 30-60-day mode is characterized by the northward propagation of approximately zonally-oriented rain bands from 5° S to 25° N [Wang et al., 2006]. This northward propagation is sometimes accompanied by eastward propagation [Wang and Rui, 1990; Lawrence and Webster, 2002]. Nevertheless, the northward propagating mode appears to be an independent regional mode of variability, rather than simply a local response in the South Asian region to the eastward-propagating disturbances [Jiang and Li, 2005], though this is still controversial in some quarters (e.g., Sperber and Annamalai, 2008). We focus here on this northward-propagating mode, assuming that the eastward-propagating mode is essentially similar to the southern summer MJO.
 Given the nearly zonal orientation of the rain bands and their nearly meridional direction of propagation, a number of studies have assumed that longitudinal structure is inessential to the dynamics of this mode, and modeled it axisymmetrically [Webster and Chou, 1980; Goswami and Shukla, 1984; Gadgil and Srinivasan, 1990; Nanjundiah et al., 1992; Srinivasan et al., 1993; Jiang et al., 2004; Drbohlav and Wang, 2005; Bellon and Sobel, 2008a, b]. These studies have obtained linearly unstable northward propagating modes which resemble the observed one to varying degrees. In earlier studies, land-atmosphere interaction was proposed as crucial to the northward propagation [Webster and Chou, 1980; Webster, 1983]. However, northward propagating modes were also later obtained in aquaplanet simulations [Goswami and Shukla, 1984; Nanjundiah et al., 1992]. The northward propagation has been attributed in several recent studies to dynamical mechanisms that involve low-level convergence north of the propagating rain band. This convergence is caused by Ekman pumping under a maximum of barotropic vorticity which itself leads the maximum convection [Jiang et al., 2004; Goswami, 2005; Bellon and Sobel, 2008b; Bellon and Sobel, 2008a]. The mechanisms explaining the generation of this barotropic vorticity maximum are still debated [Jiang et al., 2004; Drbohlav and Wang, 2005; Bellon and Srinivasan, 2006; Bellon and Sobel, 2008a].
 The question of what destabilizes the mode is distinct from that of what causes its propagation. In the model of Bellon and Sobel (2008a,b), interactive surface fluxes were found to be important to the instability of the northward propagating mode. They used the quasi-equilibrium model developed by Sobel and Neelin , which has a barotropic mode and prognostic boundary layer in addition to a first baroclinic mode in the free troposphere. Because of this more complex vertical structure, the set of possible dynamical mechanisms in this model is broader than that in the pure first baroclinic mode QE models. It is possible for linear instability to occur in this model without surface flux feedbacks. Nonetheless, Bellon and Sobel (2008a,b) found that WISHE is critical to the linear instability of the northward-propagating mode in the parameter regime which appears most justified based on observations. As usual with idealized models, one can easily challenge various details of this model (which has some similarities to earlier ones [e.g. Jiang et al., 2004] as well as some differences). The results of Bellon and Sobel [2008a,b] just show that it is possible to construct a plausible model of the northward-propagating mode of intraseasonal variability — one based on physics that is within the broad envelope of what is commonly found in idealized models of tropical atmospheric dynamics, and also broadly consistent with observations — in which surface flux feedbacks are essential.
2.3. The Near-equivalence of Surface Fluxes and Radiation in Quasi-equilibrium
 The primary radiative effects of the high clouds associated with deep convection are a cooling of the surface due to reflection and absorption of shortwave radiation and a warming of the atmosphere due to the greenhouse effect in the longwave and the absorption of shortwave. To the extent that these effects have similar magnitudes, so that they cancel at the top of the atmosphere, they lead to a cooling of the ocean and equal warming of the atmosphere. This is equivalent to a surface enthalpy flux, as far as the vertically integrated moist static energy budget of the atmosphere is concerned. QE theory provides a useful context in which to frame this equivalence.
 If the vertical structure of the atmospheric flow is assumed fixed (for example, a first baroclinic mode), and if we assume steady state and neglect horizontal advection, the budget of moist static energy requires that the large-scale vertical motion, or net vertical mass flux, is proportional to the net convergence of the vertical flux of moist static energy into the tropospheric column [e.g., Neelin and Held, 1987; Raymond, 2000; Neelin, 1997; Neelin, 2007; Sobel, 2007]. The latter is the sum of the net turbulent latent and sensible surface heat fluxes plus the vertically integrated radiative heating of the troposphere (or minus the radiative cooling).
 The proportionality factor which relates the moist static energy (or moist entropy) flux to the mass flux is known as the gross moist stability (GMS), following Neelin and Held . There is no very good theory for the value of the GMS, though some observational estimates have been made [Yu et al., 1998; Back and Bretherton, 2006]. Raymond et al.  review recent thinking on the mechanincs of the GMS. The first baroclinic mode assumption is restrictive, perhaps even qualitatively misleading in some circumstances [e.g., Sobel, 2007], but no better idea of comparable simplicity has yet appeared. In general, the GMS need not be a constant or a simple function of the temperature and humidity profiles alone (as in first baroclinic mode QE theory), because it is quite sensitive to the vertical profile of the divergent circulation [Sobel, 2007]. Since the latter can vary dynamically on a range of space and time scales, the GMS can as well. In simulations in a GCM with simplified physics [Frierson, 2007b] the GMS is strongly influenced by properties of the convective parameterization [Frierson, 2007a].
 For our immediate purpose, what matters most is that GMS be positive on average on intraseasonal time scales, so that increases in net vertical moist static energy flux convergence into the column lead (with a time lag that is either negligible or at least short by comparison to the intraseasonal timescale; storage on timescales of a few days does not significantly complicate the argument) to increases in vertical mass flux, which in turn imply increases in deep convection. This is a weaker constraint than usually assumed in QE theory, though the difference is one of degree rather than kind. Even the positivity of the gross moist stability is questionable in observations, particularly in the eastern Pacific ITCZ [Back and Bretherton, 2006], but it appears to be a reasonable assumption in the Indian and western Pacific regions for the time mean. In some models, the transient occurrence of negative GMS appears to be important to the dynamics of the simulated MJO [Raymond and Fuchs, 2009], though even there enhanced surface fluxes appear to be associated with enhanced precipitation.
 We assume that the difference in the cloud field between convectively active and suppressed precipitation regimes consists predominantly of the presence vs. absence of high clouds. Satellite observations have shown that, in the mean, these clouds produce perturbations in the net radiative energy flux at the top of the atmosphere which are small compared to their largely cancelling shortwave and longwave components [Ramanathan et al., 1989; Harrison et al., 1990; Hartmann et al., 2001]. Lin and Mapes  found that this cancellation is less close on intraseasonal time scales, with MJO-related shortwave anomalies being larger than longwave ones by as much as 30%. This is a significant difference, but still the cancellation substantially exceeds the remainder. The implication is that any anomalous radiative heating of the atmosphere due to these clouds, whether occurring in the longwave or shortwave bands, is approximately compensated by anomalous radiative cooling of the ocean. In the vertically integrated moist static energy budget, cloud-radiative heating anomalies due to deep convection are essentially similar to convectively induced perturbations to turbulent surface heat fluxes, as both amount to a net transfer of enthalpy from ocean to atmosphere in a convectively active phase. When convection is active, there is a net decrease of radiative energy flux into the ocean, accompanied by a significantly smaller change in the top-of-atmosphere balance. Thus we use the phrases “surface fluxes” or “surface flux feedbacks” to include radiative cooling feedbacks.
2.4. Ocean Coupling
 A substantial body of work over the last decade or so argues that intraseasonal SST variability is not only driven by the atmosphere, through intraseasonal variations in surface enthalpy fluxes, but that SST variability also influences the atmosphere through the influence of SST anomalies on column stability and deep convection. To the extent that these feedbacks are significant, intraseasonal variability is coupled. Most GCM studies addressing this in the context of the MJO have shown some enhancement of the simulated variability in experiments with atmospheric models coupled to a mixed-layer ocean models, as compared to models with fixed SST [Waliser et al., 1999; Kemball-Cook et al., 2002; Zheng et al., 2004; Fu et al., 2007], although at least two studies found no enhancement [Hendon, 2000; Grabowski, 2006] and and others found small enhancements [e.g., Maloney and Sobel, 2004] or mixed results, with differences in the mean climate between coupled and uncoupled runs complicating the interpretation [Inness and Slingo, 2003]. This evidence suggests that the MJO is enhanced by coupling, but is not fundamentally dependent on coupling for its existence. In virtually all models tested in this way, a simulated MJO is present to some degree without coupling.
 Observations suggest that coupling has a qualitatively similar impact on intraseasonal variability of the Asian monsoon in northern hemisphere summer, including northward-propagating rainbands and SST variability in the Arabian sea and Bay of Bengal [Vecchi and Harrison, 2002; Wang et al., 2006; Roxy and Tanimoto, 2007]. In GCM studies, ocean coupling enhances northward-propagating intraseasonal variability in the Indian Ocean to varying degrees [e.g. Zheng et al., 2004, Seo et al., 2007, Fu et al., 2007, Fu and Wang, 2004, Kemball-Cook et al., 2002]. One recent study with an idealized axisymmetric model suggests that the SST variability is largely passive, being forced by the atmosphere but having only a modest impact on the atmospheric mode [Bellon et al., 2008].
 The question of the importance of ocean coupling is related to but not the same as that of the importance of surface fluxes to the dynamics of intraseasonal variability. If ocean coupling is important, surface fluxes must be involved, since only through those fluxes can the ocean influence the atmosphere. The converse is not true: an important role for surface fluxes does not necessarily imply that coupling is important. Surface flux feedbacks can operate in models which assume fixed SST. Such models do not satisfy a surface energy budget, but their surface fluxes can still vary interactively and influence the atmosphere. Coupling can either amplify or damp intraseasonal variability, depending on the phasing of the SST anomalies relative to anomalies in atmospheric variables. For example, Shinoda et al.  found that observed SST anomalies slightly reduced the amplitude of MJO-related surface latent heat fluxes compared to what they would have been for fixed SST.
 Our interest here is in the role of surface fluxes in the dynamics of atmospheric intraseasonal variability. Ocean coupling, while also arguably important, is secondary in this discussion. However, as discussed next, the nature of the underlying surface is important to the extent that it must have sufficiently large heat capacity to allow substantial fluctuations in the net surface enthalpy flux on the intraseasonal time scale.