The Madden–Julian oscillation (MJO; Zhang, 2005) is a prominent tropical variability that many global atmospheric models still have difficulties simulating. In the case of the ECMWF Integrated Forecasting System (IFS), the forecast of the propagation of a pre-existing MJO has much improved in recent years (Vitart, 2014), typically providing persistent MJO signals well beyond the medium-range forecast. However, the IFS still suffers from some difficulties, especially in predicting the onset of MJOs. The capacity to produce extended MJO forecasts is becoming more important with increasing demand for extended forecasts up to a subseasonal range (3–4 weeks) and because the MJO is one of the most prominent and persistent tropical signals to be forecast over this timescale (see Kim et al., 2018).

From an operational point of view, the MJO is typically considered physically forced in the sense that the physical parameterizations (or “physics” for short) in the models are the key to improving the simulation of the MJO, rather than a problem of the dynamical core (e.g. Hirons et al., 2013a, b). The most crucial physical process to be considered is deep convection, which is typically parameterized as a sub-grid-scale process in global models (Plant and Yano, 2015). A majority of the existing theories for the MJO are based on a certain coupling of the large-scale dynamics with convection (e.g. Hayashi, 1970; Lindzen, 1974; Emanuel, 1987; Yano and Emanuel, 1991; Majda and Stechmann, 2009; Fuchs and Raymond, 2017; see also reviews by Zhang et al., 2020; Jiang et al., 2020a). For this reason, a general expectation is that simulations and forecasts of the MJO in the global models must be improved by improving the parametrization of deep convection (see Jiang et al., 2015, 2020b) as well as shallow convection (see Pilon et al., 2015). Thus, existing sensitivity studies on MJO simulations almost exclusively focus on convection parameterizations (e.g. Hirons et al., 2013a, b; Pilon et al., 2015).

The present study examines the sensitivity of the MJO forecasts to physics from a different perspective of Yano and Bonazzola (2009), Yano et al. (2009), Wedi and Smolarkiewicz (2010), Yano and Tribbia (2017), Rostam and Zeitlin (2019), and Wang et al. (2019). According to their perspective, the tropical large-scale dynamics in general and the MJO specifically can be understood in terms of free Rossby wave dynamics, in which model “physics” may still play a role, although secondary to the initiation and evolution. More specifically, Yano and Tribbia (2017) and Rostam and Zeitlin (2019) propose that the MJO is basically understood in terms of a dipolar vortex (vortex pair) symmetric to the Equator, described by a nonlinear analytical solution, called “modon”, which propagates eastwards as observed for the MJO. To investigate this possibility of the MJO as free dynamics in the context of the operational global forecasts, we take the ECMWF global model (IFS) as a basic framework and perform extensive physical sensitivity experiments. See Sect.  for model details.

To emulate free dynamics within the IFS, physical tendencies of some variables are selectively turned off so that the resulting sensitivities to the corresponding MJO forecasts can be examined. A key process to be turned off in order to emulate free dynamics is the surface friction (or momentum dissipation more generally). This process has been expected to potentially play a crucial role in the MJO dynamics. A classical work by Chang (1977) makes this point by invoking the surface friction as a mechanism to slow down the propagation speed of the eastward-propagating free Kelvin wave to a degree comparable to that of the MJO. The frictional wave-CISK (conditional instability of the second kind) theories by Wang (1988) and Salby et al. (1994) also invoke frictional moisture convergence as a key ingredient in addition to deep convection for explaining the basic dynamics of the MJO. Along with the surface friction, diabatic heating is another key process to be turned off in order to achieve free dynamics.

A shortcoming of the free wave theory of the MJO is that it does not explain an MJO initiation in an obvious manner. Thus, when physical forcings are turned off from a model, an initiation mechanism must be sought. For this reason, particular attention is paid to the potential importance of interactions of the MJO with higher-latitude dynamics. Weickmann et al. (1985) and Knutson and Weickmann (1987) suggest that the interactions with Rossby wave trains from and to higher latitudes are intrinsic parts of the MJO dynamics. Hsu et al. (1990), Gustafson and Weare (2004), Ray and Zhang (2010), Ray and Li (2013), Zhao et al. (2013), and Wang et al. (2019) further suggest that Rossby wave trains from the Northern Hemisphere higher latitudes initiate MJOs. The general importance of higher-latitude variability in MJO dynamics is also suggested by the modelling of MJOs under an equatorial channel configuration, in which a properly prescribed lateral boundary condition is crucial (see Hall et al., 2016, and references therein).

To investigate these aspects of the MJO dynamics, we attempt to simulate the higher-latitude dynamics as properly as possible. In the following sensitivity experiments, a weighting of cos⁡6ϕ with ϕ of the latitude is adopted so that the effects of the applied sensitivity rapidly tail off polewards of ca. 20∘. Hence, when a certain process is turned off over the tropics, the tendency due to this process is multiplied by 1-cos⁡6ϕ.

Under this general strategy, four major categories of experiments are performed, as listed in Table . These experiments are designed to address the following questions:

Can the propagation of the MJO be simulated in a complex forecast model even if the diabatic heating due to convection is turned off?

To address question 1, we turn off all of the diabatic heating in the heat equation (entropy budget) so that an adiabatic free dynamics regime is realized over the tropics. Here, it is crucial to turn off all the diabatic heating, because if the latent heating is turned off, but the radiative cooling tendency of the tropics is maintained, a steady state can only be maintained by turning the mean ascent (associated with moist convection) to a mean descent, which induces diabatic heating that balances the radiative cooling. We turn off the total diabatic heating so that the tendency to generate any vertical motion is suppressed, and a purely horizontal, quasi-non-divergent flow is realized.

To address question 2, we turn off the non-conservative processes (i.e. frictional dissipation in general) in the horizontal momentum equation, because we expect that the free Rossby wave dynamics associated with the MJO are enhanced by turning off the momentum dissipation. As a result, we also expect that Rossby wave interactions between the tropics and the higher latitudes are enhanced. The claim that the MJO is a free Rossby wave also contains another important general implication that the MJO can be principally understood in terms of non-divergent, rotational flows. Thus, an important question to be investigated is the extent to which a non-divergent (rotational) component of the MJO is still maintained by selectively turning off the physics.

The exploratory nature of the present investigation is emphasized. Unfortunately, our goal of emulating the free dynamics is not achieved in any obvious manner without any systematically identifiable trait in these sensitivity experiments. For example, the reduction of momentum-dissipation effects (“frictions”) in the model does not lead to a simple improvement or deterioration of the MJO forecast. The paper focuses on elucidating these complex sensitivities of the MJO forecasts to different configurations of the physics. Detailed descriptions of the results are presented as objectively as possible with the purpose of elucidating real operational issues in improving the MJO forecasts. This is where theoretical investigations are strongly needed to better understand the model behaviour.

For example, the role of friction in the MJO dynamics remains a key question since a pioneering study by Chang (1977); however, the majority of theoretical studies treat it simply as a Rayleigh friction (see Sect. 4 of Yano et al., 2013, for a review of this line of theoretical studies). The present study, in turn, shows that the actual contribution of friction in an operational model is far more complex. Thus, a more serious effort to fill the gap between those idealized theoretical studies and operational problems is required.

The present study is unique with respect to modelling studies, as it examines the roles of more specific physical processes in the MJO dynamics – for example, instead of turning off the whole momentum-dissipation process, individual momentum-dissipation processes are turned off one by one. This is in contrast to mechanism-denial studies (e.g. Kim et al., 2011; Ma and Kuang, 2016), in which a whole process (e.g. momentum dissipation, surface-flux evaporation) is typically turned off (see also e.g. Crueger and Stevens, 2015). The present study is also conceptually different from the mechanism-denial studies. The latter replace the turned-off processes with climatologies, whereas the present study turns off a given process with the goal of getting closer to idealized free dynamics.

However, there is a subtlety in turning off certain physics in a given model, because of their impact on the mean state and the nonlinearity of the system leading to various chain reactions and compensatory behaviour with corresponding changes to the MJO forecast skill. We find that changes in the results due to turning off different physics hardly constitute simple additive processes. Previous studies have found significant changes in the energy cascade behaviour of the IFS model, controlled by certain physics or specific parts thereof (Malardel and Wedi, 2016). A change in the tropical processes clearly influences the interactions of the tropical processes with those at higher latitudes. Therefore, subtle balances between higher latitudes and the tropics must carefully be taken into account for a full interpretation of these sensitivity results.

The main contribution of the present study is to suggest that the MJO dynamics is not just a matter of its coupling with convection, but other physical processes, including friction, actively contribute to defining its dynamics. Another important, rather non-intuitive result is the strong sensitivity of the MJO forecast to initial conditions. The following analysis is focused over the region of the Indian Ocean to the western Pacific (90–180∘ E), where the main activities of the MJO are identified. Although the original study by Madden and Julian (1972) identifies the MJO as a global mode, as the analysis by Milliff and Madden (1996) shows, the continuous mode propagating eastwards beyond the Date Line is rather identified as a free Kelvin wave.

The next section describes the model used in this study (Sect. 2.1), the forecast cases (Sect. 2.2 and 2.3) and the analysis procedure (Sect. 2.4). The results are presented in Sect. 3, and the paper concludes with a discussion in Sect. 4.

A main motivation for the present study was to examine the extent to which the MJO can be simulated with a relatively frictionless (physically unforced) setting, which is consistent with the proposed free nonlinear Rossby wave theory for the MJO by Wedi and Smolarkiewicz (2010), Yano and Tribbia (2017), Rostam and Zeitlin (2019), and Wang et al. (2019). The MJO forecast does indeed improve when the momentum dissipation is totally removed (Ma; cf., Figs. 2c and 3c); however, the tendency is hardly consistent: the degree of forecast improvements sensitively depends on the choice of the momentum-dissipation terms that are turned off. The effects are also hardly additive, and certain nonlinear interactions are clearly going on. Most disappointingly, when all of the dissipation and forcing terms both for the momentum and the entropy are turned off (QF), the features associated with MJO disappear rather rapidly (Fig. 3k). Thus, the present study does not support the proposed free nonlinear Rossby wave theory in any consistent manner. Details on the forecast behaviour based on the choice of the physical configurations of the model have been carefully documented to record the unexpected but nevertheless important impact on MJO forecast skill.

There are several lessons to learn from the present sensitivity exercise. The first is the importance of closely evaluating the details of sensitivities of physical processes for the MJO. In typical mechanism-denial studies (e.g. Kim et al., 2011; Ma and Kuang, 2016), the physical process concerned is either totally turned off or maintained. If we would have followed such an approach, the improvement in MJO forecasts due to totally removing momentum dissipation (case Ma) would have simply been interpreted as a positive result for supporting a free wave theory. However, in the present study, the momentum-dissipation processes, arising from various different physical mechanisms, are turned off selectively to verify this initial finding in a more solid manner. As it turns out, the sensitivities of MJO to momentum-dissipation processes are not that simple. Although we are short of making any definite conclusions from our sensitivity study of the MJO on the momentum-dissipation processes, the study suggests the critical importance of examining the physical sensitivities of a phenomenon in more detail rather than simply switching off the entire physical mechanism as has been done in past sensitivity studies. Second, after examining the forecast results closely, we have realized that it is not quite straightforward to simulate a free wave dynamics expected from the theory with a complex state-of-the-art global model, as originally intended. We conclude that this difficulty stems from the need to maintain a realistic background state at the same time (see Ma and Kuang, 2016).

Discussions on some specific runs make this point clearer: with the quasi-free 40 d extended forecast (QF; Fig. 5e), the pre-existing anticyclonic variability over 100–150∘ E persists almost as long as observed (7 d), albeit with weak amplitude. A weakly eastward tendency, which is consistent with the nonlinear free wave theory, may also be noticed in this simulation. In the standard 20 d forecast case, only a reminiscence of the anticyclone signature from the previous MJO event is found around 120∘ E initially in the analysis, and this feature disappears in less than 2 d (Fig. 3b). Note that no convective variability is found in the vicinity of this longitude at the initial time of this forecast period (Fig. 2a). The quasi-free forecast (QF) maintains anticyclonic variability longer than in the analysis, albeit with a weaker amplitude (Fig. 3k).

We interpret these rather subtle results with the quasi-free (QF) forecast experiments as a demonstration of the difficulties in realizing a “realistic” free dynamics experiment. The main problem with the QF forecasts in the present study is the fact that by practically turning off “all” the physical forcings, the basic state of the model also breaks down very rapidly; thus, a proper background state that may support an MJO with free dynamics is also lost very rapidly. It also follows that a free MJO mode also dissipates out very rapidly. A more appropriate manner of performing free dynamics experiments would be to maintain a background state with full physics in place but to introduce quasi-free dynamics only to a perturbation component. The basic idea of this strategy may be understood in analogy with standard perturbation analyses. However, in the present case, perturbations must be treated in a fully nonlinear manner in order to be consistent with our anticipation that the MJO is a fully nonlinear construct. A brute force approach of nudging the model towards a climatology (e.g. Ma and Kuang, 2016) may be valid, but only when the given climatology is a correct “background state” to maintain. A more delicate procedure is required, for example, by using the emerging modelling infrastructure described in Kühnlein et al. (2019) so that any constraints on the evolving nonlinearities are removed.

The present study further suggests that the MJO predictability sensitively depends on the choice of the initial condition in a rather non-intuitive manner, although this is consistent with a clear distinction between high- and low-skill MJO events identified by Kim et al. (2016): longer forecasts from an earlier phase of the MJO may not be harder than a shorter one from a later phase. In the present study, the standard forecasts are initiated (on 19 January) from an early stage of an MJO already present; thus, a successful forecast would simply capture the subsequent development and propagation of this MJO. On the other hand, the 40 d extended forecasts are initiated 10 d earlier towards the end of a previous MJO event. Presumably, the latter is harder to forecast with respect to the MJO evolution, especially the onset of a new MJO. However, an inspection of the time–longitude section suggests a different picture: the longer 40 d extended forecasts tend to regenerate the MJO signal towards the end of the forecasts, and the forecast capacity recovers. In some cases, their performance becomes even better than the shorter standard 20 d forecasts initiated 10 d later in terms of the pattern correlations of the OLR and the 150 hPa stream function (Fig. 6).

As Nakazawa (1988) originally pointed out, the MJO typically constitutes a modulation of the westward-propagating cloud clusters which have scales of a few hundred kilometres. The 9 January, the initiation time of the 40 d extended forecasts, corresponds to the end of the previous MJO event and is also the moment that the last cloud cluster over the western Pacific begins to propagate westwards, which marks the end of this MJO event (Fig. 4a). In the 40 d extended CF (Fig. 4b), this westward-propagating cloud cluster does not die out as observed but continues to propagate westwards to the Indian Ocean, which marks an initiation of a new MJO under this forecast. Although the predicted new MJO weakens out during the middle of the event, we note a recovery of the signal towards the end of the event. These initial condition sensitivities of the MJO forecasts point to the simple fact that the onset as well as the evolution of an MJO should not be considered as isolated events and are better interpreted as a part of a chain of processes in the atmosphere. It also points to the importance of better understanding detailed processes associated with the MJO – in the present case, those of the westward-propagating cloud clusters. Standard MJO indices (e.g. RMM) fail to depict those critical details (see Straub, 2013).

The present study has also elucidated active interactions of MJOs with higher-latitude Rossby wave activities (Fig. 9). Inspections of the latitude–time sections suggest that the performance of the MJO forecasts appears, at least partially, to be helped by the successfully simulated interactions of the MJO with the higher-latitude Rossby waves (Rossby wave trains).

The MJO forecast problem is often reduced to that of convection parameterizations (e.g. Hirons et al., 2013a, b; Jiang et al., 2015, 2020b; Pilon et al., 2015). However, improvement of the MJO forecast, along with the many other forecast issues, is not a matter of fixing a single physical scheme. Rather, we need to examine a forecast model as a whole with its interacting physics for achieving this goal. The present model sensitivity study has exposed the importance of physical processes other than convection for maintaining a realistic tropical mean state and for MJO forecast skill.

The complex behaviour of the IFS model sensitively depending on the choice of the physics that are turned off, as identified in the present study, should be emphasized in its own right. For example, the role of momentum friction, in general, is not simply favourable or unfavourable for MJO forecasts. The behaviour sensitively depends on the precise type of momentum friction being turned off. In other words, the operational model behaviour is not decided by a dichotomy of with or without friction, as typically assumed in theoretical as well as in some model sensitivity studies. By reporting the details of these physical sensitivities on the MJO forecast, the present study strongly suggests the need for theoretical investigations that are much more closely tied to the actual operational formulations of physical parameterization and their impact on the mean circulation rather than merely modulating the (MJO) anomaly.