Intraseasonal Variability in an Aquaplanet General Circulation Model

Abstract

[1] An aquaplanet atmospheric general circulation model simulation with a robust intraseasonal oscillation is analyzed. The SST boundary condition resembles the observed December-April average with continents omitted, although with the meridional SST gradient reduced to be one-quarter of that observed poleward of 10° latitude. Slow, regular eastward propagation at 5 m s⁻¹ in winds and precipitation with amplitude greater than that in the observed MJO is clearly identified in unfiltered fields. Local precipitation rate is a strongly non-linear and increasing function of column precipitable water, as in observations. The model intraseasonal oscillation resembles a moisture mode that is destabilized by wind-evaporation feedback, and that propagates eastward through advection of anomalous humidity by the sum of perturbation winds and mean westerly flow. A series of sensitivity experiments are conducted to test hypothesized mechanisms. A mechanism denial experiment in which intraseasonal latent heat flux variability is removed largely eliminates intraseasonal wind and precipitation variability. Reducing the lower-troposphere westerly flow in the warm pool by reducing the zonal SST gradient slows eastward propagation, supporting the importance of horizontal advection by the low-level wind to eastward propagation. A zonally symmetric SST basic state produces weak and unrealistic intraseasonal variability between 30 and 90 day timescales, indicating the importance of mean low-level westerly winds and hence a realistic phase relationship between precipitation and surface flux anomalies for producing realistic tropical intraseasonal variability.

1. Introduction

[2] The Madden-Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics, characterized by eastward-propagating coherent wind and precipitation fluctuations at 30–60 day timescales and zonal wavenumbers 1–3 [Madden and Julian, 2005]. While the existence of the MJO has been known since the early 1970s with the early pioneering work by Roland Madden and Paul Julian [Madden and Julian, 1971, 1972], the underlying dynamics of the MJO have to this point remained elusive. We still do not have a fundamental understanding of the spatial and temporal scale selection of the MJO, its slow eastward propagation, or its seasonality [Zhang, 2005]. This paper describes general circulation model (GCM) aquaplanet experiments that continue the quest for this elusive understanding of the MJO's fundamental nature.

[3] This paper details further investigations with the NCAR Community Atmosphere Model Version 3 (CAM3) that are motivated by the modeling results of Maloney [2009, hereafter M09]. In M09 a modified version of CAM3, in which a relaxed Arakawa-Schubert convection scheme was implemented [Moorthi and Suarez 1992], was used to show that horizontal advection and latent heat flux dominated the column-integrated moist static energy (MSE) budget of the model's intraseasonal oscillation. M09 showed that anomalous horizontal advection moistened the atmosphere to the east of MJO convection, incompletely opposed by suppressed latent heat fluxes, possibly explaining the slow eastward movement of the simulated MJO. Further, discharge of MSE during and after MJO convective events due to horizontal dry air advection was slowed by enhanced latent heat fluxes. It was hypothesized on the basis of these results that climate models must have realistic basic state low-level wind and humidity distributions in order to correctly simulate the intraseasonal phase relationships among precipitation, horizontal advection, and latent heat fluxes, and hence the properly simulate the MJO.

[4] A dominant mechanism of anomalous horizontal MSE advection in the modeling study of M09 was meridional advection of humidity by eddies of smaller scale than the MJO, predominantly those with synoptic space and time scales. The interpretation of this term was that in regions of MJO easterly anomalies, synoptic-scale eddies like easterly waves and tropical-depression type disturbances [e.g. Lau and Lau, 1992, Takayabu and Nitta, 1993] were suppressed, inhibiting horizontal mixing between the moister equatorial region and drier subtropics, hence leading to anomalous moistening of the equatorial region to the east of MJO convection. Likewise, during the active MJO phase synoptic eddies were more active, increasing horizontal advection from the subtropics, thus causing drying of the equatorial region and aiding MSE discharge. Observations are broadly supportive of the role of horizontal advection in moistening (drying) in advance of (subsequent to) peak MJO convection [Benedict and Randall, 2007, 2009], although the role of synoptic eddies in this anomalous advection has yet to be explicitly examined. Zonal advection was of the same order of magnitude as meridional advection in the intraseasonal MSE budget of M09, but the implications of zonal advection were not as extensively analyzed.

[5] Interest in wind-induced surface heat exchange (WISHE) as a mechanism for the development and maintenance of the MJO originated with Neelin et al. [1987] and Emanuel [1987]. While the precise details of these early linear models of WISHE, namely the requirement of easterly low-level mean flow and enhancement of surface fluxes to the east of convection, have been largely contradicted by observations [e.g. Zhang and McPhaden, 2000], increasing evidence exists that some form of WISHE may be important for MJO maintenance and possibly propagation. For example, recent mechanism denial experiments with versions of the NCAR CAM and GFDL Atmosphere Model 2 indicate a substantial decrease in intraseasonal precipitation variance when wind-induced surface flux anomalies are removed [Maloney and Sobel, 2004, Sobel et al. 2010]. Grabowski [2003] also suggested a role for WISHE in MJO organization in a simulation using the multiscale modeling framework [MMF, Randall et al., 2003]. These studies and other recent evidence from idealized models and observations suggest that non-linear forms of WISHE may actively contribute to the maintenance and propagation of the MJO [Raymond, 2001, Sugiyama, 2009a,2009b, Sobel et al., 2008, 2010]. If WISHE is important to the MJO, however, it must operate in a basic state of surface westerlies, unlike in the early linear models [Neelin et al., 1987, Emanuel, 1987]. This indicates that the real WISHE mode is either nonlinear, or has some other significant difference, as yet unclear, from that described in those early studies. A satisfactory analytic prototype for an MJO-like disturbance destabilized by WISHE on a westerly basic state remains elusive. Sugiyama [2009a,2009b] documents an informative recent effort in this direction, and Sobel et al. [2010] provides a comprehensive review of recent observational and modeling developments related to WISHE and its impact on the MJO. In the GCM integrations described here, very robust MJO-like disturbances emerge on a westerly basic state and are shown to owe their existence to WISHE. By documenting the dynamics of these disturbances, we hope (among other motivations) to provide guidance for the development of better analytical prototypes.

[6] It will be shown below that the simulated MJO in the model used here has many characteristics of a “moisture mode.” We use this term to denote disturbances of a type that have emerged in a number of studies using simplified models of the tropical atmosphere [e.g. Neelin and Yu, 1994, Sobel et al., 2001, Raymond, 2001, Fuchs and Raymond, 2007, Sugiyama, 2009a, 2009b; Raymond and Fuchs, 2009, Raymond et al., 2009], as well as mesoscale and cloud-resolving models run under idealized conditions [e.g., Tompkins 2001, Sobel and Bretherton 2003, Bretherton et al. 2005]. A moisture mode is a balanced disturbance in which the large-scale dynamics are well-described by the weak temperature gradient approximation [e.g., Held and Hoskins 1985, Sobel et al. 2001, Majda and Klein 2003], and whose other properties are determined primarily by local interactions between deep convection and tropospheric moisture anomalies. A detailed review of the properties of moisture modes can be found in Raymond et al. (2009). The essential dynamics of a moisture mode involves those processes that control the tropical moisture field, such as surface latent heat flux and horizontal advection. A moisture mode instability can develop if column moist static energy anomalies (approximately equivalent to humidity anomalies in the weak temperature gradient framework, in which free-tropospheric temperature anomalies are assumed negligible) are augmented by the actions of deep convection and processes tightly coupled to it. One way in which this can occur is if the gross moist stability (GMS), essentially the column MSE exported by the large-scale divergent flow per unit vertical mass flux [e.g. Neelin and Held 1987, Raymond et al. 2009], is negative in deep convective regions. Moisture mode instability can also exist if gross moist stability is positive, provided that surface latent heat fluxes, cloud-radiative feedbacks, and other column MSE sources can compensate for the MSE loss by large-scale motions [e.g. Bony and Emanuel 2005]. Without advection by steering currents, moisture mode instabilities would be stationary, to the extent that interactions between moisture, convection, surface fluxes, and radiation are all local [e.g. Raymond and Fuchs 2009]. In large-scale disturbances such as intraseasonal oscillations, it is reasonable to assume that moisture, convection, and radiation anomalies are locally related, while surface fluxes are in general nonlocally related to convection since the wind response to localized convective heating is nonlocal; thus surface fluxes may influence the propagation of intraseasonal oscillations, as has been found in some idealized models of poleward-propagating intraseasonal disturbances [Bellon and Sobel, 2008].

[7] Observational evidence is at least circumstantially consistent with the existence of tropical moisture modes due to the very strong relationship between column-integrated precipitable water, saturation fraction, and precipitation [e.g. Bretherton et al., 2004, Back and Bretherton, 2005, Peters et al., 2009] and the relatively weak temperature gradients observed in the tropics. It has further been documented that strengthening moisture-convection feedbacks in models improves their simulations of the MJO, as demonstrated by Grabowski and Moncrieff [2004] using a cloud resolving convection parameterization. Recent climate simulations that produce realistic intraseasonal variability (e.g. SP-CAM) exhibit a strong relationship between tropospheric relative humidity and precipitation [e.g. Thayer-Calder and Randall, 2009, Kim et al., 2009, Zhu et al., 2009].

[8] An initial motivation for this study was to test the sensitivity of the MJO simulation in the NCAR CAM3 with RAS convection to basic state using an aquaplanet configuration. In particular, a control version of the model having a realistic SST distribution is compared to a zonally-symmetric version designed to generate an easterly basic state on the equator. In work with a predecessor version of this model, WISHE was found to be important to the simulated MJO occurring in a mean state of low-level westerlies [Maloney and Sobel, 2004]. Changing the sign of the low-level flow alters the phase relationship between anomalous surface fluxes and precipitation, allowing us to gain more insight into the nature of an unstable intraseasonal WISHE mode on a westerly basic state. Further, the control version is compared to a simulation with reduced equator to pole SST and moisture gradient, designed to weaken the influence of meridional humidity advection on the intraseasonal moisture and moist static energy budgets. Contrary to what one might have expected based on the results of M09, this later simulation produces an extremely robust MJO with stronger amplitude than observed and a timescale narrowly confined around 50 days, with 5 m s⁻¹ eastward propagation in tropical warm pool regions. MSE and moisture budgets for this simulation indicate the importance of horizontal advection and wind-induced surface fluxes to this mode. An experiment with surface latent heat fluxes set to their climatology from the reduced meridional SST gradient simulation is also conducted to directly assess the importance of interactive surface fluxes on the MJO simulation. A further sensitivity experiment with a reduced zonal SST gradient and hence weakened mean low-level equatorial westerly flow is used to test whether eastward propagation of the model MJO is slowed with reduction in steering currents. We will show the model MJO to have characteristics of an intraseasonal moisture mode destabilized by WISHE, and advected eastward by the action of horizontal moisture advection.

[9] Section 2 describes the model and the experimental design. Section 3 compares the mean state among control, zonally-symmetric, and reduced meridional SST gradient aquaplanet simulations and briefly compares the space-time characteristics of the variability among these runs to observations. Section 4 provides a detailed analysis of the MSE and moisture budgets of the MJO mode in the simulation with reduced meridional SST gradient. Section 5 describes experiments in which surface latent heat fluxes are set to climatology to assess the impact of their variability on the simulation, as well as the impact of reducing the zonal SST gradient and hence mean low-level tropical zonal winds. Conclusions and discussion are presented in section 6.

2. Experiment Design

2.1. Model

[10] As further described in M09, we use a version of the NCAR CAM 3.1 with the relaxed Arakawa-Schubert convection parameterization implemented [RAS, Moorthi and Suarez, 1992]. The version of RAS we use includes a minimum entrainment threshold for the existence of convective plumes, similar to that employed in Tokioka et al. [1988]. This threshold has been demonstrated to improve intraseasonal variability in climate simulations. In this case, the minimum entrainment threshold is set to 1 × 10⁻⁴ m⁻¹. Convective rain re-evaporation is also parameterized, and a certain fraction of falling convective rainfall is exposed to the environment and allowed to evaporate [e.g. Sud and Molod, 1988]. This evaporation fraction is set to 0.6, which was demonstrated to produce realistic amplitude tropical intraseasonal variability in the study of M09. Grabowski and Moncrieff [2004] demonstrated that including convective rainfall re-evaporation increases moisture-convection feedbacks in climate models, and Bacmeister et al. [2006] present a detailed analysis of the sensitivity of a model using RAS to evaporation fraction. The Hack [1994] scheme is retained to simulate shallow convection.

[11] The simulations described below are all sixteen years in length, using a spectral dynamical core at T42 resolution, or approximately 2.8° × 2.8°. Twenty-six levels are employed in the vertical, with an integration time step of 20 minutes.

2.2. SST Boundary Conditions and Other Forcings

[12] Simulations are conducted in aquaplanet mode using perpetual March 21 insolation and ozone distributions. Three idealized SST boundary conditions are used to force the model, shown in Figure 1. The first distribution called Realistic SST (RS) is most like the observed SST during boreal Winter and Spring, the time of maximum MJO activity. RS was constructed by first averaging climatological surface temperature for December-April, taking a meridional transect of these surface temperatures from 90°S to 90°N at 155°E, creating a zonally symmetric state based on these 155° temperatures, and then adding a zonal perturbation to this zonally-symmetric state as a function of longitude that is constructed from a 5.6°S–5.6°N equatorial average at each longitude. The 155°E equatorial SST value is subtracted before the zonal perturbation is added to each longitude, such that the 155°E temperature remains at the December-April observed mean. A 1-2-1 running filter is successively applied 10 times to the zonal perturbation to remove sharp zonal SST gradients before addition to each longitude. The influence of the zonal perturbation to SST is allowed to decay with latitude ( ϕ) with a form exp[−ϕ²/(30°)²], such that the SST is nearly zonally-symmetric poleward of 30°N and 30°S.

Figure 1. SST distributions for the RS simulation, the ZS simulation, and the QM simulation. Units are degrees Celsius.

[13] The RS distribution in Figure 1 is characterized by a tropical warm pool of SSTs 29°C and higher centered just south of the equator in the Eastern Hemisphere, and cooler tropical SSTs in the Western Hemisphere. Given that the 155°E meridional gradient is used to set the SST distribution, a cold tongue does not exist in the eastern tropical Pacific. However, many aspects of this idealized tropical SST distribution resemble observations, and the nature of intraseasonal variability in the model resembles that in the simulation described in M09 which includes a realistic continental configuration.

[14] Two other idealized SST distributions are used in the initial part of this study. One is associated with the Zonally Symmetric (ZS) simulation, and is a zonally-symmetric state based on the 155°E SST transect from the RS simulation (Figure 1b). Thus, equatorial temperatures everywhere in the tropics are equal to those observed in the west Pacific warm pool. The final SST distribution is associated with the Quarter Meridional Gradient (QM) simulation (Figure 1c). Construction of this SST distribution starts with the SST boundary condition from the RS simulation, retains the same SST from 10°N to 10°S, but reduces the meridional SST gradient poleward of these latitudes to one-quarter of its value in the RS case. After some initial analysis using all three SST distributions in section 3, the QM simulation will be the primary focus of the paper given its robust intraseasonal variability.

3. Simulation Intercomparison

[15] Figure 2a shows the mean 850 hPa winds and precipitation in the three simulations. The RS simulation is characterized by precipitation maxima near 80°E and 160°E that straddle and are approximately symmetric about the equator. These precipitation maxima are accompanied by mean equatorial westerlies approaching 5 m s⁻¹ near 155°E. This mean precipitation and wind distribution in the RS simulation resembles that found during boreal winter in the model with full continental distribution and realistic boundary forcing analyzed in M09, and hence contains most of its precipitation biases as well, including the tendency to produce a double ITCZ and weaker than observed mean precipitation west of 110°E. The ZS case exhibits a double ITCZ structure that straddles the equator with mean equatorial easterly winds at low levels. The Northern Hemisphere (NH) precipitation maximum occurs near 5°N, and is slightly stronger than the corresponding Southern Hemisphere precipitation band centered near 10°S. Mean winds are also stronger in the NH than the SH. Interestingly, the QM simulation is characterized by a single ITCZ centered near 10°S, extending from 90°E past the Dateline and is accompanied by strong mean westerly flow from the equator to 15°S.

Figure 2. a) Mean 850 hPa wind (m s⁻¹) and precipitation (mm day⁻¹) for the RS simulation, the ZS simulation, and the QM simulation, and b) Intraseasonal (20–100 day) precipitation variance (mm² day⁻²) and mean 850 hPa wind (m s⁻¹) for the RS simulation, the ZS simulation, and the QM simulation. The reference wind vector is shown at the lower right.

[16] Precipitation variance at 20–100 day timescales among the simulations is shown in Figure 2b. Notice the different scale for the QM run than the other simulations. Precipitation variance in the RS simulation maximizes in regions of high mean precipitation that straddle the equator. The amplitude of the precipitation variance maximum near 150°E is comparable to that in observations during boreal winter [Kim et al., 2009], although the 60–90°E variance maximum is weaker than observed. Further, the RS simulation exhibits a pronounced minimum in precipitation variance on the equator, whereas no such equatorial minimum occurs in observations. Precipitation variance in the ZS simulation is exceedingly weak, and tends to maximize near 10°S. Intraseasonal precipitation variance in the QM simulation is strong in the region of maximum mean precipitation and background westerly flow centered near 10°S. Precipitation variance in this band exceeds 168 mm² day⁻² near 155°E. This precipitation variance maximum is stronger than the boreal winter distribution in observations, which features an Eastern hemisphere variance maximum during boreal winter approximately centered along 10°S whose peak magnitude is greater than 38 mm² day⁻² [Kim et al., 2009].

[17] Wavenumber-frequency spectra of equatorial 850 hPa zonal winds (Figure 3) and precipitation (Figure 4) are shown. In addition to the simulations we show results from the NCEP reanalysis 850 hPa winds [Kalnay et al., 1996] and Climate Prediction Center Merged Analysis of Precipitation (CMAP, Xie and Arkin, 1999] during November-April of 1979–2005. As intraseasonal zonal wind variability tends to be more equatorially confined than precipitation when considering all simulations as a whole, we use a slightly narrower equatorial averaging band for zonal winds (10°N–10°S average) than precipitation (15°S–15°N average). Spectra are computed in observations and models using 180 day non-overlapping segments for a bandwidth of 0.0056 day⁻¹. In the MJO timescale band, resolved periods are centered on 30, 36, 45, 60, and 90 days. For convenience, vertical dashed lines show 30 and 90 day periods.

Figure 3. Wavenumber-frequency spectra of equatorial (10°S–10°N averaged) 850 hPa zonal wind during November–April from NCEP-NCAR reanalysis (November–April), the RS simulation, the QM simulation, and the ZS simulation. Contour interval is 0.05 m² s⁻², starting at 0.10 m² s⁻². Values greater than 0.15 m² s⁻² are shaded. Spectra are computed on 180 day segments during November–April of each year for NCEP reanalysis, and over adjacent 180 day segments for the models, and then averaged across all realizations to compute an average spectrum. Only the climatological seasonal cycle (NCEP) or time mean (models) was removed before computation of the spectra.

Figure 4. Wavenumber-frequency spectra of equatorial (15°S–15°N averaged) precipitation during November–April from CMAP (November–April), the RS simulation, the QM simulation, and the ZS simulation. Contour interval is 0.02 mm² day⁻², starting at 0.04 m² s⁻². Values greater than 0.06 m² s⁻² are shaded. Spectra are calculated in an identical manner to Figure 3.

[18] Observed 850 hPa zonal wind variance has a broad maximum near zonal wavenumber 1 and 50 day timescale (Figure 3a). The RS simulation contains maximum variance near wavenumber 1 and about 40 days, similar to observations (Figure 3b), although the variance maximum tends to be temporally broader than that computed from observations. The ZS simulation does not have appreciable variance in the 30–90 day band, instead having maximum variance near 1/30 day⁻¹ and higher frequencies (Figure 3d). Conversely, the QM simulation is characterized by a strong spectral peak in zonal wind spanning zonal wavenumbers 1 and 2 and concentrated near a frequency of 1/50 days⁻¹ (Figure 3c). Variance is higher than observed, with relatively more power occurring near zonal wavenumber 2 than in observations. As shown below, the dominance and high magnitude of the convectively coupled wind signal in the Eastern Hemisphere relative to the Western Hemisphere radiating response in the QM simulation appear to shift the wind signal toward zonal wavenumber 2. When viewing the observed Eastern Hemisphere part of the MJO in isolation, wind anomalies are dominated by scales characteristic of zonal wavenumber 2 [e.g. Maloney and Hartmann, 1998].

[19] Observed precipitation variance peaks near zonal wavenumber 2 and a period of 50 days (Figure 4a). The RS simulation has substantial low frequency variance (>90 days) contained at both eastward and westward periods, with lower than observed variance in the 30–90 day band. This lack of modeled coherence between the intraseasonal wind and precipitation signals shown in Figures 3b and 4b is endemic to many GCM simulations of the MJO [e.g. Zhang et al., 2006]. The ZS spectrum has only weak precipitation variance in the 30–90 day band. However, the QM simulation has a highly concentrated spectral peak centered near 50 days and wavenumber 2 with variance slightly higher than observations, and more narrowly confined than observations in wavenumber and frequency space.

[20] The success of the QM simulation for producing the most robust intraseasonal variability of the ones we analyze is somewhat surprising, and casts some doubt on the claim in M09 that a strong mean meridional humidity gradient, and the action of advection by synoptic eddies across this gradient, are key to understanding the intraseasonal moisture budget and the MJO. The weaker SST gradient in the QM simulation than in the others leads to a weaker mean humidity gradient, as one would expect (not shown); the argument of M09 would then suggest that QM should have weaker intraseasonal variability than the others, the opposite of what occurs. The role of the eddy advection mechanism in the QM simulation will be diagnosed further in section 4. The results also indicate that a zonally symmetric SST distribution degrades the simulation of intraseasonal variability. A diagnosis of the MSE budget (not shown) indicates that the phase relationship between surface latent heat flux anomalies and anomalous precipitation in the ZS simulation is altered such that enhanced fluxes now lead precipitation to the east in regions of anomalous low-level easterly flow. This change in phase relationship is consistent with the basic state equatorial easterly winds in the ZS simulation. As will be diagnosed below, wind-induced latent heat fluxes appear to be an important destabilizing mechanism for the MJO in the QM simulation, and hence altering the phase relationship between precipitation and surface fluxes would be expected to modify the destabilizing effects of these surface fluxes. These findings are also consistent with those of Inness and Slingo [2003] and Inness et al. [2003], who hypothesized that basic state low-level westerly winds are necessary for a model to produce realistic tropical intraseasonal variability. It may be no coincidence that the strongest observed intraseasonal variability in the Tropics occurs in regions of low-level mean westerly flow.

[21] Time-longitude diagrams of 0°S–20°S averaged unfiltered precipitation and 850 hPa zonal winds in the QM simulation indicate a very regular oscillation that propagates eastward at approximately 5 m s⁻¹ in the Eastern Hemisphere (Figure 5). As is shown in Figure 5, 0°S–20°S averaged precipitation fluctuates in a highly regular manner from near 0 mm day⁻¹ to values greater than 35 mm day⁻¹, and then back again in the span of 50 days. Zonal winds exhibit variations from near calm conditions to zonal westerlies of 20 m s⁻¹ during the same time span. Because of the strong and highly coherent nature of intraseasonal wind and precipitation anomalies in the QM simulation, it will be the focus of analysis during much of the remainder of this paper. The strong regularity of the signal in this model and its clean nature in unfiltered fields will also allow many of the diagnostics shown below to be conducted using unfiltered data.

Figure 5. Time-longitude diagrams of 0°S–20°S averaged precipitation (mm day⁻¹) and 850 hPa zonal wind (m s⁻¹) for Days 700–900 of the QM simulation.

4. Budget Analyses of the QM Simulation

4.1. Composite Analysis

[22] Many of the analyses in this section will feature compositing. We use a combined EOF technique very similar to that of Wheeler and Hendon [2004], although we apply the EOF analysis to 20–100 day bandpass filtered fields rather than unfiltered anomalies given that we do not have the constraints of producing a real-time index. Intraseasonal precipitation anomalies, and 850 hPa and 200 hPa zonal wind anomalies are averaged from 15°S–15°N, and then each field is individually normalized by its zonal mean standard deviation. The leading EOFs explain 28% and 20% of the total variance (Figure 6), respectively, and resemble the leading EOFs in Wheeler and Hendon [2004]. The second EOF is plotted first for more direct comparison with Figure 1 of Wheeler and Hendon, 2004. Once the two leading normalized principal components are derived (the leading PCs are correlated at 0.9 at a lag of 11 days), composites are generated in an identical manner to Wheeler and Hendon [2004]. The leading PCs are combined to derive amplitude and phase information. Then, periods with amplitude greater than one standard deviation are retained, and the phase space spanning 0° to 360° is partitioned into eight equal-angle “MJO phases” into which high amplitude events are binned based on phase information derived from the PCs. For each MJO phase, days with amplitude exceeding one standard deviation are averaged together to generate a composite event, with composites for phases 1–8 averaged over the following number of days over the 16-year run, respectively: 464, 497, 494, 499, 469, 482, 476, and 451.

Figure 6. Combined EOF2 and EOF1 of 15°N–15°S averaged U850, U200, and OLR. Fields are bandpass filtered to 20–100 days before computation of the EOFs. The amplitudes are normalized.

4.2. Basic Composite Structure

[23] Figure 7 describes the eight-phase composite time evolution of the model MJO in total unfiltered 850 hPa wind and precipitation. The composite structure is characterized by an eastward- moving, zonally-elongated precipitation center centered just south of 10°S with maximum magnitude greater than 28 mm day⁻¹, alternating with suppressed precipitation periods having magnitude approaching zero. Strong westerly winds occur near and to the west of the precipitation center. Winds are very weak westerly in regions of suppressed precipitation. The entire coupled complex moves very slowly eastward, at about 4–5 m s⁻¹ on average. The initiation of model MJO precipitation occurs near 90°E, and model MJO precipitation decays past the Dateline. The structure of the MJO in this model resembles the moisture mode in the β-plane tropical channel model of Raymond [2001] and follow-up papers [e.g. Raymond 2007], consisting of a strong off-equatorial cyclonic gyre bounded on its equatorial side by a strong jet exceeding 10 m s⁻¹, with precipitation maximizing to the east of the jet core. The structure of variability (although with too large an amplitude) also resembles the observed structure of the MJO in the west Pacific during boreal winter [e.g. Araligidad and Maloney, 2008, Kim et al., 2009], although the model phase relationship near 90°E differs from observed boreal winter behavior, in that observed composite precipitation and winds tend to have more of a quadrature relationship in the Indian Ocean [e.g. Zhang and McPhaden, 2000, Sperber, 2003].

Figure 7. Unfiltered composite 850hPa wind (m s⁻¹) and precipitation (mm day⁻¹) as a function of MJO phase in the QM simulation. The reference wind vector is shown at the lower right.

[24] Figure 8a shows a snapshot of 20–100 day bandpass filtered 850 hPa wind and precipitation anomalies during Phase 5 of an MJO lifecycle in the model. This phase will be featured in many of the budget analyses presented below, and hence is shown here mainly for reference. During this phase, enhanced (suppressed) precipitation is centered near 110°E (the Dateline) with maximum westerly (easterly) wind anomalies occurring just to the west of these precipitation anomaly centers. Precipitation anomalies in the enhanced precipitation region are greater than 10 mm day⁻¹ during Phase 5, although larger when the model convective signal travels to the east. Also as a reference for some of the budget analyses shown below, and to elucidate the phase relationship between MJO 850 hPa winds and precipitation in the model a bit more clearly, Figure 9 presents composite 0°S–20°S averaged 20–100 day bandpass filtered wind and precipitation anomalies and total unfiltered wind and precipitation at 141°E. This location is near the region of strongest intraseasonal variance in the model. Note the reversal in the time axis with phase increasing from right to left, so that it can also be interpreted as approximately representative of the longitudinal structure at a fixed time, with longitude increasing to the right. Precipitation at 141°E peaks during Phase 6, followed by a peak in westerly winds one phase, or about 5 days later. The unfiltered total winds (mean state plus anomalies) never become easterly but rather are weak westerly during the suppressed phase. Figure 9 shows that total westerly winds are near 5 m s⁻¹ around Phases 4 and 5. It will be shown below that this is near the time of peak moistening by horizontal advection. This suggests the possibility that eastward horizontal advection by the zonal flow may largely determine the eastward MJO propagation speed in the model.

Figure 8. a) Composite 20–100 day bandpass filtered 850hPa wind (m s⁻¹) and precipitation (mm day⁻¹) anomalies for MJO phase 5 in the QM simulation. The reference wind vector is shown at the lower right. b) Composite 20–100 day bandpass filtered precipitation and column-integrated precipitable water (mm) anomalies for MJO phase 5 in the QM simulation. The precipitation contour interval is 4 mm day⁻¹, starting at 2 mm day⁻¹. Negative contours are dashed.

Figure 9. a) Composite 0°S–20°S averaged 20–100 day bandpass filtered 850 hPa zonal wind (red, m s⁻¹) and precipitation (blue, mm day⁻¹) anomalies at 141°E as a function of MJO phase in the QM simulation. b) Same as a), except for unfiltered fields.

[25] A very strong relationship between precipitation and column-integrated precipitable water exists in the model. Figure 8b shows that column-integrated precipitable water anomalies are nearly perfectly collocated with precipitation anomalies. In Figure 8b, the amplitude of 20–100 day bandpass filtered precipitable water anomalies is about 7 mm day⁻¹. A more general analysis of precipitation rate versus column saturation fraction for the region 0°S–20°S, 60°E–180°E is presented in Figure 10, and can be directly compared to the satellite-derived analysis of Bretherton et al. [2004]. We define saturation fraction as the vertically-integrated water vapor content of atmosphere divided by the maximum vertically-integrated water vapor content that would exist if all layers were saturated for the same temperature profile. Like in Bretherton et al. [2004], daily mean precipitation rate is a strongly increasing and nonlinear function of saturation fraction. The rise in precipitation rate in the model actually starts later and rises more sharply than that in Bretherton et al. [2004]. Figure 10 suggests strong mutual interactions between convection and column precipitable water.

Figure 10. Average daily-mean precipitation rate (solid, mm day⁻¹) versus column saturation fraction in the QM simulation. Precipitation rate is averaged within saturation fraction bins of width 0.01. The number of observations per bin (gray-dashed) is also shown.

[26] Many studies have suggested that a gradual moistening of the lower and middle troposphere, possibly by the action of shallow convection, is an important underlying mechanism that sets the MJO timescale [e.g. Benedict and Randall, 2007, 2009; Tian et al., 2010]. This can be manifest as a tilted structure in humidity anomalies whereby low-level humidity leads that in the upper troposphere [e.g. Kim et al., 2009]. Such a tilt is not apparent in our simulation. Figure 11 shows the vertical structure of 20–100 day bandpass filtered specific humidity anomalies at 141°E as a function of MJO phase. The middle and lower troposphere in this simulation appears to moisten and dry in unison. If anything, the middle troposphere appears to moisten slightly in advance of the lower troposphere. If the mechanism underlying the MJO in our model were representative of that in reality, this would cast some doubt on a gradual moistening of the troposphere from below as being essential for MJO dynamics. The design of the QM simulation and its reduced meridional humidity gradients is such that it minimizes anomalous meridional humidity advection in the lower troposphere. In M09, in which a tilted structure in humidity anomalies was apparent, meridional advection anomalies were shown to be a major anomalous moistening agent in advance of MJO convection. Shallow convection was deemed to be poorly simulated. Some have ascribed vertical advection associated with shallow convection processes to be important for lower tropospheric moistening [e.g. Thayer-Calder and Randall, 2009]. Since both anomalous meridional advection by eddies and shallow convection appear relatively unimportant in our simulation, shallow moistening by these processes is also inhibited. These processes do not appear essential to producing an MJO in this model.

Figure 11. Composite 0°S–20°S averaged 20–100 day bandpass filtered q anomalies at 141°E as a function of MJO phase and pressure in the QM simulation. The contour interval is 0.1 g kg⁻¹, starting at 0.05 g kg⁻¹. Values greater (less) than 0.05 (−0.05) are dark (light) shaded. Negative contours are dashed.

[27] We note that we have also examined the composite equatorial temperature structure of the model MJO (not shown). Cold tropospheric temperature anomalies accompany low-level easterly anomalies, and warm anomalies occur near and to the west of enhanced convection in regions of low-level westerlies. This structure is inconsistent with that of a convectively coupled equatorial Kelvin wave [Wheeler et al., 2000], and hence it appears very unlikely that Kelvin wave dynamics influence the propagation of the model variability we analyze here. The positive covariance of temperature and heating is consistent with what Hendon and Salby [1994] found for the growing phase of the MJO in the Indian Ocean, although observed temperature and heating are more in quadrature in the west Pacific. Hendon and Salby [1994] also note that positive precipitation anomalies remain within surface westerly anomalies throughout most of the observed MJO lifecycle (their Figure 9).

4.3. Moisture and Moist Static Energy Budgets

[28] Figure 12 shows composite unfiltered column integrated precipitable water (PW) tendency and precipitation as a function of MJO phase in the QM simulation. As described above, strong precipitation is initiated near 90°E, and then propagates eastward in time. The PW tendency is generally weak in advance of initiation of MJO convection near 90°E, but then as strong precipitation develops, strong precipitable water tendencies develop that flank the precipitation center, with moistening to the east and drying to the west. Composite tendency amplitudes exceed 1.4 mm day⁻¹, and can deplete or replenish the entire moisture content of the tropical atmosphere in about 40 days. The pattern of moistening and drying suggests that the processes that regulate these tendencies may help foster the eastward propagation of the model MJO, particularly given the strong relationship between column saturation fraction and precipitation exhibited by the model (Figure 10).

Figure 12. Unfiltered composite precipitation (contours) and column-integrated precipitable water tendency (colors, mm) as a function of MJO phase in the QM simulation. The precipitation contour interval is 4 mm day⁻¹, starting at 0 mm day⁻¹.

[29] Vertically-integrated intraseasonal moist static energy and moisture budgets are presented at 141°E and averaged from 0°S–20°S as a function of MJO phase. As in Neelin and Held [1987], the vertically-integrated budget for moist static energy (h) is given as:

• 

where brackets represent a vertical integral from the surface to 100 hPa, is the horizontal wind vector, the surface latent heat flux is LH, SH is the surface sensible heat flux, 〈LW〉 represents the vertically integrated longwave heating rate, and 〈SW〉 represents the vertically integrated shortwave heating rate. Before compositing, the terms in (1) are first bandpass filtered to 20–100 days. In practice, intraseasonal anomalies in 〈SW〉 are small and hence will not be displayed. Also, SH anomalies are generally an order of magnitude smaller than LH, and will not shown separately, but added to the LH term for presentation purposes.

[30] Similarly, the vertically-integrated specific humidity (q) budget is given as:

• 

where E is the surface evaporation rate, and P is the precipitation rate.

[31] As in M09, horizontal advection and latent heat flux are the largest terms in the intraseasonal moist static energy budget (Figure 13a), with anomalous horizontal advection increasing MSE in advance of MJO precipitation, and discharging it during and after the precipitation event. Anomalous latent heat fluxes tend to incompletely oppose the MSE tendency produced by horizontal advection, and to be partly in phase with the anomaly in the moist static energy itself. The terms in the intraseasonal MSE budget are dominated by humidity tendencies, consistent with the ability of the tropical atmosphere to support only weak temperature gradients. Anomalous vertical advection is negative during enhanced MJO precipitation in the model, consistent with gross moist stability in the model being positive as defined in the traditional way using vertical MSE advection [Neelin and Held, 1987]. In regions of high precipitation rates (>10 mm day⁻¹) over the region 0°S–20°S, 60°E–180°E, the column integrated MSE export due to vertical advection, normalized by dry static energy export [similar to the “normalized gross moist stability”, e.g., Raymond et al. [2009] [Raymond et al. [2009] normalize by moisture convergence instead of dry static energy export.)], is weakly positive at 0.04. Radiative cooling also approaches zero at the highest precipitation rates. Hence, the sum of latent and sensible heat fluxes can easily overwhelm export due to divergent motions and radiative cooling in regions of heavy precipitation. (Raymond et al. [2009] normalize by moisture convergence instead of dry static energy export.)

Figure 13. a) Composite 0°S–20°S averaged 20–100 day bandpass filtered vertically-integrated moist static energy budget anomalies and L times precipitation anomalies at 141°E as a function of MJO phase in the QM simulation. Terms include L times precipitation (blue, solid), latent plus sensible heat fluxes (green, solid), horizontal advection (red, solid), longwave heating (tan, dashed), vertical advection (blue, dashed), and moist static energy tendency (red, dashed). b) Composite 0°S–20°S averaged 20–100 day bandpass filtered vertically-integrated q budget anomalies at 141°E as a function of MJO phase in the QM simulation. Terms include negative one times precipitation (blue, solid), latent heat (green, solid), horizontal advection (red, solid), vertical advection (blue, dashed), precipitable water tendency (red, dashed), and vertical advection plus negative precipitation (tan, dashed).

[32] Figure 13b shows the anomalous vertically-integrated specific humidity budget. The large convergence term − 〈q∇·〉 is more than cancelled by precipitable water loss through precipitation, with a residual between these two terms that is negative during maximum precipitation. Notably, − 〈q∇·〉 anomalies are near zero during the time of peak moistening near Phase 5. Horizontal moisture advection anomalies are large and positive to the east of maximum precipitation. Evaporation anomalies are large and positive near and to the west of maximum precipitation, as observed [e.g. Zhang, 1996, Araligidad and Maloney, 2008, Grodsky et al., 2009]. Composite 0°S–20°S averaged moisture storage anomalies peak near 0.5 mm day⁻¹ in advance of MJO precipitation near Phases 4 and 5, producing a quadrature relationship between moisture tendency and precipitation. Tendencies in vertically-integrated latent heat tendency anomalies account for about 80% of the vertically-integrated MSE tendency anomalies.

[33] Maps of tendency terms in the vertically-integrated precipitable water budget help elucidate the mechanisms responsible for eastward propagation of the model MJO. Figure 14 shows 20–100 day bandpass filtered precipitable water budget terms for Phase 5 of an MJO lifecycle, including precipitation which is shown in contours on each plot. The precipitable water tendency is nearly in quadrature with precipitation, with anomalies peaking to east of enhanced precipitation at greater than 1 mm day⁻¹ (consistent with unfiltered tendencies in Figure 12). PW tendency is negative to the west of enhanced precipitation. Anomalous horizontal advection is nearly in phase with PW tendency, supporting its importance for moistening to the east of MJO precipitation. Positive (negative) latent heat flux anomalies are largest just to the west (east) of positive (negative) precipitation anomalies, consistent with the observed relationship [e.g. Araligidad and Maloney, 2008]. Vertical advection is in phase with anomalous precipitation, and is more than cancelled by PW decrease due to precipitation (as described in Figure 13).

Figure 14. Composite 20–100 day bandpass filtered precipitation anomalies and anomalous column-integrated precipitable water budget terms for MJO phase 5 in the QM simulation. Terms include column-integrated a) precipitable water tendency, b) horizontal q advection, c) vertical q advection, and d) surface evaporation. Water budget units are mm day⁻¹. The precipitation contour interval is 4 mm day⁻¹, starting at 2 mm day⁻¹. Negative contours are dashed.

[34] Figure 15 is identical to Figure 14, except that it shows total unfiltered PW tendency terms (thus including components associated with the mean state as well as anomalies). Total horizontal advection is always negative, even in locations in which precipitable water tendency is increasing. Some column drying by horizontal moisture advection occurs at all points due to the moister equatorial region relative to higher latitudes. However, substantial weakening of horizontal advection in regions of positive precipitable water tendency between 130°E–180°E allows surface evaporation, although weakened, to moisten the troposphere and lead to the onset of the next MJO convective event. It should be noted in Figures 14 and 15 that strong negative PW tendencies due to horizontal advection occur near and to the west of enhanced MJO precipitation. Sugiyama [2009b] invoked such a pattern of drying to explain how horizontal advection could foster eastward propagation of a moisture mode convective anomaly.

Figure 15. Unfiltered composite precipitation anomalies and column-integrated precipitable water budget terms for MJO phase 5 in the QM simulation. Terms include column-integrated a) precipitable water tendency, b) horizontal q advection, c) vertical q advection, and d) surface evaporation. Water budget units are mm day⁻¹. The precipitation contour interval is 4 mm day⁻¹, starting at 0 mm day⁻¹. Negative contours are dashed.

[35] Anomalous zonal and meridional moisture advection are now partitioned by decomposing variables into a time mean and perturbation about the time mean. The following partitioning is produced:

[36] For zonal advection,

• 

and for meridional advection,

• 

[37] Overbars represent the 50-day mean, and primes represent the deviation from the 50-day mean. Results are not sensitive to how the basic state is determined. For example, defining the basic state on the basis of a 100-day mean, or simulation mean, produced similar results. These terms are integrated from the surface to top of the troposphere in the plots shown below. It should be noted that the term − − was also examined, and generally provides a vertically-integrated background drying across the tropical warm pool region, primarily due to the meridional component. This term needs to be added to the anomalous advection (3) and (4) in order to get the total advection shown in Figure 15.

[38] Figure 16 shows the vertically-integrated partitioned zonal terms in (3), which are not bandpass filtered. The sum of advection of anomalous humidity by the mean zonal wind and advection of anomalous humidity by the perturbation wind largely determine the anomalous zonal advection [ − ( + u′) ], and appears to strongly influence the eastward propagation of the MJO mode in the model. Total moistening by zonal advection of up to 2 mm day⁻¹ occurs to the east of the convective center, and is approximately in quadrature with column precipitable water anomalies (Figure 8b). Maximum moistening in the model due to (3) and (4) occurs near 850 hPa (not shown). Recall also that moistening between 140°E and 150°E peaks near Phases 4 and 5 (Figure 13). Perhaps not coincidentally, total lower-tropospheric winds during Phases 4 and 5 at the leading edge of convection are on the order of 5 m s⁻¹, approximately the propagation speed of the MJO in the model (Figure 9b). These unfiltered winds are the sum of the 50-day mean wind and wind anomalies (Figure 9a) and hence their effects on advection are consistent with that shown in Figure 16.

Figure 16. Composite unfiltered partitioned vertically-integrated zonal q advection anomalies (mm day⁻¹) for MJO phase 5 in the QM simulation. Brackets represent the 50-day mean, and primes deviations from this 50 day running mean. The precipitation contour interval is 4 mm day⁻¹, starting at 0 mm day⁻¹. Tendency is in units of mm day⁻¹.

[39] The anomalous partitioned meridional advection terms (4) are shown in Figure 17. Total meridional advection anomalies tend to be shifted about 15° longitude to the east of the zonal component, such that meridional advection tends to oppose precipitation and precipitable water anomalies (see Figure 8b). An analysis of spectral coherence in the intraseasonal band verifies this lag between meridional and zonal components, with meridional advection preceding zonal advection by about 30 degrees of phase. This lag is even greater when considering only the troposphere below 800 hPa. As in M09, the term − contributes strongly to the anomalous meridional advection signal, although it is of weaker relative magnitude than in M09, given the weaker meridional basic state humidity gradient in the model. The weaker contribution of this term will also become apparent in Figure 18 below. M09 showed that eddy components with timescales less than 30 days dominated − , and this is also true in the QM simulation (not shown). The term − appears related to variations in tropical synoptic wave activity and the meridional moisture gradient. Advection of dry air from higher latitudes is increased (decreased) during periods of enhanced (suppressed) precipitation when meridional moisture gradients are also enhanced (weakened) and synoptic eddy activity is largest (smallest). Previous observational and modeling studies have hypothesized that eddy advection of this type might be idealized as a form of moisture diffusion [e.g. Sobel and Neelin, 2006, Peters et al., 2008], and the role of − here appears broadly consistent with these ideas. However, more work is necessary to determine whether this eddy advection term can truly be represented as diffusion with a well-behaved diffusivity.

Figure 17. As in Figure 16, except for meridional advection.

Figure 18. a) Composite partitioned 0°S–20°S averaged vertically-integrated perturbation zonal q advection at 141°E as a function of MJO phase in the QM simulation. Total zonal advection is black-solid, advection of mean q by the anomalous zonal wind is black-dashed, advection of anomalous q by the mean zonal wind is black-dotted, and the contribution due to advection of anomalous q by the anomalous zonal flow is gray-solid. b) Composite partitioned 0°S–20°S averaged vertically-integrated perturbation meridional q advection at 141°E as a function of MJO phase in the QM simulation. Total meridional advection is black-solid, advection of mean q by the anomalous meridional wind is black-dashed, advection of anomalous q by the mean meridional wind is black-dotted, and the contribution due to advection of anomalous q by the anomalous meridional flow is gray-solid. Overbars represent the 50-day mean, and primes deviations from this 50 day running mean.

[40] Examining the evolution of perturbation horizontal advection terms at one location is also enlightening. In this case, we examine the partitioned horizontal advection terms as a function of MJO phase at 141°E (Figure 18), near the location of strongest intraseasonal precipitation variance in the model. Recall that precipitation peaks at this location during Phase 6 (Figure 9). Perturbation zonal advection peaks near Phases 4 and 5, which is dominated by −, and partially canceled by the term . Hence, peak moistening of greater than 1 mm day⁻¹ occurs before (to the east) of MJO convection in the model and is primarily regulated by −( + u′) . The sum of the mean and anomalous flow at 850 hPa during Phases 4 and 5 at 141°E is approximately 5 m s⁻¹ (Figure 9b), and thus it is plausible that advection due to this zonal wind may be responsible for the eastward propagation seen in the model. The perturbation meridional advection budget indicates that each of the terms in (4) are of approximately equal amplitude at 141°E. This is in contrast to the modeling study of M09, where clearly dominated the meridional advection. Hence, weakening the meridional SST and humidity gradients in the QM simulation appear to have produced the desired effect of reducing the relative influence of . However, given the strong intraseasonal variability in this simulation, it is suggested that this eddy advection mechanism is not essential to the eastward propagation of the MJO, the opposite of that hypothesized by M09. In fact, MJO variability in the QM simulation is stronger than in the RS simulation (e.g. Figures 3 and 4), where is relatively more important compared to other advection terms, as in M09. Hence, may instead act as a damping term on moisture anomalies, a role supported by the negative covariance between and column humidity anomalies as inferred by comparing Figures 11 and 18. This negative covariance was also confirmed using an analysis of spectral coherence (not shown).

5. Sensitivity Tests

[41] A simulation is conducted that is identical to the QM simulation, except that latent and sensible heat fluxes are held fixed at the long term mean of the QM simulation. Technically, such an experiment removes more than wind-driven variability in surface latent and sensible heat fluxes. However, since intraseasonal variability in these fluxes is dominated by the wind-driven component in the QM simulation [and in observations, e.g. Shinoda et al., 1999, Araligidad and Maloney 2008], setting latent and sensible heat fluxes to climatology has the same essential effect. This “No-WISHE” run is motivated by the dominant role of latent heat flux and evaporation in the intraseasonal MSE and moisture budgets in the model, as well as other recent evidence in the literature suggesting an important role for WISHE in destabilizing tropical intraseasonal oscillations [e.g. Sobel et al., 2008, 2010].

[42] As a comparison to Figure 5 from the control QM simulation, Figure 19 shows that the character of precipitation variability has changed considerably in the No-WISHE simulation. No longer do high amplitude intraseasonal oscillations in precipitation occur in the model organized around zonal wavenumber 2. Instead, only higher frequency wind and precipitation variability remains, although interestingly slow eastward propagation at about 5 m s⁻¹ is still apparent, particularly in precipitation. It is possible that eastward propagation of precipitation anomalies by horizontal advection still occurs in the model. However, interactive surface fluxes appear necessary to destabilize the intraseasonal oscillation that is characterized by 50 day timescale and zonal wavenumbers 1–3 in the QM simulation.

Figure 19. Time-longitude diagrams of 0°S–20°S averaged precipitation (mm day⁻¹) and 850 hPa zonal wind (m s⁻¹) for Days 700–900 of the No-WISHE simulation.

[43] Figure 20a shows a plot of 20–100 day bandpass filtered precipitation variance and mean 850 zonal winds in the No-WISHE simulation. Compared to Figure 2 and consistent with Figure 19, intraseasonal precipitation variance decreases by greater than 50% with removal of interactive surface fluxes. Figure 20 also shows that mean winds in the No-WISHE run do not change substantially as compared to the QM simulation, suggesting that the model basic state has not significantly changed. Spectral power at wavenumber 1–3 and eastward intraseasonal timescales decreases substantially in wind and precipitation in the No-WISHE simulation, so much so that variance falls below the lowest contour intervals in the wind and precipitation spectra in Figures 3 and 4 (not shown).

Figure 20. Intraseasonal (20–100 day) precipitation variance (mm² day⁻²) and mean 850 hPa wind (m s⁻¹) for the a) No-WISHE simulation and b) Reduced zonal SST gradient simulation. The reference wind vector is shown at the lower right.

[44] To test the hypothesis that zonal advection is responsible for the eastward propagation of the MJO in the model, we conduct another experiment with the same SST distribution as the QM simulation (Figure 1), but with the zonal SST gradient reduced by one-half. This reduced zonal SST gradient reduces mean zonal westerly winds on the equator relative to the QM simulation, as seen by comparing Figure 20b to Figure 2. Intraseasonal precipitation variance is also reduced in this run. To verify that this low-level basic state wind change affects the propagation speed of precipitation anomalies in the model, we present a lag-regression analysis for the QM and reduced zonal gradient simulations (Figure 21), whereby 0°S–20°S averaged precipitation at all longitudes is regressed onto a 141°E 850 hPa intraseasonal zonal wind timeseries, and then scaled by a one-standard deviation value of this reference timeseries. Figure 21 indicates that eastward propagation is much slower in the run with reduced zonal SST gradient than in the control QM, supporting the hypothesis that zonal advection is important to eastward propagation in the model. The dominant propagation speed appears to change from about 4–5 m s⁻¹ in the QM run to about 2.5 m s⁻¹ in the reduced zonal gradient run, consistent with a weakening of advective zonal currents. A precipitation space time-spectrum confirms this shift in the reduced zonal gradient run to slower propagation speeds, with variance now concentrated in a narrow band centered on 90 days and wavenumber 3 (not shown), as compared to the spectrum from the QM simulation that has power concentrated at wavenumber 2 and 50 day period (Figure 4). An analysis like Figures 9 and 13, but for the reduced zonal gradient run, indicates that peak moistening in the model occurs when total unfiltered zonal winds at 850 hPa are eastward at about 2.5 m s⁻¹ (not shown), supporting the hypothesis that zonal advection is the propagation mechanism.

Figure 21. Lag regression of 0°S–20°S averaged intraseasonal (20–100 day) precipitation (colors) onto a reference 850 hPa zonal wind time series at 141°E in a) the QM and b) reduced zonal SST gradient simulations. Regression coefficients are scaled by a one standard deviation value of the reference time series. Precipitation anomaly units are mm day⁻¹.

[45] Figure 13 showed that the sum of latent and sensible heat flux anomalies, when combined with cloud-radiative feedbacks and other factors that influence longwave radiative cooling anomalies, is sufficient to overcome anomalous discharge of MSE by vertical advection at the time of peak precipitation. Horizontal advection is approximately in quadrature with precipitation, and supports eastward propagation. Hence, supported by the strong relationship between precipitation and precipitable water in the model, the MJO in the QM simulation resembles a moisture mode with weakly positive gross moist stability, and an effective gross moist stability (including radiative feedbacks, [e.g., Bretherton and Sobel [2002], Su et al. [2003]] very close to zero, destabilized primarily by WISHE. Without the effect of horizontal advection providing steering currents for moisture anomalies, stationary moisture modes can exist [e.g. Raymond and Fuchs, 2009]. Hence, we intend to test in future work the precise effects of horizontal advection on the model MJO mode by setting to climatology the meridional and zonal components of horizontal advection. As discussed above, meridional advection and zonal advection may have somewhat different impacts on intraseasonal tropospheric moisture anomalies, with meridional advection tending to discharge precipitable water in regions of high precipitation and humidity, and zonal advection through its quadrature relationship with precipitation tending to support propagation. The roles of horizontal and meridional advection may become clearer through future mechanism denial experiments to isolate the distinct impacts of these two advection components. We intend to further remove the impact of longwave radiative heating anomalies, to determine whether they are necessary to destabilize the model MJO.

6. Conclusions and Discussion

[46] Tropical intraseasonal variability was explored in an aquaplanet version of the NCAR Community Atmosphere Model 3 with a relaxed Arakawa-Schubert convection parameterization. First, sensitivity of intraseasonal variability to the SST basic state was examined. A simulation with zonally-symmetric SST produces only weak eastward-propagating intraseasonal variability on 30–90 day timescales, consistent with previous studies suggesting that a westerly low-level basic state is necessary for producing realistic intraseasonal variability [e.g. Inness and Slingo, 2003; Inness et al., 2003]. A zonally asymmetric SST distribution broadly similar to that observed during boreal winter produces intraseasonal variability in zonal winds that resembles observations, although with less realistic precipitation variability. The strongest intraseasonal variability in this simulation is concentrated near regions of mean low-level westerlies, as observed. To test the hypothesis of M09 that variations in meridional humidity advection produced by tropical synoptic eddies acting across the mean meridional humidity gradient are important for regulating the MJO moisture budget and hence MJO convection, a zonally-asymmetric simulation but with reduced meridional SST and humidity gradients was also conducted. While the relative impact of synoptic eddies on meridional advection was reduced in this run, intraseasonal variability in winds and precipitation is strengthened to magnitudes exceeding those observed. Precipitation and wind variability is highly concentrated near a 50-day period and zonal wavenumbers 1–2, and is clearly apparent in unfiltered precipitation and wind fields. Hence, the eddy advection mechanism proposed by M09 appears not to be essential for producing realistic intraseasonal variability, and in fact appears to damp that variability in the results presented here. However, we cannot rule out the possibility that synoptic eddies have other impacts on the model MJO [e.g. Majda and Stechmann, 2009].

[47] The simulation with reduced meridional SST gradient was analyzed throughout the rest of the paper. Given the high amplitude and high signal to noise ratio of the model MJO, many of the diagnostics were computed using unfiltered fields. The analysis indicates that the model MJO resembles a moisture mode. The model exhibits a very strong relationship between precipitable water and precipitation rate. Normalized gross moist stability in the model is positive, but weak. The intraseasonal disturbances appear to be destabilized by wind-induced surface flux anomalies, which overcompensate the vertically-integrated moist static energy export by divergent motions. Budget analyses indicate that horizontal moisture advection supports eastward propagation of the model MJO, with horizontal moisture advection approximately in quadrature with precipitation such that moistening (drying) by horizontal advection leads (lags) precipitation. Meridional advection tends to damp precipitable water anomalies that are in phase with precipitation, whereas zonal advection appears to propagate moisture anomalies eastward. In particular, zonal advection appears regulated by the term − ( + u′), where overbars represent a 50-day running mean, and primes a deviation from the 50-day running mean. At the time of peak moistening in advance of MJO precipitation, the total wind at low levels + u′ is approximately 5 m s⁻¹. This value is approximately equal to the MJO disturbances' phase speed, suggesting that horizontal advection is the propagation mechanism.

[48] The model hence appears to support an MJO resembling a moisture mode that is destabilized by wind-evaporation feedback and propagated eastward by horizontal advection. The integral role of wind-induced latent heat flux anomalies is exposed through a sensitivity test in which surface latent and sensible heat fluxes are set to their long-term climatology from the control simulation with reduced meridional SST gradient. Intraseasonal variability at zonal wave numbers 1–3 and 30–90 day periods is severely reduced when WISHE is removed, although high space and time frequency convective features that propagate slowly eastward near 5 m s⁻¹ still occur in this “No-WISHE” run. A simulation in which the zonal SST gradient is also reduced (by one-half) produces weakened mean 850 hPa westerly flow, which is accompanied by a reduction in eastward propagation speed, lending further support to the hypothesis that horizontal moisture advection by the low-level wind induces the eastward propagation.

[49] The role of wind-evaporation feedback here is fundamentally different from that in the original linear WISHE theory in which surface evaporation maximized in regions of low-level easterly anomalies, assuming an easterly basic state [Neelin et al., 1987, Emanuel, 1987]. Enhanced westerly winds occur near and to the west of MJO precipitation in our model, and warm pool evaporation anomalies maximize in regions of low-level westerly anomalies because the mean flow is from the west [as in observations, e.g. Sperber, 2003, Araligidad and Maloney, 2008]. Because a positive covariance exists between surface evaporation and precipitation anomalies in our model, and because these evaporation anomalies are sufficiently large, they support the tropospheric moisture anomalies that are collocated with precipitation and appear essential for destabilizing the MJO in this model.

[50] Because positive evaporation anomalies peak near and to the west of convection in our model as in observations, they cannot be directly responsible for eastward propagation of the MJO (although they could potentially slow it down). Our model also does not appear to support the paradigm that moistening to the east of convection occurs through frictional convergence, as has been hypothesized to be important in many modeling and observational studies over the past two decades [e.g. Wang and Li, 1994, Maloney and Hartmann, 1998, Liu et al., 2005]. Moistening to the east of MJO convection in our model is dominated by zonal horizontal advection. In fact, anomalies in −q∇· are near zero at the time of peak moistening.

[51] This study does not come without caveats. First, the composite moistening structure in our reduced meridional SST gradient simulation does not exhibit a vertical tilt like observations in which moisture anomalies first start in the lower troposphere before expanding vertically [e.g. Kiladis et al., 2005]. As mentioned earlier, simulations with realistic SST distributions do capture this vertical tilt, which appears to be strongly regulated by meridional moisture advection anomalies [Maloney, 2009].

[52] Second, the magnitude of the background 850 hPa zonal wind in the warm pool is about twice as strong as observed in the reduced meridional SST gradient simulation as compared to both observations and a simulation with realistic SST (e.g. compare Figure 2 to Figure 4 of Zhang et al., 2006]. This obviously has implications for the strength of the zonal moisture advection, a key regulator of propagation in our model. Since MJO wind anomalies also affect the zonal advection mechanism we propose here, and the strength of the model MJO is also substantially larger than observed, understanding the impact of mean zonal wind changes on the strength of advection is not entirely straightforward.

[53] Third, both the version of the model with realistic SST (e.g. Figure 2, top panels) and the model with reduced meridional SST gradient (Figure 2, bottom panels) exhibit substantial mean precipitation biases relative to the observed boreal winter and spring distribution. The simulation with realistic SST produces a strong double ITCZ in the warm pool, whereas the simulation with reduced meridional SST gradient produces a single strong Southern Hemisphere ITCZ. As the shape of the mean precipitation distribution in the model strongly influences the shape of MJO precipitation anomalies and hence the structure of the anomalous large-scale circulation response [e.g. Gill, 1980], such precipitation biases may impact the nature of anomalous moisture advection. We note that observed DJF MJO precipitation and wind anomalies have a decided preference toward the Southern Hemisphere, particularly in the west Pacific [see Wheeler and Hendon, 2004, Figure 8]. Hence, the strong Southern Hemisphere bias of MJO anomalies in our reduced meridional SST gradient run may not be unrealistic. Regardless, the caveats listed here suggest that some of the details of the model propagation mechanism could differ from reality. However, given the robust model intraseasonal variability that exhibits many characteristics of the observed MJO, propagation mechanisms related to the one we propose here are at least plausible for the real MJO and should be tested using observational diagnostics and sensitivity tests in a wider suite of models.

[54] Why the strongest intraseasonal variability in our study occurs with an SST simulation having the meridional SST gradient reduced to one-quarter of that observed is also an interesting question. One possibility is that a reduction in midlatitude baroclinic influence in the tropics could make for a cleaner and less interrupted MJO simulation. A second possibility is that because the off-equatorial Tropics in the Eastern Hemisphere are warmer, gross moist stability is also reduced there, making it easier for surface fluxes to destabilize the model MJO [e.g. Raymond et al., 2009]. Gross moist stability can also be lowered by altering the vertical profile of diabatic heating and related vertical velocities. Maloney, [2009] documented that the version of the model we use produces a very poor simulation of shallow convection and congestus. Such shallower heating modes may contribute to periods of strongly reduced or negative gross moist stability during MJO events [e.g. Peters and Bretherton, 2006, Haertel et al., 2008, Hannah, 2009]. Hence, reducing the gross moist stability by changing the SST distribution may be compensating for deficiencies in moist physics of the GCM.

[55] Future work will be conducted to extend the sensitivity tests conducted here. In particular, sensitivity tests, in which either meridional or zonal moisture advection are set to their climatology, will be conducted to test the importance of horizontal advection to MJO propagation and maintenance. Further, a sensitivity test in which longwave radiative cooling is set to climatology will be conducted to test the impact of cloud radiative feedbacks to the model MJO. The importance of cloud-radiative feedbacks to intraseasonal variability in the tropics is a subject of ongoing debate [e.g. Lin and Mapes, 2004, Bony and Emanuel, 2005]. From the standpoint of the vertically-integrated moist static energy budget, it is possible that any combination of moist diabatic sources including latent and sensible heat fluxes and column-integrated longwave and shortwave heating anomalies that add up to overcompensate export by vertical advection may lead to instability in the model [e.g. Sugiyama, 2009a,2009b]. Exploration of the MJO initiation process in the model will also be conducted. As Figure 5 shows, the model MJO is characterized by very strong and somewhat regular intraseasonal variability. Given the reduced meridional SST gradient in the model and reduced midlatitude baroclinic wave activity, extratropical forcing [e.g. Bladé and Hartmann, 1993] would appear to be a less likely candidate for MJO initiation. Hence, it is possible that alternate explanations may exist for initiation of successive MJO events in the model [e.g. excitation by circumnavigation, Matthews, 2008].

Acknowledgments

[56] The authors acknowledge Chris Bretherton and Dargan Frierson for helpful discussions on the results presented here. Two anonymous reviewers and the editor Minghua Zhang also provided insightful comments on an earlier version of this paper. This work was supported by the Climate and Large-Scale Dynamics Program of the National Science Foundation under Grant ATM-0832868 (EDM) and the Science and Technology Center for Multiscale Modeling of Atmospheric Processes, managed by Colorado State University under cooperative agreement No. ATM-0425247 (EDM, WMH). This work has also been funded by award NA08OAR4320893 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce (EDM, AHS), and by NASA MAP grant NNX09AK34G (AHS). The statements, findings, conclusions, and recommendations do not necessarily reflect the views of NSF, NASA, NOAA, or the Department of Commerce.