The sensitivity of a simulated Madden–Julian oscillation (MJO) was investigated in the NCAR Community Atmosphere Model 3.1 with the relaxed Arakawa–Schubert convection scheme by analyzing the model’s response to varying the strength of two moisture sensitivity parameters. A higher value of either the minimum entrainment rate or rain evaporation fraction results in increased intraseasonal variability, a more coherent MJO, and enhanced moisture–convection feedbacks in the model. Changes to the mean state are inconsistent between the two methods. Increasing the minimum entrainment leads to a cooler and drier troposphere, whereas increasing the rain evaporation fraction causes warming and moistening. These results suggest that no straightforward correspondence exists between the MJO and the mean humidity, contrary to previous studies.
Analysis of the mean column-integrated and normalized moist static energy (MSE) budget reveals a substantial reduction of gross moist stability (GMS) for increased minimum entrainment, while no significant changes are found for an increased evaporation fraction. However, when considering fluctuations of the normalized MSE budget terms during MJO events, both methods result in negative GMS prior to the deep convective phase of the MJO. Intraseasonal fluctuations of GMS, rather than the mean, appear to be a better diagnostic quantity for testing a model’s ability to produce an MJO.
The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics and is characterized by an eastward-propagating planetary-scale (zonal wavenumbers 1–3) disturbance in tropical convection, large-scale circulations, and tropospheric humidity with fluctuations on 30–90-day time scales (Madden and Julian 2005). Although the MJO has been observed since the early 1970s (Madden and Julian 1971) an understanding of the fundamental dynamics is lacking. Many models are plagued by incoherent intraseasonal variability (Slingo et al. 1996; Sperber et al. 1997; Wu et al. 2002; Kim et al. 2009), which further complicates obtaining a full understanding of the MJO, although recent modeling efforts have shown considerable improvements (e.g., Benedict and Randall 2009; Liu et al. 2009). This paper documents the sensitivity of the MJO simulation in the National Center for Atmospheric Research (NCAR) Community Atmospheric Model version 3.1 (CAM3.1) to variations of two moisture sensitivity parameters and explores why these modifications enhance intraseasonal variability in the model in hopes of illuminating the fundamental mechanisms that drive the MJO.
A comprehensive theory of the MJO would need to account for several attributes including a planetary-scale circulation coupled with a large-scale convective complex, a dominant spectral peak of approximately 50 days, slow eastward propagation in the eastern hemisphere with seasonally dependent poleward propagation, and a longitudinal-dependent amplification and suppression of the convective signal (Wang 2005; Zhang 2005). Several hypotheses for the MJO have been proposed. Two leading theories that are most relevant to this paper are moisture modes (Sobel et al. 2001; Fuchs and Raymond 2007) and wind-induced surface heat exchange (WISHE; Neelin et al. 1987; Emanuel 1987), which are not necessarily mutually exclusive. Other hypotheses that currently exist in the literature such as frictional wave–conditional instability of the second kind (CISK) (Wang and Li 1994) will not be discussed in detail.
Although the original linear WISHE theory for the MJO has been contradicted by observations (Lin and Johnson 1996; Zhang and McPhaden 2000), strong evidence has been presented in the literature suggesting that surface fluxes are important in some way for maintaining the MJO (Sobel et al. 2010; Araligidad and Maloney 2008). Nonlinear forms of WISHE have also been suggested by previous studies to play a role in organizing the initial MJO convective disturbance (Grabowski 2003). For a conceptual model of the MJO that includes WISHE to be viable, it will need to operate when the mean equatorial surface winds are westerly. This is unlike the original WISHE prototype, which requires the prevailing low-level equatorial winds to be easterly. Maloney et al. (2010) found that simulated MJO-like disturbances in a westerly basic state were not able to develop when surface flux feedbacks were disabled, suggesting that surface fluxes may regulate the convective organization of the MJO.
A moisture mode is a disturbance whose dynamics are controlled by the processes that regulate free tropospheric humidity. The large-scale dynamics of a moisture mode exist under a weak temperature gradient balance (WTG; Sobel et al. 2001; Raymond and Fuchs 2009) in which horizontal temperature gradients are negligible to first order and diabatic heating is balanced by adiabatic cooling. The location of convection is determined by column humidity anomalies, which are approximately equivalent to moist static energy (MSE) anomalies in regions of weak temperature gradients. Moisture modes can become destabilized when deep convection and associated processes result in growth of column MSE anomalies. A diagnostic quantity that is useful for looking at this process is gross moist stability (GMS; Neelin and Held 1987), which can be defined as the export of MSE out of the column by divergent circulations per unit vertical mass flux. If we consider an effective GMS, which we define here as including the effects of MSE sources such as surface fluxes and cloud–radiative feedbacks to the extent that they are local to convection, then a negative effective GMS in deep convective regions indicates that convection and associated processes are moistening the column and consequently augmenting the MSE anomaly. A thorough review of GMS and its roles in conceptual models of the tropical atmospheric circulation can be found in Raymond et al. (2009).
Moisture mode propagation is determined by the mechanisms that control the spatial distribution of moisture. Without the existence of steering currents or nonlocal wind-induced surface flux anomalies, moisture modes would remain stationary since feedbacks between convection, moisture, and radiation happen locally (Raymond et al. 2009). Maloney (2009) showed for a simulated MJO in a modified version of the NCAR CAM that the leading terms of the vertically integrated intraseasonal MSE budget were horizontal advection and surface latent heat flux. Anomalous horizontal advection was shown to be responsible for moistening the atmosphere to the east of MJO convection and was incompletely cancelled by the contribution of suppressed latent heat fluxes. Observational evidence has been published that supports the notion of moistening by horizontal advection being important to the MJO (i.e., Benedict and Randall 2007).
It is widely understood that many aspects of the large-scale dynamics in the tropical atmosphere are consistent with the WTG theory (Charney 1963; Held and Hoskins 1985; Sobel et al. 2001). Although there is no conclusive evidence for the existence of moisture modes, numerous observations indicate the existence of strong moisture–convection feedbacks in the atmosphere, which are manifested as a strong relationship between precipitation and free tropospheric moisture (Bretherton et al. 2004; Holloway and Neelin 2009). Grabowski and Moncrieff (2004) demonstrated that moisture–convection feedbacks can be strengthened in a model by increasing the sensitivity of the convective scheme to free tropospheric moisture with the use of a specified convective rain evaporation fraction, which also improved the MJO signal in the model. Various other parameters that inhibit convection can be implemented in a model to yield similar improvements. In some cases these parameters have been shown to be associated with a more unstable tropical atmosphere, shallower convection, and reduced GMS in the mean (Frierson et al. 2011). Several modeling efforts that utilize embedded cloud-resolving models, or superparameterization, have shown improvements to the MJO for a given model, which appears to be largely due to improved moisture–convection feedbacks (Thayer-Calder and Randall 2009; Kim et al. 2009; Zhu et al. 2009).
The present study expands on previous work in an effort to determine why an increased sensitivity of convection to free tropospheric moisture yields a more robust MJO in a GCM. In particular, we examine how the MJO signal changes in response to the strength of two different modifications to the Relaxed Arakawa–Schubert (RAS) scheme of Moorthi and Suarez (1992). Impacts on the time mean and intraseasonal scales are compared between these two methods to highlight whether moisture–convection feedbacks are realized in a consistent manner on time scales pertinent to the MJO. Looking at how these feedbacks operate during the various phases of the MJO should bring us closer to a thorough explanation of why they are essential to the existence of the MJO. Because of the current limitations of computational resources, traditional methods of parameterization will be needed both for research and operational forecasting for the foreseeable future, and so investigating why such modifications to cumulus parameterizations improve simulations of the MJO should prove to be valuable to the modeling community.
Section 2 provides a description of the model and details about the modifications made relative to the standard configuration of the CAM 3.1. Section 3 presents a sensitivity analysis detailing how changes to each moisture sensitivity parameter affect the MJO and the mean state of the model. Section 4 uses process-oriented diagnostics to investigate the causes of the changes described in section 3. A summary and discussion are presented in section 5.
a. Model description
The NCAR CAM3.1 (Collins et al. 2006) is used for this study. CAM is the atmospheric component of the Community Climate System Model version 3. The RAS convective parameterization of Moorthi and Suarez (1992) is used in place of the standard Zhang and McFarlane (1995) scheme to improve the model’s tropical intraseasonal variability (Maloney and Sobel 2004; Maloney 2009). The Hack (1994) scheme is retained to simulate shallow convection.
RAS simplifies some of the calculations made in the original Arakawa–Schubert (AS; Arakawa and Schubert 1974) scheme so that it is more computationally economical. Instead of requiring the cloud ensemble to reach quasi-equilibrium as in AS, RAS simply relaxes the state toward equilibrium each time the parameterization is invoked. The convective adjustment in RAS is still governed by a cloud work function, similar to AS, which is strongly regulated by boundary layer MSE. Although RAS is sensitive to the amount of moisture in the boundary layer, the standard version of this scheme is relatively insensitive to the amount of moisture in the free troposphere (e.g., Yang et al. 1999). The reason for this insensitivity is that cloud ensemble members in RAS are allowed unrealistically low entrainment rates, which buffer these clouds from the effects of dry free tropospheric environments. Thus, the version of RAS used in this study has been modified to include a minimum entrainment parameter similar to the method used by Tokioka et al. (1988) to address this issue. Cloud ensemble members with entrainment rates less than the prescribed minimum entrainment rate are suppressed. In this way we can make the convective parameterization more sensitive to the free tropospheric environment and more realistically simulate the suppression of deep convection in dry atmospheres, as is observed (e.g., Neelin et al. 2009).
In Tokioka et al. (1988) the prescribed minimum entrainment rate μmin was related to the location-dependent depth of the boundary layer, such that μmin= α/D, where α is a dimensionless constant, and D is the depth of the boundary layer. Using this method resulted in an enhanced MJO signal in their model. The version of RAS used here assumes a constant boundary layer depth of D = 2000 m when calculating μmin so that the minimum entrainment parameter is constant for each model run. Results based on this assumption should not significantly differ from that of Tokioka et al. (1988) since the temporal variability of boundary layer MSE is small in the model used here.
The version of RAS used here also allows a specified fraction ɛ of convective precipitation to be exposed to the environment and evaporate depending on the environmental humidity as well as microphysical assumptions such as droplet size distribution and fall velocities (Sud and Molod 1988). Previous studies have shown that a simulated MJO is sensitive to changes of this parameter (e.g., Grabowski and Moncrieff 2004; Maloney 2009). Although convective rain evaporation is not allowed to explicitly generate subgrid-scale downdrafts, it is likely to have impacts on the grid-scale vertical velocity through modifications to the vertical heating structure.
Four 16-yr simulations of CAM with the RAS convective scheme were conducted to assess the sensitivity to the minimum entrainment parameter. The primary simulations analyzed were configured with ɛ = 0.3 and α = 0.0, 0.2, 0.4, and 0.6. Two additional simulations were analyzed in section 3 in which α was held fixed at α = 0.2 and ɛ was set to 0.05 and 0.6. Simulations are integrated using a spectral dynamical core at T42 resolution (approximately 2.8° × 2.8° grid resolution) with climatological seasonal cycles of sea surface temperatures and insolation applied. Twenty-six levels are resolved in the vertical, and the model time step is 20 min.
The European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis product (ERAi; Simmons et al. 2007) is used throughout this study as an observational comparison and was obtained from the ECMWF data server. Reanalysis data provides comprehensive spatial coverage for the area of interest where observations are sparse, which makes it ideal for this type of research, although many of the reanalysis fields may be strongly constrained by the reanalysis model, especially moist variables that are parameterization dependent. The ERAi dataset has a 1.5° × 1.5° horizontal resolution and 37 available vertical levels. A subset of this dataset is used here, which includes 13 vertical levels from 975 to 100 hPa, latitudes between 15°N and 15°S, and all longitudes during 1990–2004. The Global Precipitation Climatology Project (GPCP) dataset is also used, which combines precipitation measurements from six datasets (Huffman et al. 2001). Special Sensor Microwave Imager (SSM/I) version 6 precipitation was also used and obtained from Remote Sensing Systems (http://www.remss.com/; Wentz and Spencer 1998). Total precipitable water data was acquired from the National Aeronautics and Space Administration (NASA) water vapor project (NVAP; Randel et al. 1996) dataset, which includes satellite and radiosonde measurements.
Intraseasonal anomalies in all fields are calculated by applying a linear nonrecursive digital band-pass filter with half-power points at 30- and 90-day periods. The frequency response of the filter retains nearly full power at 40–50-day time scales, which is the dominant time scale of the MJO as documented in observations (Madden and Julian 1971). Lagged composites were created using an MJO index based on the equatorial averaged filtered 850-hPa zonal wind at 155°E as in Maloney and Sobel (2004). Significant MJO events were defined on the basis of maxima in the anomalous zonal wind having amplitudes greater than one standard deviation. A comparison of alternative compositing methods (e.g., Wheeler and Hendon 2004) showed that the results were insensitive to which technique was used.
3. Model sensitivity analysis
a. Minimum entrainment rate
Mean boreal winter (November–April) 850-hPa zonal winds are shown in Fig. 1 for model runs with varying α and ERAi data. Low level easterlies prevail throughout most of the tropics in observations (Fig. 1e), although the Indo-Pacific warm-pool region consists of westerlies along and just south of the equator. This structure is partially captured in the model, but the region of westerlies over the warm pool covers a smaller zonal extent with weak easterlies over the Indian Ocean. This discrepancy may be important as MJO propagation may be strongly regulated by zonal moisture advection. The MJO destabilization mechanism may also be affected by surface fluxes and their phase relationship relative to precipitation anomalies, which is highly dependent on the sign of the background flow (Maloney et al. 2010). This is supported by the results of Inness et al. (2003) and Inness and Slingo (2003) who showed that an accurate low-level wind distribution was important for producing realistic MJO propagation in a GCM. The MJO in our simulations is weaker than observed over the Indian Ocean (see Fig. 4), consistent with a lack of mean westerlies there.
If the model’s intraseasonal variability is in fact related to moisture–convection feedbacks that are enhanced with increasing α, then there should be a detectable change in the intraseasonal variability of column moisture as the moisture trigger threshold is increased. To investigate this, the variance of 30–90-day boreal winter column saturation fraction was computed for each model run and ERAi (Fig. 2). The saturation fraction was calculated as the ratio of the column-integrated specific humidity to the column-integrated saturation specific humidity. Unlike intraseasonal variance of zonal wind or precipitation (not shown), which is overestimated in the model, saturation fraction variance in the model is generally weaker than observations. An area of very low saturation fraction variance in the Indo-Pacific warm-pool region can be observed in the control simulation (Fig. 2a), which becomes less prominent as the minimum entrainment rate is increased.
Figure 3 shows a scatterplot describing the ratio of total eastward spectral power in the MJO band to its westward counterpart over 30–90-day periods and wavenumbers 1–3 for each model run where α is varied and observations (see also Table 1 of Zhang et al. 2006; Fig. 5 of Kim et al. 2009). The precipitation variance ratio is shown on the abscissa, and the zonal wind ratio is on the ordinate. This ratio approaches the observations as the minimum entrainment is increased. The similarity of the ratios for α = 0.4 and α = 0.6 suggests that the effect of the moisture trigger saturates at these thresholds.
b. Minimum entrainment composite analysis
Figure 4 shows boreal winter composite 850-hPa zonal wind and precipitation anomalies for the models as well as ERAi winds and GPCP precipitation. Lag in days relative to the maximum zonal wind is on the ordinate and longitude is on the abscissa. Zonal wind anomalies are shown in colors and precipitation in contours. Composites based on observations indicate an average phase speed of approximately 8 m s−1 for intraseasonal westerly anomalies between 90°E and 180° (Fig. 6c), which increases past the date line to approximately 25–30 m s−1. The phase relationship between zonal wind and precipitation anomalies displays a similar quadrature relationship to the results of previous observational studies (e.g., Hendon and Salby 1994). This relationship shifts slightly around the Maritime Continent such that precipitation anomalies become closer in phase with zonal wind anomalies. The relative minimum in precipitation over the Maritime Continent (110°E) may be attributable to surface flux anomaly contrasts between land and ocean surfaces (Sobel et al. 2010).
The composite structure of the control simulation (Fig. 4a) shows a very weak amplitude stationary signal with no organized precipitation. The simulation with α = 0.2 has a higher-amplitude oscillation with coherent propagation of 5 m s−1 on average (Fig. 4b), slightly slower than observations. Higher minimum entrainment rates yield anomaly propagation speeds comparable to observations, at roughly 7 m s−1 (Fig. 6b). Zonal wind anomalies for nonzero minimum entrainment rates are stronger than observations, but precipitation anomalies are comparable in amplitude except over the Indian Ocean. The relatively weak signal in the Indian Ocean is consistent with previous analysis using related versions of the NCAR CAM (e.g., Maloney and Sobel 2004), and may be related to weak climatological westerlies there, as discussed above.
Lag composites of equatorially averaged and filtered specific humidity and diabatic heating profiles at 155°E are shown in Fig. 5. The lag in days relative to the peak westerly wind anomaly is shown on the abscissa. Peak precipitation associated with the MJO occurs around day −5. The abscissa can also be thought of as a proxy for physical position relative to 155°E, where each day roughly corresponds to 6° of longitude. The signal in the control simulation (α = 0.0) is very weak and incoherent, whereas the α = 0.2 simulation shows a more appreciable humidity signal with a noticeable westward tilt with height. Anomaly magnitudes in the models with higher minimum entrainment rates (Figs. 5c,d) are overestimated compared to observations (Fig. 5e). Low-level heating prior to the deep heating phase is likely due to the Hack (1994) shallow convection scheme. Anomalous near-surface moisture in the wake region in the models is likely due to enhanced surface fluxes driven by the westerly wind burst, although the reason why this is not seen in observations is unclear. These results were not notably sensitive to the longitude being considered.
Several previous observational studies have found a westward tilt with height to specific humidity anomalies as is shown here for ERAi data, (Fig. 5e; Sperber 2003; Kiladis et al. 2005), although this has been shown to vary between the time period and dataset under consideration (Kim et al. 2009; Myers and Waliser 2003; Tian et al. 2006). This tilt has been suggested to be an indication of low-level preconditioning possibly by shallow convection (Benedict and Randall 2007, 2009; Thayer-Calder and Randall 2009) or low-level horizontal moisture advection (Maloney 2009). Although the simulations shown here also exhibit a westward tilt with height, this tilt appears to diminish slightly as the minimum entrainment rate is increased. Simulations of the MJO in an aqua-planet version of this model and its superparameterized counterpart (i.e., SP-CAM) are not characterized by a westward tilt with height. In the simulations of Maloney et al. (2010) all levels appear to moisten simultaneously to the east of the MJO convection with low-level horizontal advection and rapid vertical redistribution of moisture anomalies being dominant. Whether the westward tilt with height is an essential feature of the MJO remains an open question.
c. Rain evaporation fraction
Maloney (2009) showed that the MJO was enhanced in a GCM with a variant of RAS (see Sud and Walker 1999) when ɛ was increased. Note that the value of this parameter for the previous simulations analyzed with varying minimum entrainment was set to ɛ = 0.3. Analysis of how this parameter influences the MJO, in a similar manner to that done for minimum entrainment, reveals that the model has a similar sensitivity to the evaporation parameter (not shown). Specifically, the spectral representation of the MJO becomes more pronounced and the intraseasonal variance of saturation fraction increases substantially as the evaporation fraction is increased.
Lagged composite profiles of specific humidity and diabatic heating (Fig. 6) for three simulations with varying ɛ and fixed minimum entrainment (α = 0.2) further show how increased evaporation parameter enhances the MJO in agreement with Maloney (2009). The ɛ = 0.05 simulation exhibits a relatively weak and incoherent signal similar to the simulation with zero minimum entrainment. Variance substantially increases with ɛ = 0.6 and a tilted structure is apparent. The dominant period of the oscillation associated with ɛ = 0.6 is longer than that produced with increased minimum entrainment, and moisture and diabatic heating anomalies are not as strong.
d. Mean-state comparison
Previous studies have presented contradictory evidence as to whether changes to the time mean humidity associated with a moisture sensitivity parameter can influence a model’s intraseasonal variability. Several of these results show that by increasing the strength of a moisture trigger, the MJO signal is improved and the time mean humidity in the tropics increases (Tokioka et al. 1988; Maloney and Hartmann 2001; Maloney 2009). On the other hand, Lin et al. (2008) show several cases in which moisture trigger strength does not produce increased time mean total precipitable water, although intraseasonal variability increases. Here, we present a comparison of how the mean state changes when both the evaporation and minimum entrainment parameters are increased.
Figure 7 shows the difference in all-season mean profiles of specific humidity, temperature, and diabatic heating between the simulations with the highest and lowest minimum entrainment thresholds (solid lines) and between the simulations with the highest and lowest rain evaporation fractions (dashed lines). These figures represent averages over the Indo-Pacific warm pool. A higher minimum entrainment results in drier and cooler conditions above the boundary layer, with the largest differences in the middle troposphere for specific humidity and the upper troposphere for temperature. Similar profiles of relative humidity are consistent with those shown here of specific humidity. A large decrease in diabatic heating owing to the suppression of deep convection is evident at upper levels. This is consistent with the mean vertical velocity, which shows a more bottom-heavy profile with higher minimum entrainment (not shown). Increasing the rain evaporation fraction produces a moister midtroposphere and a warmer upper troposphere, almost the opposite effect of increasing the minimum entrainment rate. Kim et al. (2011) found similar inconsistencies in the mean state when comparing the effects of increased moisture sensitivity between models. These results seem to belie a simple dependence of intraseasonal variability on the mean tropospheric humidity, contrary to that suggested by Maloney and Hartmann (2001).
Changes to the profile of specific humidity are different than what was found by Tokioka et al. (1988) in which the column moistened significantly as the minimum entrainment threshold is increased. One possible reason for this is that Tokioka et al. (1988) used an aquaplanet model with zonally uniform SSTs. Since the model used here has large landmasses and cold-pool regions where the tropospheric humidity is low compared to the warm pool, stronger moisture gradients are found in our model that may affect the tropical mean state through horizontal advection. This possible influence will be discussed in section 4b. Since both of the moisture sensitivity parameters foster an MJO while inducing vastly different changes to the mean climate, we argue that there is no unique relationship between the time mean tropospheric humidity and the MJO.
4. Process-oriented diagnostics
a. Moisture–convection feedbacks
Several studies have shown that there is a strong nonlinear relationship between precipitation and tropospheric water vapor using various techniques including cloud-resolving models (Derbyshire et al. 2004; Raymond and Zeng 2005), satellite observations (Bretherton et al. 2004; Peters and Neelin 2006), and conventional sounding and radar data (Raymond et al. 2007). These results support the notion that dry air can inhibit deep convection. If the effective gross moist stability is negative, then the presence of moist convection and associated processes such as enhanced surface latent heat fluxes can create a positive feedback with the environment, allowing for the growth and maintenance of column humidity anomalies and organized convection on large scales (Raymond et al. 2009).
Figure 8 shows daily total rain rate binned as a function of saturation fraction (Fig. 8a) and the distributions of saturation fraction (Fig. 8b) and precipitation (Fig. 8c) for select simulations and observations. Simulations with varying minimum entrainment are shown by the solid curves and simulations with varying rain evaporation fraction are shown by the dashed curves. Both increasing the minimum entrainment parameter and increasing the rain evaporation fraction make the dependence of precipitation on saturation fraction more nonlinear. Higher average precipitation occurring at a high saturation fraction suggests that the minimum entrainment threshold supports more vigorous convection when the column is anomalously humid, which is overestimated compared to observations. Other models that produce an MJO, such as the superparameterized CAM, show a similar precipitation overestimation when the column is anomalously humid (Zhu et al. 2009; Kim et al. 2011). The low rain evaporation simulation produces unrealistically high precipitation rates for low saturation fraction. Increasing evaporation lowers precipitation rates for most bins (Fig. 8b), which is expected since more rain is expected to evaporate into the environment.
In either case, this analysis shows that moisture–convection feedbacks are being enhanced when the strength of either moisture parameter is increased. Increasing the minimum entrainment suppresses precipitation for low saturation fractions and increases it for high saturation fractions, hence increasing the sensitivity of convection to the environmental humidity. Increased evaporation fraction generated a nonlinear and monotonically increasing dependence of precipitation on saturation fraction. For the low rain evaporation simulation, around 80% saturation, the excessive precipitation indicates that the convective moisture sensitivity is not being realistically simulated. These results were found to be qualitatively identical when only convective precipitation is considered. In both cases, the mean fraction of large-scale to convective precipitation in the warm pool becomes larger as the sensitivity parameter is increased (increases from 3% to 8% with the minimum entrainment change and from 1% to 13% with varying rain evaporation), which agrees with other sensitivity studies (e.g., Lin et al. 2008).
b. Moist static energy budget
The MSE budget is useful for describing the interaction of convection and large-scale circulation (Neelin and Held 1987), particularly in the presence of weak temperature gradients. MSE can be defined as
where s = cpT + gz is the dry static energy (DSE), cp is the specific heat at constant pressure for dry air, T is temperature, g is the gravitational constant, z is height above some reference level, Lυ is the latent heat of vaporization, and q is specific humidity. In this section we will examine the MSE budget for both the mean-state and intraseasonal time scales and how they are affected by moisture sensitivity parameters.
To interpret results in the context of WTG concepts we need to justify that WTG is a valid approximation. Filtered and vertically integrated DSE budget terms were composited over an MJO life cycle for all simulations (not shown). As expected, the resulting picture shows the DSE tendency to be negligible relative to the vertical advection, and that vertical advection of DSE is almost completely canceled by DSE generation due to precipitation, justifying the WTG approximation (Yano and Bonazolla 2009). Composites of vertically integrated intraseasonal DSE and MSE anomalies (not shown) illustrate that DSE makes up roughly 10%–20% of MSE anomalies, allowing us to consider MSE anomalies as approximately equal to latent heat anomalies on intraseasonal time scales.
where LH and SH represent the surface latent and sensible heat flux, LW and SW represent longwave and shortwave heating rates, and v is the horizontal velocity vector. Brackets represent a mass-weighted vertical integral through the troposphere. The gradient operator here only applies along constant pressure surfaces. Following Raymond and Fuchs (2009), the first term on the right-hand side of (2) represents the effect of horizontal mass convergence on MSE tendency, which is equivalent through continuity to the effect of vertical mass divergence. Therefore, integration by parts over the depth of the tropospheric column shows that we can equivalently refer to this term as the column-integrated MSE import due to vertical advection (e.g., Back and Bretherton 2006). We consider this quantity useful here since we are focused on changes to the structure of divergent motions and hence vertical advection. All terms are normalized by the column-integrated DSE s import due to divergent motions (−〈s∇ · v〉), which is generally negative in convective regions of the tropics. Given this sign convention, if the normalized terms are positive, they represent an export of MSE, and if negative, they represent an import.
GMS can be defined as the export of MSE out of the column by divergent motions per some unit measure of convective activity (often mass flux, Neelin and Held 1987; Raymond et al. 2009). This definition can be expanded to account for an effective GMS, which includes the effects of surface fluxes and radiative heating to the extent which these processes are local to convection (e.g., Sugiyama 2009; Bretherton and Sobel 2002; Su et al. 2001). Normalizing the first term on the right-hand side of (2) we can write the GMS as
This gives a measure of GMS that has been shown to be relevant to theories of precipitation (e.g., Raymond et al. 2009) and represents MSE export by vertical advection per unit DSE export.
To maintain moisture modes against dissipation requires that the effective GMS be negative (Raymond et al. 2009). This indicates that column MSE anomalies can grow in the presence of convection and the associated divergent motions, which in WTG regimes means that convection is moistening the environment rather than drying it, as is argued to be necessary in some models of the MJO (Raymond and Fuchs 2009). This also means that surface fluxes and other local MSE sources can overcompensate for the loss of MSE by divergent motions. Yu et al. (1998) estimated small positive values of GMS in regions of the tropics with active convection using prescribed vertical velocity profiles based on quasi-equilibrium assumptions. However, Back and Bretherton (2006) showed that geographic variations in MSE divergence are dominated by differences between the shapes of the vertical motion profiles. Their results found that some areas of the tropics have small values of MSE export with uncertain sign, while the west Pacific warm pool had small positive values.
Figure 9 shows the all-season mean normalized column-integrated MSE budget terms for the simulations with the lowest and highest minimum entrainment thresholds (Fig. 9a) and lowest and highest rain evaporation fractions (Fig. 9b) as a function of daily rain rate. Note that all terms are plotted with the opposite sign to that shown in (2) such that the quantities describe the amount of export rather than import. The domain was restricted to 10–50 mm day−1 since lower rain rates include subsidence regimes with weak dynamics, which complicate the interpretation of the results. Most strikingly, the normalized export of MSE due to vertical advection (i.e., GMS) is dramatically reduced at all rain rates greater than 10 mm day−1 in the α = 0.6 simulation (Fig. 9a) and even becomes negative around 10–15 mm day−1. This reduction in GMS should make it easier to grow and sustain MSE anomalies against dissipation, especially when assisted by MSE sources such as enhanced surface heat fluxes.
The more bottom-heavy mean heating profile and associated divergent circulation produce a reduced export of DSE aloft, lowering GMS. This effect overwhelms the effect of a decrease in gross moisture stratification due to a drier troposphere. For increased rain evaporation (Fig. 9b) there is no evidence for a decrease in the mean GMS as is found for an increased minimum entrainment. As Fig. 7 shows for increased rain evaporation, while the lower troposphere above the boundary layer moistens in the mean, creating larger moisture convergence per unit mass flux, the diabatic heating profile becomes more top heavy in the mean tending to increase export per unit mass flux (e.g., Peters and Bretherton 2006). These changes to the mean moisture and diabatic heating profiles apparently cancel to produce only modest changes in GMS, suggesting that the mean GMS is not useful for diagnosing a model’s ability to produce an MJO. However, it will be shown below that in the low rainfall and shallow heating period in advance of MJO convection, negative GMS can be found in either simulation with a high moisture sensitivity parameter.
MSE export due to horizontal advection increases significantly for all rain rates shown and for both moisture sensitivity parameters, consistent with the results of Maloney (2009). In addition to the cooling effects of suppressing deep convection with increased minimum entrainment rate, the increased horizontal advection per unit mass flux of cold, dry air into the equatorial region is consistent with the drier and cooler troposphere shown in Fig. 7. The dry static energy and moisture budgets indicate that cold, dry air advection into the Indo-Pacific warm-pool region is increased substantially as the minimum entrainment threshold is increased, consistent with increased wind variability (e.g., Figure 1). Horizontal negative latent heat advection also increases by 16 W m−2. Peters et al. (2008) found a greater role for horizontal advection in closing the MSE budget when the diabatic heating profile is more bottom heavy and GMS is small or negative, consistent with Fig. 7c. The import due to surface fluxes is increased at low rain rates for higher minimum entrainment thresholds, which may be attributable to an increase in variability of the low-level flow and hence wind-driven heat fluxes.
The normalized MSE tendency is slightly positive for rain rates of 10–50 mm day−1 in the α = 0.0 run, which indicates damping of moisture anomalies. The α = 0.6 simulation, on the other hand, shows negative total MSE export (i.e., positive MSE import) for rain rates of 10–15 mm day−1. The reduction in GMS appears to be the main factor in allowing MSE sources to outweigh the export and grow MSE anomalies. Increasing the rain evaporation does not have an effect on the total MSE tendency in agreement with the conclusion above that the mean MSE budget does not seem to give any information as to how well a model can simulate an MJO.
Lagged composites of the normalized MSE budget terms for vertical advection and total tendency during boreal winter are shown in Fig. 10. Simulations with the lowest and highest minimum entrainment are shown in Fig. 10a, while simulations with the lowest and highest evaporation fraction are shown in Fig. 10b. A 30-day low-pass filter is applied to all fields before normalization. Such a time-filtering method has been argued by Raymond et al. (2009) to be an appropriate means of determining GMS. Although the simulations with low rain evaporation and zero minimum entrainment do not show much agreement, the simulations with high thresholds exhibit notable similarities with respect to the fluctuations of MSE tendency and GMS. For both simulations with high moisture sensitivity parameters, a strong MSE import by divergent circulations occurs around day −20, which was shown in Fig. 6 to be a period of enhanced shallow heating. Prior to the westerly wind burst at day 0, the normalized MSE tendency in the simulations indicates a net import of MSE into the column and net export afterward. One exception to the similarities is that GMS becomes positive during and after the deep convective phase for the case with a high evaporation fraction. The reasons for this are unclear but may be due to the fact that in this case the minimum entrainment threshold is lower than in the α = 0.6 simulation and hence produces generally deeper clouds, engendering a positive export of MSE during the deep convective phase.
The differences between the lagged MJO composites (Fig. 10) and MSE budget composited as a function of precipitation (Fig. 9) may be due to the compositing method since composites only consider significant MJO events and also use a more limited geographic area. Also, a low to moderate precipitation rate in Fig. 9 can be characteristic of both the growing and declining stages of MJO precipitation in Fig. 10. Hence, two periods of very different dynamics are clearly separated in Fig. 10, whereas they are combined in Fig. 9. Recall also that these fields are normalized measures and hence do not reflect that the unnormalized moisture tendencies can be very different between simulations. For example, anomalous positive horizontal advection is the leading term in the intraseasonal MSE budget, which contributes to moistening before peak MJO convection (not shown). In spite of the contribution from horizontal export, intraseasonal fluctuations of negative GMS appear to support the growth of large moisture and convection anomalies during this phase.
5. Summary and discussion
The sensitivity of the MJO simulation in the NCAR Community Atmosphere Model 3.1 (CAM3.1) to varying thresholds of two moisture sensitivity parameters was analyzed. Using a higher threshold of either the minimum entrainment rate (i.e., Tokioka et al. 1988) or rain evaporation fraction resulted in increased intraseasonal variability and a more coherent MJO signal in the model. The increase in intraseasonal variance for higher minimum entrainment thresholds is accompanied by a reduction in mean free tropospheric moisture and temperature in the Indo-Pacific warm-pool region. Mean diabatic heating at upper levels was also reduced, associated with suppression of the deepest clouds. Increased evaporation fraction leads to a different effect on the mean state, with slight warming at upper levels and moistening throughout the troposphere. Cooling and reduced diabatic heating are found at low levels consistent with the enhanced evaporation of precipitation.
Analysis of the normalized MSE budget shows a reduction in mean GMS associated with suppressed deep convection for a higher minimum entrainment. However, GMS is not reduced for an increased evaporation fraction, and the changes to the mean MSE budget do not appear to be significant. However, considering the fluctuations of the normalized MSE budget relative the MJO reveals that increasing both moisture sensitivity parameters results in a substantial reduction in GMS prior to enhanced MJO convection. This reduction in GMS in the suppressed phase permits moisture, and hence MSE, anomalies to grow.
Since both parameters support more robust intraseasonal variability while inducing different changes to the mean state, this suggests that no straightforward correspondence exists between intraseasonal variability and the mean tropospheric humidity, in contrast to the conclusions of Maloney and Hartmann (2001) and Maloney (2009). On the other hand, Maloney et al. (2010) showed that changing the meridional and zonal SST gradients, which also affect the humidity gradient, had profound impacts on a simulated MJO, suggesting that the spatial distribution of moisture may be of more importance.
Although the existence of undilute convective plumes has been speculated about for many years (e.g., Riehl and Malkus 1958; Xu and Emanuel 1989), recent studies have suggested that dilution of the deepest clouds is unavoidable (Zipser 2003; Romps and Kuang 2010). Therefore, more realistic treatments of entrainment are crucial for simulating realistic moisture–convection feedbacks with conventional parameterizations. Enhancing moisture–convection feedbacks in the model with a minimum entrainment threshold was found to have a dramatic impact on the simulated MJO. When suppressing deep convection with a higher entrainment threshold, divergent circulations associated with convection are less effective at discharging column moisture anomalies, in agreement with the suggestion of Raymond and Fuchs (2009) that GMS is a good diagnostic quantity for investigating a model’s ability to produce a robust MJO. However, based on the analysis of the model’s response to increasing the rain evaporation fraction it seems that the fluctuations of the GMS, rather than the mean, may provide a more reliable metric for diagnosing a model’s ability to support robust intraseasonal variability.
The mechanism through which convective rain evaporation leads to negative GMS in the early phases of the MJO is unclear. One plausible explanation is that when the troposphere is anomalously dry, more of the convective rain that is exposed to the large-scale environment is evaporated. This evaporative cooling would lead to reduced deep convective heating and generate a more bottom-heavy heating profile (because of the presence of shallow convection) until the troposphere can be sufficiently moistened by other processes such as shallow convection or decreased MSE export by horizontal dry air advection due to synoptic eddy activity (Maloney 2009). This would provide an indirect means of suppressing deep convection relative to the Tokioka et al. (1988) method and may also help to explain why a positive GMS occurs during the deep convective phase of the MJO in the simulations with a high evaporation fraction and low but nonzero minimum entrainment. The deepest convective clouds that are active in this scenario during the deep convective phase would likely have entrainment rates close to the minimum threshold. The circulations induced by these deep clouds would contribute a significant export of MSE out of the column. Comparing this to the case where the minimum entrainment threshold is large and the convective rain evaporation fraction is small, it is apparent that these same very deep clouds would likely not exist, and hence, the MSE export would not be as strong, corresponding to lower GMS.
Relating entrainment to vertical velocity in a cumulus scheme has recently been investigated by Chikira and Sugiyama (2010) (see also Chikira 2010). Using this method to explicitly calculate entrainment as a function of height for each cumulus ensemble member yielded enhanced tropical variability in a GCM. Alternative methods of representing the effects of convection in GCMs by embedding cloud-resolving models into each grid cell known as a multiscale modeling framework (i.e., superparameterization; e.g., Khairoutdinov et al. 2008) have also been shown to improve many aspects of a model’s intraseasonal variability (e.g., Thayer-Calder and Randall 2009; Benedict and Randall 2009). When using such methods, convection more naturally interacts with environmental moisture. Making use of these methods to investigate entrainment and moisture–convection feedbacks in finer detail will prove beneficial. Cloud-resolving models (e.g., Romps 2010) and recent observational techniques for estimating entrainment (e.g., Luo et al. 2008; 2009) should also be utilized to refine the treatment of entrainment in conventional GCMs. Further investigations to reveal the fundamental dynamics behind the MJO will include experiments to determine the extent to which horizontal moisture advection drives its eastward propagation, such as mechanism denial simulations.
We thank three reviewers for providing insightful comments that led to improvement of the manuscript. This work encompasses a portion of the first author’s M.S. thesis. The authors thank Dave Randall and Karan Venayagamoorthy for valuable criticism on an earlier version of the manuscript. This work was supported by the Climate and Large-Scale Dynamics Program of the National Science Foundation under Grants ATM-0832868 and AGS-1025584 and the Science and Technology Center for Multi-Scale Modeling of Atmospheric Processes, managed by Colorado State University under Cooperative Agreement No. ATM-0425247. This work has also been funded by Award NA08OAR4320893 from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce. The statements, findings, conclusions, and recommendations do not necessarily reflect the views of NSF, NOAA, or the Department of Commerce.