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Better Madden-Julian Oscillations with better physics: the impact of 1

improved convection parameterizations 2

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Lei Zhou 4 Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York 5

Key Lab of Ocean Dynamic Processes and Satellite Oceanography, SOA, Hangzhou, China 6 7

Richard Neale and Markus Jochum 8 National Center for Atmospheric Research, Boulder, Colorado 9

10 Raghu Murtugudde 11

Earth System Science Interdisciplinary Center, University of Maryland, College Park, Maryland 12 13

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20 21 22 Lei Zhou 23 24 Address: 301d Oceanography 25

Lamont-Doherty Earth Observatory 26 61 Route 9W, Palisades, NY 10964 27

E-mail: lzhou@ldeo.columbia.edu 28 29

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Abstract 31

Two modifications are made to the deep convection parameterization in the NCAR Community 32

Climate System Model, version 3 (CCSM3); a dilute plume approximation and an implementation of 33

the convective momentum transports (CMT). These changes lead to significant improvement in the 34

simulated Madden-Julian Oscillations (MJOs). With the dilute plume approximation, temperature and 35

convective heating perturbations become more positively correlated. Consequently, more available 36

potential energy is generated and the intraseasonal variability (ISV) becomes stronger. The 37

organization of ISV is also improved, which is manifest in coherent structures between different MJO 38

phases and an improved simulation of the eastward propagation of MJOs with a reasonable eastward 39

speed. The improved propagation can be attributed to a better simulation of the background zonal 40

winds due to the inclusion of CMT. We posit that the large-scale zonal winds are akin to a selective 41

conveyor belt that facilitates the organization of ISVs into highly coherent structures, which are 42

important features of observed MJOs. This study provides evidence for the interaction between the 43

large-scale background state and the ISVs and concludes that it is necessary to consider MJOs in a 44

multi-scale framework to enhance their understanding. The conclusions are supported by two 45

supplementary experiments, which include the dilute plume approximation and CMT separately. 46

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1. Introduction 48

Madden-Julian Oscillations (MJOs) are the dominant source of intraseasonal variance in the 49

tropical atmosphere (Madden and Julian 1971, 1972, 1994, 2005). There have been numerous theories 50

and model studies of MJOs to date, as summarized in Wang (2005) and Zhang (2005). Some theories 51

have focused on the internal atmospheric dynamics, such as the wave-CISK (Lindzen 1974) and the 52

‘mobile wave-CISK’ (Lau and Peng 1987). Some emphasized the role of surface heat flux in the 53

development of MJOs (Sobel et al. 2008, 2010), such as the ‘wind-induced surface heat exchange’ 54

(WISHE) proposed by Emanuel (1987) and Neelin et al. (1987). Observations show that MJOs are also 55

closely related to several phenomena occurring at different temporal and spatial scales, such as ENSO 56

(Kessler and Kleeman 2000; Zavala-Garay et al. 2005), the North Atlantic Oscillation (Cassou 2008; 57

Lin et al. 2009), and even the mean climate state (Sardeshmukh and Sura 2007). Therefore, it would 58

appear necessary to study MJOs keeping in mind that their life cycle occurs in a multi-scale framework. 59

A discharge-recharge mechanism was proposed to emphasize the interactions between the large-scale 60

circulation and small-scale convections (e.g., Blade and Hartmann 1993; Hu and Randall 1995; 61

Kemball-Cook and Weare 2001). Biello and Majda (2005) established a multi-scale model which 62

resolved both the upscale and downscale energy transfer associated with MJOs. In addition, Majda and 63

Stechmann (2009) resolved convective momentum transport (CMT), which is critical for the 64

interactions between the mesoscale and the planetary scale, in a simple dynamic model and reproduced 65

major features of MJOs on multiple scales. 66

Climate model simulations of MJOs exhibit several substantial deficiencies. In particular, the 67

eastward propagation of the convection over the warm pool is not well simulated (Slingo et al. 1996) 68

and the eastward phase speed is not consistent with observations (Waliser 1999). Recently, Waliser et 69

al. (2009) summarized the MJO diagnostics. The Level 2 diagnostics they proposed highlighted the 70

organization (coherence) of MJOs between various variables and between different scales. They also 71

emphasized that climate models have difficulty simulating this high degree of coherence. Therefore, it 72

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is reasonable to argue that the observed MJOs are not only enhanced intraseasonal variabilities (ISVs) 73

but, more importantly, are also well-organized ISVs. Kim et al. (2009) analyzed 8 model outputs 74

following the standardized MJO diagnostics proposed in Waliser et al. (2009). They found that 75

ECHAM4/OPYC displayed better skill in reproducing MJOs, which they argued was attributable to “a 76

quite good mean state of precipitation and low-level wind”. In fact, possible improvement of MJO 77

simulation due to an improvement in mean state has been proposed and tested in some other previous 78

studies, such as Inness and Slingo (2003) and Sperber et al. (2005). 79

In this study, the major focus is on the influence of the background state on MJO simulations. Two 80

modifications are made to the convection scheme in the Community Climate System Model, version 3 81

(CCSM3); implementing the dilute plume approximation and the CMT. As a result, the simulated 82

MJOs become more energetic and the ISVs have more coherent structures with enhanced realism 83

compared to observed MJO events. In Section 2, CCSM3 model configurations are described and 84

differences in background states in the two model runs are highlighted. The improvements in the 85

strength and the coherence of simulated MJOs are analyzed in Section 3 and 4, respectively. 86

Conclusions are presented in Section 5. 87

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2. Model description 89

CCSM3 is a state-of-the-art, global climate model which fully couples the atmosphere, ocean, land, 90

and sea ice (Collins et al. 2006a, b). The perturbed deep convection model configurations are described 91

in detail in Neale et al. (2008). Hence, only the relevant aspects are briefly mentioned below. The 92

atmospheric component is based on the Community Atmosphere Model, version 3 (CAM3; Collins et 93

al. 2006a) with 26 vertical levels and a horizontal resolution of 1.9° latitude × 2.5° longitude. There are 94

40 vertical levels in the ocean component with a nominal horizontal resolution of 1° × 1°. The 95

parameterization of the deep convection basically follows Zhang-McFarlane scheme (Zhang and 96

McFarlane 1995), but with two modifications. One is the dilute plume approximation (Raymond and 97

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Blyth 1986, 1992), which relates the mixing between the reference parcel and the free troposphere to 98

an assumed entrainment rate. The other one is the inclusion of CMT following Kershaw and Gregory 99

(1997) which represents the compensation of convective momentum transport by atmospheric 100

subsidence. More details about these two modifications can be found in Neale et al. (2008). Two fully 101

coupled CCSM experiments were performed, one is the control run (referred to as C3OLD hereafter) 102

without the above two changes and the other one includes the two modifications (referred to as 103

C3NEW hereafter). Both experiments are conducted for 102 years and the last 20 years (Years 83 – 104

Year 102) provide the period of focus for the daily output analysis. In the following, we will show that 105

the two modifications to the Zhang-McFarlane scheme contribute in different ways to the improved 106

MJO simulations. In order to further understand the separate role of the convection changes, two 107

supplementary runs are performed; one including the dilute plume approximation (referred to as 108

C3DPA hereafter) only and one including CMT (referred to as C3CMT hereafter) only. Both 109

supplementary runs are conducted for 50 years and the last 10 years (Year 41 – Year 50) with daily 110

outputs are used for analysis. 111

With the inclusion of CMT, the easterly bias of low-level zonal winds in the tropics is reduced, 112

which has been reported in detail by Richter and Rasch (2008) and Neale et al. (2008). The 113

improvement in the mean westerly winds can be seen in Fig. 1. Generally, the mean zonal winds at 850 114

hPa are quite similar in the two model runs (Fig. 1c and 1e). However, pronounced westerly winds 115

from the central tropical Indian Ocean to the western Pacific Ocean (approximately from 50°E to 116

180°E; Fig. 1c) are reproduced, although they are still a little weaker than reality as represented by the 117

NCEP reanalysis (Kalnay et al. 1996; Fig. 1a) over the maritime continent (Fig. 1d). The 118

climatological winds in C3CMT (not shown) are very similar to those in C3NEW (Fig. 1c). In contrast, 119

the westerly winds can barely be found in the above region in C3OLD (Fig. 1e and 1f). Except for the 120

background zonal winds, other background fields are very similar in the two model runs. The mean 121

geopotential height and surface temperature in C3NEW, which are representatives of the dynamic and 122

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thermodynamic fields, respectively, are shown in Fig. 2a and 2c. The corresponding differences 123

between C3NEW and C3OLD are shown in Fig. 2b and 2d. For both quantities, relatively large 124

differences (but still very small compared with the mean state) are found over the central tropical 125

Pacific Ocean (around 200°E), northern Pacific Ocean, and the southern Indian Ocean. Over the Indo-126

Pacific warm pool, which is the region we are interested in, the differences are even smaller. Latent 127

heat flux in C3NEW, which can play a critical role in tropical ISVs (e.g., Sobel et al. 2008, 2010), is 128

shown in Fig. 2e and the differences are shown in Fig. 2f. From the tropical Indian Ocean to the 129

western tropical Pacific Ocean, the difference is generally between ±5 W m-2, which is less than 5% of 130

the mean value in this region. In addition, the vertically averaged moist static energy (MSE, h = CpT + 131

Lq + gz, where Cp is the specific heat of the air, T is the air temperature, q is the specific humidity, g is 132

the gravitational acceleration, and z is the geopotential height) in C3NEW is shown in Fig. 2g, along 133

with the difference between the two model runs (Fig. 2h). Since MSE is an indicator of the stability of 134

the air column (see further discussion below), the high similarity between the two model runs indicates 135

that the stabilities of the background state in the two model runs have no distinct differences. Note 136

however that these stabilities are reached after adjustments in the coupled systems and the state 137

variables such as winds and precipitation do display differences in spatial and temporal scales. In all, 138

the only significant difference in the background state between the two model runs resides in the 139

enhanced westerly winds over the tropical Indian Ocean and the western Pacific Ocean in C3NEW. 140

Except the mean westerly winds, all other background variables are very similar to each other in the 141

two experiments. In this study, we will show that a better organization of simulated MJOs in C3NEW 142

is closely related to the improved background westerly winds. 143

144

3. Strength of the intraseasonal variabilities 145

Following the method proposed in Slingo et al. (1999), the strength of the simulated MJOs is 146

represented by the variance of the intraseasonal zonal winds at 200 hPa over the tropical Indian Ocean 147

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(averaged from 10°S to 10°N and from 50°E to 100°E and passed through the 101-day running mean, 148

Fig. 3). In this study, all intraseasonal variables are obtained with a band-pass filtering from 20 to 100 149

days. With the same method, Zhang and Mu (2005; their Fig. 2) showed that applying a modified 150

Zhang-McFarlane scheme for deep convection could considerably increase the strength of ISVs in 151

CCSM3. In C3OLD (which uses the Zhang-McFarlane scheme with no modifications) there are indeed 152

energetic ISVs such as the peaks seen at the end of Years 91 and 95 (Fig. 3), which reaffirms that 153

adopting Zhang-McFarlane scheme can indeed produce strong ISVs in a model. Nevertheless, the ISVs 154

in C3NEW are in general stronger than those in C3OLD, e.g., in Years 84, 88, 96, 99, and 101. The 155

stronger ISVs in C3NEW can also be clearly seen in other variables, such as the intraseasonal zonal 156

winds at 850 hPa and the outgoing longwave radiation (OLR; see Neale et al. 2008). Note that the 157

impacts of model differences in monsoons, ENSO, and their interactions on the ISVs are beyond the 158

scope of this work and are not considered here. 159

At 850 hPa, the standard deviations (STDs) of the intraseasonal zonal winds in C3NEW (Fig. 4c) 160

are similar to those in NCEP reanalysis (Fig. 4a). Generally, the differences between C3NEW and 161

NCEP are smaller than 0.5 m s-1 over the tropical Indian Ocean and the western Pacific Ocean (Fig. 162

4b). However in C3OLD, the ISVs in this region are not distinctly different from other tropical regions 163

(such as the central Pacific Ocean and the Atlantic Ocean; Fig. 4e). As clearly shown in Fig. 4d and 4f, 164

the major enhancement in the intraseasonal zonal winds in C3NEW is over the Indo-Pacific warm pool. 165

Therefore, with the modifications to the deep convection parameterization (Neale et al. 2008), the 166

tropical ISVs in C3NEW become generally more energetic than those in C3OLD. 167

The mean vertically averaged deep convective heating (product of the Zhang-McFarlane scheme) 168

in the two model runs are compared in Fig. 5a and b. Over the tropical Pacific Ocean, the double ITCZ 169

problem still exists in C3NEW, although there is moderate improvement in contrast with C3OLD (note 170

the negative anomalies around 10°S in the central Pacific in Fig. 5b). It was argued in Neale et al. 171

(2008) that the current changes in convection scheme are not very helpful for removing the southern 172

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Pacific convergence zone (SPCZ) bias. Another notable feature in Fig. 5b is the negative values from 173

the tropical Indian Ocean to the western tropical Pacific Ocean, the region in which the ISVs are 174

actually stronger in C3NEW than those in C3OLD (Fig. 4d). In the intraseasonal band (20-100 days), 175

the STDs of convective heating in C3NEW (Fig. 5c) are also smaller than those in C3OLD (Fig. 5d). 176

In addition, precipitation in the two model runs displays no pronounced differences (not shown). 177

However, as emphasized in Emanuel et al. (1994), the convective heating is not the key factor for ISVs; 178

instead, the correlation between convective heating and the temperature perturbation is the key. The 179

thermodynamic equation can be written as 180

)1('''

pp C

JSwt

T=⋅−

∂∂ , 181

where T is the air temperature, w is the vertical velocity, Sp is the static stability parameter, J is 182

convective heating which is the major component of the total external heating, Cp is the heat capacity 183

of the air, and the prime denotes the intraseasonal component (between 20 days and 100 days) of the 184

variables. Multiplying T’ on both sides of Eq. (1), one has 185

)2(''''2'2

pp C

JTSwTTt

=⋅−⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂ , 186

where 2/'2T is proportional to the potential energy in the intraseasonal band, '' JT ⋅ is critical to the 187

buildup of available potential energy during convection and '' wT ⋅ determines the energy conversion 188

from potential energy to kinetic energy. The two terms '' JT ⋅ and '' wT ⋅ are distinctly different between 189

the two model runs. Similar to the method used above in Fig. 3 (Slingo et al. 1999), we calculate the 190

mean variance of J’ and '' JT ⋅ (vertically averaged, then averaged from 10°S to 10°N and from 50°E to 191

100°E and passed through a 101-day running mean). As shown in Fig. 6a, the variance of convective 192

heating is virtually indistinguishable between the two runs, which is consistent with Fig. 5. In contrast, 193

the variance of '' JT ⋅ in C3NEW is clearly larger than that in C3OLD, which explains the more 194

energetic ISVs in the former. The model performance supports the principle of the quasi-equilibrium 195

theory for convection (Emanuel et al. 1994). Due to the dilute plume approximation, the environmental 196

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air is entrained into the cloud at all levels, not only at the cloud top (Raymond and Blyth 1986). As a 197

result, the phase relations between the convective heating and the temperature perturbation are 198

modified. Although the convective heating is generally a little weaker because of the entrainment of 199

dry air in C3NEW than it is in C3OLD (Figs. 5 and 6), both the buildup of potential energy ( '' JT ⋅ ) and 200

the release to kinetic energy ( '' wT ⋅ ) become larger in C3NEW. Therefore, the ISVs in C3NEW are 201

stronger than those in C3OLD. This conclusion is also supported by the comparisons between C3DPA 202

and C3CMT in Fig. 3b. Stronger ISVs in C3DPA compared to C3CMT points to the fact that the 203

reinforcement of ISVs is attributable to the dilute plume approximation. 204

205

4 Organization of the intraseasonal variabilities 206

4.1 Composite MJO phases 207

Differences between the two model runs reside in the propagating features of the ISVs. The ISVs in 208

C3NEW are not only more energetic, but also better organized in comparison to reality. Thus, they 209

resemble the observationally-inferred MJOs, much more so than the ISVs in C3OLD. 210

Observed MJOs are composed of successive suppressed and active phases during the eastward 211

propagation (Zhang 2005). Thus, with the EOF analysis, the first two EOF modes are in quadrature, 212

which is represented with the significant cross-correlation at a time lag of 10-15 days between the 213

principal components (PCs) of the first two EOFs. This relation is well captured in C3NEW in the 214

intraseasonal zonal winds at both 200 hPa and 850 hPa, and for the intraseasonal OLR anomalies, 215

while it is not well captured in C3OLD (Fig. 7). For comparison with reality, the cross-correlation 216

between RMM1 and RMM2, which were defined in Wheeler and Hendon (2004), is superimposed in 217

the middle panel in Fig. 7. Better coherence between the first two EOF modes of the intraseasonal 218

zonal winds and OLR indicates a better eastward propagation of the ISVs during MJOs, which is a 219

major challenge for MJO simulations. The ISVs in C3OLD, although they can be energetic, do not 220

have such coherent eastward propagation. In addition, the first two EOF modes in C3NEW explain 221

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about 14% of the total variance of the intraseasonal zonal winds at 850 hPa and about 16% of the total 222

variance at 200 hPa, which are comparable with the observations (13% – 16%). As summarized in 223

Waliser et al. (2009), “many climate (model) simulations produce leading EOFs for convective fields 224

that explain relatively small amounts of the variance compared to observations”, since the ISVs in 225

many models were likely to be strong enough but not organized well enough. Cross-correlations 226

between the first two EOFs for C3CMT and C3DPA are also shown in Fig. 7. Although the ISVs in 227

C3CMT are weaker than the counterparts in C3DPA (Fig. 3b), the quadrature relation is better 228

captured in C3CMT, which implies that the CMT is more conducive to the organization of the ISVs. 229

However, the first two EOFs in C3CMT only explain about 6% and 5% respectively of the total 230

variance in the intraseasonal band, because the organized ISVs are weak due to the absence of the 231

dilute plume approximation. 232

Following Wheeler and Hendon (2004), the MJO phases can be defined with the first two PCs of 233

the multivariate EOF analysis (based on OLR, zonal winds at 850 hPa and 200 hPa) and the phase 234

diagram is shown in Fig. 8. When PC12 + PC22 is larger than 2, the ISVs are regarded as strong. 235

Canonically, an MJO event originates from the western Indian Ocean and diminishes over the eastern 236

Pacific Ocean. Thus, the line rotates counterclockwise in the phase diagram. Six MJO events are 237

defined based on the strength of the ISVs (represented with PC12 + PC22) and the eastward 238

propagation (the phase diagram shown in Fig. 8a), which are listed in Table 1. For comparison with 239

reality, the phase diagram of 4 observed MJO events are shown in Fig. 8b. The number of MJO events 240

appears to be fewer than reality in typical years. One important reason is that we intend to guarantee 241

that all selected MJO events can travel continuously around the globe from the western Indian Ocean 242

back to the western hemisphere since we want to focus on the eastward propagation of the ISVs in 243

following discussion. Thus, the selected MJO events are required to show smooth counterclockwise 244

rotation in the phase diagram as shown in Fig. 8. This criterion is much stricter than only requiring 245

large amplitudes (like PC12 + PC22 > 2). The composite intraseasonal OLR anomalies in the 8 MJO 246

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phases are shown in Fig. 9. In Phase 1, there is almost no depression in OLR over the tropics. In 247

Phases 2 and 3 when the convection center is supposed to be over the Indian Ocean, negative OLR 248

anomalies are discernible from the western tropical Indian Ocean to the central Indian Ocean. 249

Meanwhile the OLR depression becomes stronger in Phase 3 than it is in Phase 2. In Phase 4 and 5 250

when MJOs reach a mature stage over the maritime continent, the negative OLR anomalies reach their 251

maxima. Then from Phase 6 to Phase 8, negative OLR anomalies move eastward from the maritime 252

continent to the western hemisphere while they weaken along the way. The whole process of the 253

simulated composite MJO event in C3NEW is very similar to observations. Since the MJO phases can 254

only be well defined in C3NEW (ISVs in C3CMT are weak; ISVs in C3OLD and C3DPA hardly 255

propagate and the variances explained by the first two EOF modes are relatively small), all composite 256

quantities shown below are calculated with the C3NEW outputs. 257

The difference in the intraseasonal MSE between the surface and the mid-troposphere is a good 258

index for the atmospheric instability (Kemball-Cook and Weare 2001); this instability usually being a 259

necessary ingredient for the onset of MJOs. Defining ΔMSE as the intraseasonal MSE at 950 hPa 260

minus the intraseasonal MSE at 500 hPa, positive ΔMSE implies an atmosphere unstable to saturated 261

moist convection, while negative ΔMSE implies a stable atmosphere. Figure 10 shows the composite 262

ΔMSE in the 8 MJO phases during the 6 MJO events (Table 1). In Phase 3, positive ΔMSE begins to 263

occur over the Indian Ocean and the maritime continent, indicating deep convective instability in these 264

regions. In Phase 4, ΔMSE reaches a maximum over the maritime continent, where the MJOs also 265

become mature (see the OLR anomalies in Phase 4 in Fig. 9). In Phase 5 and Phase 6, positive ΔMSE 266

turns weak and the MJOs enter the decaying phases. In Phases 7 and 8, there is no clear positive ΔMSE 267

in the deep tropics, thus the MJO convective signals become weaker in the western hemisphere. One 268

may see that ΔMSE increases down the SPCZ in Phases 7 and 8 which leads to a split in negative OLR 269

anomalies during these phases. The MJO signal bifurcates too strongly here (this happens weakly in 270

observations), which may be due to cold SST biases in the central and eastern Pacific Ocean. Actually, 271

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ΔMSE is a practical and convenient measure of the convectively available potential energy (CAPE). 272

The composite intraseasonal CAPE anomalies also display a similar evolution (not shown) as shown in 273

Fig. 10. Maloney (2009) concluded that surface heat flux and horizontal advection are the dominant 274

terms in the intraseasonal MSE budget. 275

The composite intraseasonal latent heat fluxes during the 6 MJO phases are shown in Fig. 11. In 276

Phase 1, one can see positive surface heat flux in the western tropical Indian Ocean, which is enhanced 277

in Phase 2 and extends to the central and eastern Indian Ocean. In Phase 3, the surface heat fluxes are a 278

maximum over the eastern Indian Ocean and the maritime continent. Then in Phase 4, positive surface 279

heat fluxes remain over the maritime continent and the southeastern Indian Ocean, but become weaker 280

than they are in Phase 3. The maximum in surface heat fluxes (in Phase 3) is generally one phase 281

(about 5 – 7 days) earlier than the mature stage of MJOs (Phase 4), which is roughly consistent with 282

the observations (Sperber 2003). From Phase 5 to Phase 7, positive surface heat fluxes move eastward 283

to the western and central Pacific Ocean. The composite convergence of MSE ( hu ∇⋅−r ; Maloney 284

2009) in the 8 phases is shown in Fig. 12. The patterns are somewhat noisy. But some features can still 285

be clearly identified if we focus on the tropical region. In Phases 1 and 2, MSE converges over the 286

western Indian Ocean. In Phase 3, the horizontal transport of MSE increases over the whole tropical 287

Indian Ocean and the maritime continent and then becomes weaker in Phase 4. Synthesizing the 288

information from Fig. 10 to Fig. 12, it can be concluded that over the Indian Ocean and the maritime 289

continent (Phase 3 and Phase 4), the air column over the eastern Indian Ocean and the maritime 290

continent becomes unstable due to the surface heat flux and horizontal transport. As a result, the 291

increased potential energy is released and transferred to kinetic energy and the reinforced intraseasonal 292

winds occur in these regions. 293

The above analyses on MSE are consistent with the analysis of convective heating in Section 3, 294

both of which explain how the ISVs become stronger in C3NEW. However, the ISVs in C3NEW 295

propagate eastward (Fig. 7) and resemble realistic MJO events, while the ISVs in C3OLD barely 296

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propagate, although they are enhanced occasionally (Fig. 3). Naturally, the question is what leads to 297

the eastward propagation of the enhanced ISVs in C3NEW and more specifically what determines the 298

eastward propagation speed of MJOs? Since the distinct difference between C3OLD and C3NEW 299

model simulations resides in the simulated background low-level westerly winds from the tropical 300

Indian Ocean to the western Pacific Ocean (Fig. 1), the better organization of ISVs in C3NEW should 301

be attributable to the improved westerly winds in C3NEW. 302

303

4.2 Eastward propagation of MJOs 304

Several mechanisms have been proposed to explain and simulate the slow movement of the MJO 305

events, which is much slower than the free planetary waves. A friction-convergence mechanism was 306

invoked to account for the retardation in the eastward propagation of MJO events (Wang and Rui 1990; 307

Salby et al. 1994). However, the drag coefficients used in the friction-convergence theory were deemed 308

to be unrealistically large, such that the actual role of friction was also debatable (Sperber et al. 1997; 309

Moskowitz and Bretherton 2000). In a numerical model study, Chao and Chen (2001) showed that 310

friction may not be as important as claimed for the low-level convergence. Instead, friction only 311

dissipates the energy of MJOs. Studies have also shown that the enhanced surface heat flux could 312

determine the speed of the eastward-propagating ISVs, as hypothesized in the WISHE theory 313

(Emanuel 1987; Neelin et al. 1987). In practice, a weak, rather than a strong evaporation usually leads 314

the convection (Woolnough et al. 2001). Furthermore, it is nontrivial to explain why most MJO events 315

“select” to travel around a specific speed of 5 m s-1, rather than a random speed over a wide range. 316

With our model simulations and NCEP reanalysis, we will show that the large-scale zonal winds are 317

likely to play a role in pacing the eastward speed of MJOs. 318

As described above, the generation of available potential energy and kinetic energy during 319

convection is determined by '' JT ⋅ and '' wT ⋅ . Actually we can treat '' JT ⋅ and '' wT ⋅ in a similar way 320

when assessing the circumstances under which these two terms have significantly non-zero values. 321

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According to the weak temperature gradient approximation (Sobel et al. 2001; Bretherton and Sobel 322

2002) which was thoroughly tested for applications in the tropical ISVs (Bretherton and Sobel 2003), 323

variation of T’ with longitude is small and the principal thermal-dynamical balance is '' JSw p =⋅− , 324

where Sp is the static stability parameter. Since Sp is a slowly-varying quantity, w’ and J’ have similar 325

structures. The weak temperature gradient and similar structures between w’ and J’ are also reproduced 326

in C3NEW. As shown in Fig. 13, the variation patterns of J’ and w’ are similar and the variation of T’ 327

along a latitude is quite small compared with the variation of J’ and w’. In order to quantify the above 328

argument, along every latitude, we calculate the ratio )(/)( latlat XmeanXSTD , where Xlat represents the 329

STD of T’, J’, and w’ along latitudes shown in Fig. 13(a, c, e). The ratios are shown on the right 330

column of Fig. 13. For T’, the zonal variance is less than 10% of the zonal mean, while for J’ and w’, 331

the zonal variance is about 20% – 60% of the zonal mean. Therefore, the zonal oscillatory parts of 332

'' JT ⋅ and '' wT ⋅ are determined by J’ and w’, respectively. J’ and w’ are composed of oscillations with 333

various wavenumbers and frequencies (Wheeler and Kiladis 1999) and each component can be written 334

in a wavelike form, i.e. ψitekA )( , where )(kkU ωψ −= and U = x/t is the mean zonal current. Thus, 335

'' JT ⋅ can be expressed as the sum of the waves with all wavenumbers (the same argument can also be 336

applied to '' wT ⋅ ), 337

)3()('''0∫∞

=⋅ dkekATJT itψ . 338

Then integration by parts yields 339

)4(/

'/

'/

'''000∫∫∞∞∞

⎟⎟⎠

⎞⎜⎜⎝

⎛−==⋅

dkdA

ddde

itT

dkdAe

itTd

dkdAeTJT it

itit

ψψψ

ψψ

ψψ

ψψ. 340

According to the method of stationary phase (see Pedlosky 2003 for details), the term ∞

0/

'dkd

AeitT it

ψ

ψ

341

decreases with 1/t and approaches zero after a considerable period of time (when t is large). The last 342

term in Eq. (4) also decreases at least as fast as 1/t, unless ψite does not oscillate too rapidly at large t. 343

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Therefore, '' JT ⋅ has a significantly non-zero value only when ψ does not change at large t, in other 344

words, at the stationary point of ψ with respect to k. Thus, 0/ =∂∂ kψ is a necessary condition and the 345

group velocity of perturbations is Ukcg =∂∂= /ω . This relation implies that the propagation speed of 346

the perturbations, which can last for a long time, is not determined by the meso-scale variability itself. 347

Instead, it is selected by the background zonal flow. Note that we do not argue that the ISVs are simply 348

advected by the mean flow. Actually, the fluctuations caused by an individual convective event can 349

have considerably different propagation speed from the background state (Hendon and Liebmann 1994; 350

Wheeler and Kiladis 1999). These fluctuations can be very energetic in the spatio-temporal scales of 351

tropical convection (on the order of days and hundreds of kilometers), but tend to dissipate on much 352

larger spatio-temporal scales (e.g., the scale of MJOs, on the order of tens of days and thousands of 353

kilometers), because they have random phases which are prone to cancel each other (the physical 354

essence of the method of stationary phase). Only the fluctuations which have a coherent relation with 355

the background state can last for a long time and propagate over large distances. This process is 356

analogous to a selective conveyor belt (the background state), which selectively picks only the suitable 357

perturbations and discards (dissipates) the unfitting ones, organizing the former into an energetic event 358

which is much larger in space and longer in time than any individual perturbation. As a result, one can 359

observe the well-organized MJO events, which originate from the un-organized deep convection but 360

have much larger space scales and much longer time scales than any individual deep convective cell. 361

The above arguments are supported by evidence from both our model simulations and the NCEP 362

reanalysis (Kalnay et al. 1996). Intraseasonal OLR anomalies during two simulated MJO events are 363

shown in Fig. 14 (a and b). The ISVs propagate eastward at a speed of about 4 m s-1, as indicated with 364

the gray dashed lines. Contours of the background zonal winds at 4 m s-1 at 850 hPa are superimposed. 365

The eastward propagation speed of ISVs is consistent with the background zonal wind speed. As 366

shown in Fig. 3, there are also pronounced ISVs in C3OLD, but they do not propagate to the east (see 367

the flat lag-correlation coefficients in Fig. 7). Intraseasonal OLR anomalies from the end of Year 95 to 368

16

the beginning of Year 96 in C3OLD are shown in Fig. 14c. Strong negative OLR anomalies in the 369

central Indian Ocean (around 100°E) are obvious and they are comparable with those in C3NEW in 370

strength. However, the background zonal winds are very weak during this period of time and the 371

negative OLR anomalies in C3OLD do not propagate to the east. Therefore, it is reasonable to assume 372

that the distinctive difference in the eastward propagation of ISVs in the two model runs is attributable 373

to the difference in the simulations of the large-scale zonal winds. This hypothesis is also supported 374

when one looks at OLR observations and NCEP reanalysis. Figure 15 shows the intraseasonal OLR 375

anomalies (obtained from NOAA polar-orbiting series of satellites, Liebmann and Smith 1996) during 376

four MJO events, superimposed on the zonal background velocities (from NCEP reanalysis). The 377

propagation speeds of the intraseasonal OLR anomalies, which are marked with gray lines, range from 378

4 to 4.7 m s-1. The speeds are consistent with the zonal background speeds. Thus, both observations 379

and our simulations confirm that the eastward propagation speeds of MJOs are consistent with the 380

background zonal wind speed. 381

The above analyses can help us understand why the eastward propagation of ISVs in C3NEW is 382

better than those in C3OLD. As shown in Fig. 1, the background westerly winds are pronounced and 383

around 5 m s-1 in C3NEW from the tropical Indian Ocean to the western Indian Ocean. As a result, in 384

C3NEW and C3CMT, the ISVs are better organized by the large-scale flow and propagate eastward, 385

which is represented with the cross-correlation between the first two EOF PCs shown in Fig. 7 386

(especially for the intraseasonal zonal winds at 850 hPa and for intraseasonal OLR anomalies). In 387

contrast, in C3OLD and C3DPA, there are almost no background low-level westerly winds over the 388

Indo-Pacific warm pool. Therefore, although the ISVs can be enhanced by the Zhang-McFarlane deep 389

convection parameterization scheme (Zhang and Mu 2005) and the dilute plume approximation, their 390

eastward propagation tends to be rather weak. Instead, the ISVs are mostly generated locally and 391

dissipated also locally (Fig. 14c). As a result, there is no significant cross-correlation between the first 392

two EOF PCs (Fig. 7), which indicates a lack of eastward propagation. 393

17

394

5. Conclusions 395

Two modifications are made to the convection scheme in the CCSM3 model, which leads to a 396

better simulation of MJOs. The climatologies of most variables are not significantly changed by the 397

modifications to the Zhang-McFarlane scheme, except for the mean westerly winds from the Indian 398

Ocean to the western Pacific Ocean. In a coupled system, the post-adjustment states may well appear 399

proximate but the adjustment process itself may produce more distinguishable responses, as in the 400

strength and propagation of MJOs for the cases under consideration here. Inclusion of dilute plume 401

approximation improves the correlation between J’ and T’ which is critical for the buildup of the 402

available potential energy. Although the convective heating is indistinguishable between C3NEW and 403

C3OLD, '' JT ⋅ is much larger in C3NEW. Since w’ has a similar structure to J’, '' wT ⋅ is also larger in 404

C3NEW, which makes the energy conversion from potential energy to kinetic energy more efficient. 405

As a result, ISVs in C3NEW are enhanced in strength. In the additional experiment C3DPA, it is also 406

shown that inclusion of the dilute plume approximation helps to reinforce ISVs. With the inclusion of 407

CMT, the low-level background zonal winds over the Indo-Pacific warm pool are reinforced and the 408

easterly wind bias in this region is largely removed. The improved zonal winds tend to pace the 409

eastward propagation of the enhanced ISVs, acting like a selective conveyor belt. In the experiment 410

C3CMT, although the ISVs are not strong enough, the eastward propagation of ISVs is also 411

discernable due to the improved westerly winds. 412

As articulated in Waliser et al. (2009), the high degree of coherence is a very important feature of 413

MJOs. By comparing the model runs with CCSM3 with and without the dilute plume approximation 414

and the CMT, we show that a better simulation of the background westerly winds in the tropical Indian 415

Ocean and the western tropical Pacific Ocean facilitates a better organization of the simulated MJOs. 416

The quadrature relation between the first two EOF modes is well captured in C3NEW and the eastward 417

propagation is similar to the realistic MJOs. Both with the NCEP reanalysis and the model outputs, it is 418

18

shown that the eastward propagation speed of the intraseasonal signals is tuned by the background 419

zonal currents. The ISVs themselves, which can be regarded as stochastic perturbations to the 420

background state (e.g., Newman et al. 2009), are not as well organized. Nevertheless, only the ISVs 421

that are coherent with the background state can accumulate energy and propagate over a relatively long 422

distance. Thus, the ISVs are selected (not just advected) and organized by the background state. Notice 423

that the background zonal winds are not independent of the mesoscale convection, since CMT 424

represents the connection between convection and the background state. Thus, the MJO speed is 425

essentially the result of an interaction between the mesoscale convection and the background 426

circulation. With an aqua-planet model, Maloney et al. (2010) demonstrated that the synchronization 427

between peak moistening and total westerly winds at 850 hPa determines the eastward propagation 428

speed of the simulated MJOs, which was argued to also highlight the role of the coupling between 429

convection and background winds in selecting the MJO speed. 430

This conclusion confirms the importance of examining MJOs in a multi-scale framework. A better 431

simulation of the background state is helpful to achieve a better simulation of MJOs. In addition to the 432

deep convection parameterization being regarded at present to be a major requirement for improved 433

MJO simulations, this also calls for more attention to better representation and parameterization of the 434

interactions between the large-scale circulation and the mesoscale ISVs. In particular, the hypothesis 435

that the propagation speed of MJOs is closely related to the mean westerly winds is also consistent 436

with the improvement of the eastward propagation of the simulated MJOs even when they are 437

approximately resolved in a model. The background states are also affected by changes in climate 438

modes such as monsoons and ENSO. While that is consistent with the multi-scale framework we are 439

arguing for, the details of those interactions are not addressed here other than that they impact the 440

background westerlies discussed here. Further details of the monsoon-ENSO-MJO interactions will be 441

reported elsewhere. 442

443

19

444

Acknowledgments: 445

Zhou gratefully acknowledges NOAA Climate & Global Change Postdoctoral Fellowship Program. 446

Zhou is also thankful for the travelling funding support from Open Fund of Key Lab of Ocean 447

Dynamic Processes and Satellite Oceanography, SOA, under contract No. SOED1005. R. Neale and M. 448

Jochum are supported by NSF through NCAR, and computations have been performed on the NSF 449

supercomputing facilities operated by the Computational and Information Systems Laboratory at 450

NCAR and at the National Center for Computational Sciences at the DOE Oak Ridge National 451

Laboratory. R. Murtugudde was partially supported by the NASA PO grant on Decadal Mixed Layer 452

Heat Budget and the OSSST funds. We are grateful to Adam Sobel for helpful comments and 453

suggestions. 454

455

20

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591

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Captions 592

Table 1 MJO events defined with the C3NEW outputs. 593

Figure 1 Mean zonal winds at 850 hPa in the NCEP reanalysis (a), C3NEW (c), and C3OLD (e). 594

Differences between C3NEW and C3OLD, between NCEP and C3NEW, between NCEP and C3OLD 595

are shown in the right column. The unit is m s-1. 596

Figure 2 20-year mean geopotential height, surface temperature, latent heat flux, and moisture static 597

energy (MSE) in C3NEW (left column) and the corresponding differences between C3NEW and 598

C3OLD (right column; regions with positive values are shaded). 599

Figure 3 Variance of the intraseasonal zonal winds at 200 hPa averaged from 10°S to 10°N and from 600

50°E to 100°E and then passing a 101-day running mean. (a) Comparison between C3NEW and 601

C3OLD. (b) Comparison between C3CMT and C3DPA. 602

Figure 4 STDs of intraseasonal zonal winds at 850 hPa in NCEP (a), C3NEW (c), and in C3OLD (e). 603

The differences between the STDs in NCEP and C3NEW are shown in (b). The differences and the 604

ratios between the STDs in C3NEW and C3OLD are shown in (c) and (d), respectively. 605

Figure 5 (a) 20-year mean convective heating in C3NEW; (b) difference of 20-year mean convective 606

heating between C3NEW and C3OLD. (c) STD of the intraseasonal convective heating in C3NEW; (d) 607

difference of the STDs of intraseasonal convective heating between C3NEW and C3OLD. The white 608

contours mark zero. 609

Figure 6 Variance of J’ and '' JT ⋅ averaged in the vertical and within 10°S – 10°N and 50°E – 100°E, 610

then passing a 101-day running mean. The unit for J’ is K s-1 and the unit for '' JT ⋅ is K2 s-1. 611

Figure 7 Cross-correlations between PC1 and PC2 of the intraseasonal zonal winds at 200 hPa, at 850 612

hPa, and intraseasonal OLR anomalies. Cross-correlations between RMM1 and RMM2 defined in 613

Wheeler and Hendon (2004) are superimposed in the middle panel with a dot-dash line. 614

27

Figure 8 (a) Phase diagram in terms of the first two PCs of the EOF analysis for 6 MJO events in 615

C3NEW listed in Table 1. Every curve rotates anti-clockwise. The dash cycle is the unit cycle. (b) is 616

the same as (a) but for 4 observed MJO events which are used again in Fig. 15. 617

Figure 9 Composite intraseasonal OLR anomalies during 6 MJO events in C3NEW (Table 1). The unit 618

is W m-2. 619

Figure 10 Composite ΔMSE during 6 MJO events in C3NEW (Table 1). The unit is J kg-1. 620

Figure 11 Composite intraseasonal latent heat fluxes during 6 MJO events in C3NEW (Table 1). The 621

unit is W m-2. 622

Figure 12 Composite divergence of intraseasonal MSE during 6 MJO events in C3NEW (Table 1). 623

The unit is W kg-1. 624

Figure 13 STD of intraseasonal temperature (a), convective heating (c), and vertical velocity (e). The 625

unit for T’ is Kelvin, for J’ is 10-6 K/s, for w’ is 10-2 Pa/s. Ratios of )(/)( latlat XmeanXSTD , where Xlat 626

represents the STD of T’, J’, and w’ along a single latitude shown in the left column, are plotted in the 627

right column. 628

Figure 14 (a) and (b): Intraseasonal OLR anomalies (color shades) averaged between 10°N and 10°S 629

during two MJO events in C3NEW (Table 1) with a unit of W m-2. The gray dash lines mark an 630

eastward propagation speed of 4 m s-1. The black contours represent the background zonal winds (after 631

a low-pass filtering of 100 days) of 4 m s-1 in the same region. (c): Intraseasonal OLR anomalies (color 632

shades) averaged between 10°N and 10°S when the ISVs are strong in C3OLD. The black contours 633

also represent the background zonal winds of 4 m s-1 in the same region. 634

Figure 15 Intraseasonal OLR anomalies from NOAA satellite (colors) and background zonal winds at 635

850 hPa from NCEP reanalysis. The estimated eastward propagation speed of each MJO event is 636

marked in the title of each panel. It is also marked with a thick gray line in each panel. The contours of 637

OLR anomalies are from -50 W m-2 (dark blue) to 50 W m-2 (dark red) with an interval of 10 W m-2. 638

The interval for the wind speed is 1 m s-1. 639

640

28

Table and Figures 641

642

Event No. Start date End date 1 Day 52/Yr 101 Day 86/Yr 101 2 Day 27/Yr 99 Day 54/Yr 99 3 Day 65/Yr 96 Day 114/Yr 96 4 Day 39/Yr 91 Day 91/Yr 91 5 Day 60/Yr 90 Day 120/Yr 90 6 Day 65/Yr 84 Day 126/Yr 84

643

Table 1 MJO events defined with the C3NEW outputs. 644

645

29

646

647

Figure 1 Mean zonal winds at 850 hPa in the NCEP reanalysis (a), C3NEW (c), and C3OLD (e). 648

Differences between C3NEW and C3OLD, between NCEP and C3NEW, between NCEP and C3OLD 649

are shown in the right column. The unit is m s-1. 650

651

30

652

Figure 2 20-year mean geopotential height, surface temperature, latent heat flux, and moisture static 653

energy (MSE) in C3NEW (left column) and the corresponding differences between C3NEW and 654

C3OLD (right column; regions with positive values are shaded). 655

656

31

657

Figure 3 Variance of the intraseasonal zonal winds at 200 hPa averaged from 10°S to 10°N and from 658

50°E to 100°E and then passing a 101-day running mean. (a) Comparison between C3NEW and 659

C3OLD. (b) Comparison between C3CMT and C3DPA. 660

661

32

662

Figure 4 STDs of intraseasonal zonal winds at 850 hPa in NCEP (a), C3NEW (c), and in C3OLD (e). 663

The differences between the STDs in NCEP and C3NEW are shown in (b). The differences and the 664

ratios between the STDs in C3NEW and C3OLD are shown in (c) and (d), respectively. 665

666

33

667

Figure 5 (a) 20-year mean convective heating in C3NEW; (b) difference of 20-year mean convective 668

heating between C3NEW and C3OLD. (c) STD of the intraseasonal convective heating in C3NEW; (d) 669

difference of the STDs of intraseasonal convective heating between C3NEW and C3OLD. The white 670

contours mark zero. 671

672

34

673

Figure 6 Variance of J’ and '' JT ⋅ averaged in the vertical and within 10°S – 10°N and 50°E – 100°E, 674

then passing a 101-day running mean. The unit for J’ is K s-1 and the unit for '' JT ⋅ is K2 s-1. 675

676

35

677

Figure 7 Cross-correlations between PC1 and PC2 of the intraseasonal zonal winds at 200 hPa, at 850 678

hPa, and intraseasonal OLR anomalies. Cross-correlations between RMM1 and RMM2 defined in 679

Wheeler and Hendon (2004) are superimposed in the middle panel with a dot-dash line. 680

681

36

682 683

Figure 8 (a) Phase diagram in terms of the first two PCs of the EOF analysis for 6 MJO events in 684

C3NEW listed in Table 1. Every curve rotates anti-clockwise. The dash cycle is the unit cycle. (b) is 685

the same as (a) but for 4 observed MJO events which are used again in Fig. 15. 686

687

37

688 689

Figure 9 Composite intraseasonal OLR anomalies during 6 MJO events in C3NEW (Table 1). The unit 690

is W m-2. 691

692

38

693

Figure 10 Composite ΔMSE during 6 MJO events in C3NEW (Table 1). The unit is J kg-1. 694

695

39

696

Figure 11 Composite intraseasonal latent heat fluxes during 6 MJO events in C3NEW (Table 1). The 697

unit is W m-2. 698

699

40

700

Figure 12 Composite divergence of intraseasonal MSE during 6 MJO events in C3NEW (Table 1). 701

The unit is W kg-1. 702

703

41

704

Figure 13 STD of intraseasonal temperature (a), convective heating (c), and vertical velocity (e). The 705

unit for T’ is Kelvin, for J’ is 10-6 K/s, for w’ is 10-2 Pa/s. Ratios of )(/)( latlat XmeanXSTD , where Xlat 706

represents the STD of T’, J’, and w’ along a single latitude shown in the left column, are plotted in the 707

right column. 708

709

42

710 711

Figure 14 (a) and (b): Intraseasonal OLR anomalies (color shades) averaged between 10°N and 10°S 712

during two MJO events in C3NEW (Table 1) with a unit of W m-2. The gray dash lines mark an 713

eastward propagation speed of 4 m s-1. The black contours represent the background zonal winds (after 714

a low-pass filtering of 100 days) of 4 m s-1 in the same region. (c): Intraseasonal OLR anomalies (color 715

shades) averaged between 10°N and 10°S when the ISVs are strong in C3OLD. The black contours 716

also represent the background zonal winds of 4 m s-1 in the same region. 717

718

43

719

Figure 15 Intraseasonal OLR anomalies from NOAA satellite (colors) and background zonal winds at 720

850 hPa from NCEP reanalysis. The estimated eastward propagation speed of each MJO event is 721

marked in the title of each panel. It is also marked with a thick gray line in each panel. The contours of 722

OLR anomalies are from -50 W m-2 (dark blue) to 50 W m-2 (dark red) with an interval of 10 W m-2. 723

The interval for the wind speed is 1 m s-1. 724