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  • View in gallery

    A 10-yr (October–April 1979–88) mean vertical cross section of zonal (m s−1) and vertical (hPa day−1) wind averaged between 10°N and 10°S for (a) NCEP, (b) ISUCCM3, and (c) ISUCCM3-CTL. The color contour is for zonal wind.

  • View in gallery

    Longitude–height section of mean PKE in the 20–100-day period along the equator (10°N–10°S) for (a) NCEP, (b) ISUCCM3, and (c) CTL during 10 yr (October–April 1979–88). The contour interval 2.5 J kg−1; the areas with values >12.5 J kg−1 are shaded.

  • View in gallery

    As in Fig. 2, but for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL, and the areas with values >5 J kg−1 are shaded.

  • View in gallery

    The NCEP longitude–height section along the equator (10°N–10°S) for (a) barotropic conversion term, (b) (α, −ω) covariance with wave energy flux (Fx, Fz), (c) (α, Q1) covariance, (d) horizontal convergence of wave energy flux Fh, and (e) vertical convergence of wave energy flux Fp in the 20–100-day period during 10 yr (October–April 1979–88). The contour interval is 2 J kg−1 day−1. Negative areas are shaded, except in (b). The units for the wave energy flux vectors in (b) are 600 J m s−1 kg−1 for Fx and 0.35 J m s−1 kg−1 for Fz.

  • View in gallery

    As in Fig. 4, but for ISUCCM3, and the contour interval is 5 J kg−1 day−1 for (d). Also, (f) is the longitude–height section of the work done by the convection-induced momentum tendency for ISUCCM3 during 10-yr (October–April 1979–88) in a period range of 20–100 days along the equator (10°N–10°S). The contour interval is 0.5 J kg−1 day−1 in (f).

  • View in gallery

    As in Fig. 4, but for CTL, and the contour interval is 5 J kg−1 day−1 for (d).

  • View in gallery

    Longitude–height section of the barotropic conversion term in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

  • View in gallery

    Longitude–height section of in the 20–100-day period along the equator (10°N–10°S) for NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

  • View in gallery

    Mean zonal wind (m s−1) along the equator (10°N–10°S) at 200 hPa for NOTRI and CTL during 10 yr (October–April 1979–88).

  • View in gallery

    Longitude–height section of the (α, Q1) covariance in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Areas of negative (α, Q1) covariance are shaded. The contour interval is 2 J kg−1 day−1.

  • View in gallery

    Longitude–height section of horizontal convergence of Fh in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 5 J kg−1 day−1.

  • View in gallery

    Horizontal map of wave energy flux (Fh) in the 20–100-day period range for NOCMT-NOTRI during 10 yr (October–April 1979–88) at 200 hPa. The contour interval is 4 J kg−1 day−1 for horizontal convergence of Fh.

  • View in gallery

    As in Fig. 12, but for NOTRI-CTL with the contour interval 2 J kg−1 day−1.

  • View in gallery

    As in Fig. 12, but for (a) NCEP, (b) ISUCCM3, and (c) CTL with the contour interval 2 J kg−1 day−1.

  • View in gallery

    Longitude–height section of vertical convergence of Fp in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

  • View in gallery

    Longitude–height section of the work done by the convection-induced momentum tendency’s (a) and (b) components for ISUCCM3 in period range of 20–100 days during 10 yr (October–April 1979–88) along the equator (10°N–10°S). Negative areas are shaded. The contour interval is 0.5 J kg−1 day−1.

  • View in gallery

    Zonal wind in the 20–100-day period range for ISUCCM3-NOCMT along the equator (10°N–10°S) during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 0.01 m s−1.

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Physical Mechanisms for the Maintenance of GCM-Simulated Madden–Julian Oscillation over the Indian Ocean and Pacific

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  • 1 Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa, and Pacific Northwest National Laboratory, Richland, Washington
  • | 2 Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa
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Abstract

The kinetic energy budget is conducted to analyze the physical processes responsible for the improved Madden–Julian oscillation (MJO) simulated by the Iowa State University general circulation models (ISUGCMs). The modified deep convection scheme that includes the revised convection closure, convection trigger condition, and convective momentum transport (CMT) enhances the equatorial (10°S–10°N) MJO-related perturbation kinetic energy (PKE) in the upper troposphere and leads to a more robust and coherent eastward-propagating MJO signal. In the MJO source region, the Indian Ocean (45°–120°E), the upper-tropospheric MJO PKE is maintained by the vertical convergence of wave energy flux and the barotropic conversion through the horizontal shear of mean flow. In the convectively active region, the western Pacific (120°E–180°), the upper-tropospheric MJO PKE is supported by the convergence of horizontal and vertical wave energy fluxes. Over the central-eastern Pacific (180°–120°W), where convection is suppressed, the upper-tropospheric MJO PKE is mainly due to the horizontal convergence of wave energy flux. The deep convection trigger condition produces stronger convective heating that enhances the perturbation available potential energy (PAPE) production and the upward wave energy fluxes and leads to the increased MJO PKE over the Indian Ocean and western Pacific. The trigger condition also enhances the MJO PKE over the central-eastern Pacific through the increased convergence of meridional wave energy flux from the subtropical latitudes of both hemispheres. The revised convection closure affects the response of mean zonal wind shear to the convective heating over the Indian Ocean and leads to the enhanced upper-tropospheric MJO PKE through the barotropic conversion. The stronger eastward wave energy flux due to the increase of convective heating over the Indian Ocean and western Pacific by the revised closure is favorable to the eastward propagation of MJO and the convergence of horizontal wave energy flux over the central-eastern Pacific. The convection-induced momentum tendency tends to decelerate the upper-tropospheric wind, which results in a negative work to the PKE budget in the upper troposphere. However, the convection momentum tendency accelerates the westerly wind below 800 hPa over the western Pacific, which is partially responsible for the improved MJO simulation.

Corresponding author address: Liping Deng, Pacific Northwest National Laboratory, P.O. Box 999, MSIN: K9-24, Richland, WA 99352. E-mail: liping.deng@pnl.gov

Abstract

The kinetic energy budget is conducted to analyze the physical processes responsible for the improved Madden–Julian oscillation (MJO) simulated by the Iowa State University general circulation models (ISUGCMs). The modified deep convection scheme that includes the revised convection closure, convection trigger condition, and convective momentum transport (CMT) enhances the equatorial (10°S–10°N) MJO-related perturbation kinetic energy (PKE) in the upper troposphere and leads to a more robust and coherent eastward-propagating MJO signal. In the MJO source region, the Indian Ocean (45°–120°E), the upper-tropospheric MJO PKE is maintained by the vertical convergence of wave energy flux and the barotropic conversion through the horizontal shear of mean flow. In the convectively active region, the western Pacific (120°E–180°), the upper-tropospheric MJO PKE is supported by the convergence of horizontal and vertical wave energy fluxes. Over the central-eastern Pacific (180°–120°W), where convection is suppressed, the upper-tropospheric MJO PKE is mainly due to the horizontal convergence of wave energy flux. The deep convection trigger condition produces stronger convective heating that enhances the perturbation available potential energy (PAPE) production and the upward wave energy fluxes and leads to the increased MJO PKE over the Indian Ocean and western Pacific. The trigger condition also enhances the MJO PKE over the central-eastern Pacific through the increased convergence of meridional wave energy flux from the subtropical latitudes of both hemispheres. The revised convection closure affects the response of mean zonal wind shear to the convective heating over the Indian Ocean and leads to the enhanced upper-tropospheric MJO PKE through the barotropic conversion. The stronger eastward wave energy flux due to the increase of convective heating over the Indian Ocean and western Pacific by the revised closure is favorable to the eastward propagation of MJO and the convergence of horizontal wave energy flux over the central-eastern Pacific. The convection-induced momentum tendency tends to decelerate the upper-tropospheric wind, which results in a negative work to the PKE budget in the upper troposphere. However, the convection momentum tendency accelerates the westerly wind below 800 hPa over the western Pacific, which is partially responsible for the improved MJO simulation.

Corresponding author address: Liping Deng, Pacific Northwest National Laboratory, P.O. Box 999, MSIN: K9-24, Richland, WA 99352. E-mail: liping.deng@pnl.gov

1. Introduction

Simulations of the Madden–Julian oscillation (MJO) by general circulation models (GCMs) have been gradually improved in the last decade through studies on the representation of cloud systems in terms of gridscale physical variables (e.g., Wang and Schlesinger 1999; Maloney and Hartmann 2001; Sperber et al. 2005; Zhang and Mu 2005; Liu et al. 2005; Khairoutdinov et al. 2005; Ziemiański et al. 2005; Deng and Wu 2010). Some of the well-known spatial and temporal features of the MJO (Madden and Julian 1972, 1994) are reproduced by several GCMs with varying degrees of success. Wang and Schlesinger (1999) showed the enhancement of the MJO in a GCM with the use of a larger threshold of relative humidity that allows the accumulation of moist static energy to a certain amount to trigger the convection in three different convection schemes. Maloney and Hartmann (2001) improved intraseasonal variability of tropical precipitation and zonal winds by including the microphysics of cloud in the relaxed Arakawa–Schubert convection scheme (Sud and Walker 1999) in the National Center for Atmospheric Research (NCAR) Community Climate Model, version 3.6 (CCM3). Analyzing ECHAM4 coupled and uncoupled GCM simulations, Sperber et al. (2005) demonstrated that the eastward-propagating MJO zonal wind and latent heat flux are related to the horizontal resolution, realistic mean state simulation, and air–sea interaction. Zhang and Mu (2005) obtained the enhanced intraseasonal variability in the precipitation, zonal wind, and outgoing longwave radiation (OLR) and the eastward-propagating MJO from the Indian Ocean to the Pacific by modifying the closure assumption in the Zhang and McFarlane (1995) convection parameterization scheme of NCAR CCM3. Liu et al. (2005) simulated an improved mean state, intraseasonal variability, space–time power spectra, and coherent eastward propagation of MJO precipitation using a modified Tiedtke (1989) convection scheme in NCAR Community Atmosphere Model (CAM). Ziemiański et al. (2005) presented a more realistic simulation of MJO-like system including the large-scale organization of the tropical superclusters, eastward propagation, and lower-tropospheric cyclonic and upper-tropospheric anticyclonic gyres by applying the cloud-resolving convection parameterization over the western Pacific warm pool in NCAR CAM. Khairoutdinov et al. (2005) showed that the enhanced intraseasonal variability is simulated by the NCAR CAM with the cloud-resolving model in replacing the convection and cloud parameterization.

The improved simulations of intraseasonal variability allow further diagnostic analysis to investigate the physical processes responsible for the development and maintenance of the MJO. Mu and Zhang (2006, 2008) analyzed the energetics of MJO simulated by the NCAR CAM and showed that the observed mechanisms responsible for the MJO perturbation kinetic energy (PKE) production (Yanai et al. 2000; Chen and Yanai 2000) are reproduced by the simulations with the improved convection closure in the Zhang–McFarlane convection scheme (Zhang and McFarlane 1995; Zhang 2002). The interaction between the large-scale motion and convection plays a predominant role in the maintenances of PKE associated with the 30–60-day period through the conversion of perturbation available potential energy (PAPE) generated by convection heating over the Indian Ocean–western Pacific. However, over the central-eastern Pacific where the convection is suppressed, the strong equatorward fluxes of wave energy from the extratropic latitudes result in the convergence of horizontal wave energy flux in the equatorial upper troposphere, which maintains the MJO PKE.

With the inclusion of the revised closure assumption, convection trigger condition, and the convective momentum transport (CMT) in the deep convection scheme, Deng and Wu (2010) showed that the MJO simulations are improved in the amplitude, spatial distribution, eastward propagation, and horizontal and vertical structures, especially for the coherent feature of eastward-propagating convection and the precursor sign of the convective center. The revised convection closure plays a major role for improving the eastward propagation of MJO. The convection trigger enhances the amplitude of the MJO by producing less frequent but more vigorous moist convection. The inclusion of CMT results in more coherent structure of the MJO and its corresponding atmospheric variances. The relationship between the CMT and MJO has been suggested by the analysis of momentum budget residuals by Tung and Yanai (2002a,b). The CMT plays two different roles during the westerly phase of the MJO. The upgradient CMT transfers kinetic energy into large-scale zonal flow and helps maintain middle-level easterly shear at the early stage, while the downgradient CMT decelerates the large-scale zonal flow and reduces zonal wind shear. Using the analytic model and the idealized simulations produced by the cloud-resolving convection parameterization (Grabowski 2001), Moncrieff (2004) suggested the convective organization and mesoscale momentum transport appear to play a role in producing the coherence between MJO zonal wind and convective envelope. The objective of this paper is to examine the perturbation kinetic energy of the MJO and its budget over the Indian Ocean and Pacific using the GCM simulations in comparison with the observations. Consequently, the physical processes responsible for the enhanced MJO can be understood. The model simulations and observational data are described in section 2. The energetic features of the MJO are presented in section 3. The impacts of revised convection closure, convection trigger condition, and CMT on the simulated MJO PKE budgets are discussed in section 4. The summary is given in section 5.

2. Simulations and observational data

Four 10-yr (1979–88) Iowa State University GCM (ISUGCM) simulations presented in Deng and Wu (2010) are used in this paper. ISUGCM is a global climate model based on the NCAR CCM3 (Kiehl et al. 1998). It has 18 hybrid vertical levels extending from the surface to 4 hPa and a horizontal resolution of T42 (a roughly 2.8° × 2.8° Gaussian grid). Deep precipitating convection and shallow convection are treated by the Zhang and McFarlane (1995) and Hack (1994) schemes, respectively. Three modifications, that is, the revised convection closure assumption, convection trigger condition, and CMT, are made to the deep convection scheme in ISUGCM. The revised closure relates convection to the destabilization of the tropospheric layer above the planetary boundary layer by the large-scale processes (Zhang 2002). The trigger condition obtained from the cloud-resolving simulations (Wu et al. 2008) activates deep convection when the CAPE increase due to the large-scale temperature and moisture advection exceeds certain threshold (70 J kg−1 h−1; Wu et al. 2007a). The CMT parameterization validated by the cloud-resolving simulations takes into account the role of perturbation pressure field generated by the interaction of convection with large-scale circulation (Zhang and Cho 1991a,b; Wu and Yanai 1994; Wu et al. 2003, 2007b; Zhang and Wu 2003).

In Table 1, the control simulation (CTL) is conducted using ISUGCM with the original deep convection scheme in the standard CCM3, and the simulation ISUCCM3 is performed with the inclusion of all three modifications in the convection scheme. The simulation NOCMT only includes the revised closure and trigger condition in the convection scheme, and the simulation NOTRI only applies the revised closure in the scheme. National Centers for Environmental Prediction (NCEP) reanalysis datasets (Kalnay et al. 1996), including the horizontal wind, vertical velocity, and temperature, are regridded to T42 resolution for matching the model output.

Table 1.

List of four ISUGCM simulations.

Table 1.

3. Energetic characteristics of simulated MJO in comparison with observations

a. Mean vertical circulation along the equator

To illustrate the large-scale vertical circulation, the 10-yr (1979–88) October to April mean vertical cross section of zonal and vertical wind averaged across the equatorial belt (10°N–10°S) is given in Fig. 1. In NCEP, the zonal wind from the eastern Indian Ocean (~60°E) to the date line is easterly in the upper troposphere and weak westerly in the lower troposphere, and the zonal wind direction is just opposite over the central to eastern Pacific and Atlantic Ocean (Fig. 1a). The strong upper-tropospheric easterly centered at 150 hPa over the Indian Ocean and western Pacific is coupled with a strong band of upward motion and active convection reflected in the OLR field (not shown). The strong upper-tropospheric westerly centered at 150–200 hPa is over the central-eastern Pacific and Atlantic Ocean. The mean vertical circulation simulated by ISUCCM3 is in general agreement with the observations, but the upper-tropospheric westerly is stronger than that in NCEP, as well as the stronger and wider band of upward motion in ISUCCM3 (Fig. 1b). The band of upward motion exists from the Indian Ocean to central Pacific with the maximum upward velocity located over the western Pacific. The impact of modified convection scheme on the mean vertical circulation can be readily identified from the difference between ISUCCM3 and CTL presented in Fig. 1c. A notable feature is the enhanced upward vertical velocity over the western Pacific between 150°E and 180°. The lower-tropospheric westerly between 120°E and 150°W is increased from CTL to ISUCCM3 with a peak around 850 hPa and 150°E, and the easterly is increased in the upper troposphere. Outside the western and central Pacific, however, the increased westerly (easterly) is present in the upper (lower) troposphere.

Fig. 1.
Fig. 1.

A 10-yr (October–April 1979–88) mean vertical cross section of zonal (m s−1) and vertical (hPa day−1) wind averaged between 10°N and 10°S for (a) NCEP, (b) ISUCCM3, and (c) ISUCCM3-CTL. The color contour is for zonal wind.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

b. Distribution of PKE along the equator

In this section, we examine the perturbation kinetic energy associated with the MJO along the equator following the methodology of Yanai et al. (2000). The PKE is defined as , where the overbar and prime represent the time mean and the deviation from the time mean, respectively. Figure 2a illustrates the longitude–height cross section of the mean NCEP PKE for the period of 10 yr (October–April 1979–88) along the equator (10°N–10°S). A 20–100-day filter has been used to highlight the MJO-related variability of PKE. The large PKE is centered at 150 hPa and located over the Indian Ocean–western Pacific, eastern Pacific, and Atlantic Ocean (e.g., Yanai et al. 2000; Mu and Zhang 2006). The maxima of PKE in the Indian Ocean and western Pacific collocate with the upper-tropospheric easterly (Fig. 1a) and are closely related with the strong convective activity in this region (e.g., Chen and Yanai 2000). However, the maxima of PKE in the eastern Pacific, where convection is suppressed, are associated with the upper-tropospheric westerly (Fig. 1a) and are due to the accumulation of wave energy through the zonal flow (e.g., Webster and Chang 1988). The PKE distribution of ISUCCM3 (Fig. 2b) is in agreement with the observations, but the maximum centers shift slightly westward except the one over the western Pacific (e.g., Mu and Zhang 2006). The maximum of PKE near 120°E in the western Pacific is located higher than the observed peak and also has larger amplitudes, which is consistent with the higher location of the upper-tropospheric easterly center and the stronger band of upward motion in ISUCCM3 (Fig. 1b). Similar distribution of PKE is produced by CTL, but the amplitude of PKE is smaller than that in ISUCCM3 and observations, especially over the Indian Ocean (Fig. 2c). The maximum of PKE does not extend over the Maritime Continent in CTL as in ISUCCM3 and observations.

Fig. 2.
Fig. 2.

Longitude–height section of mean PKE in the 20–100-day period along the equator (10°N–10°S) for (a) NCEP, (b) ISUCCM3, and (c) CTL during 10 yr (October–April 1979–88). The contour interval 2.5 J kg−1; the areas with values >12.5 J kg−1 are shaded.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

The enhancement of MJO PKE by the modified convection scheme is more clearly documented in Fig. 3a, which shows the difference of PKE between ISUCCM3 and CTL. Four major positive centers are over the Indian Ocean around 60°E, western Pacific around 120°E, eastern Pacific around 130°W, and west coast of South America around 60°W. To further examine the impacts of each modification on the MJO PKE, the differences of MJO PKE between four ISUGCM simulations are presented in Figs. 3b–d. The comparison between ISUCCM3 and NOCMT shows that the inclusion of CMT generally reduces the upper-tropospheric MJO PKE with negative centers around 200 hPa over Africa, western Pacific, eastern Pacific, and Atlantic Ocean (Fig. 3b). The enhanced MJO PKE in the upper troposphere around 100 hPa coupled with the strong upward motion and easterly is also present near 120°E with active convection. The contribution of the convection trigger condition to the enhanced MJO PKE is demonstrated by the difference between NOCMT and NOTRI in Fig. 3c. The magnitudes of MJO PKE in NOCMT in the upper troposphere are obviously larger than that in NOTRI as shown by the positive centers over the Africa, western Indian Ocean, western Pacific, eastern Pacific, west coast of South America, and Atlantic Ocean. The PKE difference between NOCMT and NOTRI over the west coast of South America to Africa is associated with a large upper-tropospheric westerly difference (not shown). The influence of the revised closure on the MJO PKE is indicated by the difference between NOTRI and CTL in Fig. 3d. The positive peak of PKE difference over the Indian Ocean is related to the more active convection coupling with the strong easterly and upward motion (not shown) in NOTRI compared to CTL. The positive PKE differences are also present in the upper troposphere around 130° and 60°W.

Fig. 3.
Fig. 3.

As in Fig. 2, but for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL, and the areas with values >5 J kg−1 are shaded.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

4. Kinetic energy budgets of the MJO

The analysis in the last section illustrates the contributions of revised closure, convection trigger condition, and CMT to the simulations of MJO PKE in the upper troposphere. To further understand the physical processes responsible for the enhanced MJO PKE, we perform the kinetic energy budget of the MJO in this section. Following Yanai et al. (2000),
e1
In Eq. (1), v is the horizontal velocity, p is the pressure, ω = dp/dt (the vertical p velocity), is the isobaric gradient operator, α is the specific volume, and fr is the frictional force per unit mass. Here, F(Fu, Fυ) is the convection-induced momentum tendency (e.g., Wu and Yanai 1994; Wu et al. 2007a); is the horizontal wave energy flux, which includes both zonal (Fx) and meridional (Fy) components; and is the vertical wave energy flux (ϕ is the geopotential). Equation (1) shows that the local time change of PKE is due to the work done by the horizontal (term A) and vertical (term B) shear generation of the mean flow, the conversion from the perturbation available potential energy (PAPE) with the (α, −ω) correlation (term C), the horizontal (term D), and vertical (term E) convergence of wave energy fluxes, the work done by the convection-induced momentum tendency (term F), and the work done by the frictional force (term G). Term B is negligibly small for large-scale motions (e.g., Yanai et al. 2000). Term G is the work related to the frictional force, and is negligible in the upper troposphere. Therefore, the maintenance of upper-tropospheric PKE is mainly governed by the barotropic conversion through the horizontal shear generation of mean flow, the PAPE conversion, the horizontal and vertical convergence of wave energy fluxes, and the work done by the convection-induced momentum tendency. In the following presentation, the cross-spectra analysis is used to evaluate the contribution of two variables’ covariance from the period of 20–100 days with respect to the total covariance. In the calculation of MJO-related covariance terms in Eq. (1), the cospectra are integrated over the period of 20–100 days for October–April of each year from 1979 to 1988 and are then averaged over the 10 years to get the climatological mean.

a. Maintenance of the MJO PKE

Figure 4 presents the NCEP MJO PKE production due to the work done by the barotropic conversion (Fig. 4a), the PAPE conversion with the corresponding PAPE generation (Figs. 4b,c), and the convergence of horizontal and vertical wave energy fluxes (Figs. 4d,e). Large observed PKE productions due to the barotropic conversion appear in the upper level (150–200 hPa) over the Indian Ocean from 45° to 90°E, the eastern Pacific from 135° to 75°W, and the Atlantic Ocean from 30°W to 15°E (Fig. 4a) and correspond to the PKE peaks in these regions (Fig. 2a). These large PKE productions normally locate at the downstream of upper-tropospheric zonal wind center (Fig. 1a) where the zonal wind shear helps the accumulation of energy. Negative barotropic conversions are present in the upper troposphere over the western Pacific (125°E–180°) and the South America (~60°W) in NCEP. Figure 4b shows the longitude–height cross section of the partial covariance of specific volume (α) and vertical motion (−ω) in the 20–100-day period with the vertical and zonal wave energy flux superimposed on. The large band of energy conversion from PAPE to PKE occurs around 200–400 hPa over the Indian Ocean and western Pacific where the active convection and strong upward wave energy flux present. The weak point of this large energy conversion band is around the Maritime Continent. One possible explanation is that the strong land heating (cooling) during the day (night) tends to favor the variability of convections on the shorter time scales (e.g., diurnal cycle) than the 20–100-day period. As shown by previous studies (e.g., Nitta 1970, 1972; Yanai et al. 2000; Mu and Zhang 2006), the conversion from PAPE to PKE through the covariance of (α, −ω) is largely supplied by the production of PAPE through the covariance of (α, Q1), that is, [see Eq. (7) in Yanai et al. 2000], where R is the specific gas constant, cp is the isobaric specific heat capacity, is the static stability factor, θ is the potential temperature, and Q1 is the diabatic heating in which the deep convective heating is the dominant term. Figure 4c shows the covariance of specific volume and diabatic heating in NCEP data. Large PAPE generation due to the convective heating is located over the Indian Ocean and western Pacific with a small gap over the Maritime Continent, which explains most of PAPE conversion to PKE shown in Fig. 4b. Figure 4d presents the longitude–height cross section of horizontal convergence of wave energy flux along the equator in the 20–100-day period. NCEP observations indicate two major convergent zones in the upper troposphere over the central-eastern Pacific and South America and two major divergent zones over the west coast of South America and Atlantic Ocean. Further analysis of 200-hPa horizontal wave energy fluxes in the 20–100-day period from NCEP (not shown) reveals that the convergence over the central-eastern Pacific between 150° and 120°W is largely due to the meridional wave energy fluxes from three source regions, that is, the subtropical latitudes of both hemispheres and the west coast of North America, which confirms the finding of Yanai et al. (2000). The meridional wave energy fluxes from the subtropical latitudes of both hemispheres also contribute to the convergence over the east coast of South America. The vertical convergence of wave energy flux along equator is given in Fig. 4e. NCEP analysis shows the convergence above 200 hPa and the divergence below over the Indian Ocean and western Pacific, which results from the upward and downward wave energy fluxes from the peak of PAPE production near 250 hPa (Figs. 4b,c). The vertical convergence of wave energy flux apparently is a major contributor to the maintenances of upper-tropospheric PKE in these two regions (Fig. 2a).

Fig. 4.
Fig. 4.

The NCEP longitude–height section along the equator (10°N–10°S) for (a) barotropic conversion term, (b) (α, −ω) covariance with wave energy flux (Fx, Fz), (c) (α, Q1) covariance, (d) horizontal convergence of wave energy flux Fh, and (e) vertical convergence of wave energy flux Fp in the 20–100-day period during 10 yr (October–April 1979–88). The contour interval is 2 J kg−1 day−1. Negative areas are shaded, except in (b). The units for the wave energy flux vectors in (b) are 600 J m s−1 kg−1 for Fx and 0.35 J m s−1 kg−1 for Fz.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

The observed MJO PKE production due to the work done by the barotropic conversion, the PAPE conversion with the corresponding PAPE generation, and the horizontal and vertical convergence of wave energy fluxes is generally simulated by ISUCCM3 but with the difference in the amplitude (Fig. 5). ISUCCM3 has smaller positive barotropic conversions over the west coast of South America and the Atlantic Ocean but larger positive barotropic conversions over the Maritime Continent between 90° and 120°E compared to the NCEP analysis (Fig. 5a and Fig. 4a). The observed band of energy conversion from PAPE to PKE through the covariance of (α, −ω) over the Indian Ocean and western Pacific with the gap at the Maritime Continent and the upward energy flux above 300 hPa is also simulated in ISUCCM3 (Fig. 5b) but with larger amplitude. Corresponding to the PAPE conversion, the PAPE generation band through the covariance of (α, Q1) centered over the convection active area around 200–400 hPa shows the larger amplitude in ISUCCM3 (Fig. 5c). These results confirm the role of coupling between convection and large-scale circulation in the maintenance of MJO PKE over the Indian Ocean and western Pacific obtained by previous studies. The observed convergence/divergence of horizontal wave energy flux along the equator in the 20–100-day period is generally captured by ISUCCM3 but with stronger convergences over the central-eastern Pacific and South America and weaker divergences over the west coast of South America (Fig. 5d). The vertical convergence of wave energy flux along the equator is given in Fig. 5e. ISUCCM3 simulates the observed convergence–divergence pattern but with the larger amplitude over the western Pacific and Indian Ocean. This is due to the larger upward and downward wave energy fluxes from the peak of stronger PAPE production (Figs. 5b,c). The magnitude of the work done by the convection-induced momentum tendency in Fig. 5f is smaller than that for other terms in the MJO PKE budget (Figs. 5a–e), and this feature will be further discussed later.

Fig. 5.
Fig. 5.

As in Fig. 4, but for ISUCCM3, and the contour interval is 5 J kg−1 day−1 for (d). Also, (f) is the longitude–height section of the work done by the convection-induced momentum tendency for ISUCCM3 during 10-yr (October–April 1979–88) in a period range of 20–100 days along the equator (10°N–10°S). The contour interval is 0.5 J kg−1 day−1 in (f).

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Figure 6 shows the longitude–height cross section of the barotropic conversion, the PAPE conversion and generation, and the horizontal and vertical convergence of wave energy fluxes in the 20–100-day period along the equator for CTL. Comparing with the NCEP and ISUCCM3, CTL simulates the general patterns of observations but the amplitude and location are different. For example, CTL presents less PKE production owing to the barotropic conversions over the Indian Ocean (Fig. 6a). Also, CTL shows a weak conversion band from PAPE to PKE with a gap over the Indian Ocean around 90°E. This band extends to the eastern Pacific around 135°W where convection is normally suppressed (Fig. 6b). Correspondingly, the PAPE generation band due to the convective heating around 300 hPa in CTL is weaker than that in ISUCCM3, but it extends to the eastern Pacific, which does not appear in the observations (Figs. 6c, 5c, and 4c). The horizontal convergence of wave energy flux over the central-eastern Pacific along the equator is weaker in CTL compared to the NCEP and ISUCCM3 (Figs. 6d, 4d, and 5d).

Fig. 6.
Fig. 6.

As in Fig. 4, but for CTL, and the contour interval is 5 J kg−1 day−1 for (d).

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Over the Indian Ocean, the NCEP upper-tropospheric MJO PKE is mainly maintained by the barotropic conversion and the vertical convergence of wave energy flux from the PAPE generation band around 200–400 hPa through the covariance of (α, Q1). This feature is better simulated in ISUCCM3 than CTL. Over the western Pacific, both the NCEP and ISUCCM3 show stronger support to the upper-tropospheric MJO PKE through the vertical convergence of wave energy flux (coupled with the PAPE generation and conversion) when compared to the CTL. Over the central-eastern Pacific, the horizontal convergence of wave energy flux in CTL is weaker than that in NCEP and ISUCCM3. In general, the upper-tropospheric MJO PKE maintenance over the Indian Ocean and Pacific in ISUCCM3 is closer to the observations than CTL.

b. Impacts of the revised closure assumption, convection trigger and CMT on the MJO PKE

To further understand how each modification affects the MJO PKE, the differences between four simulations are examined. Figure 7 shows the MJO PKE production due to the work done by the barotropic conversion. The increased upper-tropospheric PKE from CTL to ISUCCM3 over the Indian Ocean (Fig. 7a) is mainly due to the impact of revised convection closure and trigger condition (Figs. 7d,c). The barotropic conversion consists of four parts: , , , and . The analysis of each term indicates that the zonal wind related term is the dominant term among them. Figure 8 presents the difference of between NOTRI and CTL along the equator in the 20–100-day period. It explains most features shown in Fig. 7d with the positive center in the upper troposphere over the Indian Ocean. Since NOTRI and CTL runs pose similar positive (not shown), the increases of mean easterly wind shear along the equator is the major reason for the positive difference of barotropic conversion between two runs. As shown in Fig. 9, the mean 200-hPa easterly wind difference between 45° and 110°E along the equator is 5 m s−1 in NOTRI, which is three times larger than 1.4 m s−1 in CTL. This increased mean zonal wind shear corresponds to the enhanced deep convective heating (Fig. 10d) and upper-tropospheric divergence (Fig. 9). The negative differences of barotropic conversion over the eastern Pacific and the Atlantic Ocean (Fig. 7a) can be also attributed to the horizontal wind shear, which is smaller in NOTRI than CTL (Fig. 9).

Fig. 7.
Fig. 7.

Longitude–height section of the barotropic conversion term in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 8.
Fig. 8.

Longitude–height section of in the 20–100-day period along the equator (10°N–10°S) for NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 9.
Fig. 9.

Mean zonal wind (m s−1) along the equator (10°N–10°S) at 200 hPa for NOTRI and CTL during 10 yr (October–April 1979–88).

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 10.
Fig. 10.

Longitude–height section of the (α, Q1) covariance in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Areas of negative (α, Q1) covariance are shaded. The contour interval is 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

The difference between four simulations for the PAPE production through the covariance of (α, Q1) is given in Fig. 10. The increase of PAPE production from CTL to ISUCCM3 mainly appears over the western Pacific and the Indian Ocean around 300 hPa. The CMT, through the influence on the convective heating, strengthens the positive correlation between the specific volume and convective heating from 140° to 170°E but weakens the PAPE production near 130°E (Fig. 10b). The convection trigger condition is responsible for the increase of PAPE production around 300 hPa near 130° and 90°E (Fig. 10c) since the new trigger produces more vigorous convective heating by limiting the frequent light precipitation. The use of the revised closure increases the PAPE production over the Indian Ocean, western Pacific, and eastern Pacific centered around 500 hPa (Fig. 10d).

Figure 11 presents convergence–divergence of horizontal wave energy flux along the equator in the 20–100-day period for the differences between four model simulations. A major difference between ISUCCM3 and CTL is the convergence over the central-eastern Pacific (Fig. 11a). This enhanced horizontal convergence is largely due to the impacts of the convection trigger condition and revised closure (Figs. 11c,d). The impact of convection trigger over the central-eastern Pacific can be further identified in the difference of horizontal wave energy fluxes between NOCMT and NOTRI at 200 hPa (Fig. 12). The enhanced southward (northward) wave energy fluxes to the equator from the subtropical latitudes of the Northern (Southern) Hemisphere present around 140°W and help build up the convergence along the equator, which suggests an extratropic influence to the tropical intraseasonal signal. The use of revised closure results in the enhanced eastward energy flux coupled with the divergence from the Indian Ocean to central Pacific along the equator (Fig. 13). This corresponds to the increased convective heating over the Indian Ocean and western Pacific around 500 hPa (Fig. 10d) and helps the horizontal convergence of wave energy flux over the central-eastern Pacific in the upper troposphere (Fig. 11d). It is noticed that the enhanced eastward energy flux due to the revised closure plays a role in the reversal from the westward wave energy flux over the Indian Ocean in CTL (Fig. 14c) to the eastward wave energy flux in ISUCCM3 (Fig. 14b), which is also shown in NCEP analysis (Fig. 14a). This reversal feature supports the eastward MJO signal simulated by ISUCCM3 compared to the westward signal by CTL (Fig. 4 in Deng and Wu 2010).

Fig. 11.
Fig. 11.

Longitude–height section of horizontal convergence of Fh in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 5 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 12.
Fig. 12.

Horizontal map of wave energy flux (Fh) in the 20–100-day period range for NOCMT-NOTRI during 10 yr (October–April 1979–88) at 200 hPa. The contour interval is 4 J kg−1 day−1 for horizontal convergence of Fh.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 13.
Fig. 13.

As in Fig. 12, but for NOTRI-CTL with the contour interval 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 14.
Fig. 14.

As in Fig. 12, but for (a) NCEP, (b) ISUCCM3, and (c) CTL with the contour interval 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

The vertical convergence differences of wave energy flux between four simulations are shown in Fig. 15. In comparison with CTL, the major impacts of the modified convection scheme in ISUCCM3 are over the western Pacific where the convergence of vertical wave energy fluxes is enhanced above 200 hPa (Fig. 15a), and over the central-eastern Pacific where the divergence of vertical wave energy fluxes is increased above 300 hPa because of the enhanced downward energy fluxes around 150°W (Figs. 5b and 6b). Examination of Figs. 15b–d indicates that the convection trigger condition is the major contributor to the enhanced upper-tropospheric convergence of energy fluxes over the western Pacific and Indian Ocean. The enhanced convergence (Fig. 15c) coupled with the PAPE production around 300 hPa (Fig. 10c) is responsible for the increase of MJO PKE (Fig. 3c).

Fig. 15.
Fig. 15.

Longitude–height section of vertical convergence of Fp in the 20–100-day period along the equator (10°N–10°S) for (a) ISUCCM3-CTL, (b) ISUCCM3-NOCMT, (c) NOCMT-NOTRI, and (d) NOTRI-CTL during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 2 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Finally, the ISUCCM3 simulation that includes the parameterization of convective momentum transport allows the analysis of work done by the convection-induced momentum tendency and its influence on the PKE budget. Figure 5f shows predominantly negative work above 400 hPa with the peak near 200 hPa corresponding to the large zonal wind velocity. It indicates that the impact of convective momentum transport reduces the mean upper-tropospheric PKE but with relatively small amplitude comparing to other terms in the budget equation. The dominant negative work by the convective momentum tendency is consistent with the rate of kinetic energy transfer estimated from the momentum budget residual during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) (Tung and Yanai 2002a). Figures 16a and 16b present the and components of the work done by the convection-induced momentum tendency, respectively. Comparing these two components, the work done by the momentum tendency mostly comes from the component of . As the negative indicates the tendency to decelerate the zonal wind, the sign of the zonal wind difference between ISUCCM3 and NOCMT (Fig. 17) is roughly opposite to the sign of zonal wind in NOCMT (not shown, similar to Fig. 1b) for the upper troposphere. It is noted that in the lower troposphere over the western Pacific between 150°E and 180°, a dipole pattern appears with the positive work below 800 hPa and negative above (Fig. 16a). The positive work indicates the acceleration of low-level westerly wind by the convective momentum transport (e.g., Tung and Yanai 2002b), which can be visually identified over the western Pacific from Fig. 17 and is favorable for the development and eastward propagation of MJO.

Fig. 16.
Fig. 16.

Longitude–height section of the work done by the convection-induced momentum tendency’s (a) and (b) components for ISUCCM3 in period range of 20–100 days during 10 yr (October–April 1979–88) along the equator (10°N–10°S). Negative areas are shaded. The contour interval is 0.5 J kg−1 day−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

Fig. 17.
Fig. 17.

Zonal wind in the 20–100-day period range for ISUCCM3-NOCMT along the equator (10°N–10°S) during 10 yr (October–April 1979–88). Negative areas are shaded. The contour interval is 0.01 m s−1.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3759.1

5. Summary

The Indian Ocean with active convection is the source region of the MJO. The upper-tropospheric MJO PKE maintenances not only depend on the vertical convergence of wave energy flux from the convective heating source region where large PAPE production exits but also the barotropic conversion term through the horizontal shear of mean flow. The impact of revised closure plays an important role for the enhancement of barotropic conversion through the work done by the mean zonal wind shear and in turn favors the upper-tropospheric MJO PKE production. The convection triggers condition, through its requirement that convection is only activated when the CAPE continuously increases and exceeds a certain threshold, generates stronger convective heating, which enhances the upward wave energy fluxes and leads to the increase of MJO PKE over the Indian Ocean.

Over the western Pacific, the upper-tropospheric MJO PKE is supported by the horizontal convergence of wave energy flux as well as the vertical convergence of wave energy flux from the convective heating source region around 200–400 hPa. The work done by the barotropic conversion through the horizontal shear of the mean flow appears to decrease the upper-tropospheric MJO PKE. As over the Indian Ocean, the convection trigger condition helps build up more robust deep convection and stronger upward wave energy flux and enhances the MJO PKE production in the upper troposphere over the western Pacific. The inclusion of convective momentum transport in the convection scheme reduces the upper-tropospheric MJO PKE through the work done by the convection-induced momentum tendency with the deceleration of the upper-tropospheric wind. But the convective momentum transport tends to accelerate the westerly wind below 800 hPa over the western Pacific and enhances the MJO PKE.

Over the central-eastern Pacific, although the convection is suppressed, the large-scale circulation carries on the MJO signal. The suppressed deep convection coupled with the downward wave energy flow appears to decrease the MJO PKE in the upper troposphere. The MJO PKE production is mainly due to the work done by the horizontal wave energy flux. The impact of convection trigger condition leads to the enhanced equatorward wave energy fluxes from the subtropical latitudes of both hemispheres and contributes to the horizontal convergence of wave energy flux. The equatorial eastward wave energy flux from the Indian Ocean to the central Pacific, responding to the increased convective heating due to the impact of revised closure, helps the convergence over the central-eastern Pacific and favors the eastward propagation of MJO.

Acknowledgments

Computing support by Daryl Herzmann is greatly appreciated. This research was partly supported by the Biological and Environmental Research Program (BER), U.S. Department of Energy under Grant DE-FG02-08ER64559 and by the National Science Foundation under Grant ATM-0935263. Work performed while the first author was at PNNL was funded by the Department of Energy’s Atmospheric System Research program.

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