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An internationally coordinated observational campaign, namely DYNAMO, was carried out during October 2011–March 2012. Two strong MJO events, namely MJO1 (from mid October to mid November) and MJO2 (from mid November to mid December), occurred during the period. The objective of the current study is to conduct 60day hindcast experiments for the two events with different cumulus parameterization schemes and to reveal physical mechanisms associated with the two events. The forecasts are compared with satelliteobserved outgoing longwave radiation (OLR) product from NOAA (Liebmann and Smith, 1996) and ERAInterim reanalysis dataset (Dee et al., 2011).
The model used for the hindcast experiments is Central Weather Bureau global forecast system (CWBGFS; Liou et al., 1997). The global spectrum atmospheric model has a resolution of about 25 km and 60 vertical levels. It contains a number of physical parameterization schemes listed in Table 1. This atmospheric model is coupled with a onedimensional Snow/Ice/Thermocline (SIT) ocean model (Tsuang et al., 2001, 2009; Tu and Tsuang, 2005). The SIT model is able to describe the energy exchange among ocean, ice, and snow, and predict SST change within the domain of 30°S–30°N. The horizontal grid of the SIT model is the same as that of the atmospheric model. Vertically, it has a total of 30 levels covering the upper ocean to 200m depth.
Radiation RRTMG (Rapid Radiative Transfer Model for GCMs) scheme (Clough et al., 2005; Iacono et al., 2008) Cumulus Simplified Arakawa–Schubert (SAS; Pan and Wu, 1995; Han and Pan, 2011); Tiedtke (TDK) scheme (Tiedtke, 1989; Nordeng, 1994) Large scale precipitation Predict cloud water scheme (Zhao and Carr, 1997) Shallow convection Han and Pan (2011) PBL Firstorder nonlocal scheme (Troen and Mahrt, 1986; Hong and Pan, 1996; Han and Pan, 2011) Surface flux Similarity theory (Businger et al., 1971) Land model Noah land surface model (Ek et al., 2003) Gravity wave drag Palmer et al. (1986) Table 1. List of main parameterization schemes in the CWBGFS model
Two types of cumulus convective schemes are applied for the sensitivity experiments. The first is the Tiedtke (TDK) scheme (Tiedtke, 1989; Nordeng, 1994). Another is the SAS scheme (Pan and Wu, 1995; Han and Pan, 2011). TDK scheme includes shallow, midlevel, and deep convection, and only one type of convection is allowed at one grid. The moisture convergence closure is employed for shallow convection and the convective available potential energy (CAPE) is used for closure of deep convection (Nordeng, 1994). For midlevel convection, the largescale vertical momentum is used to determine the cloud base mass flux. The SAS scheme (Pan and Wu, 1995) is based on the working concepts of Arakawa and Schubert (1974) but simplified to only one cloud type at each grid by Grell (1993). Two different types of convection, shallow and deep convection, are considered. The shallow base mass flux is parameterized from surface buoyancy flux (Han and Pan, 2011), and the quasiequilibrium assumption is used for deep convection closure. For each forecast experiment, the model was integrated for a period of 107 days from 1 October 2011 to 16 January 2012.
For a given variable X, time series at a given location may be decomposed into three components, a lowfrequency background state (LFBS) component, an MJO component, and a highfrequency (HF) component:
$$X = \bar X + X' + {X^*},$$ (1) where
$\bar X$ denotes the LFBS component,$ {X'}$ represents the MJOscale component, and$ {X^*}$ denotes HF component. A 30day running mean is applied to the original time series to obtain the LFBS component with a period longer than 60 days. Subtracting this LFBS from the original time series and then applying a 5day running mean, one may obtain the MJOscale component with a period of 10–60 days. Subtracting the 5day running mean field from the original time series, one may obtain the HF component with a period shorter than 10 days.MSE may be regarded as the sum of dry static energy (DSE) and latent heat:
$${\rm{MSE}} = {\rm{DSE}} + {L_v}q = {c_p}T + {\rm{g}} z + {L_v}q,$$ (2) where c_{p} is the specific heat (1004 J K^{−1} kg^{−1}), T is the temperature, L_{v} is the latent heat (2.5 × 10^{6} J kg^{−1}), q is the specific humidity, g is the gravity acceleration (9.8 m s^{−2}), and z is the height.
The DSE and moisture equations may be derived from atmospheric thermodynamic, continuity, hydrostatic, and moisture equations. Following Yanai et al. (1973), we have
$$ \begin{aligned} {\rm{d}}\left({{\rm{DSE}}} \right)/{\rm{d}}t & = {c_p}\left({{\rm{d}}T/{\rm{d}}t} \right)  \omega \alpha \\ & = {c_p}\left({{\rm{d}}T/{\rm{d}}t} \right) + {\rm{d}}\phi /{\rm{d}}t = {Q_1}, \end{aligned} $$ (3) $$ \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! L\left({{\rm{d}}q/{\rm{d}}t} \right) = L\left({e  c} \right) =  {Q_2}, \quad$$ (4) where Q_{1} denotes the diabatic heating (or the apparent heat source), ω is the vertical velocity in pressure coordinate, α is the specific volume, t is the time, Q_{2} is the apparent moisture sink, e and c are the evaporation rate and condensation rate, and ϕ is the potential energy (ϕ = gz).
In the above, the eddy horizontal and vertical transports of total heat and moisture are included in Q_{1} and Q_{2} of Eqs. (3) and (4) as derived in Yanai et al. (1973). Traditionally, the eddy horizontal transports are ignored since they are negligible compared to the horizontal transports by the largescale motion (Arakawa and Schubert, 1974). Therefore, the eddy vertical fluxes can be regarded as the main contributions of eddy transports in Q_{1} and Q_{2}. If the eddy vertical fluxes are assumed negligibly small at the top of the column, the columnintegrated eddy fluxes approximate to the sum of the surface sensible heat flux (SH) and latent heat flux (LH), and the columnintegrated amount of (e − c) approximates to the precipitation rate (P). The columnintegrated MSE tendency equation (Neelin and Held, 1987; Yanai and Johnson, 1993) may be written as:
$$\begin{array}{l} \left\langle {\dfrac{{\partial {\rm{MSE}}}}{{\partial t}}} \right\rangle =  \left\langle {u\dfrac{{\partial {\rm{MSE}}}}{{\partial x}}} \right\rangle  \left\langle {v\dfrac{{\partial {\rm{MSE}}}}{{\partial y}}} \right\rangle  \left\langle {\omega \dfrac{{\partial {\rm{MSE}}}}{{\partial p}}} \right\rangle + \left\langle {{Q_1}} \right\rangle  \left\langle {{Q_2}} \right\rangle \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \approx  \left\langle {u\dfrac{{\partial {\rm{MSE}}}}{{\partial x}}} \right\rangle  \left\langle {v\dfrac{{\partial {\rm{MSE}}}}{{\partial y}}} \right\rangle  \left\langle {\omega \dfrac{{\partial {\rm{MSE}}}}{{\partial p}}} \right\rangle + \left\langle {{Q_R}} \right\rangle + {\rm{SH}} + {\rm{LH,}} \end{array}$$ (5) where
$$\left\langle {{Q_1}} \right\rangle \approx \left\langle {{Q_R}} \right\rangle + {\rm{LP}} + {\rm{SH}} = \left\langle {{Q_{{\rm{clr}}}}} \right\rangle + \left\langle {{Q_{{\rm{cld}}}}} \right\rangle + {\rm{LP}} + {\rm{SH}},$$ (6) $$\hspace{148pt} \left\langle {{Q_2}} \right\rangle \approx {\rm{LP}}  {\rm{LH}}, $$ (7) $$\hspace{60pt} \left\langle {{Q_{\rm{m}}}} \right\rangle = \left\langle {{Q_1}} \right\rangle  \left\langle {{Q_2}} \right\rangle \approx \left\langle {{Q_R}} \right\rangle + {\rm{SH}} + {\rm{LH}}.$$ (8) In the equations above, 〈〉 represents a column integration from 1000 to 100 hPa. The lefthand side in Eq. (5) describes the time change rate of the columnintegrated MSE, whereas the righthand side in Eq. (5) consists of various terms that affect the MSE tendency, including the columnintegrated horizontal advection, vertical advection, radiative heating, surface sensible, and LH. The columnintegrated total diabatic heating 〈Q_{1}〉can be expressed as the sum of the columnintegrated radiative heating 〈Q_{R}〉, SH, LH, and precipitation induced condensational heating (LP). 〈Q_{R}〉 can be decomposed into a clearsky 〈Q_{clr}〉 and a cloudy 〈Q_{cld}〉 component. 〈Q_{2}〉 represents the columnintegrated net LP and evaporative cooling terms, which may be expressed as a difference between LP and LH. 〈Q_{m}〉 can be regarded as a net diabatic heating term in the MSE budget equation. Substituting Eq. (2) into Eq. (5), one may obtain
$$\begin{aligned} & \left\langle\dfrac{\partial }{{\partial t}}\left[{c_p}T + {L_v}q + {{\rm{g}}z} \right] \right\rangle =  \left\langle u\dfrac{\partial }{{\partial x}}\left[{c_p}T + {L_v}q + {{\rm{g}}z} \right] \right\rangle \\ &  \left\langle v\dfrac{\partial }{{\partial y}}\left[ {c_p}T + {L_v}q + {{\rm{g}}z} \right] \right\rangle  \left\langle \omega \dfrac{\partial }{{\partial p}}\left[{c_p}T + {L_v}q + {{\rm{g}}z} \right] \right\rangle \\ & + \left\langle {{Q_R}} \right\rangle + {\rm{SH}} + {\rm{LH}}. \end{aligned}$$ (9) Equation (9) can be used to diagnose the zonal asymmetry of MSE tendency, and to understand the MJO propagation mechanism in the “moisture mode” framework.