Forecasts of MJO Events during DYNAMO with a Coupled Atmosphere–Ocean Model: Sensitivity to Cumulus Parameterization Scheme

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  • Corresponding author: Tim LI, timli@hawaii.edu
  • Funds:

    Supported by the NOAA (NA18OAR4310298), NSF (AGS-1643297), and NSFC (41875069). This is SOEST contribution number 1234, IPRC contribution number 1234

  • doi: 10.1007/s13351-019-9062-5

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  • An operational weather forecast model, coupled to an oceanic model, was used to predict the initiation and propagation of two major Madden–Julian Oscillation (MJO) events during the dynamics of the MJO (DYNAMO) campaign period. Two convective parameterization schemes were used to understand the sensitivity of the forecast to the model cumulus scheme. The first is the Tiedtke (TDK) scheme, and the second is the Simplified Arakawa–Schubert (SAS) scheme. The TDK scheme was able to forecast the MJO-1 and MJO-2 initiation at 15- and 45-day lead, respectively, while the SAS scheme failed to predict the convection onset in the western equatorial In-dian Ocean (WEIO). The diagnosis of the forecast results indicates that the successful prediction with the TDK scheme is attributed to the model capability to reproduce the observed intraseasonal outgoing longwave radiation–sea surface temperature (OLR–SST) relationship. On one hand, the SST anomaly (SSTA) over the WEIO was induced by surface heat flux anomalies associated with the preceding suppressed-phase MJO. The change of SSTA, in turn, caused boundary layer convergence and ascending motion, which further induced a positive column-integrated moist static energy (MSE) tendency, setting up a convectively unstable stratification for MJO initiation. The forecast with the SAS scheme failed to reproduce the observed OLR–SST–MSE relation. The propagation characteristics differed markedly between the two forecasts. Pronounced eastward phase propagation in the TDK scheme is attributed to a positive zonal gradient of the MSE tendency relative to the MJO center, similar to the observed, whereas a reversed gradient appeared in the forecast with the SAS scheme with dominant westward propagation. The difference is primarily attributed to anomalous vertical and horizontal MSE advection.
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  • Fig. 1.  Time–longitude sections of OLR fields from (a) ERA-Interim reanalysis and forecasts of the CWBGFS model with (b) TDK scheme and (c) SAS scheme from 1 October to 31 December 2011. Data are averaged from 5°S to 5°N. Contour lines are from NOAA satellite-observed OLR product.

    Fig. 2.  Time series of normalized SST (red curve) and OLR (black curve) anomalies from (a) ERA-Interim and forecasts of the CWBGFS model with (b)TDK scheme and (c) SAS scheme during 1 October to 30 November 2011. Data are averaged over the initiation region (5°S–5°N, 50°–70°E).

    Fig. 3.  Time series of normalized SSTA tendency (red curve) and net surface (SFC) heat flux anomaly (black curve) derived from (a) ERA-Interim data and forecasts of the CWBGFS model with (b) TDK scheme and (c) SAS scheme from 1 October to 30 November 2011. The fields are averaged over the initiation region.

    Fig. 4.  Time series of SSTA tendency (black curve), net surface heat flux anomaly (red curve), and individual components of the surface heat flux anomalies (bars) derived from (a) ERA-Interim and forecasts of the CWBGFS model with (b) TDK and (c) SAS schemes during 1 October to 30 November 2011. All fields are averaged over the initiation region (5°S–5°N, 50°–70°E).

    Fig. 5.  (a–c) Time series of normalized SSTA (black line) and <MSE> anomaly (red curve); (d–f) time–vertical sections of anomalous divergence, (g–i) vertical velocity (ω), and (j–l) MSE tendency fields (shading) and the MSE anomaly fields (contour) during October 2011. All the fields are averaged over the initiation region. Left panels are the results from ERA-Interim, and middle and right panels are the model forecasts with the TDK and SAS schemes, respectively.

    Fig. 7.  Time series of the column integrated anomalous MSE budget terms including anomalous MSE tendency (dMSE/dt), horizontal advection of MSE (Hadvm), vertical advection of MSE (Vadvm) and net diabatic component of MSE budget (QmseF) during 1 October to 30 November 2011, calculated from (a) ERA-Interim and forecasts of the CWBGFS model with (b) TDK and (c) SAS schemes, respectively. All the fields are averaged over the initiation region (5°S–5°N, 50°–70°E)

    Fig. 6.  Time series of normalized SSTA (black) and <MSE> anomaly (red) derived from (a) ERA-Interim and the model forecasts with (b) TDK scheme and (c) SAS scheme during November 2011, averaged over the initiation region

    Fig. 8.  Longitude–time sections of anomalous rainfall (shaded; mm day−1) and OLR averaged over 10°S–10°N from (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes. The lag regression was calculated against the time series of the intraseasonal rainfall anomaly over the central equatorial Indian Ocean (5°S–5°N, 70°–90°E).

    Fig. 9.  Zonal distributions of column integrated anomalous MSE (bar) and MSE tendency (red curve) regressed against intraseasonal rainfall anomaly over the equatorial Indian Ocean (5°S–5°N, 70°–90°E) for (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes.

    Fig. 10.  As in Fig. 9, but for individual anomalous MSE budget terms including anomalous MSE tendency (dmdt), horizontal advection of MSE (hadvm), vertical advection of MSE (wdmdp), and net diabatic component of MSE budget (qmf), calculated from (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes.

    Fig. 11.  Vertical–longitude cross-sections of (a, c, e) regressed vertical pressure velocity anomalies (10−2 Pa s−1) and (b, d, f) moisture anomalies (contour interval multiplied by 4 × 10−6) averaged over 10°S–10°N for (a, b) ERA-Interim and the forecasts with (c, d) TDK and (e, f) SAS schemes.

    Fig. 12.  Vertical–longitude cross-sections of (a, c, e) regressed MSE and (b, d, f) MSE tendency anomalies averaged over 10°S–10°N for (a, b) ERA-Interim and the forecasts with (c, d) TDK and (e, f) SAS schemes.

    Table 1.  List of main parameterization schemes in the CWBGFS model

    RadiationRRTMG (Rapid Radiative Transfer Model for GCMs) scheme (Clough et al., 2005; Iacono et al., 2008)
    CumulusSimplified Arakawa–Schubert (SAS; Pan and Wu, 1995; Han and Pan, 2011); Tiedtke (TDK) scheme (Tiedtke, 1989; Nordeng, 1994)
    Large scale precipitationPredict cloud water scheme (Zhao and Carr, 1997)
    Shallow convectionHan and Pan (2011)
    PBLFirst-order nonlocal scheme (Troen and Mahrt, 1986; Hong and Pan, 1996; Han and Pan, 2011)
    Surface fluxSimilarity theory (Businger et al., 1971)
    Land modelNoah land surface model (Ek et al., 2003)
    Gravity wave dragPalmer et al. (1986)
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Forecasts of MJO Events during DYNAMO with a Coupled Atmosphere–Ocean Model: Sensitivity to Cumulus Parameterization Scheme

    Corresponding author: Tim LI, timli@hawaii.edu
  • 1. Institute of Atmospheric Physics, Department of Atmospheric Sciences, “National” Central University, Taoyuan 32001
  • 2. Key Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environmental Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing 210044
  • 3. Department of Earth and Life Science, University of Taipei, Taipei 10048
  • 4. Central Weather Bureau (CWB), Taipei 10048
Funds: Supported by the NOAA (NA18OAR4310298), NSF (AGS-1643297), and NSFC (41875069). This is SOEST contribution number 1234, IPRC contribution number 1234

Abstract: An operational weather forecast model, coupled to an oceanic model, was used to predict the initiation and propagation of two major Madden–Julian Oscillation (MJO) events during the dynamics of the MJO (DYNAMO) campaign period. Two convective parameterization schemes were used to understand the sensitivity of the forecast to the model cumulus scheme. The first is the Tiedtke (TDK) scheme, and the second is the Simplified Arakawa–Schubert (SAS) scheme. The TDK scheme was able to forecast the MJO-1 and MJO-2 initiation at 15- and 45-day lead, respectively, while the SAS scheme failed to predict the convection onset in the western equatorial In-dian Ocean (WEIO). The diagnosis of the forecast results indicates that the successful prediction with the TDK scheme is attributed to the model capability to reproduce the observed intraseasonal outgoing longwave radiation–sea surface temperature (OLR–SST) relationship. On one hand, the SST anomaly (SSTA) over the WEIO was induced by surface heat flux anomalies associated with the preceding suppressed-phase MJO. The change of SSTA, in turn, caused boundary layer convergence and ascending motion, which further induced a positive column-integrated moist static energy (MSE) tendency, setting up a convectively unstable stratification for MJO initiation. The forecast with the SAS scheme failed to reproduce the observed OLR–SST–MSE relation. The propagation characteristics differed markedly between the two forecasts. Pronounced eastward phase propagation in the TDK scheme is attributed to a positive zonal gradient of the MSE tendency relative to the MJO center, similar to the observed, whereas a reversed gradient appeared in the forecast with the SAS scheme with dominant westward propagation. The difference is primarily attributed to anomalous vertical and horizontal MSE advection.

1.   Introduction
  • The Madden–Julian Oscillation (MJO) is the most pronounced intraseasonal oscillation in the tropics. It was first discovered by Madden and Julian (1971), who analyzed zonal wind and pressure fields over Canton Island in equatorial central Pacific and found a significant 40–50-day power spectrum peak. Recent study by Li et al. (2018) pointed out that this 40–50-day oscillation was detected over the Asian monsoon regions by a Chinese scientist [Xie et al., 1963, see an English transition version (Hsieh et al., 2018)] in 8 yr before Madden and Julian’s seminal discovery.

    With use of more station data across the tropics, Madden and Julian (1972) noted that the 40–50-day signal appeared over the large tropical domain, propagating eastward along the equator. This large-scale propagation characteristic was further confirmed later with modern satellite data and global reanalysis data (e.g., Weickmann, 1983; Murakami and Nakazawa, 1985; Wang and Rui, 1990; Hendon and Salby, 1994). Observational studies showed that during its eastward propagation, MJO may interact with various weather and climate systems such as tropical cyclone, monsoon, and El Niño–Southern Oscillation (Rui and Wang, 1990; Kessler and Kleeman, 2000; Higgins and Shi, 2001; Zhang and Gottschalck, 2002; Zhang, 2005; Li, 2014).

    Numerical weather prediction (NWP) models are regarded as an important tool to predict weather and future climate change, but current state-of-the-art NWP models still have great challenging in realistically capturing the MJO mode. By analyzing 14 IPCC (Intergovernmental Panel on Climate Change) models, Lin et al. (2006) found that a better MJO simulation was achieved in models with a moisture convergence closure. Hung et al. (2013) analyzed MJO and convectively coupled equatorial waves in 20 CMIP5 (Coupled Model Intercomparison Project Phase 5) models, and found that only CNRM-CM5 (Centre National de Recherches Météorologiques) model captured the realistic eastward propagation of MJO. They attributed the much improved simulation compared to the previous version with higher resolution, a new dynamic core, a new radiative scheme, a moisture convergence closure, and a better water vapor and air mass conservation scheme. Jiang et al. (2015) and Wang et al. (2017) evaluated 20-yr climate simulations of 27 state-of-the-art global general circulation models (GCMs) around the world and found that only one fourth of these models were able to reproduce the observed eastward propagation of MJO. Therefore, in order to improve the model performance, a detailed diagnosis of dynamic and thermodynamic processes relevant to MJO propagation and initiation is needed.

    Early theories on MJO eastward propagation include 1) wave convergence–convection interaction [i.e., wave-CISK (Conditional Instability of Second Kind); Lau and Peng, 1987; Hendon, 1988], and 2) wind-induced surface heat exchange (WISHE) or evaporation–wind feedback (Emanuel, 1987; Yano and Emanuel, 1991), and frictional moisture–convective feedback (Wang, 1988; Wang and Rui, 1990; Li and Wang, 1994; Wang and Li, 1994). Other theories suggested that the oscillation may arise from cloud–radiation feedback (Hu and Randall, 1994, 1995; Raymond, 2001; Lin et al., 2004, 2007) or atmosphere–ocean interaction (Lau and Sui, 1997; Jones et al., 1998; Wang and Xie, 1998). Recently, a moisture mode theory was introduced. It emphasizes the important role of MJO-scale moisture in promoting the eastward propagation. Among the moisture mode paradigm, there are two schools of thinking. One emphasized the east–west asymmetry of planetary boundary layer (PBL) moisture anomaly (Hsu and Li, 2012). This zonal asymmetry may induce an unstable stratification in front of MJO convection, leading to eastward propagation. Another emphasized the zonal asymmetry of MJO-scale moist static energy (MSE) tendency (Sobel and Maloney, 2012, 2013; Adames and Kim, 2016)––even in the presence of a zonally symmetric perturbation moisture distribution, the MJO can still move eastward as long as the column-integrated MSE tendency is asymmetric.

    Processes relevant to MJO initiation over the western equatorial Indian Ocean (WEIO) include internal atmospheric dynamics and atmosphere–ocean interaction. The internal atmospheric processes involve PBL moistening prior to convection onset caused by anomalous horizontal advection (Zhao et al., 2013) and triggering of low-level anomalous ascending motion due to warm advection (Jiang and Li, 2005; Li et al., 2015). The atmosphere–ocean interaction mechanism involves a delayed feedback of intraseasonal sea surface temperature anomaly (SSTA), which is caused by a preceding opposite-phase MJO (Li et al., 2008). A global circumnavigating theory was suggested previously (e.g., Lau and Peng, 1987), but this theory was challenged by Li et al. (2015), who pointed out that the upper-tropospheric circumnavigating signal was still far away from the initiation region when MJO convection occurred, and major precursory signals appeared in lower troposphere, not in upper troposphere. Another theory was midlatitude triggering through equatorward Rossby wave energy propagation (Hsu et al., 1990; Matthews and Kiladis, 1999; Pan and Li, 2007), but such a theory requires further observational, theoretical, and modeling support.

    Motivated by the aforementioned studies, we intend to conduct real-case long-lead forecast experiments for the MJOs during the dynamics of the MJO (DYNAMO) period, to understand at what lead to a current NWP model is able to capture the observed MJO initiation and propagation and how sensitive the forecast is to different cumulus convective schemes. If the model forecast is indeed sensitive to the cumulus parameterization scheme, we further diagnose the model output to understand physical mechanisms behind the MJO initiation and propagation.

    The remaining part of this paper is organized as follows. In Section 2, observational data, model, and diagnosis methods are described. In Section 3, simulated MJO initiation and propagation characteristics including the associated SST change in equatorial western Indian Ocean and the zonal asymmetry of MJO-scale MSE tendency are examined. Finally, a summary is given in Section 4.

2.   Data, model, and analysis methods
  • An internationally coordinated observational campaign, namely DYNAMO, was carried out during October 2011–March 2012. Two strong MJO events, namely MJO-1 (from mid October to mid November) and MJO-2 (from mid November to mid December), occurred during the period. The objective of the current study is to conduct 60-day 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 satellite-observed outgoing longwave radiation (OLR) product from NOAA (Liebmann and Smith, 1996) and ERA-Interim 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 one-dimensional 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 200-m depth.

    RadiationRRTMG (Rapid Radiative Transfer Model for GCMs) scheme (Clough et al., 2005; Iacono et al., 2008)
    CumulusSimplified Arakawa–Schubert (SAS; Pan and Wu, 1995; Han and Pan, 2011); Tiedtke (TDK) scheme (Tiedtke, 1989; Nordeng, 1994)
    Large scale precipitationPredict cloud water scheme (Zhao and Carr, 1997)
    Shallow convectionHan and Pan (2011)
    PBLFirst-order nonlocal scheme (Troen and Mahrt, 1986; Hong and Pan, 1996; Han and Pan, 2011)
    Surface fluxSimilarity theory (Businger et al., 1971)
    Land modelNoah land surface model (Ek et al., 2003)
    Gravity wave dragPalmer 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, mid-level, 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 mid-level convection, the large-scale 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 quasi-equilibrium 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 low-frequency background state (LFBS) component, an MJO component, and a high-frequency (HF) component:

    $$X = \bar X + X' + {X^*},$$ (1)

    where $\bar X$ denotes the LFBS component, $ {X'}$ represents the MJO-scale component, and $ {X^*}$ denotes HF component. A 30-day 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 5-day running mean, one may obtain the MJO-scale component with a period of 10–60 days. Subtracting the 5-day 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 cp is the specific heat (1004 J K−1 kg−1), T is the temperature, Lv is the latent heat (2.5 × 106 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 Q1 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, Q2 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 Q1 and Q2 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 large-scale motion (Arakawa and Schubert, 1974). Therefore, the eddy vertical fluxes can be regarded as the main contributions of eddy transports in Q1 and Q2. If the eddy vertical fluxes are assumed negligibly small at the top of the column, the column-integrated eddy fluxes approximate to the sum of the surface sensible heat flux (SH) and latent heat flux (LH), and the column-integrated amount of (e − c) approximates to the precipitation rate (P). The column-integrated 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 left-hand side in Eq. (5) describes the time change rate of the column-integrated MSE, whereas the right-hand side in Eq. (5) consists of various terms that affect the MSE tendency, including the column-integrated horizontal advection, vertical advection, radiative heating, surface sensible, and LH. The column-integrated total diabatic heating 〈Q1〉can be expressed as the sum of the column-integrated radiative heating 〈QR〉, SH, LH, and precipitation induced condensational heating (LP). 〈QR〉 can be decomposed into a clear-sky 〈Qclr〉 and a cloudy 〈Qcld〉 component. 〈Q2〉 represents the column-integrated net LP and evaporative cooling terms, which may be expressed as a difference between LP and LH. 〈Qm〉 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.

3.   Diagnosis of the model forecast results
  • Figure 1 shows the time–longitude sections of OLR fields from ERA-Interim reanalysis and forecasts of the CWBGFS model with the TDK and SAS schemes during 1 October to 31 December 2011. For comparison with satellite observation, observed OLR counterpart is also plotted in contour. The observation in Fig. 1a shows clear eastward propagation of the OLR along the equator for both MJO-1 and MJO-2. While MJO-1 was initiated over WEIO within 50°–70°E around 15 October, the MJO-2 event was initiated around 15 November over the same region. This result is consistent with Li et al. (2015).

    Figure 1.  Time–longitude sections of OLR fields from (a) ERA-Interim reanalysis and forecasts of the CWBGFS model with (b) TDK scheme and (c) SAS scheme from 1 October to 31 December 2011. Data are averaged from 5°S to 5°N. Contour lines are from NOAA satellite-observed OLR product.

    The forecast with the TDK scheme captures to a certain extent the initiation timing and location, as well as the eastward propagation of the two MJO events. The forecast with the SAS scheme, on the other hand, failed to do so. In particular, the initiation of MJO-1 is completely missing, and through the entire forecast period, no clear eastward phase propagation is detected. Rather there is obvious westward phase propagation in the forecast with the SAS scheme.

    The result presented above indicates that the forecast appears very sensitive to the cumulus scheme applied. In the following, we will focus on the diagnosis of the difference between the two sensitivity experiments in MJO initiation and propagation, respectively.

  • An interesting question is why the model with the TDK scheme was able to forecast the initiations of MJO-1 and MJO-2 at 15- and 45-day lead whereas the forecast with the SAS scheme could not. To answer this question, we examine the time series of the intraseasonal (with an approximate period of 10–60 days) OLR and SST anomalies over the WEIO. Figure 2 shows that the observed OLR anomaly led the local SSTA by a few days. This implies that a positive OLR anomaly (i.e., suppressed-phase MJO) led to the development of a warm SSTA, which further led to the OLR phase transition from a positive to a negative value. Thus, the local air–sea interaction seems to play a critical role in the phase transition of both the OLR and SST anomalies over the WEIO.

    Figure 2.  Time series of normalized SST (red curve) and OLR (black curve) anomalies from (a) ERA-Interim and forecasts of the CWBGFS model with (b)TDK scheme and (c) SAS scheme during 1 October to 30 November 2011. Data are averaged over the initiation region (5°S–5°N, 50°–70°E).

    The forecast with the TDK scheme shows a similar OLR–SST evolution characteristic, comparing to the observed. For example, a transition of the OLR anomaly from a positive to a negative value occurred near 15 October for MJO-1 case and near 15 November for MJO-2 case, even though there is higher-frequency fluctuation in both the time series. The peaks of the simulated OLR anomaly led the peaks of the forecasted SSTA in both the MJO-1 and MJO-2 cases.

    On the contrary, the transition from a positive to a negative OLR anomaly was aborted near 15 October for the forecast with the SAS scheme. The second transition near mid November is also unclear. While a warm SSTA was generated in response to a positive OLR anomaly in early October, this SSTA failed to trigger and sustain the MJO-1 convection afterwards. The failure was possibly attributed to the convection closure scheme used in the SAS.

    What generated the intraseasonal SSTA? To illustrate the cause of the SSTA, we diagnose the observed and forecasted surface heat flux anomaly fields over the WEIO. Figure 3 shows the time series of the local SSTA tendency and net surface heat flux anomaly. The two curves are almost overlapped with each other, indicating that the generation of the intraseasonal SSTA is primarily attributed to the heat flux forcing. The high correlations between the SSTA tendency and the net surface heat flux anomaly appear in both the observation and the forecasts.

    Figure 3.  Time series of normalized SSTA tendency (red curve) and net surface (SFC) heat flux anomaly (black curve) derived from (a) ERA-Interim data and forecasts of the CWBGFS model with (b) TDK scheme and (c) SAS scheme from 1 October to 30 November 2011. The fields are averaged over the initiation region.

    Because the net heat flux anomaly consists of shortwave radiation, longwave radiation, LH, and SH components, we further examine the relative contributions of these components. Figure 4 clearly shows that the most important contribution arises from surface shortwave radiation, followed by the LH.

    Figure 4.  Time series of SSTA tendency (black curve), net surface heat flux anomaly (red curve), and individual components of the surface heat flux anomalies (bars) derived from (a) ERA-Interim and forecasts of the CWBGFS model with (b) TDK and (c) SAS schemes during 1 October to 30 November 2011. All fields are averaged over the initiation region (5°S–5°N, 50°–70°E).

    The diagnosis above indicates that the intraseasonal SSTA was caused by the intraseasonal surface heat flux anomalies associated with the suppressed-phase MJO. A natural question is through what processes the warm SSTA further triggered the MJO convection over the WEIO. The top panels in Fig. 5 show the time series of the SSTA and column integrated MSE anomaly averaged over the initiation region (5°S–5°N, 50°–70°E) during October 2011. Note that the observed warm SSTA led a positive column integrated MSE anomaly by a week or so (Fig. 5a). In the “moisture mode” theory, the eastward propagation of the MJO convection/precipitation overlaps well with the eastward propagation of the column integrated MSE, and thus to the first order of approximation, the MJO convective envelope may be represented by the column integrated MSE (Wang et al., 2017). Thus, the result in Fig. 7 implies that a warm SSTA in the WEIO may promote the onset of convection through strengthened local MSE and a convectively unstable stratification (Hsu and Li, 2012; Zhao et al., 2013). The forecast with the TDK scheme reproduced well the local SSTA–MSE relationship (Fig. 5b), while a much weaker MSE response was found in the forecast with the SAS scheme (Fig. 5c).

    Figure 5.  (a–c) Time series of normalized SSTA (black line) and <MSE> anomaly (red curve); (d–f) time–vertical sections of anomalous divergence, (g–i) vertical velocity (ω), and (j–l) MSE tendency fields (shading) and the MSE anomaly fields (contour) during October 2011. All the fields are averaged over the initiation region. Left panels are the results from ERA-Interim, and middle and right panels are the model forecasts with the TDK and SAS schemes, respectively.

    Figure 7.  Time series of the column integrated anomalous MSE budget terms including anomalous MSE tendency (dMSE/dt), horizontal advection of MSE (Hadvm), vertical advection of MSE (Vadvm) and net diabatic component of MSE budget (QmseF) during 1 October to 30 November 2011, calculated from (a) ERA-Interim and forecasts of the CWBGFS model with (b) TDK and (c) SAS schemes, respectively. All the fields are averaged over the initiation region (5°S–5°N, 50°–70°E)

    The lower panels in Fig. 5 illustrate step-by-step physical processes through which a positive SSTA led to the development of a positive column integrated MSE tendency. According to the Lindzen–Nigam mechanism (Lindzen and Nigam, 1987), a warm SSTA could generate a PBL convergence due to SSTA gradient induced pressure gradient force (Fig. 5d). According to mass continuation, the convergence in PBL could further induce anomalous ascending motion in lower troposphere, which, together with anomalous descending motion in the upper troposphere, caused a positive MSE tendency throughout the troposphere (Fig. 5j).

    The forecast with the TDK scheme reproduced well the observed structure and evolution of PBL divergence, vertical motion and MSE tendency. On the other hand, the forecast with the SAS scheme reproduced a relatively weak PBL convergence and vertical velocity response. As a result, the so-generated column integrated MSE anomaly is much weaker.

    A similar sequence among a warm SSTA, a PBL convergence, and an MSE tendency happened during the MJO-2 event (figure ommited). The time evolution of the observed and forecasted SSTA and MSE anomaly during November 2011 is shown in Fig. 6. Similar to the MJO-1, the forecast with the TDK scheme captured the phase relationship between the SSTA and MSE anomaly to a certain extent. Moreover, a much weaker MSE response occurred in the forecast with the SAS scheme.

    Figure 6.  Time series of normalized SSTA (black) and <MSE> anomaly (red) derived from (a) ERA-Interim and the model forecasts with (b) TDK scheme and (c) SAS scheme during November 2011, averaged over the initiation region

    From the MSE budget point of view, one may wonder what are the dominant terms controlling the <MSE> change over the initiation region. To address this question, we plotted the time series of each of <MSE> budget terms averaged over the initiation region (Fig. 7). The temporal correlations between the MSE tendency and the vertical and horizontal advection are positive (about 0.7), exceeding the 95% statistical confidence level. This suggests that the two terms played an important role in setting up a positive <MSE> anomaly. The combined radiative and surface heat flux term, on the other hand, was negatively correlated with the MSE tendency, and thus, it did not play an active role in setting up a positive <MSE> anomaly.

  • Following Jiang et al. (2015) and Wang et al. (2017), we use the “moisture mode” framework to diagnose the MJO propagation dynamics. To illustrate the dominant propagation feature from 1 October to 30 November, a lagged regression analysis was applied to the intraseasonal precipitation field averaged over the equatorial Indian Ocean (5°S–5°N, 70°–90°E) in both the observation and forecasts. All regressed patterns are normalized based on a fixed 3-mm day−1 rainfall anomaly in the region. A reference point over the equatorial central Indian Ocean (0°N, 80°E) was chosen for this lagged regression analysis. The longitude–time evolutions of anomalous rainfall and OLR are depicted in Fig. 8, consistent with the observation, and the forecast with the TDK scheme shows pronounced eastward phase propagation along the equator during the period. This is in great contrast to the forecast with the SAS scheme––marked westward phase propagation appeared during the two-month period.

    Figure 8.  Longitude–time sections of anomalous rainfall (shaded; mm day−1) and OLR averaged over 10°S–10°N from (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes. The lag regression was calculated against the time series of the intraseasonal rainfall anomaly over the central equatorial Indian Ocean (5°S–5°N, 70°–90°E).

    The cause of the distinctive phase propagation characteristics can be explained based on the column-integrated MSE budget diagnosis. By diagnosing the 27 GCMs, Jiang et al. (2015) and Wang et al. (2017) showed that for the models that are able to generate the observed eastward phase propagation, a positive MSE tendency always appears to the east of MJO convective center, while a negative MSE tendency appears to the west of MJO convective center. For those models that simulate westward phase propagation, the zonal asymmetry of the MSE tendency is reversed.

    Figure 9 illustrates the zonal distributions of column integrated MSE tendency relative to the MJO OLR center at 80°E from the observations and the forecasts. It is obvious that the forecast with the TDK scheme captured the correct MSE tendency distribution, with a positive zonal gradient of MSE tendency to the east and a negative tendency to the west of the MJO convective center. On the contrary, the forecast with the SAS generated an opposite zonal gradient with a stronger positive tendency to the west. Such distinctive zonal MSE gradients between the two forecasts are consistent with their propagation characteristics.

    Figure 9.  Zonal distributions of column integrated anomalous MSE (bar) and MSE tendency (red curve) regressed against intraseasonal rainfall anomaly over the equatorial Indian Ocean (5°S–5°N, 70°–90°E) for (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes.

    Further examination of individual MSE budget terms (Fig. 10) indicates that the difference in the MSE tendency asymmetry arose primarily from the vertical MSE advection, followed by the horizontal MSE advection. This result is consistent with Wang et al. (2017) based on the 27 GCM diagnoses. The combined radiative heating and surface heat flux term contributed negatively to the overall MSE tendency asymmetry, indicating that this term favors the westward phase propagation.

    Figure 10.  As in Fig. 9, but for individual anomalous MSE budget terms including anomalous MSE tendency (dmdt), horizontal advection of MSE (hadvm), vertical advection of MSE (wdmdp), and net diabatic component of MSE budget (qmf), calculated from (a) ERA-Interim and the forecasts with (b) TDK and (c) SAS schemes.

    While the forecast with the TDK scheme reproduced a similar zonal distribution in horizontal and vertical MSE advection fields, the forecast with the SAS scheme generated an incorrect vertical and horizontal advection distribution, with a greater positive tendency appearing to the west of MJO convective center. For further understanding the mechanisms related to the different forecast results, the regressed anomalous vertical pressure velocity and moisture distributions are diagnosed (Fig. 11). The observation (Fig. 11a) showed that there was a zonally asymmetric pattern of vertical pressure velocity relative to the convective center. Upward anomalies appeared to the east in PBL and to the west in the upper troposphere. The PBL ascent anomaly to the east was associated with boundary layer convergence (Hsu and Li, 2012). In the rear of MJO convective center, an ascent anomaly caused by the upper-tropospheric stratiform heating appeared in the upper troposphere, while a descent anomaly appeared in the lower troposphere. Such a vertical velocity distribution favors a positive (negative) vertical MSE advection anomaly to the east (west) (Wang et al., 2017) and promotes eastward propagation. The TDK scheme produced a similar but weaker vertical velocity distribution and moisture anomalies to the east in PBL compared to the observation. Such patterns induced a positive column-integrated MSE tendency to the east and led to eastward propagation. In contrast, the SAS scheme produced both the low-level moistening and the ascent anomalies in PBL to the west, and the upper-tropospheric stratiform heating was too weak to identify, resulting in a positive column-integrated MSE tendency to the west and thus westward propagation.

    Figure 11.  Vertical–longitude cross-sections of (a, c, e) regressed vertical pressure velocity anomalies (10−2 Pa s−1) and (b, d, f) moisture anomalies (contour interval multiplied by 4 × 10−6) averaged over 10°S–10°N for (a, b) ERA-Interim and the forecasts with (c, d) TDK and (e, f) SAS schemes.

4.   Conclusions and discussion
  • The initiation and propagation processes of MJOs during the DYNAMO campaign period were investigated through the sensitivity forecast experiments with the CWBGFS coupled model. Two cumulus parameterization schemes (TDK and SAS) were applied. The forecast with the TDK scheme was able to forecast the MJO-1 and MJO-2 initiation at 15- and 45-day lead, while the forecast with the SAS scheme failed to predict the convection onset in the WEIO.

    The diagnosis of the forecast results indicates that the successful prediction with the TDK scheme was attributed to the capability to reproduce the observed intraseasonal OLR–SST relationship. Both the observation and the forecast show a clear phase leading of the intraseasonal OLR anomaly to the SSTA over the WEIO. A further diagnosis of the surface heat flux anomalies indicates that the change of SSTA is primarily controlled by the surface shortwave radiation and LH anomalies associated with the preceding suppressed-phase of the MJO. The change of the SSTA, in turn, caused the PBL convergence and promoted anomalous ascending motion in the lower troposphere, which, working together with upper-tropospheric descending motion anomaly, induced a positive MSE tendency, set up a convectively unstable stratification, and triggered the onset of MJO convection over the WEIO.

    The forecast with the SAS scheme failed to reproduce the observed SSTA–MSE relation over the initiation region. While similar amplitude of the SSTA was generated, the SSTA induced a much weaker MSE tendency, and thus could not cause the convection onset.

    In addition, the propagation characteristics are very different between the two forecasts. Pronounced eastward phase propagation was found along the equator for the forecast with the TDK scheme, whereas westward phase propagation was dominant in the forecast with the SAS scheme. The cause of this difference is attributed to the distinctive zonal distributions of anomalous MSE tendency. A positive zonal gradient of the MSE tendency relative to the MJO convective center was predicted in the forecast with the TDK scheme, while a reversed gradient of the MSE tendency was found in the forecast with the SAS scheme. The sign of the zonal gradient of the MSE tendency determines the propagation direction. A positive gradient favors eastward propagation, while a negative tendency favors westward propagation. A further examination of individual MSE budget terms indicates that the MSE tendency asymmetry is primarily attributed to anomalous vertical advection in both the observation and forecasts, followed by anomalous horizontal advection.

    The distinctive forecast results from the two sensitivity runs provide valuable information about mechanisms behind the MJO initiation and propagation. In order to reproduce active air–sea interaction over the initiation region, a key element for an atmospheric model is to capture the PBL convergence and anomalous MSE setup in response to an SSTA, while a key element for the oceanic model is to generate realistic SSTA in response to atmospheric intraseasonal forcing. To predict realistic eastward phase propagation, a key element for an atmospheric model is to reproduce a realistic three-dimensional MJO dynamic and thermodynamic structure, including a westward tilted vertical velocity and moisture structure (Sperber, 2003; Hsu and Li, 2012) and lower tropospheric wind patterns associated with Kelvin and Rossby wave response to the MJO heating (Li and Wang, 1994; Wang and Li, 1994; Wang et al., 2018). Our diagnosis (Fig.11) shows that the forecast with the TDK scheme captured the westward tilting moisture structure whereas the forecast with SAS scheme generated a weak eastward tilting moisture or MSE structure (Fig.12). In addition to the MJO structure, the mean state difference, particularly in the latter forecast period, may also contribute to the forecast difference. We will further examine this possibility in future endeavor.

    Figure 12.  Vertical–longitude cross-sections of (a, c, e) regressed MSE and (b, d, f) MSE tendency anomalies averaged over 10°S–10°N for (a, b) ERA-Interim and the forecasts with (c, d) TDK and (e, f) SAS schemes.

    An interesting question is how two different cumulus schemes affect MJO forecasts. In general, convection can be viewed conceptually as being driven by two key variables, local buoyance (instability) and moisture content. The closure assumptions, in broad sense, include the approach to define the intensity of the convection and the criteria to determine convective development, i.e., “trigger functions”. Trigger functions are very important to convective parameterization, as they determine where and when the convection develops. It is worth noting that the local buoyancy or surface heating is generally weaker over the tropical oceans than over the continent regions. Therefore, to initiate and sustain the convection over the tropical oceans, low-level moisture convergence is required. TDK scheme assumes that the convection is dependent upon the moisture supply from large-scale moisture convergence and boundary layer turbulence (Tiedtke, 1989). Its trigger functions, cloud-base mass flux and closure for shallow convection are connected to moisture convergence, making this scheme as a moisture-based approach. Nordeng (1994) made further modifications in the organized entrainment based on local buoyancy and a CAPE-type adjustment closure for deep convection. The considerations of both instability and moisture controls allow TDK scheme to have better performance on MJO forecasts. On the other hand, the trigger conditions of SAS scheme are mainly dependent on the local buoyancy, the cloud-base mass flux of shallow convection is determined by the surface buoyant flux (Grant, 2001), and the quasi-equilibrium assumption for deep convection is based on a threshold cloud work function. These make SAS scheme mainly as an instability-control scheme. Over the tropical oceans, the weaker buoyant environment gives rise to the weaker simulations of surface buoyant flux, cloud-base mass flux and shallow convection in SAS scheme, leading to the weaker development of MJOs. Furthermore, a closure based on the threshold cloud work function deduced from observation (Lord, 1978) may induce the environmental instability back to a statistical equilibrium state, which influences the CAPE energy released and the development of MJO in the following life cycle.

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