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The primary observational data used in the current study include the NCEP/DOE (Department of Energy) Reanalysis II (Kanamitsu et al., 2002) and daily OLR product. Both datasets have a horizontal resolution of 2.5° × 2.5°. The analysis focuses on extended summer season (i.e., from May to October) for the period of 1979–2001.
A lagged correlation analysis is employed, with a reference box over the SCS (10°–20°N, 110°–120°E) and BoB (10°–20°N, 85°–95°E) respectively, to derive the structure and evolution features of the QBWO and ISO modes. Propagation vectors are calculated at each grid point based on the maximum lagged correlation coefficient in the surrounding region within a short time window (which is 2 days for the QBWO mode and 5 days for the ISO mode).
In addition to the lagged correlation analysis, a multivariate empirical orthogonal function (EOF) analysis is performed onto the bandpass filtered 850hPa wind and vorticity fields over the Asian monsoon domain (10°S–30°N, 50°E–180°). Based on the leading EOF modes, a composite analysis is further applied to the 850hPa wind and vorticity fields to reveal the spatial structure and evolution characteristics of the two modes.
A 2.5layer atmospheric model (Li and Wang, 1994; Wang and Li, 1994; Wang and Xie, 1997; Jiang et al., 2004) is used to investigate the most unstable mode in the offequatorial region in boreal summer. This model consists of twolevel free atmosphere and a wellmixed planetary boundary layer (PBL). This model is essentially the same as that used previously in studying the planetary zonal scale selection of the equatorial mode at the equator (Li and Zhou, 2009; Li, 2014). The model has a horizontal resolution of 5° longitudes by 2° latitudes and covers the domain of 40°S–40°N, 0°–360°.
The governing equations are linearized based on either an idealized or realistic background mean state. The perturbation condensational heating in the middle troposphere (
${ Q'_{\rm m} }$ ) depends on both the vertically integrated mean and anomalous moisture convergences,$${Q'_{\rm m}} = {\delta _1}{Q_{\rm m}}  {\delta _2}{\bar Q_{\rm m}},$$ (1) where
${Q_{\rm m}}$ represents the total heating,$${Q_{\rm m}} = \frac{{b{L_{\rm c}}}}{{\Delta p}}[  ({\omega '_{\rm m}} + {\bar \omega _{\rm m}}) \times ({\bar q_2}  {\bar q_1})  ({\omega '_{\rm e}} + {\bar \omega _{\rm e}}) \times ({\bar q_{\rm e}}  {\bar q_2})],$$ (2) and
${\bar Q_{\rm m}}$ represents the heating due to the basicstate circulation,$${\bar Q_{\rm m}} = \frac{{b{L_{\rm c}}}}{{\Delta p}}[  {\bar \omega _{\rm m}}({\bar q_2}  {\bar q_1})  {\bar \omega _{\rm e}}({\bar q_{\rm e}}  {\bar q_2})];$$ (3) and
${\delta _1}$ and${\delta _2}$ are SSTdependent heating switchon coefficients (Wang and Li, 1994; Li, 2006),$$ \begin{aligned} & {\delta _1}({\rm{ }}{\delta _2}{\rm{ }}) = \\ & \left\{ {\begin{aligned} & {1, \quad\quad\quad\quad\quad\;\;\;{\rm{ if \;SST}} > {\rm{29}}{\rm{.5, and }}\;{Q_{\rm m}}({\rm{ }}{{\bar Q}_{\rm m}}{\rm{ }}) > 0{\rm{ }}} \\ & {{\rm{(SST  26}}{\rm{.5)/3, \; if \;26}}{\rm{.5}} < {\rm{SST}} < {\rm{29}}{\rm{.5, and }}\;{Q_{\rm m}}({\rm{ }}{{\bar Q}_{\rm m}}{\rm{ }}) > 0} \\ & {0,\quad\quad\quad\quad\quad\;\;\;{\rm{ if \;SST}} < {\rm{26}}{\rm{.5, or }}\;{Q_{\rm m}}({\rm{ }}{{\bar Q}_{\rm m}}{\rm{ }}) < 0{\rm{ }}} \end{aligned}} \right. . \end{aligned} $$ (4) In Eqs. (2) and (3),
$\Delta p$ (= 400 hPa) is the mean depth between the upper and lower freeatmosphere levels, and${\bar q_1}$ ,${\bar q_2}$ , and${\bar q_{\rm e}}$ represent mean specific humidity at the upper level, lower level, and in the boundary layer, respectively. The basicstate humidity fields are the function of specific humidity at the surface, and decay exponentially with height (Wang, 1988). Variables${\omega '_{\rm m}}$ and${\omega '_{\rm e}}$ denote vertical velocities in the middle troposphere and at the top of PBL respectively, while${\bar \omega _{\rm m}}$ and${\bar \omega _{\rm e}}$ denote summer mean vertical velocities at the middle level and the top of PBL respectively. In addition,$b$ (= 0.9) is a fraction parameter measuring the efficiency of precipitation, and${L_{\rm c}}$ is the latent heat of condensation per unit mass.Although simple, this model contains essential dynamics and physics for tropical lowfrequency motion (Wang and Li, 1994). The specified basicstate fields include geopotential height, wind, sea surface temperature (SST), and surface specific humidity derived from the NCEP/DOE Reanalysis II. By integrating the model forward, one may examine the temporal evolution of initial perturbation under the specified background mean state and structure and evolution characteristics of the most unstable mode simulated by the model.