Modulation of tropical cyclone tracks over the western North Pacific by intra-seasonal Indo-western Pacific convection oscillation during the boreal extended summer

Abstract

This study investigates the effect of the intra-seasonal Indo-western Pacific convection oscillation (IPCO) on tropical cyclone (TC) tracks over the western North Pacific (WNP) during the boreal extended summer (May−October). The number of west- and northwest-moving TC tracks is found to sharply increase over the WNP in the positive intra-seasonal IPCO phase. Recurving tracks have greater weight in the negative intra-seasonal IPCO phase. Possible physical mechanisms are further examined in terms of steering flow, energy conversion, and energy propagation. When the intra-seasonal IPCO phase is positive, the first-order moment term of perturbation potential energy (PPE₁) converts into perturbation kinetic energy (PKE) at lower latitudes. The pressure trough spreads farther to the east. Meanwhile, Rossby waves emanating from the convective centers of the intra-seasonal IPCO over the WNP (Wave_WNP) and EEIO (Wave_EEIO) travel into the trough region, thereby deepening the trough. These features enhance the westward and northwestward steering flow between 20°N and about 30°N, sharply increasing the number of straight west- and northwest-moving TC tracks over the WNP. When the intra-seasonal IPCO is in a negative phase, conversion from PPE₁ to PKE at lower latitudes is suppressed and the trough weakens. More PPE₁ converts to PKE in the climatological western Pacific subtropical high (WPSH) region and the WPSH is intensified. Moreover, Wave_EEIO intensifies the north–south ridge of the WPSH over the southern Indian Peninsula. Meanwhile, part Wave_WNP propagate northeastward. These features favor northeastward motion of TCs over the WNP.

Appendices

Appendix A

1.1 The governing equations of the atmospheric layer PPE₁

The governing equations of the atmospheric layer PPE₁$\left({\hat {P}^{\prime}_{a1}},~\;\;{\hat {P}^{\prime}_{a1}}=\left\langle {{C_p}T^{\prime}} \right\rangle\right)$ and perturbation kinetic energy (PKE, $K^{\prime}$) are derived as follows (Wang et al. 2012):

$$\left\{ {\left\langle {\frac{{\partial {{\hat {P}^{\prime}}_{a1}}}}{{\partial t}}} \right\rangle } \right\}= - V{F_{PE}}+{C_k} - HF{B_{PE}}+G,$$

(7)

$$\left\{ {\left\langle {\frac{{\partial K^{\prime}}}{{\partial t}}} \right\rangle } \right\}= - V{F_K} - {C_k}+D - HF{B_K},$$

(8)

where $K^{\prime}=K - \bar {K}$ and ${\text{~}}\overline {{\left( ~ \right)}}$ is the global average; $\overline {{\left( ~ \right)}} =\frac{1}{{4\pi {a^2}}}\mathop \smallint \nolimits_{{ - \frac{\pi }{2}}}^{{\frac{\pi }{2}}} \mathop \smallint \nolimits_{0}^{{2\pi }} \left( ~ \right)d\lambda d\varphi$, where $\varphi$ is latitude and $\lambda$ longitude; $~\left\langle {} \right\rangle =\frac{1}{g}\mathop \smallint \nolimits_{{{p_1}}}^{{{p_2}}} \cdot dp$; $\{$$\}$ represents a horizontal integration with $\left\{ {} \right\}=\iint_{\sigma } {d\sigma }$, where $d\sigma ={a^2}\cos \varphi d\lambda d\varphi$; $a$ is the Earth’s radius; $V{F_{PE}}$ and $V{F_K}$ are vertical fluxes of PPE₁ and PKE, respectively; $V{F_{PE}}=\left\{ {\left\langle {\frac{\partial }{{\partial p}}\left( {\omega {{\hat {P}^{\prime}}_{a1}} - \overline {{\omega {{\hat {P}^{\prime}}_{a1}}}} } \right)} \right\rangle } \right\};~V{F_K}=\left\{ {\left\langle {\frac{\partial }{{\partial p}}\left( {\omega K - \overline {{\omega K}} } \right) - \frac{\partial }{{\partial p}}\left( {\omega \Phi - \overline {{\omega \Phi }} } \right)} \right\rangle } \right\}$, where $\omega$ is the vertical velocity in terms of the pressure coordinate; and ${C_k}=\left\{ {\left\langle {\omega \alpha - \overline {{\omega \alpha }} } \right\rangle } \right\}$ represents the energy conversion between PPE₁ and PKE, where α is the air specific volume. When ${C_k}$ < 0, PPE₁ is converted to PKE, whereas when ${C_k}$ > 0, PKE is converted to PPE₁. $G=\left\{ {\left\langle {Q - \bar {Q}} \right\rangle } \right\}$ represents the PPE tendency associated with diabatic heating of the atmosphere, where $~Q$ is the atmospheric diabatic heating rate. $~HF{B_{PE}}$ and $HF{B_K}$ are the horizontal boundary fluxes of PPE₁ and PKE, respectively, with $HFB_{{PE}} = \left\{ {\left\langle {\nabla _{h} \cdot \left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} \hat{P}_{{a1}}^{\prime } } \right)} \right\rangle } \right\}\;~{\text{and}}~HFB_{K} = \left\{ {\left\langle {\nabla _{h} \cdot \left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} K} \right)} \right\rangle + \left\langle {\nabla _{h} \cdot \left( {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} \Phi } \right)} \right\rangle } \right\},$ where the horizontal wind velocity $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} = u\vec{i} + v\vec{j}$; $u$ and $v$ are the zonal and meridional components of horizontal wind velocity, respectively; ${\nabla _h}$ is the horizontal gradient operator; ${\nabla _h}=\frac{1}{{acos\varphi }}\frac{\partial }{{\partial \varphi }}\vec {i}+\frac{1}{a}\frac{\partial }{{\partial \varphi }}\vec {j}$; $\Phi$ is geopotential; and $D$ represents viscous dissipation, with$D = \left\{ {\left\langle {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{F_{h} }} - \overline{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{V_{h} }} \cdot \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{F_{h} }} }} } \right\rangle } \right\}$ , where $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{F_{h} }}$ is the horizontal friction term.

Appendix B

2.1 Non-stationary Rossby wave ray tracing method in the horizontal non-uniform basic flow

Previous research has suggested that the barotropic vorticity equation is a useful tool to describe Rossby wave propagation (Hoskins and Karoly 1981; Branstator 1983; Hoskins and Ambrizzi 1993). By employing the Mercator projection, the perturbation method, and the Wentzel–Kramers–Brillouin (WKB) approximation, it is possible to obtain a linearized barotropic non-divergent vorticity equation in spherical coordinates (Eq. 9) and dispersion relation (Eq. 10) (Hoskins and Karoly 1981; Li and Li 2012; Li et al. 2015):

$$\left( {\frac{\partial }{{\partial t}}+{{\bar {u}}_M}\frac{\partial }{{\partial x}}+{{\bar {v}}_M}\frac{\partial }{{\partial y}}} \right)\nabla _{M}^{2}\psi ^{\prime}+{\bar {q}_y}\frac{{\partial \psi ^{\prime}}}{{\partial x}} - {\bar {q}_x}\frac{{\partial \psi ^{\prime}}}{{\partial y}}=0,$$

(9)

$$\omega ={\bar {u}_M}k+{\bar {v}_M}l+\frac{{{{\bar {q}}_x}l - {{\bar {q}}_y}k}}{{{K^2}}}~,$$

(10)

where $\psi$ is the stream function; ${\bar {u}_M}=\frac{{\bar {u}}}{{\cos \varphi }}$ and ${\bar {v}_M}=\frac{{\bar {v}}}{{\cos \varphi }}$ are the zonal and meridional components of the basic flow in a Mercator projection, respectively; $\bar {q}=\frac{{\nabla _{M}^{2}\bar {\psi }}}{{{{\cos }^2}\varphi }}+2\Omega \sin \varphi$ is the fundamental quantity of absolute vorticity; ${K^2}={l^2}+{k^2}$ is the total wavenumber, where $k$ and$l$ are the zonal and meridional wavenumbers, respectively; and ${\omega}$ is the angular frequency.

The ray path is a trajectory locally tangent to the group velocity vector (Lighthill 1978). Hence, Li and Li (2012) detected the energy dispersion by calculating the ray trajectories, further revealing the impact of meridional basic flow on the wave propagation:

$$f\left( l \right)={\bar {v}_M}{l^3}+k\left( {{{\bar {u}}_M} - {c_x}} \right){l^2}+\left( {{k^2}{{\bar {v}}_M}+{{\bar {q}}_x}} \right)l+\left[ {{k^2}\left( {{{\bar {u}}_M} - {c_x}} \right) - {{\bar {q}}_y}} \right]k=0,$$

(11)

where ${\mathbf{c}}=({c_x},{c_y})$ is the phase velocity.

The zonal and meridional components of group velocity, ${u_g}$ and ${v_g}$, respectively, take the form

$${u_g}=\left( {1+\frac{1}{{1+{l ^2}}}} \right){\bar {u}_M}+\frac{l}{{1+{l ^2}}}{\bar {v}_M} - \frac{l }{{1+{l ^2}}}\frac{l }{k} - \frac{{l \left( {{{\bar {q}}_x}+l {{\bar {q}}_y}} \right)}}{{{k^2}{{\left( {1+{l ^2}} \right)}^2}}},$$

(12)

$${v_g}=\frac{l }{{1+{l ^2}}}{\bar {u}_M}+\left( {1+\frac{{{l ^2}}}{{1+{l ^2}}}} \right){\bar {v}_M} - \frac{{{l ^2}}}{{1+{l ^2}}}\frac{\omega }{l} - \frac{{{{\bar {q}}_x}+l {{\bar {q}}_y}}}{{{k^2}{{\left( {1+{l ^2}} \right)}^2}}}.$$

(13)

Due to the longitudinal and latitudinal variation of the basic state, $l$, $k,$ and $\theta$ (phase) change along the ray paths. Their evolution is determined by kinematic wave theory (Whitham 1960) as follows:

$$\frac{{{d_g}k}}{{dt}}= - \frac{{\partial \omega }}{{\partial x}}= - k\frac{{\partial {{\bar {u}}_M}}}{{\partial y}} - l\frac{{\partial {{\bar {v}}_M}}}{{\partial x}}+\frac{{{{\bar {q}}_{xy}}k - {{\bar {q}}_{xx}}l}}{{{K^2}}},$$

(14)

$$\frac{{{d_g}l}}{{dt}}= - \frac{{\partial \omega }}{{\partial y}}= - k\frac{{\partial {{\bar {u}}_M}}}{{\partial y}} - l\frac{{\partial {{\bar {v}}_M}}}{{\partial x}}+\frac{{{{\bar {q}}_{yy}}k - {{\bar {q}}_{xy}}l}}{{{K^2}}}~,$$

(15)

$$\frac{{{d_g}\theta }}{{dt}}=\frac{{\partial \theta }}{{\partial t}}+{{\mathbf{c}}_{\mathbf{g}}} \cdot \nabla \theta ,$$

(16)

where $\frac{{{d_g}}}{{dt}}=\frac{\partial }{{\partial t}}+{u_g}\frac{\partial }{{\partial x}}+{v_g}\frac{\partial }{{\partial y}}$ denotes the Lagrangian variation moving at the group velocity; $~{{\mathbf{c}}_{\mathbf{g}}}=\left( {{u_g},{v_g}} \right)$ is local group velocity. Therefore, the ray trajectory and phase evolution can be integrated through Eqs. (14)−(16) using Runge–Kutta methods if the basic and initial states are known.