### Observation and data

We conducted radiosonde observations from the R/V Hakuho-maru during December 23–26, 2012 as a part of the Vietnam Philippines Rainfall Experiment (VPREX) 2012 (http://www.jamstec.go.jp/rigc/j/tcvrp/mhcrt/vprex.html) under the Asian Monsoon Year 2007–2012 project (Wang et al. 2010). Figure 1 shows the observation sites and the launch times of the radiosondes. We launched radiosondes at 6- or 12-h intervals during December 23–24 between 29°N and 21°N along the cruise track from north to south. At the southernmost site (21°N, 133°E), we carried out a fixed-point observation at 3-h intervals for about 1.5 days during December 24–25. We then performed an energy budget analysis with the fixed-point observation data combined with the operational radiosonde data from the nearby Japan Meteorological Agency upper-air stations, Minamidaitojima (26°N, 131°E) and Chichijima (27°N, 142°E). We also used the National Centers for Environmental Prediction (NCEP) reanalysis II (Kanamitsu et al. 2002) to examine the large-scale background fields and the Tropical Rainfall Measuring Mission (TRMM) 3B42 data set (e.g., Kummerow et al. 2000) to examine the rainfall intensity.

### Thermal and moisture budget analysis

We performed a thermal and moisture budget analysis and compared the results with those obtained by Ninomiya (1975) from AMTEX ‘74. In order to compare these results, we used the same formula and vertical coordinates as those used by Ninomiya (1975), which are briefly described below.

The heat energy and moisture continuity equations averaged over a certain area are written as follows:

$$\begin{array}{@{}rcl@{}} \frac{\delta T}{\delta t} + \frac{\partial}{\partial p} \overline{\omega ' T'} &=& \frac{d T_{R}}{d t} + \frac{L}{C_{p}} m, \end{array} $$

(1)

$$\begin{array}{@{}rcl@{}} \frac{\delta q}{\delta t} + \frac{\partial}{\partial p} \overline{\omega ' q'} &=& - m, \end{array} $$

(2)

where *T* is temperature, *p* is pressure, *ω* is the vertical *p*-velocity, *d**T*_{
R
}/*d**t* is the heating rate due to net radiation, *C*_{
p
} is the specific heat of dry air at constant pressure, *q* is the water vapor mixing ratio, *L* is the latent heat of condensation, *m* is the net condensation, the overbar \(\overline {X}\) denotes the area-averaged value of the variable *X*, and the prime *X*^{′} denotes the deviation from \(\overline {X}\). The individual changes, the changes in the area-averaged quantities following the motion, of temperature and moisture were calculated from the area-averaged thermodynamic and moisture budget equations as follows:

$$\begin{array}{@{}rcl@{}} \frac{\delta T}{\delta t} &=& \frac{\partial \overline{T}}{\partial t} + \overline{\boldsymbol{v} \cdot \nabla T} + \overline{\omega} \left(\frac{\partial \overline{T}}{\partial p} - \frac{R}{C_{p}} \frac{\overline{T}}{p} \right), \end{array} $$

(3)

$$\begin{array}{@{}rcl@{}} \frac{\delta q}{\delta t} &=& \frac{\partial \overline{q}}{\partial t} + \overline{\boldsymbol{v} \cdot \nabla q} + \overline{\omega} \frac{\partial \overline{q}}{\partial p}, \end{array} $$

(4)

where *v* is the horizontal wind and *R* is the gas constant. The individual change in the equivalent temperature is obtained by eliminating the net condensation *m* from Eqs. (1) and (2) as follows:

$$\begin{array}{@{}rcl@{}} \frac{\delta}{\delta t} \left(T+\frac{L}{C_{p}}q\right) &=& -\frac{\partial}{\partial p} \overline{\omega ' \left(T' + \frac{L}{C_{p}}q' \right)} + \frac{d T_{R}}{d t}. \end{array} $$

(5)

By integrating Eq. (5) from the surface (*p*_{SFC}) to a given pressure level (*p*), the eddy transport of the total heat energy \(F_{c} = -1/g \left (C_{p}\overline {\omega ' T'} + L\overline {\omega ' q'}\right)\) can be evaluated as follows:

$$ \begin{aligned} {}F_{c}(p) = &-\frac{1}{g} \int_{p}^{p_{\text{SFC}}} \frac{\delta}{\delta t} \left({C_{p}}T+Lq\right)dp - \frac{1}{g} F_{c}(p_{\text{SFC}})\\ &+ \frac{C_{p}}{g} \int_{p}^{p_{\text{SFC}}} \frac{d T_{R}}{d t} dp, \end{aligned} $$

(6)

where *g* is the gravitational acceleration, the second term on the right-hand side can be evaluated beforehand by integrating Eq. (5) from the surface to the top level under the assumption that the eddy heat and moisture transport vanish at the top level as described below, and the third term on the right-hand side can be evaluated by assuming that the radiative heating rate at each layer is as described below.

The area-average of the abovementioned thermodynamic quantities was calculated from the data obtained at R/V Hakuho-maru, Minamidaitojima, and Chichijima. The horizontal gradient and the horizontal divergence were calculated by fitting of the plane surface to the data from the three observation stations as in Davies-Jones (1993).

As in Ninomiya (1975), we evaluate the thermodynamic quantities in three layers: (1) between the surface and 850 hPa, (2) between 850 and 700 hPa, and (3) between 700 and 500 hPa. We assume that the eddy transport of heat and moisture vanish at 500 hPa.

The vertical *p*-velocity was estimated by accumulation of the horizontal divergence. The surface vertical *p*-velocity was calculated from the time derivative of the surface pressure. The original estimate of the vertical *p*-velocity *ω*_{org} was adjusted in order to reduce the estimate errors as follows:

$$\begin{array}{@{}rcl@{}} \omega &=& \omega_{\text{org}} - \Delta \omega \\ &=& \omega_{\text{org}} - \left(p - p_{\text{sfc}} \right) \frac{\omega_{\mathrm{org,top}} - \omega_{\text{top}}}{p_{\text{top}}-p_{\text{sfc}}}, \end{array} $$

where subscripts top and sfc denote the top level (500 hPa in this study) and the surface, respectively. The vertical *p*-velocity at the top level *ω*_{top} was estimated by

$$ \omega_{\text{top}} = - \left(\frac{\partial \overline{T}}{\partial t} + \overline{\boldsymbol{v} \cdot \nabla T} - \frac{dT_{R}}{dt} \right) \bigg/ \left(\frac{\partial \overline{T}}{\partial p} - \frac{R}{C_{p}} \frac{\overline{T}}{p} \right), $$

and assuming thermodynamic balance between the adiabatic motion and the radiative heating. This assumption is reasonable because condensation and evaporation did not seem to occur under the dry conditions observed at this level (the relative humidity was under 40%, not shown), and the eddy heat transport from the sea surface did not seem to penetrate the 700 hPa pressure level as discussed later.

For the radiative heating rate *d**T*_{
R
}/*d**t*, the climatological values near 20°N and 135°E taken from Katayama (1967) are used as in Ninomiya (1975). They are −0.042, −0.034, and −0.062 K/h for the layers between the surface and at 850 hPa, 850–700 hPa, and 700–500 hPa, respectively, and are insignificant compared with the other terms in the budget analysis of this study (e.g., the change in the equivalent temperature in the near-surface layer was estimated as about 0.5 K/hr).

The net condensation *m* was assumed to be zero, as we found no TRMM 3B42 precipitation over the analysis area during the analysis period (from 1200 UT on December 24 to 1200 UT on December 25).