: 2. $B;29MJ88%(B : $B<>=aBg5$$K$*$1$k(B 2 $B : $B<>=aBg5$$K$*$1$k(B 2 $B

• 1.1 $B1?F0J}Dx<0!&05NOJ}Dx<0!&G.$N<0!&:.9gHf$NJ]B8<0(B
• 1.2 $B1@HyJ*M}2aDx$N%Q%i%a%?%j%
• 1.3 $BJ|
• 1.4 $BMpN.:.9g$N%Q%i%a%?%j%
  • 1.4.1 $B1?F0J}Dx<0Cf$N3H;69`(B
  • 1.4.2 $BG.NO3X$N<0$N3H;69`(B
  • 1.4.3 $BMpN.1?F0%(%M%k%.!<$N<0(B
  • 1.4.4 $B;60o2CG.9`$NI=8=(B

1. $B4pACJ}Dx<07O(B

$BK\?tCM%b%G%k$O?eJ?!&1tD>$N(B 2 $B, $B1tD>J}8~$N:BI8JQ?t$r(B $z$ $B$HI=$7(B, $B;~4VJ}8~$NJQ?t$O(B $t$ $B$HI=$9(B.

1.1 $B1?F0J}Dx<0!&05NOJ}Dx<0!&G.$N<0!&:.9gHf$NJ]B8<0(B

$BNO3XE*$JOHAH$_$O(B, $B=`05=LJ}Dx<07O(B(Klemp and Wilhelmson,1978)$B$rMQ$$$k(B. $B$3$NJ}Dx<07O$G$O(B, $BM=JsJQ?t$r?eJ?0lMM$J4pK\>l$H$=$3$+$i$N$:$l$KJ,N%$7(B, $BJ}Dx<0$N@~7A2=$r9T$C$F$$$k(B. $BJ}Dx<0Cf$NJQ?t$OIUO?(B D $B$K<($9(B.

$B0J2<$K=`05=LJ}Dx<07O$N;~4VH/E8J}Dx<0$r0lMw$9$k(B. $BL)EY$N<0$G$O4%[email protected],$H<>[email protected],$NJ,;RNL$N:9$r9MN8$9$k$,(B, $BG.$N<0$G$O9MN8$7$J$$(B. $B$^$?05NOJ}Dx<0$G$OHsCGG.2CG.$K$h$kBg5$$NKDD%$H(B, $B6E=L$KH<$&05NOJQ2=$rL5;k$7$F$$$k(B.

$B1?F0J}Dx<0(B

$$\DP{u}{t} = - \left( u \DP{u}{x} + w \DP{u}{z} \right) - {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{x} + Turb.u$$ (1.1)

$$\DP{w}{t} = - \left( u \DP{u}{x} + w \DP{u}{z} \right) - {c_{p}}_{d} \bar{\theta_{v}} \DP{\pi}{z} + Turb.w$$

$$+ \left( \frac{\theta}{\bar{\theta}} + \frac{\sum q_{v}/M_{v}}{1/... ... - \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}} {1 + \sum \bar{q_{v}}} \right) g$$ (1.2)

$B05NOJ}Dx<0(B

$$\DP{\pi}{t} = - \frac{\overline{{C_{s}}^{2}}}{{c_{p}}_{d} \bar{\rho} \bar{\theta_{v}}^{2}} \DP{}{x_{j}}(\bar{\rho} \bar{\theta_{v}} u_{j})$$ (1.3)

$BG.$N<0(B

$$\DP{\theta}{t} = - \left( u \DP{\theta}{x} + w \DP{\theta}{z} \right) - w\DP{\bar{\theta}}{x} + \Dinv{\bar{\pi}} \left(Q_{cnd} + Q_{rad} + Q_{dis}\right)$$

$$+ Turb.\bar{\theta} + Turb.\theta$$ (1.4)

$B:.9gHf$NJ]B8<0(B

$$\DP{q_{v}}{t} = - \left( u \DP{q_{v}}{x} + w \DP{q_{v}}{z} \right) - w\DP{\bar{q_{v}}}{x} + Src.q_{v} + Turb.q_{v} + Turb.\bar{q_{v}},$$ (1.5)

$$\DP{q_{c}}{t} = - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right) + Src.q_{c} + Turb.q_{c}$$ (1.6)

$$\DP{q_{r}}{t} = - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right) + Src.q_{r} + Fall.q_{r} + Turb.q_{r}$$ (1.7)

$B$?$@$7(B, $\bar{~}$ $B$NIU$$$?JQ?t$O?eJ?0lMM$J4pK\>l$G$"$k$3$H$r<($7(B, $B>eIU$-E:$(;z(B $c$ mail protected],$r<($9(B.

$B%(%/%9%J!<4X?t(B $\pi$

$$\pi \equiv \left(\frac{p}{p_{0}}\right)^{R_{d}/{c_{p}}_{d}}$$ (1.8)

$B290L(B $\theta$

$$\theta \equiv T \left(\frac{p_{0}}{p}\right)^{R_{d}/{c_{p}}_{d}} = \frac{T}{\pi}$$ (1.9)

$BL)EY(B $\rho$

$$\rho = \frac{p}{R_{d}T} \left( \frac{1/{M_{d}}} {1/M_{d} + \sum{{q_{v}}/{M_{v}}}} \right) \left( 1 + \sum q_{v} + \sum q_{c} + \sum q_{r} \right)$$

$$= \frac{p}{R_{d}T_{v} } = \frac{p_{0} \pi^{{c_{v}}_{d}/R_{d}}}{R_{d} \theta_{v}}$$ (1.10)

$B2>290L(B $\theta_{v}$

$$\theta_{v} = \frac{\theta}{ \left( \frac{1/M_{d}} {1/M_{d} + \sum... ...v}}/{M_{v}}}} \right) \left( 1 + \sum q_{v} + \sum q_{c} + \sum q_{r} \right) }$$ (1.11)

$B2;GHB.EY(B ${C_{s}}^{2}$

$${C_{s}}^{2} = \frac{{c_{p}}_{d}}{{c_{v}}_{d}} R_{d} \pi \theta_{v}$$ (1.12)

1.2 $B1@HyJ*M}2aDx$N%Q%i%a%?%j%

$BJ}Dx<07O$K4^$^$l$k6E=L$K$h$k2CG.9`(B $Q_{cnd}$, $B@[email protected]`(B $Src$, $BMn2<9`(B $Fall$ $B$NI>2A$O(B, $BCfEg(B(1998)$B$GMQ$$$i$l$?(B Kessler (1969) $B$N%Q%i%a%?%j%$&(B.

$BCH$+$$1+$N%P%k%/K!$N%Q%i%a%?%j%

$B5-9f(B	$B0UL#(B	$BFbMF(B
$q_{v}$	$B5$Aj$N:.9gHf(B	$B5$BN$N>uBV$GBg5$Cf$KB8:_$9$k?e(B
$q_{c}$	$B1@?e:.9gHf(B	$BMn2
		$BDL>o(B 100 $\mu$m $B0J2<$NHy>.$JN.BNN3;R$G$"$k(B.
$q_{r}$	$B1+?e:.9gHf(B	$BM-0U$JMn2

$B$=$7$F(B, $BHyJ*M}AG2aDx$H$7$F0J2<$r9MN8$9$k(B. $B$?$@$7(B, $B$3$l$i$NNL$OA4$F@5$NCM$H$7$FDj5A$5$l(B, $B?e>x5$$,D>@\1+?e$K6E7k$9$k2aDx$OL5;k$5$l$F$$$k(B.

$B5-9f(B	$BFbMF(B
$CN_{vc}$	$B6E7k$K$h$k?e>x5$$+$i1@?e$X$NJQ49(B (condensation)
$EV_{cv}$	$B>xH/$K$h$k1@?e$+$i?e>x5$$X$NJQ49(B (evaporation)
$EV_{rv}$	$B>xH/$K$h$k1+?e$+$i?e>x5$$X$NJQ49(B (evaporation)
$CN_{cr}$	$BJ;[email protected]$K$h$k1@?e$+$i1+?e$X$NJQ49(B.
	$BJ;9g$d?e>x5$3H;6$K$h$j(B, $B1@N3;R$,1+N3$NBg$-$5$K$^[email protected]$9$k(B (autocondensation)
$CL_{cr}$	$B>WFMJ;9g$K$h$k1@?e$+$i1+?e$X$NJQ49(B. $BBg?eE)$,>.?eE)$r>WFMJ;(B $B9g$9$k(B (collection)
$PR_{r}$	$B1+?e$N=ENOMn2<$KH<$&1+?e:.9gHf$NJQ2=N((B (Precipitation)

$B$3$NHyJ*M}AG2aDx$rMQ$$$F(B (1.5) - (1.7) $B<0$r=q$-D>$9$H(B, $B0J2<$N$h$&$K$J$k(B.

$$\DP{\theta}{t} = - \left( u \DP{\theta}{x} + w \DP{\theta}{z} \right) - w\DP{\bar{... ...x} + \frac{L}{{c_{p}}_{d} \bar{\pi}} \left( CN_{vc} - EV_{cv} - EV_{rv} \right)$$

$$+ \Dinv{\bar{\pi}} \left(Q_{rad} + Q_{dis}\right) + Turb.\bar{\theta} + Turb.\theta$$ (1.13)

$$\DP{q_{v}}{t} = - \left( u \DP{q_{v}}{x} + w \DP{q_{v}}{z} \right) - w\DP{\bar{q_{v}}}{x} - \left( CN_{vc} - EV_{cv} - EV_{rv} \right)$$

$$+ Turb.q_{v} + Turb.\bar{q_{v}},$$ (1.14)

$$\DP{q_{c}}{t} = - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right) + ( CN_{vc} - EV_{cv} - CN_{cr} - CL_{cr}) + Turb.q_{c},$$ (1.15)

$$\DP{q_{r}}{t} = - \left( u \DP{q_{c}}{x} + w \DP{q_{c}}{z} \right) + (CN_{cr} + CL_{cr} - EV_{rv} ) + PR_{r} + Turb.q_{r}$$ (1.16)

$B$3$3$G(B, $\gamma = L_{v}/ ({c_{p}}_{d} \pi)$ $B$G$"$j(B, $L_{v}$ $B$O?e$N>xH/$N@xG.(B[J K$^{-1}$ kg$^{-1}$], ${c_{p}}_{d}$ $B$O4%AgBg5$$NDj05HfG.(B[J K kg$^{-1}$], $\pi$ $B$O%(%/%9%J!<4X?t$G$"$k(B.

$BHyJ*M}AG2aDx$O0J2<$N$h$&$KDj<02=$9$k(B.

$B?e>x5$$H1@?e$N4V$NJQ49(B: $-CN_{vc} + EV_{cv}$

 
$B1@?e$ON3$,>.$5$/(B, $B?e>x5$$H$N4V$G=V4VE*$KK0OBD4@a$,5/$3$k$b$N(B $B$H$9$k(B. $B$9$J$o$A(B, $B0\N.$J$I$N9`$r7W;;$7$?8e$N29EY$H?e>x5$NL$,(B $B2aK0OB>uBV$H$J$C$F$$$k>l9g$K$O(B, $B$A$g$&$IK0OB$K$J$kNL$N?e>x5$(B $B$r6E=L$5$;$k(B. $B0lJ}(B, $B0\N.$J$I$N9`$r7W;;$7$?8e$K(B, $B1@?e$,B8:_$9(B $B$k$K$b94$o$i$:L$K0OB$K$J$C$F$$$k>l=j$G$O(B, $B$A$g$&$IK0OB$K$J$k(B $BNL$N1@?e$r>xH/$5$;$k(B.

$B1@?e$NJ;[email protected](B: $CN_{cr}$

 
Kessler (1969) $B$K=>$C$F(B, $B0J2<$N$h$&$KM?$($k(B.

$$CN_{cr} = ( q_{c} - q_{c0} ) / \tau _{ac}$$ (1.17)

$B1@?e$N>WFMJ;9g(B: $CL_{cr}$

 
Kessler (1969) $B$K=>$C$F(B, $B0J2<$GDj<02=$9$k(B.

$$CL_{cr} = 2.2 q_{c} (\bar{\rho} q_{r})^{0.875} .$$ (1.18)

$B1+?e$N>xH/(B: $EV_{rv}$

 

$$EV_{rv} = 4.85 \times 10^{-2} (q_{vsw} - q_{v}) (\bar{\rho} q_{r})^{0.65}$$ (1.19)

$B1+?e$N%U%i%C%/%9(B: $PR_{r}$

 
$B1+?e$N=ENOMn2<$K$h$k:.9gHf$NJQ2=N($O(B,

$$PR_{r} = \Dinv{\bar{\rho}} \DP{}{z}(\bar{\rho} U_{r} q_{r}).$$ (1.20)

$B$G$"$j(B, $B1+?e$N=*C [m s$^{-1}$] $B$O(B

$$U_{r} = 12.2 (q_{r})^{0.125}$$ (1.21)

$B$GM?$($k(B.

1.3 $BJ|

$BJ| $B$O@5L#$N>e8~$-J| $B$rMQ$$$F(B $B0J2<$N$h$&$KI=$5$l$k(B.

$$Q_{rad} = - \frac{1}{\overline{\rho}c_{p_{d}}}\DD{F_{net}}{z}$$

$BK\%b%G%k$G$O(B $F_{net}$ $B$OM[$K7W;;$;$:(B, $Q_{rad}$ $B$O9bEY$N$_$K0MB8$9$k(B $B%Q%i%a%?$H$7$FM?$($k(B.

1.4 $BMpN.:.9g$N%Q%i%a%?%j%

1.4.1 $B1?F0J}Dx<0Cf$N3H;69`(B

Klemp and Wilhelmson (1978) $B$*$h$S(B CReSS ($BDZLZ$H:g86(B, 2001) $B$HF1MM$K(B, 1.5 $B

$$Turb.{u_{i}} = - \DP{}{x_{j}} \overline{(u_{i}^{\prime} u_{j}^{\prime})}$$

$$= - \DP{}{x_{j}} \left[ - K_{m} \left(\DP{u_{i}}{x_{j}} + \DP{u_{j}}{x_{i}}\right) + \frac{2}{3} \delta_{ij} E \right].$$ (1.22)

$B$3$3$G(B $K_{m}$ $B$O1?F0NL$KBP$9$kMpN.3H;678?t$G$"$j(B, $E$ $B$O(B $B%5%V%0%j%C%I%9%1!<%k$NMpN.1?F0%(%M%k%.!<(B

$$E = \frac{1}{2} \overline{(u^{\prime})^{2} + (w^{\prime})^{2}} = \frac{{K_{m}}^{2}}{C_{m}^{2} l^{2}}$$ (1.23)

$B$G$"$k(B.

1.4.2 $BG.NO3X$N<0$N3H;69`(B

Klemp and Wilhelmson (1978) $B$*$h$S(B CReSS ($BDZLZ$H:g86(B, 2001) $B$HF1MM$K(B, 1.5 $B

$$Turb.{\theta} = - \DP{}{x_{j}} \overline{u_{i}^{\prime} \theta^{\prime}}$$

$$= - \DP{}{x_{j}} \left(K_{h}\DP{\theta}{x_{j}}\right) .$$ (1.24)

$B$3$3$G(B $K_{h}$ $B$O290L$KBP$9$kMpN.3H;678?t$G$"$k(B.

1.4.3 $BMpN.1?F0%(%M%k%.!<$N<0(B

Klemp and Wilhelmson (1978) $B$*$h$S(B CReSS ($BDZLZ$H:g86(B, 2001) $B$HF1MM$K(B, 1.5 $B

$$\DP{K_{m}}{t} = - \left( u \DP{K_{m}}{x} + w \DP{K_{m}}{z} \right) - \frac{3 g C_{m}^{2} l^{2}}{ 2 \overline{\theta_{v}}} \left(\DP{\theta_{el}}{z} \right)$$

$$+ \left( C_{m}^{2} l^{2} \right) \left\{ \left( \DP{u}{x} \right)^{2} + \left( \DP{w}{z} \right)^{2} \right\}$$

$$+ \frac{ C_{m}^{2} l^{2} }{2} \left( \DP{u}{z} + \DP{w}{x}\right)^{2} - \frac{K_{m}}{3} \left( \DP{u}{x} + \DP{w}{z} \right)$$

$$+ \Dinv{2} \left(\DP[2]{K_{m}^{2}}{x} + \DP[2]{K_{m}^{2}}{z} \right) + \left(\DP{K_{m}}{x}\right)^{2} + \left(\DP{K_{m}}{z}\right)^{2}$$

$$- \Dinv{2 l^{2}} K_{m}^{2}$$ (1.25)

$B$3$3$G(B $C_{\varepsilon} = C_{m} = 0.2$, $B:.9g5wN%(B $l = \left(\Delta x \Delta z \right)^{1/2}$ $B$H$9$k(B. $B$?$@$7(B $\Delta x, \Delta z$ $B$O$=$l$>$l?eJ?$*$h$S1tD>3J;R4V3V$G$"$k(B. $\theta_{el}$ $B$O0J2<$N$h$&$KDj5A$9$k(B

$$\theta_{el} = \overline{ \theta_{v}} + \theta_{v}^{'} \;\;\; (for \;\; q_{c} = 0)$$ (1.26)

$$\theta_{el} = \overline{\theta_{v}} + \theta_{v}^{'} + \frac{ \sum L q_{v}}{{c_p}_{d} \bar{\pi}} \;\;\; (for \;\; q_{c} > 0)$$ (1.27)

$B$?$@$7(B,

$$\overline{\theta_{v}} + \theta_{v}^{'} = \bar{\theta_{v}} \left\{ 1 + \frac{\theta}{\bar{\theta}} + \frac{... ...} - \frac{\sum q_{v} + \sum q_{c} + \sum q_{r}} {1 + \sum \bar{q_{v}}} \right\}$$ (1.28)

$B$G$"$k(B.

1.4.4 $B;60o2CG.9`$NI=8=(B

$B;60o2CG.9`(B $Q_{dis}$ $B$O(B, $BMpN.1?F0%((B $B%M%k%.!<$N;60o9`$r$b$H$K(B, $B0J2<$N$h$&$KM?$($k(B.

$$Q_{dis} = \frac{1}{\overline{c_{p}}}\frac{C_{\varepsilon}}{l} \frac{K_{m}^{3}}{(C_{m}l)^{3}}.$$ (1.29)

$B$3$3$G(B $l=(\Delta x\Delta z)^{1/2}$ $B$G$"$k(B.

: 2. $B;29MJ88%(B : $B<>=aBg5$$K$*$1$k(B 2 $B : $B<>=aBg5$$K$*$1$k(B 2 $B