# LaTeX2HTML 2002-2-1 (1.70) # Associate images original text with physical files. $key = q/(2N_{tr}+1)(N_{tr}+1);MSF=1.6;AAT/; $cached_env_img{$key} = q| $(2N_{tr}+1) (N_{tr}+1)$ |; $key = q/displaystyleDD{S}{z}<0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DD{S}{z} < 0$ |; $key = q/p_s=hat{p_s}+Deltap_s;MSF=1.6;AAT/; $cached_env_img{$key} = q| $p_s = \hat{p_s} + \Delta p_s$ |; $key = q/displaystyle{calF}_varphi(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal F}_\varphi (\varphi, \lambda, \sigma)$ |; $key = q/f^{(n)}=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $f^{(n)}=0$ |; $key = q/displaystyle=T_k-overline{T}_k,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = T_k - \overline{T}_k,$ |; $key = q/displaystyletilde{P}_n^mequivfrac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{P}_n^m \equiv \frac{ (1-\mu^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n .$ |; $key = q/tau_{S,i}(z);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tau_{S,i}(z)$ |; $key = q/JleKle2J-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \le K \le 2J-1$ |; $key = q/dot{calA}_{dif};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\cal A}_{dif}$ |; $key = q/I=128;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/i=1,2,cdots,I.quadj=1,2,cdots,J;MSF=1.6;AAT/; $cached_env_img{$key} = q| $i=1,2,\cdots,I. \quad j=1,2,\cdots,J$ |; $key = q/displaystyle=Dinv{acosvarphi}left{DP{{u_A}_{,k}}{lambda}+DP{({v_A}_{,k}cosvarphihi}right}-nabla^{2}_{sigma}(Phi_k+C_{p}hat{kappa}_koverline{T}_kpi+(;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{{u_A}_{,k}}{\lambda} + \DP{({... ...\} - \nabla^{2}_{\sigma} ( \Phi_k + C_{p} \hat{\kappa}_k \overline{T}_k \pi + ($ |; $key = q/Dvect{D}={D_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Dvect{D}=\{ D_{k} \}$ |; $key = q/tilde{A}_n^m;(m=-M,-M+1,cdots,M,;n=|m|,|m|+1,cdots,N(m));MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{A}_n^m \; (m=-M,-M+1, \cdots,M, \; n=\vert m\vert,\vert m\vert+1,\cdots,N(m))$ |; $key = q/displaystyle=sum_{k=0}^{J-1}(2k+1)(mu-mu_j)tilde{P}_k(mu)tilde{P}_k(mu_j).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{k=0}^{J-1} (2k+1) (\mu-\mu_j) \tilde{P}_k(\mu) \tilde{P}_k(\mu_j).$ |; $key = q/displaystylenabla^{2}_{sigma};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \nabla^{2}_{\sigma}$ |; $key = q/displaystyleDP{zeta}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\zeta}{t}$ |; $key = q/A_{zeta};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{\zeta }$ |; $key = q/-1leqmuleq1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $-1 \leq \mu \leq 1$ |; $key = q/displaystylesum_{i=1}^Iexp(i(m'-m)lambda)=Idelta_{mm'},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{i=1}^I \exp(i(m'-m) \lambda) = I \delta_{mm'} ,$ |; $key = q/mu=mu_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mu=\mu_j$ |; $key = q/r;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleequivT-overline{T},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv T - \overline{T},$ |; $key = q/tau_i(z);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tau_i(z)$ |; $key = q/displaystyleequivleft[DP{}{lambda}left(sum_{m,n}tilde{f}_n^mY_n^m(lambda,varphi)right)right]_{ij}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \left[ \DP{}{\lambda} \left( \sum_{m,n} \tilde{f}_n^m Y_n^m (\lambda, \varphi) \right) \right]_{ij} .$ |; $key = q/{displaystylew_jequivfrac{(2J-1)(1-sin^2varphi_j)}{left{JP_{J-1}(sinvarphi_j)right}^2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle w_j \equiv \frac{(2J-1)(1-\sin^2 \varphi_j)} {\left\{J P_{J-1}(\sin \varphi_j)\right\}^2 } }$ |; $key = q/displaystyle=frac{I}{2}int_{-1}^{1}f_{n'}^{m}P_{n}^{m}(varphi)DD{P_{n'}^m}{varphi}dvarphidelta_{mm'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{I}{2} \int_{-1}^{1} f_{n'}^{m} P_{n}^{m}(\varphi) \DD{P_{n'}^m}{\varphi} d \varphi \delta_{m m'} .$ |; $key = q/p^{*}_{0}=1.4times10^{11};MSF=1.6;AAT/; $cached_env_img{$key} = q| $p^{*}_{0} = 1.4 \times 10^{11}$ |; $key = q/displaystyleequivfrac{1}{2Deltat}left({calA}^{t+Deltat}-{calA}^{t-Deltat}right),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \frac{1}{2 \Delta t} \left( {\cal A}^{t+\Delta t} - {\cal A}^{t-\Delta t} \right) ,$ |; $key = q/displaystyleDP{D}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{D}{t}$ |; $key = q/displaystylew_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle w_j$ |; $key = q/{displaystyleleft(int_a^bf_k(mu)f_{k'}(mu)w(mu)dmu=lambda_kdelta_{kk'}right)};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \left( \int_a^b f_k (\mu) f_{k'} (\mu) w(\mu) d \mu = \lambda_k \delta_{kk'} \right) }$ |; $key = q/displaystyle=frac{1}{2Jtilde{P}_{J-1}(mu_j)tilde{P}^{'}_{J}(mu_j)}sum_{k=0}^{J-1}(2k+1)tilde{P}_k(mu_j)int_{-1}^1tilde{P}_k(mu)dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{2 J \tilde{P}_{J-1}(\mu_j) \tilde{P}^{'}_{J} (\mu_j)} \sum_{k=0}^{J-1} (2k+1) \tilde{P}_k(\mu_j) \int_{-1}^1 \tilde{P}_k(\mu) d \mu$ |; $key = q/T^c_k=T^a_k,q^c_k=q^a_k;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}nabla_H^2Y_n^m&equivfrac{1}{r^2}left[DP{}{mu}left((1-mu^2)DP{}{mus^2varphi}DP[2]{}{lambda}right]Y_n^m&=-frac{n(n+1)}{r^2}Y_n^m{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\nabla_H^2 Y_n^m &\equiv \frac{1}{r^2} \left[ \DP{}{\... ...{\lambda} \right] Y_n^m \ &= - \frac{n(n+1)}{r^2} Y_n^m \end{split}\end{align*}$ |; $key = q/displaystyle=-frac{1}{I}sum_{i,j}f_{ij}left.DD{}{varphi}left(cos^2varphiP_n^mright)right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{I} \sum_{i,j} f_{ij} \left. \DD{}{\varphi} \left( \cos^2\varphi P_n^m \right) \right\vert _j \exp(-im \lambda_i) w_j$ |; $key = q/Jgefrac{2N_{{rmmax}}+1}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \ge \frac{2N_{{\rm max}}+1}{2}$ |; $key = q/displaystyle(hat{p_s}+Deltap_s)q,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (\hat{p_s} + \Delta p_s) q,$ |; $key = q/{displaystyle(g_{ij}=)sum_{m,n}imtilde{f}_n^mY_n^m=sum_{m,n}tilde{g}_n^mY_n^m};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle (g_{ij}=) \sum_{m,n} im \tilde{f}_n^m Y_n^m = \sum_{m,n} \tilde{g}_n^m Y_n^m }$ |; $key = q/displaystyle{calD}(q)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}q.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(q) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} q .$ |; $key = q/{align*}{split}DP{q}{t}&=-Dinv{acosvarphi}left{DP{(uq)}{lambda}+DP{(vqcosvarphi)varphi}right}+qD&quad-dot{sigma}DP{q}{sigma}+S_{q}+{calD}(q).{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{q}{t} &= - \Dinv{a \cos \varphi} \left\{ \DP{... ...uad - \dot{\sigma} \DP{q}{\sigma} + S_{q} + {\cal D}(q). \end{split}\end{align*}$ |; $key = q/[a,b];MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleDeltap_s=ginthat{rho}Deltaqdhat{z}=-ginthat{rho}Deltaqfrac{dhat{p}}{-hat{rho}g}=intDeltaqdhat{p}=hat{p_s}intDeltaqdsigma;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta p_s = g \int \hat{\rho} \Delta q d \hat{z} = -g \int \hat{... ...}}{- \hat{\rho} g} = \int \Delta q d \hat{p} = \hat{p_s} \int \Delta q d \sigma$ |; $key = q/displaystyle(n-|m|+1)tilde{P}_{n+1}^m-(2n+1)mutilde{P}_n^m+(n+|m|)tilde{P}_{n-1}^m=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (n-\vert m\vert+1) \tilde{P}_{n+1}^m - (2n+1) \mu \tilde{P}_n^m +(n+\vert m\vert) \tilde{P}_{n-1}^m = 0 .$ |; $key = q/Jslash2;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleH=lambda-lambda_{subsolar}*frac{180}{pi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle H = \lambda - \lambda_{subsolar} * \frac{180}{\pi}$ |; $key = q/displaystyleF_S(0)=sum_i^{N_S}a_i(1-alpha_g)(1-alpha_A)F_S^Iexp(-tau_{S,i}(0)seczeta),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle F_S(0) = \sum_i^{N_S} a_i (1-\alpha_g) (1-\alpha_A) F_S^I \exp ( - \tau_{S,i}(0)\sec \zeta ) ,$ |; $key = q/displaystyleDP{Dvect{T}}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\Dvect{T}}{t}$ |; $key = q/displaystyleq^a_{k+1}leftarrowq^a_{k+1}-frac{L}{C_p}DP{q^*}{T}frac{q^a_{k+1}-q^*(T^a_{k+1},p_{k+1})}{displaystyle1+frac{L}{C_p}DP{q^*}{T}},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q^a_{k+1} \leftarrow q^a_{k+1} - \frac{L}{C_p} \DP{q^*}{T} \frac{... ...1} - q^*( T^a_{k+1},p_{k+1}) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} } ,$ |; $key = q/displaystylehat{T}_{k-1}+DeltaT_{k-1}-left(hat{T}_{k}+DeltaT_{k}right)+frac{L}{C_{k-1}-q^{*}(hat{T}_{k})-left.DP{q^{*}}{T}right|_{k}DeltaT_{k}right};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k-1} + \Delta T_{k-1} - \left( \hat{T}_{k} + \Delta T_{k... ...{*} (\hat{T}_{k}) - \left. \DP{q^{*}}{T} \right\vert _{k} \Delta T_{k} \right\}$ |; $key = q/|m'-m|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\vert m'-m\vert$ |; $key = q/0lelambda<2pi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le \lambda < 2 \pi$ |; $key = q/displaystyle=Isum_{j=1}^{J}P_n^m(mu_j)P_{n'}^{m}(mu_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = I \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^{m} (\mu_j) w_j$ |; $key = q/displaystyleT_{k-1}-T_{k}+frac{L}{C_p}left{q^{*}(T_{k-1},p_{k-1})-q^{*}(T_{k},p_C_p}frac{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{T_{k-1}+T_{k}}{2}=0,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{k-1} - T_{k} + \frac{L}{C_p} \left\{ q^{*} (T_{k-1}, p_{k-1}) ... ...\frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{T_{k-1} + T_{k}}{2} = 0,$ |; $key = q/displaystylep_{ij}equivleft[DP{}{varphi}left(sum_{m,n}tilde{f}_n^mY_n^mright)right]_{ij}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle p_{ij} \equiv \left[ \DP{}{\varphi} \left( \sum_{m,n} \tilde{f}_n^m Y_n^m \right) \right]_{ij} .$ |; $key = q/I=2M+1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle{calD}(D);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(D)$ |; $key = q/tilde{B}_n^m,tilde{C}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{B}_n^m,\tilde{C}_n^m$ |; $key = q/displaystyle:qquad小規模運動過程(緯度方向),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 小規模運動過程 (緯度方向),$ |; $key = q/displaystyle=left|{array}{ll}(2n+1)xtilde{P}_n(x)-ntilde{P}_{n-1}(x)&tilde{P}_n(x)(2n+1)ytilde{P}_n(y)-ntilde{P}_{n-1}(y)&tilde{P}_n(y){array}right|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \left\vert \begin{array}{ll} (2n+1)x \tilde{P}_n(x)-n\tilde{P}_... ...1)y \tilde{P}_n(y)-n\tilde{P}_{n-1}(y) & \tilde{P}_n(y) \end{array} \right\vert$ |; $key = q/m,m',n,n';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/p_s;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/I=2M;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/k_B;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylesum_{n=0}^{J-1}P_n(mu_j)P_n(mu_{j'})=frac{1}{w_j}delta_{jj'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{n=0}^{J-1} P_n (\mu_j) P_n (\mu_{j'}) = \frac{1}{w_j} \delta_{jj'}$ |; $key = q/displaystylehspace{4em}=-S_{k-1slash2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{4em} = - S_{k-1/2}$ |; $key = q/displaystyle=frac{1}{I}sum_{m'=-M}^{M}sum_{n'=|m'|}^Nsum_{m''=-M}^{M}sum_{n''=|m''|}^Ntilde{B}_{n'}^{m'}tilde{C}_{n''}^{m''};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{m'=-M}^{M} \sum_{n'=\vert m'\vert}^N \sum_{m''=-M}^{M} \sum_{n''=\vert m''\vert}^N \tilde{B}_{n'}^{m'} \tilde{C}_{n''}^{m''}$ |; $key = q/{align*}{split}DP{tilde{q}_n^m}{t}&=-frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}imu_{ij}(lambda_i,varphi_j)w_j&quad+tilde{calD}_{H,n}^mtilde{q}_n^m.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{\tilde{q}_n^m}{t} & = - \frac{1}{I} \sum_{i=1}^{I... ... w_j \ & \quad + \tilde{\cal D}_{H,n}^m \tilde{q}_n^m . \end{split}\end{align*}$ |; $key = q/displaystyleq_{ij}=cos^2varphi_jsum_{m,n}tilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q_{ij} = \cos^2\varphi_j \sum_{m,n} \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i)$ |; $key = q/displaystyle(n-|m|+1)sqrt{frac{1}{2n+3}frac{(n+1+|m|)!}{(n+1-|m|)!}}P_{n+1}^m-(2n+1)sqrt{frac{1}{2n+1}frac{(n+|m|)!}{(n-|m|)!}}muP_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (n-\vert m\vert+1) \sqrt{ \frac{1}{2n+3} \frac{(n+1+\vert m\vert)... ...) \sqrt{ \frac{1}{2n+1} \frac{(n+\vert m\vert)!}{(n-\vert m\vert)!} } \mu P_n^m$ |; $key = q/displaystyle=hat{kappa}_{k}C_{p}overline{T}_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \hat{\kappa}_{k} C_{p} \overline{T}_{k} ,$ |; $key = q/displaystyleT_v(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_v (\varphi, \lambda, \sigma)$ |; $key = q/displaystyle=frac{1}{Deltasigma_{k}}(hat{overline{T}}_{k-1slash2}-overline{T}_{kgma_{k}}(overline{T}_{k}-hat{overline{T}}_{k+1slash2})delta_{k+1=l},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{\Delta \sigma_{k}} ( \hat{\overline{T}}_{k-1/2} - \ove... ... \sigma_{k}} ( \overline{T}_{k} - \hat{\overline{T}}_{k+1/2} ) \delta_{k+1=l} ,$ |; $key = q/displaystylequad+n(-tilde{P}_{n-1}(x)tilde{P}_n(y)+tilde{P}_{n-1}(y)tilde{P}_n(x));MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad +n (- \tilde{P}_{n-1}(x) \tilde{P}_n(y) + \tilde{P}_{n-1}(y) \tilde{P}_n(x) )$ |; $key = q/0lemleM,|m|lenleN;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le m \le M, \vert m\vert \le n \le N$ |; $key = q/{align*}{split}DP{T}{t}&=-Dinv{acosvarphi}left{DP{(uT^{prime})}{lambda}+DP{(vT^{sigma}right)+frac{Q}{C_p}+{calD}(T)+{calD}^{prime}(Dvect{v}).{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{T}{t} &= - \Dinv{a \cos \varphi} \left\{ \DP{... ...ac{Q}{C_p} + {\cal D}(T) + {\cal D}^{\prime}(\Dvect{v}). \end{split}\end{align*}$ |; $key = q/Y_n^m(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $Y_n^m(\lambda,\varphi)$ |; $key = q/k=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=q^{*}(hat{T}_{k},p_{k})+left.DP{q^{*}}{T}right|_{hat{T}_{k}}DeltaT_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = q^{*} (\hat{T}_{k},p_{k}) + \left. \DP{q^{*}}{T} \right\vert _{\hat{T}_{k}} \Delta T_{k},$ |; $key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda=frac{1}{I}sum_{n=1}^{I}g(lambda_n);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda = \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n)$ |; $key = q/displaystyledot{sigma}=0atsigma=0,1.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma} = 0 at \sigma = 0 , 1 .$ |; $key = q/displaystyle=Dinv{acosvarphi}left{DP{{v_A}_{,k}}{lambda}-DP{({u_A}_{,k}cosvarphi)}{varphi}right}+{calD}(zeta_k),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{{v_A}_{,k}}{\lambda} - \DP{({u_A}_{,k} \cos \varphi)}{\varphi} \right\} + {\cal D}(\zeta_k),$ |; $key = q/displaystylehspace{2em}=-S_{k-1slash2}-left(1+gamma_{k-1}-kappafrac{Deltap_{k-1st)frac{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{2em} = - S_{k-1/2} - \left( 1 + \gamma_{k-1} - \kappa \fr... ...rac{1}{ 1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$ |; $key = q/tilde{P}_J;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_J$ |; $key = q/I,J;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/n=0,1,cdots,n-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $n=0,1,\cdots,n-1$ |; $key = q/displaystyle=-sum_{k=1}^{K}(D_k+Dvect{v}_kcdotnablapi)Deltasigma_k,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sum_{k=1}^{K} ( D_k + \Dvect{v}_k \cdot \nabla \pi ) \Delta \sigma_k,$ |; $key = q/displaystyletilde{calD}_{M,n}^m=-K_{HD}left[left(frac{-n(n+1)}{a^{2}}right)^{N_Dslash2}-left(frac{2}{a}right)^{N_D}right].;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{\cal D}_{M,n}^m = - K_{HD} \left[ \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2} - \left( \frac{2}{a} \right)^{N_D} \right] .$ |; $key = q/displaystylehat{T}_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k-1}$ |; $key = q/{displaystylefrac{1}{r}DP{f}{varphi}left(=frac{cosvarphi}{r}DP{f}{mu}right)};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \frac{1}{r} \DP{f}{\varphi} \left( = \frac{\cos \varphi}{r} \DP{f}{\mu} \right) }$ |; $key = q/{align*}{split}hat{T}_{k-1slash2}&=frac{left[left(displaystylefrac{sigma_{k-1sla{sigma_{k-1}^{kappa}-sigma_k^{kappa}}&=a_kT_k+b_{k-1}T_{k-1},{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\hat{T}_{k-1/2} & = \frac{ \left[ \left( \displaystyl... ... - \sigma_k^{\kappa} } \ & = a_k T_k + b_{k-1} T_{k-1}, \end{split}\end{align*}$ |; $key = q/J=63,N=21;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleu_A(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle u_A (\varphi, \lambda, \sigma)$ |; $key = q/M,N;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}zeta&=frac{1}{rcosvarphi}DP{v}{lambda}-frac{1}{rcosvarphi}DP{}{varphi}(ucosvarphi).{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\zeta &= \frac{1}{r \cos \varphi} \DP{v}{\lambda} - \frac{1}{r \cos \varphi} \DP{}{\varphi}(u \cos \varphi) . \end{split}\end{align*}$ |; $key = q/displaystylew_j=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle w_j = \frac{(2J-1)(1-\mu_j^2)}{(J P_{J-1}(\mu_j))^2 }$ |; $key = q/zeta;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\zeta$ |; $key = q/0le|m'|len';MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le \vert m'\vert \le n'$ |; $key = q/{displaystylesin^{-1}left(cosfrac{j-1slash2}{J}piright)};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \sin^{-1} \left( \cos \frac{j-1/2}{J}\pi \right) }$ |; $key = q/tilde{P}_n^m(mu)(n=|m|,|m+1,cdots);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_n^m(\mu) (n=\vert m\vert,\vert m+1, \cdots)$ |; $key = q/hat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{q}$ |; $key = q/Leftrightarrow;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Leftrightarrow$ |; $key = q/displaystyle=frac{1}{2}int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{2} \int_{-1}^1 \frac{\tilde{P}_J(\mu)} {(\mu-\mu_j) \tilde{P}^{'}_J(\mu_j)} d \mu$ |; $key = q/zeta_0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\zeta_0$ |; $key = q/frac{I}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\frac{I}{2}$ |; $key = q/P_n^m(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m(\mu)$ |; $key = q/displaystyle(n+1)tilde{P}_{n+1}(mu)=(2n+1)mutilde{P}_n(mu)-ntilde{P}_{n-1}(mu)(n=0,1,2,cdots);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (n+1) \tilde{P}_{n+1}(\mu) = (2n+1) \mu \tilde{P}_n(\mu) - n \tilde{P}_{n-1}(\mu) (n=0,1,2,\cdots)$ |; $key = q/T^c_k,q^c_k;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleZequiv-sum_{k=1}^{K}Dvect{v}_kcdotnablapi.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Z \equiv - \sum_{k=1}^{K} \Dvect{v}_k \cdot \nabla \pi.$ |; $key = q/displaystyleDeltaq_{cond}=S^{cond}_{q}Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta q_{cond} = S^{cond}_{q} \Delta t$ |; $key = q/displaystylehspace{2em}+left(1+gamma_{k-1}-kappafrac{Deltap_{k-1slash2}}{2p_{k-1{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{2em} + \left( 1 + \gamma_{k-1} - \kappa \frac{\Delta p_{k... ...1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$ |; $key = q/displaystyleint_{-1}^{1}f(mu)dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^{1} f(\mu) d \mu$ |; $key = q/displaystyleS_q(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle S_q (\varphi, \lambda, \sigma)$ |; $key = q/displaystyle=;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle =$ |; $key = q/tilde{P}_0=1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_0 = 1$ |; $key = q/displaystylesum_{i=0}^{I-1}exp(imlambda_i)exp(-im'lambda_i)=Idelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{i=0}^{I-1} \exp(i m \lambda_i) \exp(-i m' \lambda_i) = I \delta_{mm'}$ |; $key = q/displaystyle:qquad放射,凝結,小規模運動過程等による加熱・温度変化,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 放射, 凝結, 小規模運動過程等による加熱・温度変化,$ |; $key = q/displaystyle:qquad温度水平拡散,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 温度水平拡散,$ |; $key = q/displaystylequadsum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}cos^2varphi_jP_{n}^{m}(varphi_j(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \cos^2\varphi_j P_{n}... ...mbda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$ |; $key = q/S;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/nabla^{N_D};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla^{N_D}$ |; $key = q/displaystyleequivfrac{1}{2}left({calA}^{t+Deltat}+{calA}^{t-Deltat}right)={calA}^{t-Deltat}+delta_{t}{calA}Deltat.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \frac{1}{2} \left( {\cal A}^{t+\Delta t} + {\cal A}^{t-\Delta t} \right) = {\cal A}^{t-\Delta t} + \delta_{t} {\cal A} \Delta t .$ |; $key = q/displaystyleequivgz:quadジオポテンシャル高度[mathrm{m}^{2}mathrm{s}^{-2}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv gz : \quad ジオポテンシャル高度 [\mathrm{m}^{2} \mathrm{s}^{-2}],$ |; $key = q/displaystyleDeltahat{Q}equivleft{hat{q}_{k-1}-q^{*}(hat{T}_{k-1})right}Deltap_{k-1}+left{hat{q}_{k}-q^{*}(hat{T}_{k})right}Deltap_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta \hat{Q} \equiv \left\{ \hat{q}_{k-1} - q^{*} (\hat{T}_{k-1... ...Delta p_{k-1} + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\} \Delta p_{k}$ |; $key = q/hat{calA}^{t+Deltat};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{\cal A}^{t+\Delta t}$ |; $key = q/{align*}{split}{u_A}_{,k}&=(zeta_k+f)v_k-frac{1}{2Deltasigma_k}[dot{sigma}_{k-1sT_{v,k}^{prime}}{acosvarphi}DP{pi}{lambda}+{calF}_{lambda,k},{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}{u_A}_{,k} & = ( \zeta_k + f ) v_k - \frac{1}{2 \Delt... ...\cos \varphi} \DP{\pi}{\lambda} + {\cal F}_{\lambda, k}, \end{split}\end{align*}$ |; $key = q/displaystyleR_k=q_kD_k-frac{1}{2Deltasigma_k}left[dot{sigma}_{k-1slash2}(q_{k-1}-q_k)+dot{sigma}_{k+1slash2}(q_k-q_{k+1})right].;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle R_k = q_k D_k - \frac{1}{2 \Delta \sigma_k} \left[ \dot{\sigma}_{k-1/2} ( q_{k-1} - q_k ) + \dot{\sigma}_{k+1/2} ( q_k - q_{k+1} ) \right].$ |; $key = q/Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta t$ |; $key = q/r_S;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleA(lambda,varphi)=sum_{m=0}^{infty}sum_{n=|m|}^{infty}tilde{A}_n^mY_n^m(lambda,varphi),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A(\lambda, \varphi) = \sum_{m=0}^{\infty} \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m Y_n^m(\lambda,\varphi) ,$ |; $key = q/{align*}{split}H_k&=T_{k}^{prime}D_{k}&quad-frac{1}{Deltasigma_{k}}[dot{sigma}_{{k}}{Deltasigma_{k}}T'_{v,k}sum_{l=k+1}^{K}D_lDeltasigma_{l}.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}H_k & = T_{k}^{\prime} D_{k} \ & \quad - \frac{1}{\D... ..._{k} } T'_{v,k} \sum_{l=k+1}^{K} D_l \Delta \sigma_{l} . \end{split}\end{align*}$ |; $key = q/displaystyletilde{h}_n^m=-frac{n(n+1)}{r^2}tilde{f}_n^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{h}_n^m = -\frac{n(n+1)}{r^2} \tilde{f}_n^m .$ |; $key = q/B;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/P_J(sinvarphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_J(\sin \varphi)$ |; $key = q/displaystyle=1-left(frac{sigma_{k+1slash2}}{sigma_k}right)^{kappa}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = 1- \left( \frac{ \sigma_{k+1/2} } { \sigma_k } \right)^{\kappa} .$ |; $key = q/hat{T};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{T}$ |; $key = q/displaystyleD;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle D$ |; $key = q/displaystyleint^{1}_{-1}f(mu)dmu=2sum_{j=1}^{J}f(mu_j)w_j,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int^{1}_{-1} f(\mu) d \mu = 2 \sum_{j=1}^{J} f(\mu_j) w_j ,$ |; $key = q/displaystyleint_{-1}^1tilde{P}_n(mu)tilde{P}_{n'}(mu)dmu=frac{2}{2n+1}delta_{nn'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 \tilde{P}_n(\mu) \tilde{P}_{n'}(\mu) d \mu = \frac{2}{2n+1} \delta_{nn'} .$ |; $key = q/dot{calA}_{phy};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\cal A}_{phy}$ |; $key = q/tilde{P}_J(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_J(\mu)$ |; $key = q/n+n'+n'';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/*;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/A;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/chi_n^m,psi_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\chi_n^m,\psi_n^m$ |; $key = q/displaystyleg(lambda)=sum_{m=-M}^{m=M}g_mexp(imlambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle g(\lambda) = \sum_{m=-M}^{m=M} g_m \exp( i m \lambda )$ |; $key = q/displaystyle:quad乾燥大気の気体定数[mathrm{Jkg}^{-1}mathrm{K}^{-1}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 乾燥大気の気体定数 [\mathrm{J kg}^{-1} \mathrm{K}^{-1}],$ |; $key = q/displaystyle=frac{1}{I}sum_{n=1}^{I}sum_{m=-M}^{M}g_mexp(imlambda_n);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{n=1}^{I} \sum_{m=-M}^{M} g_m \exp(i m \lambda_n)$ |; $key = q/displaystyle=frac{1}{I}sum_{i,j}left(cos^2varphi_jsum_{m',n'}tilde{f}_{n'}^{m'}lphi}right|_jexp(im'lambda_i)right)P_n^m(varphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} \left( \cos^2\varphi_j \sum_{m',n'} \til... ...t\vert _j \exp(i m' \lambda_i) \right) P_n^m(\varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/{calA};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\cal A}$ |; $key = q/displaystyleleft(-1-gamma_{k}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( - 1 - \gamma_{k} - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k}$ |; $key = q/displaystyle=frac{1}{Jtilde{P}_{J-1}(mu_j)tilde{P}^{'}_{J}(mu_j)};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{J \tilde{P}_{J-1}(\mu_j) \tilde{P}^{'}_{J} (\mu_j)}$ |; $key = q/displaystyle=sigma_{k-1slash2}Deltasigma_{l}-Deltasigma_{l}delta_{kleql},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sigma_{k-1/2} \Delta \sigma_{l} - \Delta \sigma_{l} \delta_{k \leq l } ,$ |; $key = q/displaystyleleft[frac{1}{cosvarphi}DP{}{varphi}left(cosvarphiDP{}{varphi}right)+frac{1}{cos^2varphi}DP[2]{}{lambda}+n(n+1)right]Y_n^m=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[ \frac{1}{\cos \varphi} \DP{}{\varphi} \left( \cos \varphi ... ...right) + \frac{1}{\cos^2 \varphi} \DP[2]{}{\lambda} + n(n+1) \right] Y_n^m =0 .$ |; $key = q/displaystyle=g_0+sum_{m=-M,mneq0}^{M}frac{g_m}{I}sum_{n=1}^{I}left(exp(frac{2piim}{I})right)^{n-1}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = g_0 + \sum_{m=-M, m\neq0}^{M} \frac{g_m}{I} \sum_{n=1}^{I} \left( \exp(\frac{2 \pi i m}{I}) \right)^{n-1} .$ |; $key = q/f_J(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $f_J(\mu)$ |; $key = q/displaystyletilde{A}_n^m=frac{1}{2}int_{-1}^1A(mu)P_n^m(mu)dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{A}_n^m = \frac{1}{2} \int_{-1}^1 A(\mu) P_n^m(\mu) d \mu$ |; $key = q/x=-1,alpha,1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $x=-1,\alpha,1$ |; $key = q/displaystyleS_{k-1slash2}equivhat{T}_{k-1}-hat{T}_{k}+frac{L}{C_p}left{q^{*}(hatc{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+hat{T}_{k}}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle S_{k-1/2} \equiv \hat{T}_{k-1} - \hat{T}_{k} + \frac{L}{C_p} \lef... ...{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$ |; $key = q/displaystyleequivsum_{m=-M}^{M}sum_{n=|m|}^{N}tilde{A}_n^mY_n^m(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \tilde{A}_n^m Y_n^m (\lambda, \varphi)$ |; $key = q/{align*}{split}DP{tilde{D}_n^m}{t}&=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}im(u_A)_}hat{kappa}_kbar{T}_kpi_n^m)+tilde{calD}_{M,n}^mtilde{D}_n^m.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{\tilde{D}_n^m}{t} & = \frac{1}{I} \sum_{i=1}^{I} ... ...{T}_k \pi_n^m ) + \tilde{\cal D}_{M,n}^m \tilde{D}_n^m . \end{split}\end{align*}$ |; $key = q/displaystyle(C_pT_{k}+Lq_{k})Deltap_{k}+(C_pT_{k-1}+Lq_{k-1})Deltap_{k-1}=(C_pha+Lhat{q}_{k})Deltap_{k}+(C_phat{T}_{k-1}+Lhat{q}_{k-1})Deltap_{k-1}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (C_p T_{k} + L q_{k}) \Delta p_{k} + (C_p T_{k-1} + L q_{k-1}) \D... ...at{q}_{k}) \Delta p_{k} + (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}.$ |; $key = q/displaystylep_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle p_n^m$ |; $key = q/displaystyleDeltaq_{evap}=F_{evap}frac{g}{LDeltap}Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta q_{evap} = F_{evap} \frac{g}{L \Delta p} \Delta t$ |; $key = q/{figure}center{picture{(300,100)(10,-10)put(20,10){vector(1,0){85}}put(30,0){vec0,-20){shortstack{三角形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{figure}\begin{center} \begin{picture}(300,100)(10,-10) \put(20 , 10){\v... ...00,-20) \{ shortstack\{三角形切断\}\} \par \end{picture}\end{center}\end{figure}$ |; $key = q/(u,v);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/P_n^mP_{n'}^{m'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m P_{n'}^{m'}$ |; $key = q/{picture}(300,150)(50,10)put(50,20){line(1,0){220}}put(50,40){line(1,0){220}}put){shortstack{{sigma=1{}}put(280,136){shortstack{{sigma=0{}}{picture};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{picture}(300,150)(50,10) \put(50,20){\line(1,0){220}} \put(50,40){\line... ...){\shortstack{$\sigma=1$}} \put(280,136){\shortstack{$\sigma=0$}} \end{picture}$ |; $key = q/Y_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}DP{T_k}{t}&=-Dinv{acosvarphi}left{DP{(u_kT^{prime}_k)}{lambda}+DPhat{H}_k&quad+frac{Q_k}{C_{p}}+{calD}(T_k)+{calD}'(Dvect{v}).{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{T_k}{t} & = - \Dinv{a \cos \varphi} \left\{ \DP{(... ...frac{Q_k}{C_{p}} + {\cal D}(T_k) + {\cal D}'(\Dvect{v}). \end{split}\end{align*}$ |; $key = q/displaystyleQ_{kl};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Q_{kl}$ |; $key = q/displaystylefrac{hat{p_{s}}sigma}{RT}hat{q}=frac{p_{s}sigma}{RT}q;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q} = \frac{p_{s} \sigma}{RT} q$ |; $key = q/mu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mu$ |; $key = q/displaystyleleft[left(-1-gamma_{k}right)-kappafrac{Deltap_{k-1slash2}}{2p_{k-1sl}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}right)right]DeltaT_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[ \left( - 1 - \gamma_{k} \right) - \kappa \frac{\Delta p_{k... ... \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} \right) \right] \Delta T_{k}$ |; $key = q/displaystyleDD{}{mu}left{(1-mu^2)DD{}{mu}P_n^mright}+left{n(n+1)-frac{m^2}{1-mu^2}right}P_n^m=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DD{}{\mu} \left\{ (1-\mu^2) \DD{}{\mu} P_n^m \right\} + \left\{ n(n+1) - \frac{m^2}{1-\mu^2} \right\} P_n^m = 0 .$ |; $key = q/displaystyleint_{-1}^1P_n^m(mu)P_{n'}^m(mu)dmu=2delta_{nn'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 P_n^m(\mu) P_{n'}^m(\mu) d \mu = 2 \delta_{nn'}$ |; $key = q/displaystyle=-sum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}left.DD{}{varphi}left(cos^2varphight)right|_jexp(-imlambda_i)P_{n'}^{m'}(varphi_j)exp(im'lambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \left. \DD{}{\varphi} \... ...ight\vert _j \exp(-im \lambda_i) P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) w_j$ |; $key = q/displaystylesigma;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sigma$ |; $key = q/displaystyleequivDD{sigma}{t}equivDP{sigma}{t}+frac{u}{acosvarphi}DP{sigma}{lambda}+frac{v}{a}DP{sigma}{varphi}+DP{sigma}{sigma},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \DD{\sigma}{t} \equiv \DP{\sigma}{t} + \frac{u}{a \cos... ... \DP{\sigma}{\lambda} + \frac{v}{a} \DP{\sigma}{\varphi} + \DP{\sigma}{\sigma},$ |; $key = q/displaystylehspace{-7em}=-left[DeltaT_{k}+frac{L}{C_p}left{q^{*}(T_{k})+left.DP{q^{*}}{T}right|_{k}DeltaT_{k}-hat{q}_{k}right}right]Deltap_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{-7em} = - \left[ \Delta T_{k} + \frac{L}{C_p} \left\{ q^{... ...}{T} \right\vert _{k} \Delta T_{k} - \hat{q}_{k} \right\} \right] \Delta p_{k},$ |; $key = q/displaystyleq^a_{k+1}>q^*(T^a_{k+1},p_{k+1});MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q^a_{k+1} > q^*( T^a_{k+1}, p_{k+1} )$ |; $key = q/2Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $2 \Delta t$ |; $key = q/displaystyleu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle u$ |; $key = q/{displaystyleint_{-1}^1fdmu};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\int_{-1}^1 f d \mu$ |; $key = q/P_{J};MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_{J}$ |; $key = q/L;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/K=2N_{tr},J=M=N_{tr};MSF=1.6;AAT/; $cached_env_img{$key} = q| $K=2N_{tr}, J=M=N_{tr}$ |; $key = q/2J-1ge{rmmax}[n+n']=2{rmmax}[N];MSF=1.6;AAT/; $cached_env_img{$key} = q| $2J-1 \ge {\rm max}[n+n'] = 2 {\rm max}[N]$ |; $key = q/alpha_A;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\alpha_A$ |; $key = q/N=64;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/Jge65;MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \ge 65$ |; $key = q/sigma=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma=0$ |; $key = q/displaystylehequivfrac{g}{rcos^2varphi}=frac{1}{rcos^2varphi}DP{f}{lambda}left[=DP{}{x}left(frac{f}{cosvarphi}right)right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle h \equiv \frac{g}{r \cos^2 \varphi} = \frac{1}{r \cos^2 \varphi} ... ...f}{\lambda} \left[ = \DP{}{x} \left( \frac{f}{\cos \varphi} \right) \right]$ |; $key = q/displaystyleoverline{coszeta}simeqA_{zeta}+B_{zeta}cos^2varphi.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{\cos \zeta} \simeq A_{\zeta} + B_{\zeta} \cos^2 \varphi .$ |; $key = q/f''=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleDP{tilde{pi}_n^m}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\tilde{\pi}_n^m}{t}$ |; $key = q/F_{evap}simLC(q^{*}-q_s)rho_s;MSF=1.6;AAT/; $cached_env_img{$key} = q| $F_{evap} \sim L C (q^{*} - q_s) \rho_s$ |; $key = q/{P_n^m|n=|m|,|m+1|,cdots};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ P_n^m \vert n=\vert m\vert,\vert m+1\vert,\cdots \}$ |; $key = q/u,v;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle:quad水平平均気温[mathrm{K}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 水平平均気温 [\mathrm{K}],$ |; $key = q/displaystylehspace*{2.5cm}-sqrt{frac{(2n+1)(2n+3)}{(n-|m|+1)(n+|m|+1)}}sqrt{frac{(n-|m|)(n+|m|)}{(2n+1)(2n-1)}}P_{n-1}^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace*{2.5cm} - \sqrt{ \frac{(2n+1)(2n+3)}{(n-\vert m\vert+1)(n... ...)} } \sqrt{ \frac{(n-\vert m\vert)(n+\vert m\vert)}{(2n+1)(2n-1)} } P_{n-1}^m .$ |; $key = q/D;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleqquad-frac{R}{C_p}frac{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+DeltaT_{k-1}+hat{T}_{k}+DeltaT_{k}}{2}=0,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \qquad - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \Delta T_{k-1} + \hat{T}_{k} + \Delta T_{k}}{2} = 0,$ |; $key = q/displaystyle(n+1)left|{array}{ll}tilde{P}_{n+1}(x)&tilde{P}_n(x)tilde{P}_{n+1}(y)&tilde{P}_n(y){array}right|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (n+1) \left\vert \begin{array}{ll} \tilde{P}_{n+1}(x) & \tilde{P}_n(x) \ \tilde{P}_{n+1}(y) & \tilde{P}_n(y) \end{array} \right\vert$ |; $key = q/M=N_{tr},N(m)=N_{tr}+|m|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $M= N_{tr}, N(m) =N_{tr}+\vert m\vert$ |; $key = q/{calT}^f(z_1,z_2);MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\cal T}^f(z_1,z_2)$ |; $key = q/A(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $A(\mu)$ |; $key = q/displaystylew_j=frac{1}{2}int_{-1}^{1}frac{P_J(mu)}{(mu-mu_j)P^{'}_J(mu_i)}dmu=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle w_j = \frac{1}{2} \int_{-1}^{1} \frac{P_J(\mu)}{(\mu-\mu_j) P^{'}_J (\mu_i)}d \mu = \frac{(2J-1)(1-\mu_j^2)}{(J P_{J-1}(\mu_j))^2 } .$ |; $key = q/displaystylehat{hat{T}}_{k+1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{\hat{T}}_{k+1}$ |; $key = q/R;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleI=sum_{k=k_B}^{k_T}(hat{q}_k-bar{q}_k^{t-Deltat})frac{Deltap_k}{g}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle I = \sum_{k=k_B}^{k_T} ( \hat{q}_k - \bar{q}_k^{t-\Delta t} ) \frac{\Delta p_k}{g} .$ |; $key = q/displaystylesum_{n=1}^{I}left(exp(frac{2piim}{I})right)^{n-1}=0(mneq0);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{n=1}^{I} \left( \exp(\frac{2 \pi i m}{I}) \right)^{n-1} =0 (m \neq 0)$ |; $key = q/{align*}{split}Deltasigma_k&equivsigma_{k-1slash2}-sigma_{k+1slash2},qquad(1|; $key = q/N_D;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/k_{S,i};MSF=1.6;AAT/; $cached_env_img{$key} = q| $k_{S,i}$ |; $key = q/displaystyle=Idelta_{nn'}delta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = I \delta_{nn'} \delta_{mm'}$ |; $key = q/S_0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyletilde{g}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{g}_n^m$ |; $key = q/displaystyle=frac{displaystyle-S_{k-1slash2}-left(1+gamma_{k-1}-kappafrac{Deltaprac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}right)};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{ \displaystyle - S_{k-1/2} - \left( 1 + \gamma_{k-1} - \k... ...+ \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} \right) }$ |; $key = q/^{-2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $^{-2}$ |; $key = q/displaystyleDD{}{mu}left{(1-mu^2)DD{}{mu}tilde{P}_n^mright}+left{n(n+1)-frac{m^2}{1-mu^2}right}tilde{P}_n^m=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DD{}{\mu} \left\{ (1-\mu^2) \DD{}{\mu} \tilde{P}_n^m \right\} + \left\{ n(n+1) - \frac{m^2}{1-\mu^2} \right\} \tilde{P}_n^m = 0 .$ |; $key = q/displaystyleleft.-alpha_g(1-alpha_A)F_S^Iexpleft(-tau_{S,i}(0)seczetaright)expleft(-(tau_{S,i}(0)-tau_i(z))seczeta_0right)right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left. - \alpha_g (1-\alpha_A) F_S^I \exp \left( - \tau_{S,i}(0) ... ... \right) \exp \left( - ( \tau_{S,i}(0)-\tau_i(z) ) \sec \zeta_0 \right) \right]$ |; $key = q/{align*}{split}(mbox{rot}Dvect{v})_r&equivfrac{1}{rcosvarphi}DP{v_2}{lambda}-frat{1-mu^2}}DP{v_2}{lambda}-frac{1}{r}DP{}{mu}(sqrt{1-mu^2}v_1){split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}(\mbox{rot} \Dvect{v})_r &\equiv \frac{1}{r \cos \var... ..._2}{\lambda} - \frac{1}{r} \DP{}{\mu}(\sqrt{1-\mu^2}v_1) \end{split}\end{align*}$ |; $key = q/(T^a_k,q^a_k);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleY_n^m(lambda,varphi)equivP_n^m(sinvarphi)exp(imlambda).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Y_n^m(\lambda, \varphi) \equiv P_n^m(\sin \varphi) \exp(i m \lambda) .$ |; $key = q/B_{ins};MSF=1.6;AAT/; $cached_env_img{$key} = q| $B_{ins}$ |; $key = q/{displaystylew_j=frac{1}{2}int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle w_j = \frac{1}{2} \int_{-1}^1 \frac{\tilde{P}_J(\mu)} {(\mu-\mu_j)\tilde{P}^{'}_J(\mu_j)} d \mu }$ |; $key = q/displaystyledot{sigma}_{k-1slash2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma}_{k-1/2}$ |; $key = q/displaystyle=-sum_{k=1}^{K}(tilde{D}_n^m)_kDeltasigma_k+frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}Z_{ij}Y_n^{m*}(lambda_i,mu_j)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sum_{k=1}^{K} (\tilde{D}_n^m)_k \Delta \sigma_k + \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} Z_{ij} Y_n^{m *} ( \lambda_i, \mu_j ) w_j.$ |; $key = q/displaystyle{calD}(q);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(q)$ |; $key = q/displaystyle=widetilde{left[DP{}{lambda}left(frac{f}{rcos^2varphi}right)right]_n^m}=imwidetilde{left(frac{f}{rcos^2varphi}right)_n^m};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \widetilde{ \left[ \DP{}{\lambda} \left( \frac{f}{r \cos^2 \var... ... \right]_n^m } = im \widetilde{ \left( \frac{f}{r \cos^2 \varphi} \right)_n^m }$ |; $key = q/displaystyleT^{prime}(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T^{\prime} (\varphi, \lambda, \sigma)$ |; $key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Ntilde{A}_n^mP_n^{m}(sinvarphi_j)exp(imlambda_i);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N \tilde{A}_n^m P_n^{m}(\sin \varphi_j) \exp(im \lambda_i)$ |; $key = q/z=z_1,z_2;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleT=hat{T}+frac{L}{C_p}frac{hat{q}-q^*(hat{T},p)}{displaystyle1+frac{L}{C_p}DP{q^*}{T}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T = \hat{T} + \frac{L}{C_p} \frac{ \hat{q} - q^*(\hat{T},p) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} }$ |; $key = q/-1|; $key = q/displaystyle=left(DP{Dvect{T}}{t}right)_{rmNG}-underline{h}Dvect{D}+{calD}_HDvect{T}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \left( \DP{\Dvect{T}}{t} \right)_{\rm NG} - \underline{h} \Dvect{D} + {\cal D}_H \Dvect{T} .$ |; $key = q/DeltaT_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta T_{k-1}$ |; $key = q/displaystylequadsum_{j=1}^{J}sum_{i=1}^{I}P_n^m(mu_j)P_{n'}^{m'}(mu_j)exp(imlambda_i)exp(-im'lambda_{i})w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \sum_{j=1}^{J} \sum_{i=1}^{I} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) \exp(i m \lambda_i) \exp(-i m' \lambda_{i}) w_j$ |; $key = q/P_n^m(sinvarphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m(\sin \varphi)$ |; $key = q/displaystyleP=frac{Deltap}{g}(hat{q}-q).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle P = \frac{\Delta p}{g} ( \hat{q} - q ) .$ |; $key = q/displaystyleP_n^mequivsqrt{frac{(2n+1)(n-|m|)!}{(n+|m|)!}}tilde{P}_n^m=sqrt{fracm|)!}}frac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle P_n^m \equiv \sqrt{ \frac{(2n+1)(n-\vert m\vert)!}{(n+\vert m\ver... ...^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n .$ |; $key = q/nabla_H^2Y^m_n(lambda,varphi)=-frac{n(n+1)}{r^2}Y^m_n(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla_H^2 Y^m_n(\lambda, \varphi) =- \frac{n(n+1)}{r^2} Y^m_n(\lambda,\varphi)$ |; $key = q/displaystylehat{rho}hat{q}=rhoq,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{\rho} \hat{q} = \rho q,$ |; $key = q/displaystyleequivDP{f}{lambda};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \DP{f}{\lambda}$ |; $key = q/displaystyleJtilde{P}_J(mu)tilde{P}_{J-1}(mu_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle J \tilde{P}_J (\mu) \tilde{P}_{J-1} (\mu_j)$ |; $key = q/displaystyleDeltaT_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta T_{k}$ |; $key = q/x=-1,1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{P_n^m}(n=|m|,|m|+1,|m|+2,cdots,N);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ P_n^m \} (n=\vert m\vert,\vert m\vert+1,\vert m\vert+2,\cdots,N)$ |; $key = q/Y_n^m(lambda',varphi');MSF=1.6;AAT/; $cached_env_img{$key} = q| $Y_n^m(\lambda',\varphi')$ |; $key = q/A_{i,j}-A_{i,J-j};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{i,j}-A_{i,J-j}$ |; $key = q/displaystyle{calD}'(Dvect{v});MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}' (\Dvect{v})$ |; $key = q/{align*}{split}Phi_k-Phi_{k-1}&=C_{p}left[left(frac{sigma_{k-1slash2}}{sigma_k}right]T_{v,k-1}&=C_{p}alpha_kT_{v,k}+C_{p}beta_{k-1}T_{v,k-1}.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\Phi_k - \Phi_{k-1} & = C_{p} \left[ \left( \frac{ \s... ... = C_{p} \alpha_k T_{v,k} + C_{p} \beta_{k-1} T_{v,k-1}. \end{split}\end{align*}$ |; $key = q/displaystylefrac{1}{rcosvarphi}DP{Y_n^m}{lambda}=frac{1}{rcosvarphi}DP{}{lambda}p(imlambda)right)=frac{im}{rcosvarphi}P_n^m(sinvarphi)exp(imlambda).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{r \cos \varphi} \DP{Y_n^m}{\lambda} = \frac{1}{r \cos \v... ...da) \right) = \frac{im}{r \cos \varphi} P_n^m (\sin \varphi) \exp(im \lambda) .$ |; $key = q/F_S^I;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/P_n^mP_{n'}^{m};MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m P_{n'}^{m}$ |; $key = q/displaystyle{calD}(T);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(T)$ |; $key = q/bar{calA};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\bar{\cal A}$ |; $key = q/chi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\chi$ |; $key = q/displaystyledelta_{t}{calA};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \delta_{t} {\cal A}$ |; $key = q/displaystyleh_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle h_{ij}$ |; $key = q/displaystyleequivpslashp_s,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv p/p_s,$ |; $key = q/displaystylesum^{KMAX}_{k=1}c_vDeltaT_{k}Deltap_{k}=sum^{KMAX}_{k=1}c_vS_{grst}(T_{Bk}-T_{k})(p_sDeltasigma_{k});MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum^{KMAX}_{k=1} c_v \Delta T_{k} \Delta p_{k} = \sum^{KMAX}_{k=1} c_v S_{grst} (T_{Bk} - T_{k}) (p_s \Delta \sigma_{k})$ |; $key = q/{displaystylesum_{i=1}^{I}sum_{j=1}^{J}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{i=1}^{I} \sum_{j=1}^{J}$ |; $key = q/displaystylehat{T}_{k}=T_{k}+S_{grst}(T_{Bk}-T_{k})-frac{sum^{KMAX}_{k=1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{KMAX}_{k=1}Deltap_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k} = T_{k} + S_{grst} (T_{Bk} - T_{k}) - \frac{ \sum^{KM... ...k=1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k} }{ \sum^{KMAX}_{k=1} \Delta p_{k} }$ |; $key = q/displaystyleequiv(zeta+f)v-dot{sigma}DP{u}{sigma}-frac{RT_v^{prime}}{acosvarphi}DP{pi}{lambda}+{calF}_{lambda},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv ( \zeta + f ) v - \dot{\sigma} \DP{u}{\sigma} - \frac{R T_v^{\prime}}{a \cos \varphi} \DP{\pi}{\lambda} + {\cal F}_{\lambda},$ |; $key = q/Deltap_s;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta p_s$ |; $key = q/P_n^0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/1leileI,1lejleJ;MSF=1.6;AAT/; $cached_env_img{$key} = q| $1 \le i \le I,1 \le j \le J$ |; $key = q/displaystyledot{sigma}=-sigmaDP{pi}{t}-int_{0}^{sigma}Ddsigma-int_{0}^{sigma}Dvect{v}_{H}cdotnabla_{sigma}pidsigma,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma} = - \sigma \DP{\pi}{t} - \int_{0}^{\sigma} D d \sigma - \int_{0}^{\sigma} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma ,$ |; $key = q/displaystylehat{T}_{k+1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k+1}$ |; $key = q/I=64,J=65;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleleft(DP{f}{varphi}right)_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left(\DP{f}{\varphi}\right)_{ij}$ |; $key = q/H;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleL(mu)equivsum_{j=1}^{J}f(mu_j)prod_{k=1,kneqj}^{J}frac{mu-mu_k}{mu_j-mu_k}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle L(\mu) \equiv \sum_{j=1}^{J} f(\mu_j) \prod_{k=1,k \neq j}^{J} \frac{ \mu-\mu_k}{\mu_j-\mu_k} .$ |; $key = q/tilde{P}_J(mu)S(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_J(\mu) S(\mu)$ |; $key = q/C_v;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleleft(DP{pi}{t}right)^{rmNG}=-sum_{k=1}^{K}Dvect{v}_{k}cdotnablapiDeltasigma_{k}=Z_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( \DP{\pi}{t} \right)^{\rm NG} = - \sum_{k=1}^{K} \Dvect{v}_{k} \cdot \nabla \pi \Delta \sigma_{k} = Z_{k} ,$ |; $key = q/overline{P_n^1}=P_n^1slashsqrt{2},overline{P_n^2}=P_n^2slashsqrt{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\overline{P_n^1} = P_n^1/\sqrt{2}, \overline{P_n^2} = P_n^2/\sqrt{2}$ |; $key = q/displaystyleg;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle g$ |; $key = q/displaystyleleft(DP{D}{t}right)^{rmNG}=Dinv{acosvarphi}left{DP{{u_A}_{,k}}{lambda}+DP{({v_A}_{,k}cosvarphi)}{varphi}right}-nabla^{2}_{sigma}(;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( \DP{D}{t} \right)^{\rm NG} = \Dinv{a \cos \varphi} \left\{... ...bda} + \DP{({v_A}_{,k} \cos \varphi)}{\varphi} \right\} - \nabla^{2}_{\sigma} ($ |; $key = q/displaystyletilde{h}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{h}_n^m$ |; $key = q/k+2;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/M=21,N=42;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle:qquad小規模運動過程(経度方向),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 小規模運動過程 (経度方向),$ |; $key = q/|m|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\vert m\vert$ |; $key = q/{displaystylesum_{i,j}Y_n^{m*}(lambda_i,varphi_j)w_j};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{i,j} Y_n^{m*}(\lambda_i,\varphi_j)w_j$ |; $key = q/f=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle:qquad発散水平拡散,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 発散水平拡散,$ |; $key = q/displaystyletilde{g}_n^m=imtilde{f}_n^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{g}_n^m = im \tilde{f}_n^m .$ |; $key = q/displaystyle)_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle )_k$ |; $key = q/displaystylequadtimesleft(sum_{m''=-M}^{M}sum_{n''=|m''|}^Ntilde{C}_{n''}^{m''}en''}^{m''}(sinvarphi_j)right)P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \times \left( \sum_{m''=-M}^{M} \sum_{n''=\vert m''\vert}^N... ...}^{m''}(\sin \varphi_j) \right) P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/displaystyleequivRslashC_p,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv R/C_p,$ |; $key = q/displaystyleP=(1-b)I.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle P = (1-b) I .$ |; $key = q/displaystylelangle;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \langle$ |; $key = q/k_{R,i};MSF=1.6;AAT/; $cached_env_img{$key} = q| $k_{R,i}$ |; $key = q/displaystyleDeltap_s=F_{evap}frac{g}{L}Deltat+hat{p_s}intS^{cond}_{q}Deltatdsigma;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta p_s = F_{evap} \frac{g}{L} \Delta t + \hat{p_s} \int S^{cond}_{q} \Delta t d \sigma$ |; $key = q/{rmmax}[N];MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\rm max}[N]$ |; $key = q/I;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylesum_{j=1}^{J}P_n^m(mu_j)P_{n'}^m(mu_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^m (\mu_j) w_j$ |; $key = q/q^c_k=q^*(T^c_k,p_k);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{figure}center{picture{(300,170)(10,-20)put(20,10){vector(1,0){95}}put(30,0){vec0,-20){shortstack{五角形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{figure}\begin{center} \begin{picture}(300,170)(10,-20) \put(20 , 10){\v... ...00,-20) \{ shortstack\{五角形切断\}\} \par \end{picture}\end{center}\end{figure}$ |; $key = q/displaystyle=sum_{k=0}^{n-1}(2k+1)(x-y)tilde{P}_k(x)tilde{P}_k(y);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{k=0}^{n-1} (2k+1)(x-y)\tilde{P}_k(x)\tilde{P}_k(y)$ |; $key = q/displaystyleoverline{F_S^I}(varphi)simeq-S_0(1-mathcal{A})(A_{ins}+B_{ins}cos^2varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{F_S^I} (\varphi) \simeq - S_0 (1 - \mathcal{A})( A_{ins} + B_{ins} \cos^2 \varphi )$ |; $key = q/displaystyle=(2n+1)(x-y)tilde{P}_n(x)tilde{P}_n(y)+nleft|{array}{ll}tilde{P}_{n}(x)&tilde{P}_{n-1}(x)tilde{P}_{n}(y)&tilde{P}_{n-1}(y){array}right|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = (2n+1)(x-y)\tilde{P}_n(x)\tilde{P}_n(y) + n \left\vert \begin{a... ...de{P}_{n-1}(x) \ \tilde{P}_{n}(y) & \tilde{P}_{n-1}(y) \end{array} \right\vert$ |; $key = q/displaystyleint_{-1}^1f(mu)P_n(mu)dmu=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 f(\mu) P_n(\mu) d \mu = 0$ |; $key = q/displaystylea;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle a$ |; $key = q/K;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/I=128,J=65;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/M,N(m);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylepi(varphi,lambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \pi (\varphi, \lambda)$ |; $key = q/displaystyle=Idelta_{mm'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = I \delta_{mm'}.$ |; $key = q/displaystyleA(mu)=sum_{n=|m|}^{infty}tilde{A}_n^mtilde{P}_n^m(mu),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A(\mu) = \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m \tilde{P}_n^m(\mu),$ |; $key = q/displaystyle(1-mu^2)DD{}{mu}tilde{P}_{n}^{m}=(n+|m|)tilde{P}_{n-1}^m-nmutilde{P}_n^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (1-\mu^2) \DD{}{\mu}\tilde{P}_{n}^{m} = (n+\vert m\vert) \tilde{P}_{n-1}^m - n \mu \tilde{P}_n^m .$ |; $key = q/{f_k(mu)}(k=0,1,2,cdots);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ f_k(\mu) \}(k=0,1,2,\cdots)$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jleft(sum_{m'=-M}^{M}sum_{n'=|m'|}^Ntilde{B}_{n'}^{m'}exp(im'lambda_i)P_{n'}^{m'}(sinvarphi_j)right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J \left( \sum_{m'=-M}^{M} \... ...}^N \tilde{B}_{n'}^{m'} \exp(im' \lambda_i) P_{n'}^{m'}(\sin \varphi_j) \right)$ |; $key = q/displaystyle=Dinv{acosvarphi}left{DP{u_A}{lambda}+DP{(v_Acosvarphi)}{varphi}right}-nabla^{2}_{sigma}(Phi+Roverline{T}pi+;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{u_A}{\lambda} + \DP{(v_A \cos \varphi)}{\varphi} \right\} - \nabla^{2}_{\sigma} ( \Phi + R \overline{T} \pi +$ |; $key = q/P_J(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_J (\mu)$ |; $key = q/displaystylesum_{j=0}^{J-1}f_k(mu_j)f_{k'}(mu_{j})w_j=lambda_kdelta_{kk'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{j=0}^{J-1} f_k (\mu_j) f_{k'} (\mu_{j}) w_j = \lambda_k \delta_{kk'}$ |; $key = q/Jgefrac{3N_{{rmmax}}+1}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \ge \frac{3N_{{\rm max}}+1}{2}$ |; $key = q/Idelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $I \delta_{mm'}$ |; $key = q/displaystyleequivsum_{m=-M}^{M}sum_{n=|m|}^{N}tilde{A}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \tilde{A}_n^m Y_n^m (\lambda_i,\varphi_j),$ |; $key = q/F_S;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyletau_{R,i}(z)=int_z^inftyk_{R,i}rhoqdz+int_z^inftybar{k}_{R,i}rhodz;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz + \int_z^\infty \bar{k}_{R,i} \rho dz$ |; $key = q/displaystyledelta_{t}Dvect{D}=left(DP{Dvect{D}}{t}right)_{rmNG}-nabla^{2}_{sigmaine{pi}^{t})+{calD}_M(Dvect{D}^{t-Deltat}+2Deltatdelta_{t}Dvect{D}),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \delta_{t} \Dvect{D} = \left( \DP{\Dvect{D}}{t} \right)_{\rm NG} ... ...} ) + {\cal D}_M ( \Dvect{D}^{t-\Delta t} + 2 \Delta t \delta_{t} \Dvect{D} ) ,$ |; $key = q/displaystylenabla^{2}_{sigma}=-frac{n(n+1)}{a^{2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \nabla^{2}_{\sigma} = - \frac{n(n+1)}{a^{2}}$ |; $key = q/displaystyleDeltaT_{k-1}-DeltaT_{k}+gamma_{k-1}DeltaT_{k-1}-gamma_{k}DeltaT_{k}-p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2}}DeltaT_{k}=-S_{k-1slash2},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta T_{k-1} - \Delta T_{k} + \gamma_{k-1} \Delta T_{k-1} - \ga... ... \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \Delta T_{k} = - S_{k-1/2},$ |; $key = q/displaystyleq_k=bar{q}_k^{t-Deltat}+bIfrac{(q^c_k-q_k)}{displaystylesum_{k=k_B}^{k_T}(q^c_k-q_k)frac{Deltap_k}{g}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q_k = \bar{q}_k^{t-\Delta t} + b I \frac{( q^c_k - q_k )} {\displaystyle \sum_{k=k_B}^{k_T} ( q^c_k - q_k ) \frac{\Delta p_k}{g} }$ |; $key = q/i;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/n=0,1,2,cdots,N|; $key = q/^{-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $^{-1}$ |; $key = q/times10^{-8};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\times 10^{-8}$ |; $key = q/S(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $S(\mu)$ |; $key = q/displaystyle=sum_{j=1}^{J}f(mu_j)int^1_{-1}frac{{displaystyleprod_{k=1}^{J}(mu-mu_k)}}{(mu-mu_j){displaystyleprod_{k=1,kneqj}^{J}(mu_j-mu_k)}}dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{j=1}^{J} f(\mu_j) \int^1_{-1} \frac{ {\displaystyle \prod... ... } { (\mu-\mu_j) {\displaystyle \prod_{k=1,k \neq j}^{J}(\mu_j-\mu_k) } } d \mu$ |; $key = q/-1|; $key = q/128times64=8192;MSF=1.6;AAT/; $cached_env_img{$key} = q| $128 \times 64 = 8192$ |; $key = q/A_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ij}$ |; $key = q/displaystyle=frac{1}{I}sum_{i,j}p_{ij}Y_n^{m*}w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} p_{ij} Y_n^{m*} w_j$ |; $key = q/displaystyleleft{1+frac{L}{C_p}left.DP{q^{*}}{T}right|_{k-1}right}DeltaT_{k-1}De}left{q^{*}(hat{T}_{k-1})-hat{q}_{k-1}right}Deltap_{k-1}hspace{-7em};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{ 1+ \frac{L}{C_p} \left. \DP{q^{*}}{T} \right\vert _{k-1} ... ...\{ q^{*} (\hat{T}_{k-1} ) - \hat{q}_{k-1} \right\} \Delta p_{k-1} \hspace{-7em}$ |; $key = q/{rmmax}[n+n'+n''];MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\rm max}[n+n'+n'']$ |; $key = q/a_i;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylesum_{j=1}^JP_n^{m}(sinvarphi_j)P_{n'}^{m}(sinvarphi_j)w_j=delta_{nn'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{j=1}^J P_n^{m}(\sin \varphi_j) P_{n'}^{m}(\sin \varphi_j) w_j = \delta_{nn'}$ |; $key = q/x;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/f-L;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/-1lemule1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $-1 \le \mu \le 1$ |; $key = q/tilde{P}_J(mu_j)=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_J(\mu_j)=0$ |; $key = q/h=nabla_H^2f;MSF=1.6;AAT/; $cached_env_img{$key} = q| $h = \nabla_H^2 f$ |; $key = q/B,C;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleC_pT+Lq=C_phat{T}+Lhat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle C_p T + L q = C_p \hat{T} + L \hat{q}$ |; $key = q/displaystyleDP{Phi}{sigma}=-frac{RT_v}{sigma}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\Phi}{\sigma} = - \frac{RT_v}{\sigma}.$ |; $key = q/displaystyleoverline{calA}^{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{\cal A}^{t}$ |; $key = q/hat{T},hat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{T}, \hat{q}$ |; $key = q/Deltaq_{evap};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta q_{evap}$ |; $key = q/B_{zeta};MSF=1.6;AAT/; $cached_env_img{$key} = q| $B_{\zeta }$ |; $key = q/j;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/J;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=-frac{1}{r}DP{psi}{varphi}+frac{1}{rcosvarphi}DP{chi}{lambda},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{r} \DP{\psi}{\varphi} + \frac{1}{r\cos\varphi} \DP{\chi}{\lambda} ,$ |; $key = q/displaystyle=-Dinv{acosvarphi}left{DP{(u_kq_k)}{lambda}+DP{(v_kq_kcosvarphi)}{varphi}right}+R_k+S_{q,k}+{calD}(q_k).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \Dinv{a \cos \varphi} \left\{ \DP{(u_k q_k)}{\lambda} + \DP{(v_k q_k \cos \varphi)}{\varphi} \right\} + R_k + S_{q,k} + {\cal D}(q_k).$ |; $key = q/displaystyle%T_{v,k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle % T_{v,k}$ |; $key = q/displaystyle=frac{{displaystylesum_{k=0}^{J-1}(2k+1)tilde{P}_k(mu)tilde{P}_k(mu_j)}}{Jtilde{P}_{J-1}(mu_j)};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{ {\displaystyle \sum_{k=0}^{J-1} (2k+1) \tilde{P}_k(\mu) \tilde{P}_k(\mu_j) } } {J \tilde{P}_{J-1}(\mu_j)}$ |; $key = q/qll1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $q \ll 1$ |; $key = q/displaystylepequivDP{f}{varphi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle p \equiv \DP{f}{\varphi}$ |; $key = q/m=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylekappa;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \kappa$ |; $key = q/displaystyle=Dinv{acosvarphi}left{DP{v_A}{lambda}-DP{(u_Acosvarphi)}{varphi}right}+{calD}(zeta),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \Dinv{a \cos \varphi} \left\{ \DP{v_A}{\lambda} - \DP{(u_A \cos \varphi)}{\varphi} \right\} + {\cal D}(\zeta),$ |; $key = q/k;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle:qquad比湿水平拡散,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 比湿水平拡散,$ |; $key = q/displaystyle=left{{array}{ll}{displaystylefrac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}}Aij}Y_n^{m*}(lambda_i,varphi_j)w_j,&1lemleM,quadmlenleN.{array}right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \left\{ \begin{array}{ll} {\displaystyle \frac{1}{I} \sum_{i=1}... ...varphi_j) w_j , & 1 \le m \le M, \quad m \le n \le N. \end{array} \right.$ |; $key = q/N_R;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylef;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle f$ |; $key = q/[];MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=frac{1}{I}sum_{i,j}q_{ij}Y_n^{m*}w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} q_{ij} Y_n^{m*} w_j$ |; $key = q/P_n^m(sinvarphi)exp(imlambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m(\sin \varphi) \exp(im \lambda)$ |; $key = q/k+1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleY^m_n(lambda,varphi)=sum_{m'=-n}^{n}A_n^{m'}Y^{m'*}_n(lambda',varphi').;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Y^m_n(\lambda, \varphi) = \sum_{m'=-n}^{n} A_n^{m'} Y^{m'*}_n(\lambda',\varphi') .$ |; $key = q/displaystylefrac{1}{I}sum_{n=1}^{I}g(lambda_n);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n)$ |; $key = q/F_R;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/A(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $A(\lambda,\varphi)$ |; $key = q/T^a_1=hat{T}_1,q^a_1=hat{q}_1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $T^a_1=\hat{T}_1, q^a_1=\hat{q}_1$ |; $key = q/nabla^{'2}_HY_n^m=-frac{n(n+1)}{r^2}Y_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla^{'2}_H Y_n^m = -\frac{n(n+1)}{r^2} Y_n^m$ |; $key = q/displaystyleequivDinv{acosvarphi}left{DP{v}{lambda}-DP{(ucosvarphi)}{varphi}right}:quad渦度[mathrm{s}^{-1}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \Dinv{a \cos \varphi} \left\{ \DP{v}{\lambda} - \DP{(u \cos \varphi)}{\varphi} \right\} : \quad 渦度 [\mathrm{s}^{-1}],$ |; $key = q/displaystyle=frac{1}{I}sum_{i,j}imleft(frac{f}{rcos^2varphi}right)_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} im \left( \frac{f}{r \cos^2 \varphi} \right)_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j$ |; $key = q/displaystylesum^{KMAX}_{k=1}DeltaT_{k}Deltap_{k}=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum^{KMAX}_{k=1} \Delta T_{k} \Delta p_{k} = 0$ |; $key = q/R_v;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/Ige2M+1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $I \ge 2M+1$ |; $key = q/sinvarphi=mu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sin \varphi = \mu$ |; $key = q/displaystyleqequivcos^2varphiDP{f}{varphi}=cos^2varphip;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q \equiv \cos^2\varphi \DP{f}{\varphi} = \cos^2\varphi p$ |; $key = q/displaystyle{calT}^f(z_1,z_2)=sum_{i=1}^{N_R}b_iexpleft(-delta_R|tau_{R,i}(z_1)-tau_{R,i}(z_2)|right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal T}^f(z_1,z_2) = \sum_{i=1}^{N_R} b_i \exp \left( - \delta_R \vert \tau_{R,i}(z_1) - \tau_{R,i}(z_2) \vert \right)$ |; $key = q/displaystylehat{q}>q^*(hat{T},p);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{q} > q^*(\hat{T},p)$ |; $key = q/displaystylehspace*{2cm}+(n+|m|)sqrt{frac{1}{2n-1}frac{(n-1+|m|)!}{(n-1-|m|)!}}P_{n-1}^m=0,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace*{2cm} +(n+\vert m\vert) \sqrt{ \frac{1}{2n-1} \frac{(n-1+\vert m\vert)!}{(n-1-\vert m\vert)!} } P_{n-1}^m = 0 ,$ |; $key = q/displaystylePhi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Phi$ |; $key = q/-frac{n(n+1)}{r^2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $- \frac{n(n+1)}{r^2}$ |; $key = q/displaystyleint_{-1}^1P_n(mu)P_n'(mu)dmu=2;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 P_n(\mu) P_n'(\mu) d \mu = 2$ |; $key = q/displaystylev=frac{1}{rcosvarphi}DP{psi}{lambda}+frac{1}{r}DP{chi}{varphi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle v = \frac{1}{r\cos\varphi} \DP{\psi}{\lambda} + \frac{1}{r} \DP{\chi}{\varphi}$ |; $key = q/M=21;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleb_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle b_k$ |; $key = q/displaystyledelta_{t}Dvect{T}=left(DP{Dvect{T}}{t}right)_{rmNG}-underline{h}overvect{D}}^{t}+{calD}_H(Dvect{T}^{t-Deltat}+2Deltatdelta_{t}Dvect{T}).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \delta_{t} \Dvect{T} = \left( \DP{\Dvect{T}}{t} \right)_{\rm NG} ... ...{t} + {\cal D}_H ( \Dvect{T}^{t-\Delta t} + 2 \Delta t \delta_{t} \Dvect{T} ) .$ |; $key = q/displaystyleDP{zeta_k}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\zeta_k}{t}$ |; $key = q/displaystyleW_{kl};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle W_{kl}$ |; $key = q/n-m;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyledot{sigma}^{rmNG}_{k-1slash2}=-sigma_{k-1slash2}left(DP{pi}{t}right)^{rmNG}-sum_{l=k}^{K}Dvect{v}_{l}cdotnablapiDeltasigma_{l},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma}^{\rm NG}_{k-1/2} = - \sigma_{k-1/2} \left( \DP{\pi}{... ...t)^{\rm NG} - \sum_{l=k}^{K} \Dvect{v}_{l} \cdot \nabla \pi \Delta \sigma_{l} ,$ |; $key = q/displaystyle=left(frac{sigma_{k-1slash2}}{sigma_k}right)^{kappa}-1,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \left( \frac{ \sigma_{k-1/2} } { \sigma_k } \right)^{\kappa} -1 ,$ |; $key = q/displaystylev_A(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle v_A (\varphi, \lambda, \sigma)$ |; $key = q/displaystyleoverline{T}(sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{T} (\sigma)$ |; $key = q/N;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylehat{T}_{k+1}+S_{grst}(T_{Bk+1}-hat{T}_{k+1})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k+1} + S_{grst} (T_{Bk+1} - \hat{T}_{k+1}) - \frac{ \sum... ..._{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k} }{ \sum^{k+2}_{k=k} \Delta p_{k} },$ |; $key = q/{Y_n^m|m=0,1,2,cdots,n=|m|,|m+1|,cdots};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ Y_n^m \vert m=0,1,2,\cdots, n=\vert m\vert,\vert m+1\vert,\cdots \}$ |; $key = q/displaystylefrac{(hat{p_s}+Deltap_s)sigma}{RT}q,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{(\hat{p_s} + \Delta p_s) \sigma}{RT} q,$ |; $key = q/displaystyle=sum_{m,n}imtilde{f}_n^mY_n^m(lambda_i,varphi_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{m,n} im \tilde{f}_n^m Y_n^m (\lambda_i,\varphi_j)$ |; $key = q/displaystyleC=sum_{m=-M}^{M}sum_{n=|m|}^{N}left(tilde{C}_n^mexp(imlambda)right)P_n^m(sinvarphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle C= \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \left( \tilde{C}_n^m \exp(im \lambda) \right) P_n^m(\sin \varphi)$ |; $key = q/2J-1ge{rmmax}[n+n'+n'']=3{rmmax}[N];MSF=1.6;AAT/; $cached_env_img{$key} = q| $2J-1 \ge {\rm max}[n+n'+n''] = 3 {\rm max}[N]$ |; $key = q/q;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/N_{{rmmax}}=M;MSF=1.6;AAT/; $cached_env_img{$key} = q| $N_{{\rm max}}=M$ |; $key = q/-1|; $key = q/displaystyle:quad気温[mathrm{K}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 気温 [\mathrm{K}],$ |; $key = q/Dvect{T}={T_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Dvect{T}=\{ T_{k} \}$ |; $key = q/bar{k}_{S,i};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\bar{k}_{S,i}$ |; $key = q/mu_j,mu_{j'}(1lej,j'leJ);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mu_j, \mu_{j'}(1 \le j,j' \le J)$ |; $key = q/A_{ij}^{odd};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ij}^{odd}$ |; $key = q/displaystylesum_{j=1}^{J}sum_{i=1}^{I}P_n^m(mu_j)P_{n'}^{m'}(mu_j)exp(imlambda_i)exp(-im'lambda_i)w_j=Idelta_{nn'}delta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{j=1}^{J} \sum_{i=1}^{I} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) \exp(i m \lambda_i) \exp(-i m' \lambda_i) w_j = I \delta_{nn'} \delta_{mm'}$ |; $key = q/sigma=1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma=1$ |; $key = q/displaystyleT(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T (\varphi, \lambda, \sigma)$ |; $key = q/J=K=M=N_{tr};MSF=1.6;AAT/; $cached_env_img{$key} = q| $J=K=M =N_{tr}$ |; $key = q/displaystyle=frac{1}{I}sum_{i,j}imf_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} im f_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j$ |; $key = q/displaystyleequiv-(zeta+f)u-dot{sigma}DP{v}{sigma}-frac{RT_v^{prime}}{a}DP{pi}{varphi}+{calF}_{varphi},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv - ( \zeta + f ) u - \dot{\sigma} \DP{v}{\sigma} - \frac{R T_v^{\prime}}{a} \DP{\pi}{\varphi} + {\cal F}_{\varphi},$ |; $key = q/m,n;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylehat{p_{s}}hat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{p_{s}} \hat{q}$ |; $key = q/{P_n}(n=0,1,2,cdots,J-1);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ P_n \}(n=0,1,2,\cdots,J-1)$ |; $key = q/tilde{B}_n^m=tilde{B}_n^{m*},{itetc.};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{B}_n^m = \tilde{B}_n^{m*}, {\it etc.}$ |; $key = q/displaystyleR_{kl};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle R_{kl}$ |; $key = q/displaystyle:quad水蒸気分子量比.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 水蒸気分子量比.$ |; $key = q/(2times21+1)times(21+1)=946;MSF=1.6;AAT/; $cached_env_img{$key} = q| $(2 \times 21 +1) \times (21+1)= 946$ |; $key = q/P_J;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}D&=frac{1}{rcosvarphi}DP{u}{lambda}+frac{1}{rcosvarphi}DP{}{varphi}(vcosvarphi).{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}D &= \frac{1}{r \cos \varphi} \DP{u}{\lambda} + \frac{1}{r \cos \varphi} \DP{}{\varphi} (v \cos \varphi) . \end{split}\end{align*}$ |; $key = q/f(mu)-L(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $f(\mu)-L(\mu)$ |; $key = q/displaystyle%(;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle % ($ |; $key = q/displaystyledot{sigma};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma}$ |; $key = q/S^{cond}_{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $S^{cond}_{q}$ |; $key = q/displaystyleF_S(z);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle F_S(z)$ |; $key = q/mathcal{A};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mathcal{A}$ |; $key = q/times10^6;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\times 10^6$ |; $key = q/{displaystylex_j=cosfrac{j-1slash2}{n}pi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $x_j=\cos \frac{j-1/2}{n}\pi$ |; $key = q/displaystylehspace{3em}=-left(1+gamma_{k}right)DeltaT_{k}Deltap_{k}+frac{L}{C_p}Deltap_{k-1}+left{hat{q}_{k}-q^{*}(hat{T}_{k})right}Deltap_{k}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{3em} = - \left( 1 + \gamma_{k} \right) \Delta T_{k} \Delt... ...{k-1} + \left\{ \hat{q}_{k} - q^{*} (\hat{T}_{k}) \right\} \Delta p_{k} \right]$ |; $key = q/f'(alpha)=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $f'(\alpha)=0$ |; $key = q/C;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/Deltasigma;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta \sigma$ |; $key = q/{align*}{split}&left{(1-2Deltat{calD}_H)(1-2Deltat{calD}_M)underline{I}-(Deltat)[pi^{t-Deltat}+Deltatleft(DP{pi}{t}right)_{rmNG}right]right}.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}& \left\{ ( 1-2\Delta t {\cal D}_H )( 1-2\Delta t {\c... ...t \left( \DP{\pi}{t} \right)_{\rm NG} \right] \right\} . \end{split}\end{align*}$ |; $key = q/displaystyle=q^{*}(T_{k},p_{k}),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = q^{*} (T_{k}, p_{k}),$ |; $key = q/{displaystylesigmaequivfrac{p}{p_s}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma \equiv \frac{p}{p_s}$ |; $key = q/displaystyle(1-mu^2)DD{}{mu}P_n^m=(n+|m|)sqrt{frac{(n-|m|)(2n+1)}{(n+|m|)(2n-1)}}P_{n-1}^m-nmuP_n^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (1-\mu^2) \DD{}{\mu} P_n^m = (n+\vert m\vert) \sqrt{ \frac{(n-\vert m\vert)(2n+1)}{(n+\vert m\vert)(2n-1)} } P_{n-1}^m - n \mu P_n^m .$ |; $key = q/displaystyle{calD}(zeta)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]zeta,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(\zeta) = - K_{HD} \left[ (-1)^{N_D/2} \nabla^{N_D} - \left( \frac{2}{a^2} \right)^{N_D/2} \right] \zeta ,$ |; $key = q/displaystylecoszeta=cosvarphicosdelta_ScosH+sinvarphisindelta_S;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \cos \zeta = \cos \varphi \cos \delta_S \cos H + \sin \varphi \sin \delta_S$ |; $key = q/P_n(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n(\mu)$ |; $key = q/(n,m);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleS_{kl};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle S_{kl}$ |; $key = q/displaystyle=-left{DeltaT_{k}+frac{L}{C_p}(q_{k}-hat{q}_{k})right}Deltap_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \left\{ \Delta T_{k} + \frac{L}{C_p} (q_{k} - \hat{q}_{k}) \right\} \Delta p_{k},$ |; $key = q/displaystylesigma_k=left{frac{1}{1+kappa}left(frac{sigma^{kappa+1}_{k-1slash2}-sh2}}{sigma_{k-1slash2}-sigma_{k+1slash2}}right)right}^{1slashkappa}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sigma_k = \left\{ \frac{1}{1+\kappa} \left( \frac{ \sigma^{\kapp... ... +1}_{k+1/2} } { \sigma_{k-1/2} - \sigma_{k+1/2} } \right) \right\}^{1/\kappa}.$ |; $key = q/n=|m|,|m|+1,cdots,|m|+J-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $n=\vert m\vert, \vert m\vert+1, \cdots, \vert m\vert+J-1$ |; $key = q/displaystyle=frac{1}{rcos^2varphi_i}g_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{r \cos^2 \varphi_i} g_{ij}$ |; $key = q/displaystyleB=sum_{m=-M}^{M}sum_{n=|m|}^{N}left(tilde{B}_n^mexp(imlambda)right)P_n^m(sinvarphi),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle B= \sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N} \left( \tilde{B}_n^m \exp(im \lambda) \right) P_n^m(\sin \varphi) ,$ |; $key = q/T^a_{k_B}=hat{T}_{k_B},q^a_{k_B}=q^*(hat{T}_{k_B},p_{k_B});MSF=1.6;AAT/; $cached_env_img{$key} = q| $T^a_{k_B} = \hat{T}_{k_B}, q^a_{k_B} = q^*( \hat{T}_{k_B}, p_{k_B} )$ |; $key = q/q^{*};MSF=1.6;AAT/; $cached_env_img{$key} = q| $q^{*}$ |; $key = q/displaystyle=sum_{j=1}^{J}f(mu_j)int_{-1}^1frac{tilde{P}_J(mu)}{(mu-mu_j)tilde{P}^{'}_J(mu_j)}dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{j=1}^{J} f(\mu_j) \int_{-1}^1 \frac{\tilde{P}_J(\mu)} {(\mu-\mu_j)\tilde{P}^{'}_J(\mu_j)} d \mu$ |; $key = q/{align*}{split}mbox{div}_HDvect{v}&equivfrac{1}{rcosvarphi}DP{v_1}{lambda}+frac{t{1-mu^2}}DP{v_1}{lambda}+frac{1}{r}DP{}{mu}(sqrt{1-mu^2}v_2){split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\mbox{div}_H \Dvect{v} &\equiv \frac{1}{r \cos \varph... ...{\lambda} + \frac{1}{r} \DP{}{\mu}( \sqrt{1-\mu^2} v_2 ) \end{split}\end{align*}$ |; $key = q/displaystyleequivnabla_H^2psi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \nabla_H^2 \psi$ |; $key = q/f'=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=frac{displaystyle(1+gamma_{k-1})Deltap_{k-1}S_{k-1slash2}+left(1+gaac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)(1+gamma_{k})Deltap_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{ \displaystyle (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2... ...pa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) (1 + \gamma_{k}) \Delta p_{k} }$ |; $key = q/(k-1);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyledot{sigma}_{1slash2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \dot{\sigma}_{1/2}$ |; $key = q/displaystyle=-left(frac{alpha_{k}}{Deltasigma_{k}}Deltasigma_{l}delta_{kleql}+fr}{Deltasigma_{k}}Deltasigma_{l}delta_{k+1leql}right)overline{T}_{k}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \left( \frac{ \alpha_{k} }{ \Delta \sigma_{k} } \Delta \sigma... ...a \sigma_{k} } \Delta \sigma_{l} \delta_{k+1 \leq l} \right) \overline{T}_{k} .$ |; $key = q/displaystylewidetilde{left(DP{f}{varphi}right)}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \widetilde{\left(\DP{f}{\varphi}\right)}_n^m$ |; $key = q/m=n=0;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleleft{1+gamma_{k-1}right}DeltaT_{k-1}Deltap_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{ 1 + \gamma_{k-1} \right\} \Delta T_{k-1} \Delta p_{k-1}$ |; $key = q/displaystyle=-sum_{i}sum_{j}f_{n'}^{m'}P_{n'}^{m'}(varphi_j)exp(im'lambda_i)left.DD{P_{n}^{m}}{varphi}right|_jexp(-imlambda_i)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sum_{i} \sum_{j} f_{n'}^{m'} P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) \left. \DD{P_{n}^{m}}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j .$ |; $key = q/displaystyle:qquad凝結,小規模運動過程等による水蒸気ソース,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 凝結, 小規模運動過程等による水蒸気ソース,$ |; $key = q/displaystylesum_{k=0}^{J-1}frac{f_k(mu_j)f_k(mu_{j'})}{lambda_k}=frac{1}{w_j}delta_{jj'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{k=0}^{J-1} \frac{f_k (\mu_j) f_k (\mu_{j'}) }{\lambda_k} = \frac{1}{w_j} \delta_{jj'}$ |; $key = q/displaystyle=frac{I}{2}int_{-1}^1P_n^m(mu)P_{n'}^{m}(mu)dmu.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{I}{2} \int_{-1}^1 P_n^m (\mu) P_{n'}^{m} (\mu) d\mu .$ |; $key = q/displaystyle=frac{1}{I}sum_{m'=-M}^{M}sum_{n'=|m'|}^Ntilde{A}_{n'}^{m'}sum_{i=1}-m)lambda)sum_{j=1}^JP_n^{m}(sinvarphi_j)P_{n'}^{m'}(sinvarphi_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{m'=-M}^{M} \sum_{n'=\vert m'\vert}^N \tilde{A... ...) \lambda) \sum_{j=1}^J P_n^{m}(\sin \varphi_j) P_{n'}^{m'}(\sin \varphi_j) w_j$ |; $key = q/displaystyle=-frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}P_{n'}^{m'}(varphi_j)exp(im'lambda_i)right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'} P_{n'}^{m'}(\varphi_j) \exp(i m' \lambda_i) \right)$ |; $key = q/displaystyle:quad経度[mathrm{deg.}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 経度 [\mathrm{deg.}],$ |; $key = q/displaystyleT^a_{k+1}>hat{T}_{k+1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T^a_{k+1} > \hat{T}_{k+1}$ |; $key = q/1leileI,1lejleJ,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $1 \le i \le I , 1 \le j \le J,$ |; $key = q/L-f;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylevarphi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \varphi$ |; $key = q/hat{rho};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{\rho}$ |; $key = q/displaystyle(1-mu^2)DP{tilde{P}_n}{mu}=ntilde{P}_{n-1}(mu)-nmutilde{P}_n(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (1-\mu^2) \DP{\tilde{P}_n}{\mu} = n \tilde{P}_{n-1}(\mu) - n \mu \tilde{P}_n(\mu)$ |; $key = q/displaystyle=alpha_kleft[1-left(frac{sigma_k}{sigma_{k-1}}right)^{kappa}right]^{-1},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \alpha_k \left[ 1- \left( \frac{ \sigma_k }{ \sigma_{k-1} } \right)^{\kappa} \right]^{-1},$ |; $key = q/g(lambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $g(\lambda)$ |; $key = q/Dvect{v};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Dvect{v}$ |; $key = q/displaystyleT_{k+1}+S_{grst}(T_{Bk+1}-T_{k+1})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{k+1} + S_{grst} (T_{Bk+1} - T_{k+1}) - \frac{ \sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k} }{ \sum^{k+1}_{k=k-1} \Delta p_{k} }$ |; $key = q/tilde{P}_n^0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_n^0$ |; $key = q/P_n;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/times10^{10};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\times 10^{10}$ |; $key = q/M=42,N=42;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{tilde{P}_n^m|n=|m|,|m+1|,cdots};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ \tilde{P}_n^m \vert n=\vert m\vert,\vert m+1\vert,\cdots \}$ |; $key = q/n=J,mu=mu_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $n=J, \mu=\mu_j$ |; $key = q/sigma_{k-1slash2}(k=1,2,cdots,K);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma_{k-1/2} (k=1,2,\cdots,K)$ |; $key = q/displaystyleA_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A_{ij}$ |; $key = q/u;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle)_{k}-nabla^{2}_{sigma}sum_{k=1}^{K}W_{kl}(T_{v,l}-T_{l})+{calD}(D_{k}),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle )_{k} - \nabla^{2}_{\sigma} \sum_{k=1}^{K} W_{kl} ( T_{v,l}-T_{l} ) + {\cal D}(D_{k}) ,$ |; $key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Ntilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i) ,$ |; $key = q/exp(imlambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\exp(im\lambda)$ |; $key = q/displaystylequadtimessum_{i=1}^Iexp(i(m'+m''-m)lambda_i)sum_{j=1}^JP_{n'}^{m'}(sinvarphi_j)P_{n''}^{m''}(sinvarphi_j)P_n^{m}(sinvarphi_j)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \times \sum_{i=1}^I \exp(i(m'+m''-m) \lambda_i) \sum_{j=1}^... ...m'}(\sin \varphi_j) P_{n''}^{m''}(\sin \varphi_j) P_n^{m}(\sin \varphi_j) w_j .$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^JB_{ij}C_{ij}P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J B_{ij} C_{ij} P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/displaystyle:quad緯度[mathrm{deg.}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 緯度 [\mathrm{deg.}],$ |; $key = q/displaystylebeta_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \beta_k$ |; $key = q/f'=2nx(x^2-1)^{n-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $f'=2nx(x^2-1)^{n-1}$ |; $key = q/displaystyle∴P_{n+1}^m=sqrt{frac{(2n+1)(2n+3)}{(n-|m|+1)(n+|m|+1)}}muP_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle ∴ P_{n+1}^m = \sqrt{ \frac{(2n+1)(2n+3)}{(n-\vert m\vert+1)(n+\vert m\vert+1)} } \mu P_n^m$ |; $key = q/displaystyleleft(DP{f}{lambda}right)_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( \DP{f}{\lambda} \right)_{ij}$ |; $key = q/{Y_n^m|m=-n,-n+1,cdots,n};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{Y_n^m \vert m= -n, -n+1,\cdots,n \}$ |; $key = q/T,q;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/tilde{P}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_n^m$ |; $key = q/frac{I-1}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\frac{I-1}{2}$ |; $key = q/J-1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/tilde{A}_n^m(-MlemleM,|m|lenleN);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{A}_n^m ( -M \le m \le M, \vert m\vert \le n \le N)$ |; $key = q/displaystyle=-Isum_{j}f_{n'}^{m}P_{n'}^{m}(varphi_j)left.DD{P_{n}^{m}}{varphi}right|_jw_jdelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - I \sum_{j} f_{n'}^{m} P_{n'}^{m}(\varphi_j) \left.\DD{P_{n}^{m}}{\varphi}\right\vert _j w_j \delta_{mm'}$ |; $key = q/M|; $key = q/sim;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sim$ |; $key = q/mu_j（j=1,2,cdots,J）;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mu_j（j=1,2,\cdots,J）$ |; $key = q/displaystylezeta(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \zeta (\varphi, \lambda, \sigma)$ |; $key = q/displaystyleF_S^I(lambda,varphi)=-S_0r_S^{-2}coszeta.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle F_S^I (\lambda, \varphi)= - S_0 r_S^{-2} \cos \zeta .$ |; $key = q/{displaystyleleft{tilde{A}^m_nexp(imlambda)right}^*=tilde{A}^{-m}_nexp(-imlambda)};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \left\{\tilde{A}^m_n \exp(im\lambda) \right\}^* = \tilde{A}^{-m}_n \exp(-im\lambda) }$ |; $key = q/displaystyle=Deltasigma_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \Delta \sigma_{k} ,$ |; $key = q/displaystylesum_{i=1}^{I}exp(imlambda_i)exp(-im'lambda_i);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{i=1}^{I} \exp(im \lambda_i) \exp(-im' \lambda_i)$ |; $key = q/P_n,P_n^1,P_n^2;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/tilde{A}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{A}_n^m$ |; $key = q/hat{T}_{k+2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{T}_{k+2}$ |; $key = q/displaystyleDeltaT_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta T_{k-1}$ |; $key = q/displaystylefrac{Deltaq_{evap}}{Deltat}=frac{F_{evap}L^{-1}rho_s^{-1}}{Deltaz}=fevap}L^{-1}rho_s^{-1}}{Deltapslash(rho_sg)}=F_{evap}frac{g}{LDeltap};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{\Delta q_{evap}}{\Delta t} = \frac{ F_{evap} L^{-1} \rho_s^... ...vap} L^{-1} \rho_s^{-1}}{\Delta p / (\rho_s g)} = F_{evap} \frac{g}{L \Delta p}$ |; $key = q/displaystyleDP{T}{z}-frac{RT}{C_pp}DP{p}{z}+frac{L}{C_p}DP{q^*}{z}<0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{T}{z} - \frac{RT}{C_p p} \DP{p}{z} + \frac{L}{C_p} \DP{q^*}{z} < 0$ |; $key = q/sigma_k(k=1,2,ldotsK);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma_k (k=1,2,\ldots K)$ |; $key = q/im'tilde{f}_{n'}^{m'}=tilde{g}_{n'}^{m'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $im' \tilde{f}_{n'}^{m'} = \tilde{g}_{n'}^{m'}$ |; $key = q/displaystylew_j=frac{1-mu_j^2}{(Jsqrt{frac{1}{2J-1}}P_{J-1}(mu_j))^2}=frac{(2J-1)(1-mu_j^2)}{(JP_{J-1}(mu_j))^2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle w_j = \frac{1-\mu_j^2} {(J \sqrt{ \frac{1}{2J-1} } P_{J-1}(\mu_j))^2 } = \frac{(2J-1)(1-\mu_j^2)} {(J P_{J-1}(\mu_j))^2 }$ |; $key = q/displaystyleA(mu)=sum_{n=|m|}^{infty}tilde{A}_n^mP_n^m(mu),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A(\mu) = \sum_{n=\vert m\vert}^{\infty} \tilde{A}_n^m P_n^m(\mu),$ |; $key = q/{displaystylefrac{I}{3}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\frac{I}{3}$ |; $key = q/displaystyleq^{*}(T,p)=p^{*}_{0}expleft(-frac{L}{RT}right)frac{1}{p};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q^{*}(T, p) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right) \frac{1}{p}$ |; $key = q/{displaystyleJgefrac{3N_{tr}+1}{2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \ge \frac{3N_{tr}+1}{2}$ |; $key = q/displaystyleY_n^m(lambda,varphi)equivP_n^m(sinvarphi)exp(imlambda),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Y_n^m(\lambda,\varphi) \equiv P_n^m(\sin \varphi) \exp(im \lambda),$ |; $key = q/f';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/equivhat{q}slashq^*(hat{T},p);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\equiv \hat{q}/q^*(\hat{T},p)$ |; $key = q/displaystylea_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle a_k$ |; $key = q/epsilon_f;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\epsilon_f$ |; $key = q/displaystyle{calD}(zeta);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(\zeta)$ |; $key = q/K=42,J=M=21;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyledelta_{t}pi=left(DP{pi}{t}right)_{rmNG}-Dvect{C}cdotoverline{Dvect{D}}^{t},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \delta_{t} \pi = \left( \DP{\pi}{t} \right)_{\rm NG} - \Dvect{C} \cdot \overline{ \Dvect{D} }^{t} ,$ |; $key = q/y;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleT_v^{prime}(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_v^{\prime} (\varphi, \lambda, \sigma)$ |; $key = q/I=64,J=64;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleoverline{F_S^I}(varphi)simeq-S_0(A_{ins}+B_{ins}cos^2varphi),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{F_S^I} (\varphi) \simeq - S_0 ( A_{ins} + B_{ins} \cos^2 \varphi ) ,$ |; $key = q/displaystyleequivlnp_s,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \ln p_s,$ |; $key = q/A{i,J-j}=A_{ij}^{even}-A_{ij}^{odd};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A{i,J-j}=A_{ij}^{even}-A_{ij}^{odd}$ |; $key = q/alpha;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\alpha$ |; $key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda$ |; $key = q/displaystyle=-sum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}left.DD{P_{n}^{m}}{varphi}right|_jexp(-imlambda_i)P_{n'}^{m'}(varphi_j)exp(im'lambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} \left. \DD{P_{n}^{m}}{\... ...ight\vert _j \exp(-im \lambda_i) P_{n'}^{m'}(\varphi_j) \exp(im' \lambda_i) w_j$ |; $key = q/{displaystylesum_{i,j}Y_{n'}^{m'*}|_{ij}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{i,j} Y_{n'}^{m'*}\vert _{ij}$ |; $key = q/I=64;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/frac{1}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\frac{1}{2}$ |; $key = q/P_0simP_{n-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_0 \sim P_{n-1}$ |; $key = q/{displaystyle-frac{I-1}{2}simfrac{I-1}{2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $-\frac{I-1}{2} \sim \frac{I-1}{2}$ |; $key = q/displaystyle=frac{displaystyle(1+gamma_{k-1})Deltap_{k-1}S_{k-1slash2}+left(1+gash2}}left{(1+gamma_{k-1})Deltap_{k-1}-(1+gamma_{k})Deltap_{k}right}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{ \displaystyle (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2... ...\{ (1 + \gamma_{k-1}) \Delta p_{k-1} - (1 + \gamma_{k}) \Delta p_{k} \right\} }$ |; $key = q/^{-4};MSF=1.6;AAT/; $cached_env_img{$key} = q| $^{-4}$ |; $key = q/alpha_g;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\alpha_g$ |; $key = q/n=J,x=mu,y=mu_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $n=J,x=\mu,y=\mu_j$ |; $key = q/delta_v=epsilon_v^{-1}-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\delta_v = \epsilon_v^{-1} - 1$ |; $key = q/varphi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\varphi$ |; $key = q/displaystyleT_{k-1}+S_{grst}(T_{Bk-1}-T_{k-1})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{k-1} + S_{grst} (T_{Bk-1} - T_{k-1}) - \frac{ \sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k} }{ \sum^{k+1}_{k=k-1} \Delta p_{k} },$ |; $key = q/displaystyle=frac{1}{I}sum_{i,j}imf_{ij}Y_n^{m*}(lambda_ivarphi_j)frac{w_j}{rcos^2varphi_j}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} im f_{ij} Y_n^{m*} (\lambda_i \varphi_j) \frac{w_j}{r \cos^2 \varphi_j} .$ |; $key = q/0leKle2J-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le K \le 2J-1$ |; $key = q/q_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $q_{k}$ |; $key = q/I=128,J=64;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle:qquad渦度水平拡散,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 渦度水平拡散,$ |; $key = q/N_{{rmmax}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $N_{{\rm max}}$ |; $key = q/displaystyle=T_{k}-hat{T}_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = T_{k} - \hat{T}_{k} ,$ |; $key = q/0le|m|len,n';MSF=1.6;AAT/; $cached_env_img{$key} = q| $0\le \vert m\vert \le n,n'$ |; $key = q/displaystyleh_{ij}=left.left(nabla_H^2sum_{m,n}tilde{f}_n^mY_n^mright)right|_{ij}=-sum_{m,n}frac{n(n+1)}{r^2}left.tilde{f}_n^mY_n^mright|_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle h_{ij} = \left. \left(\nabla_H^2 \sum_{m,n} \tilde{f}_n^m Y_n^m \... ... = - \sum_{m,n} \frac{n(n+1)}{r^2} \left. \tilde{f}_n^m Y_n^m \right\vert _{ij}$ |; $key = q/displaystyleP_n^m(mu)equivsqrt{frac{(2n+1)(n-|m|)!}{(n+|m|)!}}frac{(1-mu^2)^{frac{|m|}{2}}}{2^nn!}DD[n+|m|]{}{mu}(mu^2-1)^n,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle P_n^m(\mu)\equiv \sqrt{\frac{(2n+1)(n-\vert m\vert)!}{(n+\vert m\... ...u^2)^{\frac{\vert m\vert}{2}} }{2^n n!} \DD[n+\vert m\vert]{}{\mu} (\mu^2-1)^n,$ |; $key = q/delta_{kleql};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\delta_{k \leq l}$ |; $key = q/displaystyleq_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q_{k}$ |; $key = q/Deltaq;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta q$ |; $key = q/tilde{P}^m_n(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}^m_n(\mu)$ |; $key = q/displaystylefrac{tilde{P}_J(mu)}{mu-mu_j};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{\tilde{P}_J (\mu) }{\mu-\mu_j}$ |; $key = q/d_{mathrm{H}_2mathrm{O}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $d_{\mathrm{H}_2\mathrm{O}}$ |; $key = q/-MlemleM,|m|lenleN;MSF=1.6;AAT/; $cached_env_img{$key} = q| $-M \le m \le M, \vert m\vert \le n \le N$ |; $key = q/displaystyleT_{Bk}=frac{T_{k+1slash2}+T_{k-1slash2}}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{Bk} = \frac{T_{k+1/2} + T_{k-1/2}}{2}$ |; $key = q/displaystyle=q^{*}(hat{T}_{k-1},p_{k-1})+left.DP{q^{*}}{T}right|_{hat{T}_{k-1}}DeltaT_{k-1}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = q^{*} (\hat{T}_{k-1},p_{k-1}) + \left. \DP{q^{*}}{T} \right\vert _{\hat{T}_{k-1}} \Delta T_{k-1}.$ |; $key = q/z;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleequivnabla_H^2chi,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \nabla_H^2 \chi ,$ |; $key = q/displaystyle{calD}(T)=-(-1)^{N_Dslash2}K_{HD}nabla^{N_D}T,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(T) = - (-1)^{N_D/2} K_{HD} \nabla^{N_D} T ,$ |; $key = q/tilde{P}_n^m(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_n^m(\mu)$ |; $key = q/displaystyle=-D-DP{dot{sigma}}{sigma}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - D - \DP{\dot{\sigma}}{\sigma}.$ |; $key = q/dot{calA}_{cnd};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\cal A}_{cnd}$ |; $key = q/M=42;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/a;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylealpha_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \alpha_k$ |; $key = q/{rmmax}[n+n'];MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\rm max}[n+n']$ |; $key = q/0le|m|len;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le \vert m\vert \le n$ |; $key = q/displaystylee^{*}(T)=p^{*}_{0}expleft(-frac{L}{RT}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle e^{*}(T) = p^{*}_{0} \exp \left( - \frac{L}{RT} \right)$ |; $key = q/displaystyleA(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A(\lambda,\varphi)$ |; $key = q/displaystyle=Isum_{j}f_{n'}^{m'}P_{n}^{m}(varphi_j)left.DD{P_{n'}^{m'}}{varphi}rP_{n}^{m}(varphi_j)left.DD{P_{n'}^{m}}{varphi}right|_jw_jdelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = I \sum_{j} f_{n'}^{m'} P_{n}^{m}(\varphi_j) \left.\DD{P_{n'}^{m... ...}^{m}(\varphi_j) \left.\DD{P_{n'}^{m}}{\varphi}\right\vert _j w_j \delta_{m m'}$ |; $key = q/displaystylegamma_{k}equivfrac{L}{C_p}left.DP{q^{*}}{T}right|_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \gamma_{k} \equiv \frac{L}{C_p} \left. \DP{q^{*}}{T} \right\vert _{k}$ |; $key = q/displaystyleDP{pi}{t}+frac{u}{acosvarphi}DP{pi}{lambda}+frac{v}{a}DP{pi}{varphi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\pi}{t} + \frac{u}{a \cos \varphi} \DP{\pi}{\lambda} + \frac{v}{a} \DP{\pi}{\varphi}$ |; $key = q/Ige3M+1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $I \ge 3M+1$ |; $key = q/int_0^{2pi}exp(imlambda)dlambda;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\int_0^{2\pi} \exp(i m \lambda) d \lambda$ |; $key = q/T_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $T_{k}$ |; $key = q/M=64;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylesum_{n=1}^{I}exp(imlambda_n)=left{{array}{ll}I&(m=0),0&(0<|m||; $key = q/{displaystylefrac{pi}{2}>varphi_1>varphi_2>cdots>varphi_{J}>-frac{pi}{2}};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \frac{\pi}{2} > \varphi_1 > \varphi_2 > \cdots > \varphi_{J} > -\frac{\pi}{2} }$ |; $key = q/Y_n^mexp(imlambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $Y_n^m \exp(im\lambda)$ |; $key = q/tilde{P_n};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P_n}$ |; $key = q/T_{k+2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $T_{k+2}$ |; $key = q/varphi_j(j=1,2,3,cdots,J);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\varphi_j (j=1,2,3,\cdots,J)$ |; $key = q/displaystyleqquad+DeltaT_{k-1}-DeltaT_{k}+frac{L}{C_p}left.DP{q^{*}}{T}right|_{keltap_{k-1slash2}}{p_{k-1slash2}}frac{DeltaT_{k-1}+DeltaT_{k}}{2}=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \qquad + \Delta T_{k-1} - \Delta T_{k} + \frac{L}{C_p} \left. \DP... ...\frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\Delta T_{k-1} + \Delta T_{k}}{2} = 0.$ |; $key = q/displaystyle(T_{k}-T_{k-1})cdot(T_{k+1}-T_{k})<0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) < 0$ |; $key = q/displaystyleT_k=hat{T}_k+frac{L}{C_p}(1-b)Ifrac{(T^c_k-T_k)}{displaystylesum_{k=k_B}^{k_T}(T^c_k-T_k)frac{Deltap_k}{g}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_k = \hat{T}_k + \frac{L}{C_p} (1-b) I \frac{( T^c_k - T_k )} {\displaystyle \sum_{k=k_B}^{k_T} ( T^c_k - T_k ) \frac{\Delta p_k}{g} }$ |; $key = q/displaystylebar{calA}^{t}=(1-2epsilon_f){calA}^{t}+epsilon_fleft(bar{calA}^{t-Deltat}+{calA}^{t+Deltat}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \bar{\cal A}^{t} = ( 1-2 \epsilon_f ) {\cal A}^{t} + \epsilon_f \left( \bar{\cal A}^{t-\Delta t} + {\cal A}^{t+\Delta t} \right)$ |; $key = q/displaystylehat{T}_{k-1}-hat{T}_{k}+frac{L}{C_p}left{q^{*}(hat{T}_{k-1})-q^{*}(hc{Deltap_{k-1slash2}}{p_{k-1slash2}}frac{hat{T}_{k-1}+hat{T}_{k}}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k-1} - \hat{T}_{k} + \frac{L}{C_p} \left\{ q^{*} (\hat{T... ...{C_p} \frac{\Delta p_{k-1/2}}{p_{k-1/2}} \frac{\hat{T}_{k-1} + \hat{T}_{k} }{2}$ |; $key = q/{Y_n^m(lambda',varphi')|m=-n,-n+1,cdots,n};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{ Y_n^m(\lambda', \varphi') \vert m=-n,-n+1, \cdots, n \}$ |; $key = q/{displaystyleM=left[frac{I}{2}right]};MSF=1.6;AAT/; $cached_env_img{$key} = q| $M= \left[ \frac{I}{2} \right]$ |; $key = q/displaystylev_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle v_{ij}$ |; $key = q/Y_n^m(varphi,lambda);MSF=1.6;AAT/; $cached_env_img{$key} = q| $Y_n^m(\varphi,\lambda)$ |; $key = q/displaystyle=underline{Q}underline{S}-underline{R},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \underline{Q}\underline{S} - \underline{R} ,$ |; $key = q/Y^m_n(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $Y^m_n(\lambda, \varphi)$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^JA_{ij}P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J A_{ij} P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/displaystyleq=frac{hat{p_s}}{hat{p_s}+Deltap_s}hat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q = \frac{\hat{p_s}}{\hat{p_s} + \Delta p_s} \hat{q}$ |; $key = q/piBequivsigma_{SB}T^4;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\pi B \equiv \sigma_{SB} T^4$ |; $key = q/displaystyleF_S^I(lambda,varphi)=-S_0(1-mathcal{A})coszeta;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle F_S^I (\lambda, \varphi) = - S_0 (1 - \mathcal{A}) \cos \zeta$ |; $key = q/displaystyleD(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle D (\varphi, \lambda, \sigma)$ |; $key = q/-MlemleM,|m|lenleN(m);MSF=1.6;AAT/; $cached_env_img{$key} = q| $-M \le m \le M, \vert m\vert \le n \le N(m)$ |; $key = q/displaystyleleft[DeltaT_{k-1}+frac{L}{C_p}left{q^{*}(hat{T}_{k-1})+left.DP{q^{*}|_{k-1}DeltaT_{k-1}-hat{q}_{k-1}right}right]Deltap_{k-1}hspace{-7em};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[ \Delta T_{k-1} + \frac{L}{C_p} \left\{ q^{*} (\hat{T}_{k-1... ...1} \Delta T_{k-1} - \hat{q}_{k-1} \right\} \right] \Delta p_{k-1} \hspace{-7em}$ |; $key = q/T=overline{T}_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $T=\overline{T}_k$ |; $key = q/displaystyleT_{k+1}+S_{grst}(T_{Bk+2}-T_{k+2})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{k+1} + S_{grst} (T_{Bk+2} - T_{k+2}) - \frac{ \sum^{k+2}_{k=k} S_{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k} }{ \sum^{k+2}_{k=k} \Delta p_{k} }$ |; $key = q/displaystylerangle=frac{displaystylesum_{k=k_B}^{k_T}hat{q}frac{Deltap_k}{g}}{displaystylesum_{k=k_B}^{k_T}q^*(hat{T},p)frac{Deltap_k}{g}}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \rangle = \frac{\displaystyle \sum_{k=k_B}^{k_T} \hat{q} \frac{\D... ...{g} } {\displaystyle \sum_{k=k_B}^{k_T} q^*(\hat{T},p) \frac{\Delta p_k}{g} } .$ |; $key = q/k_T;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=-frac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}Delt}+frac{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}... ...rac{1}{ 1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}}$ |; $key = q/T^a_k=hat{T}_k,q^a_k=q^*(hat{T}_k,p_k);MSF=1.6;AAT/; $cached_env_img{$key} = q| $T^a_k = \hat{T}_k, q^a_k = q^*( \hat{T}_k, p_k )$ |; $key = q/displaystyleq^a_{k+1}=q^a_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q^a_{k+1} = q^a_k$ |; $key = q/m;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=sum_{m,n}left(frac{1}{rcosvarphi_j}imtilde{psi}_n^mP_n^m(sinvarphi_tilde{chi}_n^mleft.DD{P_n^m}{varphi}right|_{j}right)exp(imlambda_i).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{m,n} \left( \frac{1}{r\cos\varphi_j} im \tilde{\psi}_n^m ... ...i}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _{j} \right) \exp(im \lambda_i) .$ |; $key = q/pi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\pi$ |; $key = q/displaystyle{calA}^{t+Deltat}=hat{calA}^{t+Deltat}+2Deltatdot{calA}_{dis}left(haDeltat}right)+2Deltatdot{calA}_{cnd}left(hat{calA}^{t+Deltat}right).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal A}^{t+\Delta t} = \hat{\cal A}^{t+\Delta t} + 2 \Delta t \d... ...ight) + 2 \Delta t \dot{\cal A}_{cnd}\left( \hat{\cal A}^{t+\Delta t} \right) .$ |; $key = q/displaystyle:quad時間[mathrm{s}].;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 時間 [\mathrm{s}].$ |; $key = q/L(mu_j)=f(mu_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $L(\mu_j) = f(\mu_j)$ |; $key = q/{displaystyleexp(imlambda_n)=expleft(frac{2piim(n-1)}{I}right)};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \exp(i m \lambda_n) = \exp \left( \frac{2\pi i m (n-1)}{I} \right) }$ |; $key = q/displaystyleq=hat{q}-frac{L}{C_p}DP{q^*}{T}frac{hat{q}-q^*(hat{T},p)}{displaystyle1+frac{L}{C_p}DP{q^*}{T}}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q = \hat{q} - \frac{L}{C_p} \DP{q^*}{T} \frac{ \hat{q} - q^*(\hat{T},p) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} } .$ |; $key = q/varphi=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\varphi=0$ |; $key = q/P;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/(T^a_{k+1},q^a_{k+1});MSF=1.6;AAT/; $cached_env_img{$key} = q| $(T^a_{k+1}, q^a_{k+1})$ |; $key = q/{Y_n^m|n=0,1,2,cdots,m=-n,-n+1,cdots,n};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\{Y_n^m \vert n=0,1,2,\cdots, m= -n, -n+1,\cdots,n \}$ |; $key = q/displaystylequadsum_{i}sum_{j}f_{n'}^{m'}P_{n}^{m}(varphi_j)exp(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \sum_{i} \sum_{j} f_{n'}^{m'} P_{n}^{m}(\varphi_j) \exp(im \lambda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$ |; $key = q/sigma;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma$ |; $key = q/displaystyleDP{q_k}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{q_k}{t}$ |; $key = q/displaystyle=(2n+1)(x-y)tilde{P}_n(x)tilde{P}_n(y);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = (2n+1)(x-y)\tilde{P}_n(x)\tilde{P}_n(y)$ |; $key = q/displaystyle=imtilde{f}_n^m.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = im \tilde{f}_n^m .$ |; $key = q/varphi_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\varphi_j$ |; $key = q/displaystyle=-sigma_{k-1slash2}DP{pi}{t}-sum_{l=k}^{K}(D_l+Dvect{v}_lcdotnablapi)Deltasigma_l,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \sigma_{k-1/2} \DP{\pi}{t} - \sum_{l=k}^{K} ( D_l + \Dvect{v}_l \cdot \nabla \pi ) \Delta \sigma_l,$ |; $key = q/displaystyle=frac{1}{rcos^2varphi_j}sum_{m,n}imtilde{f}_n^mY_n^m(lambda_i,varphi_j).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{r \cos^2 \varphi_j} \sum_{m,n} im \tilde{f}_n^m Y_n^m (\lambda_i, \varphi_j) .$ |; $key = q/displaystyleepsilon_v;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \epsilon_v$ |; $key = q/(lambda_i,varphi_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $(\lambda_i,\varphi_j)$ |; $key = q/displaystyletilde{A}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{A}_n^m$ |; $key = q/u_{ij},v_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $u_{ij},v_{ij}$ |; $key = q/displaystyle=T_{k-1}-hat{T}_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = T_{k-1} - \hat{T}_{k-1}$ |; $key = q/(N_{tr}+1)^2;MSF=1.6;AAT/; $cached_env_img{$key} = q| $(N_{tr}+1)^2$ |; $key = q/displaystylelambda;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lambda$ |; $key = q/hat{T}_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{T}_{k}$ |; $key = q/displaystyleD^{t+Deltat}=2overline{Dvect{D}}^{t}-D^{t-Deltat};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle D^{t+\Delta t} = 2\overline{ \Dvect{D} }^{t} - D^{t-\Delta t}$ |; $key = q/K-J;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/1leqkleqKMAX;MSF=1.6;AAT/; $cached_env_img{$key} = q| $1 \leq k \leq KMAX$ |; $key = q/displaystyleunderline{h};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \underline{h}$ |; $key = q/displaystyle:quad乾燥大気の大気定圧比熱[mathrm{Jkg}^{-1}mathrm{K}^{-1}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 乾燥大気の大気定圧比熱 [\mathrm{J kg}^{-1} \mathrm{K}^{-1}],$ |; $key = q/displaystylefrac{partialDvect{D}}{partialt}=left(DP{Dvect{D}}{t}right)_{rmNG}-naa}(Dvect{Phi}_{S}+underline{W}Dvect{T}+Dvect{G}pi)+{calD}_MDvect{D},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{\partial \Dvect{D}}{\partial t} = \left( \DP{\Dvect{D}}{t} ... ...{\Phi}_{S} + \underline{W} \Dvect{T} + \Dvect{G} \pi ) + {\cal D}_M \Dvect{D} ,$ |; $key = q/i,j,m,m',n,n',I,J,M,N(m);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleg_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle g_{ij}$ |; $key = q/{displaystylelambda_i=frac{2pi(i-1)}{I}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\lambda_i=\frac{2\pi(i-1)}{I}$ |; $key = q/displaystyleS_{k-1slash2}>0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle S_{k-1/2} > 0$ |; $key = q/P_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/tilde{P}_n;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\tilde{P}_n$ |; $key = q/m=-M,cdots,M.quadn=|m|,cdots,N(m);MSF=1.6;AAT/; $cached_env_img{$key} = q| $m=-M,\cdots,M. \quad n=\vert m\vert,\cdots,N(m)$ |; $key = q/x=-1,beta_1,beta_2,1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $x=-1,\beta_1,\beta_2,1$ |; $key = q/{displaystyleP_n=frac{1}{2^nn!}DD[n]{}{mu}(mu^2-1)^n};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle P_n= \frac{1}{2^n n!} \DD[n]{}{\mu} (\mu^2-1)^n }$ |; $key = q/displaystyleint_{-1}^1P_n^m(mu)P_{n'}^m(mu)dmu=2delta_{nn'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 P_n^m(\mu) P_{n'}^m (\mu) d \mu = 2 \delta_{nn'} .$ |; $key = q/n;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/I>M;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleDP{pi}{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\pi}{t}$ |; $key = q/displaystyle=sum_{m=-M}^{M}frac{1}{2pi}g_mint_0^{2pi}exp(imlambda)dlambda=g_0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{m=-M}^{M} \frac{1}{2\pi} g_m \int_0^{2\pi} \exp(i m \lambda) d \lambda =g_0$ |; $key = q/w(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $w(\mu)$ |; $key = q/displaystyleleft{DeltaT_{k-1}+frac{L}{C_p}(q_{k-1}-hat{q}_{k-1})right}Deltap_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left\{ \Delta T_{k-1} + \frac{L}{C_p} (q_{k-1} - \hat{q}_{k-1} ) \right\} \Delta p_{k-1}$ |; $key = q/displaystyle=Isum_{j=1}^{J}P_n^m(mu_j)P_{n'}^{m'}(mu_j)w_jdelta_{mm'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = I \sum_{j=1}^{J} P_n^m (\mu_j) P_{n'}^{m'} (\mu_j) w_j \delta_{mm'} .$ |; $key = q/displaystyle=int_{-1}^1L(mu)dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \int_{-1}^1 L(\mu) d \mu$ |; $key = q/{calF}_lambda,{calF}_varphi,Q,S_q;MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\cal F}_\lambda, {\cal F}_\varphi, Q, S_q$ |; $key = q/mu_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mu_j$ |; $key = q/A_{ins};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ins}$ |; $key = q/displaystyleC_p;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle C_p$ |; $key = q/w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/nabla_H^2;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla_H^2$ |; $key = q/displaystyleu_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle u_{ij}$ |; $key = q/displaystyleDeltaT_{k}equivhat{T}_{k}-T_{k}=S_{grst}(T_{Bk}-T_{k});MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Delta T_{k} \equiv \hat{T}_{k} - T_{k} = S_{grst} (T_{Bk} - T_{k})$ |; $key = q/displaystylehat{T}_{k}=T_{k}+S_{grst}(T_{Bk}-T_{k});MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k} = T_{k} + S_{grst} (T_{Bk} - T_{k})$ |; $key = q/p;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle(C_pT_{k-1}+Lq_{k-1})Deltap_{k-1}-(C_phat{T}_{k-1}+Lhat{q}_{k-1})Deltap_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (C_p T_{k-1} + L q_{k-1}) \Delta p_{k-1} - (C_p \hat{T}_{k-1} + L \hat{q}_{k-1}) \Delta p_{k-1}$ |; $key = q/Dvect{v}=(v_1,v_2);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Dvect{v}=(v_1,v_2)$ |; $key = q/displaystyleT_{k}+S_{grst}(T_{Bk}-T_{k})-frac{sum^{k+1}_{k=k-1}S_{grst}(T_{Bk}-T_{k})Deltap_{k}}{sum^{k+1}_{k=k-1}Deltap_{k}},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T_{k} + S_{grst} (T_{Bk} - T_{k}) - \frac{ \sum^{k+1}_{k=k-1} S_{grst} (T_{Bk} - T_{k}) \Delta p_{k} }{ \sum^{k+1}_{k=k-1} \Delta p_{k} },$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}A_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} A_{ij} Y_n^{m*} (\lambda_i,\varphi_j) w_j ,$ |; $key = q/int_0^{2pi}exp(imlambda)exp(-im'lambda)dlambda=2pidelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\int_0^{2 \pi} \exp(im\lambda) \exp(-im'\lambda) d \lambda = 2 \pi \delta_{mm'}$ |; $key = q/displaystylequadhspace{1.5cm}timesleft.DD{}{varphi}left(cos^2varphiP_n^mright)right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \quad \hspace{1.5cm} \times \left. \DD{}{\varphi} \left( \cos^2\varphi P_n^m \right) \right\vert _j \exp(-im \lambda_i) w_j$ |; $key = q/displaystyleF_R(z)=left(piB(T_g)-piB(T_s)right){calT}^f(z,0)+piB(T(z_T)){calT}^f(z,z_T)-int_0^{z_T}DD{piB}{xi}{calT}^f(z,xi)dxi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle F_R(z) = \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(z,0) +... ...(z_T)) {\cal T}^f(z,z_T) - \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi$ |; $key = q/J=65;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/b_i;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}left.DD{P_{n'}phi}right|_jexp(im'lambda_i)right)P_n^m(varphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'} ... ...t\vert _j \exp(i m' \lambda_i) \right) P_n^m(\varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/displaystyle{calD}(D)=-K_{HD}left[(-1)^{N_Dslash2}nabla^{N_D}-left(frac{2}{a^2}right)^{N_Dslash2}right]D,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal D}(D) = - K_{HD} \left[ (-1)^{N_D/2} \nabla^{N_D} - \left( \frac{2}{a^2} \right)^{N_D/2} \right] D ,$ |; $key = q/{displaystylesum_{m=-M}^{M}sum_{n=|m|}^{N}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{m=-M}^{M} \sum_{n=\vert m\vert}^{N}$ |; $key = q/overline{Dvect{D}_n^m}^{t};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\overline{ \Dvect{D}_n^m }^{t}$ |; $key = q/displaystyle=frac{v^{2}_k+v^{2}_k}{2}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{v^{2}_k + v^{2}_k}{2}.$ |; $key = q/displaystyleqquadsum_{i=1}^Isum_{j=1}^Jf_{n'}^{m'}P_{n}^{m}(varphi_j)exp(imlambda_i)left.DD{P_{n'}^{m'}}{varphi}right|_jexp(-im'lambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \qquad \sum_{i=1}^I \sum_{j=1}^J f_{n'}^{m'} P_{n}^{m}(\varphi_j)... ...mbda_i) \left. \DD{P_{n'}^{m'}}{\varphi}\right\vert _j \exp(-im' \lambda_i) w_j$ |; $key = q/delta;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\delta$ |; $key = q/4pi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $4 \pi$ |; $key = q/displaystylefrac{1}{r}DP{Y_n^m}{varphi}=frac{1}{r}DP{}{varphi}left(P_n^m(sinvarplambda)right)=frac{sqrt{1-mu^2}}{r}DD{}{mu}P_n^{m}(mu)exp(imlambda).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{r} \DP{Y_n^m}{\varphi} = \frac{1}{r} \DP{}{\varphi} \lef... ...\right) = \frac{\sqrt{1-\mu^2} }{r} \DD{}{\mu} P_n^{m} (\mu) \exp(im \lambda) .$ |; $key = q/N_S;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=frac{(2J-1)(1-sin^2varphi_j)}{(JP_{J-1}(sinvarphi_j))^2}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{(2J-1)(1-\sin^2 \varphi_j)} {(J P_{J-1}(\sin \varphi_j))^2 } .$ |; $key = q/2J+2|m|-2;MSF=1.6;AAT/; $cached_env_img{$key} = q| $2J+2\vert m\vert-2$ |; $key = q/displaystyle(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (\varphi, \lambda, \sigma)$ |; $key = q/displaystylefrac{1}{2pi}int_0^{2pi}g(lambda)dlambda=frac{1}{I}sum_{n=1}^{I}g(lambda_n),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{1}{2\pi} \int_0^{2\pi} g(\lambda) d \lambda = \frac{1}{I} \sum_{n=1}^{I} g(\lambda_n) ,$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}A_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^{I} \sum_{j=1}^{J} A_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j .$ |; $key = q/displaystyle=-frac{1}{I}sum_{i,j}left(sum_{m',n'}tilde{f}_{n'}^{m'}P_{n'}^{m'}(v(im'lambda_i)right)left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{I} \sum_{i,j} \left( \sum_{m',n'} \tilde{f}_{n'}^{m'... ...bda_i) \right) \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j$ |; $key = q/delta_S;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\delta_S$ |; $key = q/lambda_k;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\lambda_k$ |; $key = q/lambda_{subsolar};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\lambda_{subsolar}$ |; $key = q/M=N_{tr},N=N_{tr};MSF=1.6;AAT/; $cached_env_img{$key} = q| $M= N_{tr}, N =N_{tr}$ |; $key = q/displaystylenleft|{array}{ll}tilde{P}_n(x)&tilde{P}_{n-1}(x)tilde{P}_n(y)&tilde{P}_{n-1}(y){array}right|;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle n \left\vert \begin{array}{ll} \tilde{P}_n(x) & \tilde{P}_{n-1}(x) \ \tilde{P}_n(y) & \tilde{P}_{n-1}(y) \end{array} \right\vert$ |; $key = q/{displaystylesum_{m,n}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{m,n}$ |; $key = q/m,n,n';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleequivT_v-overline{T},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv T_v - \overline{T},$ |; $key = q/displaystylehspace{2em}+left(1+gamma_{k-1}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{{1}{1+gamma_{k-1}}frac{L}{C_p}Deltahat{Q}frac{1}{Deltap_{k-1}}right);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{2em} + \left( 1 + \gamma_{k-1} - \frac{R}{C_p} \frac{\Del... ...1 + \gamma_{k-1}} \frac{L}{C_p} \Delta \hat{Q} \frac{1}{\Delta p_{k-1}} \right)$ |; $key = q/displaystyle(T_{k}-T_{k-1})cdot(T_{k+1}-T_{k})geq0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle (T_{k} - T_{k-1}) \cdot (T_{k+1} - T_{k}) \geq 0$ |; $key = q/displaystyle=-(C_pT_{k}+Lq_{k})Deltap_{k}+(C_phat{T}_{k}+Lhat{q}_{k})Deltap_{k},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - (C_p T_{k} + L q_{k}) \Delta p_{k} + (C_p \hat{T}_{k} + L \hat{q}_{k}) \Delta p_{k},$ |; $key = q/mathaccentV{tilde}07E{P}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\mathaccentV {tilde}07E{P}_n^m$ |; $key = q/m,m';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/f(x)=(x-1)^n(x+1)^n;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $(\lambda, \varphi)$ |; $key = q/displaystyleequivTleft{1+left(epsilon_v^{-1}-1right)qright},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv T \left\{ 1 + \left(\epsilon_v^{-1} - 1\right) q \right\},$ |; $key = q/nabla_H^2equivfrac{1}{r^2}left[DP{}{varphi}left(cosvarphiDP{}{varphi}right)+frac{1}{cos^2varphi}DP[2]{}{lambda}right];MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla_H^2 \equiv \frac{1}{r^2} \left[ \DP{}{\varphi} \left( \cos \varphi \DP{}{\varphi} \right) + \frac{1}{\cos^2 \varphi} \DP[2]{}{\lambda} \right]$ |; $key = q/displaystyleoverline{seczeta}simeqfrac{1}{A_{zeta}+B_{zeta}cos^2varphi}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \overline{\sec \zeta} \simeq \frac{1}{A_{\zeta} + B_{\zeta} \cos^2 \varphi} .$ |; $key = q/{displaystyleMleleft[frac{I}{2}right],N(m)leJ-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle M \le \left[ \frac{I}{2} \right] , N(m) \le J-1 }$ |; $key = q/f;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle∴h_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle ∴ h_{ij}$ |; $key = q/{align*}{split}DP{tilde{T}_n^m}{t}&=-frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}imu_{ijj=1}^{J}{calD}'_{ij}(Dvect{v})Y_n^{m*}(lambda_i,varphi_j)w_j.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{\tilde{T}_n^m}{t} & = - \frac{1}{I} \sum_{i=1}^{I... ...{ij}(\Dvect{v}) Y_n^{m *} ( \lambda_i, \varphi_j ) w_j . \end{split}\end{align*}$ |; $key = q/Jge3N_{tr}+1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $J \ge 3N_{tr}+1$ |; $key = q/displaystyleleft[DD{}{mu}left{(1-mu^2)DD{}{mu}right}+J(J+1)right]P_J(mu)=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[ \DD{}{\mu} \left\{ (1-\mu^2) \DD{}{\mu} \right\} + J(J+1) \right] P_J(\mu) = 0$ |; $key = q/displaystyleequivsum_{m=-M}^Msum_{n=|m|}^Nimtilde{f}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \sum_{m=-M}^M \sum_{n=\vert m\vert}^N im \tilde{f}_n^m Y_n^m (\lambda_i,\varphi_j) ,$ |; $key = q/displaystyleleft(-1-gamma_{k}-kappafrac{Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( - 1 - \gamma_{k} - \kappa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k}$ |; $key = q/kappa=RslashC_p;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\kappa = R/C_p$ |; $key = q/(q,T);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/n-1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/-1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/f(mu_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $f(\mu_j)$ |; $key = q/displaystyleequivwidetilde{(BC)_n^m};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \widetilde{(BC)_n^m}$ |; $key = q/P_n^m(mu)(n=|m|,|m+1,cdots);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P_n^m(\mu) (n=\vert m\vert,\vert m+1, \cdots)$ |; $key = q/displaystyletilde{A}_n^m=frac{1}{4pi}int_{-1}^1d(sinvarphi)int_0^{2pi}dlambdaA(lambda,varphi)Y_n^{m*}(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{A}_n^m = \frac{1}{4 \pi} \int_{-1}^1 d (\sin \varphi) \int_0^{2 \pi} d \lambda A(\lambda, \varphi) Y_n^{m*}(\lambda, \varphi)$ |; $key = q/displaystylelambda_n=frac{2pi(n-1)}{I}(n=1,2,cdots,I);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lambda_n = \frac{2\pi (n-1)}{I} (n=1,2,\cdots,I)$ |; $key = q/displaystyleq=q^*(T,p);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q = q^*( T,p )$ |; $key = q/DeltaT_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\Delta T_{k}$ |; $key = q/chi,psi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\chi ,\psi$ |; $key = q/displaystyletilde{A}_n^m=frac{2n+1}{2}frac{(n-|m|)!}{(n+|m|)!}int_{-1}^1A(mu)tilde{P}_n^m(mu)dmu;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{A}_n^m = \frac{2n+1}{2} \frac{(n-\vert m\vert)!}{(n+\vert m\vert)!} \int_{-1}^1 A(\mu) \tilde{P}_n^m(\mu) d \mu$ |; $key = q/m(n-1);MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/K+frac{1}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $K+\frac{1}{2}$ |; $key = q/displaystyletilde{f}_{n'}^{m'}=-frac{n(n+1)}{r^2}tilde{h}_{n'}^{m'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{f}_{n'}^{m'} = -\frac{n(n+1)}{r^2} \tilde{h}_{n'}^{m'}$ |; $key = q/f(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $f(\mu)$ |; $key = q/g=DP{f}{lambda};MSF=1.6;AAT/; $cached_env_img{$key} = q| $g = \DP{f}{\lambda}$ |; $key = q/displaystyleh_{ij}=sum_{m,n}left.tilde{h}_n^mY_n^mright|_{ij};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle h_{ij} = \sum_{m,n} \left. \tilde{h}_n^m Y_n^m \right\vert _{ij}$ |; $key = q/displaystyle=-left(1+gamma_{k}right)DeltaT_{k}Deltap_{k}+frac{L}{C_p}Deltahat{Q},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \left( 1 + \gamma_{k} \right) \Delta T_{k} \Delta p_{k} + \frac{L}{C_p} \Delta \hat{Q},$ |; $key = q/nabla^2_Hf=-frac{n(n+1)}{r^2}f;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\nabla^2_H f = -\frac{n(n+1)}{r^2} f$ |; $key = q/f(lambda,varphi);MSF=1.6;AAT/; $cached_env_img{$key} = q| $f(\lambda,\varphi)$ |; $key = q/{align*}{split}nabla^2_Hf&equivfrac{1}{r^2}left[frac{1}{cosvarphi}DP{}{varphi}le{(1-mu^2)DP{}{mu}right}+frac{1}{1-mu^2}DP[2]{}{lambda}right]f{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\nabla^2_H f &\equiv \frac{1}{r^2} \left[ \frac{1}{\c... ...\right\} + \frac{1}{1-\mu^2} \DP[2]{}{\lambda} \right] f \end{split}\end{align*}$ |; $key = q/M;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/_2;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/psi;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\psi$ |; $key = q/sigma_{SB};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sigma_{SB}$ |; $key = q/displaystyletilde{calD}_{H,n}^m=-K_{HD}left(frac{-n(n+1)}{a^{2}}right)^{N_Dslash2}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{\cal D}_{H,n}^m = - K_{HD} \left( \frac{-n(n+1)}{a^{2}} \right)^{N_D/2} .$ |; $key = q/{displaystylekappa=frac{R}{C_p}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\kappa=\frac{R}{C_p}$ |; $key = q/displaystyleleft[DP{}{mu}left((1-mu^2)DP{}{mu}right)+frac{1}{1-mu^2}DP[2]{}{lambda}+n(n+1)right]Y_n^m=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left[ \DP{}{\mu} \left( (1-\mu^2) \DP{}{\mu} \right) + \frac{1}{1-\mu^2} \DP[2]{}{\lambda} + n(n+1) \right] Y_n^m =0$ |; $key = q/f_k（k=0,1,2,cdots,K-1）;MSF=1.6;AAT/; $cached_env_img{$key} = q| $f_k（k=0,1,2,\cdots,K-1）$ |; $key = q/A_{ij}^{even};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ij}^{even}$ |; $key = q/A_{i,j}+A_{i,J-j};MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{i,j}+A_{i,J-j}$ |; $key = q/kappa;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\kappa$ |; $key = q/displaystyle:qquad摩擦熱.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \qquad 摩擦熱.$ |; $key = q/dot{calA}_{adv};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\cal A}_{adv}$ |; $key = q/{calA}^{t+Deltat};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\cal A}^{t+\Delta t}$ |; $key = q/displaystylehspace{-7em}=-left[1+frac{L}{C_p}left.DP{q^{*}}{T}right|_{k}right]Deap_{k}-frac{L}{C_p}left{q^{*}(hat{T}_{k})-hat{q}_{k}right}Deltap_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hspace{-7em} = - \left[ 1 + \frac{L}{C_p} \left. \DP{q^{*}}{T} \... ...- \frac{L}{C_p} \left\{ q^{*} (\hat{T}_{k}) - \hat{q}_{k} \right\} \Delta p_{k}$ |; $key = q/displaystyle)_k)+{calD}(D_k).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle )_k ) + {\cal D}(D_k).$ |; $key = q/displaystylesum^{KMAX}_{k=1}hat{T}_{k}Deltap_{k}=sum^{KMAX}_{k=1}left{S_{grst}(TT_{Bk}-T_{k})Deltap_{k}}{sum^{KMAX}_{k=1}Deltap_{k}}Deltap_{k}right};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum^{KMAX}_{k=1} \hat{T}_{k} \Delta p_{k} = \sum^{KMAX}_{k=1} \l... ...- T_{k}) \Delta p_{k} }{ \sum^{KMAX}_{k=1} \Delta p_{k} } \Delta p_{k} \right\}$ |; $key = q/N_{{rmmax}}=2M;MSF=1.6;AAT/; $cached_env_img{$key} = q| $N_{{\rm max}}=2M$ |; $key = q/C_p;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/v;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}hat{H}_k&equivT_k'D_k-frac{1}{Deltasigma_k}[dot{sigma}_{k-1slash2vect{v}_lcdotnablapi)Deltasigma_lfrac{T_{v,k}}{Deltasigma_k},{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\hat{H}_k & \equiv T_k' D_k - \frac{1}{\Delta \sigma_... ...a \pi ) \Delta \sigma_l \frac{T_{v,k}}{\Delta \sigma_k}, \end{split}\end{align*}$ |; $key = q/{displaystylesum_{i,j}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sum_{i,j}$ |; $key = q/displaystyleequivfrac{1}{a^{2}cos^2varphi}DP[2]{}{lambda}+frac{1}{a^{2}cosvarphi}DP{}{varphi}left(cosvarphiDP{}{varphi}right),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \frac{1}{a^{2} \cos^2 \varphi} \DP[2]{}{\lambda} + \frac{1}{a^{2} \cos \varphi} \DP{}{\varphi} \left( \cos \varphi \DP{}{\varphi} \right),$ |; $key = q/h;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/bar{k}_{R,i};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\bar{k}_{R,i}$ |; $key = q/displaystyleq_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q_{k-1}$ |; $key = q/delta_R=1.5;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\delta_R = 1.5$ |; $key = q/displaystylesum_i^{N_S}a_ileft[(1-alpha_A)F_S^Iexpleft(-tau_{S,i}(z)seczetaright)right.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_i^{N_S} a_i \left[ (1-\alpha_A) F_S^I \exp \left( - \tau_{S,i}(z) \sec \zeta \right) \right.$ |; $key = q/displaystyle=-frac{I}{2}int_{-1}^{1}f_{n'}^{m}P_{n'}^{m}(varphi)DD{P_n^m}{varphi}dvarphidelta_{mm'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{I}{2} \int_{-1}^{1} f_{n'}^{m} P_{n'}^{m}(\varphi) \DD{P_n^m}{\varphi} d \varphi \delta_{m m'}$ |; $key = q/3slash4;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/kleql;MSF=1.6;AAT/; $cached_env_img{$key} = q| $k \leq l$ |; $key = q/dot{sigma};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\sigma}$ |; $key = q/{align*}{split}hat{kappa}_k&=frac{sigma_{k-1slash2}(sigma^{kappa}_{k-1slash2}-sima_{k-1slash2}alpha_k+sigma_{k+1slash2}beta_k}{Deltasigma_k},{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\hat{\kappa}_k & = \frac{ \sigma_{k-1/2}( \sigma^{\ka... ...\alpha_k + \sigma_{k+1/2} \beta_k } { \Delta \sigma_k }, \end{split}\end{align*}$ |; $key = q/J=63,N=42;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=sum_{m,n}left(-frac{1}{r}tilde{psi}_n^mleft.DD{P_n^m}{varphi}right|cosvarphi_j}imtilde{chi}_n^mP_n^m(sinvarphi_j)right)exp(imlambda_i).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{m,n} \left( - \frac{1}{r} \tilde{\psi}_n^m \left. \DD{P_n... ...arphi_j} im \tilde{\chi}_n^m P_n^m(\sin \varphi_j) \right) \exp(im \lambda_i) .$ |; $key = q/t+Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $t+\Delta t$ |; $key = q/displaystylesum_{m=-frac{I}{2}+1}^{frac{I}{2}}exp(imlambda_i)exp(-imlambda_{i'})=Idelta_{ii'};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum_{m=-\frac{I}{2}+1}^{\frac{I}{2}} \exp(i m \lambda_i) \exp(-i m \lambda_{i'}) = I \delta_{ii'}$ |; $key = q/displaystyletilde{q}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tilde{q}_n^m$ |; $key = q/g;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/q_{k-1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $q_{k-1}$ |; $key = q/displaystyleb=left{{array}{ll}left(frac{1-langlembox{RH}rangle}{1-mbox{RH}_c}rig{RH}ranglegembox{RH}_c1&langlembox{RH}rangle|; $key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jimf_{ij}Y_n^{m*}(lambda_i,varphi_j)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J im f_{ij} Y_n^{m*} (\lambda_i, \varphi_j) w_j .$ |; $key = q/(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $(\varphi, \lambda, \sigma)$ |; $key = q/overline{seczeta};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\overline{\sec \zeta}$ |; $key = q/displaystyle:quadコリオリパラメータ[mathrm{s}^{-1}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad コリオリパラメータ [\mathrm{s}^{-1}],$ |; $key = q/displaystyleint_{-1}^1Y_n^m(lambda,varphi)Y_{n'}^{m'*}(lambda,varphi)d(sinvarphi)dlambda=4pidelta_{mm'}delta_{nn'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 Y_n^m(\lambda, \varphi) Y_{n'}^{m'*} (\lambda, \varphi) d (\sin \varphi) d \lambda = 4 \pi \delta_{mm'} \delta_{nn'} .$ |; $key = q/displaystylehat{T}_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k}$ |; $key = q/displaystylecoszeta=sinvarphisindelta+cosvarphicdotsqrt{1-sin^2delta}cdotcosH;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \cos \zeta = \sin \varphi \sin \delta + \cos \varphi \cdot \sqrt{1 - \sin^2 \delta} \cdot \cos H$ |; $key = q/displaystyleDP{pi}{t}=-int_{0}^{1}Dvect{v}_{H}cdotnabla_{sigma}pidsigma-int_{0}^{1}Ddsigma,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\pi}{t} = - \int_{0}^{1} \Dvect{v}_{H} \cdot \nabla_{\sigma} \pi d \sigma - \int_{0}^{1} D d \sigma ,$ |; $key = q/rho;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\rho$ |; $key = q/lambda;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\lambda$ |; $key = q/{displaystylefrac{1}{rcosvarphi}DP{f}{lambda}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\frac{1}{r \cos \varphi} \DP{f}{\lambda}$ |; $key = q/displaystylehat{T}_{k+2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k+2}$ |; $key = q/seczeta_0=1.66;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\sec \zeta_0 = 1.66$ |; $key = q/displaystyle:quad比湿[mathrm{kg}mathrm{kg}^{-1}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 比湿 [\mathrm{kg} \mathrm{kg}^{-1}],$ |; $key = q/overline{coszeta};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\overline{\cos \zeta}$ |; $key = q/{align*}{split}DP{tilde{zeta}_n^m}{t}&=frac{1}{I}sum_{i=1}^{I}sum_{j=1}^{J}im(v_c{w_j}{acosvarphi_j}&quad+tilde{calD}_{M,n}^mtilde{zeta}_n^m,{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\DP{\tilde{\zeta}_n^m}{t} & = \frac{1}{I} \sum_{i=1}^... ... \ & \quad + \tilde{\cal D}_{M,n}^m \tilde{\zeta}_n^m , \end{split}\end{align*}$ |; $key = q/K=J+M;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleq(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle q (\varphi, \lambda, \sigma)$ |; $key = q/displaystyle:quad惑星半径[mathrm{m}],;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle : \quad 惑星半径 [\mathrm{m}],$ |; $key = q/w_j=w(mu_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $w_j=w(\mu_j)$ |; $key = q/displaystylelambda_i=frac{2pi(i-1)}{I}(i=1,2,cdots,I);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \lambda_i = \frac{2 \pi (i-1)}{I} \ (i=1,2,\cdots,I)$ |; $key = q/displaystyleT^a_{k+1}leftarrowT^a_{k+1}+frac{L}{C_p}frac{q^a_{k+1}-q^*(T^a_{k+1},p_{k+1})}{displaystyle1+frac{L}{C_p}DP{q^*}{T}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T^a_{k+1} \leftarrow T^a_{k+1} + \frac{L}{C_p} \frac{ q^a_{k+1} - q^*( T^a_{k+1},p_{k+1}) } {\displaystyle 1 + \frac{L}{C_p} \DP{q^*}{T} }$ |; $key = q/displaystyleC_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle C_{k}$ |; $key = q/L=f;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/-;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylesum^{I}_{n=1}expleft{imfrac{2pi(n-1)}{I}right}=frac{1-left(e^{frac{i)^I}{1-e^{frac{im2pi}{I}}}=frac{1-e^{im2pi}}{1-e^{frac{im2pi}{I}}}=0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \sum^{I}_{n=1} \exp \left\{ im \frac{2 \pi (n-1)}{I} \right\} = \... ...im 2 \pi}{I} } } = \frac{1 - e^{im 2 \pi} } {1 - e^{ \frac{im 2 \pi}{I} } } = 0$ |; $key = q/displaystylev;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle v$ |; $key = q/T^a_{k+1},q^a_{k+1};MSF=1.6;AAT/; $cached_env_img{$key} = q| $T^a_{k+1}, q^a_{k+1}$ |; $key = q/displaystyletau_{S,i}(z)=int_z^inftyk_{S,i}rhoqdz+int_z^inftybar{k}_{S,i}rhodz;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \tau_{S,i}(z) = \int_z^\infty k_{S,i} \rho q dz + \int_z^\infty \bar{k}_{S,i} \rho dz$ |; $key = q/displaystylewidetilde{left(DP{f}{lambda}right)}_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \widetilde{ \left( \DP{f}{\lambda} \right) }_n^m$ |; $key = q/displaystyle=-frac{1}{I}sum_{i=1}^Isum_{j=1}^Jf_{ij}left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J f_{ij} \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j .$ |; $key = q/2J-1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyle=beta_kleft[left(frac{sigma_k}{sigma_{k+1}}right)^{kappa}-1right]^{-1}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \beta_k \left[ \left( \frac{ \sigma_k }{ \sigma_{k+1} } \right)^{\kappa} - 1 \right]^{-1} .$ |; $key = q/1+(2times1+1)+cdots+(2times42+1)=43^2=1849;MSF=1.6;AAT/; $cached_env_img{$key} = q| $1+ (2 \times1 +1) + \cdots + (2 \times 42 +1) = 43^2 = 1849$ |; $key = q/displaystyle=q^*(T_{k-1},p_{k-1}),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = q^* (T_{k-1}, p_{k-1}),$ |; $key = q/displaystyle=sum_{m=0}^{M}sum_{n=m}^{N}Retilde{A}_n^mY_n^m(lambda_i,varphi_j),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \sum_{m=0}^{M} \sum_{n=m}^{N} \Re \tilde{A}_n^m Y_n^m(\lambda_i, \varphi_j),$ |; $key = q/1;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/A_{ij}=A(lambda_i,varphi_j);MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ij}=A(\lambda_i,\varphi_j)$ |; $key = q/{displaystyleM=left[frac{I-1}{3}right]};MSF=1.6;AAT/; $cached_env_img{$key} = q| $M= \left[ \frac{I-1}{3} \right]$ |; $key = q/0le|m|,|m'|leM,|m|lenleN,|m'|len'leN;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le \vert m\vert,\vert m'\vert \le M, \vert m\vert \le n \le N, \vert m'\vert \le n' \le N$ |; $key = q/epsilon_v;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\epsilon_v$ |; $key = q/Depsf[10cm]{spectralslashspl-spherical-harmonics-imagesslashlegendre1.ps};AAT/; $cached_env_img{$key} = q| $\Depsf[10cm]{spectral/spl-spherical-harmonics-images/legendre1.ps}$ |; $key = q/displaystyle=delta_{nn'},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \delta_{nn'},$ |; $key = q/displaystyleQ(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle Q (\varphi, \lambda, \sigma)$ |; $key = q/displaystylep_{ij}=sum_{m,n}tilde{f}_n^mleft.DD{P_n^m}{varphi}right|_jexp(imlambda_i);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle p_{ij} = \sum_{m,n} \tilde{f}_n^m \left. \DD{P_n^m}{\varphi} \right\vert _j \exp(im \lambda_i)$ |; $key = q/displaystyle=dot{sigma}_{K+1slash2}=0.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \dot{\sigma}_{K+1/2} = 0.$ |; $key = q/displaystylef(mu)-L(mu)=tilde{P}_J(mu)S(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle f(\mu) - L(\mu) = \tilde{P}_J(\mu) S(\mu)$ |; $key = q/displaystylet;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle t$ |; $key = q/displaystyleequivfrac{u^{2}+v^{2}}{2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \frac{u^{2}+v^{2}}{2 }$ |; $key = q/dot{calA}_{dis};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\dot{\cal A}_{dis}$ |; $key = q/displaystyleleft(DP{T_{k}}{t}right)^{rmNG}=-frac{1}{a(1-mu^{2})}DP{U_kT'_k}{lambc{1}{a}DP{V_kT'_k}{mu}+H_{k}+{calD}(T_{k})+{calD}^{prime}(Dvect{v}),;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( \DP{T_{k}}{t} \right)^{\rm NG} = - \frac{1}{a(1-\mu^{2})} ... ...} \DP{V_k T'_k}{\mu} + H_{k} + {\cal D}(T_{k}) + {\cal D}^{\prime}(\Dvect{v}) ,$ |; $key = q/displaystyle=frac{1}{I}sum_{i=1}^Isum_{j=1}^Jleft(sum_{m'=-M}^{M}sum_{n'=|m'|}^Nvarphi_j)exp(im'lambda)right)P_n^{m}(sinvarphi_j)exp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{I} \sum_{i=1}^I \sum_{j=1}^J \left( \sum_{m'=-M}^{M} \... ...hi_j) \exp(im' \lambda) \right) P_n^{m}(\sin \varphi_j) \exp(-im \lambda_i) w_j$ |; $key = q/displaystylehat{hat{T}}_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{\hat{T}}_{k}$ |; $key = q/displaystyleint_{-1}^1tilde{P}_n^m(mu)tilde{P}_{n'}^m(mu)dmu=frac{2}{2n+1}frac{(n+|m|)!}{(n-|m|)!}delta_{nn'}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \int_{-1}^1 \tilde{P}_n^m(\mu) \tilde{P}_{n'}^m (\mu) d \mu = \frac{2}{2n+1} \frac{(n+\vert m\vert)!}{(n-\vert m\vert)!} \delta_{nn'} .$ |; $key = q/{figure}center{picture{(300,170)(10,-20)put(20,10){vector(1,0){85}}put(30,0){vec0){shortstack{平方四辺形切断}}{par{picture{center{{{{figure};MSF=1.6;FSF=1.6;AAT/; $cached_env_img{$key} = q| $\begin{figure}\begin{center} \begin{picture}(300,170)(10,-20) \put(20 , 10){\v... ...20) \{ shortstack\{平方四辺形切断\}\} \par \end{picture}\end{center}\end{figure}$ |; $key = q/displaystyle=2sum_{j=1}^{J}f(mu_j)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = 2 \sum_{j=1}^{J} f(\mu_j) w_j$ |; $key = q/A,B,C;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/hat{p_s};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\hat{p_s}$ |; $key = q/N_{tr};MSF=1.6;AAT/; $cached_env_img{$key} = q| $N_{tr}$ |; $key = q/{align*}{split}{v_A}_{,k}&=-(zeta_k+f)u_k-frac{1}{2Deltasigma_k}[dot{sigma}_{k-1ac{C_{p}hat{kappa}_kT_{v,k}'}{a}DP{pi}{mu}+{calF}_{varphi,k},{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}{v_A}_{,k} & = - ( \zeta_k + f ) u_k - \frac{1}{2 \De... ...a}_k T_{v,k}'}{a} \DP{\pi}{\mu} + {\cal F}_{\varphi, k}, \end{split}\end{align*}$ |; $key = q/0le|m|len-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0\le \vert m\vert \le n-1$ |; $key = q/Depsf[][7cm]{spectralslashspl-spherical-harmonics-imagesslashlegendre2.ps};AAT/; $cached_env_img{$key} = q| $\Depsf[][7cm]{spectral/spl-spherical-harmonics-images/legendre2.ps}$ |; $key = q/displaystyleG_{k};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle G_{k}$ |; $key = q/A_n^m;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/{align*}{split}Phi_{1}&=Phi_{s}+C_{p}(sigma_{1}^{-kappa}-1)T_{v,1}&=Phi_{s}+C_{p}alpha_{1}T_{v,1}.{split}{align*};AAT/; $cached_env_img{$key} = q| $\begin{align*}\begin{split}\Phi_{1} & = \Phi_{s} + C_{p} ( \sigma_{1}^{-\kappa} - 1 ) T_{v,1} \ & = \Phi_{s} + C_{p} \alpha_{1} T_{v,1}. \end{split}\end{align*}$ |; $key = q/(lambda',varphi');MSF=1.6;AAT/; $cached_env_img{$key} = q| $(\lambda', \varphi')$ |; $key = q/displaystyle=C_{p}alpha_{l}delta_{kgeql}+C_{p}beta_{l}delta_{k-1geql},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = C_{p} \alpha_{l} \delta_{k \geq l} + C_{p} \beta_{l} \delta_{k-1 \geq l} ,$ |; $key = q/mneq0;MSF=1.6;AAT/; $cached_env_img{$key} = q| $m \neq 0$ |; $key = q/displaystyleDP{pi}{t}=left(frac{partialpi}{partialt}right)_{rmNG}-Dvect{C}cdotDvect{D},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \DP{\pi}{t} = \left( \frac{\partial \pi}{\partial t} \right)_{\rm NG} - \Dvect{C} \cdot \Dvect{D} ,$ |; $key = q/P^m_n(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $P^m_n(\mu)$ |; $key = q/displaystyle=frac{displaystyleS_{k-1slash2}+left(1+gamma_{k-1}-kappafrac{Deltap_ight)frac{1+gamma_{k}}{1+gamma_{k-1}}frac{Deltap_{k}}{Deltap_{k-1}}};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{ \displaystyle S_{k-1/2} + \left( 1 + \gamma_{k-1} - \kap... ...frac{ 1 + \gamma_{k} }{ 1 + \gamma_{k-1}} \frac{\Delta p_{k}}{\Delta p_{k-1}} }$ |; $key = q/displaystyleequivDinv{acosvarphi}left{DP{u}{lambda}+DP{(vcosvarphi)}{varphi}right}:quad発散[mathrm{s}^{-1}].;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \equiv \Dinv{a \cos \varphi} \left\{ \DP{u}{\lambda} + \DP{(v \cos \varphi)}{\varphi} \right\} : \quad 発散 [\mathrm{s}^{-1}].$ |; $key = q/{displaystyletilde{P}_{J-1}=sqrt{frac{1}{2(mbox{J}-1)+1}}P_{J-1}};MSF=1.6;AAT/; $cached_env_img{$key} = q| ${\displaystyle \tilde{P}_{J-1} =\sqrt{ \frac{1}{2(\mbox{J}-1)+1} } P_{J-1} }$ |; $key = q/M=32;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystylefrac{hat{p_{s}}sigma}{RT}hat{q};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \frac{\hat{p_{s}} \sigma}{RT} \hat{q}$ |; $key = q/displaystylehat{calA}^{t+Deltat}=bar{calA}^{t-Deltat}+2Deltatdot{calA}_{adv}leftDeltat}right)+2Deltatdot{calA}_{phy}left(bar{calA}^{t-Deltat}right).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{\cal A}^{t+\Delta t} = \bar{\cal A}^{t-\Delta t} + 2 \Delta ... ...ight) + 2 \Delta t \dot{\cal A}_{phy}\left( \bar{\cal A}^{t-\Delta t} \right) .$ |; $key = q/A_{ij};(i=1,2,cdots,I,;j=1,2,cdots,J);MSF=1.6;AAT/; $cached_env_img{$key} = q| $A_{ij} \; (i=1,2,\cdots,I, \; j=1,2,\cdots,J)$ |; $key = q/displaystyleT^a_{k+1}=T^a_kleft(frac{p_{k+1}}{p_k}right)^{kappa};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle T^a_{k+1} = T^a_k \left( \frac{p_{k+1}}{p_k} \right)^{\kappa}$ |; $key = q/displaystyleR;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle R$ |; $key = q/displaystyle=frac{1}{rcosvarphi}DP{psi}{lambda}+frac{1}{r}DP{chi}{varphi};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1}{r\cos\varphi} \DP{\psi}{\lambda} + \frac{1}{r} \DP{\chi}{\varphi}$ |; $key = q/displaystyleDvect{v}cdotnablapi=frac{u}{acosvarphi}DP{pi}{lambda}+frac{v}{a}DP{pi}{varphi}.;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \Dvect{v} \cdot \nabla \pi = \frac{u}{a \cos \varphi} \DP{\pi}{\lambda} + \frac{v}{a} \DP{\pi}{\varphi}.$ |; $key = q/displaystylehat{T}_{k}+S_{grst}(T_{Bk}-hat{T}_{k})-frac{sum^{k+2}_{k=k}S_{grst}(T_{Bk}-hat{T}_{k})Deltap_{k}}{sum^{k+2}_{k=k}Deltap_{k}},;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \hat{T}_{k} + S_{grst} (T_{Bk} - \hat{T}_{k}) - \frac{ \sum^{k+2}... ..._{grst} (T_{Bk} - \hat{T}_{k}) \Delta p_{k} }{ \sum^{k+2}_{k=k} \Delta p_{k} },$ |; $key = q/displaystyleT^c_k|; $key = q/0leKleJ-1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $0 \le K \le J-1$ |; $key = q/displaystyle=-frac{1}{I}sum_{i,j}f_{ij}left.DD{P_n^m}{varphi}right|_jexp(-imlambda_i)w_j;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = - \frac{1}{I} \sum_{i,j} f_{ij} \left. \DD{P_n^m}{\varphi}\right\vert _j \exp(-im \lambda_i) w_j$ |; $key = q/L(mu);MSF=1.6;AAT/; $cached_env_img{$key} = q| $L(\mu)$ |; $key = q/displaystyle)+{calD}(D).;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle ) + {\cal D}(D).$ |; $key = q/Ige3N_{tr}+1;MSF=1.6;AAT/; $cached_env_img{$key} = q| $I \ge 3N_{tr}+1$ |; $key = q/(hat{q},hat{T});MSF=1.6;AAT/; $cached_env_img{$key} = q| $(\hat{q}, \hat{T})$ |; $key = q/t-Deltat;MSF=1.6;AAT/; $cached_env_img{$key} = q| $t-\Delta t$ |; $key = q/displaystylezeta;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \zeta$ |; $key = q/displaystyleleft(-1-gamma_{k}-frac{R}{C_p}frac{Deltap_{k-1slash2}}{2p_{k-1slash2Deltap_{k-1slash2}}{2p_{k-1slash2}}right)DeltaT_{k-1}=-S_{k-1slash2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle \left( - 1 - \gamma_{k} - \frac{R}{C_p} \frac{\Delta p_{k-1/2}}{2... ...{C_p} \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}} \right) \Delta T_{k-1} = - S_{k-1/2}$ |; $key = q/displaystyle{calF}_lambda(varphi,lambda,sigma);MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle {\cal F}_\lambda (\varphi, \lambda, \sigma)$ |; $key = q/64times64=4096;MSF=1.6;AAT/; $cached_env_img{$key} = q| $64 \times 64 = 4096$ |; $key = q/n+n';MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/2M;MSF=1.6;AAT/; $cached_env_img{$key} = q|

|; $key = q/displaystyleA=BC,;MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle A= BC ,$ |; $key = q/displaystyle=frac{1-mu_j^2}{(Jtilde{P}_{J-1}(mu_j))^2};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle = \frac{1-\mu_j^2}{(J \tilde{P}_{J-1}(\mu_j))^2 }$ |; $key = q/displaystyleu=-frac{1}{r}DP{psi}{varphi}+frac{1}{rcosvarphi}DP{chi}{lambda};MSF=1.6;AAT/; $cached_env_img{$key} = q| $\displaystyle u = - \frac{1}{r} \DP{\psi}{\varphi} + \frac{1}{r\cos\varphi} \DP{\chi}{\lambda}$ |; 1;