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    101. 

  101. <a href="legsym_8f90.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">! ************************************************************************</span>
    102. 

  102. <a name="l00002"></a>00002 <span class="comment">! * module legsym - direct and indirect Legendre transformation routines *</span>
    103. 

  103. <a name="l00003"></a>00003 <span class="comment">! * using symmetric and antisymmetric fourier coefficients               *</span>
    104. 

  104. <a name="l00004"></a>00004 <span class="comment">! * E. Kirk 08-Sep-2010 tested for T21 - T682 resolutions 32 &amp; 64 bit    *</span>
    105. 

  105. <a name="l00005"></a>00005 <span class="comment">! ************************************************************************</span>
    106. 

  106. <a name="l00006"></a>00006 
    107. 

  107. <a name="l00007"></a><a class="code" href="classlegsym.html">00007</a> <span class="keyword">module</span> <a class="code" href="classlegsym.html">legsym</a>
    108. 

  108. <a name="l00008"></a>00008 <span class="comment">! ************************</span>
    109. 

  109. <a name="l00009"></a>00009 <span class="comment">! * Legendre Polynomials *</span>
    110. 

  110. <a name="l00010"></a>00010 <span class="comment">! ************************</span>
    111. 

  111. <a name="l00011"></a>00011 
    112. 

  112. <a name="l00012"></a><a class="code" href="classlegsym.html#a9f44e2174fc92267b46632e481acce37">00012</a> <span class="keywordtype">integer</span> :: ntru
    113. 

  113. <a name="l00013"></a><a class="code" href="classlegsym.html#a3de2526b7367430bf2925e4d9e293b8d">00013</a> <span class="keywordtype">integer</span> :: ntp1
    114. 

  114. <a name="l00014"></a><a class="code" href="classlegsym.html#a1cc07c984867c3dc3b122ac8fce446e2">00014</a> <span class="keywordtype">integer</span> :: ncsp
    115. 

  115. <a name="l00015"></a><a class="code" href="classlegsym.html#a8d1597f9974455b1abb4b57e34a77625">00015</a> <span class="keywordtype">integer</span> :: nesp
    116. 

  116. <a name="l00016"></a><a class="code" href="classlegsym.html#adc6b16f2626e9dcb618d2d950e2db17a">00016</a> <span class="keywordtype">integer</span> :: nlon
    117. 

  117. <a name="l00017"></a><a class="code" href="classlegsym.html#a296b840ee1daf32583f78f3b8136acb0">00017</a> <span class="keywordtype">integer</span> :: nlpp
    118. 

  118. <a name="l00018"></a><a class="code" href="classlegsym.html#a2ca038107ed480d5443db9a2f0322ce1">00018</a> <span class="keywordtype">integer</span> :: nhpp
    119. 

  119. <a name="l00019"></a><a class="code" href="classlegsym.html#a48c28c34fad8572472b4994bf99da184">00019</a> <span class="keywordtype">integer</span> :: nlat
    120. 

  120. <a name="l00020"></a><a class="code" href="classlegsym.html#a8b4c67467362c9d324d5ad7bf5b6e78e">00020</a> <span class="keywordtype">integer</span> :: nlev
    121. 

  121. <a name="l00021"></a><a class="code" href="classlegsym.html#adb777017fc0833c5be3bbe40fb789d9f">00021</a> <span class="keywordtype">real</span>    :: plavor
    122. 

  122. <a name="l00022"></a>00022 
    123. 

  123. <a name="l00023"></a><a class="code" href="classlegsym.html#a35897a5a32d0ac4f7193e2c6df059430">00023</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qi(:,:) <span class="comment">! P(m,n) = Associated Legendre Polynomials</span>
    124. 

  124. <a name="l00024"></a><a class="code" href="classlegsym.html#a3fd3514e19855e9c94debeb13d1c0a3c">00024</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qj(:,:) <span class="comment">! Q(m,n) = Used for d/d(mu)</span>
    125. 

  125. <a name="l00025"></a><a class="code" href="classlegsym.html#a8da266cccc13b41ffb15d593f3cfbda1">00025</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qc(:,:) <span class="comment">! P(m,n) * gwd              used in fc2sp</span>
    126. 

  126. <a name="l00026"></a><a class="code" href="classlegsym.html#a27a404e273f903a7a9fa790dd2440605">00026</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qe(:,:) <span class="comment">! Q(mn,) * gwd / cos2       used in mktend</span>
    127. 

  127. <a name="l00027"></a><a class="code" href="classlegsym.html#ae957dbe2cb8c53bef3e92d64bbea2785">00027</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qq(:,:) <span class="comment">! P(m,n) * gwd / cos2 * n * (n+1) / 2  &quot;</span>
    128. 

  128. <a name="l00028"></a><a class="code" href="classlegsym.html#a9e9b5d567f315f6cf660a0b44ffb4889">00028</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qu(:,:) <span class="comment">! P(m,n) / (n*(n+1)) * m    used in dv2uv</span>
    129. 

  129. <a name="l00029"></a><a class="code" href="classlegsym.html#a9a8f54ece20fd3aacb5d1f1570450ee0">00029</a> <span class="keywordtype">real</span>   , <span class="keywordtype">allocatable</span> :: qv(:,:) <span class="comment">! Q(m,n) / (n*(n+1))        used in dv2uv</span>
    130. 

  130. <a name="l00030"></a><a class="code" href="classlegsym.html#aff59025facb5c5b3d3717ca32328f587">00030</a> <span class="keywordtype">complex</span>, <span class="keywordtype">allocatable</span> :: qx(:,:) <span class="comment">! P(m,n) * gwd / cos2 * m   used in mktend</span>
    131. 

  131. <a name="l00031"></a>00031 <span class="keyword">end module legsym</span>
    132. 

  132. <a name="l00032"></a>00032 
    133. 

  133. <a name="l00033"></a>00033 <span class="comment">! =================</span>
    134. 

  134. <a name="l00034"></a>00034 <span class="comment">! SUBROUTINE LEGINI</span>
    135. 

  135. <a name="l00035"></a>00035 <span class="comment">! =================</span>
    136. 

  136. <a name="l00036"></a>00036 
    137. 

  137. <a name="l00037"></a><a class="code" href="legsym_8f90.html#a86bc436e65d6c4ddde72bb3cce7dc8c8">00037</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a86bc436e65d6c4ddde72bb3cce7dc8c8">legini</a>(klat,klpp,kesp,klev,vorpla,sid,gwd)
    138. 

  138. <a name="l00038"></a>00038 use <span class="keywordflow">legsym</span>
    139. 

  139. <a name="l00039"></a>00039 <span class="keyword">implicit none</span>
    140. 

  140. <a name="l00040"></a>00040 
    141. 

  141. <a name="l00041"></a>00041 <span class="keywordtype">integer</span> :: klat
    142. 

  142. <a name="l00042"></a>00042 <span class="keywordtype">integer</span> :: klpp
    143. 

  143. <a name="l00043"></a>00043 <span class="keywordtype">integer</span> :: kesp
    144. 

  144. <a name="l00044"></a>00044 <span class="keywordtype">integer</span> :: klev
    145. 

  145. <a name="l00045"></a>00045 
    146. 

  146. <a name="l00046"></a>00046 <span class="keywordtype">real</span>          :: vorpla   <span class="comment">! planetary vorticity</span>
    147. 

  147. <a name="l00047"></a>00047 <span class="keywordtype">real (kind=8)</span> :: sid(*)   <span class="comment">! sin(phi)</span>
    148. 

  148. <a name="l00048"></a>00048 <span class="keywordtype">real (kind=8)</span> :: gwd(*)   <span class="comment">! Gaussian weight (phi)</span>
    149. 

  149. <a name="l00049"></a>00049 
    150. 

  150. <a name="l00050"></a>00050 <span class="keywordtype">integer</span> :: jlat <span class="comment">! Latitude</span>
    151. 

  151. <a name="l00051"></a>00051 <span class="keywordtype">integer</span> :: lm
    152. 

  152. <a name="l00052"></a>00052 <span class="keywordtype">integer</span> :: m
    153. 

  153. <a name="l00053"></a>00053 <span class="keywordtype">integer</span> :: n
    154. 

  154. <a name="l00054"></a>00054 
    155. 

  155. <a name="l00055"></a>00055 <span class="keywordtype">real (kind=8)</span> :: amsq
    156. 

  156. <a name="l00056"></a>00056 <span class="keywordtype">real (kind=8)</span> :: z1
    157. 

  157. <a name="l00057"></a>00057 <span class="keywordtype">real (kind=8)</span> :: z2
    158. 

  158. <a name="l00058"></a>00058 <span class="keywordtype">real (kind=8)</span> :: z3
    159. 

  159. <a name="l00059"></a>00059 <span class="keywordtype">real (kind=8)</span> :: f1m
    160. 

  160. <a name="l00060"></a>00060 <span class="keywordtype">real (kind=8)</span> :: f2m
    161. 

  161. <a name="l00061"></a>00061 <span class="keywordtype">real (kind=8)</span> :: znn1
    162. 

  162. <a name="l00062"></a>00062 <span class="keywordtype">real (kind=8)</span> :: zsin    <span class="comment">! sin</span>
    163. 

  163. <a name="l00063"></a>00063 <span class="keywordtype">real (kind=8)</span> :: zcsq    <span class="comment">! cos2</span>
    164. 

  164. <a name="l00064"></a>00064 <span class="keywordtype">real (kind=8)</span> :: zcos    <span class="comment">! cos</span>
    165. 

  165. <a name="l00065"></a>00065 <span class="keywordtype">real (kind=8)</span> :: zgwd    <span class="comment">! gw</span>
    166. 

  166. <a name="l00066"></a>00066 <span class="keywordtype">real (kind=8)</span> :: zgwdcsq <span class="comment">! gw / cos2</span>
    167. 

  167. <a name="l00067"></a>00067 <span class="keywordtype">real (kind=8)</span> :: zpli(kesp)
    168. 

  168. <a name="l00068"></a>00068 <span class="keywordtype">real (kind=8)</span> :: zpld(kesp)
    169. 

  169. <a name="l00069"></a>00069 
    170. 

  170. <a name="l00070"></a>00070 nlat = klat
    171. 

  171. <a name="l00071"></a>00071 nlpp = klpp
    172. 

  172. <a name="l00072"></a>00072 nhpp = klpp / 2
    173. 

  173. <a name="l00073"></a>00073 nlon = klat + klat
    174. 

  174. <a name="l00074"></a>00074 ntru = (nlon - 1) /3
    175. 

  175. <a name="l00075"></a>00075 ntp1 = ntru + 1
    176. 

  176. <a name="l00076"></a>00076 ncsp = ((ntru + 1) * (ntru + 2)) / 2
    177. 

  177. <a name="l00077"></a>00077 nesp = kesp
    178. 

  178. <a name="l00078"></a>00078 nlev = klev
    179. 

  179. <a name="l00079"></a>00079 
    180. 

  180. <a name="l00080"></a>00080 plavor = vorpla
    181. 

  181. <a name="l00081"></a>00081 
    182. 

  182. <a name="l00082"></a>00082 <span class="keyword">allocate</span>(qi(ncsp,nhpp))
    183. 

  183. <a name="l00083"></a>00083 <span class="keyword">allocate</span>(qj(ncsp,nhpp))
    184. 

  184. <a name="l00084"></a>00084 <span class="keyword">allocate</span>(qc(ncsp,nhpp))
    185. 

  185. <a name="l00085"></a>00085 <span class="keyword">allocate</span>(qe(ncsp,nhpp))
    186. 

  186. <a name="l00086"></a>00086 <span class="keyword">allocate</span>(qx(ncsp,nhpp))
    187. 

  187. <a name="l00087"></a>00087 <span class="keyword">allocate</span>(qq(ncsp,nhpp))
    188. 

  188. <a name="l00088"></a>00088 <span class="keyword">allocate</span>(qu(ncsp,nhpp))
    189. 

  189. <a name="l00089"></a>00089 <span class="keyword">allocate</span>(qv(ncsp,nhpp))
    190. 

  190. <a name="l00090"></a>00090 
    191. 

  191. <a name="l00091"></a>00091 <span class="keyword">do</span> jlat = 1 , nhpp
    192. 

  192. <a name="l00092"></a>00092 
    193. 

  193. <a name="l00093"></a>00093 <span class="comment">! set p(0,0) and p(0,1)</span>
    194. 

  194. <a name="l00094"></a>00094 
    195. 

  195. <a name="l00095"></a>00095    zgwd    = gwd(jlat)            <span class="comment">! gaussian weight - from inigau</span>
    196. 

  196. <a name="l00096"></a>00096    zsin    = sid(jlat)            <span class="comment">! sin(phi) - from inigau</span>
    197. 

  197. <a name="l00097"></a>00097    zcsq    = 1.0_8 - zsin * zsin  <span class="comment">! cos(phi) squared</span>
    198. 

  198. <a name="l00098"></a>00098    zgwdcsq = zgwd / zcsq          <span class="comment">! weight / cos squared</span>
    199. 

  199. <a name="l00099"></a>00099    zcos    = sqrt(zcsq)           <span class="comment">! cos(phi)</span>
    200. 

  200. <a name="l00100"></a>00100    f1m     = sqrt(1.5_8)
    201. 

  201. <a name="l00101"></a>00101    zpli(1) = sqrt(0.5_8)
    202. 

  202. <a name="l00102"></a>00102    zpli(2) = f1m * zsin
    203. 

  203. <a name="l00103"></a>00103    zpld(1) = 0.0
    204. 

  204. <a name="l00104"></a>00104    lm      = 2
    205. 

  205. <a name="l00105"></a>00105 
    206. 

  206. <a name="l00106"></a>00106 <span class="comment">! loop over wavenumbers</span>
    207. 

  207. <a name="l00107"></a>00107 
    208. 

  208. <a name="l00108"></a>00108    <span class="keyword">do</span> m = 0 , ntru
    209. 

  209. <a name="l00109"></a>00109       <span class="keyword">if</span> (m &gt; 0) <span class="keyword">then</span>
    210. 

  210. <a name="l00110"></a>00110          lm  = lm + 1
    211. 

  211. <a name="l00111"></a>00111          f2m = -f1m * sqrt(zcsq / (m+m))
    212. 

  212. <a name="l00112"></a>00112          f1m =  f2m * sqrt(m+m + 3.0_8)
    213. 

  213. <a name="l00113"></a>00113          zpli(lm) = f2m
    214. 

  214. <a name="l00114"></a>00114          <span class="keyword">if</span> (lm &lt; ncsp) <span class="keyword">then</span>
    215. 

  215. <a name="l00115"></a>00115             lm = lm + 1
    216. 

  216. <a name="l00116"></a>00116             zpli(lm  ) =       f1m * zsin
    217. 

  217. <a name="l00117"></a>00117             zpld(lm-1) =  -m * f2m * zsin
    218. 

  218. <a name="l00118"></a>00118          <span class="keyword">endif</span> <span class="comment">! (lm &lt; ncsp)</span>
    219. 

  219. <a name="l00119"></a>00119       <span class="keyword">endif</span> <span class="comment">! (m &gt; 0)</span>
    220. 

  220. <a name="l00120"></a>00120 
    221. 

  221. <a name="l00121"></a>00121       amsq = m * m
    222. 

  222. <a name="l00122"></a>00122 
    223. 

  223. <a name="l00123"></a>00123       <span class="keyword">do</span> n = m+2 , ntru
    224. 

  224. <a name="l00124"></a>00124          lm = lm + 1
    225. 

  225. <a name="l00125"></a>00125          z1 = sqrt(((n-1)*(n-1) - amsq) / (4*(n-1)*(n-1)-1))
    226. 

  226. <a name="l00126"></a>00126          z2 = zsin * zpli(lm-1) - z1 * zpli(lm-2)
    227. 

  227. <a name="l00127"></a>00127          zpli(lm  ) = z2 * sqrt((4*n*n-1) / (n*n-amsq))
    228. 

  228. <a name="l00128"></a>00128          zpld(lm-1) = (1-n) * z2 + n * z1 * zpli(lm-2)
    229. 

  229. <a name="l00129"></a>00129       <span class="keyword">enddo</span> <span class="comment">! n</span>
    230. 

  230. <a name="l00130"></a>00130 
    231. 

  231. <a name="l00131"></a>00131       <span class="keyword">if</span> (lm &lt; ncsp) <span class="keyword">then</span> <span class="comment">! mode (m,ntru)</span>
    232. 

  232. <a name="l00132"></a>00132          z3 = sqrt((ntru*ntru-amsq) / (4*ntru*ntru-1))
    233. 

  233. <a name="l00133"></a>00133          zpld(lm)=-ntru*zsin*zpli(lm) + (ntru+ntru+1)*zpli(lm-1)*z3
    234. 

  234. <a name="l00134"></a>00134       <span class="keyword">else</span>                <span class="comment">! mode (ntru,ntru)</span>
    235. 

  235. <a name="l00135"></a>00135          zpld(lm)=-ntru*zsin*zpli(lm)
    236. 

  236. <a name="l00136"></a>00136       <span class="keyword">endif</span>
    237. 

  237. <a name="l00137"></a>00137    <span class="keyword">enddo</span> <span class="comment">! m</span>
    238. 

  238. <a name="l00138"></a>00138 
    239. 

  239. <a name="l00139"></a>00139    lm = 0
    240. 

  240. <a name="l00140"></a>00140    <span class="keyword">do</span> m = 0 , ntru
    241. 

  241. <a name="l00141"></a>00141       <span class="keyword">do</span> n = m , ntru
    242. 

  242. <a name="l00142"></a>00142            lm = lm + 1
    243. 

  243. <a name="l00143"></a>00143            znn1 = 0.0
    244. 

  244. <a name="l00144"></a>00144            <span class="keyword">if</span> (n &gt; 0) znn1 = 1.0_8 / (n*(n+1))
    245. 

  245. <a name="l00145"></a>00145            qi(lm,jlat) = zpli(lm)
    246. 

  246. <a name="l00146"></a>00146            qj(lm,jlat) = zpld(lm)
    247. 

  247. <a name="l00147"></a>00147            qc(lm,jlat) = zpli(lm) * zgwd
    248. 

  248. <a name="l00148"></a>00148            qu(lm,jlat) = zpli(lm) * znn1 * m
    249. 

  249. <a name="l00149"></a>00149            qv(lm,jlat) = zpld(lm) * znn1
    250. 

  250. <a name="l00150"></a>00150            qe(lm,jlat) = zpld(lm) * zgwdcsq
    251. 

  251. <a name="l00151"></a>00151            qq(lm,jlat) = zpli(lm) * zgwdcsq * n * (n+1) * 0.5_8
    252. 

  252. <a name="l00152"></a>00152            qx(lm,jlat) = zpli(lm) * zgwdcsq * m * (0.0,1.0)
    253. 

  253. <a name="l00153"></a>00153       <span class="keyword">enddo</span> <span class="comment">! n</span>
    254. 

  254. <a name="l00154"></a>00154    <span class="keyword">enddo</span> <span class="comment">! m</span>
    255. 

  255. <a name="l00155"></a>00155 <span class="keyword">enddo</span> <span class="comment">! jlat</span>
    256. 

  256. <a name="l00156"></a>00156 return
    257. 

  257. <a name="l00157"></a>00157 <span class="keyword">end</span>
    258. 

  258. <a name="l00158"></a>00158 
    259. 

  259. <a name="l00159"></a>00159 
    260. 

  260. <a name="l00160"></a>00160 <span class="comment">! ================</span>
    261. 

  261. <a name="l00161"></a>00161 <span class="comment">! SUBROUTINE FC2SP</span>
    262. 

  262. <a name="l00162"></a>00162 <span class="comment">! ================</span>
    263. 

  263. <a name="l00163"></a>00163 
    264. 

  264. <a name="l00164"></a><a class="code" href="legsym_8f90.html#a04d46a94caf6c743547ac25cfa3058d4">00164</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a04d46a94caf6c743547ac25cfa3058d4">fc2sp</a>(fc,sp)
    265. 

  265. <a name="l00165"></a>00165 use <span class="keywordflow">legsym</span>
    266. 

  266. <a name="l00166"></a>00166 <span class="keyword">implicit none</span>
    267. 

  267. <a name="l00167"></a>00167 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in )</span> :: fc(nlon,nhpp)
    268. 

  268. <a name="l00168"></a>00168 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(out)</span> :: sp(nesp/2)
    269. 

  269. <a name="l00169"></a>00169 
    270. 

  270. <a name="l00170"></a>00170 <span class="keywordtype">integer</span> :: l <span class="comment">! Index for latitude</span>
    271. 

  271. <a name="l00171"></a>00171 <span class="keywordtype">integer</span> :: m <span class="comment">! Index for zonal wavenumber</span>
    272. 

  272. <a name="l00172"></a>00172 <span class="keywordtype">integer</span> :: w <span class="comment">! Index for spherical harmonic</span>
    273. 

  273. <a name="l00173"></a>00173 <span class="keywordtype">integer</span> :: e <span class="comment">! Index for last wavenumber</span>
    274. 

  274. <a name="l00174"></a>00174 
    275. 

  275. <a name="l00175"></a>00175 sp(:) = (0.0,0.0)
    276. 

  276. <a name="l00176"></a>00176 
    277. 

  277. <a name="l00177"></a>00177 <span class="keyword">do</span> l = 1 , nhpp
    278. 

  278. <a name="l00178"></a>00178    w = 1
    279. 

  279. <a name="l00179"></a>00179    <span class="keyword">do</span> m = 1 , ntp1
    280. 

  280. <a name="l00180"></a>00180       e = w + ntp1 - m
    281. 

  281. <a name="l00181"></a>00181       sp(w  :e:2) = sp(w  :e:2) + qc(w  :e:2,l) * (fc(m,l) + fc(m+nlat,l))
    282. 

  282. <a name="l00182"></a>00182       sp(w+1:e:2) = sp(w+1:e:2) + qc(w+1:e:2,l) * (fc(m,l) - fc(m+nlat,l))
    283. 

  283. <a name="l00183"></a>00183       w = e + 1
    284. 

  284. <a name="l00184"></a>00184    <span class="keyword">enddo</span> <span class="comment">! m</span>
    285. 

  285. <a name="l00185"></a>00185 <span class="keyword">enddo</span> <span class="comment">! l</span>
    286. 

  286. <a name="l00186"></a>00186 return
    287. 

  287. <a name="l00187"></a>00187 <span class="keyword">end</span>
    288. 

  288. <a name="l00188"></a>00188 
    289. 

  289. <a name="l00189"></a>00189 
    290. 

  290. <a name="l00190"></a>00190 <span class="comment">! ================</span>
    291. 

  291. <a name="l00191"></a>00191 <span class="comment">! SUBROUTINE SP2FC</span>
    292. 

  292. <a name="l00192"></a>00192 <span class="comment">! ================</span>
    293. 

  293. <a name="l00193"></a>00193 
    294. 

  294. <a name="l00194"></a><a class="code" href="legsym_8f90.html#aec404fc15930c6e4584c088a399ea099">00194</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#aec404fc15930c6e4584c088a399ea099">sp2fc</a>(sp,fc) ! Spectral to Fourier
    295. 

  295. <a name="l00195"></a>00195 use <span class="keywordflow">legsym</span>
    296. 

  296. <a name="l00196"></a>00196 <span class="keyword">implicit none</span>
    297. 

  297. <a name="l00197"></a>00197 
    298. 

  298. <a name="l00198"></a>00198 <span class="keywordtype">complex</span> :: sp(ncsp)      <span class="comment">! Coefficients of spherical harmonics</span>
    299. 

  299. <a name="l00199"></a>00199 <span class="keywordtype">complex</span> :: fc(nlon,nhpp) <span class="comment">! Fourier coefficients</span>
    300. 

  300. <a name="l00200"></a>00200 
    301. 

  301. <a name="l00201"></a>00201 <span class="keywordtype">integer</span> :: l <span class="comment">! Loop index for latitude</span>
    302. 

  302. <a name="l00202"></a>00202 <span class="keywordtype">integer</span> :: m <span class="comment">! Loop index for zonal wavenumber m</span>
    303. 

  303. <a name="l00203"></a>00203 <span class="keywordtype">integer</span> :: w <span class="comment">! Index for spectral mode</span>
    304. 

  304. <a name="l00204"></a>00204 <span class="keywordtype">integer</span> :: e <span class="comment">! Index for last wavenumber</span>
    305. 

  305. <a name="l00205"></a>00205 
    306. 

  306. <a name="l00206"></a>00206 <span class="keywordtype">complex</span> :: fs,fa
    307. 

  307. <a name="l00207"></a>00207 
    308. 

  308. <a name="l00208"></a>00208 fc(:,:) = (0.0,0.0)
    309. 

  309. <a name="l00209"></a>00209 
    310. 

  310. <a name="l00210"></a>00210 <span class="keyword">do</span> l = 1 , nhpp
    311. 

  311. <a name="l00211"></a>00211   w = 1  
    312. 

  312. <a name="l00212"></a>00212   <span class="keyword">do</span> m = 1 ,ntp1
    313. 

  313. <a name="l00213"></a>00213     e = w + ntp1 - m
    314. 

  314. <a name="l00214"></a>00214     fs = dot_product(qi(w  :e:2,l),sp(w  :e:2))
    315. 

  315. <a name="l00215"></a>00215     fa = dot_product(qi(w+1:e:2,l),sp(w+1:e:2))
    316. 

  316. <a name="l00216"></a>00216     fc(m     ,l) = fs + fa
    317. 

  317. <a name="l00217"></a>00217     fc(m+nlat,l) = fs - fa
    318. 

  318. <a name="l00218"></a>00218     w = e + 1
    319. 

  319. <a name="l00219"></a>00219   <span class="keyword">enddo</span> <span class="comment">! m</span>
    320. 

  320. <a name="l00220"></a>00220 <span class="keyword">enddo</span> <span class="comment">! l</span>
    321. 

  321. <a name="l00221"></a>00221 return
    322. 

  322. <a name="l00222"></a>00222 <span class="keyword">end</span>
    323. 

  323. <a name="l00223"></a>00223 
    324. 

  324. <a name="l00224"></a>00224 
    325. 

  325. <a name="l00225"></a>00225 <span class="comment">! ===================</span>
    326. 

  326. <a name="l00226"></a>00226 <span class="comment">! SUBROUTINE SP2FCDMU</span>
    327. 

  327. <a name="l00227"></a>00227 <span class="comment">! ===================</span>
    328. 

  328. <a name="l00228"></a>00228 
    329. 

  329. <a name="l00229"></a><a class="code" href="legsym_8f90.html#ac25a3c42ee19118b299203d2747cb59e">00229</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#ac25a3c42ee19118b299203d2747cb59e">sp2fcdmu</a>(sp,fc) ! Spectral to Fourier d/dmu
    330. 

  330. <a name="l00230"></a>00230 use <span class="keywordflow">legsym</span>
    331. 

  331. <a name="l00231"></a>00231 <span class="keyword">implicit none</span>
    332. 

  332. <a name="l00232"></a>00232 
    333. 

  333. <a name="l00233"></a>00233 <span class="keywordtype">complex</span> :: sp(ncsp)      <span class="comment">! Coefficients of spherical harmonics</span>
    334. 

  334. <a name="l00234"></a>00234 <span class="keywordtype">complex</span> :: fc(nlon,nhpp) <span class="comment">! Fourier coefficients</span>
    335. 

  335. <a name="l00235"></a>00235 
    336. 

  336. <a name="l00236"></a>00236 <span class="keywordtype">integer</span> :: l <span class="comment">! Loop index for latitude</span>
    337. 

  337. <a name="l00237"></a>00237 <span class="keywordtype">integer</span> :: m <span class="comment">! Loop index for zonal wavenumber m</span>
    338. 

  338. <a name="l00238"></a>00238 <span class="keywordtype">integer</span> :: w <span class="comment">! Index for spectral mode</span>
    339. 

  339. <a name="l00239"></a>00239 <span class="keywordtype">integer</span> :: e <span class="comment">! Index for last wavenumber</span>
    340. 

  340. <a name="l00240"></a>00240 
    341. 

  341. <a name="l00241"></a>00241 <span class="keywordtype">complex</span> :: fs,fa
    342. 

  342. <a name="l00242"></a>00242 
    343. 

  343. <a name="l00243"></a>00243 fc(:,:) = (0.0,0.0)
    344. 

  344. <a name="l00244"></a>00244 
    345. 

  345. <a name="l00245"></a>00245 <span class="keyword">do</span> l = 1 , nhpp
    346. 

  346. <a name="l00246"></a>00246   w = 1  
    347. 

  347. <a name="l00247"></a>00247   <span class="keyword">do</span> m = 1 , ntp1
    348. 

  348. <a name="l00248"></a>00248     e = w + ntp1 - m
    349. 

  349. <a name="l00249"></a>00249     fs = dot_product(qj(w  :e:2,l),sp(w  :e:2))
    350. 

  350. <a name="l00250"></a>00250     fa = dot_product(qj(w+1:e:2,l),sp(w+1:e:2))
    351. 

  351. <a name="l00251"></a>00251     fc(m     ,l) = fa + fs
    352. 

  352. <a name="l00252"></a>00252     fc(m+nlat,l) = fa - fs
    353. 

  353. <a name="l00253"></a>00253     w = e + 1
    354. 

  354. <a name="l00254"></a>00254   <span class="keyword">enddo</span> <span class="comment">! m</span>
    355. 

  355. <a name="l00255"></a>00255 <span class="keyword">enddo</span> <span class="comment">! l</span>
    356. 

  356. <a name="l00256"></a>00256 return
    357. 

  357. <a name="l00257"></a>00257 <span class="keyword">end</span>
    358. 

  358. <a name="l00258"></a>00258 
    359. 

  359. <a name="l00259"></a>00259 
    360. 

  360. <a name="l00260"></a>00260 <span class="comment">! ================</span>
    361. 

  361. <a name="l00261"></a>00261 <span class="comment">! SUBROUTINE DV2UV</span>
    362. 

  362. <a name="l00262"></a>00262 <span class="comment">! ================</span>
    363. 

  363. <a name="l00263"></a>00263 
    364. 

  364. <a name="l00264"></a>00264 <span class="comment">! This is an alternative subroutine for computing U and V from Div and Vor.</span>
    365. 

  365. <a name="l00265"></a>00265 <span class="comment">! It looks much prettier than the regular one, but unfortunately it is slower</span>
    366. 

  366. <a name="l00266"></a>00266 <span class="comment">! if compiling with &quot;gfortran&quot;. </span>
    367. 

  367. <a name="l00267"></a>00267 <span class="comment">! I leave it (unused) in this module for educational purposes.</span>
    368. 

  368. <a name="l00268"></a>00268 
    369. 

  369. <a name="l00269"></a><a class="code" href="legsym_8f90.html#a581747beee32c3386dfc0b9b1cfa4e0f">00269</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a581747beee32c3386dfc0b9b1cfa4e0f">dv2uv_alt</a>(pd,pz,pu,pv)
    370. 

  370. <a name="l00270"></a>00270 use <span class="keywordflow">legsym</span>
    371. 

  371. <a name="l00271"></a>00271 <span class="keyword">implicit none</span>
    372. 

  372. <a name="l00272"></a>00272 <span class="keywordtype">complex</span>, <span class="keywordtype">parameter</span> :: i = (0.0,1.0)
    373. 

  373. <a name="l00273"></a>00273 <span class="keywordtype">complex</span> :: pd(nesp/2)    <span class="comment">! Spherical harmonics  of divergence</span>
    374. 

  374. <a name="l00274"></a>00274 <span class="keywordtype">complex</span> :: pz(nesp/2)    <span class="comment">! Spherical harmonics  of vorticity</span>
    375. 

  375. <a name="l00275"></a>00275 <span class="keywordtype">complex</span> :: pu(nlon,nhpp) <span class="comment">! Fourier coefficients of u</span>
    376. 

  376. <a name="l00276"></a>00276 <span class="keywordtype">complex</span> :: pv(nlon,nhpp) <span class="comment">! Fourier coefficients of v</span>
    377. 

  377. <a name="l00277"></a>00277 <span class="keywordtype">complex</span> :: zsave,uds,vds,uzs,vzs,uda,vda,uza,vza
    378. 

  378. <a name="l00278"></a>00278 
    379. 

  379. <a name="l00279"></a>00279 <span class="keywordtype">integer</span> :: l <span class="comment">! Loop index for latitude</span>
    380. 

  380. <a name="l00280"></a>00280 <span class="keywordtype">integer</span> :: m <span class="comment">! Loop index for zonal wavenumber m</span>
    381. 

  381. <a name="l00281"></a>00281 <span class="keywordtype">integer</span> :: w <span class="comment">! Loop index for spectral mode</span>
    382. 

  382. <a name="l00282"></a>00282 <span class="keywordtype">integer</span> :: e <span class="comment">! End index</span>
    383. 

  383. <a name="l00283"></a>00283 
    384. 

  384. <a name="l00284"></a>00284 pu(:,:) = (0.0,0.0)
    385. 

  385. <a name="l00285"></a>00285 pv(:,:) = (0.0,0.0)
    386. 

  386. <a name="l00286"></a>00286 
    387. 

  387. <a name="l00287"></a>00287 zsave = pz(2)                      <span class="comment">! Save mode(0,1) of vorticity</span>
    388. 

  388. <a name="l00288"></a>00288 pz(2) = zsave - cmplx(plavor,0.0)  <span class="comment">! Convert pz from absolute to relative vorticity</span>
    389. 

  389. <a name="l00289"></a>00289 
    390. 

  390. <a name="l00290"></a>00290 <span class="keyword">do</span> l = 1 , nhpp
    391. 

  391. <a name="l00291"></a>00291   w = 1  
    392. 

  392. <a name="l00292"></a>00292   <span class="keyword">do</span> m = 1 ,ntp1
    393. 

  393. <a name="l00293"></a>00293     e = w + ntp1 - m
    394. 

  394. <a name="l00294"></a>00294     uds = i * dot_product(qu(w  :e:2,l),pd(w:  e:2))
    395. 

  395. <a name="l00295"></a>00295     vds =     dot_product(qv(w  :e:2,l),pd(w:  e:2))
    396. 

  396. <a name="l00296"></a>00296     uzs = i * dot_product(qu(w  :e:2,l),pz(w:  e:2))
    397. 

  397. <a name="l00297"></a>00297     vzs =     dot_product(qv(w  :e:2,l),pz(w:  e:2))
    398. 

  398. <a name="l00298"></a>00298     uda = i * dot_product(qu(w+1:e:2,l),pd(w+1:e:2))
    399. 

  399. <a name="l00299"></a>00299     vda =     dot_product(qv(w+1:e:2,l),pd(w+1:e:2))
    400. 

  400. <a name="l00300"></a>00300     uza = i * dot_product(qu(w+1:e:2,l),pz(w+1:e:2))
    401. 

  401. <a name="l00301"></a>00301     vza =     dot_product(qv(w+1:e:2,l),pz(w+1:e:2))
    402. 

  402. <a name="l00302"></a>00302     pu(m     ,l) =  vzs - uds + vza - uda
    403. 

  403. <a name="l00303"></a>00303     pu(m+nlat,l) = -vzs - uds + vza + uda
    404. 

  404. <a name="l00304"></a>00304     pv(m     ,l) = -vds - uzs - vda - uza
    405. 

  405. <a name="l00305"></a>00305     pv(m+nlat,l) =  vds - uzs - vda + uza
    406. 

  406. <a name="l00306"></a>00306     w = e + 1
    407. 

  407. <a name="l00307"></a>00307   <span class="keyword">enddo</span> <span class="comment">! m</span>
    408. 

  408. <a name="l00308"></a>00308 <span class="keyword">enddo</span> <span class="comment">! l</span>
    409. 

  409. <a name="l00309"></a>00309 pz(2) = zsave
    410. 

  410. <a name="l00310"></a>00310 return
    411. 

  411. <a name="l00311"></a>00311 <span class="keyword">end</span>
    412. 

  412. <a name="l00312"></a>00312 
    413. 

  413. <a name="l00313"></a>00313 
    414. 

  414. <a name="l00314"></a>00314 <span class="comment">! ================</span>
    415. 

  415. <a name="l00315"></a>00315 <span class="comment">! SUBROUTINE DV2UV</span>
    416. 

  416. <a name="l00316"></a>00316 <span class="comment">! ================</span>
    417. 

  417. <a name="l00317"></a>00317 
    418. 

  418. <a name="l00318"></a><a class="code" href="legsym_8f90.html#af9cbedf7e87d9d5b2360c204237cc698">00318</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#af9cbedf7e87d9d5b2360c204237cc698">dv2uv</a>(pd,pz,pu,pv)
    419. 

  419. <a name="l00319"></a>00319 use <span class="keywordflow">legsym</span>
    420. 

  420. <a name="l00320"></a>00320 <span class="keyword">implicit none</span>
    421. 

  421. <a name="l00321"></a>00321 
    422. 

  422. <a name="l00322"></a>00322 <span class="keywordtype">real</span> :: pd(2,nesp/2)    <span class="comment">! Spherical harmonics  of divergence</span>
    423. 

  423. <a name="l00323"></a>00323 <span class="keywordtype">real</span> :: pz(2,nesp/2)    <span class="comment">! Spherical harmonics  of vorticity</span>
    424. 

  424. <a name="l00324"></a>00324 <span class="keywordtype">real</span> :: pu(2,nlon,nhpp) <span class="comment">! Fourier coefficients of u</span>
    425. 

  425. <a name="l00325"></a>00325 <span class="keywordtype">real</span> :: pv(2,nlon,nhpp) <span class="comment">! Fourier coefficients of v</span>
    426. 

  426. <a name="l00326"></a>00326 <span class="keywordtype">real</span> :: zsave
    427. 

  427. <a name="l00327"></a>00327 <span class="keywordtype">real</span> :: unr,uni,usr,usi,vnr,vni,vsr,vsi
    428. 

  428. <a name="l00328"></a>00328 <span class="keywordtype">real</span> :: zdr,zdi,zzr,zzi
    429. 

  429. <a name="l00329"></a>00329 
    430. 

  430. <a name="l00330"></a>00330 <span class="keywordtype">integer</span> :: l <span class="comment">! Loop index for latitude</span>
    431. 

  431. <a name="l00331"></a>00331 <span class="keywordtype">integer</span> :: m <span class="comment">! Loop index for zonal wavenumber m</span>
    432. 

  432. <a name="l00332"></a>00332 <span class="keywordtype">integer</span> :: n <span class="comment">! Loop index for total wavenumber n</span>
    433. 

  433. <a name="l00333"></a>00333 <span class="keywordtype">integer</span> :: w <span class="comment">! Loop index for spectral mode</span>
    434. 

  434. <a name="l00334"></a>00334 
    435. 

  435. <a name="l00335"></a>00335 pu(:,:,:) = 0.0
    436. 

  436. <a name="l00336"></a>00336 pv(:,:,:) = 0.0
    437. 

  437. <a name="l00337"></a>00337 
    438. 

  438. <a name="l00338"></a>00338 zsave = pz(1,2)           <span class="comment">! Save mode(0,1) of vorticity</span>
    439. 

  439. <a name="l00339"></a>00339 pz(1,2) = zsave - plavor  <span class="comment">! Convert pz from absolute to relative vorticity</span>
    440. 

  440. <a name="l00340"></a>00340 
    441. 

  441. <a name="l00341"></a>00341 <span class="keyword">do</span> l = 1 , nhpp
    442. 

  442. <a name="l00342"></a>00342    w = 1
    443. 

  443. <a name="l00343"></a>00343    <span class="keyword">do</span> m = 1 , ntp1
    444. 

  444. <a name="l00344"></a>00344       unr = 0.0 <span class="comment">! u - north - real</span>
    445. 

  445. <a name="l00345"></a>00345       uni = 0.0 <span class="comment">! u - north - imag</span>
    446. 

  446. <a name="l00346"></a>00346       usr = 0.0 <span class="comment">! u - south - real</span>
    447. 

  447. <a name="l00347"></a>00347       usi = 0.0 <span class="comment">! u - south - imag</span>
    448. 

  448. <a name="l00348"></a>00348       vnr = 0.0 <span class="comment">! v - north - real</span>
    449. 

  449. <a name="l00349"></a>00349       vni = 0.0 <span class="comment">! v - north - imag</span>
    450. 

  450. <a name="l00350"></a>00350       vsr = 0.0 <span class="comment">! v - south - real</span>
    451. 

  451. <a name="l00351"></a>00351       vsi = 0.0 <span class="comment">! v - south - imag</span>
    452. 

  452. <a name="l00352"></a>00352 
    453. 

  453. <a name="l00353"></a>00353 <span class="comment">!     process two modes per iteration, one symmetric (m+n = even) and one anti</span>
    454. 

  454. <a name="l00354"></a>00354 <span class="comment">!     we start the loop with (n=m), so the starting mode is always symmetric</span>
    455. 

  455. <a name="l00355"></a>00355 
    456. 

  456. <a name="l00356"></a>00356       <span class="keyword">do</span> n = m , ntru , 2
    457. 

  457. <a name="l00357"></a>00357          zdr = qu(w,l) * pd(1,w)  <span class="comment">! symmetric mode</span>
    458. 

  458. <a name="l00358"></a>00358          zdi = qu(w,l) * pd(2,w)
    459. 

  459. <a name="l00359"></a>00359          zzr = qv(w,l) * pz(1,w)
    460. 

  460. <a name="l00360"></a>00360          zzi = qv(w,l) * pz(2,w)
    461. 

  461. <a name="l00361"></a>00361          unr = unr + zzr + zdi
    462. 

  462. <a name="l00362"></a>00362          uni = uni + zzi - zdr
    463. 

  463. <a name="l00363"></a>00363          usr = usr - zzr + zdi
    464. 

  464. <a name="l00364"></a>00364          usi = usi - zzi - zdr
    465. 

  465. <a name="l00365"></a>00365          zzr = qu(w,l) * pz(1,w)
    466. 

  466. <a name="l00366"></a>00366          zzi = qu(w,l) * pz(2,w)
    467. 

  467. <a name="l00367"></a>00367          zdr = qv(w,l) * pd(1,w)
    468. 

  468. <a name="l00368"></a>00368          zdi = qv(w,l) * pd(2,w)
    469. 

  469. <a name="l00369"></a>00369          vnr = vnr + zzi - zdr
    470. 

  470. <a name="l00370"></a>00370          vni = vni - zzr - zdi
    471. 

  471. <a name="l00371"></a>00371          vsr = vsr + zzi + zdr
    472. 

  472. <a name="l00372"></a>00372          vsi = vsi - zzr + zdi
    473. 

  473. <a name="l00373"></a>00373          w = w + 1
    474. 

  474. <a name="l00374"></a>00374          zdr = qu(w,l) * pd(1,w)  <span class="comment">! antisymmetric mode</span>
    475. 

  475. <a name="l00375"></a>00375          zdi = qu(w,l) * pd(2,w)
    476. 

  476. <a name="l00376"></a>00376          zzr = qv(w,l) * pz(1,w)
    477. 

  477. <a name="l00377"></a>00377          zzi = qv(w,l) * pz(2,w)
    478. 

  478. <a name="l00378"></a>00378          unr = unr + zzr + zdi
    479. 

  479. <a name="l00379"></a>00379          uni = uni + zzi - zdr
    480. 

  480. <a name="l00380"></a>00380          usr = usr + zzr - zdi
    481. 

  481. <a name="l00381"></a>00381          usi = usi + zzi + zdr
    482. 

  482. <a name="l00382"></a>00382          zzr = qu(w,l) * pz(1,w)
    483. 

  483. <a name="l00383"></a>00383          zzi = qu(w,l) * pz(2,w)
    484. 

  484. <a name="l00384"></a>00384          zdr = qv(w,l) * pd(1,w)
    485. 

  485. <a name="l00385"></a>00385          zdi = qv(w,l) * pd(2,w)
    486. 

  486. <a name="l00386"></a>00386          vnr = vnr + zzi - zdr
    487. 

  487. <a name="l00387"></a>00387          vni = vni - zzr - zdi
    488. 

  488. <a name="l00388"></a>00388          vsr = vsr - zzi - zdr
    489. 

  489. <a name="l00389"></a>00389          vsi = vsi + zzr - zdi
    490. 

  490. <a name="l00390"></a>00390          w = w + 1
    491. 

  491. <a name="l00391"></a>00391       <span class="keyword">enddo</span>
    492. 

  492. <a name="l00392"></a>00392       <span class="keyword">if</span> (n == ntp1) <span class="keyword">then</span>         <span class="comment">! additional symmetric mode</span>
    493. 

  493. <a name="l00393"></a>00393          zdr = qu(w,l) * pd(1,w)  <span class="comment">! if (ntp1-m) is even</span>
    494. 

  494. <a name="l00394"></a>00394          zdi = qu(w,l) * pd(2,w)
    495. 

  495. <a name="l00395"></a>00395          zzr = qv(w,l) * pz(1,w)
    496. 

  496. <a name="l00396"></a>00396          zzi = qv(w,l) * pz(2,w)
    497. 

  497. <a name="l00397"></a>00397          unr = unr + zzr + zdi
    498. 

  498. <a name="l00398"></a>00398          uni = uni + zzi - zdr
    499. 

  499. <a name="l00399"></a>00399          usr = usr - zzr + zdi
    500. 

  500. <a name="l00400"></a>00400          usi = usi - zzi - zdr
    501. 

  501. <a name="l00401"></a>00401          zzr = qu(w,l) * pz(1,w)
    502. 

  502. <a name="l00402"></a>00402          zzi = qu(w,l) * pz(2,w)
    503. 

  503. <a name="l00403"></a>00403          zdr = qv(w,l) * pd(1,w)
    504. 

  504. <a name="l00404"></a>00404          zdi = qv(w,l) * pd(2,w)
    505. 

  505. <a name="l00405"></a>00405          vnr = vnr + zzi - zdr
    506. 

  506. <a name="l00406"></a>00406          vni = vni - zzr - zdi
    507. 

  507. <a name="l00407"></a>00407          vsr = vsr + zzi + zdr
    508. 

  508. <a name="l00408"></a>00408          vsi = vsi - zzr + zdi
    509. 

  509. <a name="l00409"></a>00409          w = w + 1
    510. 

  510. <a name="l00410"></a>00410       <span class="keyword">endif</span>
    511. 

  511. <a name="l00411"></a>00411       pu(1,m     ,l) = unr
    512. 

  512. <a name="l00412"></a>00412       pu(2,m     ,l) = uni
    513. 

  513. <a name="l00413"></a>00413       pu(1,m+nlat,l) = usr
    514. 

  514. <a name="l00414"></a>00414       pu(2,m+nlat,l) = usi
    515. 

  515. <a name="l00415"></a>00415       pv(1,m     ,l) = vnr
    516. 

  516. <a name="l00416"></a>00416       pv(2,m     ,l) = vni
    517. 

  517. <a name="l00417"></a>00417       pv(1,m+nlat,l) = vsr
    518. 

  518. <a name="l00418"></a>00418       pv(2,m+nlat,l) = vsi
    519. 

  519. <a name="l00419"></a>00419    <span class="keyword">enddo</span> <span class="comment">! m</span>
    520. 

  520. <a name="l00420"></a>00420 <span class="keyword">enddo</span> <span class="comment">! l</span>
    521. 

  521. <a name="l00421"></a>00421 pz(1,2) = zsave <span class="comment">! Restore pz to absolute vorticity</span>
    522. 

  522. <a name="l00422"></a>00422 return
    523. 

  523. <a name="l00423"></a>00423 <span class="keyword">end</span>
    524. 

  524. <a name="l00424"></a>00424 
    525. 

  525. <a name="l00425"></a>00425 
    526. 

  526. <a name="l00426"></a>00426 <span class="comment">! =================</span>
    527. 

  527. <a name="l00427"></a>00427 <span class="comment">! SUBROUTINE MKTEND</span>
    528. 

  528. <a name="l00428"></a>00428 <span class="comment">! =================</span>
    529. 

  529. <a name="l00429"></a>00429 
    530. 

  530. <a name="l00430"></a><a class="code" href="legsym_8f90.html#ab97cf272bad63e9bdd87a01317bb71c9">00430</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#ab97cf272bad63e9bdd87a01317bb71c9">mktend</a>(d,t,z,tn,fu,fv,ke,ut,vt)
    531. 

  531. <a name="l00431"></a>00431 use <span class="keywordflow">legsym</span>
    532. 

  532. <a name="l00432"></a>00432 <span class="keyword">implicit none</span>
    533. 

  533. <a name="l00433"></a>00433 
    534. 

  534. <a name="l00434"></a>00434 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: tn(nlon,nhpp)
    535. 

  535. <a name="l00435"></a>00435 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: fu(nlon,nhpp)
    536. 

  536. <a name="l00436"></a>00436 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: fv(nlon,nhpp)
    537. 

  537. <a name="l00437"></a>00437 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: ke(nlon,nhpp)
    538. 

  538. <a name="l00438"></a>00438 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: ut(nlon,nhpp)
    539. 

  539. <a name="l00439"></a>00439 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(in)</span> :: vt(nlon,nhpp)
    540. 

  540. <a name="l00440"></a>00440 
    541. 

  541. <a name="l00441"></a>00441 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(out)</span> :: d(nesp/2)
    542. 

  542. <a name="l00442"></a>00442 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(out)</span> :: t(nesp/2)
    543. 

  543. <a name="l00443"></a>00443 <span class="keywordtype">complex</span>, <span class="keywordtype">intent(out)</span> :: z(nesp/2)
    544. 

  544. <a name="l00444"></a>00444 
    545. 

  545. <a name="l00445"></a>00445 <span class="keywordtype">integer</span> :: l <span class="comment">! Loop index for latitude</span>
    546. 

  546. <a name="l00446"></a>00446 <span class="keywordtype">integer</span> :: m <span class="comment">! Loop index for zonal wavenumber m</span>
    547. 

  547. <a name="l00447"></a>00447 <span class="keywordtype">integer</span> :: w <span class="comment">! Loop index for spectral mode</span>
    548. 

  548. <a name="l00448"></a>00448 <span class="keywordtype">integer</span> :: e <span class="comment">! End index for w</span>
    549. 

  549. <a name="l00449"></a>00449 
    550. 

  550. <a name="l00450"></a>00450 <span class="keywordtype">complex</span> :: fus,fua,fvs,fva,kes,kea,tns,tna,uts,uta,vts,vta
    551. 

  551. <a name="l00451"></a>00451 
    552. 

  552. <a name="l00452"></a>00452 d(:) = (0.0,0.0) <span class="comment">! divergence</span>
    553. 

  553. <a name="l00453"></a>00453 t(:) = (0.0,0.0) <span class="comment">! temperature</span>
    554. 

  554. <a name="l00454"></a>00454 z(:) = (0.0,0.0) <span class="comment">! vorticity</span>
    555. 

  555. <a name="l00455"></a>00455 
    556. 

  556. <a name="l00456"></a>00456 <span class="keyword">do</span> l = 1 , nhpp  <span class="comment">! process pairs of Nort-South latitudes</span>
    557. 

  557. <a name="l00457"></a>00457    w = 1
    558. 

  558. <a name="l00458"></a>00458    <span class="keyword">do</span> m = 1 , ntp1
    559. 

  559. <a name="l00459"></a>00459       kes = ke(m,l) + ke(m+nlat,l) ; kea = ke(m,l) - ke(m+nlat,l)
    560. 

  560. <a name="l00460"></a>00460       fvs = fv(m,l) + fv(m+nlat,l) ; fva = fv(m,l) - fv(m+nlat,l)
    561. 

  561. <a name="l00461"></a>00461       fus = fu(m,l) + fu(m+nlat,l) ; fua = fu(m,l) - fu(m+nlat,l)
    562. 

  562. <a name="l00462"></a>00462       uts = ut(m,l) + ut(m+nlat,l) ; uta = ut(m,l) - ut(m+nlat,l)
    563. 

  563. <a name="l00463"></a>00463       vts = vt(m,l) + vt(m+nlat,l) ; vta = vt(m,l) - vt(m+nlat,l)
    564. 

  564. <a name="l00464"></a>00464       tns = tn(m,l) + tn(m+nlat,l) ; tna = tn(m,l) - tn(m+nlat,l)
    565. 

  565. <a name="l00465"></a>00465       e = w + ntp1 - m    <span class="comment">! vector of symmetric modes</span>
    566. 

  566. <a name="l00466"></a>00466       d(w:e:2) = d(w:e:2) + qq(w:e:2,l) * kes - qe(w:e:2,l) * fva + qx(w:e:2,l) * fus
    567. 

  567. <a name="l00467"></a>00467       t(w:e:2) = t(w:e:2) + qe(w:e:2,l) * vta + qc(w:e:2,l) * tns - qx(w:e:2,l) * uts
    568. 

  568. <a name="l00468"></a>00468       z(w:e:2) = z(w:e:2) + qe(w:e:2,l) * fua + qx(w:e:2,l) * fvs
    569. 

  569. <a name="l00469"></a>00469       w = w + 1           <span class="comment">! vector of antisymmetric modes</span>
    570. 

  570. <a name="l00470"></a>00470       d(w:e:2) = d(w:e:2) + qq(w:e:2,l) * kea - qe(w:e:2,l) * fvs + qx(w:e:2,l) * fua
    571. 

  571. <a name="l00471"></a>00471       t(w:e:2) = t(w:e:2) + qe(w:e:2,l) * vts + qc(w:e:2,l) * tna - qx(w:e:2,l) * uta
    572. 

  572. <a name="l00472"></a>00472       z(w:e:2) = z(w:e:2) + qe(w:e:2,l) * fus + qx(w:e:2,l) * fva
    573. 

  573. <a name="l00473"></a>00473       w = e + 1
    574. 

  574. <a name="l00474"></a>00474    <span class="keyword">enddo</span> <span class="comment">! m</span>
    575. 

  575. <a name="l00475"></a>00475 <span class="keyword">enddo</span> <span class="comment">! l</span>
    576. 

  576. <a name="l00476"></a>00476 return
    577. 

  577. <a name="l00477"></a>00477 <span class="keyword">end</span>
    578. 

  578. <a name="l00478"></a>00478 
    579. 

  579. <a name="l00479"></a>00479 
    580. 

  580. <a name="l00480"></a>00480 <span class="comment">! ==================</span>
    581. 

  581. <a name="l00481"></a>00481 <span class="comment">! SUBROUTINE REG2ALT</span>
    582. 

  582. <a name="l00482"></a>00482 <span class="comment">! ==================</span>
    583. 

  583. <a name="l00483"></a>00483 
    584. 

  584. <a name="l00484"></a><a class="code" href="legsym_8f90.html#a4a468562c0549b4ca3ec6ea34f87545a">00484</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a4a468562c0549b4ca3ec6ea34f87545a">reg2alt</a>(pr,klev)
    585. 

  585. <a name="l00485"></a>00485 use <span class="keywordflow">legsym</span>
    586. 

  586. <a name="l00486"></a>00486 <span class="keyword">implicit none</span>
    587. 

  587. <a name="l00487"></a>00487 
    588. 

  588. <a name="l00488"></a>00488 <span class="keywordtype">real</span> :: pr(nlon,nlat,klev)
    589. 

  589. <a name="l00489"></a>00489 <span class="keywordtype">real</span> :: pa(nlon,nlat,klev)
    590. 

  590. <a name="l00490"></a>00490 
    591. 

  591. <a name="l00491"></a>00491 <span class="keywordtype">integer</span> :: jlat
    592. 

  592. <a name="l00492"></a>00492 <span class="keywordtype">integer</span> :: klev
    593. 

  593. <a name="l00493"></a>00493 
    594. 

  594. <a name="l00494"></a>00494 <span class="keyword">do</span> jlat = 1 , nlat / 2
    595. 

  595. <a name="l00495"></a>00495   pa(:,2*jlat-1,:) = pr(:,jlat       ,:)
    596. 

  596. <a name="l00496"></a>00496   pa(:,2*jlat  ,:) = pr(:,nlat-jlat+1,:)
    597. 

  597. <a name="l00497"></a>00497 <span class="keyword">enddo</span>
    598. 

  598. <a name="l00498"></a>00498 
    599. 

  599. <a name="l00499"></a>00499 pr = pa
    600. 

  600. <a name="l00500"></a>00500 
    601. 

  601. <a name="l00501"></a>00501 return
    602. 

  602. <a name="l00502"></a>00502 <span class="keyword">end</span>
    603. 

  603. <a name="l00503"></a>00503 
    604. 

  604. <a name="l00504"></a>00504 
    605. 

  605. <a name="l00505"></a>00505 <span class="comment">! ==================</span>
    606. 

  606. <a name="l00506"></a>00506 <span class="comment">! SUBROUTINE ALT2REG</span>
    607. 

  607. <a name="l00507"></a>00507 <span class="comment">! ==================</span>
    608. 

  608. <a name="l00508"></a>00508 
    609. 

  609. <a name="l00509"></a><a class="code" href="legsym_8f90.html#a308819246e409c8dbe1e778d304ef415">00509</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a308819246e409c8dbe1e778d304ef415">alt2reg</a>(pa,klev)
    610. 

  610. <a name="l00510"></a>00510 use <span class="keywordflow">legsym</span>
    611. 

  611. <a name="l00511"></a>00511 <span class="keyword">implicit none</span>
    612. 

  612. <a name="l00512"></a>00512 
    613. 

  613. <a name="l00513"></a>00513 <span class="keywordtype">real</span> :: pa(nlon,nlat,klev)
    614. 

  614. <a name="l00514"></a>00514 <span class="keywordtype">real</span> :: pr(nlon,nlat,klev)
    615. 

  615. <a name="l00515"></a>00515 
    616. 

  616. <a name="l00516"></a>00516 <span class="keywordtype">integer</span> :: jlat
    617. 

  617. <a name="l00517"></a>00517 <span class="keywordtype">integer</span> :: klev
    618. 

  618. <a name="l00518"></a>00518 
    619. 

  619. <a name="l00519"></a>00519 <span class="keyword">do</span> jlat = 1 , nlat / 2
    620. 

  620. <a name="l00520"></a>00520   pr(:,jlat       ,:) = pa(:,2*jlat-1,:)
    621. 

  621. <a name="l00521"></a>00521   pr(:,nlat-jlat+1,:) = pa(:,2*jlat  ,:)
    622. 

  622. <a name="l00522"></a>00522 <span class="keyword">enddo</span>
    623. 

  623. <a name="l00523"></a>00523 
    624. 

  624. <a name="l00524"></a>00524 pa = pr
    625. 

  625. <a name="l00525"></a>00525 
    626. 

  626. <a name="l00526"></a>00526 return
    627. 

  627. <a name="l00527"></a>00527 <span class="keyword">end</span>
    628. 

  628. <a name="l00528"></a>00528 
    629. 

  629. <a name="l00529"></a>00529 
    630. 

  630. <a name="l00530"></a>00530 <span class="comment">! ================</span>
    631. 

  631. <a name="l00531"></a>00531 <span class="comment">! SUBROUTINE ALTCS</span>
    632. 

  632. <a name="l00532"></a>00532 <span class="comment">! ================</span>
    633. 

  633. <a name="l00533"></a>00533 
    634. 

  634. <a name="l00534"></a><a class="code" href="legsym_8f90.html#a6ba5b0b99819bcbad73f2e2eb49c62bb">00534</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#a6ba5b0b99819bcbad73f2e2eb49c62bb">altcs</a>(pcs)
    635. 

  635. <a name="l00535"></a>00535 use <span class="keywordflow">legsym</span>
    636. 

  636. <a name="l00536"></a>00536 <span class="keyword">implicit none</span>
    637. 

  637. <a name="l00537"></a>00537 <span class="keywordtype">real</span> :: pcs(nlat,nlev)
    638. 

  638. <a name="l00538"></a>00538 <span class="keywordtype">real</span> :: pal(nlat,nlev)
    639. 

  639. <a name="l00539"></a>00539 <span class="keywordtype">integer</span> :: jlat
    640. 

  640. <a name="l00540"></a>00540 
    641. 

  641. <a name="l00541"></a>00541 <span class="keyword">do</span> jlat = 1 , nlat / 2
    642. 

  642. <a name="l00542"></a>00542   pal(jlat       ,:) = pcs(2*jlat-1,:)
    643. 

  643. <a name="l00543"></a>00543   pal(nlat-jlat+1,:) = pcs(2*jlat  ,:)
    644. 

  644. <a name="l00544"></a>00544 <span class="keyword">enddo</span>
    645. 

  645. <a name="l00545"></a>00545 
    646. 

  646. <a name="l00546"></a>00546 pcs = pal
    647. 

  647. <a name="l00547"></a>00547 
    648. 

  648. <a name="l00548"></a>00548 return
    649. 

  649. <a name="l00549"></a>00549 <span class="keyword">end</span>
    650. 

  650. <a name="l00550"></a>00550 
    651. 

  651. <a name="l00551"></a>00551 
    652. 

  652. <a name="l00552"></a>00552 <span class="comment">! =================</span>
    653. 

  653. <a name="l00553"></a>00553 <span class="comment">! SUBROUTINE ALTLAT </span>
    654. 

  654. <a name="l00554"></a>00554 <span class="comment">! =================</span>
    655. 

  655. <a name="l00555"></a>00555 
    656. 

  656. <a name="l00556"></a><a class="code" href="legsym_8f90.html#ae810767bcafdac840ab48c420efcb49a">00556</a> <span class="keyword">subroutine </span><a class="code" href="legsym_8f90.html#ae810767bcafdac840ab48c420efcb49a">altlat</a>(pr,klat)
    657. 

  657. <a name="l00557"></a>00557 <span class="keyword">implicit none</span>
    658. 

  658. <a name="l00558"></a>00558 <span class="keywordtype">integer</span> :: jlat
    659. 

  659. <a name="l00559"></a>00559 <span class="keywordtype">integer</span> :: klat
    660. 

  660. <a name="l00560"></a>00560 <span class="keywordtype">real</span>    :: pr(klat)  <span class="comment">! regular     grid</span>
    661. 

  661. <a name="l00561"></a>00561 <span class="keywordtype">real</span>    :: pa(klat)  <span class="comment">! alternating grid</span>
    662. 

  662. <a name="l00562"></a>00562 
    663. 

  663. <a name="l00563"></a>00563 <span class="keyword">do</span> jlat = 1 , klat / 2
    664. 

  664. <a name="l00564"></a>00564   pa(2*jlat-1) = pr(jlat       )
    665. 

  665. <a name="l00565"></a>00565   pa(2*jlat  ) = pr(klat-jlat+1)
    666. 

  666. <a name="l00566"></a>00566 <span class="keyword">enddo</span>
    667. 

  667. <a name="l00567"></a>00567 
    668. 

  668. <a name="l00568"></a>00568 pr(:) = pa(:)
    669. 

  669. <a name="l00569"></a>00569 
    670. 

  670. <a name="l00570"></a>00570 return
    671. 

  671. <a name="l00571"></a>00571 <span class="keyword">end</span>
    672. 

  672. </pre></div></div>
    673. 

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