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Warning, /pkg/atm_phys/old_doc/flux_exchange.tech.ps is written in an unsupported language. File is not indexed.

view on githubraw file Latest commit 9816fea6 on 2016-12-01 18:57:40 UTC
9816fea64a Jean*0001 %!PS-Adobe-2.0
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                0877 %%EndProlog
                0878 %%BeginSetup
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                0881 %%PaperSize: A4
                0882 
                0883 %%EndSetup
                0884 %%Page: 1 1
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                0889 %%Page: 1 2
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                0920 y Fd(L)2386 3033 y Fh(\))1013 b(\(1\))1428 3277 y Fe(c)1470
                0921 3292 y Fd(L)1522 3277 y Fe(@)5 b(T)1635 3292 y Fd(L)1688
                0922 3277 y Fe(=@)g(t)29 b Fh(=)e Fg(\000)p Fe(F)14 b Fh(\()p
                0923 Fe(T)2209 3292 y Fd(A)2267 3277 y Fe(;)j(T)2368 3292
                0924 y Fd(L)2420 3277 y Fh(\))979 b(\(2\))324 3466 y(The)43
                0925 b(atmosphere)g(and)g(the)g(land)f(exc)m(hange)i(the)f(heat)g(\015ux)g
                0926 Fe(F)14 b Fh(.)74 b(As)43 b(the)g(simplest)324 3598 y(case,)38
                0927 b(set)g Fe(F)14 b Fh(\()p Fe(T)891 3613 y Fd(A)948 3598
                0928 y Fe(;)j(T)1049 3613 y Fd(L)1101 3598 y Fh(\))34 b(=)h
                0929 Fg(\000)p Fe(\015)5 b Fh(\()p Fe(T)1512 3613 y Fd(A)1594
                0930 3598 y Fg(\000)26 b Fe(T)1754 3613 y Fd(L)1806 3598 y
                0931 Fh(\).)55 b(In)37 b(the)g(uncoupled)h(case)f(\()p Fe(T)3000
                0932 3613 y Fd(L)3087 3598 y Fh(=constan)m(t\))324 3730 y(the)c(simplest)e
                0933 (forw)m(ard)i(time)e(step)j(is)1443 3966 y Fe(c)1485
                0934 3981 y Fd(A)1552 3899 y Fh(\()p Fe(T)1661 3858 y Fd(i)p
                0935 Fc(+1)1647 3926 y Fd(A)1801 3899 y Fg(\000)23 b Fe(T)1972
                0936 3863 y Fd(i)1958 3924 y(A)2015 3899 y Fh(\))p 1552 3943
                0937 501 4 v 1744 4035 a(\001)p Fe(t)2091 3966 y Fh(=)k Fg(\000)p
                0938 Fe(\015)5 b(T)2398 3925 y Fd(i)2384 3991 y(A)3437 3966
                0939 y Fh(\(3\))324 4168 y(whic)m(h)41 b(blo)m(ws)h(up)f(if)f
                0940 Fe(\030)1179 4183 y Fd(A)1278 4168 y Fe(>)i Fh(2)f(and)g(pro)s(duces)h
                0941 (oscillatory)d(rather)i(than)g(monotonic)324 4300 y(deca)m(y)32
                0942 b(for)f(1)c Fe(<)h(\030)964 4315 y Fd(A)1048 4300 y Fe(<)g
                0943 Fh(2,)j(where)h Fe(\030)1582 4315 y Fd(A)1666 4300 y
                0944 Fg(\021)d Fe(\015)5 b Fh(\001)p Fe(t=c)2035 4315 y Fd(A)2092
                0945 4300 y Fh(.)43 b(This)31 b(is)g(unacceptable.)44 b(A)31
                0946 b(cen)m(tered)324 4433 y(step,)c(with)e(0)p Fe(:)p Fh(5)p
                0947 Fe(\015)5 b Fh(\()p Fe(T)1056 4392 y Fd(i)p Fc(+1)1042
                0948 4460 y Fd(A)1180 4433 y Fh(+)i Fe(T)1334 4397 y Fd(i)1320
                0949 4458 y(A)1377 4433 y Fh(\))25 b(on)g(the)h(RHS,)f(is)f(stable)h(in)g
                0950 (the)g(sense)i(that)e(all)e(solutions)324 4565 y(are)41
                0951 b(damp)s(ed,)i(but)f(when)g Fe(\030)1398 4580 y Fd(A)1497
                0952 4565 y Fe(>)h Fh(2)e(it)f(pro)s(duces)i(oscillatory)d(deca)m(y)-8
                0953 b(,)45 b(whic)m(h)d(is)f(still)324 4698 y(unacceptable.)j(The)34
                0954 b(standard)f(pro)s(cedure)g(is)f(to)g(use)i(a)e(bac)m(kw)m(ard)i(time)e
                0955 (step)1406 4934 y Fe(c)1448 4949 y Fd(A)1515 4866 y Fh(\()p
                0956 Fe(T)1624 4825 y Fd(i)p Fc(+1)1610 4893 y Fd(A)1764 4866
                0957 y Fg(\000)23 b Fe(T)1935 4830 y Fd(i)1921 4892 y(A)1978
                0958 4866 y Fh(\))p 1515 4911 V 1707 5002 a(\001)p Fe(t)2053
                0959 4934 y Fh(=)28 b Fg(\000)p Fe(\015)5 b(T)2361 4893 y
                0960 Fd(i)p Fc(+1)2347 4961 y Fd(A)3437 4934 y Fh(\(4\))1918
                0961 5251 y(1)p eop
                0962 %%Page: 2 3
                0963 2 2 bop 324 548 a Fh(whic)m(h)27 b(is)f(stable)h(and)g(deca)m(ys)h
                0964 (monotonically)c(in)i(all)e(cases.)43 b(\(In)27 b(fact,)h(in)e(some)g
                0965 (atmo-)324 680 y(spheric)39 b(mo)s(dels,)g(the)g(surface)g(\015uxes)i
                0966 (are)d(computed)h(with)f(a)g("sup)s(er)i(bac)m(kw)m(ards")324
                0967 813 y(sc)m(heme,)34 b(in)e(whic)m(h,)h(on)f(the)h(RHS,)g
                0968 Fe(T)1724 828 y Fd(A)1809 813 y Fg(!)27 b Fe(\013)q(T)2070
                0969 772 y Fd(i)p Fc(+1)2056 840 y Fd(A)2210 813 y Fh(+)22
                0970 b(\(1)g Fg(\000)g Fe(\013)q Fh(\))p Fe(T)2688 777 y Fd(i)2674
                0971 838 y(A)2731 813 y Fh(,)33 b(with)f Fe(\013)c(>)g Fh(1\))470
                0972 945 y(The)50 b(same)f(argumen)m(t)g(holds)g(for)g(the)g(coupled)g
                0973 (system,)55 b(\(1\))49 b(and)g(\(2\).)93 b(The)324 1078
                0974 y(fully)45 b(explicit)g(forw)m(ard)i(sc)m(heme)h(is)e(unstable)h(for)f
                0975 (either)g(large)g Fe(\030)2904 1093 y Fd(A)3007 1078
                0976 y Fh(or)g Fe(\030)3183 1093 y Fd(L)3235 1078 y Fh(,)k(where)324
                0977 1210 y Fe(\030)367 1225 y Fd(L)458 1210 y Fg(\021)40
                0978 b Fe(\015)5 b Fh(\001)p Fe(t=c)838 1225 y Fd(L)890 1210
                0979 y Fh(,)42 b(and)d(the)h('half)7 b(')39 b(explicit)f(sc)m(hemes)j
                0980 Fe(F)14 b Fh(\()p Fe(T)2507 1169 y Fd(i)p Fc(+1)2493
                0981 1237 y Fd(A)2625 1210 y Fe(;)j(T)2740 1174 y Fd(i)2726
                0982 1235 y(L)2778 1210 y Fh(\))p Fe(;)g(F)d Fh(\()p Fe(T)3046
                0983 1174 y Fd(i)3032 1235 y(A)3088 1210 y Fe(;)j(T)3203 1169
                0984 y Fd(i)p Fc(+1)3189 1237 y Fd(L)3321 1210 y Fh(\))40
                0985 b(also)324 1342 y(do)23 b(not)g(allo)m(w)f(arbitrary)g(time)g(steps)j
                0986 (or)e(heat)g(capacities.)40 b(The)24 b(fully)e(implicit)d(sc)m(heme)324
                0987 1475 y Fe(F)14 b Fh(\()p Fe(T)510 1434 y Fd(i)p Fc(+1)496
                0988 1502 y Fd(A)627 1475 y Fe(;)j(T)742 1434 y Fd(i)p Fc(+1)728
                0989 1502 y Fd(L)860 1475 y Fh(\))33 b(is)f(the)h(preferred)g(c)m(hoice.)470
                0990 1607 y(\(If)26 b(conserv)-5 b(ation)26 b(w)m(ere)h(not)f(a)g
                0991 (requiremen)m(t,)i(other)e(options)g(w)m(ould)g(b)s(e)g(a)m(v)-5
                0992 b(ailable,)324 1740 y(suc)m(h)34 b(as)1282 1989 y Fe(c)1324
                0993 2004 y Fd(A)1391 1921 y Fh(\()p Fe(T)1500 1880 y Fd(i)p
                0994 Fc(+1)1486 1948 y Fd(A)1640 1921 y Fg(\000)23 b Fe(T)1811
                0995 1885 y Fd(i)1797 1947 y(A)1854 1921 y Fh(\))p 1391 1966
                0996 501 4 v 1583 2057 a(\001)p Fe(t)1929 1989 y Fh(==)28
                0997 b Fe(F)14 b Fh(\()p Fe(T)2295 1948 y Fd(i)p Fc(+1)2281
                0998 2016 y Fd(A)2413 1989 y Fe(;)j(T)2528 1948 y Fd(i)2514
                0999 2013 y(L)2566 1989 y Fh(\))833 b(\(5\))1246 2394 y Fe(c)1288
                1000 2409 y Fd(L)1350 2327 y Fh(\()p Fe(T)1459 2286 y Fd(i)p
                1001 Fc(+1)1445 2354 y Fd(L)1599 2327 y Fg(\000)23 b Fe(T)1770
                1002 2291 y Fd(i)1756 2352 y(L)1808 2327 y Fh(\))p 1350 2372
                1003 497 4 v 1540 2463 a(\001)p Fe(t)1884 2394 y Fh(=)k Fg(\000)p
                1004 Fe(F)14 b Fh(\()p Fe(T)2250 2353 y Fd(i)p Fc(+1)2236
                1005 2421 y Fd(A)2369 2394 y Fe(;)j(T)2484 2353 y Fd(i)p Fc(+1)2470
                1006 2421 y Fd(L)2601 2394 y Fh(\))798 b(\(6\))324 2628 y(whic)m(h)40
                1007 b(has)h(the)g(adv)-5 b(an)m(tage)40 b(of)g(decoupling)f(the)i(t)m(w)m
                1008 (o)g(equations.)66 b(W)-8 b(e)41 b(require)f(the)324
                1009 2761 y(FMS)33 b(\015ux)g(exc)m(hange)h(mo)s(dule)d(to)i(conserv)m(e)h
                1010 (exactly)-8 b(,)33 b(ruling)e(out)i(suc)m(h)h(options.\))470
                1011 2893 y(Returning)e(to)g(a)g(general)g(expression)h(for)f
                1012 Fe(F)14 b Fh(\()p Fe(T)2272 2852 y Fd(i)p Fc(+1)2258
                1013 2920 y Fd(A)2390 2893 y Fe(;)j(T)2505 2852 y Fd(i)p Fc(+1)2491
                1014 2920 y Fd(L)2623 2893 y Fh(\),)32 b(w)m(e)h(replace)g(it)e(b)m(y)i(the)
                1015 324 3026 y(\014rst)g(term)f(in)g(its)g(T)-8 b(a)m(ylor)32
                1016 b(expansion)h(ab)s(out)f(its)g(v)-5 b(alue)32 b Fe(F)2497
                1017 3041 y Fc(0)2569 3026 y Fh(at)g(the)h(time)f(step)h Fe(i)p
                1018 Fh(:)1177 3211 y Fe(c)1219 3226 y Fd(A)p 1168 3255 117
                1019 4 v 1168 3347 a Fh(\001)p Fe(t)1295 3278 y Fh(\001)p
                1020 Fe(T)1433 3293 y Fd(A)1518 3278 y Fh(=)27 b Fe(F)1684
                1021 3293 y Fc(0)1746 3278 y Fh(+)1873 3211 y Fe(@)5 b(F)p
                1022 1854 3255 172 4 v 1854 3347 a(@)g(T)1967 3362 y Fd(A)2035
                1023 3278 y Fh(\001)p Fe(T)2173 3293 y Fd(A)2253 3278 y Fh(+)2377
                1024 3211 y Fe(@)g(F)p 2361 3255 167 4 v 2361 3347 a(@)g(T)2474
                1025 3362 y Fd(L)2537 3278 y Fh(\001)p Fe(T)2675 3293 y Fd(L)3437
                1026 3278 y Fh(\(7\))1141 3615 y Fe(c)1183 3630 y Fd(L)p 1130
                1027 3660 117 4 v 1130 3751 a Fh(\001)p Fe(t)1257 3683 y Fh(\001)p
                1028 Fe(T)1395 3698 y Fd(L)1475 3683 y Fh(=)27 b Fg(\000)p
                1029 Fe(F)1718 3698 y Fc(0)1781 3683 y Fg(\000)1909 3615 y
                1030 Fe(@)5 b(F)p 1890 3660 172 4 v 1890 3751 a(@)g(T)2003
                1031 3766 y Fd(A)2071 3683 y Fh(\001)p Fe(T)2209 3698 y Fd(A)2289
                1032 3683 y Fg(\000)2415 3615 y Fe(@)g(F)p 2398 3660 167 4
                1033 v 2398 3751 a(@)g(T)2511 3766 y Fd(L)2575 3683 y Fh(\001)p
                1034 Fe(T)2713 3698 y Fd(L)3437 3683 y Fh(\(8\))324 3943 y(where)36
                1035 b(\001)p Fe(T)45 b Fg(\021)32 b Fe(T)971 3907 y Fd(i)p
                1036 Fc(+1)1113 3943 y Fg(\000)24 b Fe(T)1285 3907 y Fd(i)1313
                1037 3943 y Fh(.)50 b(Note)35 b(that)g(this)f(linearization)e(do)s(es)j(not)
                1038 g(destro)m(y)h(exact)324 4075 y(energy)47 b(conserv)-5
                1039 b(ation;)53 b(w)m(e)47 b(ha)m(v)m(e)g(simply)e(mo)s(di\014ed)g(the)i
                1040 (form)d(of)i(the)h(exc)m(hanged)324 4208 y(\015ux)35
                1041 b(sligh)m(tly)-8 b(.)47 b(The)36 b(linearization)31 b(is)j(a)g(device)h
                1042 (to)f(a)m(v)m(oid)g(iterating)f(for)h(the)g(implicit)324
                1043 4340 y(solution.)43 b(Once)34 b(one)f(has)h(c)m(hosen)h(a)d(bac)m(kw)m
                1044 (ards)k(sc)m(heme,)e(the)g(iterated)e(solution)g(is,)324
                1045 4472 y(in)38 b(general,)i(no)f(more)f(accurate)i(than)f(the)h(solution)
                1046 d(with)i(linearized)e(\015uxes.)65 b(The)324 4605 y(only)37
                1047 b(disadv)-5 b(an)m(tage)38 b(of)f(the)h(latter)f(is)g(a)h("diagnostic")
                1048 e(one:)54 b(the)38 b(\015uxes)i(exc)m(hanged)324 4737
                1049 y(b)s(et)m(w)m(een)h(the)f(t)m(w)m(o)g(mo)s(dels)e(cannot)i(b)s(e)f
                1050 (considered)h(precisely)g(as)f(a)g(function)g Fe(F)53
                1051 b Fh(of)324 4870 y(atmospheric)34 b(and)h(land)f(states)i(at)f
                1052 (particular)e(times;)i(they)h(are)f(also)f(a)h(function)f(of)324
                1053 5002 y(the)f(c)m(hange)g(in)f(state)h(from)e(one)i(time)e(step)j(to)e
                1054 (the)h(next.)1918 5251 y(2)p eop
                1055 %%Page: 3 4
                1056 3 3 bop 470 548 a Fh(W)-8 b(e)43 b(no)m(w)h(ha)m(v)m(e)g(t)m(w)m(o)f
                1057 (equations)g(that)f(can)h(b)s(e)g(solv)m(ed)h(sim)m(ultaneously)d(for)h
                1058 (the)324 680 y(t)m(w)m(o)j(unkno)m(wns)h(\001)p Fe(T)1125
                1059 695 y Fd(A)1227 680 y Fh(and)e(\001)p Fe(T)1566 695 y
                1060 Fd(L)1619 680 y Fh(.)79 b(This)44 b(is)g(straigh)m(tforw)m(ard,)j(of)d
                1061 (course,)k(but)d(w)m(e)324 813 y(w)m(ould)d(lik)m(e)f(to)g(form)m
                1062 (ulate)f(things)i(so)g(that)g(the)g(t)m(w)m(o)g(mo)s(dels)f(remain)g
                1063 (as)h(mo)s(dular)324 945 y(as)c(p)s(ossible,)h(without)e(b)s(eing)h
                1064 (unnecesarily)g(in)m(tert)m(wined.)60 b(F)-8 b(or)37
                1065 b(this)h(purp)s(ose,)i(it)d(is)324 1078 y(useful)27 b(to)f(think)h(of)g
                1066 (\014rst)g(solving)f(the)i(atmospheric)e(equation,)i(whic)m(h)f(pro)m
                1067 (vides)h(\001)p Fe(T)3504 1093 y Fd(A)324 1210 y Fh(as)33
                1068 b(a)f(\(linear\))f(function)h(of)g(\001)p Fe(T)1503 1225
                1069 y Fd(L)1555 1210 y Fh(.)1572 1420 y(\001)p Fe(T)1710
                1070 1435 y Fd(A)1795 1420 y Fh(=)c Fe(e)p Fh(\001)p Fe(T)2082
                1071 1435 y Fd(L)2157 1420 y Fh(+)22 b Fe(f)1134 b Fh(\(9\))324
                1072 1631 y(In)33 b(this)f(case)1765 1841 y Fe(f)39 b Fg(\021)28
                1073 b Fh(\000)p Fe(F)2081 1856 y Fc(0)3388 1841 y Fh(\(10\))324
                1074 2052 y(and)1730 2274 y Fe(e)g Fg(\021)g Fh(\000)1995
                1075 2207 y Fe(@)5 b(F)p 1979 2251 167 4 v 1979 2343 a(@)g(T)2092
                1076 2358 y Fd(L)3388 2274 y Fh(\(11\))324 2513 y(where)1536
                1077 2736 y(\000)28 b Fg(\021)g Fh(\()1787 2669 y Fe(c)1829
                1078 2684 y Fd(A)p 1778 2713 117 4 v 1778 2804 a Fh(\001)p
                1079 Fe(t)1926 2736 y Fg(\000)2055 2669 y Fe(@)5 b(F)p 2036
                1080 2713 172 4 v 2036 2804 a(@)g(T)2149 2819 y Fd(A)2217
                1081 2736 y Fh(\))2255 2695 y Fb(\000)p Fc(1)3388 2736 y Fh(\(12\))470
                1082 2975 y(Using)28 b(this)f(linear)f(relation,)h(\001)p
                1083 Fe(T)1710 2990 y Fd(A)1796 2975 y Fh(can)h(b)s(e)g(eliminated)d(and)j
                1084 (the)g(land)f(mo)s(del)f(can)324 3107 y(b)s(e)33 b(recast)g(in)m(to)f
                1085 (the)h(form)1441 3250 y Fe(c)1483 3265 y Fd(L)p 1430
                1086 3295 117 4 v 1430 3386 a Fh(\001)p Fe(t)1556 3317 y Fh(\001)p
                1087 Fe(T)1694 3332 y Fd(L)1775 3317 y Fh(=)27 b Fg(\000)p
                1088 Fh(\()p Fe(\013)c Fh(+)f Fe(\014)6 b Fh(\001)p Fe(T)2375
                1089 3332 y Fd(L)2428 3317 y Fh(\))922 b(\(13\))324 3541 y(whic)m(h)33
                1090 b(is)f(then)h(easily)f(solv)m(ed)h(for)f(\001)p Fe(T)1772
                1091 3556 y Fd(L)1825 3541 y Fh(.)43 b(Here)1609 3783 y Fe(\013)28
                1092 b Fg(\021)g Fe(F)1867 3798 y Fc(0)1929 3783 y Fh(+)2056
                1093 3716 y Fe(@)5 b(F)p 2037 3761 172 4 v 2037 3852 a(@)g(T)2150
                1094 3867 y Fd(A)2218 3783 y Fe(f)1122 b Fh(\(14\))1575 4167
                1095 y Fe(\014)33 b Fg(\021)1794 4100 y Fe(@)5 b(F)p 1778
                1096 4145 167 4 v 1778 4236 a(@)g(T)1891 4251 y Fd(L)1976
                1097 4167 y Fh(+)2103 4100 y Fe(@)g(F)p 2084 4145 172 4 v
                1098 2084 4236 a(@)g(T)2197 4251 y Fd(A)2265 4167 y Fe(e)1078
                1099 b Fh(\(15\))324 4412 y(Once)33 b(\001)p Fe(T)711 4427
                1100 y Fd(L)796 4412 y Fh(is)f(kno)m(wn)i(w)m(e)g(can)f(return)g(to)f(\(9\))
                1101 g(and)h(compute)f(\001)p Fe(T)2823 4427 y Fd(A)470 4544
                1102 y Fh(T)-8 b(o)33 b(summarize)e(this)h(pro)s(cedure)i({)324
                1103 4677 y Fg(\017)e Fh(Compute)1659 4919 y Fe(F)1722 4934
                1104 y Fc(0)1762 4919 y Fe(;)1834 4851 y(@)5 b(F)p 1815 4896
                1105 V 1815 4987 a(@)g(T)1928 5002 y Fd(A)1996 4919 y Fe(;)2066
                1106 4851 y(@)g(F)p 2050 4896 167 4 v 2050 4987 a(@)g(T)2163
                1107 5002 y Fd(L)3388 4919 y Fh(\(16\))1918 5251 y(3)p eop
                1108 %%Page: 4 5
                1109 4 4 bop 324 548 a Fg(\017)32 b Fh(compute)h Fe(e)f Fh(and)h
                1110 Fe(f)11 b Fh(,)32 b(and)h(then)g Fe(\013)h Fh(and)e Fe(\014)6
                1111 b Fh(.)324 680 y Fg(\017)p Fh(ask)45 b(the)g(surface)g(mo)s(del\(s\))e
                1112 (to)h(compute)g(the)h(c)m(hange)h(in)d(surface)j(temp)s(erature,)324
                1113 813 y(giv)m(en)32 b(a)h(\015ux)g(of)f(the)h(form)f Fe(\013)22
                1114 b Fh(+)g Fe(\014)6 b Fh(\001)p Fe(T)1743 828 y Fd(L)324
                1115 945 y Fg(\017)25 b Fh(giv)m(en)h(this)g(c)m(hange)h(in)e(the)h(surface)
                1116 h(temp)s(erature,)g(ask)f(the)h(atmosphere)f(to)f(up)s(date)324
                1117 1078 y(the)33 b(atmospheric)f(temp)s(erature)g(using)g(\(9\).)324
                1118 1429 y Ff(2)161 b(Implicit)55 b(\015uxes)e(within)h(the)f(atmosphere)
                1119 324 1660 y Fh(W)-8 b(e)24 b(need)h(sev)m(eral)g(generalization)d(of)i
                1120 (this)f(pro)s(cedure)i(for)f(the)g(\015ux)h(exc)m(hange)h(mo)s(dule)324
                1121 1792 y(in)31 b(FMS.)h(W)-8 b(e)32 b(\014rst)g(in)m(terpret)g
                1122 Fe(T)1530 1807 y Fd(A)1619 1792 y Fh(as)g(referring)f(to)h(the)g("lo)m
                1123 (w)m(est)g(atmospheric)f(mo)s(del)324 1925 y(la)m(y)m(er".)43
                1124 b(\(In)31 b(the)h(simplest)e(energy)i(balance)e(atmospheric)h(mo)s
                1125 (dels,)f(this)h(la)m(y)m(er)g(could)324 2057 y(b)s(e)37
                1126 b(the)g(en)m(tire)g(atmosphere.\))57 b(W)-8 b(e)37 b(no)m(w)h(need)g
                1127 (to)e(lea)m(v)m(e)i(op)s(en)f(the)g(p)s(ossibilit)m(y)e(that)324
                1128 2189 y(there)h(are)g(atmospheric)f(\015uxes)i(in)m(to)e(this)g
                1129 (atmospheric)g(b)s(o)m(x)h(from)e(ab)s(o)m(v)m(e)i(that)g(are)324
                1130 2322 y(treated)d(implicitly)-8 b(.)470 2454 y(When)48
                1131 b(there)f(are)f(t)m(w)m(o)i(distinct)d(pro)s(cesses)k(in)d(a)g(mo)s
                1132 (del)f(that)h(m)m(ust)h(b)s(oth)f(b)s(e)324 2587 y(treated)35
                1133 b(implicitly)-8 b(,)31 b(it)j(is)g(not)h(necessarily)g(a)g(requiremen)m
                1134 (t)g(that)g(the)g(implicit)c(com-)324 2719 y(putations)h(b)s(e)h
                1135 (coupled.)43 b(One)33 b(can)g(instead)f(use)i(some)e(time-splitting)d
                1136 (pro)s(cedure)k(in)324 2852 y(whic)m(h)e(one)f(computes)h(the)g
                1137 (e\013ects)h(of)e(pro)s(cess)h(A)g(as)g(if)e(pro)s(cess)i(B)g(w)m(ere)h
                1138 (not)e(presen)m(t)324 2984 y(or)e(in)f(whic)m(h)i(B)f(is)g(treated)h
                1139 (explicitly)-8 b(,)27 b(then)i(uses)h(the)e(resulting)f(state)i(of)f
                1140 (the)h(system)324 3116 y(as)k(input)f(in)m(to)f(an)i(implicit)c
                1141 (computation)i(of)h(the)h(e\013ects)h(of)e(B.)470 3249
                1142 y(In)25 b(a)g(GCM)g(the)g(v)m(ertical)f(di\013usiv)m(e)h(\015uxes)h
                1143 (are)f(generally)f(treated)h(implicitly;)e(fur-)324 3381
                1144 y(thermore,)28 b(the)h(di\013usiv)m(e)f(\015ux)h(across)f(the)h(top)f
                1145 (of)f(the)h(lo)m(w)m(est)h(atmospheric)e(grid)g(b)s(o)m(x)324
                1146 3514 y(can)35 b(b)s(e)g(closely)f(related)g(to)h(the)g(surface)h
                1147 (\015ux,)g(esp)s(ecially)e(when)i(this)e(lo)m(w)m(est)h(atmo-)324
                1148 3646 y(spheric)26 b(b)s(o)m(x)g(is)f(v)m(ery)h(thin.)41
                1149 b(\(Quite)25 b(often)g(w)m(e)i(pretend)f(that)f(the)h(lo)m(w)m(est)g
                1150 (atmospheric)324 3778 y(la)m(y)m(er)j(lies)f(completely)g(within)g(the)
                1151 i("constan)m(t)g(\015ux)g(la)m(y)m(er")f(within)f(the)h(atmospheric)324
                1152 3911 y(turbulen)m(t)38 b(b)s(oundary)h(la)m(y)m(er,)h(so)f(as)f(to)g
                1153 (justify)g(the)h(use)g(of)f(Monin-Obukho)m(v)h(simi-)324
                1154 4043 y(larit)m(y)d(theory)-8 b(,)40 b(in)d(whic)m(h)h(case)h(the)f
                1155 (di\013usiv)m(e)g(\015ux)g(at)g(the)g(top)g(of)f(the)h(lo)m(w)m(est)g
                1156 (la)m(y)m(er)324 4176 y(should)33 b(b)s(e)h(essen)m(tially)f(the)g
                1157 (same)h(as)f(the)h(surface)g(\015ux.\))47 b(Therefore,)35
                1158 b(not)e(only)g(is)g(it)324 4308 y(desirable)g(to)h(treat)g(the)g(v)m
                1159 (ertical)g(di\013usion)f(within)g(the)h(planetary)g(b)s(oundary)g(la)m
                1160 (y)m(er)324 4441 y(implicitly)-8 b(,)33 b(but)k(w)m(e)h(need)f(to)g
                1161 (treat)f(the)h(surface)h(\015uxes)g(and)f(the)g(v)m(ertical)f
                1162 (di\013usiv)m(e)324 4573 y(\015uxes)e(near)f(the)g(surface)g(as)g(part)
                1163 f(of)g(the)h Fa(same)40 b Fh(implicit)28 b(step.)470
                1164 4705 y(Consider,)33 b(therefore,)1175 4937 y Fe(c)1217
                1165 4952 y Fd(A)1274 4937 y Fe(@)5 b(T)1387 4952 y Fd(A)1445
                1166 4937 y Fe(=@)g(t)29 b Fh(=)e Fe(F)14 b Fh(\()p Fe(T)1889
                1167 4952 y Fd(A)1946 4937 y Fe(;)j(T)2047 4952 y Fd(L)2099
                1168 4937 y Fh(\))22 b(+)g Fe(F)2320 4952 y Fd(A)2377 4937
                1169 y Fh(\()p Fe(T)2472 4952 y Fd(A)2529 4937 y Fe(;)17 b(\030)2616
                1170 4952 y Fd(A)2673 4937 y Fh(\))677 b(\(17\))1918 5251
                1171 y(4)p eop
                1172 %%Page: 5 6
                1173 5 5 bop 324 548 a Fh(where)35 b Fe(F)670 563 y Fd(A)761
                1174 548 y Fh(is)f(a)f(\015ux)i(in)m(to)f(the)g(b)s(o)m(x)g(from)f(ab)s(o)m
                1175 (v)m(e)i(whic)m(h)g(dep)s(ends)g(on)f Fe(T)3057 563 y
                1176 Fd(A)3148 548 y Fh(and)g(other)324 680 y(atmospheric)h(v)-5
                1177 b(ariables)35 b Fe(\030)1326 695 y Fd(A)1418 680 y Fh(\(for)g(the)i
                1178 (most)e(relev)-5 b(an)m(t)36 b(example)f(of)g(a)h(lo)s(cal)e
                1179 (di\013usiv)m(e)324 813 y(\015ux,)g Fe(\030)587 828 y
                1180 Fd(A)677 813 y Fh(is)e(the)i(temp)s(erature)f(at)g(the)g(lev)m(el)g(ab)
                1181 s(o)m(v)m(e)h(the)g(lo)m(w)m(est)g(mo)s(del)d(lev)m(el\).)45
                1182 b(Ev)-5 b(al-)324 945 y(uate)33 b(all)d(v)-5 b(ariables)31
                1183 b(on)i(the)g(RHS)g(at)f Fe(t)c Fh(=)f Fe(i)c Fh(+)f(1,)32
                1184 b(and)h(pro)s(ceed)g(with)g(a)f(linear)f(T)-8 b(a)m(ylor)324
                1185 1078 y(expansion)33 b(as)g(ab)s(o)m(v)m(e.)44 b(The)33
                1186 b(\015ux)h Fe(F)1667 1093 y Fd(A)1757 1078 y Fh(is)e(no)m(w)h(appro)m
                1187 (ximated)f(b)m(y)918 1342 y Fe(F)981 1357 y Fd(A)1038
                1188 1342 y Fh(\()p Fe(T)1133 1357 y Fd(A)1191 1342 y Fe(;)17
                1189 b(\030)1278 1357 y Fd(A)1334 1342 y Fh(\))27 b(=)h Fe(F)1566
                1190 1357 y Fd(A)1623 1342 y Fh(\()p Fe(T)1732 1300 y Fd(i)1718
                1191 1366 y(A)1775 1342 y Fe(;)17 b(\030)1867 1300 y Fd(i)1862
                1192 1366 y(A)1919 1342 y Fh(\))22 b(+)2087 1274 y Fe(@)5
                1193 b(F)2206 1289 y Fd(A)p 2087 1319 178 4 v 2090 1410 a
                1194 Fe(@)g(T)2203 1425 y Fd(A)2274 1342 y Fh(\001)p Fe(T)2412
                1195 1357 y Fd(A)2491 1342 y Fh(+)2599 1274 y Fe(@)g(F)2718
                1196 1289 y Fd(A)p 2599 1319 V 2609 1410 a Fe(@)g(\030)2708
                1197 1425 y Fd(A)2786 1342 y Fh(\001)p Fe(\030)2910 1357 y
                1198 Fd(A)3388 1342 y Fh(\(18\))324 1606 y(W)-8 b(e)31 b(no)m(w)h(need)g(to)
                1199 f(assume)g(the)h(existence)g(of)f(a)g(precomputation)f(within)g(the)h
                1200 (atmo-)324 1739 y(spheric)i(mo)s(del)e(whic)m(h)i(relates)f(\001)p
                1201 Fe(\030)1657 1754 y Fd(A)1747 1739 y Fh(to)g(\001)p Fe(T)2004
                1202 1754 y Fd(A)2062 1739 y Fh(:)1525 1971 y(\001)p Fe(\030)1649
                1203 1986 y Fd(A)1734 1971 y Fh(=)27 b Fe(e)1882 1986 y Fd(A)1940
                1204 1971 y Fh(\001)p Fe(T)2078 1986 y Fd(A)2157 1971 y Fh(+)22
                1205 b Fe(f)2303 1986 y Fd(A)3388 1971 y Fh(\(19\))324 2203
                1206 y(with)32 b(the)h(result)1279 2447 y Fe(F)1342 2462 y
                1207 Fd(A)1400 2447 y Fh(\()p Fe(T)1495 2462 y Fd(A)1552 2447
                1208 y Fe(;)17 b(\030)1639 2462 y Fd(A)1695 2447 y Fh(\))28
                1209 b(=)f(\()p Fe(F)1965 2462 y Fd(A)2022 2447 y Fh(\))2060
                1210 2462 y Fc(0)2122 2447 y Fh(+)2230 2380 y Fe(dF)2344 2395
                1211 y Fd(A)p 2230 2424 171 4 v 2233 2516 a Fe(dT)2341 2531
                1212 y Fd(A)2411 2447 y Fh(\001)p Fe(T)2549 2462 y Fd(A)3388
                1213 2447 y Fh(\(20\))324 2708 y(where)1483 2885 y Fe(dF)1597
                1214 2900 y Fd(A)p 1483 2929 V 1486 3021 a Fe(dT)1594 3036
                1215 y Fd(A)1691 2952 y Fg(\021)1806 2885 y Fe(@)5 b(F)1925
                1216 2900 y Fd(A)p 1806 2929 178 4 v 1809 3021 a Fe(@)g(T)1922
                1217 3036 y Fd(A)2015 2952 y Fh(+)22 b Fe(e)2158 2967 y Fd(A)2226
                1218 2885 y Fe(@)5 b(F)2345 2900 y Fd(A)p 2226 2929 V 2236
                1219 3021 a Fe(@)g(\030)2335 3036 y Fd(A)3388 2952 y Fh(\(21\))1321
                1220 3384 y(\()p Fe(F)1422 3399 y Fd(A)1479 3384 y Fh(\))1517
                1221 3399 y Fc(0)1584 3384 y Fg(\021)28 b Fe(F)1752 3399 y
                1222 Fd(A)1809 3384 y Fh(\()p Fe(T)1918 3343 y Fd(i)1904 3409
                1223 y(A)1961 3384 y Fe(;)17 b(\030)2053 3343 y Fd(i)2048
                1224 3409 y(A)2105 3384 y Fh(\))22 b(+)g Fe(f)2311 3399 y
                1225 Fd(A)2378 3317 y Fe(@)5 b(F)2497 3332 y Fd(A)p 2378 3361
                1226 V 2388 3452 a Fe(@)g(\030)2487 3467 y Fd(A)3388 3384
                1227 y Fh(\(22\))470 3649 y(W)-8 b(e)33 b(can)f(no)m(w)g(solv)m(e)h(our)f
                1228 (coupled)g(atmosphere-land)f(system)i(exactly)f(as)h(b)s(efore)324
                1229 3781 y(b)m(y)g(mo)s(difying)d(the)j(de\014nion)g(of)f(\000:)1380
                1230 4045 y(\000)27 b Fg(\021)i Fh(\()1630 3978 y Fe(c)1672
                1231 3993 y Fd(A)p 1622 4022 117 4 v 1622 4114 a Fh(\001)p
                1232 Fe(t)1770 4045 y Fg(\000)1898 3978 y Fe(@)5 b(F)p 1880
                1233 4022 172 4 v 1880 4114 a(@)g(T)1993 4129 y Fd(A)2083
                1234 4045 y Fg(\000)2193 3978 y Fe(dF)2307 3993 y Fd(A)p 2193
                1235 4022 171 4 v 2196 4114 a Fe(dT)2304 4129 y Fd(A)2373
                1236 4045 y Fh(\))2411 4004 y Fb(\000)p Fc(1)3388 4045 y Fh(\(23\))324
                1237 4311 y(and)32 b(replacing)g Fe(F)994 4326 y Fc(0)1066
                1238 4311 y Fh(b)m(y)h Fe(F)1264 4326 y Fc(0)1326 4311 y Fh(+)22
                1239 b(\()p Fe(F)1525 4326 y Fd(A)1582 4311 y Fh(\))1620 4326
                1240 y Fc(0)470 4444 y Fh(F)-8 b(or)37 b(the)g(relev)-5 b(an)m(t)37
                1241 b(case)h(of)f(v)m(ertical)g(di\013usion,)g(the)h(atmospheric)e
                1242 (precomputa-)324 4576 y(tion)43 b(is)g(easily)h(accomplished.)77
                1243 b(The)45 b(tridiagonal)40 b(matrix)j(that)h(results)g(from)f(the)324
                1244 4708 y(implicit)25 b(di\013usion)k(op)s(erator)g(is)g(most)g(e\016cien)
                1245 m(tly)h(solv)m(ed)g(b)m(y)g(a)f(standard)h(t)m(w)m(o-sw)m(eep)324
                1246 4841 y(algorithm.)55 b(Starting)36 b(at)i(the)g(top)f(of)g(the)h
                1247 (atmosphere,)h(one)f(uses)h(the)f(matrix)e(ele-)324 4973
                1248 y(men)m(ts)28 b(to)f(recursiv)m(ely)i(generate)f(the)g(co)s(e\016cien)m
                1249 (ts)h Fe(e)2281 4988 y Fd(k)2351 4973 y Fh(and)f Fe(f)2584
                1250 4988 y Fd(k)2654 4973 y Fh(that)g(one)g(can)f(then)i(use)1918
                1251 5251 y(5)p eop
                1252 %%Page: 6 7
                1253 6 6 bop 324 548 a Fh(to)29 b(generate)h(the)h(temp)s(erature)e
                1254 (incremen)m(ts)h(in)f(an)h(up)s(ew)m(ard)h(recursiv)m(e)g(sw)m(eep)g
                1255 (of)f(an)324 680 y(equation)i(of)g(the)h(form)1502 888
                1256 y(\001)p Fe(T)1640 903 y Fd(k)r Fb(\000)p Fc(1)1800 888
                1257 y Fh(=)28 b Fe(e)1949 903 y Fd(k)1992 888 y Fh(\001)p
                1258 Fe(T)2130 903 y Fd(k)2195 888 y Fh(+)22 b Fe(f)2341 903
                1259 y Fd(k)3388 888 y Fh(\(24\))324 1096 y(where)35 b(the)g(index)g
                1260 Fe(k)i Fh(increases)e(do)m(wn)m(w)m(ards.)51 b(If)34
                1261 b(the)h(last)f(grid)f(b)s(o)m(x)i(is)e Fe(k)h Fh(=)d
                1262 Fe(N)10 b Fh(,)35 b(then)324 1229 y Fe(e)369 1244 y Fd(N)480
                1263 1229 y Fh(and)44 b Fe(f)729 1244 y Fd(N)839 1229 y Fh(pla)m(y)g(the)g
                1264 (role)f(of)g Fe(e)1609 1244 y Fd(A)1710 1229 y Fh(and)g
                1265 Fe(f)1958 1244 y Fd(A)2059 1229 y Fh(ab)s(o)m(v)m(e.)78
                1266 b(The)44 b(\015ux)h(exc)m(hange)g(mo)s(dule)324 1361
                1267 y(do)s(es)37 b(not)f(need)i(to)e(kno)m(w)i(the)f(details)e(of)i(this)f
                1268 (computation;)h(it)f(only)g(requires)h(the)324 1493 y(resulting)31
                1269 b(mo)s(di\014ed)h(\015ux)h(and)g(deriv)-5 b(ativ)m(e)32
                1270 b(de\014ned)i(b)m(y)f(\(21\))f(and)h(\(22\).)324 1841
                1271 y Ff(3)161 b(Leapfrog)324 2072 y Fh(W)-8 b(e)38 b(also)f(need)i(to)f
                1272 (allo)m(w)e(for)i(the)g(p)s(ossibilit)m(y)e(that)i(the)g(atmosphere)g
                1273 (is)g(in)m(tegrated)324 2204 y(with)30 b(a)h(leapfrog)e(step)j(and)e
                1274 (the)i(land)e(with)g(a)g(forw)m(ard)h(step)h({)e(a)h(common)e(com)m
                1275 (bina-)324 2337 y(tion)i(in)h(practice.)44 b(W)-8 b(e)33
                1276 b(then)g(ha)m(v)m(e,)h(lea)m(ving)d Fe(F)2080 2352 y
                1277 Fd(A)2170 2337 y Fh(out)h(for)g(simplicit)m(y)-8 b(,)1280
                1278 2593 y Fe(c)1322 2608 y Fd(A)1389 2525 y Fe(T)1460 2484
                1279 y Fd(i)p Fc(+1)1446 2552 y Fd(A)1601 2525 y Fg(\000)22
                1280 b Fe(T)1771 2484 y Fd(i)p Fb(\000)p Fc(1)1757 2552 y
                1281 Fd(A)p 1389 2570 500 4 v 1557 2661 a Fh(2\001)p Fe(t)1927
                1282 2593 y Fh(=)28 b Fe(F)14 b Fh(\()p Fe(T)2217 2551 y Fd(i)p
                1283 Fc(+1)2203 2620 y Fd(A)2334 2593 y Fe(;)j(T)2449 2551
                1284 y Fd(i)p Fc(+1)2435 2620 y Fd(L)2567 2593 y Fh(\))783
                1285 b(\(25\))1323 2973 y Fe(c)1365 2988 y Fd(L)1427 2905
                1286 y Fe(T)1498 2864 y Fd(i)p Fc(+1)1484 2932 y Fd(L)1638
                1287 2905 y Fg(\000)23 b Fe(T)1809 2869 y Fd(i)1795 2930 y(L)p
                1288 1427 2950 421 4 v 1579 3041 a Fh(\001)p Fe(t)1885 2973
                1289 y Fh(=)k Fe(F)14 b Fh(\()p Fe(T)2174 2931 y Fd(i)p Fc(+1)2160
                1290 3000 y Fd(A)2292 2973 y Fe(;)j(T)2407 2931 y Fd(i)p Fc(+1)2393
                1291 3000 y Fd(L)2525 2973 y Fh(\))825 b(\(26\))324 3194 y(Energy)33
                1292 b(will)e(still)f(b)s(e)j(conserv)m(ed)i(ev)m(ery)f(t)m(w)m(o)f(time)e
                1293 (steps)j(in)e(the)h(sense)i(that)934 3450 y Fe(c)976
                1294 3465 y Fd(A)1043 3382 y Fe(T)1114 3341 y Fd(i)p Fc(+2)1100
                1295 3409 y Fd(A)1254 3382 y Fh(+)22 b Fe(T)1423 3341 y Fd(i)p
                1296 Fc(+1)1409 3409 y Fd(A)p 1043 3427 499 4 v 1268 3518
                1297 a Fh(2)1573 3450 y(+)g Fe(c)1713 3465 y Fd(L)1765 3450
                1298 y Fe(T)1836 3408 y Fd(i)p Fc(+2)1822 3477 y Fd(L)1982
                1299 3450 y Fh(=)28 b Fe(c)2128 3465 y Fd(A)2195 3382 y Fe(T)2266
                1300 3346 y Fd(i)2252 3407 y(A)2331 3382 y Fh(+)22 b Fe(T)2500
                1301 3341 y Fd(i)p Fb(\000)p Fc(1)2486 3409 y Fd(A)p 2195
                1302 3427 424 4 v 2382 3518 a Fh(2)2650 3450 y(+)g Fe(c)2790
                1303 3465 y Fd(L)2842 3450 y Fe(T)2913 3408 y Fd(i)2899 3474
                1304 y(L)3388 3450 y Fh(\(27\))324 3687 y(W)-8 b(e)33 b(no)m(w)g(expand)h
                1305 Fe(F)46 b Fh(ab)s(out)32 b(the)h(temp)s(eratures)g Fe(T)2255
                1306 3646 y Fd(i)p Fb(\000)p Fc(1)2241 3714 y Fd(A)2406 3687
                1307 y Fh(and)f Fe(T)2666 3651 y Fd(i)2652 3712 y(L)840 3934
                1308 y Fe(F)14 b Fh(\()p Fe(T)1026 3893 y Fd(i)p Fc(+1)1012
                1309 3961 y Fd(A)1144 3934 y Fe(;)j(T)1259 3893 y Fd(i)p Fc(+1)1245
                1310 3961 y Fd(L)1376 3934 y Fh(\))28 b Fg(\031)g Fe(F)14
                1311 b Fh(\()p Fe(T)1733 3893 y Fd(i)p Fb(\000)p Fc(1)1719
                1312 3961 y Fd(A)1851 3934 y Fe(;)j(T)1966 3893 y Fd(i)1952
                1313 3959 y(L)2004 3934 y Fh(\))22 b(+)2191 3867 y Fe(@)5
                1314 b(F)p 2172 3911 172 4 v 2172 4003 a(@)g(T)2285 4018 y
                1315 Fd(A)2353 3934 y Fh(\001)p Fe(T)2491 3949 y Fd(A)2571
                1316 3934 y Fh(+)2695 3867 y Fe(@)g(F)p 2679 3911 167 4 v
                1317 2679 4003 a(@)g(T)2792 4018 y Fd(L)2855 3934 y Fh(\001)p
                1318 Fe(T)2993 3949 y Fd(L)3388 3934 y Fh(\(28\))324 4170
                1319 y(where)34 b(no)m(w)1529 4378 y(\001)p Fe(T)1667 4393
                1320 y Fd(A)1752 4378 y Fg(\021)28 b Fe(T)1928 4337 y Fd(i)p
                1321 Fc(+1)1914 4405 y Fd(A)2068 4378 y Fg(\000)23 b Fe(T)2239
                1322 4337 y Fd(i)p Fb(\000)p Fc(1)2225 4405 y Fd(A)3388 4378
                1323 y Fh(\(29\))1571 4662 y(\001)p Fe(T)1709 4677 y Fd(L)1789
                1324 4662 y Fg(\021)28 b Fe(T)1965 4621 y Fd(i)p Fc(+1)1951
                1325 4689 y Fd(L)2106 4662 y Fg(\000)22 b Fe(T)2276 4621 y
                1326 Fd(i)2262 4686 y(L)3388 4662 y Fh(\(30\))324 4870 y(The)j(rest)g(of)f
                1327 (the)h(deriv)-5 b(ation)22 b(pro)s(ceeds)k(exactly)e(as)h(b)s(efore.)41
                1328 b(W)-8 b(e)25 b(need)g(only)f(b)s(e)g(careful)324 5002
                1329 y(that)32 b(2\001)p Fe(t)h Fh(is)f(substituted)i(for)e(\001)p
                1330 Fe(t)h Fh(in)e(the)i(expression)h(for)e(\000.)1918 5251
                1331 y(6)p eop
                1332 %%Page: 7 8
                1333 7 7 bop 324 548 a Ff(4)161 b(Ev)-9 b(ap)t(oration)324
                1334 779 y Fh(No)m(w)32 b(consider)g(the)g(case)h(in)e(whic)m(h)h(w)m(e)h
                1335 (ha)m(v)m(e)g(ev)-5 b(ap)s(oration)30 b(as)i(w)m(ell)f(as)h(sensible)f
                1336 (heat)324 911 y(\015ux.)45 b(The)33 b(ev)-5 b(ap)s(oration)31
                1337 b Fe(E)6 b Fh(,)33 b(migh)m(t)f(b)s(e)g(a)h(function)f(of)g(a)h(v)-5
                1338 b(ariet)m(y)32 b(of)h(things,)f(but)h(the)324 1044 y(only)26
                1339 b(functional)e(dep)s(endence)29 b(w)m(e)f(are)e(concerned)i(with)e(is)g
                1340 (that)g(part)g(that)g(is)g(treated)324 1176 y(implicitly)-8
                1341 b(.)38 b(In)32 b(the)g(curren)m(t)g(implemen)m(tation)c(of)j(FMS)g
                1342 (\(Eugene\))i Fe(E)k Fh(as)31 b(an)g(implicit)324 1309
                1343 y(function)i(of)g Fe(q)862 1324 y Fd(A)919 1309 y Fh(,)h(the)f(sp)s
                1344 (eci\014c)i(h)m(umidit)m(y)d(in)h(the)g(atmosphere,)h(and)g
                1345 Fe(T)2984 1324 y Fd(L)3036 1309 y Fh(,)g(the)g(surface)324
                1346 1441 y(temp)s(erature.)1462 1806 y Fe(c)1504 1821 y Fd(A)1561
                1347 1806 y Fe(@)5 b(T)1674 1821 y Fd(A)1732 1806 y Fe(=@)g(t)28
                1348 b Fh(=)g Fe(F)14 b Fh(\()p Fe(T)2176 1821 y Fd(A)2233
                1349 1806 y Fe(;)j(T)2334 1821 y Fd(L)2386 1806 y Fh(\))964
                1350 b(\(31\))1524 2137 y Fe(@)5 b(q)1623 2152 y Fd(A)1682
                1351 2137 y Fe(=@)g(t)28 b Fh(=)g Fe(E)6 b Fh(\()p Fe(q)2113
                1352 2152 y Fd(A)2170 2137 y Fe(;)17 b(T)2271 2152 y Fd(L)2323
                1353 2137 y Fh(\))1027 b(\(32\))1130 2469 y Fe(c)1172 2484
                1354 y Fd(L)1224 2469 y Fe(@)5 b(T)1337 2484 y Fd(L)1391 2469
                1355 y Fe(=@)g(t)28 b Fh(=)g Fg(\000)p Fe(F)14 b Fh(\()p Fe(T)1912
                1356 2484 y Fd(A)1969 2469 y Fe(;)j(T)2070 2484 y Fd(L)2122
                1357 2469 y Fh(\))22 b Fg(\000)h Fe(LE)6 b Fh(\()p Fe(q)2507
                1358 2484 y Fd(A)2564 2469 y Fe(;)17 b(T)2665 2484 y Fd(L)2717
                1359 2469 y Fh(\))633 b(\(33\))470 2701 y(After)33 b(a)f(T)-8
                1360 b(a)m(ylor's)33 b(expansion)g(as)g(ab)s(o)m(v)m(e,)g(w)m(e)h(can)e
                1361 (solv)m(e)h(the)g(atmospheric)f(equa-)324 2833 y(tion)f(for)h(\001)p
                1362 Fe(T)811 2848 y Fd(A)901 2833 y Fh(as)h(a)f(function)g(of)h(\001)p
                1363 Fe(T)1734 2848 y Fd(L)1819 2833 y Fh(as)f(b)s(efore:)1522
                1364 3065 y(\001)p Fe(T)1660 3080 y Fd(A)1745 3065 y Fh(=)c
                1365 Fe(e)1894 3080 y Fd(T)1949 3065 y Fh(\001)p Fe(T)2087
                1366 3080 y Fd(L)2162 3065 y Fh(+)22 b Fe(f)2308 3080 y Fd(T)3388
                1367 3065 y Fh(\(34\))324 3298 y(where)34 b(a)e(subscript)h
                1368 Fe(T)47 b Fh(has)32 b(b)s(een)i(added)f(to)f Fe(e)h Fh(and)g
                1369 Fe(f)43 b Fh(W)-8 b(e)33 b(can)g(also)e(solv)m(e)i(for)1546
                1370 3530 y(\001)p Fe(q)1670 3545 y Fd(A)1755 3530 y Fh(=)28
                1371 b Fe(e)1904 3545 y Fd(q)1942 3530 y Fh(\001)p Fe(T)2080
                1372 3545 y Fd(L)2155 3530 y Fh(+)22 b Fe(f)2301 3545 y Fd(q)3388
                1373 3530 y Fh(\(35\))324 3762 y(The)34 b(equation)f(for)g
                1374 Fe(e)1119 3777 y Fd(q)1190 3762 y Fh(and)g Fe(f)1428
                1375 3777 y Fd(q)1500 3762 y Fh(is)g(the)g(same)g(as)h(that)f(for)g
                1376 Fe(e)g Fh(and)g Fe(f)11 b Fh(,)33 b(substituting)g(the)324
                1377 3894 y(ev)-5 b(ap)s(oration)36 b Fe(E)43 b Fh(for)37
                1378 b Fe(F)14 b Fh(.)58 b(If)37 b(the)h(atmosphere)g(uses)g(a)g(leapfrog)e
                1379 (time)g(step)i(w)m(e)g(m)m(ust)324 4026 y(once)44 b(again)e(remem)m(b)s
                1380 (er)h(to)h(use)g(2\001)p Fe(t)g Fh(as)g(the)g(time)e(step)j(in)e(these)
                1381 i(computations.)324 4159 y(Implciit)27 b(atmospheric)i(\015uxes)i(can)f
                1382 (b)s(e)g(treated)g(just)g(as)g(b)s(efore.)43 b(W)-8 b(e)30
                1383 b(can)g(also)e(de\014ne)1579 4423 y Fe(\013)1641 4438
                1384 y Fd(q)1707 4423 y Fg(\021)g Fe(E)1884 4438 y Fc(0)1945
                1385 4423 y Fh(+)2065 4355 y Fe(@)5 b(E)p 2053 4400 158 4
                1386 v 2053 4491 a(@)g(q)2152 4506 y Fd(A)2221 4423 y Fe(f)2269
                1387 4438 y Fd(q)3388 4423 y Fh(\(36\))1546 4855 y Fe(\014)1601
                1388 4870 y Fd(q)1667 4855 y Fg(\021)1798 4787 y Fe(@)g(E)p
                1389 1782 4832 167 4 v 1782 4923 a(@)g(T)1895 4938 y Fd(L)1981
                1390 4855 y Fh(+)2100 4787 y Fe(@)g(E)p 2089 4832 158 4 v
                1391 2089 4923 a(@)g(q)2188 4938 y Fd(A)2256 4855 y Fe(e)2301
                1392 4870 y Fd(q)3388 4855 y Fh(\(37\))1918 5251 y(7)p eop
                1393 %%Page: 8 9
                1394 8 8 bop 324 548 a Fh(The)34 b(job)g(of)f(the)h(surface)h(mo)s(del)d(is)
                1395 h(unc)m(hanged)i({)e(compute)h(the)g(c)m(hange)h(in)e(surface)324
                1396 680 y(temp)s(erature)f(giv)m(en)h(a)f(surface)i(energy)f(\015ux)h(of)e
                1397 (the)h(form:)1726 912 y Fe(\013)23 b Fh(+)f Fe(\014)6
                1398 b Fh(\001)p Fe(T)2108 927 y Fd(L)3388 912 y Fh(\(38\))324
                1399 1144 y(The)33 b(di\013erence)h(is)e(that)g(no)m(w)h(the)g(v)-5
                1400 b(alues)33 b(passed)h(to)e(the)h(surface)g(mo)s(del)e(are)1677
                1401 1377 y Fe(\013)d Fh(=)g Fe(\013)1933 1392 y Fd(T)2010
                1402 1377 y Fh(+)22 b Fe(\013)2170 1392 y Fd(q)3388 1377 y
                1403 Fh(\(39\))324 1609 y(and)1685 1841 y Fe(\014)33 b Fh(=)28
                1404 b Fe(\014)1932 1856 y Fd(T)2009 1841 y Fh(+)22 b Fe(\014)2162
                1405 1856 y Fd(q)3388 1841 y Fh(\(40\))324 2192 y Ff(5)161
                1406 b(Long)53 b(w)l(a)l(v)l(e)f(radiation)j(at)f(the)f(surface)324
                1407 2423 y Fh(In)29 b(a)f(climate)e(mo)s(del,)i(there)i(are)e(radiativ)m(e)
                1408 g(\015uxes)i(as)f(w)m(ell)f(as)g(\015uxes)j(of)d(sensible)g(and)324
                1409 2555 y(laten)m(t)g(heat)h(at)f(the)h(surface,)h(whic)m(h)g(m)m(ust)e(b)
                1410 s(e)h(accoun)m(ted)h(for)e(in)g(the)h(surface)h(energy)324
                1411 2688 y(balance.)51 b(T)m(ypically)-8 b(,)35 b(short)h(w)m(a)m(v)m(e)h
                1412 (\015uxes)g(are)e(treated)h(explicitly)-8 b(,)34 b(but)i(the)f(up)m(w)m
                1413 (ard)324 2820 y(longwsa)m(v)m(e)28 b(\015ux)f(is)g(treated)g
                1414 (implicitly)-8 b(,)24 b(as)j(it)f(can)h(b)s(e)g(the)g(dominan)m(t)f
                1415 (damping)f(agen)m(t)324 2952 y(of)36 b(surface)i(temp)s(erature)e(in)g
                1416 (some)h(regions.)55 b(The)38 b(only)e(c)m(hangse)i(in)e(the)h
                1417 (equations)324 3085 y(that)i(are)h(required)h(are)f(the)g(mo)s
                1418 (di\014cations)e(to)h Fe(\013)i Fh(and)f Fe(\014)45 b
                1419 Fh(resulting)39 b(from)f(the)j(\015ux)324 3217 y(and)32
                1420 b(its)g(deriv)-5 b(ativ)m(e)33 b(with)f(resp)s(ect)i(to)e(surface)h
                1421 (temp)s(erature.)470 3350 y(\(There)k(are)e(issues)h(here)g(wtih)f
                1422 (regard)g(to)g(the)h(fact)f(the)h(atmospheric)f(radiativ)m(e)324
                1423 3482 y(computation)h(in)h(FMS)h(is)g(explicit,)f(and)h(generates)h
                1424 (heating)e(rates)i(whic)m(h)f(are)g(not)324 3615 y(mo)s(di\014ed)31
                1425 b(when)i(the)g(surface)g(mo)s(dules)e(determine)h(\001)p
                1426 Fe(T)2447 3630 y Fd(L)2532 3615 y Fh(and)g(the)h(corresp)s(ondingly)324
                1427 3747 y(mo)s(di\014ed)27 b(up)m(w)m(ard)i(long)e(w)m(a)m(v)m(e)j
                1428 (\015ux.)43 b(In)28 b(e\013ect,)i(this)e(mo)s(di\014cation)d(to)j(the)h
                1429 (long)e(w)m(a)m(v)m(e)324 3879 y(\015ux)h(is)g(assumed)g(to)f(pass)i
                1430 (through)f(the)g(atmosphere)g(to)f(space)i(without)e(absorption.)324
                1431 4012 y(A)32 b(b)s(etter)h(assumption)f(migh)m(t)f(b)s(e)i(to)g(absorb)f
                1432 (this)h(mo)s(di\014cation)d(to)i(the)h(\015ux)g(in)f(the)324
                1433 4144 y(lo)m(w)m(est)h(atmospheric)f(la)m(y)m(er?\))324
                1434 4495 y Ff(6)161 b(The)53 b(exc)l(hange)f(grid)324 4726
                1435 y Fh(No)m(w)35 b(supp)s(ose)h(that)f(the)g(atmosphere)h(and)f(the)g
                1436 (land)f(or)h(ice)f(mo)s(dels)g(are)h(on)g(di\013er-)324
                1437 4859 y(en)m(t)h(grids.)50 b(W)-8 b(e)36 b(de\014ne)g(an)f(exc)m(hange)i
                1438 (grid)d(whose)j(b)s(oundaries)e(are)g(determined)g(b)m(y)324
                1439 4991 y(o)m(v)m(erla)m(ying)h(the)h(b)s(oundaries)g(of)f(the)h
                1440 (atmosphere)g(cells)g(with)f(those)h(of)g(the)g(surface)1918
                1441 5251 y(8)p eop
                1442 %%Page: 9 10
                1443 9 9 bop 324 548 a Fh(mo)s(dels.)84 b(\(See)48 b(do)s(cumen)m(tation)e
                1444 (of)g(exc)m(hange)i(grid)e(mo)s(dule)f(for)h(further)h(discus-)324
                1445 680 y(sion)34 b(of)h(this)f(exc)m(hange)j(grid.\))49
                1446 b(An)35 b(atmospheric)f(cell,)h(or)f(ice,)h(land,)g(or)g(o)s(cean)g
                1447 (cell,)324 813 y(con)m(tains)42 b(a)g(\014nite)g(set)h(of)f(exc)m
                1448 (hange)i(grid)e(cells.)72 b(As)43 b(long)e(as)h(the)h(\015ux)g(is)f
                1449 (de\014ned)324 945 y(unam)m(biguously)34 b(on)i(the)g(exc)m(hange)h
                1450 (grid,)e(and)h(if)e(the)i(\015ux)h(in)m(to)e(an)g(atmosphere)h(or)324
                1451 1078 y(land)c(surface)i(cell)f(is)f(just)i(the)g(area-w)m(eigh)m(ted)f
                1452 (mean)g(o)m(v)m(er)h(the)g(exc)m(hange)h(grid)d(cells)324
                1453 1210 y(that)g(it)g(con)m(tains,)g(then)i(the)f(\015uxed)h(quan)m(tit)m
                1454 (y)f(will)d(b)s(e)j(conserv)m(ed.)470 1342 y(Assume)h(\014rst)f(that)f
                1455 (the)h(\015uxes)h(are)f(computed)g(explicitly)1663 1507
                1456 y Fe(c)1705 1522 y Fd(A)p 1654 1552 117 4 v 1654 1643
                1457 a Fh(\001)p Fe(t)1781 1575 y Fh(\001)p Fe(T)1919 1590
                1458 y Fd(A)2004 1575 y Fh(=)p 2107 1494 77 4 v 27 w Fe(F)2184
                1459 1513 y Fd(A)3388 1575 y Fh(\(41\))1670 1893 y Fe(c)1712
                1460 1908 y Fd(L)p 1659 1938 117 4 v 1659 2029 a Fh(\001)p
                1461 Fe(t)1786 1961 y Fh(\001)p Fe(T)1924 1976 y Fd(L)2004
                1462 1961 y Fh(=)p 2107 1881 77 4 v 27 w Fe(F)2184 1899 y
                1463 Fd(L)3388 1961 y Fh(\(42\))324 2206 y(The)j(o)m(v)m(erlines)g(refer)f
                1464 (to)g(a)m(v)m(erages)i(o)m(v)m(er)g(the)e(exc)m(hange)j(cells)c(within)
                1465 g(either)i(the)f(at-)324 2339 y(mosphere)e(or)f(the)h(surface)h(cell)
                1466 470 2471 y(There)j(are)e(some)h(problematic)d(asp)s(ects)k(of)e(this)g
                1467 (in)m(terp)s(olation)e(sc)m(heme)k(\(whic)m(h)324 2603
                1468 y(are)c(una\013ected)i(b)m(y)g(implicit)29 b(corrections)34
                1469 b(to)f(these)i(\015uxes\).)48 b(Most)35 b(relev)-5 b(an)m(t)33
                1470 b(in)g(this)324 2736 y(con)m(text)g(is)f(that)g(the)g(staggering)f(of)h
                1471 (the)g(grid)g(and)g(the)g(resulting)f(a)m(v)m(eraging)h(results)324
                1472 2868 y(in)24 b(arti\014cial)d(horizon)m(tal)i(mixing.)39
                1473 b(A)25 b(disturbance)g(initally)d(lo)s(calized)g(at)i(one)h(grid)f
                1474 (cell)324 3001 y(on)37 b(the)g(surface)h(will)d(spread)j(to)f(other)g
                1475 (surface)h(cells)e(ev)m(en)j(though)e(the)g(exc)m(hanges)324
                1476 3133 y(in)32 b(the)h(unappro)m(ximated)f(mo)s(del)f(are)h(completely)g
                1477 (lo)s(cal.)470 3266 y(If)27 b(w)m(e)g(no)m(w)h(try)f(to)f(mak)m(e)h
                1478 (the)g(mo)s(del)e(fully)g(implicit)e(as)k(b)s(efore,)h(w)m(e)g(are)e
                1479 (in)g(trouble)324 3398 y(b)s(ecause)e(of)f(this)g(coupling.)39
                1480 b(The)24 b(\015ux)g(sensitivities)e(as)i(w)m(ell)e(as)i(the)f(\015uxes)
                1481 i(themselv)m(es)324 3530 y(m)m(ust)32 b(b)s(e)h(de\014ned)h(on)f(the)g
                1482 (exc)m(hange)h(grid,)e(and)g(the)h(equations)g(w)m(ould)g(b)s(e)1091
                1483 3766 y Fe(c)1133 3781 y Fd(A)p 1083 3810 117 4 v 1083
                1484 3902 a Fh(\001)p Fe(t)1209 3833 y Fh(\001)p Fe(T)1347
                1485 3848 y Fd(A)1432 3833 y Fh(=)p 1536 3753 103 4 v 28 w
                1486 Fe(F)1599 3848 y Fc(0)1638 3772 y Fd(A)1717 3833 y Fh(+)p
                1487 1815 3685 192 4 v 1844 3766 a Fe(@)5 b(F)p 1825 3810
                1488 172 4 v 1825 3902 a(@)g(T)1938 3917 y Fd(A)2006 3703
                1489 y(A)2063 3833 y Fh(\001)p Fe(T)2201 3848 y Fd(A)2281
                1490 3833 y Fh(+)p 2379 3685 377 4 v 2405 3766 a Fe(@)g(F)p
                1491 2389 3810 167 4 v 2389 3902 a(@)g(T)2502 3917 y Fd(L)2565
                1492 3833 y Fh(\001)p Fe(T)2703 3848 y Fd(L)2756 3703 y(A)3388
                1493 3833 y Fh(\(43\))324 4094 y(and)1103 4310 y Fe(c)1145
                1494 4325 y Fd(L)p 1092 4354 117 4 v 1092 4446 a Fh(\001)p
                1495 Fe(t)1219 4377 y Fh(\001)p Fe(T)1357 4392 y Fd(L)1437
                1496 4377 y Fh(=)p 1541 4297 103 4 v 28 w Fe(F)1604 4392 y
                1497 Fc(0)1643 4315 y Fd(L)1717 4377 y Fh(+)p 1815 4229 387
                1498 4 v 1844 4310 a Fe(@)g(F)p 1825 4354 172 4 v 1825 4446
                1499 a(@)g(T)1938 4461 y Fd(A)2006 4377 y Fh(\001)p Fe(T)2144
                1500 4392 y Fd(A)2202 4247 y(L)2276 4377 y Fh(+)p 2374 4229
                1501 187 4 v 2401 4310 a Fe(@)g(F)p 2384 4354 167 4 v 2384
                1502 4446 a(@)g(T)2497 4461 y Fd(L)2560 4247 y(L)2613 4377
                1503 y Fh(\001)p Fe(T)2751 4392 y Fd(L)3388 4377 y Fh(\(44\))324
                1504 4638 y(In)31 b(general,)g(all)e(grid)h(p)s(oin)m(ts)g(in)g(the)i
                1505 (atmosphere)f(are)g(no)m(w)g(coupled)h(with)e(all)f(p)s(oin)m(ts)324
                1506 4770 y(in)c(the)i(surface)g(mo)s(del\(s\).)40 b(Solution)25
                1507 b(w)m(ould)h(require)h(iteration,)e(whic)m(h)i(is)f(a)g(source)h(of)324
                1508 4902 y(complexit)m(y)k(that)h(is)g(totally)e(inappropriate)g(giv)m(en)j
                1509 (that)f(the)g(underlying)g(dynamics)1918 5251 y(9)p eop
                1510 %%Page: 10 11
                1511 10 10 bop 324 548 a Fh(is)23 b(purely)i(lo)s(cal.)38
                1512 b(As)25 b(w)m(e)g(ha)m(v)m(e)g(seen,)i(explicit)c(\015ux)i(computation)
                1513 d(also)h(generates)i(arti-)324 680 y(\014cial)f(non-lo)s(cal)e
                1514 (coupling)i(as)i(a)f(function)f(of)h(time)f({)h(the)h(fully)e(implicit)
                1515 d(computation)324 813 y(spreads)34 b(the)f(in\015uence)g(widely)f
                1516 (within)g(one)h(time)e(step.)470 945 y(One)g(straighforw)m(ard)e
                1517 (alternativ)m(e)h(is)g(to)f(do)i(ev)m(erything)g(related)f(to)g(the)g
                1518 (implicit)324 1078 y(time-stepping)43 b(on)j(the)f(exc)m(hange)i(grid,)
                1519 h(pro)s(ducing)c(temp)s(erature)h(and)h(moisture)324
                1520 1210 y(incremen)m(ts)30 b(de\014ned)i(on)e(the)h(exc)m(hange)h(grid,)d
                1521 (and,)i(as)g(a)e(last)h(step,)h(a)m(v)m(eraging)f(these)324
                1522 1342 y(on)m(to)47 b(the)g(grids)f(of)h(the)g(resp)s(ectiv)m(e)i(mo)s
                1523 (dels.)85 b(One)47 b(di\016cult)m(y)g(with)g(this)f(sc)m(heme)324
                1524 1475 y(is)36 b(that)h(in)f(actual)f(mo)s(dels)h(the)h(pro)s(cesses)i
                1525 (in)m(v)m(olv)m(ed)e(in)f(the)h(implicit)c(computation)324
                1526 1607 y(of)48 b(surface)h(temp)s(eratures)f(and)g(\015uxes)i(can)f(b)s
                1527 (e)f(rather)g(complicated,)j(and)d(these)324 1740 y(parts)d(of)g(the)g
                1528 (mo)s(dels)f(w)m(ould)h(ha)m(v)m(e)h(to)f(compute)g(on)g(the)g(exc)m
                1529 (hange)i(grid,)g(whose)324 1872 y(dimensions)39 b(can)h(get)g(quite)g
                1530 (large.)65 b(It)40 b(turns)h(out)f(that)g(one)g(can)g(a)m(v)m(oid)g
                1531 (doing)f(the)324 2005 y(atmospheric)d(di\013usion)f(computation)g(on)i
                1532 (the)g(exc)m(hange)h(grid,)f(but)f(one)h(still)d(ends)324
                1533 2137 y(up)40 b(with)g(the)g(surface)h(comp)s(onen)m(t)g(mo)s(dels)d
                1534 (split)h(in)m(to)h(a)f(part)h(computing)f(on)h(the)324
                1535 2269 y(exc)m(hange)47 b(grid)c(and)j(a)e(part)h(on)g(the)g(mo)s(del's)f
                1536 (o)m(wn)i(grid,)h(in)d(a)h(w)m(a)m(y)h(that)f(causes)324
                1537 2402 y(considerable)34 b(confusion.)48 b(\(An)34 b(earlier)f(v)m
                1538 (ersion)h(of)g(our)g(mo)s(del)e(w)m(as)k(constructed)f(in)324
                1539 2534 y(this)30 b(w)m(a)m(y)h(and)g(rejected)h(for)d(these)j(reasons.\))
                1540 44 b(It)30 b(is)g(preferable)h(that)f(the)h(comp)s(onen)m(t)324
                1541 2667 y(mo)s(dels)g(kno)m(w)j(nothing)e(ab)s(out)g(the)h(exc)m(hange)h
                1542 (grid.)470 2799 y(While)f(it)g(is)h(not)g(clear)f(that)h(it)f(is)h(the)
                1543 g(ideal)f(solution,)g(the)h(follo)m(wing)e(sc)m(heme)j(is)324
                1544 2932 y(the)f(one)h(curren)m(tly)g(implemen)m(ted)e(in)g(FMS)i
                1545 (\(Eugene\).)50 b(It)34 b(treats)h(the)f(atmospheric)324
                1546 3064 y(side)40 b(of)f(the)h(mo)s(del)e(di\013eren)m(tly)i(from)e(the)j
                1547 (surface)f(compnen)m(t)h(mo)s(dels)d(\(whic)m(h)j(w)m(e)324
                1548 3196 y(refer)33 b(to)f(as)h("land")e(here\).)470 3329
                1549 y(Fluxes)g(and)g(deriv)-5 b(ativ)m(es)31 b(of)f(\015uxes)i(are)f
                1550 (computed)g(on)f(the)h(exc)m(hange)i(grid.)42 b(The)324
                1551 3461 y(\015ux)33 b(is)f(de\014ned)i(on)f(the)g(exc)m(hange)h(grid)e(to)
                1552 g(b)s(e)1390 3704 y Fe(F)1453 3719 y Fc(0)1514 3704 y
                1553 Fh(+)1641 3636 y Fe(@)5 b(F)p 1622 3681 172 4 v 1622
                1554 3772 a(@)g(T)1735 3787 y Fd(A)1803 3704 y Fh(\001)p Fe(T)1955
                1555 3663 y Fb(\003)1941 3728 y Fd(A)2021 3704 y Fh(+)2145
                1556 3636 y Fe(@)g(F)p 2129 3681 167 4 v 2129 3772 a(@)g(T)2242
                1557 3787 y Fd(L)2305 3704 y Fh(\001)p Fe(T)2443 3719 y Fd(L)3388
                1558 3704 y Fh(\(45\))324 3943 y(where)27 b(\001)p Fe(T)751
                1559 3907 y Fb(\003)737 3968 y Fd(A)794 3943 y Fh(,)g(computed)f(as)g
                1560 (describ)s(ed)h(b)s(elo)m(w,)g(v)-5 b(aries)25 b(across)h(exc)m(hange)i
                1561 (cells)d(within)324 4075 y(one)33 b(atmospheric)f(cell,)f(while)h(\001)
                1562 p Fe(T)1644 4090 y Fd(L)1729 4075 y Fh(is)g(uniform)f(across)i(the)g
                1563 (en)m(tire)g(land)f(cell.)470 4208 y(Start)41 b(as)h(if)f(one)h(w)m
                1564 (ere)h(computing)d(the)i(implicit)c(temp)s(erature)k(tendencies)h(on)
                1565 324 4340 y(the)29 b(exc)m(hange)h(grid)d(and)i(compute)f(explicit)f
                1566 (\015uxes)j(and)f(\015ux)g(deriv)-5 b(ativ)m(es)28 b(on)g(the)h(ex-)324
                1567 4472 y(c)m(hange)24 b(grid.)39 b(Con)m(tin)m(ue)25 b(b)m(y)f(computing)
                1568 e Fe(e)i Fh(and)f Fe(f)34 b Fh(\(9\))23 b(and)h(then)g
                1569 Fe(\013)g Fh(and)f Fe(\014)29 b Fh(\(15\))23 b(on)g(the)324
                1570 4605 y(exc)m(hange)35 b(grid.)46 b Fa(A)n(ver)-5 b(age)35
                1571 b Fe(\013)h Fa(and)g Fe(\014)41 b Fa(over)35 b(the)h(surfac)-5
                1572 b(e)36 b(mo)-5 b(del)35 b(grid.)46 b Fh(Then)35 b(instruct)324
                1573 4737 y(the)40 b(surface)g(mo)s(del)f(to)g(use)i(these)f(a)m(v)m(eraged)
                1574 h(\015uxes)h(and)d(deriv)-5 b(ativ)m(es)40 b(to)g(compute)324
                1575 4870 y(its)i(new)h(surface)g(temp)s(erature)g(implicitly)-8
                1576 b(.)68 b(Cop)m(y)44 b(this)e(surface)h(temp)s(erature)g(in-)324
                1577 5002 y(cremen)m(t)c(to)e(the)i(exc)m(hange)h(grid)d(and)h(then)h
                1578 (compute)f(the)h(atmospheric)f(tendency)1894 5251 y(10)p
                1579 eop
                1580 %%Page: 11 12
                1581 11 11 bop 324 548 a Fh(in)40 b(the)h(lo)m(w)m(est)h(mo)s(del)d(lev)m
                1582 (el)i(on)g(the)g(exc)m(hange)i(grid.)68 b(Av)m(erage)42
                1583 b(this)e(atmospheric)324 680 y(tendency)h(o)m(v)m(er)f(the)f
                1584 (atmospheric)g(grid)f(as)h(the)h(\014nal)e(step.)64 b(The)40
                1585 b(only)e(distinction)324 813 y(b)s(et)m(w)m(een)h(this)e(sc)m(heme)h
                1586 (and)f(that)g(in)f(\(43\))h(is)g(that)f(the)i(\015uxes)h(are)e
                1587 (consisten)m(t)h(with)324 945 y(the)e(atnmospheric)f(incremen)m(ts)h
                1588 (on)g(the)g(exc)m(hange)h(grid)e(\(\001)p Fe(T)2718 909
                1589 y Fb(\003)2704 970 y Fd(A)2761 945 y Fh(\))h(b)s(efore)g(a)m(v)m
                1590 (eraging,)324 1078 y(rather)c(than)h(with)f(the)h(\014nal)f(a)m(v)m
                1591 (eraged)i(incremen)m(ts.)324 1429 y Ff(7)161 b(Algorithm)324
                1592 1660 y Fh(Summarizing)30 b(the)j(\014nal)e(algorithm:)324
                1593 1887 y Fg(\017)40 b Fh(W)-8 b(e)40 b(start)h(with)e(the)i(state)g(of)e
                1594 (all)g(comp)s(onen)m(t)h(mo)s(dels)f(de\014ned)i(at)f(time)f(step)i
                1595 Fe(i)p Fh(,)324 2019 y(or)33 b Fe(i)23 b Fg(\000)h Fh(1)33
                1596 b(in)g(the)i(case)f(of)g(leapfrog)e(mo)s(dels.)46 b(The)35
                1597 b(\014rst)f(step)h(is)e(to)g(mo)m(v)m(e)i(ev)m(erything)324
                1598 2152 y(that)26 b(is)h(needed)h(to)f(compute)g(the)g(surface)h(sensible)
                1599 f(heat)g(\015ux,)h Fe(H)8 b Fh(,)28 b(and)f(ev)-5 b(ap)s(oration,)324
                1600 2284 y Fe(E)6 b Fh(,)42 b(the)f(deriv)-5 b(ativ)m(es)40
                1601 b(of)g Fe(H)48 b Fh(with)40 b(resp)s(ect)h(to)f Fe(T)2143
                1602 2299 y Fd(A)2241 2284 y Fh(and)g Fe(T)2495 2299 y Fd(L)2547
                1603 2284 y Fh(,)j(and)d(the)h(deriv)-5 b(ativ)m(es)40 b(of)324
                1604 2416 y Fe(E)49 b Fh(with)43 b(resp)s(ect)i(to)e Fe(q)1196
                1605 2431 y Fd(A)1297 2416 y Fh(and)h Fe(T)1555 2431 y Fd(L)1607
                1606 2416 y Fh(,)i(and)e(the)g(deriv)-5 b(ativ)m(e)43 b(of)g(the)h(up)m(w)m
                1607 (ard)h(longw)m(a)m(v)m(e)324 2549 y(\015ux)g(at)g(the)g(surface)g(with)
                1608 g(resp)s(ect)h(to)e Fe(T)1949 2564 y Fd(L)2001 2549 y
                1609 Fh(,)k(on)m(to)d(the)g(exc)m(hange)h(grid.)79 b(W)-8
                1610 b(e)45 b(then)324 2681 y(compute)31 b(the)g(explicit)f(estimate)g(of)g
                1611 (these)j(\015uxes)f(on)f(the)g(exc)m(hange)i(grid)d(and)h(all)e(of)324
                1612 2814 y(the)38 b(relev)-5 b(an)m(t)37 b(deriv)-5 b(ativ)m(es.)59
                1613 b(One)38 b(m)m(ust)g(k)m(eep)h(in)e(mind)f(that)i(these)h(\015ux)f(v)-5
                1614 b(alues)38 b(are)324 2946 y(temp)s(orary)-8 b(,)42 b(and)g(will)d(b)s
                1615 (e)i(corrected)i(b)m(y)f(the)f(implicit)d(part)j(of)f(the)i
                1616 (computation,)324 3078 y(using)47 b(these)j(deriv)-5
                1617 b(ativ)m(es.)90 b(This)48 b(w)m(ork)h(is)e(mostly)g(p)s(erformed)h(b)m
                1618 (y)h(a)e(call)g(to)g(the)324 3211 y(subroutine)39 b Fa(\015ux)p
                1619 973 3211 30 4 v 36 w(c)-5 b(alculation)p Fh(,)40 b(whic)m(h)g
                1620 (e\013ectiv)m(ely)f(computes)h(ev)m(erything)g(that)e(can)324
                1621 3343 y(b)s(e)33 b(computed)f(b)s(efore)h(the)g(start)g(of)f(the)h
                1622 (atmospheric)f(time)f(step.)324 3570 y Fg(\017)40 b Fh(Assume)h(that)f
                1623 (the)g(atmospheric)g(mo)s(del)e(has)j(computed)f(the)h(incremen)m(t)f
                1624 (in)f(the)324 3703 y(atmospheric)33 b(temp)s(erature)i(and)f(sp)s
                1625 (eci\014c)h(h)m(umidit)m(y)e(due)i(to)f(all)e(terms)j(treated)f(ex-)324
                1626 3835 y(plicitly)k(\(more)i(precisely)-8 b(,)43 b(all)c(explicit)h
                1627 (terms)g(that)h(are)g(included)f(b)s(efore)h(the)h(im-)324
                1628 3967 y(plicit)26 b(v)m(ertical)h(di\013usion)g(is)g(applied.\))41
                1629 b(F)-8 b(rom)27 b(the)h(m)m(y)m(opic)g(viewp)s(oin)m(t)g(of)f(the)i
                1630 (surface)324 4100 y(exc)m(hange)36 b(mo)s(dule,)e(the)i(only)e(quan)m
                1631 (tities)h(of)f(in)m(terest)h(are)g(the)g(incremen)m(ts)g(in)g(tem-)324
                1632 4232 y(p)s(erature)c(and)g(sp)s(eci\014c)g(h)m(umidit)m(y)f(in)g(the)i
                1633 (lo)m(w)m(est)f(atmospheric)f(la)m(y)m(er.)43 b(If)31
                1634 b(the)g(mo)s(del)324 4365 y(includes)i(v)m(ertical)f(di\013usion,)g
                1635 (these)i(incremen)m(ts)f(include)f(the)i(e\013ect)f(of)g(the)g
                1636 (explicit)324 4497 y(di\013usiv)m(e)41 b(\015ux)g(across)g(the)h(top)e
                1637 (of)g(the)h(lo)m(w)m(est)h(atmospheric)e(la)m(y)m(er)h(If)f(the)h(v)m
                1638 (ertical)324 4630 y(di\013usion)34 b(is)i(implicit,)c(then)37
                1639 b(this)e(incremen)m(t)h(m)m(ust)g(b)s(e)g(computed)g(with)f(the)h(mo)s
                1640 (di-)324 4762 y(\014ed)31 b(\015ux)h(\(22\))e(and)h(one)g(m)m(ust)g
                1641 (also)f(pro)m(vide)h(the)g("total")e(deriv)-5 b(ativ)m(e)30
                1642 b(\(21\),)h(for)f(b)s(oth)324 4894 y(temp)s(erature)35
                1643 b(and)h(moisture.)52 b(If)36 b(there)g(is)f(no)h(implicit)31
                1644 b(\015ux)37 b(across)f(the)g(top)g(of)f(the)1894 5251
                1645 y(11)p eop
                1646 %%Page: 12 13
                1647 12 12 bop 324 548 a Fh(lo)m(w)m(est)33 b(atmospheric)f(la)m(y)m(er,)h
                1648 (then)g(these)h(deriv)-5 b(ativ)m(es)32 b(m)m(ust)h(b)s(e)g(set)g(to)f
                1649 (zero.)324 775 y Fg(\017)38 b Fh(The)i(surface)f(exc)m(hange)i(mo)s
                1650 (dule)c(assumes)i(that)g(the)g(resulting)e(incremen)m(ts)i(and)324
                1651 907 y(deriv)-5 b(ativ)m(es)26 b(are)g(pac)m(k)-5 b(aged)26
                1652 b(in)g(a)f(particular)f(w)m(a)m(y)k(within)c(an)i(atmosp)s(ehric)f(b)s
                1653 (oundary)324 1040 y(data)35 b(t)m(yp)s(e)h(de\014ned)h(and)f(allo)s
                1654 (cated)d(within)h(the)i(atmospheric)f(mo)s(del.)51 b(In)35
                1655 b(addition)324 1172 y(to)g(a)g(v)-5 b(ariet)m(y)36 b(of)f(other)h
                1656 (\014eld)f(included)g(in)g(this)g(t)m(yp)s(e)i(that)e(are)h(not)f(in)m
                1657 (v)m(olv)m(ed)h(in)f(the)324 1305 y(implicit)e(computation)j(\(suc)m(h)
                1658 i(as)g(precipitation)d(or)h(the)i(net)g(short)m(w)m(a)m(v)m(e)h
                1659 (\015ux\),)g(\014v)m(e)324 1437 y(spatial)f(\014elds)i(of)f
                1660 (information)e(are)j(passed)h(for)e(this)h(implicit)c(algorithm:)55
                1661 b(b)s(esides)324 1569 y(the)32 b(t)m(w)m(o)h(incremen)m(ts)f(and)g(the)
                1662 g(t)m(w)m(o)h(deriv)-5 b(ativ)m(es,)32 b(the)g(atmospheric)f(time)g
                1663 (step)h(\(2\001)p Fe(t)324 1702 y Fh(for)46 b(leapfrog\))g(divided)h(b)
                1664 m(y)h(the)g(mass)f(of)g(the)g(lo)m(w)m(est)h(atmospheric)e(la)m(y)m(er)
                1665 i(is)f(also)324 1834 y(required.\))324 2061 y Fg(\017)29
                1666 b Fh(Next,)j(compute)e Fe(\013)1122 2076 y Fd(T)1177
                1667 2061 y Fh(,)g Fe(\013)1296 2076 y Fd(q)1335 2061 y Fh(,)g
                1668 Fe(\014)1447 2076 y Fd(T)1502 2061 y Fh(,)h Fe(\014)1615
                1669 2076 y Fd(q)1683 2061 y Fh(on)f(the)g(exc)m(hange)i(grid)c(and)j(a)m(v)
                1670 m(erage)f(these)i(on)m(to)324 2194 y(the)22 b(land)f(and)h(ice)f
                1671 (grids.)40 b(This)21 b(is)h(p)s(erformed)f(b)m(y)i(subroutine)f
                1672 Fa(\015ux)p 2786 2194 30 4 v 36 w(down)p 3042 2194 V
                1673 35 w(fr)-5 b(om)p 3273 2194 V 35 w(atmos)324 2420 y Fg(\017)36
                1674 b Fh(Assume)i(that)f(the)g(land)f(and)h(ice)g(mo)s(dels)f(are)h(no)m(w)
                1675 g(instructed)h(to)e(compute)h(the)324 2553 y(new)c(surface)h(temp)s
                1676 (eratures.)324 2780 y Fg(\017)45 b Fh(Mo)m(v)m(e)j(the)e(incremen)m(ts)
                1677 g(in)f(surface)i(temp)s(erature)f(to)f(the)i(exc)m(hange)g(grid,)h(and)
                1678 324 2912 y(compute)42 b(the)g(incremen)m(t)g(in)f(the)h(temp)s(erature)
                1679 g(and)g(moisture)e(of)i(the)g(lo)m(w)m(est)g(at-)324
                1680 3045 y(mospheric)i(la)m(y)m(er.)82 b(Also)44 b(correct)i(the)f(surface)
                1681 h(sensible)f(heat,)k(ev)-5 b(ap)s(oration,)46 b(and)324
                1682 3177 y(longw)m(a)m(v)m(e)33 b(radiation.)324 3404 y Fg(\017)j
                1683 Fh(Av)m(erage)h(the)f(incremen)m(ts)g(of)g(temp)s(erature)g(and)g
                1684 (moisture)f(in)g(the)i(lo)m(w)m(est)f(atmo-)324 3536
                1685 y(sp)s(ehric)d(la)m(y)m(er)f(on)m(to)h(the)g(atmospheric)f(grid.)324
                1686 3763 y Fg(\017)40 b Fh(Assume)h(that)f(the)g(atmospheric)g(mo)s(del)e
                1687 (can)j(no)m(w)f(tak)m(e)h(these)h(lo)m(w)m(est)f(la)m(y)m(er)f(in-)324
                1688 3896 y(cremen)m(ts)48 b(and)f(\014nalize)f(the)i(up)m(w)m(ard)g(sw)m
                1689 (eep)h(of)e(the)g(tridiagonal)d(elimination)f(to)324
                1690 4028 y(complete)32 b(the)h(implicit)28 b(computation)j(of)h(v)m
                1691 (ertical)g(di\013usion.)1894 5251 y(12)p eop
                1692 %%Trailer
                1693 end
                1694 userdict /end-hook known{end-hook}if
                1695 %%EOF
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