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flux_exchange.tech.ps
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flux_exchange.tech.ps
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(that)f(the)h(at-)324 2845 y(mospheric)32 b(and)h(land)e(grids)h(are)h
(iden)m(tical)e(for)h(the)h(time)e(b)s(eing.)1462 3033
y Fe(c)1504 3048 y Fd(A)1561 3033 y Fe(@)5 b(T)1674 3048
y Fd(A)1732 3033 y Fe(=@)g(t)28 b Fh(=)g Fe(F)14 b Fh(\()p
Fe(T)2176 3048 y Fd(A)2233 3033 y Fe(;)j(T)2334 3048
y Fd(L)2386 3033 y Fh(\))1013 b(\(1\))1428 3277 y Fe(c)1470
3292 y Fd(L)1522 3277 y Fe(@)5 b(T)1635 3292 y Fd(L)1688
3277 y Fe(=@)g(t)29 b Fh(=)e Fg(\000)p Fe(F)14 b Fh(\()p
Fe(T)2209 3292 y Fd(A)2267 3277 y Fe(;)j(T)2368 3292
y Fd(L)2420 3277 y Fh(\))979 b(\(2\))324 3466 y(The)43
b(atmosphere)g(and)g(the)g(land)f(exc)m(hange)i(the)f(heat)g(\015ux)g
Fe(F)14 b Fh(.)74 b(As)43 b(the)g(simplest)324 3598 y(case,)38
b(set)g Fe(F)14 b Fh(\()p Fe(T)891 3613 y Fd(A)948 3598
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Fg(\000)p Fe(\015)5 b Fh(\()p Fe(T)1512 3613 y Fd(A)1594
3598 y Fg(\000)26 b Fe(T)1754 3613 y Fd(L)1806 3598 y
Fh(\).)55 b(In)37 b(the)g(uncoupled)h(case)f(\()p Fe(T)3000
3613 y Fd(L)3087 3598 y Fh(=constan)m(t\))324 3730 y(the)c(simplest)e
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3981 y Fd(A)1552 3899 y Fh(\()p Fe(T)1661 3858 y Fd(i)p
Fc(+1)1647 3926 y Fd(A)1801 3899 y Fg(\000)23 b Fe(T)1972
3863 y Fd(i)1958 3924 y(A)2015 3899 y Fh(\))p 1552 3943
501 4 v 1744 4035 a(\001)p Fe(t)2091 3966 y Fh(=)k Fg(\000)p
Fe(\015)5 b(T)2398 3925 y Fd(i)2384 3991 y(A)3437 3966
y Fh(\(3\))324 4168 y(whic)m(h)41 b(blo)m(ws)h(up)f(if)f
Fe(\030)1179 4183 y Fd(A)1278 4168 y Fe(>)i Fh(2)f(and)g(pro)s(duces)h
(oscillatory)d(rather)i(than)g(monotonic)324 4300 y(deca)m(y)32
b(for)f(1)c Fe(<)h(\030)964 4315 y Fd(A)1048 4300 y Fe(<)g
Fh(2,)j(where)h Fe(\030)1582 4315 y Fd(A)1666 4300 y
Fg(\021)d Fe(\015)5 b Fh(\001)p Fe(t=c)2035 4315 y Fd(A)2092
4300 y Fh(.)43 b(This)31 b(is)g(unacceptable.)44 b(A)31
b(cen)m(tered)324 4433 y(step,)c(with)e(0)p Fe(:)p Fh(5)p
Fe(\015)5 b Fh(\()p Fe(T)1056 4392 y Fd(i)p Fc(+1)1042
4460 y Fd(A)1180 4433 y Fh(+)i Fe(T)1334 4397 y Fd(i)1320
4458 y(A)1377 4433 y Fh(\))25 b(on)g(the)h(RHS,)f(is)f(stable)h(in)g
(the)g(sense)i(that)e(all)e(solutions)324 4565 y(are)41
b(damp)s(ed,)i(but)f(when)g Fe(\030)1398 4580 y Fd(A)1497
4565 y Fe(>)h Fh(2)e(it)f(pro)s(duces)i(oscillatory)d(deca)m(y)-8
b(,)45 b(whic)m(h)d(is)f(still)324 4698 y(unacceptable.)j(The)34
b(standard)f(pro)s(cedure)g(is)f(to)g(use)i(a)e(bac)m(kw)m(ard)i(time)e
(step)1406 4934 y Fe(c)1448 4949 y Fd(A)1515 4866 y Fh(\()p
Fe(T)1624 4825 y Fd(i)p Fc(+1)1610 4893 y Fd(A)1764 4866
y Fg(\000)23 b Fe(T)1935 4830 y Fd(i)1921 4892 y(A)1978
4866 y Fh(\))p 1515 4911 V 1707 5002 a(\001)p Fe(t)2053
4934 y Fh(=)28 b Fg(\000)p Fe(\015)5 b(T)2361 4893 y
Fd(i)p Fc(+1)2347 4961 y Fd(A)3437 4934 y Fh(\(4\))1918
5251 y(1)p eop
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2 2 bop 324 548 a Fh(whic)m(h)27 b(is)f(stable)h(and)g(deca)m(ys)h
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(atmo-)324 680 y(spheric)39 b(mo)s(dels,)g(the)g(surface)g(\015uxes)i
(are)d(computed)h(with)f(a)g("sup)s(er)i(bac)m(kw)m(ards")324
813 y(sc)m(heme,)34 b(in)e(whic)m(h,)h(on)f(the)h(RHS,)g
Fe(T)1724 828 y Fd(A)1809 813 y Fg(!)27 b Fe(\013)q(T)2070
772 y Fd(i)p Fc(+1)2056 840 y Fd(A)2210 813 y Fh(+)22
b(\(1)g Fg(\000)g Fe(\013)q Fh(\))p Fe(T)2688 777 y Fd(i)2674
838 y(A)2731 813 y Fh(,)33 b(with)f Fe(\013)c(>)g Fh(1\))470
945 y(The)50 b(same)f(argumen)m(t)g(holds)g(for)g(the)g(coupled)g
(system,)55 b(\(1\))49 b(and)g(\(2\).)93 b(The)324 1078
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(either)g(large)g Fe(\030)2904 1093 y Fd(A)3007 1078
y Fh(or)g Fe(\030)3183 1093 y Fd(L)3235 1078 y Fh(,)k(where)324
1210 y Fe(\030)367 1225 y Fd(L)458 1210 y Fg(\021)40
b Fe(\015)5 b Fh(\001)p Fe(t=c)838 1225 y Fd(L)890 1210
y Fh(,)42 b(and)d(the)h('half)7 b(')39 b(explicit)f(sc)m(hemes)j
Fe(F)14 b Fh(\()p Fe(T)2507 1169 y Fd(i)p Fc(+1)2493
1237 y Fd(A)2625 1210 y Fe(;)j(T)2740 1174 y Fd(i)2726
1235 y(L)2778 1210 y Fh(\))p Fe(;)g(F)d Fh(\()p Fe(T)3046
1174 y Fd(i)3032 1235 y(A)3088 1210 y Fe(;)j(T)3203 1169
y Fd(i)p Fc(+1)3189 1237 y Fd(L)3321 1210 y Fh(\))40
b(also)324 1342 y(do)23 b(not)g(allo)m(w)f(arbitrary)g(time)g(steps)j
(or)e(heat)g(capacities.)40 b(The)24 b(fully)e(implicit)d(sc)m(heme)324
1475 y Fe(F)14 b Fh(\()p Fe(T)510 1434 y Fd(i)p Fc(+1)496
1502 y Fd(A)627 1475 y Fe(;)j(T)742 1434 y Fd(i)p Fc(+1)728
1502 y Fd(L)860 1475 y Fh(\))33 b(is)f(the)h(preferred)g(c)m(hoice.)470
1607 y(\(If)26 b(conserv)-5 b(ation)26 b(w)m(ere)h(not)f(a)g
(requiremen)m(t,)i(other)e(options)g(w)m(ould)g(b)s(e)g(a)m(v)-5
b(ailable,)324 1740 y(suc)m(h)34 b(as)1282 1989 y Fe(c)1324
2004 y Fd(A)1391 1921 y Fh(\()p Fe(T)1500 1880 y Fd(i)p
Fc(+1)1486 1948 y Fd(A)1640 1921 y Fg(\000)23 b Fe(T)1811
1885 y Fd(i)1797 1947 y(A)1854 1921 y Fh(\))p 1391 1966
501 4 v 1583 2057 a(\001)p Fe(t)1929 1989 y Fh(==)28
b Fe(F)14 b Fh(\()p Fe(T)2295 1948 y Fd(i)p Fc(+1)2281
2016 y Fd(A)2413 1989 y Fe(;)j(T)2528 1948 y Fd(i)2514
2013 y(L)2566 1989 y Fh(\))833 b(\(5\))1246 2394 y Fe(c)1288
2409 y Fd(L)1350 2327 y Fh(\()p Fe(T)1459 2286 y Fd(i)p