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

view on githubraw file Latest commit 672ec4d5 on 2016-12-01 17:05:48 UTC
672ec4d5cf Jean*0001 %!PS-Adobe-2.0
                0002 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
                0003 %%Title: monin_obukhov.dvi
                0004 %%Pages: 14
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                1188 %%Page: 1 1
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                1295 %%Page: 3 3
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                1302 2158 857 a(z)2203 872 y Fd(0)2253 789 y Fj(\))1146 b(\(7\))324
                1303 984 y(where)42 b Fg(u)f Fj(is)g(the)h(wind)g(comp)s(onen)m(t)f(in)g
                1304 (the)h(direction)e(of)h(the)h(surface)g(stress,)j(and)324
                1305 1105 y Fg(z)369 1120 y Fd(0)440 1105 y Fj(is)31 b(the)g("roughness)i
                1306 (heigh)m(t")d(,)i(de\014ned)h(as)e(the)h(heigh)m(t)f(at)g(whic)m(h)h
                1307 (the)f(logarithmic)324 1225 y(pro\014le)25 b(w)m(ould)h(yield)g(zero)g
                1308 (wind.)42 b(\(The)27 b(turning)e(of)h(the)g(wind)g(is)g(assumed)h(to)e
                1309 (b)s(e)i(neg-)324 1345 y(ligible)h(within)j(this)h(surface)h(la)m(y)m
                1310 (er.\))43 b(The)33 b(roughness)h(heigh)m(t)e(is)f(the)i(k)m(ey)g
                1311 (parameter)324 1466 y(describing)f(the)h(macroscopic)f(e\013ects)i(of)e
                1312 (the)h(surface)g(t)m(yp)s(e)h(on)e(the)h(stress.)324
                1313 1681 y(The)i("neutral)e(drag)h(co)s(e\016cien)m(t")g(,)g(giv)m(en)h
                1314 (the)f(\015o)m(w)h(at)e(heigh)m(t)h(z,)h Fg(C)2925 1696
                1315 y Fe(n)2972 1681 y Fj(\()p Fg(z)t Fj(\),)g(is)e(de\014ned)324
                1316 1801 y(so)g(that,)f(in)g(the)h(neutral)f(case,)h(the)g(surface)h
                1317 (stress)g(v)m(ector)g(is)e(giv)m(en)g(b)m(y)1660 1976
                1318 y Fg(\034)39 b Fj(=)28 b Fg(\032)1895 1991 y Fe(s)1932
                1319 1976 y Fg(C)2002 1991 y Fe(n)2049 1976 y Fc(j)p Fi(v)r
                1320 Fc(j)p Fi(v)1212 b Fj(\(8\))1448 2139 y Fc(j)p Fg(\034)11
                1321 b Fc(j)p 1448 2183 109 4 v 1459 2274 a Fg(\032)1509 2289
                1322 y Fe(s)1594 2206 y Fj(=)28 b Fg(u)1754 2165 y Fd(2)1754
                1323 2231 y Ff(\003)1820 2206 y Fj(=)g Fg(C)1994 2221 y Fe(n)2041
                1324 2206 y Fj(\()p Fg(z)t Fj(\))p Fc(j)p Fi(v)r Fj(\()p Fg(z)t
                1325 Fj(\))p Fc(j)2408 2165 y Fd(2)3437 2206 y Fj(\(9\))324
                1326 2406 y(so)33 b(that)1525 2526 y Fg(C)1595 2541 y Fe(n)1642
                1327 2526 y Fj(\()p Fg(z)t Fj(\))28 b(=)f([)2082 2459 y Fg(\024)p
                1328 1935 2503 349 4 v 1935 2595 a(l)r(n)p Fj(\()p Fg(z)t(=z)2205
                1329 2610 y Fd(0)2246 2595 y Fj(\))2294 2526 y(])2321 2485
                1330 y Fd(2)3388 2526 y Fj(\(10\))324 2732 y(The)39 b(neutral)f(drag)g(co)s
                1331 (e\016cien)m(t)i(is)e(a)g(function)g(of)g(the)h(heigh)m(t)f(at)g(whic)m
                1332 (h)h(the)g(winds)324 2852 y(are)f(supplied.)60 b(Giv)m(en)39
                1333 b(the)f(roughness)i(heigh)m(t)e(and)g(the)h(heigh)m(t)f
                1334 Fg(z)43 b Fj(of)38 b(the)h(sp)s(eci\014ed)324 2973 y(wind,)34
                1335 b(w)m(e)h(ha)m(v)m(e)h(simple)c(expressions)k(for)e(the)g(drag)g(co)s
                1336 (e\016cien)m(t)h(and)f(surface)h(stress.)324 3093 y(\(Quite)30
                1337 b(often)h(in)f(meteorology)-8 b(,)30 b(the)i(term)e("surface)i(winds")f
                1338 (refers)h(to)e(the)i(winds)f(at)324 3213 y(a)h(heigh)m(t)h(of)f(10)h
                1339 (m,)f(and)h(drag)f(co)s(e\016cien)m(ts)i(are)f(quoted)h(with)e(the)i
                1340 (assumption)e(that)324 3334 y(they)h(refer)g(to)f(winds)h(at)g(this)f
                1341 (heigh)m(t.\))324 3710 y Fh(1.3)135 b(Strati\014cation)324
                1342 3990 y Fj(In)30 b(the)g(strati\014ed)f(case,)i(the)f(k)m(ey)h
                1343 (assumption)e(in)g(MOS)h(is)f(that)h(the)g(pro\014le)f(can)h(also)324
                1344 4110 y(dep)s(end)k(on)e Fg(\020)j Fc(\021)28 b Fg(z)t(=L)p
                1345 Fj(.)44 b(It)33 b(is)f(con)m(v)m(en)m(tional)h(to)f(write)1626
                1346 4267 y Fg(\024z)p 1626 4311 106 4 v 1631 4403 a(u)1687
                1347 4418 y Ff(\003)1752 4267 y Fg(@)5 b(u)p 1752 4311 113
                1348 4 v 1755 4403 a(@)g(z)1902 4335 y Fj(=)28 b(\010)2076
                1349 4350 y Fe(m)2143 4335 y Fj(\()p Fg(\020)8 b Fj(\))1118
                1350 b(\(11\))324 4550 y(where)44 b(\010)686 4565 y Fe(m)797
                1351 4550 y Fj(is)f(presumed)h(to)f(b)s(e)h(a)f(univ)m(ersal)h(function)f
                1352 (of)g Fg(\020)8 b Fj(.)75 b(\010)2884 4565 y Fe(m)2997
                1353 4550 y Fc(!)46 b Fj(1)d(as)h Fg(\020)53 b Fc(!)324 4670
                1354 y Fj(0,)42 b(so)f(that)g(the)g(logarithmic)c(pro\014le)j(is)g(ac)m
                1355 (hiev)m(ed)j(as)e(the)g(surface)g(is)g(approac)m(hed.)324
                1356 4791 y(In)m(tegrating)32 b(from)f Fg(z)1103 4806 y Fd(0)1175
                1357 4791 y Fj(to)i Fg(z)t Fj(,)g(w)m(e)h(\014nd)1242 4984
                1358 y Fg(u)p Fj(\()p Fg(z)t Fj(\))28 b(=)1565 4916 y Fg(u)1621
                1359 4931 y Ff(\003)p 1565 4960 95 4 v 1584 5052 a Fg(\024)1670
                1360 4984 y Fj(\()p Fg(F)1771 4999 y Fe(m)1837 4984 y Fj(\()p
                1361 Fg(z)t(=L)p Fj(\))23 b Fc(\000)g Fg(F)2263 4999 y Fe(m)2329
                1362 4984 y Fj(\()p Fg(z)2412 4999 y Fd(0)2452 4984 y Fg(=L)p
                1363 Fj(\)\))745 b(\(12\))1918 5251 y(3)p eop
                1364 %%Page: 4 4
                1365 4 3 bop 324 548 a Fj(where)1507 668 y Fg(F)1570 683 y
                1366 Fe(m)1637 668 y Fj(\()p Fg(\020)8 b Fj(\))27 b Fc(\021)1896
                1367 551 y Fb(Z)1996 668 y Fg(\020)2047 627 y Ff(\000)p Fd(1)2140
                1368 668 y Fj(\010)2210 683 y Fe(m)2277 668 y Fg(d\020)1017
                1369 b Fj(\(13\))324 864 y(The)32 b(assumption)e(is)h(that)f
                1370 Fg(z)1388 879 y Fd(0)1459 864 y Fj(is)h(not)g(a)f(function)h(of)f
                1371 (stabilit)m(y)-8 b(,)30 b(whic)m(h)h(is)g(plausible)e(as)324
                1372 984 y(long)i(as)i Fg(z)700 999 y Fd(0)767 984 y Fg(<<)28
                1373 b Fc(j)p Fg(L)p Fc(j)p Fj(.)324 1199 y(The)g(problem)e(no)m(w)i(b)s
                1374 (ecomes)f(that)g(of)g(generating)f(the)i(sim)m(ultaneous)e(surface)i
                1375 (\015uxes)324 1320 y(of)39 b(buo)m(y)m(ancy)j(and)e(momen)m(tum)f(from)
                1376 g(the)h(v)-5 b(alues)40 b(of)g Fg(u)f Fj(and)h Fg(b)h
                1377 Fj(at)e(some)h(heigh)m(t)g Fg(z)t Fj(;)324 1440 y(the)d(determination)e
                1378 (of)h(the)h(wind)g(pro\014le)f(is)h(coupled)g(to)f(that)h(of)f
                1379 (determining)f(the)324 1560 y(buo)m(y)m(ancy)f(pro\014le.)324
                1380 1775 y(Therefore,)c(b)m(y)g(the)f(same)f(scaling)f(argumen)m(t,)i(one)g
                1381 (writes)g(the)g(buo)m(y)m(ancy)h(pro\014le)e(as,)1645
                1382 1964 y Fg(\024z)p 1645 2009 106 4 v 1657 2100 a(b)1698
                1383 2115 y Ff(\003)1775 1964 y Fg(@)5 b(b)p 1771 2009 107
                1384 4 v 1771 2100 a(@)g(z)1916 2032 y Fj(=)27 b(\010)2089
                1385 2047 y Fe(b)2124 2032 y Fj(\()p Fg(\020)8 b Fj(\))1137
                1386 b(\(14\))324 2285 y(In)m(tegrating)32 b(as)h(b)s(efore,)1147
                1387 2541 y Fg(b)p Fj(\()p Fg(z)t Fj(\))23 b Fc(\000)g Fg(b)p
                1388 Fj(\(0\))28 b(=)1743 2474 y Fg(b)1784 2489 y Ff(\003)p
                1389 1743 2518 81 4 v 1756 2610 a Fg(\024)1834 2541 y Fj(\()p
                1390 Fg(F)1935 2556 y Fe(b)1970 2541 y Fj(\()p Fg(z)t(=L)p
                1391 Fj(\))23 b Fc(\000)f Fg(F)2395 2556 y Fe(b)2430 2541
                1392 y Fj(\()p Fg(z)2513 2556 y Fe(b)2547 2541 y Fg(=L)p Fj(\)\))650
                1393 b(\(15\))324 2779 y(where)35 b Fg(z)652 2794 y Fe(b)720
                1394 2779 y Fj(is)f(the)g(roughness)h(length)f(for)f(b)s(ouy)m(ancy)-8
                1395 b(,)36 b(de\014ned)f(so)f(that)g Fg(b)g Fj(w)m(ould)g(tak)m(e)324
                1396 2900 y(on)d(its)g(surface)h(v)-5 b(alue)31 b(at)g Fg(z)1334
                1397 2915 y Fe(b)1369 2900 y Fj(.)43 b(In)32 b(the)g(neutral)e(limit,)f(b)s
                1398 (oth)i Fg(F)2613 2915 y Fe(m)2711 2900 y Fj(and)h Fg(F)2963
                1399 2915 y Fe(b)3028 2900 y Fj(should)g(equal)324 3020 y
                1400 Fg(l)r(n)p Fj(\()p Fg(\020)8 b Fj(\).)324 3235 y(In)34
                1401 b(general,)f(there)h(is)g(no)f(reason)h(to)f(exp)s(ect)i
                1402 Fg(z)2077 3250 y Fd(0)2151 3235 y Fj(and)e Fg(z)2386
                1403 3250 y Fe(b)2455 3235 y Fj(to)g(b)s(e)h(the)g(same.)46
                1404 b(T)m(ypically)324 3356 y Fg(z)369 3371 y Fd(0)436 3356
                1405 y Fg(>)28 b(z)585 3371 y Fe(b)642 3356 y Fj(b)s(ecause)23
                1406 b(momen)m(tum)e(can)h(b)s(e)h(transferred)g(to)f(the)g(surface)i
                1407 (through)e(pressure)324 3476 y(forces)k(as)g(w)m(ell)e(as)i(molecular)e
                1408 (viscosit)m(y)-8 b(,)27 b(whereas)g(temp)s(erature)e(and)h(h)m(umidit)m
                1409 (y)e(m)m(ust)324 3596 y(b)s(e)k(transferred)g(b)m(y)h(molecular)d
                1410 (di\013usion)g(at)i(the)g(surface)h(\(except)g(when)g(there)g(is)e(sea)
                1411 324 3717 y(spra)m(y)33 b(etc\))h(One)e(sometimes)g(uses)i(the)f
                1412 (notation)1658 3929 y Fg(n)28 b Fc(\021)g Fg(l)r(n)p
                1413 Fj(\()p Fg(z)2021 3944 y Fd(0)2061 3929 y Fg(=z)2155
                1414 3944 y Fe(b)2190 3929 y Fj(\))1160 b(\(16\))324 4142
                1415 y(F)-8 b(or)32 b(example,)g(Garratt)f(suggests)j(that)e
                1416 Fg(n)c Fc(\031)g Fj(2)33 b(o)m(v)m(er)g(t)m(ypical)f(land)g(surfaces.)
                1417 324 4568 y Fk(2)161 b(Solving)54 b(F)-13 b(or)54 b(Surface)f(Fluxes)324
                1418 4882 y Fj(Giv)m(en)36 b(the)g(form)f(of)g(the)h(stabilit)m(y)e
                1419 (functions)i Fg(F)2170 4897 y Fe(m)2273 4882 y Fj(and)g
                1420 Fg(F)2529 4897 y Fe(b)2563 4882 y Fj(,)h(one)f(can)g(obtain)f(a)h(con-)
                1421 324 5002 y(sistency)e(condition)d(b)m(y)i(computing)f
                1422 Fg(L)1918 5251 y Fj(4)p eop
                1423 %%Page: 5 5
                1424 5 4 bop 820 703 a Fg(L)28 b Fj(=)g Fc(\000)p Fg(u)1151
                1425 661 y Fd(2)1151 727 y Ff(\003)1190 703 y Fg(=)p Fj(\()p
                1426 Fg(\024b)1374 718 y Ff(\003)1414 703 y Fj(\))f(=)1803
                1427 635 y Fg(u)p Fj(\()p Fg(z)t Fj(\))1984 599 y Fd(2)2023
                1428 635 y Fj(\()p Fg(F)2124 650 y Fe(b)2159 635 y Fj(\()p
                1429 Fg(\020)8 b Fj(\))21 b Fc(\000)h Fg(F)2469 650 y Fe(b)2504
                1430 635 y Fj(\()p Fg(\020)8 b(z)2638 650 y Fe(b)2671 635
                1431 y Fg(=z)t Fj(\)\))p 1593 679 1463 4 v 1593 771 a(\()p
                1432 Fg(b)p Fj(\()p Fg(z)t Fj(\))23 b Fc(\000)g Fg(b)p Fj(\(0\)\)\()p
                1433 Fg(F)2225 786 y Fe(m)2291 771 y Fj(\()p Fg(\020)8 b Fj(\))22
                1434 b Fc(\000)g Fg(F)2602 786 y Fe(m)2669 771 y Fj(\()p Fg(\020)8
                1435 b(z)2803 786 y Fd(0)2842 771 y Fg(=z)t Fj(\)\))3016 742
                1436 y Fd(2)3388 703 y Fj(\(17\))324 901 y(or)1322 1051 y
                1437 Fg(R)1396 1066 y Fe(b)1458 1051 y Fj(=)28 b Fg(\020)1714
                1438 984 y(F)1777 999 y Fe(b)1812 984 y Fj(\()p Fg(\020)8
                1439 b Fj(\))21 b Fc(\000)h Fg(F)2122 999 y Fe(b)2157 984
                1440 y Fj(\()p Fg(\020)8 b(z)2291 999 y Fe(b)2325 984 y Fg(=z)t
                1441 Fj(\))p 1622 1028 932 4 v 1622 1120 a(\()p Fg(F)1723
                1442 1135 y Fe(m)1789 1120 y Fj(\()p Fg(\020)g Fj(\))22 b
                1443 Fc(\000)g Fg(F)2100 1135 y Fe(m)2167 1120 y Fj(\()p Fg(\020)8
                1444 b(z)2301 1135 y Fd(0)2340 1120 y Fg(=z)t Fj(\)\))2514
                1445 1091 y Fd(2)3388 1051 y Fj(\(18\))324 1276 y(where)48
                1446 b Fg(R)694 1291 y Fe(b)775 1276 y Fj(is)e(the)h("Bulk)f(Ric)m(hardson)h
                1447 (n)m(um)m(b)s(er")g(b)s(et)m(w)m(een)i(the)e(surface)g(and)g(the)324
                1448 1397 y(heigh)m(t)32 b Fg(z)1055 1566 y(R)1129 1581 y
                1449 Fe(b)1192 1566 y Fc(\021)1307 1499 y Fg(z)t Fj(\()p Fg(b)p
                1450 Fj(\()p Fg(z)t Fj(\))24 b Fc(\000)e Fg(b)p Fj(\(0\)\))p
                1451 1307 1543 581 4 v 1487 1635 a Fg(u)p Fj(\()p Fg(z)t Fj(\))1668
                1452 1606 y Fd(2)1925 1566 y Fj(=)2039 1499 y Fg(g)t(z)t Fj(\(\002)2253
                1453 1514 y Fe(v)2293 1499 y Fj(\()p Fg(z)t Fj(\))h Fc(\000)g
                1454 Fj(\002)2617 1514 y Fe(v)2657 1499 y Fj(\(0\)\))p 2039
                1455 1543 782 4 v 2198 1635 a(\002)2274 1650 y Fe(v)2315 1635
                1456 y Fj(\(0\))p Fg(u)p Fj(\()p Fg(z)t Fj(\))2621 1606 y
                1457 Fd(2)3388 1566 y Fj(\(19\))324 1797 y(Eq)33 b(\(18\))f(can)h(then)g(b)s
                1458 (e)g(solv)m(ed)g(iterativ)m(ely)e(for)h Fg(\020)8 b Fj(,)32
                1459 b(giv)m(en)h Fg(R)2558 1812 y Fe(b)2593 1797 y Fj(,)f
                1460 Fg(z)2697 1812 y Fd(0)2737 1797 y Fg(=z)t Fj(,)h(and)g
                1461 Fg(z)3130 1812 y Fe(b)3164 1797 y Fg(=z)t Fj(.)324 2011
                1462 y(Giv)m(en)f Fg(\020)8 b Fj(,)32 b(one)h(can)g(then)g(compute)1411
                1463 2281 y Fg(u)1467 2296 y Ff(\003)1534 2281 y Fj(=)1909
                1464 2213 y Fg(\024)p Fc(j)p Fg(u)p Fj(\()p Fg(z)t Fj(\))p
                1465 Fc(j)p 1648 2258 817 4 v 1648 2349 a Fg(F)1711 2364 y
                1466 Fe(m)1777 2349 y Fj(\()p Fg(\020)8 b Fj(\))21 b Fc(\000)i
                1467 Fg(F)2088 2364 y Fe(m)2155 2349 y Fj(\()p Fg(\020)8 b(z)2289
                1468 2364 y Fd(0)2328 2349 y Fg(=z)t Fj(\))3388 2281 y(\(20\))324
                1469 2551 y(and)1448 2702 y Fg(b)1489 2717 y Ff(\003)1557
                1470 2702 y Fj(=)1755 2634 y Fg(\024)p Fj(\()p Fg(b)p Fj(\()p
                1471 Fg(z)t Fj(\))24 b Fc(\000)e Fg(b)p Fj(\(0\)\))p 1670
                1472 2678 758 4 v 1670 2770 a Fg(F)1733 2785 y Fe(b)1768 2770
                1473 y Fj(\()p Fg(\020)8 b Fj(\))21 b Fc(\000)h Fg(F)2078
                1474 2785 y Fe(h)2123 2770 y Fj(\()p Fg(\020)8 b(z)2257 2785
                1475 y Fe(b)2291 2770 y Fg(=z)t Fj(\))3388 2702 y(\(21\))324
                1476 2926 y(These)34 b(v)-5 b(alues)33 b(corresp)s(ond)g(to)f(the)h(drag)f
                1477 (co)s(e\016cien)m(ts)1333 3200 y Fg(C)1403 3215 y Fe(m)1497
                1478 3200 y Fj(=)2029 3133 y Fg(\024)2085 3096 y Fd(2)p 1611
                1479 3177 932 4 v 1611 3268 a Fj(\()p Fg(F)1712 3283 y Fe(m)1778
                1480 3268 y Fj(\()p Fg(\020)8 b Fj(\))21 b Fc(\000)i Fg(F)2089
                1481 3283 y Fe(m)2156 3268 y Fj(\()p Fg(\020)8 b(z)2290 3283
                1482 y Fd(0)2329 3268 y Fg(=z)t Fj(\)\))2503 3240 y Fd(2)3388
                1483 3200 y Fj(\(22\))324 3470 y(and)957 3625 y Fg(C)1027
                1484 3640 y Fe(b)1089 3625 y Fj(=)2013 3558 y Fg(\024)2069
                1485 3521 y Fd(2)p 1203 3602 1716 4 v 1203 3693 a Fj(\()p
                1486 Fg(F)1304 3708 y Fe(m)1370 3693 y Fj(\()p Fg(\020)g Fj(\))22
                1487 b Fc(\000)g Fg(F)1681 3708 y Fe(m)1748 3693 y Fj(\()p
                1488 Fg(\020)8 b(z)1882 3708 y Fd(0)1921 3693 y Fg(=z)t Fj(\)\)\()p
                1489 Fg(F)2196 3708 y Fe(b)2231 3693 y Fj(\()p Fg(\020)g Fj(\))21
                1490 b Fc(\000)h Fg(F)2541 3708 y Fe(b)2576 3693 y Fj(\()p
                1491 Fg(\020)8 b(z)2710 3708 y Fe(b)2744 3693 y Fg(=z)t Fj(\)\))3388
                1492 3625 y(\(23\))324 3944 y(In)40 b(implemen)m(ting)d(this)i(theory)-8
                1493 b(,)42 b(once)f(one)f(has)g(c)m(hosen)h(similarit)m(y)c(functions,)k
                1494 (one)324 4065 y(has)31 b(a)f(c)m(hoice)h(of)f(iterating)e(to)i(a)h
                1495 (solution)d(whenev)m(er)34 b(it)29 b(is)h(needed,)j(or)d(of)g
                1496 (tabulating)324 4185 y(the)46 b(solution)f(for)g(the)i(relev)-5
                1497 b(an)m(t)46 b(range)g(of)g(inputs,)j(and,)h(p)s(oten)m(tially)-8
                1498 b(,)47 b(\014tting)e(the)324 4305 y(results)28 b(with)g(easly)g(ev)-5
                1499 b(aluated)27 b(functions.)42 b(Giv)m(en)28 b(that)g(there)h(are)f
                1500 (three)g(inputs,)h(the)324 4426 y(t)m(ypical)i(\(but)g(not)h(univ)m
                1501 (ersal\))f(c)m(hoice)h(is)f(to)g(iterate.)43 b(If)31
                1502 b(there)h(w)m(ere)h(only)e(t)m(w)m(o)i(inputs)324 4546
                1503 y(-)27 b(i.e.,)h(if)f(one)h(could)f(assume)h(that)g(the)g(ratio)e(of)h
                1504 Fg(z)2159 4561 y Fd(0)2227 4546 y Fj(to)g Fg(z)2386 4561
                1505 y Fe(h)2459 4546 y Fj(w)m(ere)i(\014xed,)h(tabulation)25
                1506 b(and)324 4666 y(curv)m(e)j(\014tting)e(w)m(ould)h(b)s(e)h(more)e
                1507 (straighforw)m(ard.)41 b(In)27 b(FMS,)h(the)f(solution)f(is)g(obtained)
                1508 324 4787 y(b)m(y)33 b(iteration.)1918 5251 y(5)p eop
                1509 %%Page: 6 6
                1510 6 5 bop 324 548 a Fj(F)-8 b(or)26 b(the)i(purp)s(ose)g(of)f(iteration)f
                1511 (using)h(Newton-Raphson,)i(w)m(e)f(note)g(that)f(the)h(needed)324
                1512 668 y(deriv)-5 b(ativ)m(e)32 b(is)502 926 y Fg(@)5 b(R)632
                1513 941 y Fe(b)668 926 y Fg(=@)g(\020)35 b Fj(=)28 b Fg(R)1029
                1514 941 y Fe(b)1080 780 y Fb( )1156 858 y Fj(1)p 1156 902
                1515 51 4 v 1156 994 a Fg(\020)1238 926 y Fj(+)1346 858 y(\010)1416
                1516 873 y Fe(b)1451 858 y Fj(\()p Fg(\020)8 b Fj(\))21 b
                1517 Fc(\000)h Fj(\010)1768 873 y Fe(b)1803 858 y Fj(\()p
                1518 Fg(\020)8 b(z)1937 873 y Fd(0)1976 858 y Fg(=z)t Fj(\))p
                1519 1346 902 767 4 v 1356 994 a Fg(F)1419 1009 y Fe(b)1453
                1520 994 y Fj(\()p Fg(\020)g Fj(\))21 b Fc(\000)i Fg(F)1764
                1521 1009 y Fe(b)1798 994 y Fj(\()p Fg(\020)8 b(z)1932 1009
                1522 y Fe(b)1966 994 y Fg(=z)t Fj(\))2145 926 y Fc(\000)22
                1523 b Fj(2)2303 858 y(\010)2373 873 y Fe(m)2440 858 y Fj(\()p
                1524 Fg(\020)8 b Fj(\))21 b Fc(\000)i Fj(\010)2758 873 y Fe(m)2825
                1525 858 y Fj(\()p Fg(\020)8 b(z)2959 873 y Fd(0)2998 858
                1526 y Fg(=z)t Fj(\))p 2303 902 832 4 v 2313 994 a Fg(F)2376
                1527 1009 y Fe(m)2443 994 y Fj(\()p Fg(\020)g Fj(\))21 b Fc(\000)h
                1528 Fg(F)2753 1009 y Fe(m)2820 994 y Fj(\()p Fg(\020)8 b(z)2954
                1529 1009 y Fe(b)2988 994 y Fg(=z)t Fj(\))3144 780 y Fb(!)3388
                1530 926 y Fj(\(24\))324 1378 y Fk(3)161 b(The)53 b(Stabilit)l(y)j(F)-13
                1531 b(unctions)324 1691 y Fj(Ideally)26 b(there)h(w)m(ould)g(b)s(e)g(a)f
                1532 (generally)g(accepted)j(theory)e(for)f(the)h(stabilit)m(y)f(functions,)
                1533 324 1812 y(but)45 b(no)f(suc)m(h)i(theory)g(exists,)i(and)d(they)g(are)
                1534 g(ev)-5 b(aluated)44 b(from)g(atmospheric)g(\014eld)324
                1535 1932 y(studies.)e(The)26 b(forms)f(that)g(receiv)m(e)i(the)f(most)f
                1536 (supp)s(ort,)j(and)d(that)h(are)f(recommended)324 2053
                1537 y(b)m(y)33 b(Garratt,)f(are)g(for)g(the)h(unstable)g(case)h
                1538 Fg(\020)g(<)28 b Fj(0,)1529 2273 y(\010)1599 2288 y Fe(m)1694
                1539 2273 y Fj(=)f(\(1)22 b Fc(\000)h Fj(16)p Fg(\020)8 b
                1540 Fj(\))2193 2231 y Ff(\000)p Fd(1)p Fe(=)p Fd(4)3388 2273
                1541 y Fj(\(25\))1545 2493 y(\010)1615 2508 y Fe(b)1678 2493
                1542 y Fj(=)27 b(\(1)22 b Fc(\000)h Fj(16)p Fg(\020)8 b Fj(\))2177
                1543 2451 y Ff(\000)p Fd(1)p Fe(=)p Fd(2)3388 2493 y Fj(\(26\))324
                1544 2667 y(and)32 b(in)g(the)h(stable)g(case)g Fg(\020)i(>)27
                1545 b Fj(0,)1557 2887 y(\010)1627 2902 y Fe(m)1721 2887 y
                1546 Fj(=)h(\010)1895 2902 y Fe(b)1957 2887 y Fj(=)g(1)22
                1547 b(+)g(5)p Fg(\020)1066 b Fj(\(27\))324 3107 y(These)34
                1548 b(are)f(considered)g(to)f(ha)m(v)m(e)i(empirical)c(supp)s(ort)j(in)f
                1549 (the)h(range)f Fc(\000)p Fj(5)c Fg(<)g(\020)35 b(<)27
                1550 b Fj(1.)324 3490 y Fh(3.1)135 b(The)45 b(unstable)g(case)324
                1551 3769 y Fj(Consider)31 b(the)g(limit)c(that)k(the)g(mean)f(wind,)h(and)g
                1552 (therefore,)h(the)f(surface)g(stress)h(and)324 3890 y(the)38
                1553 b(friction)d(v)m(elo)s(cit)m(y)j Fg(u)1262 3905 y Ff(\003)1338
                1554 3890 y Fj(tend)g(to)f(zero.)59 b(With)37 b(the)h(c)m(hoice)g(of)f
                1555 (stabilit)m(y)f(functions)324 4010 y(presen)m(ted)i(ab)s(o)m(v)m(e,)f
                1556 (the)f(result)g(will)d(b)s(e)j(zero)g(buo)m(y)m(ancy)h(\015ux)g(as)e(w)
                1557 m(ell.)52 b(This)36 b(will)d(b)s(e)324 4131 y(true)g(as)f(long)g(as)h
                1558 (\010)1051 4146 y Fe(b)1113 4131 y Fc(!)27 b Fj(0)33
                1559 b(more)f(rapidly)f(than)h Fg(\020)2177 4094 y Ff(\000)p
                1560 Fd(1)p Fe(=)p Fd(3)2374 4131 y Fj(as)h Fc(j)p Fg(\020)8
                1561 b Fc(j)26 b(!)h(1)p Fj(.)324 4345 y(T)-8 b(o)26 b(see)g(wh)m(y)h(\010)
                1562 880 4360 y Fe(b)943 4345 y Fc(/)h(j)p Fg(\020)8 b Fc(j)1155
                1563 4309 y Ff(\000)p Fd(1)p Fe(=)p Fd(3)1344 4345 y Fj(is)25
                1564 b(sp)s(ecial,)i(lo)s(ok)d(at)h(the)i(buo)m(y)m(ancy)g(pro\014le)f(and)f
                1565 (ask)i(under)324 4466 y(what)g(conditions)g(it)f(approac)m(hes)j(a)e(w)
                1566 m(ell-de\014ned)g(limit)d(as)k Fg(u)2616 4481 y Ff(\003)2682
                1567 4466 y Fc(!)g Fj(0.)41 b(W)-8 b(e)28 b(can)g(rewrite)324
                1568 4586 y(\(14\))k(as)714 4801 y Fg(@)5 b(b)p 710 4845 107
                1569 4 v 710 4937 a(@)g(z)854 4869 y Fj(=)1028 4801 y Fg(B)p
                1570 968 4845 201 4 v 968 4937 a(\024u)1080 4952 y Ff(\003)1119
                1571 4937 y Fg(z)1178 4869 y Fj(\010)1248 4884 y Fe(b)1283
                1572 4869 y Fj(\()p Fg(\020)j Fj(\))27 b(=)1611 4801 y Fg(B)p
                1573 1550 4845 V 1550 4937 a(\024u)1662 4952 y Ff(\003)1702
                1574 4937 y Fg(z)1761 4869 y Fj(\010)1831 4884 y Fe(b)1883
                1575 4722 y Fb( )1958 4801 y Fc(\000)p Fg(\024z)t(b)2181 4816
                1576 y Ff(\003)p 1958 4845 265 4 v 2043 4937 a Fg(u)2099 4908
                1577 y Fd(2)2099 4961 y Ff(\003)2233 4722 y Fb(!)2326 4869
                1578 y Fj(=)2500 4801 y Fg(B)p 2439 4845 201 4 v 2439 4937
                1579 a(\024u)2551 4952 y Ff(\003)2591 4937 y Fg(z)2650 4869
                1580 y Fj(\010)2720 4884 y Fe(b)2772 4722 y Fb( )2847 4801
                1581 y Fc(\000)p Fg(\024z)t(B)p 2847 4845 263 4 v 2931 4937
                1582 a(u)2987 4908 y Fd(3)2987 4961 y Ff(\003)3120 4722 y
                1583 Fb(!)3388 4869 y Fj(\(28\))1918 5251 y(6)p eop
                1584 %%Page: 7 7
                1585 7 6 bop 324 548 a Fj(where)27 b Fg(B)j Fj(is)25 b(here)h(the)g(buo)m(y)
                1586 m(ancy)i(\015ux)e(divided)f(b)m(y)h(the)g(surface)h(densit)m(y)-8
                1587 b(.)42 b(In)26 b(order)f(for)324 668 y(this)32 b(pro\014le)g(to)h(b)s
                1588 (e)f(w)m(ell-de\014ned)h(as)g Fg(u)1774 683 y Ff(\003)1841
                1589 668 y Fc(!)27 b Fj(0)33 b(and)g Fg(\020)i Fc(!)27 b(\0001)p
                1590 Fj(,)33 b(w)m(e)h(need)f(\010)3123 683 y Fe(b)3186 668
                1591 y Fc(/)28 b(j)p Fg(\020)8 b Fc(j)3398 632 y Ff(\000)p
                1592 Fd(1)p Fe(=)p Fd(3)324 789 y Fj(so)33 b(that)f(the)h(factors)f(of)h
                1593 Fg(u)1308 804 y Ff(\003)1379 789 y Fj(cancel,)g(leading)e(to)1723
                1594 1002 y Fg(@)5 b(b)p 1718 1046 107 4 v 1718 1138 a(@)g(z)1863
                1595 1069 y Fc(/)1978 1002 y Fg(B)2057 966 y Fd(2)p Fe(=)p
                1596 Fd(3)p 1978 1046 190 4 v 1993 1138 a Fg(z)2042 1109 y
                1597 Fd(4)p Fe(=)p Fd(3)3388 1069 y Fj(\(29\))324 1315 y(whic)m(h)33
                1598 b(is)f(referred)h(to)g(as)f(the)h(free-con)m(v)m(ection)h(limit.)324
                1599 1530 y(With)f(the)i(recommended)f(stabilit)m(y)f(function)g(\(26\))h(w)
                1600 m(e)h(ha)m(v)m(e)g(instead)f(\010)3118 1545 y Fe(b)3183
                1601 1530 y Fc(/)d(j)p Fg(\020)8 b Fc(j)3398 1494 y Ff(\000)p
                1602 Fd(1)p Fe(=)p Fd(2)324 1650 y Fj(for)36 b(large)f Fc(j)p
                1603 Fg(\020)8 b Fc(j)p Fj(.)54 b(T)-8 b(o)37 b(see)h(that)e(this)g(results)
                1604 h(in)f(zero)h(buo)m(y)m(ancy)i(\015ux)e(in)f(the)h(free)g(con-)324
                1605 1770 y(v)m(ectiv)m(e)d(limit,)29 b(w)m(e)34 b(note)e(that)h(in)f(the)h
                1606 (large)e Fc(j)p Fg(\020)8 b Fc(j)31 b Fj(limit)e(w)m(e)34
                1607 b(ha)m(v)m(e)1588 2050 y Fg(B)f Fj(=)1881 1982 y Fg(\024)1937
                1608 1946 y Fd(2)1976 1982 y Fj(\001)p Fg(b)p Fc(j)p Fi(v)r
                1609 Fc(j)p 1808 2026 480 4 v 1808 2118 a Fg(F)1871 2133 y
                1610 Fe(m)1938 2118 y Fj(\()p Fg(\020)8 b Fj(\))p Fg(F)2128
                1611 2133 y Fe(b)2161 2118 y Fj(\()p Fg(\020)g Fj(\))3388
                1612 2050 y(\(30\))324 2320 y(where)31 b(\001)p Fg(b)f Fj(is)f(the)h(buo)m
                1613 (y)m(ancy)i(di\013erence)f(b)s(et)m(w)m(een)g(the)f(surface)h(and)f
                1614 (lev)m(el)f Fg(z)34 b Fj(and)c Fg(\020)37 b Fj(is)324
                1615 2440 y(determined)32 b(b)m(y)1503 2610 y Fg(R)1577 2625
                1616 y Fe(b)1640 2610 y Fj(=)1753 2543 y Fg(z)t Fj(\001)p
                1617 Fg(b)p 1753 2587 173 4 v 1759 2679 a Fc(j)p Fi(v)r Fc(j)1876
                1618 2650 y Fa(2)1963 2610 y Fj(=)2088 2543 y Fg(\020)8 b(F)2202
                1619 2558 y Fe(b)2235 2543 y Fj(\()p Fg(\020)g Fj(\))p 2077
                1620 2587 296 4 v 2077 2679 a Fg(F)2140 2694 y Fe(m)2207 2679
                1621 y Fj(\()p Fg(\020)g Fj(\))2334 2650 y Fd(2)3388 2610
                1622 y Fj(\(31\))324 2835 y(Eliminating)28 b Fg(F)919 2850
                1623 y Fe(m)1018 2835 y Fj(w)m(e)34 b(ha)m(v)m(e)1651 3009
                1624 y Fg(B)1730 2968 y Fd(2)1797 3009 y Fc(/)1925 2942 y
                1625 Fg(z)t Fj(\(\001)p Fg(b)p Fj(\))2172 2905 y Fd(3)p 1912
                1626 2986 314 4 v 1912 3077 a Fg(\020)8 b(F)2026 3092 y Fe(b)2060
                1627 3077 y Fj(\()p Fg(\020)g Fj(\))2187 3048 y Fd(3)3388
                1628 3009 y Fj(\(32\))324 3250 y(If)40 b(\010)499 3265 y Fe(b)574
                1629 3250 y Fc(/)g(j)p Fg(\020)8 b Fc(j)798 3214 y Ff(\000)p
                1630 Fd(1)p Fe(=)p Fd(2)1002 3250 y Fj(for)39 b(large)g Fc(j)p
                1631 Fg(\020)8 b Fc(j)38 b Fj(then)j(w)m(e)g(also)e(ha)m(v)m(e)i
                1632 Fg(F)2428 3265 y Fe(b)2503 3250 y Fc(/)g(j)p Fg(\020)8
                1633 b Fc(j)2728 3214 y Ff(\000)p Fd(1)p Fe(=)p Fd(2)2891
                1634 3250 y Fj(.)66 b(So)39 b Fg(B)46 b Fc(!)40 b Fj(0)f(as)324
                1635 3371 y Fc(j)p Fg(\020)8 b Fc(j)26 b(!)h(1)p Fj(.)324
                1636 3586 y(This)33 b(is)g(unsatisfactory)g({)g(either)g(one)h(m)m(ust)f
                1637 (use)i(a)e(stabilit)m(y)e(function)i(that)g(is)g(con-)324
                1638 3706 y(sisten)m(t)h(with)g(the)g(free-con)m(v)m(ectiv)m(e)i(limit,)31
                1639 b(or)j(one)g(m)m(ust)g(not)g(allo)m(w)e(the)j(wind)e(sp)s(eed)324
                1640 3826 y(that)40 b(is)f(used)i(in)e(the)i(similarit)m(y)36
                1641 b(theory)41 b(to)f(approac)m(h)g(0.)66 b(The)40 b(latter)f(alternativ)m
                1642 (e)324 3947 y(is)33 b(the)i(c)m(hoice)f(made)f(in)g(our)h(mo)s(del)e
                1643 (and)i(in)g(man)m(y)f(others.)49 b(The)34 b(picture)g(is)g(that)f(in)
                1644 324 4067 y(the)d(con)m(v)m(ectiv)m(e)h(limit,)c(eddies)j(transp)s
                1645 (orting)e(buo)m(y)m(ancy)k(across)e(lev)m(el)f Fg(z)34
                1646 b Fj(ha)m(v)m(e)d(length)324 4188 y(scales)42 b(that)g(scale)g(not)g
                1647 (with)f Fg(z)47 b Fj(but)42 b(with)f(the)i(depth)f(of)g(the)g(con)m(v)m
                1648 (ectiv)m(e)i(la)m(y)m(er)e Fg(h)p Fj(,)324 4308 y(whic)m(h)c(violates)g
                1649 (the)g(assumptions)g(of)g(the)g(original)d(similarit)m(y)g(theory)-8
                1650 b(.)61 b(These)40 b(ed-)324 4428 y(dies)32 b(pro)s(duce)i(wind)e(sp)s
                1651 (eed)i(p)s(erturbations)e(\("gusts"\))h(of)f(magnitude)1678
                1652 4648 y Fg(G)c Fj(=)f(\()p Fg(B)5 b(h)p Fj(\))2097 4607
                1653 y Fd(1)p Fe(=)p Fd(3)3388 4648 y Fj(\(33\))324 4868 y(whic)m(h)39
                1654 b(is)f(the)h(only)e(v)m(elo)s(cit)m(y)i(scale)f(that)g(one)h(can)g
                1655 (generate)g(from)e Fg(B)44 b Fj(and)38 b Fg(h)p Fj(.)61
                1656 b(One)324 4989 y(can)43 b(no)m(w)g(visualize)e(using)h(the)h(similarit)
                1657 m(y)d(theory)j(on)f(smaller)f(scales)i(than)f(these)1918
                1658 5251 y(7)p eop
                1659 %%Page: 8 8
                1660 8 7 bop 324 548 a Fj(gusts,)42 b(implying)37 b(that)j(the)g(gusts)h(m)m
                1661 (ust)f(b)s(e)g(included)f(in)g(the)i(wind)e(sp)s(eed)i(that)f(is)324
                1662 668 y(input)34 b(in)m(to)g(MOS.)g(F)-8 b(rom)33 b(the)i(viewp)s(oin)m
                1663 (t)f(of)g(the)h(MOS)g(mo)s(dule)e(itself,)h(it)f(need)j(not)324
                1664 789 y(b)s(e)30 b(concerned)i(with)e(the)g(free-con)m(v)m(ectiv)m(e)j
                1665 (limit)26 b({)k(it)f(assumes)i(that)f(the)h(input)f(wind)324
                1666 909 y(sp)s(eed)k(will)c(b)s(e)j(b)s(ounded)g(a)m(w)m(a)m(y)h(from)d
                1667 (zero)i(b)m(y)h(some)e(theory)h(of)f("gustiness".)324
                1668 1124 y(The)g(stabilit)m(y)e(functions)h(\(25\))g(and)h(\(26\))f(ha)m(v)
                1669 m(e)h(the)g(prop)s(ert)m(y)h(that)e(\010)2988 1088 y
                1670 Fd(2)2988 1149 y Fe(m)3083 1124 y Fj(=)c(\010)3256 1139
                1671 y Fe(h)3301 1124 y Fj(.)43 b(This)324 1244 y(implies)27
                1672 b(that)i(the)i(lo)s(cal)c(\(as)j(opp)s(osed)g(to)g(the)g(bulk\))f(Ric)m
                1673 (hardson's)h(n)m(um)m(b)s(er)h(is)e(equal)324 1365 y(to)j
                1674 Fg(\020)8 b Fj(,)32 b(and,)h(in)f(particular,)f(that)h
                1675 Fg(R)q(i)h Fj(is)f(a)h(linear)e(function)h(of)g Fg(z)t
                1676 Fj(.)45 b(If)32 b(there)i(w)m(ere)g(some)324 1485 y(dynamical)26
                1677 b(argumen)m(t)h(for)g(this)h(simple)e(structure,)k(it)d(w)m(ould)h
                1678 (help)f(in)g(justifying)g(this)324 1605 y(c)m(hoice)33
                1679 b(of)f(stabilit)m(y)f(functions,)h(but)h(w)m(e)h(are)e(not)h(a)m(w)m
                1680 (are)g(of)f(suc)m(h)i(an)f(argumen)m(t.)324 1820 y(These)i(forms)d(ha)m
                1681 (v)m(e)j(the)e(con)m(v)m(enien)m(t)i(prop)s(ert)m(y)f(that)f(w)m(e)h
                1682 (can)g(ev)-5 b(aluate)33 b(the)g(in)m(tegral)324 1941
                1683 y(stabilit)m(y)45 b(functions,)50 b Fg(F)1246 1956 y
                1684 Fe(m)1360 1941 y Fj(and)d Fg(F)1627 1956 y Fe(b)1708
                1685 1941 y Fj(analytically)-8 b(.)83 b(One)47 b(\014nds,)k(with)c
                1686 (considerable)324 2061 y(e\013ort,)35 b(that)g(\(using)g(the)g
                1687 (notation)f Fg(F)14 b Fj(\()p Fg(\020)8 b Fj(;)17 b Fg(\020)1937
                1688 2076 y Fd(0)1974 2061 y Fj(\))32 b(=)f Fg(F)14 b Fj(\()p
                1689 Fg(\020)8 b Fj(\))23 b Fc(\000)h Fg(F)14 b Fj(\()p Fg(\020)2637
                1690 2076 y Fd(0)2676 2061 y Fj(\))35 b(where)h Fg(\020)3076
                1691 2076 y Fd(0)3147 2061 y Fj(=)31 b Fg(z)3299 2076 y Fd(0)3339
                1692 2061 y Fg(=L)h Fj(=)324 2182 y Fg(\020)8 b(z)420 2197
                1693 y Fd(0)459 2182 y Fg(=z)t Fj(\))374 2409 y Fg(F)437 2424
                1694 y Fe(m)503 2409 y Fj(\()p Fg(\020)g Fj(;)17 b Fg(\020)679
                1695 2424 y Fd(0)717 2409 y Fj(\))28 b(=)f(ln\()1033 2341
                1696 y Fg(z)p 1016 2385 85 4 v 1016 2477 a(z)1061 2492 y Fd(0)1110
                1697 2409 y Fj(\))5 b Fc(\000)g Fj(2)17 b(ln)o(\()1449 2341
                1698 y(1)22 b(+)g Fg(x)p 1430 2385 264 4 v 1430 2477 a Fj(1)g(+)g
                1699 Fg(x)1654 2492 y Fd(0)1703 2409 y Fj(\))5 b Fc(\000)g
                1700 Fj(ln)o(\()1957 2341 y(1)22 b(+)g Fg(x)2181 2305 y Fd(2)p
                1701 1957 2385 V 1957 2477 a Fj(1)g(+)g Fg(x)2181 2443 y Fd(2)2181
                1702 2499 y(0)2231 2409 y Fj(\))5 b(+)g(2\(tan)2582 2367 y
                1703 Ff(\000)p Fd(1)2676 2409 y Fj(\()p Fg(x)p Fj(\))g Fc(\000)g
                1704 Fj(tan)3035 2367 y Ff(\000)p Fd(1)3130 2409 y Fj(\()p
                1705 Fg(x)3223 2424 y Fd(0)3263 2409 y Fj(\)\))49 b(\(34\))324
                1706 2640 y(where)34 b Fg(x)28 b Fc(\021)g Fj(\(1)22 b Fc(\000)g
                1707 Fj(16)p Fg(\020)8 b Fj(\))1189 2604 y Fd(1)p Fe(=)p Fd(4)1298
                1708 2640 y Fj(;)33 b(while)e(for)h(buo)m(y)m(ancy)1269 2853
                1709 y Fg(F)1332 2868 y Fe(b)1367 2853 y Fj(\()p Fg(\020)8
                1710 b Fj(;)17 b Fg(\020)1543 2868 y Fe(b)1575 2853 y Fj(\))28
                1711 b(=)f(ln\()1889 2785 y Fg(z)p 1874 2829 80 4 v 1874 2921
                1712 a(z)1919 2936 y Fe(b)1963 2853 y Fj(\))22 b Fc(\000)h
                1713 Fj(2)17 b(ln)o(\()2333 2785 y(1)22 b(+)g Fg(y)p 2318
                1714 2829 251 4 v 2318 2921 a Fj(1)f(+)h Fg(y)2534 2936 y
                1715 Fe(b)2578 2853 y Fj(\))772 b(\(35\))324 3082 y(where)34
                1716 b Fg(y)c Fc(\021)f Fj(\(1)21 b Fc(\000)i Fj(16)p Fg(\020)8
                1717 b Fj(\))1185 3046 y Fd(1)p Fe(=)p Fd(2)1294 3082 y Fj(.)324
                1718 3297 y(These)26 b(expressions)f(are)f(su\016cien)m(tly)h(costly)f(to)g
                1719 (compute,)i(esp)s(ecially)d Fg(F)3023 3312 y Fe(m)3089
                1720 3297 y Fj(,)j(that)e(there)324 3417 y(migh)m(t)30 b(b)s(e)i(v)-5
                1721 b(alue)32 b(in)f(using)h(a)f(table)h(lo)s(ok)e(up)j(for)e(them,)h(ev)m
                1722 (en)i(as)e(part)g(of)f(the)i(o)m(v)m(erall)324 3538 y(iteration.)45
                1723 b(A)m(t)35 b(presen)m(t,)h(they)f(are)e(simply)g(computed)h(directly)f
                1724 (from)g(these)i(expres-)324 3658 y(sions)d(within)g(FMS.)324
                1725 4034 y Fh(3.2)135 b(The)45 b(stable)h(case)324 4313 y
                1726 Fj(It)29 b(is)g(not)g(di\016cult)f(to)h(sho)m(w)h(that)f(with)g(\010)
                1727 1896 4328 y Fe(b)1958 4313 y Fc(\021)f Fj(\010)2133 4328
                1728 y Fe(m)2200 4313 y Fj(,)i(and,)g(therefore,)h Fg(F)2968
                1729 4328 y Fe(b)3030 4313 y Fc(\021)d Fg(F)3198 4328 y Fe(m)3294
                1730 4313 y Fj(on)h(the)324 4433 y(stable)37 b(side)h(that)f(the)h(drag)f
                1731 (co)s(e\016cien)m(ts)i(drop)f(to)f(zero)h(close)g(to)f
                1732 Fg(R)q(i)2966 4448 y Fe(b)3037 4433 y Fg(<)f Fj(0)p Fg(:)p
                1733 Fj(2,)i(giv)m(en)324 4554 y(the)32 b(form)e(\(27\).)43
                1734 b(This)31 b(critical)e(Ric)m(harsons's)k(n)m(um)m(b)s(er)f(w)m(ould)f
                1735 (b)s(e)h(exactly)g(0.2)f(if)f(one)324 4674 y(set)j Fg(z)521
                1736 4689 y Fd(0)589 4674 y Fj(=)27 b Fg(z)737 4689 y Fe(h)783
                1737 4674 y Fj(.)43 b(T)-8 b(o)33 b(see)h(this,)e(note)h(that,)g(with)f
                1738 (\(27\))g(w)m(e)i(ha)m(v)m(e)g Fg(F)2688 4689 y Fe(b)2750
                1739 4674 y Fj(=)28 b Fg(F)2917 4689 y Fe(m)3011 4674 y Fj(=)g
                1740 Fg(l)r(n)p Fj(\()p Fg(\020)8 b Fj(\))22 b(+)g Fg(\014)6
                1741 b(\020)324 4794 y Fj(with)32 b Fg(\014)h Fj(=)28 b(5,)k(so)h(that)1383
                1742 4959 y Fg(R)1457 4974 y Fe(b)1520 4959 y Fj(=)2038 4891
                1743 y Fg(\020)p 1633 4935 860 4 v 1633 5027 a(l)r(n)p Fj(\()p
                1744 Fg(z)t(=z)1903 5042 y Fd(0)1944 5027 y Fj(\))22 b(+)g
                1745 Fg(\014)6 b Fj(\()p Fg(\020)29 b Fc(\000)22 b Fg(\020)2415
                1746 5042 y Fd(0)2454 5027 y Fj(\))3388 4959 y(\(36\))1918
                1747 5251 y(8)p eop
                1748 %%Page: 9 9
                1749 9 8 bop 324 548 a Fj(As)46 b Fg(\020)52 b Fj(increases,)e(this)45
                1750 b(in)f(b)s(ounded)i(ab)s(o)m(v)m(e)h(b)m(y)f Fg(R)2279
                1751 563 y Fe(cr)r(it)2447 548 y Fj(=)j Fg(\014)2633 512 y
                1752 Ff(\000)p Fd(1)2727 548 y Fj(.)82 b(Therefore,)49 b(as)d
                1753 Fg(R)3527 563 y Fe(b)324 668 y Fj(approac)m(hes)29 b
                1754 Fg(R)895 683 y Fe(cr)r(it)1013 668 y Fj(,)f Fg(\020)35
                1755 b Fc(!)27 b(1)p Fj(,)i(and,)f(therefore,)h Fg(F)2136
                1756 683 y Fe(m)2203 668 y Fg(;)17 b(F)2310 683 y Fe(t)2367
                1757 668 y Fc(!)28 b(1)f Fj(as)g(w)m(ell.,)h(implying)d(that)324
                1758 789 y(the)33 b(drag)f(co)s(e\016cien)m(ts)i Fc(!)27 b
                1759 Fj(0)324 1004 y(While)34 b(0)p Fg(:)p Fj(2)h(is)g(close)g(to)g(the)h
                1760 (0.25)f(stabilit)m(y)e(criterion)h(for)h(linear)f(Kelvin)g(Helmholtz)
                1761 324 1124 y(instabilit)m(y)-8 b(,)23 b(it)h(is)g(inconsisten)m(t)h(with)
                1762 f(\014eld)g(data)g(to)g(set)h(the)g(\015uxes)h(to)e(zero)h(at)f(this)g
                1763 (lo)m(w)324 1244 y(a)40 b(bulk)h(Ric)m(hardson's)g(n)m(um)m(b)s(er.)68
                1764 b(In)m(termitten)m(t)40 b(turbulence)h(still)e(exists)i(at)f(higher)324
                1765 1365 y(stabilit)m(y)-8 b(,)44 b(asso)s(ciated)f(with)g(breaking)g(gra)m
                1766 (vit)m(y)g(w)m(a)m(v)m(es)i(lik)m(ely)d(related)h(to)g(inhomo-)324
                1767 1485 y(geneities)j(in)h(the)g(surface)h(whose)g(e\013ects)g(are)f(not)g
                1768 (represen)m(table)h(in)e(terms)h(of)g(a)324 1605 y(surface)33
                1769 b(roughness.)324 1820 y(Since)42 b(the)h(v)-5 b(alue)42
                1770 b Fg(\014)51 b Fj(=)44 b(5)e(seems)i(to)e(agree)g(with)h(data)f(in)f
                1771 (the)i(mo)s(derately)f(stable)324 1941 y(range,)48 b(one)c(generally)g
                1772 (mo)s(di\014es)g(\010)1714 1956 y Fe(b)1793 1941 y Fj(and)h(\010)2065
                1773 1956 y Fe(m)2177 1941 y Fj(so)f(that)h(they)g(ha)m(v)m(e)h(this)f(form)
                1774 e(for)324 2061 y(small)30 b Fg(\020)39 b Fj(but)32 b(allo)m(w)f
                1775 (non-zero)h(\015uxes)i(for)e(larger)f Fg(R)q(i)2293 2076
                1776 y Fe(b)2328 2061 y Fj(.)43 b(Di\013eren)m(t)32 b(mo)s(del)e(use)j(v)-5
                1777 b(arious)324 2182 y(forms)27 b(for)g(this)g(purp)s(ose.)43
                1778 b(The)29 b(simplest)d(w)m(ould)i(seem)g(to)g(b)s(e)g(the)g(most)f
                1779 (desirable.)42 b(It)324 2302 y(is)33 b(also)h(v)m(ery)h(con)m(v)m
                1780 (enien)m(t)h(to)e(ha)m(v)m(e)i(a)e(form)f(that)h(allo)m(ws)f(one)h(to)g
                1781 (in)m(tegrate)g(\010)3270 2317 y Fe(m)3337 2302 y Fj(\()p
                1782 Fg(\020)8 b Fj(\))p Fg(=\020)324 2422 y Fj(analytically)28
                1783 b(so)i(that)h(one)g(has)g(a)f(relativ)m(ely)g(simple)f(expression)j
                1784 (for)e Fg(F)3007 2437 y Fe(m)3074 2422 y Fj(.)43 b(The)31
                1785 b(MOS)324 2543 y(mo)s(dule)g(has)i(t)m(w)m(o)g(options:)324
                1786 2758 y(V)-8 b(ersion)32 b(1)g(is)1431 2902 y(\010)1501
                1787 2917 y Fe(m)1596 2902 y Fj(=)c(\010)1770 2917 y Fe(b)1832
                1788 2902 y Fj(=)g(1)21 b(+)h Fg(\020)2165 2835 y Fj(5)f(+)h
                1789 Fg(\014)6 b(\020)p 2165 2879 280 4 v 2195 2971 a Fj(1)22
                1790 b(+)g Fg(\020)3388 2902 y Fj(\(37\))324 3117 y(This)43
                1791 b(approac)m(hes)i(1)29 b(+)g Fg(\014)6 b(\020)50 b Fj(for)43
                1792 b(large)f Fg(\020)50 b Fj(while)43 b(preserving)h(the)f(observ)m(ed)j
                1793 (small)41 b Fg(\020)324 3237 y Fj(b)s(eha)m(vior.)58
                1794 b(One)38 b(can)f(use)i Fg(\014)k Fj(as)37 b(a)h(tunable)f(parameter)g
                1795 (to)g(mo)s(dify)f(the)i(p)s(o)s(orly)e(un-)324 3358 y(dersto)s(o)s(d)d
                1796 (surface)g(mixing)e(in)h(v)m(ery)i(stable)f(conditions.)43
                1797 b(In)33 b(the)g(co)s(de,)g(the)g(namelist)324 3478 y(parameter)f(is)g
                1798 (ric)m(h)p 1054 3478 30 4 v 35 w(crit)g Fc(\021)c Fj(1)p
                1799 Fg(=\014)324 3693 y Fj(V)-8 b(ersion)30 b(2,)i(whic)m(h)f(w)m(e)h(no)m
                1800 (w)g(fa)m(v)m(or,)f(in)f(that)h(it)f(pro)m(vides)i(additional)c(con)m
                1801 (trols)i(on)h(the)324 3813 y(mixing,)f(is)i(piecewise)i(linear)1362
                1802 4022 y(\010)1432 4037 y Fe(m)1527 4022 y Fj(=)27 b(\010)1700
                1803 4037 y Fe(b)1763 4022 y Fj(=)g(1)22 b(+)g(5)p Fg(\020)8
                1804 b Fj(;)82 b Fg(\020)35 b(<)28 b(\020)2469 4037 y Fe(T)3388
                1805 4022 y Fj(\(38\))1103 4231 y(\010)1173 4246 y Fe(m)1268
                1806 4231 y Fj(=)f(\010)1441 4246 y Fe(b)1504 4231 y Fj(=)g(1)22
                1807 b(+)g(\(5)g Fc(\000)h Fg(\014)6 b Fj(\))p Fg(\020)2127
                1808 4246 y Fe(c)2183 4231 y Fj(+)22 b Fg(\014)6 b(\020)i
                1809 Fj(;)82 b Fg(\020)34 b Fc(\025)29 b Fg(\020)2728 4246
                1810 y Fe(T)3388 4231 y Fj(\(39\))324 4400 y(Here)g Fg(\014)34
                1811 b Fj(con)m(trols)28 b(the)h(critical)e(Ri)g(as)i(b)s(efore,)g(while)f
                1812 Fg(\020)2340 4415 y Fe(T)2423 4400 y Fj(con)m(trols)g(the)h(p)s(oin)m
                1813 (t)f(at)g(whic)m(h)324 4521 y(a)e(transition)e(is)h(made)h(from)f(the)h
                1814 (established)g(stabilit)m(y)f(function)g(for)h(the)g(fully)f(tubu-)324
                1815 4641 y(len)m(t)k(b)s(oundary)g(la)m(y)m(er)h(to)f(the)g(presumably)g
                1816 (in)m(termiten)m(t)f(turbulence)i(at)f(high)g(stabil-)324
                1817 4761 y(it)m(y)-8 b(.)53 b(With)36 b(this)g(v)m(ersion)g(one)h(can)f
                1818 (generate)h(drag)e(co)s(e\016cien)m(ts)j(that)d(are)i(small)c(but)324
                1819 4882 y(non-zero)g(for)g(a)g(large)g(range)g(of)g(Ri)f(\(see)j(the)f
                1820 (follo)m(wing)c(section\).)47 b(In)33 b(the)h(namelist,)324
                1821 5002 y Fg(\020)367 5017 y Fe(T)454 5002 y Fj(is)e(denoted)i(b)m(y)f
                1822 (zeta)p 1235 5002 V 36 w(trans.)1918 5251 y(9)p eop
                1823 %%Page: 10 10
                1824 10 9 bop 324 548 a Fj(The)33 b(in)m(tegrals)f(of)g(\010\()p
                1825 Fg(\020)8 b Fj(\))p Fg(=\020)39 b Fj(can)33 b(once)g(again)e(b)s(e)i
                1826 (computed)f(analytically)-8 b(.)324 973 y Fk(4)161 b(Di\013usion)54
                1827 b(co)t(e\016cien)l(ts)324 1287 y Fj(The)48 b(pro\014les)g(of)f(wind)g
                1828 (and)h(buo)m(y)m(ancy)i(obtained)d(in)g(this)g(w)m(a)m(y)i(can)f(b)s(e)
                1829 f(though)m(t)324 1407 y(of)39 b(as)h(determining)e(di\013usivities)g
                1830 (that)h(w)m(ould)h(result)f(in)g(these)i(pro\014les)f(if)e(v)m(ertical)
                1831 324 1528 y(di\013usion)45 b(w)m(ere)j(the)f(only)f(pro)s(cess)i(acting)
                1832 e({)g(whic)m(h)h(the)g(surface)h(\015ux)f(similarit)m(y)324
                1833 1648 y(theory)34 b(e\013ectiv)m(ely)h(assumes)g(in)e(an)m(y)h(case.)49
                1834 b(T)-8 b(o)33 b(obtain)g(this)h(equiv)-5 b(alen)m(t)33
                1835 b(di\013usivit)m(y)-8 b(,)324 1768 y(one)23 b(can)h(equate)h(the)f
                1836 (surface)g(\015ux)g(with)f(the)h(di\013usivit)m(y)f(m)m(ultiplied)d(b)m
                1837 (y)k(the)g(gradien)m(t.)324 1889 y(In)33 b(particular,)e(the)i
                1838 (kinematic)e(di\013usivit)m(y)g(for)i(momen)m(tum)e Fg(K)2738
                1839 1904 y Fe(m)2837 1889 y Fj(is)h(then)1454 2150 y Fg(K)1537
                1840 2165 y Fe(m)1632 2150 y Fj(=)1771 2083 y Fg(u)1827 2047
                1841 y Fd(2)1827 2108 y Ff(\003)p 1745 2127 147 4 v 1745 2219
                1842 a Fg(@)1796 2234 y Fe(z)1837 2219 y Fg(u)1930 2150 y
                1843 Fj(=)2132 2083 y Fg(\024u)2244 2098 y Ff(\003)2283 2083
                1844 y Fg(z)p 2043 2127 378 4 v 2043 2219 a Fj(\010)2113 2234
                1845 y Fe(m)2180 2219 y Fj(\()p Fg(z)t(=L)p Fj(\))3388 2150
                1846 y(\(40\))324 2509 y(The)j(di\013usivit)m(y)e(for)g(buo)m(y)m(ancy)j
                1847 (\(ie)d(p)s(oten)m(tial)f(temp)s(erature)h(or)h(dry)g(static)g
                1848 (energy\))324 2629 y(is)1472 2774 y Fg(K)1555 2789 y
                1849 Fe(b)1617 2774 y Fj(=)1731 2706 y Fg(u)1787 2721 y Ff(\003)1826
                1850 2706 y Fg(b)1867 2721 y Ff(\003)p 1731 2751 176 4 v 1752
                1851 2842 a Fg(@)1803 2857 y Fe(z)1844 2842 y Fg(b)1944 2774
                1852 y Fj(=)2130 2706 y Fg(\024u)2242 2721 y Ff(\003)2281
                1853 2706 y Fg(z)p 2058 2751 346 4 v 2058 2842 a Fj(\010)2128
                1854 2857 y Fe(b)2163 2842 y Fj(\()p Fg(z)t(=L)p Fj(\))3388
                1855 2774 y(\(41\))324 2999 y(corresp)s(onding)e(to)h(a)f(Prandtl)g(ratio,)f
                1856 Fg(P)14 b(r)30 b Fc(\021)e Fg(K)2109 3014 y Fe(m)2175
                1857 2999 y Fg(=K)2307 3014 y Fe(b)2369 2999 y Fj(=)g(\010)2543
                1858 3014 y Fe(b)2578 2999 y Fg(=)p Fj(\010)2697 3014 y Fe(m)2763
                1859 2999 y Fj(.)324 3214 y(If)f(one's)h(GCM)g(has)f(su\016cien)m(t)i(v)m
                1860 (ertical)d(resolution)g(to)h(p)s(enetrate)h(this)f(surface)h(la)m(y)m
                1861 (er,)324 3334 y(and)36 b(assuming)g(that)g(the)h(GCM)g(is)f
                1862 (di\013using)f(in)h(the)h(v)m(ertical,)f(then)h(its)f(di\013usivit)m(y)
                1863 324 3454 y(and)c(viscosit)m(y)h(should)g(approac)m(h)g(these)h(v)-5
                1864 b(alues)32 b(as)h(the)g(surface)g(is)g(approac)m(hed.)324
                1865 3669 y(In)26 b(the)g(stable)g(planetary)g(b)s(oundary)g(la)m(y)m(er)g
                1866 (ab)s(o)m(v)m(e)h(the)f(surface)h(la)m(y)m(er,)g(the)f(di\013usivit)m
                1867 (y)324 3790 y(in)32 b(GCMs)h(is)f(often)h(mo)s(deled)e(as)i(b)s(eing)f
                1868 (lo)s(cal)e(in)i(the)h(v)m(ertical,)f(of)g(the)h(form)1698
                1869 4041 y Fg(K)i Fj(=)27 b Fg(`)1960 4000 y Fd(2)2000 4041
                1870 y Fc(j)2038 3974 y Fg(@)5 b(u)p 2038 4018 113 4 v 2041
                1871 4110 a(@)g(z)2160 4041 y Fc(j)1200 b Fj(\(42\))324 4275
                1872 y(where)34 b Fg(`)e Fj(is)g(a)g(mixing)f(length.)43 b(In)33
                1873 b(the)g(neutral)f(surface)h(la)m(y)m(er,)g(w)m(e)h(ha)m(v)m(e)1236
                1874 4536 y Fg(K)1319 4551 y Fe(m)1414 4536 y Fj(=)27 b Fg(K)1600
                1875 4551 y Fe(b)1662 4536 y Fj(=)1890 4469 y Fg(u)1946 4433
                1876 y Fd(2)1946 4493 y Ff(\003)p 1776 4513 324 4 v 1776 4604
                1877 a Fc(j)p Fg(@)5 b(u=@)g(z)t Fc(j)2137 4536 y Fj(=)27
                1878 b(\()p Fg(\024z)t Fj(\))2421 4495 y Fd(2)2461 4536 y
                1879 Fc(j)2499 4469 y Fg(@)5 b(u)p 2499 4513 113 4 v 2502
                1880 4604 a(@)g(z)2621 4536 y Fc(j)739 b Fj(\(43\))324 4794
                1881 y(so)33 b(in)e(this)i(limit,)c Fg(`)e Fj(=)h Fg(\024z)t
                1882 Fj(.)44 b(In)33 b(the)g(strati\014ed)g(case,)g(w)m(e)h(write)1627
                1883 5002 y Fg(`)28 b Fj(=)f Fg(\024z)t(f)11 b Fj(\()p Fg(R)q(i)p
                1884 Fj(\))2147 4961 y Fd(1)p Fe(=)p Fd(2)3388 5002 y Fj(\(44\))1894
                1885 5251 y(10)p eop
                1886 %%Page: 11 11
                1887 11 10 bop 324 548 a Fj(so)33 b(that)1506 693 y Fg(K)i
                1888 Fj(=)27 b(\()p Fg(\024z)t Fj(\))1908 652 y Fd(2)1949
                1889 693 y Fc(j)1987 625 y Fg(@)5 b(u)p 1987 670 113 4 v 1990
                1890 761 a(@)g(z)2109 693 y Fc(j)p Fg(f)11 b Fj(\()p Fg(R)q(i)p
                1891 Fj(\))1008 b(\(45\))324 893 y(In)31 b(terms)h(of)e(our)i(stabilit)m(y)d
                1892 (function)i(\010,)h(assumed)g(to)f(b)s(e)g(the)h(same)f(for)g(momen)m
                1893 (tum)324 1013 y(and)h(buo)m(y)m(ancy)-8 b(,)35 b(w)m(e)f(ha)m(v)m(e)g
                1894 (for)e(the)h(strati\014ed)f(case)1464 1287 y Fg(K)1547
                1895 1302 y Fe(m)1641 1287 y Fj(=)27 b Fg(K)1827 1302 y Fe(b)1889
                1896 1287 y Fj(=)2003 1219 y(\()p Fg(\024z)t Fj(\))2184 1183
                1897 y Fd(2)p 2003 1263 222 4 v 2059 1355 a Fj(\010)2129 1326
                1898 y Fd(2)2234 1287 y Fc(j)2272 1219 y Fg(@)5 b(u)p 2272
                1899 1263 113 4 v 2275 1355 a(@)g(z)2394 1287 y Fc(j)966 b
                1900 Fj(\(46\))324 1532 y(Therefore,)34 b(w)m(e)f(can)g(set)1572
                1901 1652 y Fg(f)11 b Fj(\()p Fg(R)q(i)p Fj(\))28 b(=)f(\(\010\()p
                1902 Fg(\020)8 b Fj(\)\))2219 1611 y Ff(\000)p Fd(2)3388 1652
                1903 y Fj(\(47\))324 1827 y(where,)34 b(w)m(e)f(recall,)f(the)h
                1904 (relationship)d(b)s(et)m(w)m(een)35 b Fg(R)q(i)e Fj(and)f
                1905 Fg(\020)40 b Fj(is)1609 2091 y Fg(R)q(i)28 b Fj(=)f Fg(\020)1924
                1906 2023 y Fj(\010)1994 2038 y Fe(b)p 1908 2067 138 4 v 1908
                1907 2159 a Fj(\010)1978 2130 y Fd(2)1978 2184 y Fe(m)2083
                1908 2091 y Fj(=)2207 2023 y Fg(\020)p 2196 2067 71 4 v 2196
                1909 2159 a Fj(\010)3388 2091 y(\(48\))324 2361 y(giv)m(en)34
                1910 b(the)g(assumed)h(equalit)m(y)e(of)g(\010)1696 2376 y
                1911 Fe(m)1797 2361 y Fj(and)h(\010)2058 2376 y Fe(b)2093
                1912 2361 y Fj(.)47 b(Solving)33 b(this)g(last)g(expression)i(for)f
                1913 Fg(\020)324 2481 y Fj(as)d(a)h(function)f(of)g Fg(R)q(i)p
                1914 Fj(,)h(one)f(can)h(substitute)g(in)m(to)f(\(47\))g(to)g(obtain)f
                1915 Fg(f)42 b Fj(as)32 b(a)f(function)g(of)324 2602 y Fg(R)q(i)p
                1916 Fj(.)324 2816 y(If)h(one)h(simply)e(used)j(\010)28 b(=)g(1)22
                1917 b(+)g Fg(\014)6 b(\020)39 b Fj(one)33 b(w)m(ould)f(\014nd)h(that)1528
                1918 3036 y Fg(f)11 b Fj(\()p Fg(R)q(i)p Fj(\))28 b(=)f(\(1)22
                1919 b Fc(\000)h Fg(\014)6 b(R)q(i)p Fj(\))2318 2995 y Fd(2)3388
                1920 3036 y Fj(\(49\))324 3256 y(The)37 b(analogous)f(expression)i(for)e(v)m
                1921 (ersion)h(1)f(in)m(v)m(olv)m(es)i(the)f(p)s(ositiv)m(e)f(solution)f(of)
                1922 h(the)324 3377 y(quadratic)1203 3497 y(\()p Fg(R)q(i)1349
                1923 3456 y Ff(\000)p Fd(1)1466 3497 y Fc(\000)22 b Fg(\014)6
                1924 b Fj(\))p Fg(\020)29 b Fj(+)22 b(\()p Fg(R)q(i)1980 3456
                1925 y Ff(\000)p Fd(1)2097 3497 y Fj(+)g(6\))p Fg(\020)29
                1926 b Fc(\000)23 b Fj(1)k(=)h(0)705 b(\(50\))324 3672 y(One)33
                1927 b(can)g(then)g(set)g Fg(K)i Fj(=)27 b(\010)1374 3635
                1928 y Ff(\000)p Fd(2)1469 3672 y Fj(,)33 b(where)h(\010)f(is)f(giv)m(en)g
                1929 (b)m(y)i(\(37\).)324 3886 y(F)-8 b(or)32 b(v)m(ersion)h(2)f(one)h
                1930 (simply)e(gets)1270 4106 y Fg(f)11 b Fj(\()p Fg(R)q(i)p
                1931 Fj(\))27 b(=)h(\(1)22 b Fc(\000)g Fj(5)p Fg(R)q(i)p Fj(\))2047
                1932 4065 y Fd(2)2087 4106 y Fj(;)99 b Fg(R)q(i)28 b(<)f(R)q(i)2560
                1933 4121 y Fe(T)3388 4106 y Fj(\(51\))324 4326 y(and)1101
                1934 4501 y Fg(f)11 b Fj(\()p Fg(R)q(i)p Fj(\))27 b(=)1475
                1935 4355 y Fb( )1668 4433 y Fj(1)21 b Fc(\000)i Fg(\014)6
                1936 b(R)q(i)p 1550 4477 574 4 v 1550 4569 a Fj(1)22 b(+)g(\(5)g
                1937 Fc(\000)h Fg(\014)6 b Fj(\))p Fg(\020)2070 4584 y Fe(T)2134
                1938 4355 y Fb(!)2200 4378 y Fd(2)2256 4501 y Fj(;)99 b Fg(R)q(i)28
                1939 b(>)f(R)q(i)2729 4516 y Fe(T)3388 4501 y Fj(\(52\))324
                1940 4732 y(where)1627 4877 y Fg(R)q(i)1735 4892 y Fe(T)1818
                1941 4877 y Fc(\021)2042 4809 y Fg(\020)2085 4824 y Fe(T)p
                1942 1933 4853 316 4 v 1933 4945 a Fj(1)22 b(+)g(5)p Fg(\020)2194
                1943 4960 y Fe(T)3388 4877 y Fj(\(53\))1894 5251 y(11)p eop
                1944 %%Page: 12 12
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                1961 
                1962 %%BeginProlog
                1963 % MathWorks dictionary
                1964 /MathWorks 160 dict begin
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                1967 /ldef {load def} bind def
                1968 /xdef {exch def} bdef
                1969 /xstore {exch store} bdef
                1970 % operator abbreviations
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                1972 /cc /concat ldef
                1973 /cp /closepath ldef
                1974 /gr /grestore ldef
                1975 /gs /gsave ldef
                1976 /mt /moveto ldef
                1977 /np /newpath ldef
                1978 /cm /currentmatrix ldef
                1979 /sm /setmatrix ldef
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                1981 /rl /rlineto ldef
                1982 /s /show ldef
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                1987 /j /setlinejoin ldef
                1988 /cap /setlinecap ldef
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                1990 /rf {rectfill} bdef
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                2010 /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse
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                2012 /csm {1 dpi2point div -1 dpi2point div scale neg translate
                2013  dup landscapeMode eq {pop -90 rotate}
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                2042   0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef
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                2044   0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef
                2045 /FAn {newpath tMatrix currentmatrix pop translate scale
                2046   0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef
                2047 /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale
                2048   0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef
                2049 /vradius 0 def /hradius 0 def /lry 0 def
                2050 /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def
                2051 /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef
                2052   /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly
                2053   vradius add translate hradius vradius scale 0 0 1 180 270 arc 
                2054   tMatrix setmatrix lrx hradius sub uly vradius add translate
                2055   hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix
                2056   lrx hradius sub lry vradius sub translate hradius vradius scale
                2057   0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub
                2058   translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix
                2059   closepath} bdef
                2060 /FRR {MRR stroke } bdef
                2061 /PRR {MRR fill } bdef
                2062 /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def
                2063   newpath tMatrix currentmatrix pop ulx rad add uly rad add translate
                2064   rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad
                2065   sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix
                2066   closepath} bdef
                2067 /FlrRR {MlrRR stroke } bdef
                2068 /PlrRR {MlrRR fill } bdef
                2069 /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def
                2070   newpath tMatrix currentmatrix pop ulx rad add uly rad add translate
                2071   rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad
                2072   sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix
                2073   closepath} bdef
                2074 /FtbRR {MtbRR stroke } bdef
                2075 /PtbRR {MtbRR fill } bdef
                2076 /stri 6 array def /dtri 6 array def
                2077 /smat 6 array def /dmat 6 array def
                2078 /tmat1 6 array def /tmat2 6 array def /dif 3 array def
                2079 /asub {/ind2 exch def /ind1 exch def dup dup
                2080   ind1 get exch ind2 get sub exch } bdef
                2081 /tri_to_matrix {
                2082   2 0 asub 3 1 asub 4 0 asub 5 1 asub
                2083   dup 0 get exch 1 get 7 -1 roll astore } bdef
                2084 /compute_transform {
                2085   dmat dtri tri_to_matrix tmat1 invertmatrix 
                2086   smat stri tri_to_matrix tmat2 concatmatrix } bdef
                2087 /ds {stri astore pop} bdef
                2088 /dt {dtri astore pop} bdef
                2089 /db {2 copy /cols xdef /rows xdef mul dup 3 mul string
                2090   currentfile exch readhexstring pop
                2091   dup 0 3 index getinterval /rbmap xdef
                2092   dup 2 index dup getinterval /gbmap xdef
                2093   1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef
                2094 /it {gs np dtri aload pop moveto lineto lineto cp c
                2095   cols rows 8 compute_transform 
                2096   rbmap gbmap bbmap true 3 colorimage gr}bdef
                2097 /il {newpath moveto lineto stroke}bdef
                2098 currentdict end def
                2099 %%EndProlog
                2100 
                2101 %%BeginSetup
                2102 MathWorks begin
                2103 
                2104 0 cap
                2105 
                2106 end
                2107 %%EndSetup
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                2117 bplot
                2118 
                2119 /dpi2point 12 def
                2120 portraitMode 0216 7344 csm
                2121 
                2122    95   207  6387  4926 MR c np
                2123 91 dict begin %Colortable dictionary
                2124 /c0 { 0 0 0 sr} bdef
                2125 /c1 { 1 1 1 sr} bdef
                2126 /c2 { 1 0 0 sr} bdef
                2127 /c3 { 0 1 0 sr} bdef
                2128 /c4 { 0 0 1 sr} bdef
                2129 /c5 { 1 1 0 sr} bdef
                2130 /c6 { 1 0 1 sr} bdef
                2131 /c7 { 0 1 1 sr} bdef
                2132 c0
                2133 1 j
                2134 1 sg
                2135    0    0 6918 5185 PR
                2136 6 w
                2137 0 4226 5361 0 0 -4226 899 4614 4 MP
                2138 PP
                2139 -5361 0 0 4226 5361 0 0 -4226 899 4614 5 MP stroke
                2140 4 w
                2141 DO
                2142 SO
                2143 6 w
                2144 0 sg
                2145  899 4614 mt 6260 4614 L
                2146  899  388 mt 6260  388 L
                2147  899 4614 mt  899  388 L
                2148 6260 4614 mt 6260  388 L
                2149  899 4614 mt 6260 4614 L
                2150  899 4614 mt  899  388 L
                2151  899 4614 mt  899 4560 L
                2152  899  389 mt  899  442 L
                2153 %%IncludeResource: font Helvetica
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                2155 
                2156  833 4871 mt 
                2157 (0) s
                2158 1971 4614 mt 1971 4560 L
                2159 1971  389 mt 1971  442 L
                2160 1805 4871 mt 
                2161 (0.2) s
                2162 3043 4614 mt 3043 4560 L
                2163 3043  389 mt 3043  442 L
                2164 2877 4871 mt 
                2165 (0.4) s
                2166 4115 4614 mt 4115 4560 L
                2167 4115  389 mt 4115  442 L
                2168 3949 4871 mt 
                2169 (0.6) s
                2170 5187 4614 mt 5187 4560 L
                2171 5187  389 mt 5187  442 L
                2172 5021 4871 mt 
                2173 (0.8) s
                2174 6260 4614 mt 6260 4560 L
                2175 6260  389 mt 6260  442 L
                2176 6194 4871 mt 
                2177 (1) s
                2178  899 4614 mt  952 4614 L
                2179 6260 4614 mt 6206 4614 L
                2180  731 4703 mt 
                2181 (0) s
                2182  899 2501 mt  952 2501 L
                2183 6260 2501 mt 6206 2501 L
                2184  397 2590 mt 
                2185 (0.05) s
                2186  899  389 mt  952  389 L
                2187 6260  389 mt 6206  389 L
                2188  531  478 mt 
                2189 (0.1) s
                2190  899 4614 mt 6260 4614 L
                2191  899  388 mt 6260  388 L
                2192  899 4614 mt  899  388 L
                2193 6260 4614 mt 6260  388 L
                2194 gs 899 389 5362 4226 MR c np
                2195 1 0 54 0 54 0 53 0 54 0 54 0 53 0 54 0 
                2196 53 0 54 0 54 0 53 0 54 0 53 0 54 0 54 0 
                2197 53 0 54 0 53 0 54 0 54 0 53 0 54 0 54 0 
                2198 53 0 54 0 53 0 54 0 54 0 53 0 54 0 53 0 
                2199 54 0 54 0 53 0 54 0 53 0 54 0 54 0 53 0 
                2200 54 0 54 0 53 0 54 0 53 0 54 0 54 0 53 0 
                2201 54 0 53 0 54 0 54 0 53 0 54 0 53 0 54 0 
                2202 54 0 53 0 54 0 53 0 54 0 54 0 53 0 54 0 
                2203 54 0 53 0 54 0 53 0 54 0 54 0 53 0 54 0 
                2204 53 0 54 0 54 0 53 0 54 0 53 0 54 0 54 0 
                2205 53 0 54 106 54 317 53 528 54 739 53 951 54 1162 16 422 
                2206 1633 389 89 MP stroke
                2207 /c8 { 0.000000 0.000000 1.000000 sr} bdef
                2208 c8
                2209 1 0 54 0 54 0 53 0 54 0 54 0 53 0 54 0 
                2210 53 0 54 0 54 0 53 0 54 0 53 0 54 0 54 0 
                2211 53 0 54 0 53 0 54 0 54 0 53 0 54 0 54 0 
                2212 53 0 54 0 53 0 54 0 54 0 53 0 54 0 53 0 
                2213 54 0 54 0 53 0 54 0 53 0 54 0 54 0 53 0 
                2214 54 0 54 0 53 0 54 0 53 0 54 0 54 0 53 0 
                2215 54 0 53 0 54 0 54 2 53 3 54 5 53 9 54 10 
                2216 54 14 53 16 54 20 53 23 54 26 54 31 53 35 54 40 
                2217 54 45 53 51 54 58 53 66 54 73 54 84 53 94 54 107 
                2218 53 122 54 139 54 160 53 183 54 210 53 244 54 284 54 330 
                2219 53 385 54 451 54 528 32 377 1831 389 85 MP stroke
                2220 1 0 54 1 54 0 53 1 54 1 54 2 53 2 54 2 
                2221 53 3 54 3 54 3 53 4 54 4 53 4 54 5 54 6 
                2222 53 6 54 6 53 6 54 7 54 8 53 8 54 8 54 9 
                2223 53 9 54 10 53 11 54 10 54 12 53 12 54 12 53 13 
                2224 54 14 54 15 53 15 54 15 53 17 54 17 54 18 53 18 
                2225 54 20 54 20 53 22 54 22 53 23 54 25 54 25 53 27 
                2226 54 28 53 29 54 31 54 33 53 34 54 35 53 38 54 40 
                2227 54 42 53 45 54 48 53 50 54 54 54 57 53 61 54 66 
                2228 54 71 53 76 54 83 53 90 54 97 54 107 53 117 54 129 
                2229 53 143 54 159 54 178 53 199 54 225 53 254 54 290 54 331 
                2230 53 380 13 104 1958 389 83 MP stroke
                2231 1 0 54 9 54 10 53 10 54 10 54 10 53 10 54 11 
                2232 53 10 54 11 54 12 53 11 54 11 53 12 54 12 54 12 
                2233 53 13 54 12 53 13 54 14 54 13 53 14 54 14 54 15 
                2234 53 14 54 15 53 16 54 16 54 16 53 16 54 17 53 18 
                2235 54 18 54 18 53 19 54 19 53 20 54 21 54 21 53 22 
                2236 54 22 54 23 53 24 54 25 53 26 54 27 54 28 53 28 
                2237 54 30 53 32 54 32 54 34 53 36 54 37 53 39 54 42 
                2238 54 43 53 46 54 48 53 52 54 54 54 59 53 62 54 66 
                2239 54 72 53 77 54 83 53 90 54 97 54 107 53 117 54 129 
                2240 53 142 54 158 54 175 53 197 54 221 53 249 54 284 25 150 
                2241 2053 389 81 MP stroke
                2242 /c9 { 1.000000 0.000000 0.000000 sr} bdef
                2243 c9
                2244 1 0 54 6 54 6 53 6 54 6 54 6 53 6 54 6 
                2245 53 6 54 6 54 6 53 6 54 7 53 6 54 6 54 6 
                2246 53 7 54 6 53 6 54 7 54 6 53 7 54 6 54 7 
                2247 53 6 54 7 53 6 54 7 54 6 53 7 54 7 53 7 
                2248 54 6 54 7 53 7 54 7 53 7 54 7 54 7 53 7 
                2249 54 7 54 7 53 7 54 7 53 7 54 7 54 7 53 7 
                2250 54 8 53 7 54 7 54 8 53 7 54 7 53 8 54 7 
                2251 54 8 53 7 54 8 53 7 54 8 54 7 53 8 54 8 
                2252 54 7 53 8 54 8 53 8 54 8 54 7 53 8 54 8 
                2253 53 8 54 8 54 8 53 8 54 8 53 8 54 8 54 8 
                2254 53 9 54 8 54 8 53 8 54 519 53 951 54 1162 16 422 
                2255 1633 389 89 MP stroke
                2256 1 1 54 16 54 17 53 18 54 17 54 17 53 17 54 18 
                2257 53 17 54 18 54 18 53 18 54 17 53 18 54 18 54 19 
                2258 53 18 54 18 53 18 54 19 54 18 53 19 54 19 54 19 
                2259 53 18 54 19 53 19 54 20 54 19 53 19 54 20 53 19 
                2260 54 20 54 19 53 20 54 20 53 20 54 20 54 20 53 20 
                2261 54 20 54 20 53 21 54 20 53 21 54 21 54 20 53 21 
                2262 54 21 53 21 54 21 54 21 53 22 54 21 53 21 54 22 
                2263 54 21 53 22 54 22 53 22 54 22 54 22 53 22 54 22 
                2264 54 22 53 23 54 22 53 22 54 23 54 23 53 23 54 22 
                2265 53 23 54 23 54 23 53 24 54 23 53 23 54 24 54 23 
                2266 53 24 54 24 54 23 53 24 54 24 53 24 54 371 16 422 
                2267 1633 389 89 MP stroke
                2268 1 0 54 4 54 4 53 4 54 4 54 5 53 4 54 4 
                2269 53 4 54 4 54 4 53 4 54 4 53 4 54 5 54 4 
                2270 53 4 54 4 53 4 54 4 54 5 53 4 54 4 54 4 
                2271 53 5 54 4 53 4 54 4 54 5 53 4 54 4 53 5 
                2272 54 4 54 4 53 5 54 4 53 5 54 4 54 4 53 5 
                2273 54 4 54 5 53 4 54 4 53 5 54 4 54 5 53 4 
                2274 54 5 53 4 54 5 54 4 53 5 54 4 53 5 54 5 
                2275 54 4 53 5 54 4 53 5 54 5 54 4 53 5 54 4 
                2276 54 5 53 5 54 4 53 5 54 5 54 5 53 4 54 5 
                2277 53 5 54 4 54 5 53 5 54 5 53 5 54 4 54 5 
                2278 53 5 54 5 54 5 53 4 54 518 53 951 54 1162 16 422 
                2279 1633 389 89 MP stroke
                2280 1 1 54 11 54 12 53 12 54 12 54 11 53 12 54 12 
                2281 53 12 54 12 54 12 53 12 54 12 53 12 54 12 54 12 
                2282 53 12 54 13 53 12 54 12 54 12 53 13 54 12 54 12 
                2283 53 13 54 12 53 13 54 12 54 13 53 12 54 13 53 12 
                2284 54 13 54 12 53 13 54 13 53 13 54 12 54 13 53 13 
                2285 54 13 54 13 53 13 54 13 53 13 54 13 54 13 53 13 
                2286 54 13 53 13 54 13 54 13 53 13 54 14 53 13 54 13 
                2287 54 13 53 14 54 13 53 14 54 13 54 13 53 14 54 13 
                2288 54 14 53 14 54 13 53 14 54 13 54 14 53 14 54 14 
                2289 53 13 54 14 54 14 53 14 54 14 53 14 54 14 54 14 
                2290 53 14 54 14 54 14 53 14 54 14 53 14 54 364 16 422 
                2291 1633 389 89 MP stroke
                2292 gr
                2293 
                2294 c9
                2295 0 sg
                2296 2405 5077 mt 
                2297 (Richardsons number) s
                2298  323 2727 mt  -90 rotate
                2299 (f\(Ri\)) s
                2300 90 rotate
                2301 -455 252 4010 1336 2 MP stroke
                2302 12 21 51 -55 -74 14 11 20 3555 1588 5 MP
                2303 PP
                2304 0 0 12 21 51 -55 -74 14 11 20 3555 1588 6 MP stroke
                2305 4112 1369 mt 
                2306 (v2\(0.5,5.0\) ) s
                2307 4349 1675 mt 
                2308 (v2\(0.5,3.0\) ) s
                2309 3161 2540 mt 
                2310 (v1\(2.0\) ) s
                2311 3348 2930 mt 
                2312 (v1\(1.0\) ) s
                2313 3602 3210 mt 
                2314 (v1\(0.5\) ) s
                2315 -212 142 3144 2520 2 MP stroke
                2316 13 20 47 -60 -73 20 13 20 2932 2662 5 MP
                2317 PP
                2318 0 0 13 20 47 -60 -73 20 13 20 2932 2662 6 MP stroke
                2319 -469 360 3314 2897 2 MP stroke
                2320 15 19 42 -62 -71 24 14 19 2845 3257 5 MP
                2321 PP
                2322 0 0 15 19 42 -62 -71 24 14 19 2845 3257 6 MP stroke
                2323 -954 800 3568 3183 2 MP stroke
                2324 16 18 40 -64 -71 28 15 18 2614 3983 5 MP
                2325 PP
                2326 0 0 16 18 40 -64 -71 28 15 18 2614 3983 6 MP stroke
                2327 4875 3307 mt 
                2328 (v2\(1.0,5.0\) ) s
                2329 5223 3535 mt 
                2330 (v2\(1.0,3.0\) ) s
                2331 -62 300 5215 3528 2 MP stroke
                2332 23 4 -8 -75 -38 66 23 5 5153 3828 5 MP
                2333 PP
                2334 0 0 23 4 -8 -75 -38 66 23 5 5153 3828 6 MP stroke
                2335 -83 308 4858 3320 2 MP stroke
                2336 23 6 -5 -75 -41 63 23 6 4775 3628 5 MP
                2337 PP
                2338 0 0 23 6 -5 -75 -41 63 23 6 4775 3628 6 MP stroke
                2339 -550 340 4332 1648 2 MP stroke
                2340 12 20 49 -58 -74 18 13 20 3782 1988 5 MP
                2341 PP
                2342 0 0 12 20 49 -58 -74 18 13 20 3782 1988 6 MP stroke
                2343 
                2344 end
                2345 
                2346 eplot
                2347 %%EndObject
                2348 
                2349 epage
                2350 end
                2351 
                2352 showpage
                2353 
                2354 %%Trailer
                2355 %%EOF
                2356 
                2357 %%EndDocument
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                2363 (of)g Fg(R)q(i)p Fj(.)43 b(The)32 b(notation)e(is)g Fg(v)t
                2364 Fj(1\()p Fg(x)p Fj(\))e Fc(!)i Fj(v)m(ersion)i(1)f(with)324
                2365 2408 y Fg(x)d Fj(=)f Fg(R)q(i)618 2423 y Fe(cr)r(it)764
                2366 2408 y Fj(=)h(1)p Fg(=\014)6 b Fj(,)32 b Fg(v)t Fj(2\()p
                2367 Fg(x;)17 b(y)t Fj(\))26 b Fc(!)32 b Fj(v)m(ersion)h(2)g(with)f
                2368 Fg(x)c Fj(=)g Fg(\020)2436 2423 y Fe(T)2523 2408 y Fj(and)k
                2369 Fg(y)f Fj(=)d Fg(R)q(i)3003 2423 y Fe(cr)r(it)324 2698
                2370 y Fj(One)36 b(can)g(see)h(from)e(the)h(\014gure)h(that)e(v)m(ersion)i
                2371 (2)e(allo)m(ws)g(one)i(to)e(matc)m(h)h(the)g(empiri-)324
                2372 2819 y(cally)26 b(observ)m(ed)j(stabilit)m(y)d(function)h(for)g(w)m
                2373 (eakly)h(stable)f(conditions)g(while)f(still)f(b)s(eing)324
                2374 2939 y(able)35 b(to)h(tune)g(the)h(mixing)c(at)j(large)f(stabilit)m(y)
                2375 -8 b(,)35 b(for)g(whic)m(h)i(there)g(is)e(little)e(empirical)324
                2376 3059 y(guidance)k(and)g(for)f(whic)m(h)i(MOS)f(is)g(presumably)g(in)m
                2377 (v)-5 b(alid)35 b(in)h(an)m(y)i(case.)58 b(In)37 b(v)m(ersion)324
                2378 3180 y(1,)c(if)g(one)g(tries)h(to)f(increase)h(the)g(mixing)d(at)i
                2379 (high)g(stabilities)e(one)j(b)s(egins)f(to)g(depart)324
                2380 3300 y(substan)m(tially)e(from)h(the)h(empirical)c(relation)i(at)h(w)m
                2381 (eak)i(stabilit)m(y)-8 b(.)324 3515 y(In)48 b(addition)e(to)h(pro)m
                2382 (viding)g(a)g(w)m(a)m(y)i(of)e(matc)m(hing)f(an)i(in)m(terior)e
                2383 (di\013usivit)m(y)h(of)g(the)324 3635 y(form)31 b(\(45\),)h(these)i
                2384 (expressions)h(also)d(pro)m(vide)h(a)f(useful)h(w)m(a)m(y)h(of)e
                2385 (thinking)g(ab)s(out)g(the)324 3756 y(strength)g(of)f(the)i(mixing)c
                2386 (in)i(the)h(surface)h(la)m(y)m(er)f(implied)d(b)m(y)j(the)g(similarit)m
                2387 (y)d(pro\014les.)324 4183 y Fk(5)161 b(Implemen)l(tation)52
                2388 b(Notes)324 4496 y Fj(F)-8 b(our)32 b(in)m(terfaces)h(are)f(pro)m
                2389 (vided)h(\(see)h(FMS)f(do)s(cumen)m(tation)e(for)h(details\))469
                2390 4819 y Fc(\017)49 b Fi(mo)p 725 4819 34 4 v 39 w(drag)42
                2391 b Fj(returns)g(drag)f(co)s(e\016cien)m(ts)h(for)e(momen)m(tum,)i(heat,)
                2392 i(and)d(sp)s(eci\014c)568 4940 y(h)m(umidit)m(y)j(using)h(as)h(input)f
                2393 (the)g(heigh)m(t)h(z,)j(the)c(e\013ectiv)m(e)i(wind)e(sp)s(eed)i(at)e
                2394 Fg(z)1894 5251 y Fj(12)p eop
                2395 %%Page: 13 13
                2396 13 12 bop 568 548 a Fj(\(incorp)s(orating)37 b(gustiness\),)43
                2397 b(and)e(the)f(virtual)f(p)s(oten)m(tial)f(temp)s(erature)i(at)g
                2398 Fg(z)568 668 y Fj(and)e(at)g(the)h(surface.)62 b(In)39
                2399 b(addition)d(to)i(the)h(three)g(drag)f(co)s(e\016cien)m(ts,)j(output)
                2400 568 789 y(also)31 b(includes)i Fg(u)1194 804 y Ff(\003)1265
                2401 789 y Fj(and)g Fg(b)1496 804 y Ff(\003)469 992 y Fc(\017)49
                2402 b Fi(mo)p 725 992 34 4 v 39 w(pro\014le)39 b Fj(returns)h(the)f
                2403 (pro\014les)g(of)g(momen)m(tum,)g(heat,)i(and)e(sp)s(eci\014c)g(h)m(u-)
                2404 568 1112 y(midit)m(y)28 b(b)s(elo)m(w)j(heigh)m(t)f Fg(z)t
                2405 Fj(,)i(giv)m(en)e(the)h(three)g(roughness)h(lengths)e(as)h(w)m(ell)f
                2406 (as)g Fg(u)p Fc(\003)p Fj(,)568 1233 y Fg(b)p Fc(\003)p
                2407 Fj(,)35 b(and)g Fg(q)t Fc(\003)p Fj(.)49 b(\(while)34
                2408 b Fg(u)1437 1248 y Ff(\003)1511 1233 y Fj(and)g Fg(b)1743
                2409 1248 y Ff(\003)1818 1233 y Fj(are)h(a)m(v)-5 b(ailable)32
                2410 b(as)j(output)f(from)g(mo)p 3199 1233 30 4 v 34 w(drag,)h
                2411 Fg(q)3522 1248 y Ff(\003)568 1353 y Fj(m)m(ust)d(b)s(e)h(computed)g(b)m
                2412 (y)g(dividing)e(the)i(ev)-5 b(ap)s(oration)31 b(b)m(y)j
                2413 Fg(u)2795 1368 y Ff(\003)2834 1353 y Fj(\))469 1557 y
                2414 Fc(\017)49 b Fi(mo)p 725 1557 34 4 v 39 w(di\013)31 b
                2415 Fj(returns)g(the)g(di\013usivities)e(consisten)m(t)i(with)g(the)f
                2416 (similarit)m(y)e(pro\014les,)568 1677 y(as)k(describ)s(ed)i(b)m(y)f
                2417 (Eqs.)45 b(\(40\))32 b(and)h(\(41\),)f(giv)m(en)g Fg(u)2420
                2418 1692 y Ff(\003)2492 1677 y Fj(and)h Fg(b)2723 1692 y
                2419 Ff(\003)469 1880 y Fc(\017)49 b Fi(stable)p 862 1880
                2420 V 40 w(mix)31 b Fj(returns)j(the)f(function)f Fg(f)11
                2421 b Fj(\()p Fg(R)q(i)p Fj(\))32 b(describ)s(ed)h(b)m(y)h(Eq.)44
                2422 b(\(45\))324 2203 y(The)36 b(relev)-5 b(ance)35 b(of)f(this)h(theory)g
                2423 (to)g(b)s(oundary)g(la)m(y)m(er)g(\015uxes)i(is)d(t)m(ypically)g
                2424 (limited)e(to)324 2324 y Fc(\031)f Fj(10\045)i(of)h(the)h(planetary)e
                2425 (b)s(oundary)i(la)m(y)m(er)f(depth)h(\(PBL\).)g(This)f(n)m(um)m(b)s(er)
                2426 g(seem)h(to)324 2444 y(arise)g(from)f(the)i(fact)f(that)h(O\(1\))e
                2427 (wind)i(turning)f(and)g(stress)i(c)m(hanges)g(o)s(ccur)f(on)f(the)324
                2428 2564 y(scale)25 b(of)h(the)g(PBL,)g(so)g(these)g(are)g(lik)m(ely)f(to)g
                2429 (b)s(e)h(O\(1/10\))e(o)m(v)m(er)j(ther)f(lo)m(w)m(est)g(10)f(p)s(ercen)
                2430 m(t)324 2685 y(of)j(the)i(PBL.\))f(This)h(pro)m(vides)g(strong)f(motiv)
                2431 -5 b(ation)26 b(to)i(place)h(the)h(lo)m(w)m(est)f(mo)s(del)f(lev)m(el)
                2432 324 2805 y(close)k(to)h(the)g(surface,)g(preferably)g(less)g(than)f(50)
                2433 g(meters.)324 3020 y(The)d(assumption)e(is)h(that)g(the)g(di\013eren)m
                2434 (tial)f(stabilit)m(y)f(functions)i(for)g(tracers,)i(suc)m(h)f(as)324
                2435 3140 y(sp)s(eci\014c)k(h)m(umidit)m(y)-8 b(,)32 b(are)g(the)h(same)g
                2436 (as)g(those)g(for)f(buo)m(y)m(ancy)-8 b(,)34 b(or)f(p)s(oten)m(tial)e
                2437 (temp)s(era-)324 3261 y(ture.)42 b(Ho)m(w)m(ev)m(er,)30
                2438 b(the)d(roughness)h(length)e(for)g(tracers)h(can)g(b)s(e)g(di\013eren)m
                2439 (t)f(from)g(that)g(for)324 3381 y(buo)m(y)m(ancy)35 b(or)f(momen)m
                2440 (tum,)e(so)i(that)f(the)h(\014nal)f(pro\014les,)h(and)f(drag)h(co)s
                2441 (e\013cien)m(ts,)g(can)324 3502 y(b)s(e)h(di\013eren)m(t.)51
                2442 b(The)37 b(monin-obukho)m(v)d(length)h Fg(L)g Fj(and)g(the)h(drag)f(co)
                2443 s(e\013cien)m(ts)g(for)g(mo-)324 3622 y(men)m(tum)29
                2444 b(and)h(buo)m(y)m(ancy)j(\(heat\))d(are)g(functions)g(of)f(the)i(momen)
                2445 m(tum)d(and)j(buo)m(y)m(ancy)324 3742 y(roughness)j(lengths.)44
                2446 b(The)34 b(The)f(drag)g(co)s(e\016cien)m(t)g(for)f(tracers)i(is)e(then)
                2447 h(a)g(function)f(of)324 3863 y Fg(L)h Fj(and)f(the)h(roughness)h
                2448 (length)e(for)g(tracer.)324 4078 y(The)e(con)m(v)m(ergence)i(criterion)
                2449 c(is)h(that)g(the)h(c)m(hange)h(in)d Fg(\020)37 b Fj(from)28
                2450 b(the)i(previous)g(iteration)324 4198 y Fg(\016)t(\020)8
                2451 b Fj(,)31 b(satis\014es)j Fg(min)p Fj(\()p Fc(j)p Fg(\016)t(\020)8
                2452 b Fc(j)p Fg(;)17 b Fc(j)p Fg(\016)t(\020)8 b(=\020)g
                2453 Fc(j)p Fj(\))24 b Fg(<)j Fj(1)p Fg(:e)22 b Fc(\000)h
                2454 Fj(04)324 4413 y(Con)m(v)m(ergence)31 b(of)c(the)i(in)m(teration)e(can)
                2455 h(b)s(e)g(slo)m(w)h(when)g Fg(R)2436 4428 y Fe(b)2499
                2456 4413 y Fj(is)e(close)h(to)g Fg(R)3010 4428 y Fe(cr)r(it)3129
                2457 4413 y Fj(.)42 b(T)-8 b(o)28 b(a)m(v)m(oid)324 4533 y(this,)k
                2458 Fg(R)q(i)649 4548 y Fe(b)716 4533 y Fj(is)g(arbitrarily)e(set)j(to)g
                2459 Fg(R)q(i)1663 4548 y Fe(cr)r(it)1814 4533 y Fj(whenev)m(er)i
                2460 Fg(R)q(i)28 b(>)f Fj(0)p Fg(:)p Fj(95)p Fg(R)2729 4548
                2461 y Fe(cr)r(it)324 4748 y Fj(The)35 b(v)-5 b(alue)34 b(of)g(v)m(on)p
                2462 1050 4748 30 4 v 36 w(Karman's)f(constan)m(t)j(is)e(tak)m(en)h(from)e
                2463 (constan)m(ts)p 2925 4748 V 37 w(mo)s(d,)h(as)g(is)g(the)324
                2464 4868 y(v)-5 b(alue)38 b(of)g Fg(g)t Fj(,)i(required)f(to)f(compute)h
                2465 (buo)m(y)m(ancy)i(from)c(the)i(p)s(oten)m(tial)e(temp)s(eratures)324
                2466 4989 y(input)32 b(in)m(to)g(mo)p 919 4989 V 34 w(drag.)1894
                2467 5251 y(13)p eop
                2468 %%Page: 14 14
                2469 14 13 bop 1894 5251 a Fj(14)p eop
                2470 %%Trailer
                2471 end
                2472 userdict /end-hook known{end-hook}if
                2473 %%EOF
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