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<br />EM 1110-2-1406
<br />5 Jan 60
<br />
<br />2-<08. CONVECTION MELT. Tile principal variables affecting convcctive heat exchange are
<br />thc temperature gradient of the atmosDh"rc measured above the snow surfaec and the corresponding
<br />wind sp('('d. A seeondary factor iG the density of the atmosphere, which may be expressed as a
<br />function of all' presnrc, Thc folle,wing cq\:ation expresses the melt of a ripe snowpack (thermal
<br />quality=0.(7) by convection:
<br />
<br />e
<br />
<br />J1I,~O.OOr,~O(ii/p,J (Z"b)-I!G(T,-' 1',) (l'b)
<br />
<br />(11)
<br />
<br />wLen ~~fc is lhe daily snowmelt by convection in inches; p ilnd Po arc the air pressures at the location
<br />and at sea level, respectively; Za ilnd z~ arc the heights of mc,lsuremcnt, in feet above the sno\v sur-
<br />facc, of :lir t.emperature and 'wind 3p(~cd, rrspcdivply; 1:1 is the nil' temperature in of.; Ts is the
<br />snow surface temperature in of. (bere 320 F.); and Vb is the wind sp('(>d in miles per hour.
<br />
<br />2-09. CONDENSATION MELT. The cquation for computing condensation melt is similar in
<br />form to that for ron'.'l,ctioIl melt. The VltpOr prrssuro gradieIlt and the wind speed are the prime
<br />v;1'''iables, as ShO\VIl in the following C'q ua tio1l:
<br />
<br />Jf~:= 0.05..:1- (::a:::'~) -l/U(e a -. e 8) I"b
<br />
<br />(12)
<br />
<br />v.:hcn JJe is the daily snowmelt hy cOIHlc'Tbation in illch('s.. 2a and 2b arc the heights of meaSlll'Cment
<br />in feet above the snow surface, of t.he airvapor pressurp and wind speed, fesp<.'ctivdy; ea is the
<br />air vapor pressure in i~l('l1('s,: and ('s is t.he snow surface Ya[lOl' pressure in mb (G.II mb for a melting
<br />snow surface); and 1'" is the wind speed in miles p('r hOllr.
<br />
<br />2-10. SIMPLIFIED EQUATION FOR CO:\TVECTION-CONDENSATION MELT.
<br />bined equation for cOflvection-condpllsatioIl melt (.lIef) is obtained frorn equations
<br />above, to give
<br />
<br />The eom-
<br />II and 1~,
<br />
<br />.M,,= 0.00629 (z"z,) -I/O[ (1',-- :J2) 1'.'1'0'- S..30 (c"- G.l1'!]r,
<br />
<br />(13)
<br />
<br />e
<br />
<br />where Jfce is the total conYection-(,oI}{len~atioll Itwlt in i~lcll('s per Jay. It is possible to simplify
<br />this equation by mnking ('ert,lin approxim:Jtions \vhich an' \n,ll within the limit:-> of hydrologic
<br />accuracy. The air dt>nsity factor, (xpl'cssrd by t 11(' ratio pipo. may vury from 1.0 at sea le\-el to 0.7
<br />at lO,OO(J fed in C'1C'vation. For Illountainous al'l'n~, ,1 COI13ttWt value of 0.8 l\lay be assumed, \vhich
<br />is adequate for gl'Ill'I'al use when con::::idcring thllt it afi"t,t'ts only cOIlV('cti\"e melt, and that COIlH'cti,:m
<br />is small I'l'htive to uther mPlt. factors. AlIotlwr simplifying nssumption is allowing dcwpoint
<br />ternpcratul'(.g to represent vnpor prC:'>SUfCS, by liSt' of :In averagc> lirH'nr relationship \vitbin the
<br />range normally CllC.clHltf>rcd in sno,," hydrology. The lIlrIt ('quat ion may also be simplified -by
<br />specifying the levels of mcasun>IlH'nts of the metC'ornlogic variables. "[Tnder these assumptions,
<br />equation 13 becomes
<br />
<br />M,,~ O.0084r[O.~~ (1', --3~) + 0 ~s (T,,- :3~)]
<br />
<br />(14)
<br />
<br />when Ta and Td 111'(' the mean air I.tnd dewpoint tcmperature's, n'spectivcly, in
<br />level; and v is the It1l'an \vind speerl in miles pCI' hour nt. the 50-foot level.
<br />
<br />OF. at tbe 10-foot
<br />
<br />8
<br />
<br />e
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