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<br />EM 1ll~2--1406
<br />5 Jan 60
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<br />CHAPTER 2
<br />THEORY OF S]\'OWMELT AT A POINT
<br />
<br />2-01. GENERAL. Evaluating snowmelt on a theoretical basis is a problem of heat transfer involv-
<br />ing radiation, cOllypctiorl, find conduetioll. The relat.ive importance of each of these processes of
<br />hpnt trnnsfl~r is highly vnrinblt', depending upon conditions of weather and local environment.
<br />Heat transfer is ulmost Ill'Vel' a measured quantity ill project basins, and knowledge of its magnitude
<br />has lwrll drrived primurily from laboratory experiments. From such measurements, however, the
<br />gencral equations and coefficients have bCP!l derived for point evaluation of snowmelt.
<br />
<br />2-02. SOURCES OF HEAT. The natural sources of heat in melting snolV are:
<br />a. Absorbed solar radiation, fIrs.
<br />b. Xct longw:lYc (tcrrestial) radiatioH, I-ITl'
<br />e, Convection beat transfer from the air, H,.
<br />d. La tent heat of vapoJ'ization by condensation from the air, Fl"
<br />c. Conduction of IH'at from the ground, IIg.
<br />f. H{lnt contrllt of rain \Yuter, Hp.
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<br />Of thesc, held, from the ground is lIsunIly Jlcgligible. The summation of the net exchange lrom
<br />nIl sources of heat l'('prc'sC'nts the alllollnt of energy available for melting the snowpnck, and may
<br />he rxpl'l'ssed by the g(\tH'ral formula,
<br />
<br />:Ell
<br />M~20:W
<br />
<br />(I)
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<br />in \d,irh J[ is snowmelt in inch,'s of water equivalent, :EH is the ulgebrnic snm of all heat compo-
<br />11(,llt~" in calories per squnrr ccntimctrr, and B is the "thermal quality," which is equal to the
<br />!',ltio of hent required to melt a unit ,yeight of the snow to that of ice at 00 C. The constant 203
<br />is the numlH'l' of caloril's per square centimC'ter required to melt 1 inch of ,vater equivalent of ice
<br />nl no C. (SO cal,/gmX2.5.! ('Ill/in).
<br />
<br />2-03. THEIC\IAL Q{;ALITY. A melting snowpack cousists of a mixture of ice and a small
<br />qnnntity of free lmter. The relative proportion of ice is the thermal qllality of such a snowpaek,
<br />The latent heat of fusion of \\"111('1' (the ('!lergy required to change its state from ice to water) is 80
<br />cnloril\s })('1' gralll, aud a sllowpack containing no freo water has a thermal quality of 1.0. After
<br />llldt. has brgull, there is SOllie water held within the snow matrix after drainage. Heat energy
<br />melting th(' ~IlO\rp(ll'k will tIH-'l'l'[Ol'l' rdr:lsr the free wairI' held within it, so that t.he amount of
<br />IH'ut I't'quil't'd to r('l('a~(' 1 gram of \yatel' is sOIlH'what less tha1l80 calories. For a melting snowpack,
<br />aftN' [['('t' drainage b~? grayily for srvt'I'nl hOllr~, the thermal quality normally avrragcs between
<br />0.D5 and (I,Di, corresponding to :3 to 5 percent liquid water. The thermal quality may be far
<br />loweI' ill l'xtrClllf' case::; when' watet' Cllllllot drain freely, as in shallmv snowpacks in the plains.
<br />
<br />2-04. SOLAR RADIATIOX. ClII"(" (,IIO,.t\\"a1'c) radiation is the primc source of all energy at
<br />tlll' Cllrth's sUl'face. TIll' alllOlIllt of beat traIlsferred to the stlowpack by solar radiation varies
<br />with latitude, f'('n~oll. tillH' of (h~~, atrnosph('rie conditions, forC'st cover, and reflectivity of the snow.
<br />The intensity oj' incident ~()Lr 'l{li,ltion just aboye the earth's atmosphere and normal to the
<br />path of radiation is virtu'llly C,I[\,t'\Ilt at UH langleys (ral(sq cm) per minute. Eigure 1 shows
<br />tIw 8(';(50Ilnl and latitudinal variation of solar radiation on a horizontal surface, just ahove the
<br />(,<l1'tl1'5 atJl]o:~:']\I'l'l'. Fig'lIJ'(' 2 indicates the av{'rag-c atlllosphC'ric depIction of insolation \vith
<br />cl~udl('ss skil'''' :It C(,Hlml ~i()I'I'n Sno\v Laboratory (lat. 39022' N). By far the hlrgrst yarintions
<br />in tl", portioJl III ",la,. nllliation transmitted by the atmo,plll'r(' are cansed by clouds, alld direct
<br />nH'<l~lln'llH\nr .! ,-,oIar LldiiLtion principally reflects the efl'ect of ckplctioll by clouds. Inllsmuch
<br />HS s\I('11 Jll'.:i.,:ll'l'Jl\cnh <In' not gt'Il('ndly available for a project basiIl) it is usually ncccssllry to
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