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<br />EM 1110-2-1406
<br />5 Jan 60
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<br />Precise computation of back radiat: <, -;lll :11' atmosphere with clear skies is complex and
<br />far too cumbersome for practical use in . [,', r1""'ogy. It has been found experimentally that,
<br />over snow, a simple air temperature functie.j"[ if', :l([l.'t/uate to express downward longwave radiation
<br />with clear skies, because of the fest (~ct(',' " -_~~p j;l vapor pre~sure norma.lly experi(~nced in tbese
<br />conditions. This j-g expressed by the rqu<ltion
<br />
<br />R,~- (1 7G~n (lysfmin)
<br />
<br />(5)
<br />
<br />The net exchange by long""nvl'; raJiat.l':ljl i..;; then
<br />
<br />l? -"-GoT:-OA,59 (h'sfmin)
<br />
<br />(6)
<br />
<br />\Vith low clouds or und~l' t~;, ;'\'fcst, the downward longwave radiation is a function of the
<br />temperature of the under "u:t..':. : :'1 tbe r",.linting body, The !let excbange is given by tbe formula
<br />
<br />R.=uT:---O..l59 (l.ve/min)
<br />
<br />(7)
<br />
<br />It may usuall, '.". "-"""..r1 tliat the undersurface forest temperature is equal to the free air
<br />tempe;ature, '1'1"," at'" "tJiles to low clouds whose base is less than 1,000 feet above the surface.
<br />E':aJ""tic.,' of he"'- ,'-.;c;lllnge to the snowpack by longwave radiation can be further simplified
<br />by assilming u linenr relationship between longwave radiation and air temperature. This is very
<br />nearly irue .)1' the i",,;u',: range of temperature (in degrees absolute) that is normally experienced
<br />in '.:nowflJdt eorql1JiatlOr:.. \Vith clear skies in the open, the simplified formula for heat exchange
<br />to n mdtiIl~~ s :'\\'.':1:1('k by longwave radiation ('l:in be expressed as
<br />
<br />M,,=0,0212(T.-32) -0.84
<br />
<br />(8)
<br />
<br />where M" is the daily snowmelt in inches and T. is the air temperature over the snow surface at
<br />tbe 10-foot level, in OF, The daily snowmelt by longwave radiation under the forest canopy for
<br />a melting snowpack is
<br />
<br />M,,=O,029(T.-32)
<br />
<br />(9)
<br />
<br />Similarly, with low clouds with a complete cloud cover (as would be experienced during rain-on-
<br />snow),
<br />
<br />M,,~0.029(T,-32)
<br />
<br />(10)
<br />
<br />where T, is the temperature of the cloud base, in OF. The cloud base temperature may be esti-
<br />mated from atmospheric soundings, or by applying temperature lapse rate corrections to surface
<br />air temperatures. For cases where the cloud base is less than 1,000 feet above the snow surface,
<br />it may be assumed that the cloud base temperature is equal to the surface air temperature at
<br />normal instrument height level.
<br />
<br />2-07. ENERGY EXCHANGE FROM THE ATMOSPHERE. For c!ear-weather, springtime
<br />snowmelt, energy exchange by the process of turbulent exchange from the atmosphere is of secondary
<br />importance compared with radiation, In winter rain-on-snow conditions, howeyer, turbulent
<br />exchange is the dominant heat exchange process. It involves the transfer of sensible heat from
<br />warm air advccted over the snowfield (convection), and also the heat of condensation of water
<br />vapor from the atmosphere condensed on the snow surfaces (condensation). Computation of
<br />heat exchange from the atmosphere is complex from a theoretical standpoint, and exchange coeffi-
<br />cients arc derived empirically from controlled cxperiments, The following pragraphs present
<br />equations of convection and condensation melt, including coefficients derived from observations
<br />of t.he snow investigations. .F'inally, a simplified combined general equation of convection-conden-
<br />sation melt, in terms of commonly observed data, is shown. Reference is made to chapter 5 of
<br />the summary report for a description of the theory,
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