Energy Balance
Climate Local Meteorology Surface Mass And Energy Exchange Net Mass Balance Dynamic Response Effect on Landscape Changes In Geometry Water Flow
Climate Local Meteorology Surface Mass And Energy Exchange Net Mass Balance Dynamic Response Effect on Landscape Changes In Geometry Water Flow
Accumulation - Ablation = Mass Change Calving Wind Erosion Sublimation Melt
Mass Balance IN OUT Mass Analogy for heat balance
Surface Energy Balance Radiation Turbulent (wind) exchange Mass Conduction
Surface Energy Balance Radiation Mass Shortwave Longwave
Surface Energy Balance Turbulent (wind) exchange 1. Sensible Heat Mass 2. Latent Heat
FLUXES: ATMOSPHERE - GLACIER 0 = S (1 ) + L - L + Q H + Q L + Q m S a L L Q H Q L Q m short-wave incoming radiation flux albedo of the surface long-wave incoming radiation flux long-wave outgoing radiation flux sensible heat flux latent heat flux phase change Greuell, 2003
Short Wave Radiation S ( 1 α ).net shortwave radiation S α short-wave incoming radiation flux albedo of the surface
Antarctic Snow ~ 0.8
Clean Ice ~ 0.5
DIRTY ICE ~ 0.2 Pasterzeglet
Midtalsbreen 2009
Long Wave Radiation L - L L L long-wave incoming radiation flux long-wave outgoing radiation flux
SHORT- AND LONG-WAVE RADIATION 1 Black body radiation Q = T 4 Normalized irradiance 0.8 0.6 0.4 0.2 0 T = 5780 K sun T = 290 K Earth Q flux (irradiance) Stefan Boltzmann constant (5.67. 10-8 W m -2 K -4 ) temperature Q = ε T 4 0.1 1 10 100 Wavelength (µm) ε emmisivity Greuell, 2003
TURBULENT FLUXES Q H + Q L Vertical transport of properties of the air by eddies Turbulence is generated by wind shear (du/dz) Turbulent fluxes increase with wind speed Heat: sensible heat flux, Q H Water vapor: latent heat flux, Q L Greuell, 2003
SENSIBLE HEAT FLUX (Q H ) Q H a C pa ln z z 0 2 mz L ob u T T s ln z hz z T calculated with the bulk method L ob a C pa air density specific heat capacity of air k von Karman constant u wind speed T air temperature at height z T s surface temperature z 0 momentum roughness length z T roughness length for temperature m, h constants L ob Monin-Obukhov length (depends on u and T-T s ) z Greuell, 2003
LATENT HEAT FLUX (Q L ) Q L a L s 2 u q q s ln z z m ln z z 0 L ob z q calculated with the bulk method h z L ob a L s air density latent heat of sublimation k von Karman constant u wind speed q specific humidity at height z q s surface specific humidity z 0 roughness length for velocity z q roughness length for water vapor m, h constants L ob Monin-Obukhov length (depends on u and T-T s ) Greuell, 2003
measure short-wave radiation with a pyranometer (glass dome) INSTRUMENTS measure sensible heat flux with a sonic anemometer measure long-wave radiation with a pyrgeometer (silicon dome) Greuell, 2003
ZERO-DEGREE ASSUMPTION Assumption: surface temperature = 0 C Leads to: Q 0 > 0: Q 0 is consumed in melting Q 0 0: nothing occurs Assumption okay when melting conditions are frequent Not okay when positive Q 0 causes heating of the snow (spring, early morning, higher elevation)
1000 Diurnal Variation site on glacier ice in summer 800 short wave in Energy flux (W/m 2 ) 600 400 200 0 sensible heat long wave in latent heat -200 long wave out short wave out -400 0 4 8 12 16 20 24 Time Greuell, 2003
NET FLUXES Energy flux (W/m 2 ) 700 600 500 400 300 200 100 0-100 net short wave sensible heat latent heat net long wave 0 4 8 12 16 20 24 Time
R = net radiation S = sensible heat L = latent heat G = ground heat flux M = melt POSTIVE FLUX IS TOWARDS THE SURFACE
ENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher Energy flux in W/m 2 300 250 200 150 100 50 net shortwave net longwave sensible heat latent heat 0-50 A1 2205 m =0.21 T=6.8ÞC U2 2310 m =0.29 T=6.4ÞC U3 2420 m =0.25 T=7.1ÞC U4 2945 m =0.59 T=3.5ÞC U5 3225 m =0.59 T=3.2ÞC o C o C o C o C o C Greuell, 2003
Effect of Solar Radiation Google Maps Rueters
Effect of Solar Radiation 200 Stream flow 200 Stream flow 150 150 Discharge (l/s) 100 Discharge (l/s) 100 50 50 0 Anderson Stream 6:00 12:00 18:00 0:00 6:00 0 Canada Stream 6:00 12:00 18:00 0:00 6:00 N W E S Bomblies (2000) Jan 2, 1994
Effect of Solar Radiation, Turbulent Exchange Dec-Jan 1996-1997 Ablation 27.4 cm Sublimation 1.8 cm Melt 25.7 cm Ablation 5.2 cm Sublimation 3.5 cm Melt 1.7 cm Cliff area accounts for 2% of the ablation zone. But cliff melt accounts for 15-20% of the runoff Lewis et al. (1999)
Effect of Solar Radiation, Turbulent Exchange 1.5m Penitentes are the name of the caps of the nazarenos; literally Neve Penitentes Upper Rio Blanco, Argentina Photo: Arvaki those doing penance for their sins. Photo: Sanbec Wikipedia Wikipedia Mount Rainier Notice the tilt angle 0.5 m tall. person Photo: Mark Sanderson Wikipedia
Statistical Model 1 of 2 DEGREE-DAY METHOD M = T pdd M: melt : degree-day factor [mm day -1 K -1 ] T pdd : sum of positive daily mean temperatures Why does it work: - net long-wave radiative flux, and sensible and latent heat flux ~ proportional to T - feedback between mass balance and albedo Advantages: - computationally cheap - input: only temperature needed Disadvantages: - more tuning to local conditions needed: e.g. b depends on mean solar zenith angle - only sensitivity to temperature can be calculated
Statistical Model 2 of 2 REGRESSION MODELS M n = c 0 + c 1 T s + c 2 P w M n : c i : T s : P w : mean specific mass balance coefficients determined by regression analysis Annual mean summer temperature Winter Precipitation
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