Energy Balance
WaterFlow
Climate
Local Meteorology
Surface MassAnd
Energy Exchange
Net Mass Balance
Dynamic Response
Changes In
GeometryEffect onLandscape
WaterFlow
Climate
Local Meteorology
Surface MassAnd
Energy Exchange
Net Mass Balance
Dynamic Response
Changes In
GeometryEffect onLandscape
Accumulation - Ablation = Mass Change
CalvingWind Erosion
SublimationMelt
Mass
Mass Balance
IN OUT
Analogy for heat balance
Mass
Surface Energy Balance
Conduction
Radiation
Turbulent (wind) exchange
Mass
Surface Energy Balance Radiation
Shortwave Longwave
Mass
Turbulent (wind) exchange
Surface Energy Balance
1. Sensible Heat
2. Latent Heat
S short-wave incoming radiation fluxa albedo of the surfaceL long-wave incoming radiation fluxL long-wave outgoing radiation fluxQH sensible heat fluxQL latent heat fluxQm phase change
FLUXES: ATMOSPHERE - GLACIER
0 = S ( 1 – ) + L - L + QH + QL + Qm
Greuell, 2003
S ( 1 – α ) ….net shortwave radiation
Short Wave Radiation
S short-wave incoming radiation flux
α albedo of the surface
Antarctic Snow
~ 0.8
~ 0.5Clean Ice
DIRTY ICE~ 0.2
Pasterzeglet
Midtalsbreen 2009
L - L
Long Wave Radiation
L long-wave incoming radiation flux
L long-wave outgoing radiation flux
SHORT- AND LONG-WAVE RADIATION
Q = T4
Q flux (irradiance) Stefan Boltzmann
constant (5.67.10-8 W m-2 K-4)
temperature
0
0.2
0.4
0.6
0.8
1
0.1 1 10 100
Black body radiation
Nor
mal
ized
irra
dian
ce
Wavelength (µm)
T = 5780 Ksun
T = 290 KEarth
Greuell, 2003
Q = εT4
ε emmisivity
TURBULENT FLUXES
Vertical transport of properties of the air by eddiesTurbulence is generated by wind shear (du/dz)Turbulent fluxes increase with wind speed
Heat: sensible heat flux, QH
Water vapor: latent heat flux, QL
Greuell, 2003
QH + QL
SENSIBLE HEAT FLUX (QH)
QH a Cpa 2 u T Ts
ln zz0
mzLob
ln zzT
hzLob
a air densityCpa specific heat capacity of airk von Karman constantu wind speedT air temperature at height zTs surface temperaturez0 momentum roughness lengthzT roughness length for temperaturem, h constantsLob Monin-Obukhov length (depends on u and T-Ts)
calculated with the “bulk method”
Greuell, 2003
z
QL a Ls 2 u q qs
lnz
z0
mzLob
lnzzq
hzLob
LATENT HEAT FLUX(QL)
a air densityLs latent heat of sublimationk von Karman constantu wind speedq specific humidity at height zqs surface specific humidityz0 roughness length for velocityzq roughness length for water vaporm, h constantsLob Monin-Obukhov length (depends on u and T-Ts)
calculated with the “bulk method”
Greuell, 2003
INSTRUMENTSmeasure short-wave radiation
with a pyranometer (glass dome)
measure long-wave radiationwith a pyrgeometer (silicon
dome)
measure sensible heat fluxwith a sonic anemometer
Greuell, 2003
ZERO-DEGREE ASSUMPTION
Assumption: surface temperature = 0˚C
Leads to:Q0 > 0: Q0 is consumed in meltingQ0 ≤ 0: nothing occurs
Assumption okay when melting conditions are frequent
Not okay when positive Q0 causes heating of the snow (spring, early morning, higher elevation)
Diurnal Variation
site on glacier ice in summer
-400
-200
0
200
400
600
800
1000
0 4 8 12 16 20 24
Ener
gy fl
ux (W
/m2 )
Time
short wave in
short wave out
long wave in
long wave out
sensible heat
latent heat
Greuell, 2003
NET FLUXES
-100
0
100
200
300
400
500
600
700
0 4 8 12 16 20 24
Ener
gy fl
ux (W
/m2 )
Time
net short wave
net long wave
sensible heat
latent heat
R = net radiation
S = sensible heat
L = latent heat
G = ground heat flux
M = melt
POSTIVE FLUX IS TOWARDSTHE SURFACE
ENERGY BALANCE AT 5 ELEVATIONSPasterzegletscher
U53225 m=0.59
T=3.2ÞC
-50
0
50
100
150
200
250
300net shortwavenet longwavesensible heatlatent heat
Ener
gy fl
ux in
W/m
2
A12205 m=0.21
T=6.8ÞC
U22310 m=0.29
T=6.4ÞC
U32420 m=0.25
T=7.1ÞC
U42945 m=0.59
T=3.5ÞCGreuell, 2003
oCoC oC oC oC
Effect of Solar Radiation
Google Maps Rueters
0
50
100
150
200
6:00 12:00 18:00 0:00 6:00
Dis
char
ge (l
/s)
Canada Stream0
50
100
150
200
6:00 12:00 18:00 0:00 6:00
Disc
harg
e (l/
s)
Anderson Stream
N
EW
S
Jan 2, 1994Bomblies (2000)
Effect of Solar Radiation
Stream flow Stream flow
Cliff area accounts for 2% of the ablation zone.
But cliff melt accounts for15-20% of the runoff
Ablation 27.4 cmSublimation 1.8 cmMelt 25.7 cm
Ablation 5.2 cmSublimation 3.5 cmMelt 1.7 cm
Dec-Jan 1996-1997
Lewis et al. (1999)
Effect of Solar Radiation, Turbulent Exchange
Penitentes are the name of the caps of the nazarenos; literally Neve Penitentes Upper Rio Blanco, Argentina Photo: Arvakithose doing penance for their sins. Photo: Sanbec Wikipedia Wikipedia
1.5m
Effect of Solar Radiation, Turbulent Exchange
Mount Rainier Notice the tilt angle0.5 m tall.
person
Photo: Mark Sanderson Wikipedia
DEGREE-DAY METHOD
M = Tpdd M: melt: degree-day factor [mm day-1 K-1]Tpdd: 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 1 of 2
REGRESSION MODELS
Mn = c0 + c1Ts + c2Pw
Mn: mean specific mass balance
ci: coefficients determined by regression analysis
Ts: Annual mean summer temperature
Pw: Winter Precipitation
Statistical Model 2 of 2
End