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Page 1: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Energy Balance

Page 2: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

WaterFlow

Climate

Local Meteorology

Surface MassAnd

Energy Exchange

Net Mass Balance

Dynamic Response

Changes In

GeometryEffect onLandscape

Page 3: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

WaterFlow

Climate

Local Meteorology

Surface MassAnd

Energy Exchange

Net Mass Balance

Dynamic Response

Changes In

GeometryEffect onLandscape

Page 4: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Accumulation - Ablation = Mass Change

CalvingWind Erosion

SublimationMelt

Page 5: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Mass

Mass Balance

IN OUT

Analogy for heat balance

Page 6: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Mass

Surface Energy Balance

Conduction

Radiation

Turbulent (wind) exchange

Page 7: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Mass

Surface Energy Balance Radiation

Shortwave Longwave

Page 8: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Mass

Turbulent (wind) exchange

Surface Energy Balance

1. Sensible Heat

2. Latent Heat

Page 9: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 10: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

S ( 1 – α ) ….net shortwave radiation

Short Wave Radiation

S short-wave incoming radiation flux

α albedo of the surface

Page 11: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Antarctic Snow

~ 0.8

Page 12: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

~ 0.5Clean Ice

Page 13: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

DIRTY ICE~ 0.2

Pasterzeglet

Page 14: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Midtalsbreen 2009

Page 15: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

L - L

Long Wave Radiation

L long-wave incoming radiation flux

L long-wave outgoing radiation flux

Page 16: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 17: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 18: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 19: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 20: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 21: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible
Page 22: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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)

Page 23: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 24: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 25: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

R = net radiation

S = sensible heat

L = latent heat

G = ground heat flux

M = melt

POSTIVE FLUX IS TOWARDSTHE SURFACE

Page 26: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 27: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

Effect of Solar Radiation

Google Maps Rueters

Page 28: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 29: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 30: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 31: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 32: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

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

Page 33: Energy Balance - Portland State UniversityENERGY BALANCE AT 5 ELEVATIONS Pasterzegletscher U5 3225 m =0.59 T=3.2ÞC-50 0 50 100 150 200 250 300 net shortwave net longwave sensible

End