Karthaus, September 2005

Wouter Greuell

Institute for Marine and Atmospheric Research Utrecht (IMAU)Utrecht University, the Netherlands

AIM:

Calculate surface mass balance from data collected at a

climate station (not on the glacier)

MASS-BALANCE MODELLING

SURFACE ENERGY BALANCE

Energy exchangewith atmosphere

melting /freezing

heating / coolingof the ice or snow

Q0 =L f

dmdt

+M icpi

dTi

dt [Wm−2]

Q0 energy flux atmosphere to glacierLf latent heat of fusion (0.334.10-6 J kg-1)m amount of melt waterMi mass of the icecpi specific heat capacity of ice (2009 J kg-1 K-1)Ti ice temperature

S short-wave incoming radiative flux albedo of the surfaceL long-wave incoming radiative fluxL long-wave outgoing radiative flux

QH turbulent flux of sensible heat

QL turbulent flux of latent heat

QR heat flux supplied by rain.

FLUXES ATMOSPHERE TO GLACIER

Q0 = S ( 1 – ) + L - L + QH + QL + QR

-50

0

50

100

150

200

A4 A5 I6 U8 U9 R2 R5

E meltSWnetLWnetturb flux

energy flux (W m

-2 )

(1100) (1140)(715)(279) (381) (1210) (870)

COMPONENTS OF THE ENERGY BALANCE7 LOCATIONS - VATNAJOKULL

QuickTime™ and a

Photo CD Decompressor

are needed to use this picture AUTOMATIC WEATHER STATION

MODEL INPUTMEASUREMENTS AND OBSERVATIONS AT A CLIMATE STATION NEAR THE GLACIER

In case of energy-balance model, input may consist of:

To determine ablation- 2 m temperature- 2 m wind speed- 2 m humidity- cloud amount

To determine accumulation- precipitation

TRANSFER FORCING FROM CLIMATE STATION TO GLACIER

T, u, q, n, p

T, u, q, n, p

T, u, q, n, p

T, u, q, n, p

glacier

TRANSFER FORCING FROM CLIMATE STATION TO GLACIER

Variable assumption

temperature constant lapse rate, i.e. dT/dz constant

wind speed constant

humidity constant relative humidity

cloud amount constant

precipitation linear in elevation (used for tuning)

Some commonly used assumptions

2 D PICTURE OF THE TEMPERATURE

In case the surface is melting

Surface: temperature = 0 ˚C

Boundary layer: temperature compromise between

surface (0 ˚C) and free atmosphere (> 0 ˚C)Free atmosphere

dT/dz = constant (e.g. -0.007 K/m)

dT/dz = 0

dT/dz = ?

ACTUAL TEMPERATURE VARIATION

3.5

4

4.5

5

5.5

6

6.5

7

7.5

2000 2200 2400 2600 2800 3000 3200 3400

Temperature on glacier (˚C)Sonnblick

2 m temperature (˚C)

Elevation (m a.s.l.)

stations along the glacier

A1

U3

U2

stations alongthe glacier

U5U4

Sonnblickclimate station

averages over 46 days of the ablation season, Pasterze, Austria

Constant lapse-rate

can be a bad

description,

because:

gentleslope

steepslope

gentleslope

ACTUAL TEMPERATURE VARIATION

3.5

4

4.5

5

5.5

6

6.5

7

7.5

2000 2200 2400 2600 2800 3000 3200 3400

Temperature on glacier (˚C)Sonnblick

2 m temperature (˚C)

Elevation (m a.s.l.)

stations along the glacier

A1

U3

U2

stations alongthe glacier

U5U4

Sonnblickclimate station

averages over 46 days of the ablation season, Pasterze, Austria

Constant lapse-rate

can be a bad

description,

because:

1) Air over glacier

colder than over

snow-free terrain

2) No constant lapse

rate over glacier

gentleslope

steepslope

gentleslope

4

5

6

7

8

9

10

-2 0 2 4 6 8Temperature (˚C) on glacier (2205 m a.s.l.)Temperature (˚C) at climate station (3106 m a.s.l.)

MEASURED CLIMATE SENSITIVITY

Constant lapse-rate

can be a bad

description,

because:

3) Climate

sensitivity over

glacier smaller

than over snow-

free terrain

46 daily means during the ablation season, Pasterze, Austria

ALTERNATIVE DESCRIPTIONS TEMPERATURE ALONG GLACIER

De Ruyter de Wildt, M. S., J. Oerlemans and H. Björnsson, 2003: A calibrated mass balance model for Vatnajökull, Iceland. Jökull, 52, 1-20.

Greuell, W. and R. Böhm, 1998: Two-metre temperatures along melting mid-latitude glaciers and implications for the sensitivity of the mass balance to variations in temperature. J. Glaciol., 44 (146), 9-20.

Oerlemans, J. and B. Grisogono, 2000: Glacier wind and parameterisation of the related surface heat flux. Tellus, A54, 440-452.

SHORT-WAVE INCOMING RADIATIVE FLUX

Calculation of:

- Incidence angle (date, time, location, slope)

- Transmission through clear-sky atmosphere (water vapour)

- Multiple reflection (surface albedo)

- Cloud transmission (cloud amount)

CLOUD FACTOR

causes largest uncertainty in calculated incoming short-wave radiation

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 0.2 0.4 0.6 0.8 1

Cloud factor

Cloud amount

PasterzeAustria2205 m Greenland

250 m

Greenland2000 m

Antarctica1200 m

αsnow(i) = αfirn + (αfrsno - αfirn) exp s-it*

α(i) = αsnow(i) + {αice - αsnow(i)} exp -dd*

This model has five parameters:

αice

αfrsno

αfirn

d*

t*Oerlemans and Knap, 1999

ALBEDO PARAMETERISATION

DIRTY ICE - PASTERZE

~ 0.2

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CLEAN ICE - GREENLAND ICE SHEET

~ 0.45

FEEDBACK ALBEDO SNOW AND ICE MELT

Lower albedo

More melt

1) Faster metamorphosis of snow

2) Ice appears earlier3) More meltwater on top of ice4) More water between snow grains

Net short-wave radiation

GLACIER SHOULD THEORETICALLY NOT BE SENSITIVE TO TEMPERATURE CHANGE

Because

i) Net short-wave

radiation dominates the

surface energy balance

ii) Net short-wave

radiation is not a

function of the

temperature

HOWEVER: GLACIERS ARE VERY SENSITIVE TO TEMPERATURE CHANGE!!!

-50

0

50

100

150

200

A4 A5 I6 U8 U9 R2 R5

E meltSWnetLWnetturb flux

energy flux (W m

-2 )

(1100) (1140)(715)(279) (381) (1210) (870)

DIRECT IMPACT OF TEMPERATURE INCREASE ON MELT

Higher temperature

More melt

Turbulent fluxesIncoming long-

wave radiation

SENSITIVITY INCREASES DUE TO ALBEDO FEEDBACK

Higher temperature

Lower albedo

More melt

1) Faster metamorphosis of snow

2) Ice appears earlier3) More meltwater on top of ice4) More water between snow grains

Turbulent fluxesIncoming long-

wave radiationNet short-wave

radiation

LONG-WAVE INCOMING IS DETERMINED BY …

L varies with the entire vertical profiles of temperature and water vapour

and with cloud-base height, cloud-base temperature and cloud amount

But in this case we only know:T2m temperature at 2 me2m water-vapour pressure at 2 mn cloud amount

εcs =0.23+cL e2m

T2m

⎛

⎝ ⎜

⎞

⎠ ⎟

1/8

L ↓ = εcs 1−na( )+εocn

a[ ] σ T2m

4

LONG-WAVE INCOMING, PARAMETERISATION

clear-skyterm (cs)

overcastterm (oc)

emittance (): is 1.0 for a black body

Three tunable parameters: a, oc and cL

LONG-WAVE OUTGOING RADIATION

L = s Ts4

where s and Ts are the emissivity and temperature of the surface

but since s is close to 1.0:

L = Ts4

SENSIBLE HEAT FLUX (QH)

QH = ρa Cpa κ2 u T −Ts( )

lnzz0

+αmzL ob

⎛ ⎝ ⎜

⎞ ⎠ ⎟ ln

zzT

+αhzL ob

⎛ ⎝ ⎜

⎞ ⎠ ⎟

a air densityCpa specific heat capacity of airk von Karman constantu wind speed at height zT 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”

ROUGHNESS LENGTHS

Distinguish:

z0 = momentum roughness length (wind)

zT = roughness length for temperature (depends on z0 and

wind speed)

zq = roughness length for water vapour (depends on z0 and

wind speed)

Momentum roughness length (z0) is a function of the surface

geometry only.

z0 increases with the roughness of the surface. Most values

for ice and for melting snow are in the range 1 to 10 mm.

DETERMINE MOMENTUM ROUGHNESS LENGTH

0 2 4 6 8 10

2

4

6

8

10

12

14

Wind speed (m/s)

Height above surface (m)

neutralconditions

stableconditions(katabatic

wind)

0 2 4 6 8 100.001

0.01

0.1

1

10

100

Wind speed (m/s)

Height above surface (m)

neutralconditions

stableconditions(katabatic

wind)

The momentum roughness length is defined as the height above the surface, where the semi-logarithmic profile of u reaches its surface values (0 m/s). It is determined by extrapolation of measurements.

QL = ρa Ls κ2 u q−qs( )

lnzz0

+αmzL ob

⎛

⎝ ⎜

⎞

⎠ ⎟ ln

zzq

+αhzL ob

⎛

⎝ ⎜ ⎞

⎠ ⎟

LATENT HEAT FLUX

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 vapourm, h constantsLob Monin-Obukhov length (depends on u and T-Ts)

ZERO-DEGREE ASSUMPTION

Assumption: surface temperature = 0 ˚C

If this leads toQ0 > 0: Q0 is consumed in meltingQ0 ≤ 0: nothing occurs

Assumption ok when melting conditions are frequent

wrong when positive Q0 causes heating of the snow (spring, early morning, higher elevation)

SUB-SURFACE PROCESSES

Alternative to zero-degree assumption: model sub-surface processes on a vertical grid

Relevant processes:

- penetration of short-wave radiation; absorption below the surface

- refreezing of percolating melt water in snow with T < 0˚C ( = internal accumulation)

- retention of percolating melt water by capillary forces

- when slope is small: accumulation of water on top of ice; leads to superimposed-ice formation when T < 0˚C

- conduction

- metamorphosis

Output: mass balance, but also surface temperature

DEGREE-DAY METHOD

N = Tpdd N: ablation: 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 and easier to model- input: only temperature needed

Disadvantages:- more tuning to local conditions needed: e.g. depends on mean solar zenith

angle- only sensitivity to temperature can be calculated

ACCUMULATION

Treated in a very simple way:

Precipitation = snow for T < 2˚CPrecipitation = rain for T ≥ 2˚C

ROLE OF DATA AUTOMATIC WEATHER STATIONS (AWS) AND MASS BALANCE MEASUREMENTS

AWS data:- develop parameterizations for incoming short- and

long-wave radiation- Determine relation between temperature at climate

station and temperature over glacier- Determine wind speed - Determine roughness lengths- Test energy balance model

Mass-balance data- tune the model, mainly with precipitation amount

and gradient - validate the model (correct simulation of interannual

variation?)

SUM UP

- surface energy balance fundamental

- motivation for forcing from climate station; role of AWS’es

- transfer forcing to glacier

- parameterisations of radiative and turbulent fluxes

- sub-surface models and zero-degree assumption

- degree-day models

- intermezzo: understand apparent paradox about sensitivity of

glaciers

READING AND MODELLING

Review about mass balance modelling:

Greuell, W., and C. Genthon, 2004: Modelling land-ice surface

mass balance. In Bamber, J.L. and A.J. Payne, eds. Mass

balance of the cryosphere: observations and modelling of

contemporary and future changes. Cambridge University

Press.

Mass balance model that includes sub-surface module:

http://www.phys.uu.nl/%7Egreuell/massbalmodel.html

SOME INSTRUMENTSmeasure short-wave radiation

with a pyranometer (glass dome)

measure long-wave radiationwith a pyrgeometer (silicon

dome)

measure sensible heat fluxwith a sonic anemometer

ENERGY BALANCE AT 5 ELEVATIONS

U53225 m=0.59=3.2˚T C

-50

0

50

100

150

200

250

300net shortwavenet longwave

sensible heatlatent heat

/Energy flux in W m

2

1A2205m=0.21=6.8˚T C

2U2310m=0.29=6.4˚T C

3U2420m=0.25=7.1˚T C

4U2945m=0.59=3.5˚T C

ATMOSPHERIC MODELS

Advantages:- include all of the physics contained in a surface energy-balance model- forcing outside the thermal influence of the glacier or ice sheet- effect of entire atmosphere on long-wave incoming radiation

considered- clouds computed- accumulation computed

Disadvantages:- grid size- computer time

e.g. a General Circulation Model (GCM)or an operational weather forecast model (e.g. ECMWF)

REGRESSION MODELS

Mn = c0 + c1 Twcs + c2 Pwcs

Mn: mean specific mass balanceci: coefficients determined by regression analysisTwcs: annual mean temperature at climate station with

weights varying per monthPwcs: idem, for precipitation

SHORT-WAVE INCOMING RADIATION

example for site on glacier tongue Pasterze,

Austriaaverages over 46

summer days

S = I0 cos(s) Tg+a Fms Fho Frs Tc

FIGURES BUOYANCY AND ROUGHNESS

0

20

40

60

80

100

0.01 0.1 1 10 100

Sensible heat flux (W/m

2 )

Roughness length (mm)

temperature = 5 ˚Cwind speed = 4 m/s

-20

0

20

40

60

80

100

0 2 4 6 8 10

Sensible heat flux (W/m

2 )

Wind speed at 2 m (m/s)

temperature = 5 ˚Croughness length =1 mm

laminar flow

0

10

20

30

40

50

60

0 2 4 6 8 10

Sensible heat flux (W/m

2 )

Temperature at 2 m (˚C)

wind speed = 4 m/sroughness length =1 mm

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1

1

2

3

4

5

6

7

8

9

10

11

12

CT,k

(mwe K-1)

Month

Vatnajökull, Iceland

CP,k

/10 (mwe)

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1

1

2

3

4

5

6

7

8

9

10

11

12

CT,k

(mwe K-1)

Month

Devon Ice Cap, Canada

CP,k

/10 (mwe)

SEASONAL SENSITIVITY CHARACTERISTICS

LIMITATIONS OF DEGREE-DAY METHOD

Calculation of degree-day factors for various points on the Greenland ice sheet with a sophisticated atmospheric and snow model (thesis Filip Lefebre)

snow ice

SEPARATION OF SHORT- AND LONG-WAVE RADIATION

Q = T4

Q flux (irradiance) Stefan Boltzmann

constant (5.67.10-8 W m-2 K-4)

temperature0

0.2

0.4

0.6

0.8

1

0.1 1 10 100

Black body radiation

Normalized irradiance

Wavelength (µm)

T = 5780 KSun

T = 290 KEarth

TURBULENT FLUXES

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

Water vapour: latent heat flux

DAILY COURSE

site on glacier tongue (ice) in summer

-400

-200

0

200

400

600

800

1000

0 4 8 12 16 20 24

Energy flux (W/m

2 )

Time

short wave in

short wave out

long wave in

long wave out

sensible heat

latent heat

NET FLUXES

Daily course at single site

-100

0

100

200

300

400

500

600

700

0 4 8 12 16 20 24

Energy flux (W/m

2 )

Time

net short wave

net long wave

sensible heat

latent heat