Transcript Document

MASS-BALANCE MODELLING
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)
SURFACE ENERGY BALANCE
dm
dTi
Q0  L f
 Mic pi
dt
dt
Energy exchange
with atmosphere
Q0
Lf
m
Mi
cpi
Ti
melting /
freezing
2
[Wm ]
heating / cooling
of the ice or snow
energy flux atmosphere to glacier
latent heat of fusion (0.334.10-6 J kg-1)
amount of melt water
mass of the ice
specific heat capacity of ice (2009 J kg-1 K-1)
ice temperature
FLUXES ATMOSPHERE TO GLACIER
Q0 = S ( 1 – a ) + L - L + QH + QL + QR
S
a
L
L
QH
QL
QR
short-wave incoming radiative flux
albedo of the surface
long-wave incoming radiative flux
long-wave outgoing radiative flux
turbulent flux of sensible heat
turbulent flux of latent heat
heat flux supplied by rain.
COMPONENTS OF THE ENERGY BALANCE
7 LOCATIONS - VATNAJOKULL
E melt
SWnet
LWnet
turb flux
-2
energy flux (W m )
200
150
100
50
0
-50
A4
A5
(279)
(381)
I6
U8
U9
R2
R5
(715)
(1210)
(870)
(1100)
(1140)
uickTime™ and a
CD Decompressor
ed to use this picture
AUTOMATIC WEATHER STATION
MODEL INPUT
MEASUREMENTS 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
TRANSFER FORCING FROM CLIMATE
STATION TO GLACIER
Some commonly used assumptions
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)
2 D PICTURE OF THE TEMPERATURE
In case the surface is melting
dT/dz = constant (e.g. -0.007 K/m)
Free atmosphere
dT/dz = ?
dT/dz = 0
ACTUAL TEMPERATURE VARIATION
Temperature on glacier (ÞC)
Son nblick
averages over 46 days of the ablation season, Pasterze, Austria
7.5
7
A1
6.5
2 m temperature (ÞC)
stations along the glacier
U3
Constant lapse-rate
can be a bad
U2
description,
Sonnblick
climate station
6
because:
5.5
5
gentle
slope
steep
slope
gentle
slope
4.5
stations along
the glacier
4
U4
U5
3.5
2000
2200
2400
2600
2800
Elevation (m a.s.l.)
3000
3200
3400
ACTUAL TEMPERATURE VARIATION
Temperature on glacier (ÞC)
Son nblick
averages over 46 days of the ablation season, Pasterze, Austria
7.5
7
A1
6.5
2 m temperature (ÞC)
stations along the glacier
U3
Constant lapse-rate
can be a bad
U2
description,
Sonnblick
climate station
6
because:
5.5
5
gentle
slope
steep
slope
1) Air over glacier
gentle
slope
colder than over
snow-free terrain
4.5
stations along
the glacier
4
U4
2) No constant lapse
rate over glacier
U5
3.5
2000
2200
2400
2600
2800
Elevation (m a.s.l.)
3000
3200
3400
MEASURED CLIMATE SENSITIVITY
Temperature (ÞC) on glacier (2205 m a.s.l.)
46 daily means during the ablation season, Pasterze, Austria
10
Constant lapse-rate
9
can be a bad
8
description,
7
because:
3) Climate
6
sensitivity over
5
glacier smaller
4
-2
0
2
4
6
Temperature (ÞC) at climate station (3106 m a.s.l.)
8
than over snowfree terrain
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
1.1
1
Greenland
2000 m
Cloud factor
0.9
Antarctica
1200 m
0.8
Pasterze
Austria
2205 m
0.7
Greenland
250 m
0.6
0.5
0.4
0.3
0
0.2
0.4
0.6
Cloud amount
0.8
1
ALBEDO PARAMETERISATION
asnow(i) = afirn + (afrsno - afirn) exp s-i
t*
a (i) = asnow(i) + {aice - asnow(i)} exp -d
d*
This model has five parameters:
afrsno
afirn
aice
d*
t*
Oerlemans and Knap, 1999
DIRTY ICE - PASTERZE
a~ 0.2
CLEAN ICE - GREENLAND ICE SHEET
a~ 0.45
Q uickTim e™ and a
Phot o CD decom pr essor
ar e needed t o see t his pict ur e.
Q uickTim e™ and a
Phot o CD decom pr essor
ar e needed t o see t his pict ur e.
FEEDBACK ALBEDO  SNOW AND ICE MELT
1) Faster metamorphosis of
snow
2) Ice appears earlier
3) More meltwater on top of ice
4) More water between snow grains
Lower albedo
Net short-wave
radiation
More melt
GLACIER SHOULD THEORETICALLY NOT
BE SENSITIVE TO TEMPERATURE CHANGE
E melt
SWnet
LWnet
turb flux
-2
energy flux (W m )
200
150
i) Net short-wave
radiation dominates the
100
surface energy balance
50
ii) Net short-wave
0
-50
Because
radiation is not a
A4
A5
(279)
(381)
I6
U8
U9
R2
R5
(715)
(1210)
(870)
(1100)
(1140)
function of the
temperature
HOWEVER: GLACIERS ARE VERY
SENSITIVE TO TEMPERATURE CHANGE!!!

DIRECT IMPACT OF TEMPERATURE INCREASE ON
MELT
Higher temperature
Turbulent fluxes
Incoming longwave radiation
More melt
SENSITIVITY INCREASES DUE TO ALBEDO
FEEDBACK
Higher temperature
1) Faster metamorphosis of
snow
Turbulent fluxes
Incoming longwave radiation
2) Ice appears earlier
3) More meltwater on top of ice
4) More water between snow grains
Lower albedo
Net short-wave
radiation
More melt
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 m
e2m water-vapour pressure at 2 m
n
cloud amount
LONG-WAVE INCOMING, PARAMETERISATION


L    cs 1  n   ocn  T2m
clear-sky
term (cs)
a
a
4
overcast
term (oc)
emittance (): is 1.0 for a black body
1/ 8
e 2m 
 cs  0.23  c L  
T2m 
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
calculated with the “bulk method”
SENSIBLE HEAT FLUX (QH)
 u T  Ts 
2
QH  a C pa
a
Cpa
k
u
T
Ts
z0
zT
am, ah
Lob
 z a m z   z a h z 


ln
 ln

 z0 L ob   z T L ob 
air density
specific heat capacity of air
von Karman constant
wind speed at height z
air temperature at height z
surface temperature
momentum roughness length
roughness length for temperature
constants
Monin-Obukhov length (depends on u and T-Ts)
ROUGHNESS LENGTHS
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.
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)
DETERMINE MOMENTUM ROUGHNESS LENGTH
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.
100
12
Height above surface (m)
Height above surface (m)
14
neutral
conditions
10
8
6
stable
conditions
(katabatic
wind)
4
stable
conditions
(katabatic
wind)
10
1
neutral
conditions
0.1
0.01
2
0.001
0
2
4
6
Wind speed (m/s)
8
10
0
2
4
6
Wind speed (m/s)
8
10
LATENT HEAT FLUX
QL  a Ls
a
Ls
k
u
q
qs
z0
zq
am, ah
Lob
 2 u q  q s 
 z a m z   z a h z 


ln
 ln
 z 0 L ob   zq L ob 

air density
latent heat of sublimation
von Karman constant
wind speed
specific humidity at height z
surface specific humidity
roughness length for velocity
roughness length for water vapour
constants
Monin-Obukhov length (depends on u and T-Ts)
ZERO-DEGREE ASSUMPTION
Assumption: surface temperature = 0 ˚C
If this leads to
Q0 > 0: Q0 is consumed in melting
Q0 ≤ 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 = b Tpdd
N: ablation
b:
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. b 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˚C
Precipitation = 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
measure short-wave radiation
with a pyranometer (glass
dome)
SOME INSTRUMENTS
measure sensible heat flux
with a sonic anemometer
measure long-wave radiation
with a pyrgeometer (silicon
dome)
ENERGY BALANCE AT 5 ELEVATIONS
300
Energy flux in W/m
2
250
net sh ortwave
net lon gwave
sens ible heat
latent heat
200
150
100
50
0
-50
A1
U2
U3
U4
U5
2205 m 2310 m 2420 m 2945 m 3225 m
a=0.21 a=0.29 a=0.25 a=0.59 a=0.59
T=6.8Þ C T=6.4Þ C T=7.1Þ C T=3.5Þ C T=3.2Þ C
ATMOSPHERIC MODELS
e.g. a General Circulation Model (GCM)
or an operational weather forecast model (e.g. ECMWF)
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
REGRESSION MODELS
Mn = c0 + c1 Twcs + c2 Pwcs
Mn: mean specific mass balance
c i:
coefficients determined by regression analysis
Twcs: annual mean temperature at climate station with
weights varying per month
Pwcs: idem, for precipitation
SHORT-WAVE INCOMING RADIATION
S = I0 cos(s) Tg+a Fms Fho Frs Tc
example for site on
glacier tongue Pasterze,
Austria
averages over 46
summer days
10 0
2
Sensible heat flux (W/m )
FIGURES BUOYANCY
AND ROUGHNESS
laminar flow
60
40
20
temperature = 5 ÞC
roughness length =1 mm
0
-20
0
2
Sensible heat flux (W/m )
60
80
50
2
4
6
8
10
Wind speed at 2 m (m/s)
40
10 0
2
Sensible heat flux (W/m )
30
20
wind speed = 4 m/s
roughness length =1 mm
10
0
0
2
4
6
8
Temperature at 2 m (ÞC)
10
80
temperature = 5 ÞC
wind speed = 4 m/s
60
40
20
0
0.01
0.1
1
10
Roughness length (mm)
100
SEASONAL SENSITIVITY CHARACTERISTICS
Devon Ice Cap, Canada
12
12
11
11
10
10
9
9
8
8
Month
Month
Vatnajökull, Iceland
7
6
7
6
5
5
4
4
3
3
2
2
1
1
-0.2
-0.15
-0.1
C
T,k
-0.05
-1
(mwe K )
0
0.05
C
P,k
/10 (mwe)
0.1
-0.2
-0.15
-0.1
C
T,k
-0.05
-1
(mwe K )
0
0.05
C
P,k
/10 (mwe)
0.1
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
Black body radiation
Normalized irradiance
1
Q = T4
0.8
0.6
Q

0.4
0.2
T = 5780 K
Sun
T = 290 K
Earth

0
0.1
1
10
Wavelength (µm)
100
flux (irradiance)
Stefan Boltzmann
constant (5.67.10-8
W m-2 K-4)
temperature
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
1000
2
Energy flux (W/m )
800
short wave in
600
400
long wave in
200
sensible heat
0
latent heat
short wave out
-200
long wave out
-400
0
4
8
12
Time
16
20
24
NET FLUXES
Daily course at single site
700
2
Energy flux (W/m )
600
500
net short wave
400
300
200
100
sensible heat
latent heat
0
net long wave
-100
0
4
8
12
Time
16
20
24