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Glacier meteorologySurface energy balance
• How does ice and snow melt ?
• Where does the energy come from ?
• How to model melt ?
Melting of snow and ice
• Ice and snow melt at 0°C (but not necessarily at air temperature >= 0° C)
• Depends on energy balance which is controlled by
meteorological conditions
properties of the surface
Summary: Properties of snow and ice• Surface temperature can not exceed 0°C
- stable stratification in melt season
- glacier wind (katabatic wind) - max surface vapor pressure 611 Pa - max longwave outgoing radiation = 316 Wm2
• Transmission of short wave radiation • down to 10 m for ice and 1 m for snow
- important for subsurface melting
• High and variable albedo
Warming of snow/ice
• First, snow/ ice needs to be warmed to melting point
• Second, melt can occur
Cold
conten
t
Snow temp
De
pth
Cold content Ground heat flux= energy needed to
bring the snow / ice to 0 °C.
1 g water refreezes 160 grams of snow will be warmed by 1 K
SURFACE ENERGY BALANCE
Energy flux atmosphere to glacier surface
Energy available for melting
Qatm = QM + QG
Change in internal energy (heating / coolingof the ice or snow)
G
R L
L
Sensible heat flux
& latent heat flux
Wind
Precipitation
GLACIER
ATMOSPHERE
Conduction
(snow & ice)
MELTING
Energy balance
QN Net radiation
QH sensible heat flux
QL latent heat flux
QG ground heat flux (heat flux in the
ice/snow)
QR sensible heat supplied by rain
-----------------------------------------------
G Global radiation
albedo
L longwave incoming radiation
L longwave outgoing radiation
GLOBAL RADIATION or shortwave incoming radiationTop of atmosphere radiation
•solar constant = amount of incoming solar electromagnetic radiation per unit area, measured on the outer surface of Earth's atmosphere, in a plane perpendicular to the rays.
•roughly 1366 W/m2, fluctuates by about 7% during a year - 1412 W/m2 to 1321 W/m2 in early July varying distance from the sun
•the average incoming solar radiation is one fourth the solar constant or ~342 W/m .
GLOBAL RADIATION or shortwave incoming radiation
• Wavelength: 0.15-5 μm
• 2 components: Direct / diffuse component:
• Scattering by air moleculesscattering and absorption by liquid and solid particles
• Selective absorption by water vapour and ozone
Direct & diffuse
only diffuse
Direct solar radiation
Strong spatial variation
• Controlling factors: - site characteristics: slope, aspect, solar geometry - atmosphere: transmissivity (cloudiness, pollutants ...)
• I increases with - decreasing angle of incidence - increasing transmissivity (affected by volcanoes, pollution, clouds) - increasing elevation (decreasing mass, less shading, multiple reflection)
I0= solar constant=1368 Wm-2
R= Earth-Sun radius (m=mean)
= atmospheric transmissivity
P= atmospheric pressure (0=at sea level)
= slope angle, sun slope=solar and slope azimuth angle
cos (angle of incidence )
zeni
th, Z
Spatial variation of potential solar direct radiation(clear-sky conditions)
Topographic shading Potential direct radiation averaged over melt season
The large spatial variability of the direct component of global radiation in complex topography is responsible for much of the spatial variability in observed melt
Svartisen, Norway
Engabreen
38 km2
5-1600 m a.s.l.
Potential direct solar radiation DEM of 25m resolution
• Clear-sky days= D approx. 15% of global radiation,Overcast days 100%
• Sources: sky and surrounding topography
• 3 components: 1) scattered from direct radiation (sky radiation)2) backscattered radiation3) reflected from adjacent slopes
• Two opposing topographic effects: - D is reduced by obscured sky - enhanced by reflection from slopes
• D controlled by - atmospheric conditions (clouds) - spatially: albedo, skyview factor, V
• Less variable spatially than direct radiation
Diffuse radiationQM= (I+ Ds+Dt )(1- )+(Ls+Lt+L)+QH+QL+QR+QG
D =D0V + G(1-V)
glacier
Modelled direct and diffuse radiation on Storglaciaren
Jun 7 – Sep 17, 1993
20-90 Wm2
Extrapolation of global radiation
• Ratio is small under cloudy
conditions
• Ratio is large under clear-sky
conditions
• Ratio is proxy for cloudiness
and assumed to be the same
across glacier
G
R L
L
Sensible heat flux
& latent heat flux
Wind
Precipitation
GLACIER
ATMOSPHERE
Conduction
(snow & ice)
MELTING
Albedo
new snow 0.75 – 0.95
old snow 0.4 – 0.7
glacier ice 0.3 – 0.45
soil, dark 0.1
grass 0.2
rain forest 0.15
= average reflectivity over the spectrum 0.35-2.8 μm
ALBEDO
• Large variability in space and time
• Key variable in glacier melt modelling
• Ice albedo less variable than snow albedo, but often modified by sediment and debris cover
Large wavelength dependency
Typical values:
= ratio between reflected and incoming solar radiation
Hourly discharge
Incident shortwave radiation• Cloudiness ( increase since clouds
preferentially absorb near-infrared radiation higher fraction of visible light which has higher reflectivity); effect enhanced by multiple reflection, increase up to 15%
effect is small over ice surfaces
• Zenith angle ( increase when sun is
low, due to Mie scattering properties of the grains)
Jonsell et al., 2003, J. Glac.
Surface properties• Grain size (large grain size decreases albedo)
• Water content (water increases grain size decreases albedo)
• Impurity content • Surface roughness• Crystal orientation/structure
CONTROLS ON GLACIER ALBEDO
How to model snow albedo ?• Radiative transfer models including effects of grain size (most
important control) and atmospheric controls large data requirements, not practicable for operational purposes
• Empirical relationshipsAging curve approach: function of time after snowfall (Corps of Engineers, 1956)
variants include temperature, snow depth …
b, k = coefficients
0=minimum snow albedo
Snow albedo parameterisations
1) U.S. Army Corps of Engineers (1956)
function snow age n and temperature (through k)
2) Brock et al. (2000)
Snow albedo is computed as a function of accumulated maximum daily temperature since snowfall
Daily albedo Pelliciotti et al., J. Glaciol. 2005
Jonsell et al, 2003, J.Glaciol., 164
Parallel-levelled instrument
Horizontally levelled
Slope effect albedo
No
diu
rna
l
vari
ati
on
diu
rnal
vari
ati
on
Cryoconite holes
G
R L
L
Sensible heat flux
& latent heat flux
Wind
Precipitation
GLACIER
ATMOSPHERE
Conduction
(snow & ice)
MELTING
Longwave incoming radiation• Wavelengths 4-120μm
• Emitted by atmosphere (water vapour, CO2, ozone)
• Function of air temperature and humidity (cloudiness)
• High values compared to shortwave radiation
• Longwave rad. balance < 0, when fog ca 0 W/m2
• Spatial variation: Topographic effects: - reduced by obscured sky - enhanced by radiation from slopes and air inbetween
• Climate change: Temp increase or more cloudiness
glacier
L acts day & night
L = eff T4
The longwave incoming radiation is the largest contribution to melt (~ 70%)
About 70 % of the longwave incoming radiation originates from within the first 100m of the atmosphere
Variations of screen-level temperatures can be regarded as representative of this boundary layer
L = eff T4
PARAMETERISATION OF LONG-WAVE INCOMING RADIATION
clear-skyterm (cs)
overcastterm (oc)
L =F clear-sky T4= eff T4
INPUTair temperature (T)
vapour pressure (e) (air humidity)
Cloudiness (n) (can e.g. be parameterized as function of global radiation and top of atmosphere radiation)
eff=effective emissivityT=air temperaturen= cloud fraction (0-1)e=vapour pressure
cs=clear-sky emissivity
oc=overcase emissivity
L = clear (T,e) F T4
Longwave outgoing radiation
L = T4+(1- )LLongwave reflectance of snow: < 0.05Emissivity > 0.95
Often assumed =1
L = 315.6 W m-2 • = 5.67x10-8 W m-2 K-4
• Assume black body radiation -> =1
TURBULENT HEAT FLUXES
G
R L
L
Sensible heat flux
& latent heat flux
Wind
Precipitation
GLACIER
Conduction (snow & ice)
MELTING
Turbulent heat fluxes - Eddy correlation
Turbulent motion is irregular
Description by Reynolds decomposition
Eddy correlation =The covariance between two variables, associated
with turbulent motions .
e.g. eddy correlation of vertical velocity w and potential temperature , i =data indexN =number of data points.
Fluctuating quantity X = sum of the mean value (overbar) and perturbation (prime) from this mean
Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange
Turbulent heat fluxes
Turbulent heat fluxes =
Ability to transfer x gradient of relevant property
Eddy diffusivity
Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange
Turbulent heat fluxes
Sensible heat flux• Function of temperature gradient
• Function of wind speed
Latent heat flux ( the energy released or absorbed during a change of state)
• Function of vapour pressure gradient
• Function of wind speed
Fluxes also affected by• Surface roughness• Atmospheric stability
Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange
wind speed
surface roughness
turb
ule
nt
mix
ing
How to determine turbulent heat fluxes:
• Profile method
• Bulk aerodynamic method
Turbulent exchange
Turbulent heat fluxes
Win
d s
peed
Temperature difference
Humidity difference
Exch
an
ge
co
eff
icie
nt
Sensible heat flux
Latent heat flux
Exchange coefficient is function of surface roughness and stability function (empirical expressions to define stability functions)
Turbulent heat fluxes
Temperature difference
Specific humidity difference
Sensible heat flux
Latent heat flux
wind speed
P=air pressure, Z0=roughness length, =stability function,
L=Monin-Obukhov length
Turbulent heat fluxesSensible heat flux
Latent heat flux
Roughness lengthsZ0 = momentum roughness length, function of the
surface geometry only, increases with the roughness of the surface, ice/snow often 1-10 mm (but also much lower and higher values reported)
z0T= roughness length for temperature (depends on z0
and wind speed)
Z0e = roughness length for water vapour
(depends on z0 and wind speed)
wind speed
Turbulent heat fluxesSensible heat flux
Latent heat flux
Bulk aerodynamic method
• On melting surface
• Surface temperature and vapour pressure are known
• Measurements at only one level needed
• Exchange coefficient unknown (roughness length)
Turbulent heat fluxesSensible heat flux
Latent heat flux
Problems:
• Difficult to measure surface roughness and stability functions, vary in time and space, even more difficult to extrapolate across glacier, often treated as model tuning parameters (residuals in closing energy balance)
• Monin-Obukhov theory on which profile and bulk methods are based not applicable over sloping glaciers ? Violation of assumptions of homogeneous, infinite, flat terrain and constant flux with height
Sublimation
• To melt 1 kg snow/ice requires 334 000 J kg-1
Latent heat of fusion
• To sublimate 1 kg of snow requires 2 848 000 J kg-1
Latent heat of sublimation (8x Lf !!!)
Positive vapour gradient
Condensation• To melt 1 kg snow/ice requires 334 000 J kg-1 = Latent heat of fusion
Latent heat flux
Negative vapour gradient
Sublimation•To sublimate 1 kg snow/ice requires 2 848 000 J kg-1 = Latent heat of sublimation
Typical for during dry periods in the outer tropicsSublimation occurs Ls = 8*Lf 8x less ablation than under wet conditions for same energy input
Sensible heat flux by rain
Tr = rain temperature
Ts = surface temperature
R = rain fall rate
= Density of water
Cp=Specific heat of water
A 10 mm/day at 10°C on melting surface provides 2.4 Wm-2
• Negligible compared to 30-180 W/m2 net radiation averaged over longer periods
• But rainfall has indirect effects: changes albedo, mechanical removal of snow …
Photo: T. Schuler, Austonna
radiation components (S , S , L , L )
temperature humidity
wind speed & direction
1) Temp
sensible heat flux latent heat flux rain heat flux (longwave incoming
radiation)
2) Humidity latent heat
flux(longwave incoming radiation)
3) Wind speed
sensible heat flux latent heat flux
4) Global radiation
Temporal variation of
energy balance
components
Energy partitioning (%)
Glacier QN QH QL QG QM
Aletschgletscher, Switzerland
92 8 -6 0 -94
Hintereisferner, Austria
90 10 -2 0 -98
Peytoglacier, Canada 44 48 8 0 -100
Storglaciären, Sweden 66 30 5 -3 -97
Ohmura, 2001
Importance of individual components
sources
longwave incoming radiation ~ 75%
absorbed global radiation ~ 20%
sensible heat flux < 10 %
sinks
longwave outgoing radiation ~ 70 – 80%
melt ~ 10 – 30 %
ground heat flux < 10 %
Melt energy – weather patterns
QM = QN+QH+QL+…
Net radiation
Sensible heat
Latent heat
day-to-day variability in melt is often determined by the turbulent fluxes
Summary (Part I)
How to model melt ?1. Physically based energy-balance models:
each of the relevant energy fluxes at the glacier surface is computed from physically based calculations using direct measurements of the necessary meteorological variables
2. Temperature-index or degree-day models: melt is calculated from an empirical formula as a function of air temperature alone
Melt modelling
Mass balance modelsM
od
el
typ
e
S
pa
tia
l d
isc
reti
za
tio
n
Temp-index regression
Temp-index or simplified energy balance
Energybalance
0-Dim elevation bands fully distributed
Increasing model sophistication
• Assume a relationship between air temperature and melt: M=f(T), M=f(T+)
Temperature-index melt models
Data by R. Braithwaite
Relationship melt - air temperature
• Assume a relationship between air temperature and melt: M=f(T), M=f(T+)
Temperature-index melt models
Relationship melt –
degree-day sum
Positive degree-day sum
PDD = T+
Degree-day factors M = DDFice/snow * T+[mm/day/K]
Aletschgletscher, Switzerland 5.3
John Evans Glacier, Canada 5.5
4.1
2.7
7.6
8.1
5.5
Alfotbreen, Norway 4.5 6.0
Storglaciaren, Sweden 3.2 6.0
Dokriani Glacier, Himalaya 5.7 7.4
Yala Glacier, Himalaya
Glacier AX010 11.6
10.1
Thule Ramp, Greenland 12, 7.0
Camp IV-EGIG, Greenland 18.6
GIMES profile, Greenland 8.7
9.2
20.0
Qamanarssup sermia, 2.8 7.3
Snow Ice
Air temperature directly affects several components of the surface energy balance
L = T4 f(T)
Longwave incoming rad Sensible heat flux
f(e(T))
Physical basis of temp-index models
Latent heat flux
• L is the largest contribution to melt (~ 70%) (Ohmura, 2001, Physical basis of temperature-index models)
• L has low variability compared to other fluxes
• L is poorly correlated to air temperature when cloud emissions dominate its variability (usual in mountains)(Sicart et al., 2008, JGR)
Degree-day factors M = DDFice/snow * T+[mm/day/K]
Spatial and diurnal variationDerived from energy balance modeling
Hock, 1999, J.Glaciol.
SPATIAL VARIABILITY OF DEGREE-DAY FACTORS
Calculation of degree-day factors for various points on the Greenland ice sheet with an atmospheric and snow model (thesis Filip Lefebre)
snow ice
Performance of degree-day model
Melt = DDFice/snow * T+
Model captures seasonal variations but not diurnal melt fluctuations
Modified temperature-index model
Classical degree-day factor
M = DDFice/snow
* T+
Including pot. direct radiation
M = (MF + aice/snow*DIR) * T+
Including potential direct solar radiation
Model introduces • a spatial variation in melt factors • a diurnal variation in melt factors
Hock 1999, J. Glaciol
Simulated cumulative
Model comparison
Gornergletscher outburst floods
Photo: Shin SugiyamaHuss et al., 2007, J. Glaciol.
Extended temperature-index models including other
data than temperature
M = DDFice/snow * T+
M = a * R + melt factor * T
Net radiation
Shortwave bal
Degree-day model
Energy balance model
Extended temperature-index model including radiation
Gradual transition from degree-day models to energy balance-type expressions
by increasing the number of climate input variables
Simplified energy balance model
M = (1- )G+c0+c1TShortwave radiation balance
Longwave balance and turbulent fluxes
Oerlemans (2001)
Gradual transition from degree-day models to
energy balance-type expressions by increasing the number of climate input variables
M = a * R + melt factor * T
Distributed temp-index model by Pelliciotti et al, 2005, J.Glaciol.
Temperature
Model only requires air temperatureGlobal radiation and albedo parameterized
Albedo Incoming shortwave radiation
Pellicciotti et al, 2005, J. Glaciology
Brock et al. (2000)
Computed as function of accumulated maximum daily temperature since
snowfall
Brock et al. (2000)
Computed as function of daily temperature range
Spatial patterns of hourly melt rate (mm w.e. h-1)
10.00 13.00 17.00
27 A
ugu
st 2
001
27 J
uly
200
1
18.00
Melt is function of • Global radiation, and thus topography (in particular shading)
• Surface properties and particularly albedo• Temperature extrapolation
Haut d’Arolla Glacier
Pellicciotti et al, 2005, J. GlaciologyWith courtesy of Francesca Pellicciotti
Temperature-index versus energy balance
• Wide availability of Temp-data
• Easy interpolation and forecasting
• Good model performance
• Computational simplicity
• Physical based – describe physical processes more
adequately
• Projections more reliable
•Empirical, not physically based
• DDF vary, works on ‘average conditions
• Does not work in tropics
• Model parameter stability under different climate
conditions ?
• Large data requirements (often not available)
Temperature index Energy balance
Sh
ort
co
min
gs A
dvan
tag
es
Runoff peak: melt or subglacial drainage event ?
Energy balance on Storglaciären
Net radiation
Sensible heat
Latent heat
Wrong conclusion if temperature taken as sole
index,
Energy balance needed to solve
problem
SUMMARY
• Both temp-index and energy balance models are useful tools, choice depends on data availability
• Awareness of limitations
• Need for more approaches of intermediate complexity and moderate data input
• Both temp-index and energy balance models need calibration (parameter tuning)
Literature
Energy balance:
Hock, R., 2005. Glacier melt: A review on processes and their modelling. Progress in Physical Geography 29(3), 362-391.
Temperature-index methods:
Hock, R., 2003. Temperature index melt modelling in mountain regions. Journal of Hydrology 282(1-4), 104-115. doi:10.1016/S0022-1694(03)00257-9.