Glacier meteorology Surface energy balance

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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

conten

Snow temp

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)

Sensible heat flux

& latent heat flux

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 )

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

Sensible heat flux

& latent heat flux

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

Cryoconite holes

Sensible heat flux

& latent heat flux

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

Sensible heat flux

& latent heat flux

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

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

wind speed

surface roughness

How to determine turbulent heat fluxes:

• Profile method

• Bulk aerodynamic method

Turbulent exchange

Temperature difference

Humidity difference

Sensible heat flux

Latent heat flux

Exchange coefficient is function of surface roughness and stability function (empirical expressions to define stability functions)

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

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)

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 %

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

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

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

Thule Ramp, Greenland 12, 7.0

Camp IV-EGIG, Greenland 18.6

GIMES profile, Greenland 8.7

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

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

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

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.

Glacier meteorology Surface energy balance

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