Glacier meteorology Surface energy balance. How does ice and snow melt? Where does the energy come from? How to model melt?

Transcription

1 Glacier meteorology Surface energy balance How does ice and snow melt? Where does the energy come from? How to model melt?

2 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

3 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 Wm 2 Transmission of short wave radiation down to 10 m for ice and 1 m for snow - important for subsurface melting High and variable albedo

4 Warming of snow/ice First, snow/ ice needs to be warmed to melting point Second, melt can occur Snow temp Cold content 1 g water refreezes 160 grams of snow Depth will be warmed by 1 K = energy needed to Cold content bring the snow / ice Ground heat flux to 0 C.

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6 SURFACE ENERGY BALANCE Qatm = QM + QG Energy flux atmosphere to glacier surface Energy available for melting Change in internal energy (heating / cooling of the ice or snow)

7 Energy balance Q N Net radiation ATMOSPHERE Q H sensible heat flux Q L latent heat flux Q G ground heat flux (heat flux in the ice/snow) Q R sensible heat supplied by rain G Global radiation albedo L longwave incoming radiation G R L L Precipitation Sensible heat flux & latent heat flux Wind L longwave outgoing radiation GLACIER Conduction (snow & ice) MELTING

8 GLOBAL RADIATION or shortwave incoming radiation Top 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 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.

9 GLOBAL RADIATION or shortwave incoming radiation Direct & diffuse only diffuse Wavelength: μm 2 components: Direct / diffuse component: Scattering by air molecules scattering and absorption by liquid and solid particles Selective absorption by water vapour and ozone

10 Direct solar radiation I 0 = solar constant=1368 Wm -2 cos (angle of incidence ) R= Earth-Sun radius (m=mean) = atmospheric transmissivity P= atmospheric pressure (0=at sea level) = slope angle, sun slope =solar and slope azimuth angle zenith, Z 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)

11 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

12 Svartisen, Norway Engabreen 38 km m a.s.l.

13 Potential direct solar radiation DEM of 25m resolution

14 Diffuse radiation Q M = (I+ D s +D t )(1- )+(L s +L t +L)+Q H +Q L +Q R +Q G D =D 0 V + G(1-V) 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 radiation 3) 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 glacier

15 Modelled direct and diffuse radiation on Storglaciaren Jun 7 Sep 17, Wm2

16 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

17 Albedo ATMOSPHERE R L Precipitation Sensible heat flux & latent heat flux G L Wind GLACIER Conduction (snow & ice) MELTING

18 ALBEDO = average reflectivity over the spectrum μm = ratio between reflected and incoming solar radiation Typical values: new snow old snow glacier ice soil, dark 0.1 grass 0.2 rain forest 0.15 Large wavelength dependency 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

19 Hourly discharge

20 CONTROLS ON GLACIER ALBEDO Surface properties Grain size (large grain size decreases albedo) Water content (water increases grain size decreases albedo) Impurity content Surface roughness Crystal orientation/structure 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.

21 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 relationships Aging curve approach: function of time after snowfall (Corps of Engineers, 1956) variants include temperature, snow depth b, k = coefficients 0 =minimum snow albedo

22 Snow albedo parameterisations 1) U.S. Army Corps of Engineers (1956) 2) Brock et al. (2000) function snow age n and temperature (through k) Snow albedo is computed as a function of accumulated maximum daily temperature since snowfall Daily albedo Pelliciotti et al., J. Glaciol. 2005

23 Slope effect albedo Parallel-levelled instrument Horizontally levelled diurnal variation No diurnal variation Jonsell et al, 2003, J.Glaciol., 164

24 Cryoconite holes

25 Longwave incoming radiation Wavelengths 4-120μm Emitted by atmosphere (water vapour, CO 2, 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 L = eff T 4 glacier ATMOSPHERE Precipitation R L Sensible heat flux & latent heat flux L acts day & night G L GLACIER Wind MELTING Conduction (snow & ice)

26 The longwave incoming radiation is the largest contribution to melt (~ 70%) L = eff T 4 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

27 PARAMETERISATION OF LONG-WAVE INCOMING RADIATION L =F clear-sky T 4 = eff T 4 eff =effective emissivity T=air temperature n= cloud fraction (0-1) e=vapour pressure clear-sky term (cs) overcast term (oc) cs =clear-sky emissivity oc =overcase emissivity L = clear (T,e) F T 4 INPUT air temperature (T) vapour pressure (e) (air humidity) Cloudiness (n) (can e.g. be parameterized as function of global radiation and top of atmosphere radiation)

28 Longwave outgoing radiation L = T 4 +(1- )L Longwave reflectance of snow: < 0.05 Emissivity > 0.95 Often assumed =1 L = W m -2 = 5.67x10-8 W m -2 K -4 Assume black body radiation -> =1

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31 TURBULENT HEAT FLUXES Precipitation R L Sensible heat flux & latent heat flux G L Wind GLACIER Conduction (snow & ice) MELTING

32 Turbulent heat fluxes - Eddy correlation Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange Turbulent motion is irregular Description by Reynolds decomposition Fluctuating quantity X = sum of the mean value (overbar) and perturbation (prime) from this mean Eddy correlation = The covariance between two variables, associated with turbulent motions. e.g. eddy correlation of vertical velocity w and potential temperature, i =data index N =number of data points.

33 Turbulent heat fluxes Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange Turbulent heat fluxes = Ability to transfer x gradient of relevant property Eddy diffusivity

34 Sensible heat flux Turbulent heat fluxes Driven by temperature and moisture gradients between air and surface and by turbulence as mechanism of vertical air exchange 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

35 Turbulent exchange wind speed turbulent mixing surface roughness How to determine turbulent heat fluxes: Profile method Bulk aerodynamic method

36 Turbulent heat fluxes Sensible heat flux Temperature difference Latent heat flux Exchange coefficient Wind speed Exchange coefficient is function of surface roughness and stability function (empirical expressions to define stability functions) Humidity difference

37 Turbulent heat fluxes Sensible heat flux Latent heat flux Temperature difference Specific humidity difference wind speed P=air pressure, Z0=roughness length, =stability function, L=Monin-Obukhov length

38 Turbulent heat fluxes Sensible heat flux Latent heat flux wind speed Roughness lengths Z 0 = 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) z 0T = roughness length for temperature (depends on z0 and wind speed) Z 0e = roughness length for water vapour (depends on z0 and wind speed)

39 Turbulent heat fluxes Sensible 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)

40 Turbulent heat fluxes Sensible 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

41 Sublimation To melt 1 kg snow/ice requires J kg -1 Latent heat of fusion To sublimate 1 kg of snow requires J kg -1 Latent heat of sublimation (8x L f!!!)

42 Latent heat flux Positive vapour gradient Condensation To melt 1 kg snow/ice requires J kg -1 = Latent heat of fusion Negative vapour gradient Sublimation To sublimate 1 kg snow/ice requires J kg -1 = Latent heat of sublimation

43 Typical for during dry periods in the outer tropics Sublimation occurs L s = 8*L f 8x less ablation than under wet conditions for same energy input

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45 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 W/m 2 net radiation averaged over longer periods But rainfall has indirect effects: changes albedo, mechanical removal of snow

46 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 Photo: T. Schuler, Austonna

47 Temporal variation of energy balance components

48 Energy partitioning (%) Glacier Q N Q H Q L Q G Q M Aletschgletscher, Switzerland Hintereisferner, Austria Peytoglacier, Canada Storglaciären, Sweden

49 Importance of individual components sources Ohmura, 2001 longwave incoming radiation ~ 75% absorbed global radiation ~ 20% sensible heat flux < 10 % sinks longwave outgoing radiation ~ 70 80% melt ~ % ground heat flux < 10 %

50 Melt energy weather patterns day-to-day variability in melt is often determined by the turbulent fluxes Net radiation Sensible heat Latent heat Q M = Q N +Q H +Q L +

51 Summary (Part I)

52 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

53 Melt modelling

54 Mass balance models Model type Spatial discretization 0-Dim elevation bands fully distributed Temp-index regression Temp-index or simplified energy balance Increasing model sophistication Energy balance

55 Temperature-index melt models Assume a relationship between air temperature and melt: M=f(T), M=f(T + ) Relationship melt - air temperature Data by R. Braithwaite

56 Temperature-index melt models Assume a relationship between air temperature and melt: M=f(T), M=f(T + ) Positive degree-day sum PDD = T + Relationship melt degree-day sum

57 Degree-day factors [mm/day/k] M = DDF ice/snow * T + Aletschgletscher, Switzerland 5.3 John Evans Glacier, Canada Alfotbreen, Norway Storglaciaren, Sweden Dokriani Glacier, Himalaya Yala Glacier, Himalaya Glacier AX010 Snow Ice Thule Ramp, Greenland 12, 7.0 Camp IV-EGIG, Greenland 18.6 GIMES profile, Greenland Qamanarssup sermia,

58 Physical basis of temp-index models Air temperature directly affects several components of the surface energy balance Longwave incoming rad L = T 4 f(t) Sensible heat flux Latent heat flux f(e(t)) 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)

59 Degree-day factors [mm/day/k] M = DDF ice/snow * T + Spatial and diurnal variation Derived from energy balance modeling Hock, 1999, J.Glaciol.

60 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

61 Performance of degree-day model Melt = DDF ice/snow * T + Model captures seasonal variations but not diurnal melt fluctuations

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64 Modified temperature-index model Including potential direct solar radiation Classical degree-day factor M = DDF ice/snow * T + Hock 1999, J. Glaciol Including pot. direct radiation M = (MF + a ice/snow *DIR) * T + Model introduces a spatial variation in melt factors a diurnal variation in melt factors

65 Simulated cumulative

66 Model comparison

67 Gornergletscher outburst floods Huss et al., 2007, J. Glaciol. Photo: Shin Sugiyama

68 Extended temperature-index models including other data than temperature Degree-day model M = DDF ice/snow * T + Extended temperature-index model including radiation M = a * R + melt factor * T Shortwave bal Net radiation Energy balance model Gradual transition from degree-day models to energy balance-type expressions by increasing the number of climate input variables

69 Simplified energy balance model Oerlemans (2001) M = a * R + melt factor * T M = (1- )G+c 0 +c 1 T Shortwave radiation balance Longwave balance and turbulent fluxes Gradual transition from degree-day models to energy balance-type expressions by increasing the number of climate input variables

70 Distributed temp-index model by Pelliciotti et al, 2005, J.Glaciol. Temperature Albedo Incoming shortwave radiation Computed as function of accumulated maximum daily temperature since snowfall Brock et al. (2000) Brock et al. (2000) Computed as function of daily temperature range Model only requires air temperature Global radiation and albedo parameterized Pellicciotti et al, 2005, J. Glaciology

71 Spatial patterns of hourly melt rate (mm w.e. h-1) Haut d Arolla Glacier 27 August July Melt is function of Global radiation, and thus topography (in particular shading) Surface properties and particularly albedo Temperature extrapolation With courtesy of Francesca Pellicciotti Pellicciotti et al, 2005, J. Glaciology

72 Temperature-index versus energy balance Temperature index Energy balance Shortcomings Advantages Wide availability of Temp-data Easy interpolation and forecasting Good model performance Computational simplicity Empirical, not physically based DDF vary, works on average conditions Does not work in tropics Model parameter stability under different climate conditions? Physical based describe physical processes more adequately Projections more reliable Large data requirements (often not available)

73 Runoff peak: melt or subglacial drainage event?

74 Energy balance on Storglaciären Wrong conclusion if temperature taken as sole index, Energy balance needed to solve problem Net radiation Sensible heat Latent heat

75 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)

76 Literature Energy balance: Hock, R., Glacier melt: A review on processes and their modelling. Progress in Physical Geography 29(3), Temperature-index methods: Hock, R., Temperature index melt modelling in mountain regions. Journal of Hydrology 282(1-4), doi: / S (03)