MASS-BALANCE MODELLING

# MASS-BALANCE MODELLING

## MASS-BALANCE MODELLING

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1. 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)

2. SURFACE ENERGY BALANCE Energy exchange with atmosphere melting / freezing heating / cooling of the ice or snow Q0 energy flux atmosphere to glacier Lf latent heat of fusion (0.334.10-6 J kg-1) m amount of melt water Mi mass of the ice cpi specific heat capacity of ice (2009 J kg-1 K-1) Ti ice temperature

3. FLUXES ATMOSPHERE TO GLACIER Q0 = S ( 1 –  ) + L - L + QH + QL + QR S short-wave incoming radiative flux a albedo of the surface L long-wave incoming radiative flux L long-wave outgoing radiative flux QH turbulent flux of sensible heat QL turbulent flux of latent heat QR heat flux supplied by rain.

4. COMPONENTS OF THE ENERGY BALANCE7 LOCATIONS - VATNAJOKULL

5. AUTOMATIC WEATHER STATION

6. 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

7. 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

8. TRANSFER FORCING FROM CLIMATE STATION TO GLACIER Some commonly used assumptions

9. 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 = ? Boundary layer: temperature compromise between surface (0 ˚C) and free atmosphere (> 0 ˚C) Surface: temperature = 0 ˚C dT/dz = 0

10. ACTUAL TEMPERATURE VARIATION averages over 46 days of the ablation season, Pasterze, Austria Constant lapse-rate can be a bad description, because: gentle slope steep slope gentle slope

11. ACTUAL TEMPERATURE VARIATION averages over 46 days of the ablation season, Pasterze, Austria Constant lapse-rate can be a bad description, because: Air over glacier colder than over snow-free terrain No constant lapse rate over glacier gentle slope steep slope gentle slope

12. MEASURED CLIMATE SENSITIVITY 46 daily means during the ablation season, Pasterze, Austria Constant lapse-rate can be a bad description, because: 3) Climate sensitivity over glacier smaller than over snow-free terrain

13. 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.

14. 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)

15. CLOUD FACTOR causes largest uncertainty in calculated incoming short-wave radiation

16. ALBEDO PARAMETERISATION This model has five parameters: Oerlemans and Knap, 1999

17. DIRTY ICE - PASTERZE ~ 0.2

18. CLEAN ICE - GREENLAND ICE SHEET ~ 0.45

19. FEEDBACK ALBEDO  SNOW AND ICE MELT 2) Ice appears earlier 3) More meltwater on top of ice 4) More water between snow grains 1) Faster metamorphosis of snow Lower albedo Net short-wave radiation More melt

20. GLACIER SHOULD THEORETICALLY NOT BE SENSITIVE TO TEMPERATURE CHANGE Because Net short-wave radiation dominates the surface energy balance Net short-wave radiation is not a function of the temperature HOWEVER: GLACIERS ARE VERY SENSITIVE TO TEMPERATURE CHANGE!!! 

21. DIRECT IMPACT OF TEMPERATURE INCREASE ON MELT Higher temperature Turbulent fluxes Incoming long-wave radiation More melt

22. SENSITIVITY INCREASES DUE TO ALBEDO FEEDBACK Higher temperature 2) Ice appears earlier 3) More meltwater on top of ice 4) More water between snow grains 1) Faster metamorphosis of snow Turbulent fluxes Incoming long-wave radiation Lower albedo Net short-wave radiation More melt

23. 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

24. LONG-WAVE INCOMING, PARAMETERISATION clear-sky term (cs) overcast term (oc) emittance (e): is 1.0 for a black body Three tunable parameters: a, eoc and cL

25. LONG-WAVE OUTGOING RADIATION L = es Ts4 where es and Ts are the emissivity and temperature of the surface but since es is close to 1.0: L =  Ts4

26. SENSIBLE HEAT FLUX (QH) calculated with the “bulk method” ra air density Cpa specific heat capacity of air k von Karman constant u wind speed at height z T air temperature at height z Ts surface temperature z0 momentum roughness length zT roughness length for temperature am, ah constants Lob Monin-Obukhov length (depends on u and T-Ts)

27. 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)

28. 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.

29. LATENT HEAT FLUX ra air density Ls latent heat of sublimation k von Karman constant u wind speed q specific humidity at height z qs surface specific humidity z0 roughness length for velocity zq roughness length for water vapour am, ah constants Lob Monin-Obukhov length (depends on u and T-Ts)

30. 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)

31. 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

32. 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

33. ACCUMULATION Treated in a very simple way: Precipitation = snow for T < 2˚C Precipitation = rain for T ≥ 2˚C

34. 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?)

35. 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

36. 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

37. SOME INSTRUMENTS measure short-wave radiation with a pyranometer (glass dome) measure sensible heat flux with a sonic anemometer measure long-wave radiation with a pyrgeometer (silicon dome)

38. ENERGY BALANCE AT 5 ELEVATIONS

39. 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

40. REGRESSION MODELS Mn = c0 + c1 Twcs + c2 Pwcs Mn: mean specific mass balance ci: coefficients determined by regression analysis Twcs: annual mean temperature at climate station with weights varying per month Pwcs: idem, for precipitation

41. 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

42. FIGURES BUOYANCY AND ROUGHNESS

43. SEASONAL SENSITIVITY CHARACTERISTICS

44. 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

45. SEPARATION OF SHORT- AND LONG-WAVE RADIATION Q = T4 • Q flux (irradiance) • Stefan Boltzmann constant (5.67.10-8 W m-2 K-4)  temperature

46. 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

47. DAILY COURSE site on glacier tongue (ice) in summer

48. NET FLUXES Daily course at single site