Create Presentation
Download Presentation

Download Presentation
## MASS-BALANCE MODELLING

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**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**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.**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**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**TRANSFER FORCING FROM CLIMATE STATION TO GLACIER**Some commonly used assumptions**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**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**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**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**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**ALBEDO PARAMETERISATION**This model has five parameters: Oerlemans and Knap, 1999**DIRTY ICE - PASTERZE**~ 0.2**CLEAN ICE - GREENLAND ICE SHEET**~ 0.45**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**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!!! **DIRECT IMPACT OF TEMPERATURE INCREASE ON MELT**Higher temperature Turbulent fluxes Incoming long-wave radiation More melt**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**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**clear-sky term (cs) overcast term (oc) emittance (e): is 1.0 for a black body Three tunable parameters: a, eoc and cL**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**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)**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.**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)**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**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)**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 ci: 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**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**Q = T4 • Q 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**NET FLUXES**Daily course at single site