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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 dm dTi 2 Q0 L f Mic pi [Wm ] dt dt Energy exchange melting / heating / cooling with atmosphere freezing 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 – a ) + 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. COMPONENTS OF THE ENERGY BALANCE 7 LOCATIONS - VATNAJOKULL E melt SWnet 200 LWnet turb flux energy flux (W m ) -2 150 100 50 0 -50 A4 A5 I6 U8 U9 R2 R5 (279) (381) (715) (1210) (870) (1100) (1140) uickTime™ and a o CD D ecompress or ed to use this picture AUTOMATIC WEATHER STATION MODEL INPUT MEASUREMENTS 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 TRANSFER FORCING FROM CLIMATE STATION TO GLACIER Some commonly used assumptions Variable assumption temperature constant lapse rate, i.e. dT/dz constant wind speed constant humidity constant relative humidity cloud amount constant precipitation linear in elevation (used for tuning) 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 = ? dT/dz = 0 ACTUAL TEMPERATURE VARIATION Temperature on glacier (ÞC) averages over 46 days of the ablation season, Pasterze, Austria Sonnblick 7.5 stations along the glacier 7 U3 Constant lapse-rate 6.5 A1 U2 can be a bad description, 2 m temperature (ÞC) Sonnblick 6 climate station because: 5.5 gentle steep gentle 5 slope slope slope 4.5 stations along the glacier 4 U4 U5 3.5 2000 2200 2400 2600 2800 3000 3200 3400 Elevation (m a.s.l.) ACTUAL TEMPERATURE VARIATION Temperature on glacier (ÞC) averages over 46 days of the ablation season, Pasterze, Austria Sonnblick 7.5 stations along the glacier 7 U3 Constant lapse-rate 6.5 A1 U2 can be a bad description, 2 m temperature (ÞC) Sonnblick 6 climate station because: 5.5 1) Air over glacier gentle steep gentle 5 slope slope slope colder than over 4.5 snow-free terrain stations along the glacier 2) No constant lapse 4 U4 U5 rate over glacier 3.5 2000 2200 2400 2600 2800 3000 3200 3400 Elevation (m a.s.l.) MEASURED CLIMATE SENSITIVITY 46 daily means during the ablation season, Pasterze, Austria Temperature (ÞC) on glacier (2205 m a.s.l.) 10 Constant lapse-rate 9 can be a bad 8 description, 7 because: 3) Climate 6 sensitivity over 5 glacier smaller 4 -2 0 2 4 6 8 than over snow- Temperature (ÞC) at climate station (3106 m a.s.l.) 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 1.1 1 Greenland 2000 m 0.9 Antarctica 1200 m Cloud factor 0.8 Pasterze Austria 0.7 2205 m Greenland 250 m 0.6 0.5 0.4 0.3 0 0.2 0.4 0.6 0.8 1 Cloud amount ALBEDO PARAMETERISATION asnow(i) = afirn + (afrsno - afirn) exp s-i t* a (i) = asnow(i) + {aice - asnow(i)} exp -d d* This model has five parameters: afrsno afirn aice d* t* Oerlemans and Knap, 1999 DIRTY ICE - PASTERZE a~ 0.2 CLEAN ICE - GREENLAND ICE SHEET a~ 0.45 c i m Q ui kT e™ and a hot D P o C decompressor s c ar e needed t o see t hi pi t ure. c i m Q ui kT e™ and a hot D P o C decompressor s c ar e needed t o see t hi pi t ure. FEEDBACK ALBEDO SNOW AND ICE MELT 2) Ice appears earlier 1) Faster metamorphosis of 3) More meltwater on top of ice snow 4) More water between snow grains Lower albedo Net short-wave radiation More melt GLACIER SHOULD THEORETICALLY NOT BE SENSITIVE TO TEMPERATURE CHANGE E melt SWnet Because 200 LWnet turb flux i) Net short-wave energy flux (W m ) -2 150 radiation dominates the 100 surface energy balance 50 ii) Net short-wave 0 radiation is not a -50 A4 (279) A5 I6 U8 U9 R2 (1100) R5 (1140) function of the (381) (715) (1210) (870) 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 1) Faster metamorphosis of 3) More meltwater on top of ice snow 4) More water between snow grains Turbulent fluxes Lower albedo Incoming long- wave radiation 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 L cs n ocn T2m 1 a a 4 clear-sky overcast term (cs) term (oc) emittance (): is 1.0 for a black body 1/ 8 e 2m cs 0.23 c L T2m Three tunable parameters: a, oc and cL LONG-WAVE OUTGOING RADIATION L = s Ts4 where s and Ts are the emissivity and temperature of the surface but since s is close to 1.0: L = Ts4 SENSIBLE HEAT FLUX (QH) calculated with the “bulk method” u Ts 2 T QH a C pa z am z z ah z ln z L ln z L 0 ob T ob a 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. 14 100 12 Height above surface (m) Height above surface (m) 10 stable neutral conditions 10 conditions (katabatic 1 wind) neutral 8 conditions 6 stable 0.1 conditions 4 (katabatic wind) 0.01 2 0.001 0 2 4 6 8 10 0 2 4 6 8 10 Wind speed (m/s) Wind speed (m/s) LATENT HEAT FLUX 2 u q q s QL a Ls z a m z z ah z ln ln z 0 L ob zq L ob a 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 measure short-wave radiation with a pyranometer (glass SOME INSTRUMENTS dome) measure sensible heat flux with a sonic anemometer measure long-wave radiation with a pyrgeometer (silicon dome) ENERGY BALANCE AT 5 ELEVATIONS 300 net shortwave net longwave 250 sensible heat latent heat 2 Energy flux in W/m 200 150 100 50 0 -50 A1 U2 U3 U4 U5 2205 m 2310 m 2420 m 2945 m 3225 m a=0.21 a=0.29 a=0.25 a=0.59 a=0.59 T=6.8ÞC T=6.4ÞC T=7.1ÞC T=3.5ÞC T=3.2ÞC 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 c i: 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 10 0 FIGURES BUOYANCY Sensible heat flux (W/m ) 2 80 AND ROUGHNESS 60 laminar flow 40 20 temperature = 5 ÞC 0 roughness length =1 mm 60 -2 0 0 2 4 6 8 10 Sensible heat flux (W/m ) 2 50 Wind speed at 2 m (m/s) 40 30 10 0 Sensible heat flux (W/m ) 2 20 80 wind speed = 4 m/s temperature = 5 ÞC 10 roughness length =1 mm wind speed = 4 m/s 60 0 0 2 4 6 8 10 40 Temperature at 2 m (ÞC) 20 0 0.01 0.1 1 10 100 Roughness length (mm) SEASONAL SENSITIVITY CHARACTERISTICS Vatnajökull, Iceland Devon Ice Cap, Canada 12 12 11 11 10 10 9 9 8 8 Month Month 7 7 6 6 5 5 4 4 3 3 2 2 1 1 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 -1 -1 C (mwe K ) C /10 (mwe) C (mwe K ) C /10 (mwe) T,k P,k T,k P,k 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 Black body radiation 1 0.8 Q = T4 Normalized irradiance 0.6 Q flux (irradiance) 0.4 Stefan Boltzmann constant (5.67.10-8 0.2 W m-2 K-4) T = 5780 K T = 290 K Sun Earth temperature 0 0.1 1 10 100 Wavelength (µm) 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 1000 800 short wave in Energy flux (W/m ) 600 2 400 long wave in 200 sensible heat 0 latent heat short wave out -200 long wave out -400 0 4 8 12 16 20 24 Time NET FLUXES Daily course at single site 700 600 Energy flux (W/m ) 500 2 net short wave 400 300 200 100 sensible heat latent heat 0 net long wave -100 0 4 8 12 16 20 24 Time

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