Why modelling? Glacier mass balance modelling
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1 Why modelling? Glacier mass balance modelling GEO 4420 Glaciology Thomas V. Schuler global mean temperature Background Glaciers have retreated world-wide during the last century and are expected to continue retreating How can we investigate the glacier-climate relationship? Glacier retreat has socio-economic implications: - sea-level rise - hazard mitigation (floods) - hydropower (e.g. Norway 99% of power generation, 10% is glacier derived) Mass of Vernagtferner, Austrian Alps significant contributor to streamflow: modify runoff quantity and timing (glacier as water storage ) 1
2 Reasoning Side effect: optimization of stake network Climate provides upper boundary conditions of the ice sheets/ glaciers: accumulation, ablation geometry changes Thermodynamics effects: Internal ice temperature Flow law coupling (cold ice is more stiff) Surface melt water Water resource, Sea level change Glacier surface mass balance glaciologist Accumulation: gain of mass (e.g. snow deposition) Accumulation area: acc > abl Ablation: loss of mass (e.g. snow/ ice melting) Equilibrium line altitude (ELA) in (m a.s.l.) hydrologist Ablation area: acc < abl Equilibrium line: acc = abl 2
3 Methods Simple integrated schemes Regression models Mass-balance models driven by specified/modelled climate: Degree day methods Energy balance models Guidelines for Model Selection 1. Operation and calibration data availability 2. Expected physiographic and climatic conditions 3. Detail and type of results required. Primary approaches to modeling Regression Analysis (linear or multiple) Temperature Index Approach Energy Balance Approach Data: Engabreen, Norway, NVE 3
4 a regression model using winter precipitation and summer temperature may work well but only for diagnostic applications! for prognostic applications we need a deterministic model! At ELA: T summer = P winter m r=0.81 But how to determine mass balance?? MB = *T(jun-sep) *P(oct-mar) Regression analysis 4
5 Regression analysis Simple integrated approaches Advantages: Provides an estimate of total discharge from basin Simple Minimum data requirements Provide a good index for water resource managers Disadvantages: Does not provide information on factors such as peak discharge. Threshold effects may occur. Assumes stationarity. Climate boundary conditions can t change. Advantages: Very simple indeed Migration of ELA may be linked to climate change Attractive for use in situations where there is little data Disadvantages: Entirely empirical In reality, ELA depends on local climate, aspect, etc. A blunt instrument for a complex problem 0 = Q + Q + Q + Q + Q + Q R Energy balance H Q R L G P = S S + L L M SURFACE ENERGY BALANCE Q 0 = L f dm dt + M i c pi dt i dt [Wm 2 ] ATMOSPHERE MELTING S S Glacier surface L L Precipitation Sensible heat flux & latent heat flux Wind Conduction (snow & ice) ground Energy exchange with atmosphere melting / freezing heating / cooling of the ice or snow Q 0 energy flux atmosphere to glacier L f latent heat of fusion ( J kg -1 ) m amount of melt water M i mass of the ice c pi specific heat capacity of ice (2009 J kg -1 K -1 ) T i ice temperature 5
6 TRANSFER FORCING FROM CLIMATE STATION TO GLACIER TRANSFER FORCING FROM CLIMATE STATION TO GLACIER T, u, q, n, p Some commonly used assumptions T, u, q, n, p Variable assumption T, u, q, n, p temperature constant lapse rate, i.e. dt/dz constant glacier wind speed humidity constant constant relative humidity T, u, q, n, p cloud amount precipitation constant linear in elevation (used for tuning) 2 D PICTURE OF THE TEMPERATURE In case the surface is melting MEASURED CLIMATE SENSITIVITY 46 daily means during the ablation season, Pasterze, Austria Free atmosphere dt/dz = constant (e.g K/m) Boundary layer: temperature compromise between surface (0 C) and free atmosphere (> 0 C) Surface: temperature = 0 C dt/dz = 0 dt/dz =? Temperature (ÞC) on glacier (2205 m a.s.l Temperature (ÞC) at climate station (3106 m a.s.l.) Constant lapse-rate can be a bad description, because: Climate sensitivity over glacier smaller than over snow-free terrain 6
7 SHORT-WAVE INCOMING RADIATION DIRTY ICE - PASTERZE α ~ 0.2 S = I 0 cos(θ s ) T g+a F ms F ho F rs T c FEEDBACK ALBEDO SNOW AND ICE MELT SENSITIVITY INCREASES DUE TO ALBEDO FEEDBACK Higher temperature 1) Faster metamorphosis of snow 2) Ice appears earlier 3) More meltwater on top of ice 4) More water between snow grains 1) Faster metamorphosis of snow 2) Ice appears earlier 3) More meltwater on top of ice 4) More water between snow grains Lower albedo More melt Net short-wave radiation Turbulent fluxes Incoming long-wave radiation Lower albedo More melt Net short-wave radiation 7
8 0 Point or spatially distributed Energy Balance Models = Q + Q + Q + Q + Q + Q R H L Run on measured data contrast to empirical models, which run on only a few measured parameters and which rely on calibration parameters at the heart of the model. G P M Energy Balance problems Energy Balance model (parameterizations of turbulent exchange) Spatial distribution Precipitation Snowpack model (refreezing, metamorphism, water retention) Only as good as your measured data and understanding of the system Includes some empirism anyway (turbulent exchange ) Sacrifice simplicity for complicated measurements and algorithms. Energy balance models: + physical basis: good quality control - huge data demand - scaling problem: point to catchment Temperature-Index Methods Based on the concept that changes in air temperature provide an index of snowmelt. T-index approach: M = C * (T T 0 ) Air temperature commonly measured meteorological variable. secondary meteorological variable that provides an integrated measure of heat energy. Photo: Schuler 8
9 Temperature-Index Methods Based on the concept that changes in air temperature provide an index of snowmelt. T-index approach: M = C * (T T 0 ) 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 Air temperature commonly measured meteorological variable. secondary meteorological variable that provides an integrated measure of heat energy. Advanced T-index models Strategy: include the second most important energy source (global radiation) Hock 1999: M = (C 1 + C 2 *I) * (T-T 0 ) melt-factor variable in space and time Q (m 3 s -1 ) Q (m 3 s -1 ) Degree-day Temp-index incl. direct radiation Modelling: Discharge Storglaciären Measured Simulated Pellicciotti et al. (2005): M = C 1 *(T-T 0 ) + C 2 *(1-α)*I I potential clear-sky solar radiation α - albedo radiation term temperature term Q (m 3 s -1 ) Energy balance 19-Jul 29-Jul 8-Aug 18-Aug 28-Aug 7-Sep 1994 Hock
10 Importance of individual components sources longwave incoming radiation ~ 70% absorbed global radiation ~ 20% sensible heat flux < 10 % Ohmura, 2001 More trouble... The sensible heat flux contributes < 10% T-index approach: M = C * (T T 0 ) sinks longwave outgoing radiation melt ground heat flux ~ 70 % ~ % < 10 % Why does the T-index approach perform that well?? 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 LONG-WAVE INCOMING, PARAMETERISATION L = [ ε cs ( 1 n a )+ε oc n a 4 ] σ T 2m clear-sky term (cs) overcast term (oc) emittance (ε): is 1.0 for a black body 1/ 8 e ε cs = c 2m L T 2m Three tunable parameters: a, ε oc and c L 10
11 Temperature-index models: + low data demand + applicable in all scales - trouble with quality control Accumulation Treated in a very simple way: Precipitation = snow for T < 2 C Precipitation = rain for T 2 C Linear distribution with elevation Photo: Schuler Snow radar: GPR mapping of snow thickness s vs z s vs y Radar profiles s vs x s = F(x,y,z) F is a multiple regression function 11
12 radar data multiple regression: using x,y,z position scaling: avg(snow) = 1 multiple regression: radar data using x,y,z position Accumulation model Spatial distribution using an index map Temporal distribution using a scaled precipitation series from Ny-Ålesund Scales & snow distribution micro meso macro Surface roughness Surface cover (vegetation) Wind exposure Microclimate Transition Large-scale topography (mountain range) Distance to moisture source geogr. latitude acc = C3*(Pnå/ΣPnå)*C4 acc-index annual accumulation precipitation roughness 12
13 Energy exchange with atmosphere SURFACE ENERGY BALANCE Q 0 = L f dm dt + M i c pi dt i dt melting / freezing [Wm 2 ] heating / cooling of the ice or snow Q 0 energy flux atmosphere to glacier L f latent heat of fusion ( J kg -1 ) m amount of melt water M i mass of the ice c pi specific heat capacity of ice (2009 J kg -1 K -1 ) T i ice temperature Melt physics 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!!!) To warm 1 kg of snow 1 K requires 2009 J kg -1 K -1 ; ice: 2097 J kg -1 K -1 Specific heat capacity Refreezing of 1 g water warms 160 g snow by 1 K Removing cold content Stake data vs model ablation stake melt-water T w = 0 C We measure mass balance, but model melt snow V s = 1 m 3 T s = -1 C Condition for melt: snow must be at melting temperature, otherwise refreezing will occur Cold content = energy needed to bring the snow / ice to 0 C. internal accumulation superimposed ice In the given example, refreezing of 2.5 l melt-water is needed to compensate for the cold content of the snow pack (snow density, ρ s =400 kg m -3 ). ice ice ice 13
14 refreezing Using a simple model: p max = 0.6 the proportion of the winter snow pack that refreezes within one year if (si+melt<pmax*ini_snow) si=si+melt & abl=0 & snow = snow-melt Alternative: Woodward model (pmax is a function of MAAT) Summary + predictive power, assessability - complexity, data demand, distribution Interpolation Regression models T-index model Enhanced T-index Energy balance models 14
15 Climate sensitivity Static sensitivity: Apply a change to the climate data set, the glacier geometry does not change Dynamic sensitivity: Changes of the glacier geometry are considered as well Uniform temperature or precipitation changes to the input data: Temp increase m a -1 K -1 (-0.99) Prec increase m a -1 (10%) -1 (+0.35) Change in mass balance (m WE) Temperature changes b n b w b s Precipitation changes b n b s Seasonal sensitivity characteristic Sensitivity varies with season Continuous time series from 1974 to date Model input: meteo data SSC (Oerlemans & Reichert, 2000): Monthly perturbations in precipitation or temperature Devon Ice Cap, Canada Month C T,k (mwe K -1 ) C P,k /10 (mwe) DNMI station Glomfjord, ca. 20 km N of Engabreen at 39 m a.s.l. 15
16 Potential clear-sky solar radiation DEM of 25m resolution Model output: glacier mass balance Mass balance measurements Massbalance data (NVE) available since 1970 Model performance r 2 = n =
17 Model performance Model performance r 2 = 0.74 Winter balance r 2 =0.91 Net balance r 2 = measured - modelled Summer balance r 2 = measured - modelled Calibration period 17
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