Claridenfirn, Switzerland, 1916
1914 • Terminology, Definitions, Units • Specific mass balance, surface mass balance, net balance ... • Concepts: conventional and reference surface mass balance • Firn line, snow line, ELA • Mass-balance sensitivities Background General reference for mass-balance terminology has been Anonymous,1969, J. Glaciology 8(52). in practice diverging and inconsistent and confusing use of terminology new methods, e.g. remote sensing, require update New initiative by International Association of Cryospheric Sciences (IACS)
aims to update and revise Anonymous (1969) and to provide a consistent terminology for all glaciers (i.e. mountain glaciers, ice caps and ice sheets)
Can be downloaded from: http://www.cryosphericsciences.org/mass_balance_glossary/ massbalanceglossary Glacier mass balance The change in the mass of a glacier or ice body, or part thereof, over a stated span of time
=mass budget t . ‘mass imbalance’ M = Mdt t1
t . . b = c + a = (c+ a)dt t1
Net gain of mass Net loss of mass
Firn line Accumulation area: acc > abl Long-term ELA
Ablation area: acc < abl
Equilibrium line: acc = abl t . . b = c + a = (c+ a)dt t1 Precipitation - Surface accumulation precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier Melt - Runoff Precipitation Melt water may refreeze and does not Surface accumulation contribute to meltwater runoff melt
Net
Melt
Rain
Sublimation
accumulation
Internal internal accumulation accumulation Internal ablation
GLACIER Calving Basal ablation
Meltwater runoff Basal accumulation Runoff • based on Regional Atmospheric Climate Model (RACMO2/GR) • 11 km spatial resolution • forced by ERA-40 and ECMWF operational analyses
Precip
Melt
Runoff
Tide gaugesSurface mass balance
Ettema et al., 2009, GRL Precipitation - Surface accumulation precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier Melt - Runoff Precipitation Melt water may refreeze and does not Surface accumulation contribute to meltwater runoff melt Meltwater runoff - Runoff Runoff includes rain water
Net
Melt
Rain
Sublimation Accumulation - Net accumulation accumulation Net acc is a balance, acc not Internal internal accumulation accumulation Internal ablation
GLACIER Calving Basal ablation
Meltwater runoff Basal accumulation Runoff Accumulation - Winter balance Ablation - Summer balance
Ba = Bw+Bs = C + A
Bw= C ??? Bs= A ??? Implications for comparison of field measurements with model results? C, A can be modeled, but what is measured often is Bw, Bs Ice discharge MB=SMB-D Mass flux or volumetric flux of ice through a glacier cross-section or “gate”. The gate can be anywhere on the glacier, but is often at the glacier terminus. If the terminus is a calving front, ice discharge is usually in discrete pieces that, when discharged into a body of water, become icebergs, and the ice discharge is equivalent to the calving flux. Avalanching, for example from the terminus of a hanging glacier, may constitute ice discharge; --> dry calving.
Figure by G. Cogley What is surface mass balance?
Mass balance of a column c = accumulation a = ablation
b = csfc + asfc + ci + ai + cb + ab + qin + qout
Surface internal basal flux divergence
SMB ? Climatic balance Surface Climatic-basal balance
internal (Total) mass balance qin qout
basal What is mass balance?
Mass balance of a column c = accumulation a = ablation
b = csfc + asfc + ci + ai + cb + ab + qin + qout
Surface internal basal flux divergence
Continuity equation Mass balance ? SMB ? Surface . . . internal q h= bQ qin out
Thickness change basal Mass balance Change in mass over a stated period of time
Mass balance of a column c = accumulation a = ablation
b = csfc + asfc + ci + ai + cb + ab + qin + qout
Surface internal basal flux divergence
Climatic balance
Climatic-basal balance
. (Total) mass balance . . h= bQ • stratigraphic system Time systems • fixed-date system • floating-date system • combined system
The winter season (w) and the mass- balance year (a) in three time systems (STR: stratigraphic; FXD: fixed-date; FLT: floating-date) on Silvrettagletscher, Switzerland, 2005–06. Thick line: evolution of cumulative mass balance, B(t–t0), with B(0) = 0 at t0 = 1 October 2005. After Huss et al. 2009. Distributions of differences between (a) annual and (b) winter balance measured in different time systems on two Swiss glaciers during 1960–2007 (after Huss et al. 2009). Bars range from the 2.5 to the 97.5 percentile and boxes cover the 25th to the 75th percentile of each distribution. The central thick line is the median and is the standard deviation. Time Systems of Annual Measurements of Mass Balance Reported to World Glacier Monitoring System WGMS (Cumulative to 2008)
No information provided 1519
Fixed-date system 917
Stratigraphic system 931
Combined system 265
Other 188
Total of reported annual measurements 3820 Net mass balance
Appendix B – Terms Defined in Anonymous (1969)
Term Symbol* Definition STRATIGRAPHIC MEASUREMENT SYSTEM BASED ON SYSTEM EXISTENCE OF AN OBSERVABLE SUMMER SURFACE Balance year Time span between formation of two successive summer surfaces Total ablation at Integral of ablation a(t) over balance year Winter balance bw Change in mass during winter season Summer balance bs Change in mass during summer season
Net balance bn catt ; also bbws Annual balance FIXED-DATE MEASUREMENT SYSTEM BASED ON SYSTEM SPECIFIC CALENDAR DATES Measurement Time between start and end of year measurement Total ablation Aa
Annual balance ba caaa What about floating-date system ? What is specific mass balance ?
1. The mass balance at a specific location ? 2. The mass balance of the entire glacier ? 3. The mass balance expressed in m w.e. ?
Definition: Mass balance expressed per unit area, that is, with dimension [M L–2 T–1] or [M L–2] kg m–2
The prefix “specific” is not necessary. The units make clear whether or not it is specific.
Specific mass balance may be reported for a point on the surface (if it is a surface mass balance), a column of unit cross-section, or a larger volume such as the entire glacier. Balances reported for a point are always specific. Mass-balance units Mass balance = Mass change over stated period of time • Mass [M] kg, Gt (=1012 kg) • mass change per unit area [M L-2] --> kg m-2 (specific unit) • m or mm water equivalent (w.e.): -> 1 kg of water (density 1000 kg m-3) has thickness of 1 mm when distributed over 1 m2 -> kg m-2 and mm are numerically identical -> 1 m w.e. = 1000 kg m-2 / density of water • m3 w.e. or km3 w.e. (1 km3 w.e. = 1 Gt) --> important to add w.e. or i.e. (ice equiv.) • Sea-level equivalent: kg m-2 x glacier area /-(density of water x area of the ocean) (362x106 km2)
Mass balance is often expressed as an average rate over the stated time span Mass balance as climate indicator ?
Stable climate Climate change Stable climate Bn = 0 Bn < 0 Bn = 0 Steady-state Glacier retreat Steady-state Glaciers are indicators of climate change ?
B=V / A
• conventional mass balance glacier area/hypsometry is updated annually • reference surface balance glacier area/hypsometry is kept constant
Harrison, W., Elsberg, Cox and March, 2005. Different balances for climatic and hydrological applications. J. Glaciol., page 176. Conventional mass balance Time 1 Time 2 (50 yrs later)
Relevant for hydrological purposes Measurement 1 sites B = b dA 1 (h1) t1 B = b(h 2)dAt 2 A t1 At2 Reference surface mass balance
Relevant for climatological purposes 1 1 B b dA B = b(h1)dAt1 = (h1) t1 A At1 t1 Note also the surface elevation changes Mass balance as climate indicator ?
Stable climate Climate change Stable climate Bn = 0 Bn < 0 Bn = 0 Steady-state Glacier retreat Steady-state
Reference surface mass balance does not go to 0 Firn line, equilibrium line, snow line: transient, annual, balanced budget ... FIRN LINE FIRN ICE Wetted snow that has survived Interconnecting air passages one summer without being between the grains are sealed off transformed to ice (at 830 kg/m3)
The set of points on the surface of a glacier delineating the firn area and, at the end of the mass-balance year, separating firn (usually above) from glacier ice (usually below).
FIRN
ICE
Implications for mass balance (density, albedo effect) and runoff (water routing) FIRN LINE can be seen on radar profiles Snow surfaceMass balance Snowlines Snow line = Boundary separating snow from ice or firn at any time t Equilibrium line The set of points on the surface of the glacier where the climatic mass balance is zero at a given moment. The equilibrium line separates the accumulation zone from the ablation zone.
Equi.line Equilibrium line altitude (ELA)
Snowline/Equilibrium line (if no superimposed ice)
Approximate ELA Balanced-budget ELA The ELA with a climatic mass balance = 0 on average over a number of years.
Steady-state ELA The ELA of a glacier in steady state.
Equ
Dyurgerov et al., 2009, J. Glaciol.
ELAs from space: Remote sensing
Landsat image of Vatnajoekull (Iceland)
Where is the firn line, EL, snow line?
firn
firn firn Storglaciaren ELA AAR --> high --> high --> AAR ELA Low --> Low --> Low --- - Annual mass balance Mass balance sensitivity The change in mass balance due to a change in a climatic variable such as air temperature or precipitation Affected by • Glacier size • Glacier geometry • Climate Sensitivities to climate change •expressed in terms of static or dynamic mass balance sensitivities •Static sensitivities assume constant glacier size and geometry and refer only to the change in mean specific mass balance •dynamic sensitivities consider the volume and geometry changes following climate change and are thus more realistic •Sensitivities vary among regions (e.g. maritime climates more sensitive) Bn = mean specific mass balance x = perturbation of the climate, i.e. temperature or precipitation A = glacier area, V=glacier volume, T= temperature change during period t-t0 Static mass balance sensitivities using energy balance (EB) or temperature-index (TI) melt models Static mass Static mass balance Method balance sensitivity Reference Glaciers sensitivity T +1 K (m a-1) P +10 % (m a-1) 3 Norwegian glaciers EB -0.72 to -1.11 Oerlemans (1992) 12 glaciers EB -0.12 to -1.15 Oerlemans and Fortuin (1992) 12 glaciers EB -0.40 (average) Oerlemans (1993) 3 Norwegian glaciers TI -0.54 to -1.04 +0.14 to +0.39 Laumann and Reeh (1993) 2 Svalbard glaciers EB -0.61 (average) Fleming et al. (1997) 2 Icelandic glaciers TI -0.6 to -0.9 Jóhannesson (1997) 12 glaciers TI, EB -0.4 to -1.35 Oerlemans et al. (1998) 37 glaciers TI -0.1 to -1.3 Braithwaite and Zhang (1999) 5 Swiss glaciers TI -0.44 to -0.89 Braithwaite and Zhang (2000) 6 Scandinavian TI -0.68 to -1.13 +0.26 to +0.50 Nesje et al. (2000) glaciers 61 glaciers TI -0.13 to -1.22 +0.04 to +0.37 Braithwaite et al. (2002) 9 Icelandic glaciers EB -0.49 to -0.80 +0.27 to +0.35 de Ruyter de Wildt et al. (2003) 17 glaciers TI -0.2 to -1.5 Schneeberger et al. (2003) 42 Arctic glaciers TI -0.20 to -2.01 +0.03 to +0.36 de Woul and Hock (2005) 12 Scandinavian TI -0.30 to -1.01 +0.16 to +0.41 Rasmussen and Conway (in glaciers press) Hock et al., 2009, GRL Global average (area-weighted) = -0.68 m a-1 Hock et al., 2009, GRL Mass balance sensitivities Global mean static mass balance -1 -1 • -0.39 m a K (Oerlemans, 1993) -1 -1 • -0.37 m a K (Dyurgerov and Meier, 2000) -1 -1 • -0.68 m a K (Hock et al., 2009) Seasonal sensitivity characteristic Sensitivity varies with season • applies temperature and precipitation perturbations employed individually for each month while leaving the data for the remaining months unchanged. SSC (Oerlemans & Reichert, 2000): Monthly perturbations in precipitation or temperature Seasonal mass balance sensitivities • applies temperature and precipitation perturbations employed individually for each month while leaving the data for the remaining months unchanged. Future volume changes using mass balance sensitivities ST = Mass balance sensitivity to +1 K warming SP = Mass balance sensitivity to 1% precipitation increase T = predicted temperature increase P = precipitation increase (%) Assumptions: • Assumption that glacier initially are in steady-state • Constant sensitivities with time Summary