Glacier summer school 2018, McCarthy, Alaska What is mass balance ? Regine Hock Claridenfirn, Switzerland, 1916 1914 • Terminology, Definitions, Units • Conventional and reference surface mass balance • Firn line, snow line, ELA • Glacier runoff • Global mass changes PART I Terminology Claridenfirn, Switzerland, 1916 1914 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 Working group (2008-2012) by GLOSSARY International Association of OF GLACIER Cryospheric Sciences (IACS) MASS BALANCE aims to update and revise Anonymous (1969) AND and to provide a consistent terminology for all RELATED glaciers (i.e. mountain glaciers, ice caps and ice sheets) TERMS Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris. Can be downloaded from: http://www.cryosphericsciences.org/mass_balance_glossary/ massbalanceglossary Glacier mass balance Mass balance is the change in the mass of a glacier, or part of the glacier, over a stated span of time: =mass budget t . • SPACE: study volume needs to be ‘mass imbalance’ ΔM = ∫ Mdt defined t1 • mass balance is often quoted for volumes other than that of the whole glacier, for example a column of unit cross section • important to report the domain ! •TIME: the time period (esp important € for comparison with model results) • mass change can be studied over any period Net gain of mass • often done over a year or winter/summer seasons --> Annual mass balance (formerly ‘Net’) Firn line Long-term ELA Accumulation area: acc > abl Net loss of mass Ablation area: acc < abl Equilibrium line: acc = abl t . ΔM = ∫ Mdt t1 t . Δmb= c+ a = ∫ (c+ a)dt t ACCUMULATION, (c, C) 1 € • Snow fall ABLATION (a, A) • Deposition of hoar, freezing rain •Melting • Windborne blowing snow/ •Sublimation drifting snow •Loss of windborne blowing • Avalanching snow/drifting snow € •Avalanching •Calving, submarine melt ... internal acc internal melt Calving Submarine melt basal freeze-on basal melt Mass balance components: It’s more than snowfall and melt Total mass budget: sum of climatic balance and frontal ablation Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris. Mass balance components Precipitation - Surface accumulation precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier Accumulation - Net accumulation - Net acc is a balance, acc is not Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris. Winter balance <--> accumulation Summer balance <--> ablation What is measured in ice cores? Ba = Bw+Bs = Acc + Abl Bw= Accw Bs= Ablw Implications for comparison of field measurements with model results? C, A can be modeled, but what is measured often is Bw, Bs Mass balance components Precipitation - Surface accumulation precipitation includes rain; rain water is not accumulation; water is not considered to be part of the glacier Accumulation - Net accumulation - Net acc is a balance, acc is not Melt - meltwater runoff Melt water may refreeze and does not contribute to meltwater runoff Meltwater runoff - Runoff Runoff includes rain water Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris. What is mass balance? Mass balance of a column csfc LAYERS asfc surface ρ snow? compressible? internal ρ firn? ai c h i qin qout basal cb ab !11 What is mass balance? Change of the mass over a stated span of time Mass balance of a column c = accumulation a = ablation (is negative) Δmb= csfc + asfc + ci + ai + cb + ab + qin + qout csfc Surface internal basal flux divergence LAYERS asfc surface ρ € snow? compressible? internal ρ firn? ai Surface c h i qin qout internal qin qout basal !12 cb ab basal Terminology ‘mess’ Mass balance of a column c = accumulation a = ablation Δmb= csfc + asfc + ci + ai + cb + ab + qin + qout Surface internal basal flux divergence Continuity equation € Mass balance ? SMB ? Surface . → q internal q h = b− ∇Q in out Thickness change basal € What is mass balance? Mass balance of a column c = accumulation a = ablation Δmb= csfc + asfc + ci + ai + cb + ab + qin + qout surface Surface internal basal flux divergence q internal q Climatic balance, bclim in € out Climatic-basal balance, b basal (Total) mass balance, Δm . → h = b− ∇Q € What do you measure with GPS vs with a stake? Δmb= csfc + asfc + ci + ai + cb + ab + qin + qout Surface internal basal flux divergence Climatic balance Climatic-basal balance € (Total) mass balance GPS Stake . → h = b− ∇Q € What do you measure with GPS vs with a stake? Δmb= csfc + asfc + ci + ai + cb + ab + qin + qout Surface internal basal flux divergence Climatic balance Climatic-basal balance € (Total) mass balance GPS Stake •GPS --> total mass balance (but partitioning in components unknown) •Stake --> only surface mass balance, measurement relative to top of the stake What do you measure with GPS vs with a stake? GPS Point/part of glacier Glacier-wide Interpolating point data over entire glacier •GPS --> total mass •total mass balance balance --> geodetic balance Stake •Stake --> only surface •total mass balance mass balance, (for land-terminating non- measurement relative to calving glaciers) top of the stake Why does the geodetic method work? Surface - Does not need any ice velocity measurements internal q qout Over an entire glacier (no ice in flowing into another ice mass) the flux divergence is zero, i.e. height changes equal the climatic-basal basal mass balance (accounting for density); assuming no changes at the glacier bed Does an elevation change at point always indicate a change in mass? • changes in elevation dVh dMm dSL can occur without ≠ ≠ changes in mass or dt dt dt visa versa Calving flux • only includes mass loss due to calving •BUT: >50% of the mass loss at the glacier front can be due to submarine melting (even if grounded) ---> frontal ablation • mass loss at the glacier front (includes calving, submarine melting, arial melt/ sublimation ...) What is ice discharge? 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. Time systems: Annual mass balance, i.e. balance over (roughly) one year • stratigraphic system • fixed-date system • floating-date system • combined system Ablation area Accumulation areaAccumulation area Ablation fixed-date fixed-date fixed-date system system system Summer Summer Winter Winter stratigraphic system • End winter snow probing: What system? • Stratigraphic system: dates are unknown !21 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 --> comparing observations with model results problematic if time system not known 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] or as a rate [M L–2 T–1] often kg m–2 or m w.e. 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 [M] kg, Gt (=109 kg, 1 billion tonnes) • 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) Often not included: • changes in ocean area; any delay and storage in transport of water in the terrestrial water cycle • isostatic adjustment of the land surface, tectonic movements • differentiate between grounded and floating ice (floating ice does not contribute to sea-level; grounded ice contributes only to a small fraction since the ice already displaces water) Mass balance time series look different in different units Black Rapids Glacier -1 -1 Gt a by Christian Kienholz a m w.e. PART II Concept of conventional and reference surface balance Claridenfirn, Switzerland, 1916 1914 Mass balance as climate indicator ? Stable climate Step change in Stable climate Ba = 0 climate Ba = 0 Steady-state Ba < 0 Steady-state Glacier retreat 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.