PRINCIPLES OF GLACIOLOGY ESS 431 - MASS and ENERGY BUDGETS - IN THE CRYOSPHERE OCTOBER 17, 2006 Steve Warren sgw@atmos.washington.edu
Sources Paterson, W.S.B. 1994. The Physics of Glaciers. 3 rd ed. Pergamon. Lecture notes from C.F. Raymond and E.D. Waddington Rolf Tremblay http://tea.armadaproject.org/tremblay/12.1.2000.html HASAS http://www.geo.ed.ac.uk/~hasas/introen.html
Mass and Energy Budgets The Big Picture Mass budget driven by winter snowfall and summer melting, fundamentally different processes Energy budget dominated by solar radiation
Geological Survey of Canada, Map 1257A
Mass budget seasonal snow At Schefferville, Quebec (last stand of Laurentide ice sheet) Snow accumulates slowly, melts fast All snow gone in early summer Accumulation rate varies with location, microclimate. (Figure from Adams& Rogerson, Eastern Snow Conference, 1968.
Mass-Balance Definitions Accumulation c ablation a Snow Depth Time
Mass budget high on a glacier Snow on surface at all times Accumulation c is greater than ablation a This is the situation high on Easton Glacier -Site with seasonal snow -- site in glacier accumulation area
Mass budget low on a glacier No snow on surface in late summer Accumulation c is less than ablation a This is the situation at Easton Glacier terminus
How does a Glacier Work?
For glacier with terminus above sea level In accumulation area: c>a In ablation area: a>c W(x) is glacier width L is terminus position Steady-State Glacier c a = L c( x) W ( x) dx 0 = L a( x) W ( x) dx 0 c = a If then glacier is in balance (steady state), not growing, or shrinking
Alternative Glacier Behavior Not all glaciers behave this way In Antarctica: a ~ 0 Almost no melting (on the surface) Why does Antarctic Ice Sheet not keep growing?
Alternative Glacier Behavior Not all glaciers behave this way In Antarctica: a ~ 0 Almost no melting (on the surface) Why does Antarctic Ice Sheet not keep growing? Melting on the underside of floating ice shelves Icebergs calve off, drift away, and melt (this is the dominant mass-loss mechanism by far)
c and a are fundamentally different Many factors, both local and distant, can affect accumulation Local factors (energy) affect melting
c and a are fundamentally different Many factors, both local and distant, can affect snow accumulation Moisture source Storm tracks Local temperature Local wind Local factors (energy) affect melting Sunlight Infrared (IR) radiation Sensible heat (warm air)
Achieving the balance Small accumulation, little melting Glaciers in the polar regions Large accumulation, much melting Glaciers in tropics and temperate regions Glaciers in maritime climates Or not Climate can be cold with no glaciers Alaska North Slope (too dry)
Conditions favoring glaciation High snowfall, usually in winter, but there are exceptions, e.g. Himalayas (why?) Cool summers We will now look at net mass balance of a glacier Then we will look at the melting portion in more detail
Mass-balance Terminology Accumulation All processes by which mass is gained Ablation All processes by which mass is lost To fully characterize a glacier, we need this information at many points on its surface
Mass-balance Terminology c(t) b(t) b n a(t) To fully characterize a glacier, we need this information at many points on its surface Mass balance terms (J.T. Andrews)
Zones on a Glacier Can superimposed ice form if firn temperature is 0 o C? Temperate glaciers have only wet-snow zone and ablation zone (W.S.B.Paterson. 1994, based on C. Benson (1961)
Measurements in Accumulation Area (Not all snow melts) Winter Accumulation Dig snow pit at start of summer Find previous summer surface (how?) Measure density ρ(z) Net Mass Balance Dig snow pit at end of summer Find previous summer surface Measure density ρ(z) Net balance (+) End of previous summer Beginning of summer End of summer (Firn is snow that has survived through a complete year)
Measurements in Ablation Area (Some ice from previous years also melts) Winter Accumulation Install poles into ice in fall Measure height above ice Find snow depth in spring Measure density ρ(z) Net Mass Balance Measure height of pole above ice Net balance (-)
Caveats These measurements apply to a temperate Glacier like Easton Glacier at Mt. Baker (at melting temperature throughout) Why? (superimposed ice is not lost from glacier) Easier to measure net mass balance than accumulation or ablation separately Why? (they can occur simultaneously) Other complications frost deposition, sublimation, wind drifting summer accumulation (e.g. monsoon)
Works in polar regions too Net Mass Balance Dig snow pit Find previous summer surfaces (how?) Measure density ρ(z) back-lit snow pit at Siple Dome (Rolf Tremblay ) http://tea.armadaproject.org/tremblay/12.1.2000.html
Balance Year Mass Balance b(t) = c(t) a(t) b(t) reaches maximum at end of winter net balance b n is balance at end of summer End of balance year is when ablation rate no longer exceeds accumulation rate In practice it is easier to define a fixed date each year for each glacier October 1 is a convenient date in Washington
Snow Line Transient boundary on glacier surface between snow and ice/firn glacier is snow-covered by spring snow line moves upward during summer uppermost location of snow line at end of summer (on average) is called firn line or equilibrium line b n =0 at equilibrium line
Late-summer snow line on Blue Glacier, Mt. Olympus
Steady State Mass Balance b(t) = c(t) a(t) net balance b n is balance at end of summer x L E bn ( x) W ( x) dx = 0 x For Steady State: Amount of snow (mass) left above ELA at end of summer is exactly equal to mass of ice lost in ablation area. E b n ( x) W ( x) dx Or stated another way, b ( x) W ( x) dx = 0 0 L n x=0 is head of glacier x E is Equilibrium line x=l is terminus W(x) is glacier width
Mass-balance Gradient on Blue Glacier, Mt. Olympus Mass loss Mass gain
AAR (Accumulation-Area Ratio) AAR = Accum._ Area Total _ Area Net accumulation Balanced by flow Net ablation
Accumulation-Area Ratio Balanced glaciers (that end on land) have AAR ~ 0.5 0.8 Why is AAR 0.5?
AAR 0.5 Balanced glaciers (that end on land) have AAR ~ 0.5 0.8 Why is AAR 0.5? Glaciers tend to start in broad snow fields, then funnel into glacier tongues Tongues tend to descend long distances into regions of very high ablation With high ablation rate, ablation area must be small in order to achieve balance
AAR and Glacier Health If AAR 0.5 (for a glacier that ends on land) Glacier is in trouble, unless it has a highly unusual accumulation/ablation pattern
AAR and Past Climate Geologists use AAR ~0.6 to reconstruct ELA (Equilibrium Line Altitude) and climate for past glaciers However, AAR is only an approximate gauge of glacier balance
AAR in Antarctica What is AAR of East Antarctic Ice Sheet? What would AAR be if Antarctica was still a part of Gondwana?
AAR in Antarctica What is AAR of East Antarctic Ice Sheet? AAR ~ 1.0 (There is almost no ablation area, even when including melt under ice shelves) When part of Gondwana? Terminus was on land so there was a sizeable ablation area probably had AAR ~ 0.6
Equilibrium A glacier in Steady State has flow that exactly balances b n (x)
Disequilibrium Ablation and Accumulation are not exactly balanced 0 L b n ( x) W ( x) dx Glacier will grow or shrink in volume Elevation changes due to flow will no longer exactly balance elevation changes due to melting or accumulation Glacier length will change 0
Glaciers as indicators of Global Warming Glaciers are retreating. How much has Earth warmed? J. Oerlemans used measured retreat rates of 48 glaciers from 1850 to 1990. Model of surface energy balance to relate melting rate to temperature Model of glacier flow to relate length changes to melting changes Result 0.65 o C/century Thermometers give 0.5 o C/century Is this good or bad agreement? Oerlemans, J. 1994. Quantifying global warming from the retreat of glaciers. Science 264, 243-245.
Thermometers Measure Global Warming P.D. Jones. 1988. Journal of Climate.
Energy Balance - Sources Melting of snow or ice surface is determined by energy balance Sources of energy for snow pack: Net radiation sensible heat latent heat R + SH + LH Sunlight, (+) heat from air (+) frost deposition, Infrared to snow condensation on ice, (+) by day (-) heat from snow riming (-) by night to air (-) sublimation, (usually) evaporation (LH of melting will be on r.h.s.)
Energy Balance - Sinks Sinks of energy in snow pack: If (R+SH+LH) >0 Raise temperature of snow if T<0 o C Melt snow (or ice) if T=0 o C If (R+SH+LH) <0 Cool snow Freeze pore water (can be 2-3% water by volume in temperate ice)
Energy in Melt Season Typical Blue Glacier (Mt. Olympus): Radiation R 50-85% 57% Sensible heat SH 34% }15-50% Latent heat LH 9% Typically R > SH > LH
Radiation Balance at Snow Surface Avalanche Handbook
Types of Radiation Radiation is the dominant source of energy in snow Incident and reflected solar radiation - sunlight short wave (SW), wavelengths 0.2-4 μm Infrared radiation - heat energy emitted by surface and atmosphere (greenhouse) longwave (LW) 4-50 μm --------Longwave-------- ------Shortwave------ emitted by emitted by incident reflected atmosphere surface R = SW - SW + LW - LW
Typical Radiation Fluxes R = SW - SW + LW - LW Approx. average over Earth s surface 200 W m -2-30 + 330-390 +110 W m -2 (balanced by SH, LH to atmosphere) Typical melting glacier in summer 200 W m -2-120 + 280-310 +50 W m -2 Lower sun but longer days Brighter surface Colder clouds and air Colder surface (0 C ) (used for melting)
SW α = SW Albedo (α) 0 < α < 1 Black Reflective white Clean snow typically reflects 80% of sunlight α = 0.8 Old melting snow α = 0.65 Glacier ice α = 0.4-0.6 High albedo of snow helps to maintain snow (keeps it cold): albedo-temperature feedback Energy-balance equation becomes: R = SW ( 1 α) + LW LW
R = SW ( 1 α) + LW LW What does each term depend on? SW - season, latitude,time of day, clouds α - snow vs. ice, age of snow, depth of snow, impurities LW - air temperature, clouds, humidity LW - snow-surface temperature
Longwave Radiation Usually compared to an ideal black body A black body emits radiation depending on its temperature: 4 LW = σt Stefan-Boltzmann constant: σ= 5.67 10-8 W m -2 K -4 (K = deg Kelvin) Non-black body: Emissivity 0 < ε < 1 LW = εσt 4 ε = 1 for perfect black body Snow has emissivity ~0.98 (If we had infrared eyes, snow would look black!)
Radiative Cooling I LW determined by temperature of clouds or air Thick cloud is a blackbody in infrared Cloud impedes surface cooling at night Clear night sky encourages surface cooling At night, SW =0, R<0 R = 0 + ε σt 4 ε σt 4 air air snow snow On a long clear night (e.g. in Antarctica) R 0 (equilibration with atmosphere; SH and LH are small) 4 air ε T = air ε snow T 4 snow
Radiative Cooling II On clear nights 4 air ε T = air ε snow T 4 snow Snow is more emissive than atmosphere ε < ε air snow 1 Surface must be colder than air Inversion layer can be tens to hundreds of meters thick T > T air snow 500 Height (m) T 0
Temperature profiles in winter at South Pole Station (Hudson & Brandt, J. Climate 2005) lowest 8000 m lowest 500 m lowest 2 m
Sensible and Latent Heat Air cold warm dry humid (warm) SH SH LH sublim n LH depos n Snow warm evap n condens n cold humid humid (cold)
Latent Heat
Latent Heat II Importance of transitions varies with location: Sublimation -2830 J g -1 Antarctic slopes, 50% of annual snowfall Frost Deposition +2830 J g -1 Antarctic plateau, adds energy, not much mass Freezing (rime) +330 J g -1 Mt. Olympus, adds both mass and energy Keeps glacier warm Condensation (dew) +2500 J g -1 warm humid winds over melting glacier Adds energy but no solid mass Evaporation of Meltwater -2500 J g -1 Warm dry air over melting glacier
Shrinking Tropical Glaciers Tropical Glaciers are shrinking rapidly in New Guinea, East Africa, Andes Mid-latitude glaciers melt Smooth ablation areas Supraglacial streams Tropical glaciers sublimate Penitentes
Penitentes Río Plomo Glaciers, Argentina http://www.geo.ed.ac.uk/~hasas/introen.html
Energy Budget for a Jogger Humans stay cool by sweating when in bright sun The sunlight evaporates sweat rather than cooking the person Heating: R (+ SH, but SH << R) Energy comes from sunlight Cooling: LH Energy is used up changing liquid to vapor R (heating by sun) LH (evaporation of sweat)
An increase of relative humidity was suggested as a cause for rapid retreat of tropical glaciers, but recent measurements show instead a decrease of upper-tropospheric relative humidity in tropics. Energy Budget for a Tropical Glacier Air is generally very dry over tropical glaciers Sunlight can sublimate ice rather than melting Sublimation (2830 J g -1 ) vs. melting (330 J g -1 ) Each Joule of sunlight eliminates less than 1/8 as much ice if it causes sublimation rather than melting. Tropical glaciers may exist only because the air is dry and ablation is dominated by sublimation. If air becomes more humid, glaciers may convert to melting regime; rate of mass loss would increase by factor of 8.
Homework problem discussion: You found that the imbalance of radiation necessary to melt the North American Ice Sheet in 10,000 years is just 0.05 W m -2. This implies that latent heat of melting does not limit the rapidity of ice-sheet retreat. To understand this, rewrite the energy-balance equation, moving the upward longwave (LW ) to the right-hand side to be a response rather than a forcing. Define M as the energy used for melting. SW (1-α) + LW + SH + LH = LW + M On the ice sheet, if T<0 C, M=0. Also, LW =σt 4. So SW (1-α) + LW + SH + LH = σt 4
SW (1-α) + LW + SH + LH = σt 4 If there is excess energy supplied, increasing the left-hand-side (e.g. if the sun gets brighter), then the temperature will rise, increasing the right-hand side until balance is again achieved. Or if the LHS decreases, temperature will drop to regain balance. So there is no melting until T reaches 0 C; then T can't rise anymore as long as there is still ice. So an energy imbalance can't melt ice unless T=0 C. In the Earth's climate system, the melting of an ice sheet is an indicator of warmer temperature rather than a sink for excess energy.
Can we estimate mass balance from energy budget? Difficult to observe energy terms directly on glacier Use correlations to nearby weather stations e.g. Forks for glaciers in Olympic Mountains Accumulation related to winter precipitation at Forks Ablation related to summer temperature at Forks