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Glacier mass and energy balance 1. Introduction 2. The mass balance concept Accumulation and ablation Mass balance years 3. Snow metamorphism 4. Measurement of mass balance 5. Glacier energy balance Energy balance equations Geographic variability of energy balance terms

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glacier mass and energy balance
Glacier mass and energy balance

1. Introduction

2. The mass balance concept

  • Accumulation and ablation
  • Mass balance years

3. Snow metamorphism

4. Measurement of mass balance

5. Glacier energy balance

  • Energy balance equations
  • Geographic variability of energy balance terms

6. Glacier movement

  • Responses to changes in mass balance
  • Glacier surges
slide2
References

Benn, D.I. and Evans, D.J.A. (1998) Glaciers and glaciation. Chapter 2.

Sugden, D.E. and John, B.S. (1976) Glaciers and Landscape. Edward Arnold, London Chapter 3 Glacier Systems

Bennett, M.R. and Glasser, N.F. (1996) Glacial Geology: Ice Sheets and Landforms. Wiley, Chichester. Chapter 3 p 29-37.

introduction
Introduction

Input/output relationships of ice, firn & snow

  • hydrological budget

Importance

  • Catchment hydrology
  • Climate change indicator
  • Sea level rise
  • Global albedo
slide4

A simple throughput model

Regional

climate

Local

climate

Energy

balance

Mass balance

Glacier

Response

Geological

Record

slide5

Introduction (ctd.)

Principal controls

Winter precipitation and temperature

Summer insolation and temperature

The former controls accumulation

The later controls ablation

Terms

Snow unaltered since deposition ±

Firn wetted snow that has survived more than one summer

Ice no interconnecting passages

typical densities
Typical densities

Substance Density (kg m3)

___________________________________________

New snow 50-70

Damp new snow 100-200

Settled snow 200-300

Depth hoar 100-300

Wind packed snow 350-400

Firn 400-830

Very wet snow and firn 700-800

Glacier ice 830-910

Water 1000

Basal ice 900-c1200

___________________________________________

the mass balance concept
The mass balance concept

AS.SN=AEL.V=Ai.IN

where

AS = accumulation zone area

SN =snow (liquid equivalent)

AEL = area of the equilibrium line section

V = mean annual velocity

Ai = area of ablation zone

IN = ice (liquid equivalent)

if

SN =S.r(snow)

IN =I.r(ice)

where r = density

If positive the glacier thickens and/or advances

If negative the glacier thins and/or retreats

a balance year
A balance year

Begins in late summer or autumn

End of winter season

  • late spring or summer ablation>accumulation

End of balance year

  • when accumulation>ablation

Net balance is given by:

bn= bw+bs

or

bn= ct-at

where

bn = net balance

bw = winter balance

bs = summer balance

ct = total accumulation over a year

at = total ablation over a year

slide11
Summer balance

Melted snow and ice lost

Measured by a network of stakes

Temperate glaciers

  • most ice lost by melt and runoff
  • ablation stakes and density corrections

Cold glaciers

  • refreezing of meltwater
  • density change
  • heat input during refreezing
  • superimposed ice
  • internal accumulation
the equilibrium line
The equilibrium line

Temperate glaciers

  • Edge of the previous winter snowline after the end of summer
  • aka firn line

Polar glaciers

  • Boundary between glacial ice of the of the ablation zone and superimposed ice
  • Winter snowline lies above the equilibrium line
slide13
Accumulation
  • snowfall
  • rainfall
  • superimposed ice
  • regelation ice

Ablation

  • surface melt
  • basal and englacial melt
  • evaporation
  • sublimation
  • deflation
  • calving
  • avalanching
snow metamorphism
Snow metamorphism

The dry snow zone

Settling, packing change 0.4-550kg m-3

Changes in crystal size and shape

Deformation, compression

Water

Melting, transportation, refreezing

Increase in grain size

Superimposed ice

Internal accumulation

Depth hoar

Temperature gradient metamorphism

Evaporation at depth, condensation further up

Coarse grained firn

measurement of mass balance
Measurement of mass balance

Direct measurement

Hydrologic

Photogrammetric and geodetic

Remote sensing

slide17
Direct measurement

Most common: sampling ablation & accumulation at sites over the glacier

  • 20 per km2 recommended
  • 1 per 1000 km2 in practice on large ice masses

Winter balance

  • establishing snow pits at different elevations
  • density measurements
  • combine with a network of probed snow depths
slide18
Boas Glacier, Baffin Island
  • 35 density measurements
    • mean = 0.328 g.cm-3 ± 0.04
  • 21 probed cross-sections
    • mean = 1.289m ± 0.32
  • bw = 0.328 x 1.289 = 0.422 (mm H2O)

Area integration:

  • glacier area = 1.45 x 106 m2
  • bw= 1.45x106 x 0.422 = 61x104 m3 H2O
slide20
Photogrammetric

Sequential digital elevation models

Density correction

Snow fields difficult to map

slide21
Hydrologic

Hydrological budget

Precipitation input

Runoff output

Calculate stored water

Depends on reliability of estimates

slide22

San Rafael Glacier

DEM

0-2000m

Hrz resolution 15m

Vert resolution 10m

Velocity

dark blue < 6 cm per day

light blue 6-20 cm per day

green 20-45 cm per day

yellow 45-85 cm per day orange 85-180 cm per day

red >180 cm

(accurate to within 5 mm per day).

Remote sensing

eg Satellite interferometry

general energy balance equation
General energy balance equation

Qs¯+QL¯+Qc+Ql+Qe=Qm+QE+Qs­+QL­+QC

where

Qs = Short-wave radiation

QL = Long-wave radiation

Qc = Heat gained from condensation

Ql = Eddy transfer of sensible heat

Qe = Heat gained by refreezing or melt

Qm = Heat used to melt ice or snow

QE = Heat used for sublimation

QC = Heat conducted into the or ice and used to raise temperature

variability in space and time
Variability in space and time

Latitude and radiation receipt

  • Geographic differences in the proportion of different energy transfers
variability in space and time25
Variability in space and time

Latitude and radiation receipt

  • Geographic differences in the proportion of different energy transfers

Major heat sources Qs, QL, Qc, Ql

  • High latitude and high altitude glaciers net radiation impt.
  • Wide geographic scatter of sites net radiation & sensible heat transfer impt.
  • Coastal high latitudes latent heat transfer important
slide27
Major heat sinks Qm, QE, QC
  • Melting dominant (Qm) - temperate glaciers
  • Sublimation dominant (QC) - polar arid
  • Sublimation & condensation co-dominant (QC & QC) - some polar and subpolar ice masses
glacier movement
Glacier movement

Responses to changes in mass balance

Direct responses and lagged responses

Scale dependency

  • Big glaciers respond more slowly than small glaciers
  • transmission time

Velocity dependency

  • ice temperature
  • bed gradient
  • glacier hydrology

Directional dependency

  • Negative responses fast
  • Positive responses slow
slide32
eg West Coast/East Coast of NZ

Typical response times

  • Valley glaciers 10-60 yrs
  • East Antarctic ice sheet 2,500-5,000yrs

Kinematic waves

  • Development of bulges that travel down glacier 3-5 times faster than average velocity
slide33

Transient flow phenomena: surging

Major perturbations in steady state flow

Characteristics:

  • rapid advances of the terminus over short periods
  • Long periods of quiescent behaviour (years to centuries)
  • Short periods of rapid advance and ice motion (months to a few years)
  • Terminus advance
  • Flattening of upper profile
  • Steepening of lower profile
  • Crevassing
slide35
Hypotheses

Water implicated

Linked cavity mechanism

Subglacial sediment sensitivity

glacier energy balance
Glacier energy balance

Mass balance vs. energy balance

Simplified heat balance:

FT=Fr+Fc+Fl+Fp+Ff

where

FT = Total heat content of the snow/ice

Fr = Radiative heat flux

Fc = Sensible heat flux

Fl = Latent heat flux

Fp = Heat flux from precipitation

Ff = Heat content from freezing