Small Glaciers: Uncertainties, Measurements, Potential

Improvements

J. Graham Cogley, Geography, Trent University, Peterborough, Canada

gcogley@trentu.ca

www.trentu.ca/geography/glaciology/glaciology.htm

andMark B. Dyurgerov, INSTAAR, University of Colorado,

Boulder, CO, U.S.A.mark.dyurgerov@colorado.edu

Thanks to the Organizing Committee and sponsors of the Sea-Level Rise Workshop, and to the U.S. National Science Foundation (MBD).

Thanks also to Georg Kaser, Mark Meier and Atsumu Ohmura.

Scope and Format

Small-glacier mass balance

Types of measurementDefinition of terms

Sources of uncertainty Possible remedies

Small-glacier observationsAnnualPentadal

NeedsImmediateMedium-term

Types of Mass-balance Measurement

Kinematic: measure ice dischargeGeodetic: measure Δ(volume) and supply densityDirect: at each of many stakes, vertical datum is top

of stake; the aim, as always, is to measure∫(glacier) Δ(ρh) da / (A Δt)

Uncertainties: Internal Accumulation

• Impractical to measure

• Difficult to model

• Difficult to map

• May augment total accumulation by 10-100% on “cold” glaciers

• (Equal to 0 on “temperate” glaciers)

Uncertainties: Local Variability

On any one typical (small enough) small glacier, stake time series are strongly correlated

— so we have ~1-2 degrees of freedom for the whole glacier;

therefore a prudent estimate of error in whole-glacier balance is 100-200 kg m-2 a-1

— which is rather large, and is unlikely to be reducible in practice

Uncertainties: Regional Variability

Whole-glacier balances decorrelate with a length scale of ~600 km

So we can estimate regional balances with fair accuracy where we have a moderate number of measured glaciers

In remote regions, no estimate is likely to be much better than, e.g., the global average

And correlation between balances does not mean equality of balances

Uncertainties: Spatial Interpolation

Accumulation Standard Error ofAccumulation

A polynomial algorithm can estimate errors of interpolation quite well

But every algorithm has 2 or more tunable parameters, for trading smoothness and fidelity

And the location of any solution in a >2-D tuning space is not objectively constrained

Uncertainties: The Incomplete WGI

The World Glacier Inventory covers <1/3 of the ice, even after recent renewed efforts

The GLIMS project (Global Land Ice Monitoring from Space) will help, but perhaps not quickly enough

Uncertainties: Shrinkage of Glacier Ice

• The smallest glaciers are shrinking fastest, and data are incomplete

• But, roughly, we may have lost 1/6 of the extent since the 1950s

A ∫ [f(s) da(s)/dt] ds

= -2624 km2 a-1

Measurements: Source Data

Measured glaciers:325 in total

≤100 in any one year(a shifting population)

significant spatial bias towards northern mid-latitudes

Annual: Time Series

• Arithmetic-average series: seems innocuous; can go badly astray

• Area-weighted series: noisy; may contain interesting structure

Annual: Trends, Anomalies, Variability

• Decadal trends, year by year – so any one year affects ten (only 3-4 degrees of freedom)

• Mass loss tends to accelerate (i.e., trend is growing)

• — but there may also be some decadal variability

• Acceleration: recently, about 0.04-0.08 mm a-2 (definitely not zero)

• Censoring eruption years has a distinct, but moderate, effect

• Natural variability (+ noise): of the order of 0.2-0.3 mm a-1

Annual: Exploratory Analysis of Forcing

• Three eruptions appear each to affect two following years, so censor six years of each forcing

• Volcanos (and perhaps solar irradiance) apart, the small-glacier system seems to mask “external” forcing with its own internal variability

Censor 6 Years of Deviation from Trend

(std. errors)

Total Effect on Sea Level

(mm SLE) No removals 0.0 0.00.0 Volcanic eruptions -3.3 -1.61.1 Solar (high) 1.5 1.41.3 Solar (low) -1.2 -0.91.7 El Niño -0.2 -0.22.1 La Niña 0.1 0.11.8 NAO large -0.8 -0.71.4 NAO small 0.5 0.31.6

Pentadal: General Considerations

• In series which are serially uncorrelated, a sacrifice of temporal resolution yields a substantial reduction of uncertainty

• Three current mass-balance analyses, when viewed together, yield a picture which is broadly concordant

• Many, but not all, sources of error are addressed

• The average of the analyses, and their errors when combined conservatively, yield a rugged (not a rigorous) “consensus estimate” of the evolution of mass balance

Pentadal: Mass Balance with Error Bars

Global small-glacier balance(mm SLE a-1) was 0.39±0.20 in 1961-1990 1.01±0.20 in 2001-2004

Trend (mm SLE a-2)is 0.018±0.002 over 1971-2004

Immediate and Medium-term Needs

• Internal accumulation, Calving glaciers– field studies; modelling studies

• More measurements; more coverage

• New technology, especially:– laser-altimetric geodetic measurements– passive-microwave monitoring of melt

• More reliable basic facts– a complete World Glacier Inventory

• More rigorous analysis of errors– especially errors of interpolation

Conclusion

For twenty years we have struggled toextract a mass-balance signal from avery noisy glaciological record

Now, Nature seems to be solvingour problem by sending a muchstronger signal

But, if anything, the methodologicalneeds have become more pressing,as we struggle to keep up