Small Glaciers: Uncertainties, Measurements, Potential Improvements

1. Small Glaciers: Uncertainties, Measurements, Potential Improvements J. Graham Cogley, Geography, Trent University, Peterborough, Canada gcogley@trentu.ca www.trentu.ca/geography/glaciology/glaciology.htm and Mark 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.

2. Scope and Format Small-glacier mass balance Types of measurement Definition of terms Sources of uncertainty Possible remedies Small-glacier observations Annual Pentadal Needs Immediate Medium-term

3. Types of Mass-balance Measurement Kinematic: measure ice discharge Geodetic: measure Δ(volume) and supply density Direct: at each of many stakes, vertical datum is top of stake; the aim, as always, is to measure ∫(glacier) Δ(ρh) da / (A Δt)

4. 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: Internal Accumulation

5. 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

6. 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

7. Uncertainties: Spatial Interpolation 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 Accumulation Standard Error of Accumulation

8. 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

9. The smallest glaciers are shrinking fastest, and data are incomplete But, roughly, we may have lost 1/6 of the extent since the 1950s Uncertainties: Shrinkage of Glacier Ice A ∫ [f(s) da(s)/dt] ds = -2624 km2 a-1

10. Measurements: Source Data Measured glaciers: 325 in total ≤100 in any one year (a shifting population) significant spatial bias towards northern mid-latitudes

11. Annual: Time Series • Arithmetic-average series: seems innocuous; can go badly astray • Area-weighted series: noisy; may contain interesting structure

12. 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: Trends, Anomalies, Variability

13. 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

14. 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

15. 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

16. 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

17. Conclusion For twenty years we have struggled to extract a mass-balance signal from a very noisy glaciological record Now, Nature seems to be solving our problem by sending a much stronger signal But, if anything, the methodological needs have become more pressing, as we struggle to keep up