WAIS Elevation changes estimated form the ICESat mission (so far)

1. WAIS Elevation changes estimated form the ICESat mission (so far) B. E. Smith C. R. Bentley C. F. Raymond

2. Plan • Study area • Data • Elevation rate estimates • Discussion

3. Study area • Ross Embayment divided into 28 regions • Regions assumed to have constant, uniform dz/dt. Image: Joughin+Tulaczyk:2002

4. Elevations from GLA12 L2A and L3A campaigns have best pointing models. Other campaigns may have sub-decimeter-scale biases Saturation corrections from GLA01 GLA01 Waveform Energy values before version 19 must be corrected for background levels Data L3C L3A L2A L3B L2C L1 L2B L3C L3A L2A L2C L3B L2B L1 • Data filtering for apparent reflectivity, pulse shape rejects 46% of all data: leaves

5. Techniques za-zd Elevation rate estimates • Assume elevations follow: • as a matrix equation: • The generalized inverse is: • Estimate the elevation rate as • With formal error:

6. Techniques Covariance matrix estimates • Assume that errors are correlated for each pass • Find on-diagonal C from short-period cross-overs: • (s2pass + s2shot)1/2¼ 0.31 m • Find off-diagonal C by finding “best” bias for each track: reduction of variance is spass • spass¼ 0.16 m

7. apparent Analysis Elevation change + e S=0 in steady state Seasonal / unsteady effects · Instrumental errors • Flux divergence • Snowfall • Firn densification • Bed elevation changes

8. Analysis Unsteady and Seasonal effects • Snowfall and firn densification variability lead to short-term elevation changes • Random component: • Treated as significance level • Seasonal component: • Estimate influence by calculating correlation with d (from Wingham:2000)

9. Recovered elevation rates Sensitivities • Formal errors ¼ 0.02 - 0.03 m a-1 • d has no strong correlation with seasonal cycles • Best-fitting seasonal cycle explains ~ 3% of variance • Correcting for best-fitting seasonal cycle does not significantly change dz/dt estimates • dz/dt sensitivity to decimeter-scale laser ranging biases ~ 0.04 m a-1. • Calculated assuming that L2A and L2B campaigns have ~0 bias, L1, L2B, L2C, L3B, L3C have uncorrelated 0.1 m biases. • Sensitivity to L3C bias ~ 0.02-0.03 m a-1.

10. Recovered elevation rates

11. AREA RATE MISW 0.10 § 0.02 MISM 0.01 § 0.02 MISE -0.10 § 0.02 CIRSW -0.14 § 0.02 CIRSE -0.12 § 0.01 CIRN -0.10 § 0.02 WIStrunk 0.10 § 0.02 WISW 0.14 § 0.02 WISS -0.13 § 0.02 WISN -0.10 § 0.02 EIRS -0.05 § 0.02 EIRN -0.02 § 0.01 EIRE 0.20 § 0.03 AREA RATE KIStrunk 0.04 § 0.02 KISjunc 0.36 § 0.02 KISS 0.38 § 0.03 KISN 0.40 § 0.02 SipleDome -0.01 § 0.02 RIRW 0.07 § 0.03 RIRE 0.32 § 0.02 BIStrunk -0.09 § 0.03 BISS -0.02 § 0.03 BISN 0.03 § 0.02 SIR -0.05 § 0.03 MIStrunk -0.03 § 0.03 MISS 0.06 § 0.02 MISN 0.11 § 0.05 HIR -0.01 § 0.03 Recovered elevation rates Less thickening more thickening Less thickening

12. Recovered elevation rates Patterns • Area-weighted mean elevation rate: All regions: +0.057 § 0.025 m a-1 Trimmed mean: +0.023 § 0.026 m a-1 Ignores the three largest and three smallest rates • Conway Ridge is thinning • MIS and WIS are thinning faster upstream • KIS, BIS, and EIS are thinning faster downstream • Thickening in upper KIS appears to affect the adjacent ridges

13. Recovered elevation rates Outstanding Issues • Conway ridge elevation rates do not agree with ground-based GPS measurements • GPS velocities for NW Conway ridge (2001-03) show flux divergence + accumulation ~ 0 (H. Conway, Pers. Comm.), • cross-overs for the same region show dz/dt ¼ –0.08 § 0.07 m a-1 . • The stagnant part of KIS trunk should be thickening at the accumulation rate, instead is approximately in balance • Thinning on BIS, EIS not predicted by flux box calculations (Joughin+Tulaczyk:2002)