# Presentation: 076975

##   Estimating surface elevation changes on WAIS from GLAS altimetry

- Ben Smith
- U of W
- 9/30/04

## Program

- Technique
- Cross-overs
- Estimating errors
- Estimating biases
- Estimating elevation change rates
- Results
- Elevation change by region
- Caveats

## Cross-over technique

- GLAS measures z(lat, lon) on tracks
- The cross-over point is the point whose elevation is measured by both tracks
- Elevation found by interpolation at adjacent points for each track
- Rate of elevation change estimated by (zA-zD)/(tA-tD)
- Get a better estimate by combining many cross-over measurements

- A

- D

## Estimating errors

- Three kinds of errors
- Shot-to-shot errors
- 40 Hz
- instrumental noise
- Estimated (2 cm) from apparent surface roughness
- Pass-to-pass errors
- minutes-hours
- orbital/atmospheric error
- Estimated from cross-over residuals and shot-to-shot error
- Instrumental bias
- Weeks-months
- thermal / pointing problems
- Quantified from regression

## Masking bad data (temporary fix)

- GLAS cloud detection is not necessarily an exact science, but we can filter out the obviously flawed returns.
- Require that return-pulse match a model of a return from a smooth, flat, white surface
- Clouds cause deviations from this model that appear in the GLAS data-parameters
- A conservative set of requirements rejects about 80% of all cross-overs (60% of all data)
- Help is on the way!
-  LIDAR-based cloud-clearing has been implemented, I haven’t used it yet

## Elevation change detection

- The philosophy:
- If the data speak rot, then let them speak rot!
-  Look for elevation changes in glaciologically significant regions
- Plot TA-TD vs. ZA-ZD, take the slope to get z/t
- Eliminate bad data with filters and a convergent 3  edit
- Treat pass/shot errors with a covariance matrix

- TA-TD

- ZA-ZD

## Significance of derived elevation changes

- Accumulation variability can mask long-term elevation changes
- Accumulation rates are on the order of 0.1 m/a (§ 20 %) m/a
- Interannual variability is at least 0.34 A
- This translates to an error of 0.9 T-1/2 A, or about 0.07 m/a.
- We will derive formal errors for rates of elevation change, ignore elevation changes smaller than 2 or smaller than the accumulation error.

## Example: cross-overs on Mercer ice stream

## Instrumental bases

- GLAS has collected data with two lasers, in a total of 4 different configurations:
- Laser 1  : Feb 20 2003 to Mar 30 2003
- Laser 2a: Sep 8   2003 to Nov 20 2003
- Laser 2b: Feb 16 2004 to May 17 2004
- Laser 2c: May 18 2004 to present
- Each period of operation may have a different ranging bias.
- One component of bias steady, one reverses sign for ascenting/descending tracks
- Can try to solve for ranging biases:
-  dest=a(t2-t1)+ (bL2 – bL1) + (bL2A – bL1D )

- z /  t

- Difference in laser biases

- Difference in laser AD biases

## Matrix for bias estimates

- Mean dz/dt

- Range biases

- A/D biases

- Time difference

- Laser difference

- Laser A/D difference

- £

- £

- Constraints

- LaGrange multiplier

- =

- Elevation differences

- Zero

## Cross-over locations/residuals

## Calculated biases

- Increasing  decreases the calculated biases, increases the residual:
- Pick  by requiring that R<1.01 Rmin:
- Laser 1  :   0.068  m (constant) 		0.004 m (AD bias)
- Laser 2a:  -0.151			0.045
- Laser 2b:  -0.047			0.098
- Laser 2c:   0.131			0.022
- Formal errors are on the order of 0.004 m

- 101.5

## Regions for elevation differences

- Elevation changes will be calculated for glaciologically significant regions

## Calculating regional elevation differences

- For all points within a region of the ice sheet, calculate the rate of elevation change
- Data are estimated:
- zest = **T**(dz/dt)est
- Inverse:
- (dz/dt)est =(TT C-1 T)-1 TT C-1z
- T is a vector of time differences
- C is an estimate of the data covariance matrix
- Diagonal elements = RMS residual
- Off-diagonal elements  for same pass =                          [ (RMS residual)2 – (shot error)2 ]1/2
- Z is a vector of elevation differences
- For T-g=(TT C-1 T)-1 TT , the formal error estimate is the square root of the diagonal of  T-gTC-1T-g

## Regions for elevation differences

- Elevation changes will be calculated for glaciologically significant regions

## Elevation changes: results

## Trunk elevation changes

_**Location**__**	**__**Rate (m/a)**_
**Mercer Trunk****	**** -0.11 ****§**** 0.05**
**Whillans Trunk****	****  0.20 ****§**** 0.07**
- Kamb trunk	  0.10 § 0.08
- Bind. trunk	 -0.18 § 0.10
- Macayeal	  0.13 § 0.07

## Tributary elevation changes

_**Location**__**	**__** Rate (m/a)**_
**Whillans 1****	****  0.18 ****§**** 0.06**
**Whillans 2 ****	**** -0.12 ****§**** 0.06**
- Kamb junction	  0.08 § 0.12
**Kamb 1****	****	****  0.46 ****§**** 0.07 **
**Kamb 2****	**** ****	****  0.51 ****§**** 0.09 **
- Bind. 1	 	 -0.01 § 0.07
- Bind. 2	 	  0.05 § 0.08

## Interstream ridge elevation changes

_**Location**__**	**__**  Rate (m/a)**_
**Conway IR****	****  -0.13 ****§**** 0.05**
- Engelhardt IR	  0.08 § 0.05
- Siple Dome	  0.03 § 0.06
- Siple IS	 	  0.24 § 0.13
**Raymond IR****	****  0.31 ****§**** 0.06**
- Shabtaie IR 	  0.11 § 0.11
- Harrison IR	  0.09 § 0.10

## Aggregate elevation changes for catchments

- Mercer	 	 -0.12 § 0.02
- Whillans 1	 -0.08 § 0.02
- Whillans 2	  0.03 § 0.02
- Kamb	 	  0.12 § 0.03
- Bindschadler	  0.07 § 0.04
- Macayeal	  0.06 § 0.04
- Echelmeyer	  0.06 § 0.10

## Reliability test: Bootstrap tests

- To estimate the sampling error on my dz/dt estimates, I
- Generate N synthetic data-sets **X**i by resampling cross-overs *with replacement*.  Require that we have the right number of cross-overs from each period.
- Recalculate dz/dt(**X**i) from each re-sampled data-set.
- dz/dt(Xi) should have the same distribution as dz/dt would if the experiment were repeated.
- Allows assessment of the whole dz/dt process.
- May run into problems with covariance matrix estimates.

## Bootstrap results

- Bootstrap estimates of sampling errors are relatively large.  For the significant rates of change:
- _Region__	__	__Rate Estimate__	__	__Bootstrap error_
- Mercer Trunk	 -0.11 § 0.05 		 0.36
- Whillans Trunk	  0.20 § 0.07 		 0.61
- Whillans 1	  0.18 § 0.06  		 0.54
- Whillans 2 	 -0.12 § 0.06  		 0.54
- Kamb 1		  0.46 § 0.07 		 0.41
- Kamb 2	 	  0.51 § 0.09 		 0.34
- Conway IR	 -0.13 § 0.05    		 0.34
- Raymond IR	  0.31 § 0.06		 0.52
- => This means that the arbitrary nature of the sampling may have had a strong role in determining the elevation change seen!

## Caveats

- More data are on the way (New data take in October)
- The choice of LaGrange multipliers is somewhat arbitrary-  laser bias solution is not unique
- Sampling of cross-overs is random- bootstrap shows that different samples would give different results
- Some of the ridges appear to be changing at a decimeter/year level- perhaps indicates accumulation anomalies for 2003-04

## Conclusions

- There are signs of elevation change, particularly thickening in the Kamb tributaries
- We can rule out elevation changes larger than 1 m/a (at the 2- level) for ice-stream-sized areas.