E rrors in the com putation of line-of-sight velocity

This section aims to quantify potential errors in the nine computations of Austfonna's line- of-sight velocity field that were obtained as described in section 3.4. The sensitivity o f the results to phase error will first be established. The effects of topographic error and baseline error will then be discussed.

4.3.1 Sensitivitv to phase error

Using equations (2.7) and (2.9), line of sight velocity can be differentiated with respect to the phase-difference 0%2 determine its sensitivity to phase error. Thus we obtain :

(4.15) where Avr0 is the error that is due to phase error.

So for a temporal baseline At of 3 days, a 2;rphase error would produce a 3.5m/yr error in v^. Correspondingly, the same phase error in an interferogram with a 1 day temporal baseline would result in a 10.5m/yr error in v,..

Based on the analysis in Section 4.1.1 Figure 4.7 quantifies the contribution to Vr

error that is due to the scattering component of phase error

4.3.2 Sensitivitv to height and baseline errors

Again referring to equations (2.7) and (2.9) it can be seen that our ability to calculate also depends on our ability to determine the topographic range-difference At^2- As shown in

equation (3.2) At^^ is comprised of a linear term, Ar^^, that is strongly dependent on baseline, and a superimposed topography dependent term Af^^. Therefore errors in will introduce into a linear, baseline dependent error and a superimposed height- related error Av,^. Joughin et al. (1996b) derive the following expressions for these errors :

(4.16)

-(^ » ,2 sin % + ^g„,cos6>^,)

(4.17)

where Azt is the height error in the DEM that was used to extract the topographic effects from each single-pair interferogram. These errors will now be considered separately.

a) 1 3th /16th F eb . ‘9 2

■ _ W " '

b) 16th/19th F eb . ‘9 2 c ) 2 0 th /2 3 rd M ar. ‘9 2

d) 6 th /9 th Jan. ‘9 4 e ) 9 th /1 2 th Jan. ‘94 0 12th /15th Jan. ‘9 4

g ) 2 4 th /2 7 th Jan. ‘94 h) 5th /8th F eb . ‘9 4 2 0 km

I_____ I

t i

C orrelation related lin e o f sig h t v e lo c ity error Avr^s

0 0.4 > 0 .4 (m /y )

i) 15th /16th D e c . ‘9 5

&

/

Figure 4.7 L ine-of-sight velocity error that is due to p h a se scatter error, i.e. p o o r correlation. The associated correlation images can be seen in Figure 3.5. The errors are generally below 0.4m/y.

a) 13th/16th F eb. ‘92 b) 16th/19th F eb . ‘92 c ) 2 0 th /2 3 rd M ar. ‘9 2

d) 6th /9th Jan. ‘94 e ) 9 th /1 2 t b Jan. ‘9 4 0 12th/15th Jan. ‘94

g) 24th/27th Jan. '94 h) 5th/8th F eb. ‘9 4 i) 15th/16th D e c. ‘95

2 0 km

I______ I (m /y )

□

F igure 4.8 E rro r in lin e-o f-sig h t velocity that arises due to to p o g ra p h ic error, assum ing that topographic error is as show n in Figure 4.4h (Section 5.1 w ill show that this is a reasonable assumption).

Sensitivity to height error

Table 4.2 quantifies for each of the nine interferometric pairs used in section 3.4 to calculate Austfonna's line-of-sight velocity field. It shows that the results are reasonably insensitive to height error. In section 5.1.3 the mean accuracy of the corresponding DEM is established as 10m, resulting in errors of just a few tens o f cm/y, depending on the temporal and spatial baselines of individual image pairs. If phase scatter error is assumed to be the dominant source of height error (Figure 4.4b), then can be quantified more specifically, as shown in Figure 4.8.

Primary image PsLci(i) Secondary image PsLC2(i) Av,^ / Azt (cm y-i m*0 At (days)

First Ice Phase 13th Feb. '92 16th Feb. '92 -2.7 3

16th Feb. '92 19th Feb. '92 7.6 3

20th Mar. '92 23rd Mar. '92 -3.1 3

Second Ice Phase 6th Jan. '94 9th Jan. '94 -3.0 3

9th Jan. '94 12th Jan. '94 3.8 3

12th Jan. '94 15th Jan. '94 6 .0 3

24th Jan. '94 27th Jan. '94 5.0 3

5th Feb. '94 8th Feb. '94 -0.3 3

Tandem Phase 15th Dec. '95 16th Dec. '95 7.5 1

Table 4.2 Line-of-sight velocity error in cm/y per metre o f topographic error fo r each o f the interferometric pairs used in this research. Values are based on mid-scene baseline and range measurements , with variations occurring in the fir s t decimal place.

Sensitivity to baseline error

Figure 4.9 is a plot of the baseline dependent error Av^b per centimetre of baseline error (using equation 4.17), assuming equal errors in and Bp^^. As in Figure 4.6, the form of this error is an azimuth varying ramp, though it can be seen that the effect o f baseline error on the velocity results is far less than the corresponding error in the topography results.

The tie-points used to constrain the baseline param eters o f the single-pair interferograms (Figure 3.7b) were not so well distributed as those used to constrain the topography results. In order to determine the effect of this the simulation experiments perform ed in Section 4.2.3 were repeated using the nine single-pair baseline geometries, and the alternative tie-point distribution. Errors in the assumption of zero velocity at these tie-point locations were also simulated. In all cases the residual baseline errors were, at most, just a few centimetres. We can therefore be confident that baseline error will account

Far-range N ear-range

Figure 4.9 P red icted v, error p e r centim etre o f baseline error (assum ing =

in equation 4.17). A large zero-offset has been removed, since any such offset w ould be com pensated in the com putation o f the unw rapping constant by the use o f tie-points (see A ppendix 2).