2005; Zhang et al., 2006; Miller et al., 2009). This presents new 
challenges for how such datasets should be reliably combined, 
particularly under scenarios where direct access to the region of 
interest can prove difficult in terms of collecting control data. 
The goal of surface matching is to register an uncontrolled 
surface, in this case the historic DEM, to a reference surface in a 
way that differences between them are minimized (Mills et al., 
2005). 
In this research, a surface matching algorithm developed at 
Newcastle University is used to reconcile the DEM surfaces. 
This was initially developed for assessment of coastal change 
(Mills et al., 2005) and was subsequently applied to estimate 
glacier volume change in the Arctic (Miller et al., 2009). The 
underlying concept is that one surface is selected as the fixed 
reference surface, while the other surface provides the ‘floating’ 
matching surface. The goal of the algorithm is to recover the 
unknown transformation parameters which will allow the 
matching surface to be rigorously aligned with the reference 
surface (Mills et al., 2005). The algorithm globally minimises 
the distance between points on the matching surface and 
corresponding patches on the reference surface through iterative 
least squares adjustment. The solution, which is applied to the 
matching surface, is a seven parameter 3D  Helmert 
transformation (Tx, Ty, Tz, o, ©, x, s). In this research, the 
algorithm was further enhanced to facilitate minimisation of 
Euclidian distances (as well as vertical distances). Furthermore, 
a capacity to extend the transformation to nine parameters to 
account for independent scale distortions has also been 
implemented Such distortions may occur in the form of 
elevation dependent biases (Nuth and Kääb, 2010). Robustness 
of the solution is achieved by applying an M-estimator to the 
residuals, allowing outliers to be detected and down-weighted 
accordingly. 
The matching was performed only for DEM regions which 
coincided with stable terrain, i.e. rock outcrops. Glacier or snow 
covered areas were excluded from the matching as they would 
bias the result due to a likely surface change. Convergence was 
achieved within less than 10 iterations and the final 
transformation parameters where then applied to all surface 
points for the archival DEMs. Finally, the surface elevation 
differences were computed and glacier change could be 
assessed. The accuracy and precision can be directly estimated 
from the matching statistics. 
5. RESULTS 
5.1. Surface Matching Performance 
The surface matching was successfully applied between the 
historic and modern DEMs and resulted in a significant 
improvement in the accuracy. This is evidenced through the 
histograms of pre- and post-match elevation differences for 
points over stable terrain (Figure 4) at the Nemo glacier site. 
This indicates that following surface matching, mean difference 
value have been reduced to close to zero and are normally 
distributed, suggesting that systematic biases have been 
removed. Figure 4 also details the final transformation 
parameters which were applied to align the 1969 DEM with the 
2005 surface. Table 1 details the difference statistics, and 
further supports this conclusion, with a mean elevation offset of 
-16.17 m prior to matching reduced to close to zero after the 
match. The remaining differences are attributed to the different 
spatial resolutions and random errors. 
    
  
  
500 r 
-—:- Pre-Match Transformations: 
Post-Match Tx = -5.084 M 
Ty - -6.843 m 
T2 = —4.828 m 
n 020.218? 
8 y s -0.086 ^ 
5 - o 
ol. x = —0.030 
en s = 0.999 
d 
0 (hs In } 
-100 -50 50 id 
  
  
Difference [m] 
Figure 4: Histogram of level differences for points over stable 
terrain, at Nemo glacier, between 1969 USGS and 2005 aerial 
photography DEM before and after surface matching. 
The final transformation parameters reflect the uncertainty 
which existed through the initial absolute orientation. In the 
case of registering the USGS data to the present-day aerial 
imagery, the translations were relatively small and the scale is 
relatively stable. The rotational offsets may reflect an imperfect 
distribution of the ‘artificial’ GCPs. However, the matching 
provides a very good fit with the reference data. The derived 
solution is highly rigorous and benefits from the redundancy 
achieved through utilising a large number of DEM points, as 
well a solution which provides a global ‘best fit’ in a least 
squares sense. 
  
  
  
  
  
  
  
  
  
  
dh Pre-Match | Post-Match 
Mean (m) -16.17 -0.99 
o (m) 13.13 10.09 
RMSE (m) 22.72 14.91 
Min. (m) -89.41 -54.05 
Max. (m) 90.66 59.08 
  
Table 1: Statistics of elevation differences over stable terrain, at 
Nemo glacier, between 1969 USGS and 2005 BAS DEM before 
and after surface matching. 
Similar results were found for the matching of the historic DEM 
to the ASTER data at the Leonardo glacier site. The translations 
for the final registration in this case are larger due to the lower 
accuracy and spatial resolution provided by the ASTER data. 
Pre-match offsets of up to = 50 m are not unusual but could be 
successfully corrected with the technique applied here. An 
elevation dependent bias in the ASTER DEM was not observed. 
Given the steep and mountainous terrain of the Antarctic 
Peninsula the minimisation of the Euclidean distance between 
surfaces might be preferred over minimising the vertical 
distance, especially if most of the stable terrain shows steep 
   
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