The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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£(cr ,) = (<?,- +CT*‘) + 
4 Var(h) 4 R n 
- tan 2 0, (tan 2 S„ + tan 2 S ± ) 
(2) 
where Var(h) is the height variance. 
Therefore the local surface roughness can be derived by 
applying correction terms as follows 
roughness nns = 0.5cja corr 2 -^j-tan 2 0,(tan 2 S„ + tan 2 S ± ) ^ 
In (3), CT C orr is the corrected pulse width which is recorded in the 
MOLA PEDR data record where correction refers to filter 
characteristics and threshold settings, as determined by the 
receiver model (one sigma value, with the minimum limited by 
the filter response; Neumann et al., 2003). The extracted a corr 
value is corrected in two stages: (1) Removal of noisy tracks 
which is shown in Figure 1 a. compared with some noisy free 
reference planes such as HRSC DTMs; (b) slope correction by 
Eq (3). However the extracted a corr values or local surface 
roughness even after noisy track removal and slope correction 
using MOLA height values which is corrected by crossover 
check (Neumann et al., 2001) revealed strong across track 
artefacts which can be observed in Figure 1 b) and c). The 
reason for these across track artifacts is that some of the vertical 
range errors within individual tracks were not corrected. 
The height of the surface can be determined from the MOLA 
measurements and the spacecraft tracking information (Abshire 
et al., 2000) as 
K - [««os 2 + * 2 - ZSAgs cos 2 m 2 - R,„ < 4 > 
where R MCS is the radius of the MGS spacecraft orbit, R^ is 
the radius of reference. The error in R MCS or possibly error of 
the off nadir angle produces a deviation from the surface and 
creates a false across-track slope effect. 
(a) height values 
using MOLA 
uncorrected 
planet radius 
(b) The received 
pulse width after 
removing bad 
orbits 
(c) local roughness 
after slope 
correction using 
500m MOLA 
Gridded DTM 
Figure 1. The influence of noisy MOLA tracks on topographic 
height values, received pulse widths and local 
surface roughness 
Now there is one more correction term in equation (3) 
roughness rmi = 0.5c 
tan 2 0, (tan 2 S luncorrt 
+ tan 2 S„ + tan 2 S x ) 
(5) 
where S Luncorrt is the false slope which is produced by some 
tracking information. 
In this study, the slope correction procedure can be performed 
in two ways. 
1) Apply a slope correction using the height differences 
between un-crossover corrected MOLA tracks and the MOLA 
Grid DTM. 
2) Apply a slope correction in the along track and across 
direction using HRSC & CTX DTMs. The slope values are 
extracted using nearest height points in the across and along end 
side of individual MOLA footprints. This has the added 
advantage of correcting for a local slope error. One very 
important factor is the value of the nominal divergence angle. 
Abshire et al. (2000) stated this value as 93grad. However, 
Neumann et al., (2003) used an approximation consisting of 
fitting 0.5 times the nominal angle from inflight data. The 
nominal divergence angle largely influences the amount of 
slope correction. We tried to find optimal values using 
saturations of the slope correction and height variation of 
HiRISE DTMs and found the optimal values as 33 grad. 
3. RESULTS AND ASSESSMENT 
Our study site is in the Athabasca valley. The main channel of 
the Athabasca valley is covered by HRSC orbit 2099 and CTX 
stereo pair (P01_001540_1889 and P02_001804_1889). Part 
of the valley is covered by HiRISE stereo image pair 
(PSP 001540 1890 and PSP_002371_1890). First of all, 
various stereo DTMs were generated and then the correction 
term was applied to the MOLA beam pulse width. Finally, 
corrected MOLA local surface roughness tracks were compared 
with ortho images and the standard deviation of height values 
derived from the HiRISE DTM. 
3.1 Stereo processing results 
Over the central part of the Athabasca area, four different 
resolution DTMs were extracted (Figure 3). These consists of a 
50m HRSC stereo DTM; 18m CTX stereo DTM; 3.5m HiRISE 
DTM for the whole HiRISE stereo area and a 70cm DTM over 
some selected area. 
Coarse resolution DTMs and ORIs were used for the geodetic 
control of the next stage as described in the previous section, so 
that registration between different DTMs and ORIs can be 
guaranteed so long as the non-rigorous sensor model is 
working. When the ORI products are superimposed from 
different products they appear to be seamlessly co-registered. 
This suggests that the geodetic control accuracy in this research 
is sufficient to allow completion of this analysis (Figure 2). 
Close-up images over a few areas (Figure 3(b)-(f)) using 
different data resolutions, clearly show the kind of information 
which is available from individual DTM sources. For example 
50m resolution HRSC usually show the general outline of the 
overall slope.