Common use of Statistical measures Clause in Contracts

Statistical measures. Table 4-1 and Table 4-2 show height statistics figures for the CTX MER-A DTM from UCL and UoS. As described above, the HRSC DTM was resampled to fit to the data to be validated. Due to the different resolutions delivered between UCL and UoS, there is a discrepancy in the number of pixel elements evaluated. The UCL DTM (Table 4-1) has a height minimum that is 60 m lower in comparison to the HRSC DTM. In contrast the Maximum is 32 m higher in elevation than the maximum value of the HRSC DTM. As a consequence, the range of heights of the UCL DTM is 90 m larger compared to the HRSC DTM. This could be attributed to the better resolution the UCL DTM is provided in and thus the higher detail to be expected. However, the average height value is comparable with the HRSC DTM value and differs by only 6 metres. The observed standard deviation for the UCL CTX DTM is higher compared to the HRSC DTM. This could be due to the pattern observed that introduces additional noise to the scene. Another source for the higher standard deviation could be the increased detail of the CTX DTM in comparison to HRSC. Though, this appears to be unlikely since the observed effective resolution of the DTM is in the order of 75 m/pixel, as was reported in the previous section. Number of Elements: 4,593,037 4,593,037 4,593,016 Minimum [m]: -3891.83 -3951.59 -121.331 Maximum [m]: -3362.11 -3330.80 125.094 Height range [m]: 529.72 620.79 246.425 Average DN Value [m]: -3678.36 -3672.06 -6.29933 Standard Deviation [m]: 46.6395 54.9509 17.7338 The UoS DTM (Table 4-2), on the other hand, shows a comparable standard deviation with respect to the HRSC DTM. The minimum / maximum heights that are in a similar range to the height range of the HRSC DTM. Only the minimum height value is approximately 60 m below the minimum of the HRSC DTM. The source is seen in the bowl shape of the DTM and the noise in the central parts that have been observed in the colour overlay and the shaded relief. Number of Elements: 2,261,653 2,261,653 2,261,642 Minimum: -3891.82 -3951.42 -321.006 Maximum: -3362.09 -3361.91 106.930 Height range [m]: 529.73 589.51 427.936 Average DN Value: -3684.68 -3678.82 -5.85485 Standard Deviation: 45.6996 46.2945 24.9589 The equivalent figures for the HiRISE and its comparison with the validated CTX DTM are shown in Table 4-3. This indicates that there may be a height offset here which is not fully accounted for by the co-registration process. The standard deviation is very small. CTX DTM HiRISE DTM CTX – HiRISE DTM Number of Elements: 88,182,234 88,182,234 88,182,234 Height range [m]: 101.63 120.84 126.348 Average Height [m]: -3688.85 -3669.31 -19.539 Standard Deviation [m]: 14.078 14.056 5.851

Statistical measures. Table 4-1 3 and Table 4-2 4 show height statistics figures results of the statistical data analysis for the CTX MER-A B DTM from UCL and UoS. UoS, respectively. As described above, the HRSC DTM was resampled to fit to the data to be validated. Due to the different resolutions delivered between UCL and UoS, there is a discrepancy in the number of pixel elements evaluated. The UCL DTM (Table 4-13) has a height slightly lower minimum that is 60 m lower in comparison to the HRSC DTM. In contrast DTM while the Maximum is 32 m higher in elevation than the height maximum value of the HRSC DTM. As a consequence, the range of heights of the UCL DTM is 90 m larger compared differs by 400 metres with respect to the HRSC DTM. This could be attributed to the better resolution the UCL DTM is provided in and thus the higher detail to be expectedvalue. However, since the average height value is comparable with the HRSC DTM value and differs by only 6 26 metres, it is assumed that this maximum height value can be attributed to outliers in either of the two data sets. The observed standard deviation for the UCL CTX DTM is higher compared to in the same order as for the HRSC DTM. This could It would be due to expected that the pattern observed that introduces additional noise to the scene. Another source for the higher standard deviation could be also correlates with the increased detail data set resolution, however, the observed noise in parts of the CTX DTM in comparison scene will significantly contribute to HRSCthis number. Though, this appears to be unlikely since the observed effective resolution of the DTM is in the order of 75 m/pixel, as was reported in the previous section. Number of Elements: 4,593,037 4,593,037 4,593,016 Minimum [m]: -3891.83 -3951.59 -121.331 -2445.93 -2458.73 -540.707 Maximum [m]: -3362.11 -3330.80 125.094 -1690.43 -1285.77 143.094 Height range [m]: 529.72 620.79 246.425 755.50 1172.96 683.801 Average DN Value [m]: -3678.36 -3672.06 -6.29933 -1946.81 -1972.58 25.7694 Standard Deviation [m]: 46.6395 54.9509 17.7338 129.835 122.475 22.8423 The UoS DTM (Table 4-2), 4) on the other hand, hand shows a comparable standard deviation with respect to the HRSC DTM. The minimum / much larger difference in minimum/ maximum heights that are in height values and consequently has a similar range to the height much larger range of the HRSC DTM. Only the minimum height value is approximately 60 m below the minimum of heights in comparison to the HRSC DTM. The source is seen in the bowl shape of the DTM and the noise in the central parts that have been observed in the colour overlay and the shaded relief. The average of the height values of both DTMs differs by about 150 metres indicating that the UoS DTM is on average 150 meters lower than the HRSC DTM. Number of Elements: 2,261,653 2,261,653 2,261,642 2493197 2493197 2493197 Minimum: -3891.82 -3951.42 -321.006 -2445.87 -2702.33 -951.115 Maximum: -3362.09 -3361.91 106.930 -1690.14 -911.927 651.683 Height range [m]: 529.73 589.51 427.936 755.73 1790.40 1602.798 Average DN Value: -3684.68 -3678.82 -5.85485 -1949.88 -1801.35 -148.529 Standard Deviation: 45.6996 46.2945 24.9589 The equivalent figures for the HiRISE and its comparison with the validated CTX DTM are shown in Table 4-3. This indicates that there may be a height offset here which is not fully accounted for by the co-registration process. The standard deviation is very small. CTX DTM HiRISE DTM CTX – HiRISE DTM 130.911 132.611 35.2642 Number of Elements: 88,182,234 88,182,234 88,182,234 53,853,617 53,853,617 53,853,137 Height range [m]: 101.63 120.84 126.348 81.07 338.44 352.922 Average Height [m]: -3688.85 -3669.31 -19.539 -1883.53 -1883.57 0.0468 Standard Deviation [m]: 14.078 14.056 5.85110.317 11.401 7.745 The HiRISE DTM is compared with the corresponding CTX DTM and is shown in Table 4-5. The average height difference is tiny and the standard deviation is also very small.