Improving the TanDEM-X Digital Elevation Model for flood modelling using flood extents from Synthetic Aperture Radar images. Remote Sensing

The topography of many floodplains in the developed world has now been surveyed with 13 high resolution sensors such as airborne LiDAR (Light Detection and Ranging), giving 14 accurate Digital Elevation Models (DEMs) that facilitate accurate flood inundation 15 modelling. This is not always the case for remote rivers in developing countries. However, 16 the accuracy of DEMs produced for modelling studies on such rivers should be enhanced in 17 the near future by the high resolution TanDEM-X WorldDEM. 18 In a parallel development, increasing use is now being made of flood extents derived from 19 high resolution Synthetic Aperture Radar (SAR) images for calibrating, validating and 20 assimilating observations into flood inundation models in order to improve these. This paper 21 discusses an additional use of SAR flood extents, namely to improve the accuracy of the 22 TanDEM-X DEM in the floodplain covered by the flood extents, thereby permanently 23 improving this DEM for future flood modelling and other studies. 24


Introduction
al., 2012)), the TanDEM-X DEM might be spatially averaged to produce a DEM of lower 150 resolution and higher accuracy, in others (e.g. modelling of urban flooding) the full resolution 151 of the TanDEM-X DEM might be required. If it is required to extract WLOs from the SAR 152 flood extents, these would be most accurate using the highest resolution of the TanDEM-X 153 DEM.

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The objective of the paper is to investigate the increase in height accuracy in the TanDEM-X 155 IDEM that can be achieved in the floodplain area covered by the SAR flood extents using 156 these extents. due to combination of different coverages is present for the IDEM. The error is considered to 165 be a random error, but DLR (2011) cautions that there will be phase unwrapping errors that 166 will only be resolved in the final DEM. The average slope of the river over this length was 167 approximately 1 x 10 -4 . Fig. 3 shows a land cover map of the area, which is largely rural with 168 the town of Pershore just to the north of centre.

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The test was based on an approximately 1-in-10-year flood event that occurred on the river in         3.2. Pre-processing. 269 The 12.5 m resolution IDEM and its height error map were re-sampled to the 2.5 m resolution 270 of the CSK images using nearest neighbour interpolation, so that blocks of 5x5 pixels in each 271 downscaled map contained the same values (see section 3.5).

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The SAR images were processed to level 1C-GEC, which meant that they were geo-corrected 273 to approximately100 m. It was necessary to register the images to British National Grid 274 coordinates using ground control points and a digital map, when a registration accuracy of 275 better than 2 pixels (of size 2.5 m) was obtained. The height error at a waterline pixel due to 276 mis-registration should be small compared to the random error on an IDEM pixel height.

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It was important to minimise inaccuracies in the SAR flood extents extracted, as these might 279 give rise to inaccuracies in the corrected IDEM.

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In the absence of significant surface water turbulence due to wind, rain or currents, flood 281 water generally appears dark in a SAR image because the water acts as a specular reflector, backscatter that were long, thin, fairly straight and adjacent to flood regions were 300 automatically reclassified as flooded. It was verified that no urban areas (which might also 301 have had high backscatter) were misclassified as flooded in this step. The backscatter 302 threshold was also raised to include in the flood category regions of flooding adjacent to the 303 flood class that had slightly higher mean backscatter than the original threshold (e.g., due to 304 wind ruffling the water surface in more exposed parts of the floodplain). Note that no DTM 305 information was used in the segmentation process.

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Using contemporaneous aerial photographs, the algorithm has been shown to produce    However, this was felt to be too elaborate for the current study given the likely short 351 vegetation heights, and it was assumed that any height error due to the failure to remove short 352 vegetation heights would be small compared to the IDEM random height error.

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Finally, candidate water line pixels were required to lie within a certain height range centred 354 on the mean water height in the area. In order to find the allowed waterline level range in the 355 area, a histogram was constructed of the waterline levels, and the position of the mean was 356 found. A normal distribution N(µ, σ 2 ) was fitted around the mean µ, and candidate waterline 357 points with levels more than 2.5σ away from µ were suppressed. capable of choosing an optimal window size (e.g. Kervrann, 2004).

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A value for n of 11 in the 12.5 m IDEM space was chosen by experiment. This ensured that 376 adjacent heights were sufficiently local that they were likely to form an isoline section, but 377 also that close to the maximum possible number of candidate pixel heights were corrected.

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Values of n less than 11 tended to produced higher height standard deviations and correct 379 fewer pixels (because a minimum of 4 adjacent heights was required), whereas values greater 380 than 11 produced little reduction in standard deviation compared to that for n = 11. The latter 381 is likely to be because the waterline is only a quasi-contour because there is a fall in water 382 elevation moving downstream along the river, and this fall may not be linear over a long 383 distance. The average number of adjacent heights employed was 11. 384 3.6. Adjustment of the IDEM between adjacent higher and lower waterlines. 385 Each pair of adjacent waterlines in the time sequence was examined to update the section of 386 IDEM between the current pair of waterlines if possible. No averaging of height was 387 performed in correcting heights between waterlines, so that spatial resolution was maintained.

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The updating process was based on the heights and height errors associated with the 389 candidate waterline pixels on the waterline pair. All IDEM pixels between the waterlines in  where σ i ' is obtained by equating the two sides of equation [5].

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However, a complication arises because the situation for IDEM pixels below the lower 422 waterline is not the same as that for pixels above the higher waterline. In the latter case, 423 pixels must be at least no higher than the corrected heights along the higher waterline, 424 otherwise they would emerge from the flood extent. The method for the lower waterline 425 assumes that there is a monotonic increase in height between the lower and higher waterlines.

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Another possible scenario is that, moving away from the lower waterline, there is initially a 427 rise in height that is followed by a fall to below the lower waterline, before the IDEM rises was significantly lower than that of the local waterline.

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An important requirement of the method was that locally the higher waterline of the pair 441 should never be lower than the lower waterline, and to this end lower waterline candidate 442 pixels higher than nearby higher waterline candidate pixels were suppressed in a pre-443 processing step.

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In addition, any IDEM pixels enclosed within the lowest waterline boundary were assessed 445 for possible modification so that locally they did not exceed this waterline height. On the 446 other hand, no attempt was made to modify IDEM pixels outside the boundary of the highest 447 waterline that were lower than the highest waterline. This was because, for example, an 448 embankment might have been present at the edge of the highest flood extent, so that, even if 449 lower areas of floodplain were present beyond the embankment, these would not be covered 450 by water.

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In the above method, pixel heights between the waterlines were only modified if they lay 452 above the higher or below the lower waterline of a pair. One consequence of this was that the 453 upper and lower height errors associated with a height could be different. An alternative 454 method that was also studied involved modifying the height to lie at the centre of its 455 associated error range, so that the upper and lower height errors once again became the same.

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On average about 45% of the waterline pixels in each flood extent became candidate pixels 458 able to satisfy the selection criteria of having a low/medium slope, not being a height outlier, 459 and coinciding with short vegetation.

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Original and corrected IDEM candidate waterline pixel heights were compared to 461 corresponding airborne LiDAR heights (  The results for the alternative method of height correction in which a corrected IDEM height 542 was modified to lie at the centre of its associated error range, so that its upper and lower 543 height errors were symmetric, are given in table 5. For the 63% of pixels between the 544 waterlines in the grassland/arable class whose heights were modified, the symmetric error For the 23% of pixels between the waterlines whose heights were not modified but reduced in at the equator (in interferometric wide-swath mode assuming that ascending and descending 564 passes and overlaps are used). Table 6 shows that, if IDEM heights both above the higher and 565 below the lower waterline are modified, the standard deviation of the difference between the 566 Simplest of all to acquire would be a single SAR image obtained near the peak of the flood.

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In this case IDEM heights within the flood extent could only be corrected above the 578 waterline. A surprising result was how much correction could be achieved using only the 579 single SAR image of 27/11/2015. Table 6 shows that, for this case, the standard deviation of 580 the difference between the corrected IDEM heights and the corresponding LiDAR heights 581 was 66% that of the original IDEM heights. This is only slightly worse than for the 2-image 582 case, though the latter is able to modify heights below the lower waterline for IDEM pixels 583 lying between the higher and lower waterlines, and also should be able to modify more using two images rather than one has in this case introduced more errors that have tended to 605 offset the increased accuracy that should be obtainable. Fig. 7 shows, for the red square of  or down to the relevant waterline to maintain spatial resolution, though methods involving 658 smoothing followed if necessary by rounding could also be considered.

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A caveat regarding the method is its effect on dykes adjacent to the river, which the water