3.1.

Fishlake Flood of 8–20 November 2019

Fishlake is a village in Yorkshire, England, near the river Don east and downstream of Doncaster. It was originally a fishing village on the Don (now diverted to the south). It has a population of 700 and is surrounded by farmland. Some parts of Fishlake have high housing density (30 houses/hectare), though the average density over the whole village is 15 houses/hectare. The flooding was caused by an extreme weather event due to an area of low pressure stalling over the north of England. The river Don and its tributary burst their banks into an area that was already heavily sodden from rain over a period of weeks. More than 1000 homes from the village and surrounding area had to be evacuated, leaving many residents homeless for days.⁵⁰ According to the EA flood risk map, the area flooded has a low risk of flooding with an annual exceedance probability (AEP) between 0.1% and 1%, as the river Don is constrained within 7-m high flood barriers as it flows past Fishlake. The flooding was imaged by S-1 on November 11, 2019, and November 14, 2019 (Table 1). There was little flooding on the image of November 08, 2019.

A number of aerial photos showing the urban flooding were available for validation [e.g., Figs. 3(a) and 3(b)]. The flood hydrograph is shown in Fig. 3(c) and indicates that the SAR images were obtained on the falling limb.

Fig. 3

(a) Flooding in Fishlake on November 11, 2019, looking from E (©SWNS); (b) flooding on November 14, 2019, from NE (©PA); and (c) levels for river Don at Fishlake (Ref. 51, vertical dashed lines mark overpass times).

3.2.

Pontypridd Flood of 15-16 February 2020

Pontypridd is a former coal-mining town to the north of Cardiff on the river Taff in Wales, with narrow streets and dense Victorian terraced housing. It has a population of 33,000 and sits in a steep-sided valley, at the confluence of the Taff and its tributary the Rhondda. In the east of the old town next to the river Taff, the housing density is 75 houses/hectare. More than 1000 homes and businesses were damaged after rivers flooded when Storm Dennis hit communities in south and mid-Wales on February 15, 2020, to February 16, 2020. The storm was classed as a weather bomb due to the large drop in pressure associated with it. The center of Pontypridd was extensively affected after the river Taff flooded [Figs. 4(a) and 4(b)].⁵² From the Natural Resources Wales flood risk map, the area flooded has a low risk of flooding, with an AEP between 0.1% and 1%. Although the duration of the flooding was not long, an S-1image was acquired at 6.31 am on February 16, 2020 (Table 1), only an hour or so after the flood peak, which, coupled with the fact that validation photos were taken the same morning, make this an ideal data set for study. The flood hydrograph is shown in Fig. 4(c).

Fig. 4

(a) Flooding in Taff Street, Pontypridd town center (© BBC News); (b) flooding in Sion Street adjacent to river (© Richard Swingler); (c) levels for river Taff at Pontypridd (Ref. 51, vertical dashed line marks overpass time).

4.1.

Estimation of Water Levels Away from High DSM Slopes

Flooded areas in the DSM are first mapped using the ‘bare soil flood mapping’ algorithm developed in Ref. 42. This compares backscatter intensities from an S-1 post-flood image with those from a preflood image. The algorithm has been implemented as the HASARD system on the ESA Grid Processing on Demand platform.

Prior to the application of the algorithm, the HASARD system first performs all the preprocessing steps that need to be applied to each SAR image, using the ESA SNAP toolbox. The preprocessing steps include precise orbit correction, radiometric calibration, thermal noise removal, speckle reduction, terrain correction, and reprojection to the WGS84 coordinate system.

The HASARD flood mapping algorithm is based on adaptive thresholding of the SAR backscatter using a hierarchical approach, such that regions falling below the threshold in the postflood image are classed as flooded, while those above are unflooded. The method exploits multitemporal information to detect changes and contextual information through region growing. Permanent water bodies are suppressed using change detection.

The HASARD system outputs a binary flood extent map, which is subjected to further processing. Waterlines are detected in the map by applying the Sobel edge detector.⁵³ To increase accuracy and suppress false alarms, waterline levels in regions that are sufficiently far (11 m) from high ($>0.5$) DSM slopes are selected, provided they are within the expected height range of flooding. A waterline level is likely to be determined more accurately on a low slope. This also avoids false alarms near high DSM slopes, which may give rise to shadow/layover areas. These waterlines away from high DSM slopes will largely occur in rural areas, but may also be found in urban areas.

These regions are unlikely to occur on completely bare soils but rather in fields that are vegetated to some extent. The heights of their WLOs may be slightly under estimated due to vegetation height not being taken into account in the bare soil algorithm. Pixels adjacent to low-slope flooded regions may have high rather than low backscatter because of double scattering in vegetation that is flooded but still emergent. To cope with this, these flood regions are modified by merging into them pixels that are adjacent to them and have high scattering ratios between post- and preflood images.

Figure 6 shows the flood extent determined by HASARD for Fishlake on November 14, 2019, together with post- and preflood S-1 subimages after preprocessing. Figure 6 shows flooding in the rural areas surrounding the village, but little flooding in the urban area because backscatter here is higher than the threshold used in HASARD.

Fig. 6

(a) Postflood S-1 intensity subimage of Fishlake flood of November 14, 2019; (b) preflood S-1 subimage of Fishlake of September 15, 2019; and (c) “bare-earth” flood map produced by HASARD (flood-water = blue; WGS84 coordinate system).

4.2.

Estimation of Water Levels from Double Scattering in Urban Areas

In dense urban areas, there would be little flooding identified by HASARD because of the high postflood backscatter that often occurs there due to double scattering between flooded roads and adjacent building walls. This mechanism may be used to identify urban flooding.

Strong edges in the DSM (mainly corresponding to building edges) are first detected using a Roberts edge detector.⁵³ This calculates the magnitude and direction of the local gradient at a pixel using a small $2\times 2\text{-}\text{pixel}$ window centered on the pixel. The Roberts detector is used rather than a more robust one having a larger kernel (e.g., Sobel) because the width of streets in dense urban areas may be comparable to the DSM pixel size. Edges having too large an aspect angle φ to the satellite direction of travel ($>35\mathrm{deg}$) are suppressed, as the SAR image is unlikely to exhibit substantial double scattering at these edges. Because the aspect angle calculated may be rather noisy using the Roberts operator, selected pixels are also required to have not too low a backscatter in the preflood image, on the basis that a correctly oriented double scatterer should give a reasonable backscatter even in the preflood image. A caveat is that such pixels should not have too high an elevation to avoid selecting pixels of high backscatter from sloping roofs.

At each edge pixel, the pixel and the immediate neighbor on either side of it along a line centered on the edge pixel and perpendicular to its edge direction are selected. These three pixels are examined to find the maximum intensity ratio between the postflood and the preflood images, the maximum DSM height (assumed to be from a building roof), and the minimum DSM height. The minimum height is required to be in the height range expected for flooding to reduce outliers from heights above reasonable flood levels. It is assumed that the minimum height is the local ground height where the DSM and the Digital Terrain Model (DTM) coincide, so that there is no need to generate a separate DTM from the DSM prior to the processing. As a check, at this stage, the DTM heights of the edge pixels are regressed against their intensity ratios, as DTM heights should in general fall as intensity ratios rise.

A set of strong edge pixels is chosen that have high intensity ratios and are likely to be mainly flooded, together with another set whose members have ratios close to 1 and are likely mainly unflooded. A condition of set membership is that each member of the first set must be spatially close to a member of the second set, and vice versa. This condition ensures that the flooded double scattering pixels are chosen to be near the flood edge, so that their flood depths are likely to be shallow, as required by Eq. (3). The average DTM heights are estimated for pixels in both sets. The averaging process is essential to reduce the noise in the DTM heights of the individual double scatterers.⁵⁴ It is assumed that double scattering is largely from unvegetated roads and pavement, and that the DTM varies reasonably slowly in the vicinity of the flood edge. To test this latter hypothesis, a t-test is performed on the two averages to check that they are not significantly different. Provided this is so, the local flood height is then chosen as the mean of the flooded and unflooded average DTM heights. The idea in estimating this local flood height is to try to find WLOs at double scattering pixels on both sides of the waterline and close to it in the urban area. This is somewhat analogous to finding WLOs on waterlines in rural areas.

If there are insufficient pixels with intensity ratios close to 1, this indicates that all of the urban area is flooded. In this case, the method will give no result, and it is assumed that a water level threshold can be constructed from flooding of nearby rural areas. If there are insufficient pixels with large intensity ratios, this indicates that none of the urban area is flooded and the local flood height is set to the DSM height below which only a small percentage of lower heights in the urban area lie.

In regions that are predominantly urban, the number of WLOs that are far from high slopes in the DSM may fall, but the number of WLOs from double scattering should rise to compensate.

Figure 7 shows the accepted double scattering points for flooded and unflooded pixels for the Fishlake urban area for the image of November 14, 2019, superimposed on the WorldDEM DSM. This is a descending pass image and S-1 is right-looking, so that most of the double scattering points should lie immediately to the east of buildings, which does appear to generally be the case.

Fig. 7

WorldDEM DSM for Fishlake urban area, with double scattering points for descending-pass S-1 image of November 14, 2019, superimposed (height range = 0 to 19 m, lighter gray = higher, blue/red = flooded/unflooded double scatterers; BNG coordinate system).

It should be noted that the polarization of the S-1 images in IW mode is Vertical-Vertical (VV). Considering a double scattering wall-ground combination and assuming a brick wall of complex dielectric constant 4.53 – j0.31 as given in Ref. 41, its Brewster angle is 65 deg. If the SAR incidence angle at the ground is 25 deg, it will be incident on the wall at the Brewster angle.⁴⁵ At this angle, reflection from the wall will be extinguished, and the wall-ground combination will no longer act as a high-intensity double scatterer, in either the pre- or postflood image. It is, therefore, important that the local incidence angle at the study sites considered is $>25\mathrm{deg}$. In fact, the S-1 incidence angle range in IW mode is 29.1 deg to 46 deg, and in Table 1 it is shown that the local incidence angles are greater than the minimum.

A further point is that the range position of the double reflection from a building in the postflood image is shifted toward the near range compared to its position in the preflood image,⁴¹ due to the depth of the floodwater ($h_W-h_G$). According to Eq. (9) of Ref. 41, the slant range is reduced by ($h_W-h_G$) $\cos \theta$. However, as it has been assumed that the flooding depth is small near the flood edge, the reduction is small compared to the slant range pixel size after multilooking.

Coherence between pre- and postflood images has been shown to be a useful adjunct for detecting flooding in urban areas, though SAR intensity still appears to be the dominant measure.^4,37–39 Compared to using double scattering, coherence may not be so useful in high density urban housing because of the averaging operation over a large window required to measure it and the consequent reduction in spatial resolution, especially using S-1 images. However, it might still be useful in urban areas where the buildings are not oriented to produce much double scattering. While coherence has not been used here, the method could easily be modified to accept coherence as an additional measure of urban flooding.

4.3.

Combining Water Levels

At this stage, the WLOs from pixels away from high slopes in the DSM are combined with the WLOs estimated by double scattering in urban areas.

To take into account the fall-off of water level down the reach and that different parts of a domain may be flooded to different depths, a local combination method is used in which the domain is subdivided into nonoverlapping rectangular $m\times n\text{-}\text{pixel}$ subdomains of $\sim 1\text{-}\mathrm{km}$ side. Within each subdomain, an average water level is calculated from WLOs of pixels away from high slopes, together with a further average of WLOs from double scattering. The combined water level for the subdomain is calculated as the weighted mean of these two averages, with the weighting being determined by the number of WLOs of each type. If there are only WLOs of one type available in a subdomain, the average water level for that type is taken as the average for the subdomain. If there are no WLOs of either type available for a subdomain, its water level is set to that of the nearest subdomain with a high proportion of urban coverage. A water level surface $\mathrm{O}(x,y)$ for the whole domain is then obtained by performing linear interpolation between the water levels of the individual subdomains.

4.4.

Modification of the DSM by Flood Return Period Maps

If FRP maps are available, they can be used to modify the DSM, if necessary, in a preprocessing operation.³⁶ The advantage of FRP maps is that if there are urban areas that are lower than the flooding but protected from it (e.g., by embankments), this information should be contained in the maps, which would assign high return periods to such areas.

Details of the method are given in Ref. 36. The first stage is to estimate the return period $rp(x,y)$ of each point in the floodplain using the FRP maps provided by public bodies. Usually, 3 to 5 maps are made available, and for each pair of contiguous maps, an interpolation technique is applied to derive intermediate FRP maps. Regions classed as flooded due to low backscatter in the postflood SAR image are used to estimate a return period for the flood. Floodplain pixels having return periods $rp(x,y)$ less than this estimate are classed as flooded. If some portion of the urban area is protected, this will be encapsulated in the FRP maps as high return periods at the protected pixels, which will result in these not being classed as flooded. It is worth noting that a disadvantage of the FRP maps is they do not contain information about any temporary barriers erected to mitigate the flooding.

A further difficulty with FRP maps is that it may be difficult to access them rapidly in an emergency. However, it would still be possible to obtain an urban flood detection accuracy without the FRP data, though it may be an overestimate of the urban flooding because protected urban areas are not screened out from the flooding.

4.5.

Flood Detection in Urban Areas

The final stage is to extract urban water regions from the effective height image $eff\_h(x,y)$ using the water level surface $O(x,y)$. For pixels in urban areas

5.1.

Fishlake

Table 1 gives details of the two postflood images analyzed for Fishlake on November 11, 2019, and November 14, 2019, together with their associated preflood images.

Both these image pairs were processed by the HASARD system, with the small object size limit set to 10 pixels (Sec. 4.1). The flood extent map produced by HASARD for November 14, 2019, shows flooding in the rural area surrounding Fishlake, but little flooding in the urban area itself because of double scattering raising the SAR backscatter here (Fig. 6). The flood extent map for November 11, 2019, was very similar to Fig. 6.

The SNAP toolbox was used to collocate the WorldDEM DSM and SAR intensity maps, and to reproject these from WGS84 to the British National Grid (BNG) coordinate system, for comparison with the EA LiDAR data at the validation stage.

In the double scattering analysis (Sec. 4.2), edges in the DSM were required to be at least 2-m high. Correctly oriented edge pixels were defined as having high intensity ratios (${{\sigma }^0}_w/{{\sigma }^0}_g$) if their ratios were $>2.5$, and having ratios close to 1 if these were $<2$. An edge pixel having high (low) intensity ratio was required to be within 150 m of a pixel of low (high) intensity ratio to be included in the set of high (low) ratio edges. For both postflood image dates, the slopes of the regression line of the DTM heights of the double-scattering edge pixels against their intensity ratios were slightly negative, in keeping with the expectation that DTM heights should fall as intensity ratios rise.

At the stage of combining water levels from both types of WLO (Sec. 4.3), the $3\times 3{\mathrm{km}}^2$ domain of the Fishlake area [Fig. 8(a)] was subdivided into nonoverlapping square subdomains of 1-km sides.

Fig. 8

(a) WorldDEM DSM of Fishlake area [$3\times 3{\mathrm{km}}^3$, urban area visible in aerial photos masked out (black)]; (b) correspondence between SAR image of November 11, 2019, and aerial photo flood extent in urban area that is visible in aerial photos, superimposed on the WorldDEM image (lighter gray = higher; yellow, wet in SAR and aerial photos; red, wet in SAR only; and cyan, wet in aerial photos only); and (c) as (b) but for SAR image of November 14, 2019.

From the EA flood risk map,⁵⁵ the area flooded has a low risk of flooding, with an AEP of between 0.1% and 1%, as the river Don is constrained within high flood barriers as it flows past Fishlake. Because there were no sharp discontinuities in risk in the urban area, there was no need to use the flood risk map to modify the DSM to account for high return periods in protected areas (Sec. 4.4).

The aerial photos were used in conjunction with the 2-m EA LiDAR data to construct validation flood images. It was found by manual inspection that a simple flood-fill of the LiDAR DSM up to the level of the waterline in the aerial photos could match the flooding in the aerial photos for each postflood S-1 image date. This was a straightforward way of extracting the waterline from the aerial photos without having to resort to manual digitization. The validation image for each postflood S-1 image date was constructed at the WorldDEM DSM resolution by applying the relevant flood-fill height threshold in the WorldDEM DSM. There appeared to be little bias between the WorldDEM and LiDAR DSMs over this area. The mean flood height was slightly lower in the image of November 14, 2019, than that of November 11, 2019, as the flood was slowly receding during this period.

The urban area of Fishlake turned out to have a mixture of WLOs from nearby rural areas and WLOs from urban double scatterers. Table 2 gives the mean flood heights of the two types of WLO, together with those of the validation images, for the central $1\times 1{\mathrm{km}}^2$ subdomain of the Fishlake area containing the village. It can be seen that, for both flood image dates, the mean height of water levels away from high DSM slopes is lower than the mean of the flooded and unflooded double scatterer average heights, in the case of November 11, 2019, significantly so. A possible reason for this is that the water levels of WLOs away from high slopes were being underestimated due to the vegetation height corrections to the HASARD bare soil algorithm being too small. The correction was only a few cm, whereas it might be expected to be 10 to 20 cm or so.

Table 2

Flood heights of both WLO types and validation images, for central 1×1  km2 subdomain of Fig. 8(a). Errors quoted are standard errors on the means.

Figure 8(b) shows the class correspondence between the S-1 image of November 11, 2019, and the aerial photo flood extent in the urban area that was visible in the aerial photography, superimposed on the WorldDEM image. Figure 8(c) shows the correspondence for the S-1 image of November 14, 2019.

The performance measures used to assess the flood detection accuracy were the flood detection rate [i.e., $\text{Recall}=t_p/(t_p+f_n)$], the Precision $[=t_p/(t_p+f_p)]$, and the critical success index [$\mathrm{CSI}=t_p/(t_p+f_p+f_n)$], where $t_p$ = true positives, $f_n$ = false negatives, and $f_p$ = false positives.

Table 3 gives the performance measures in the urban area for November 11, 2019, and November 14, 2019. For both dates, there was a good flood detection rate (87% and 100%, respectively), with associated high rates of Precision and CSI.

Table 3

Urban flood detection accuracy.

The relationship between the intensity ratio and the angle $\phi$ between the wall of the double scatterer and the SAR direction of travel was also examined. The object was to measure how fast the ratio fell as $\phi$ increased from 0 deg. If the fall was very rapid, this might reduce the number of double scatterers that could be distinguished as flooded or unflooded in the postflood image. A set of 10 reasonably isolated unambiguous flooded double scatterers was identified in the Fishlake image of November 14, 2019. These had building heights in the range 4 to 6 m and flood heights $<1\mathrm{m}$. For each building, the angle $\phi$ and building height were measured manually in the 2-m LiDAR DSM. This approach was taken because these variables measured using the WorldDEM DSM were rather inaccurate. Figure 9 shows the relationship between the ratio and $\phi$. Although the sample size is small, the data are not inconsistent with a peak at $\phi =0\mathrm{deg}$ with a rapid fall off as predicted by Ref. 37, though there are still a significant number of ratios $>2.5$ at angles $>10\mathrm{deg}$.

Fig. 9

Relationship between S-1 intensity ratio and angle $\phi$ to satellite track.

5.2.

Pontypridd

The postflood image of February 16, 2020, and its preflood associate (Table 1) were processed by the HASARD system, with the small object size limit set to 10 pixels. Figure 10 shows the flood extent map produced by HASARD, together with post- and preflood S-1 subimages after preprocessing. HASARD detected flooding in the rural part of the valley north of Pontypridd, but little flooding in the urban area itself because of double scattering raising the SAR backscatter here.

Fig. 10

(a) Postflood S-1 intensity subimage of Pontypridd flood of February 16, 2020; (b) preflood S-1 subimage of Pontypridd of February 14, 2020; and (c) “bare-earth” flood map produced by HASARD (flood-water = blue; WGS84 coordinate system).

The urban area of Pontypridd proved to be a stiff test of the method because of its narrow streets of terraced houses with high housing density, set in a valley with steep-sloping sides (Fig. 11). Figure 11(b) shows an extract from the WorldDEM DSM covering the center of Pontypridd, and Fig. 11(c) shows the LiDAR DSM averaged to the same 12-m scale. While it is to be expected that many streets will be missing in the WorldDEM DSM because their widths are less than the WorldDEM resolution, it is also apparent that there is more sensible structure and less noise in the downscaled LiDAR.

Fig. 11

(a) WorldDEM DSM of Pontypridd area; (b) expanded view of WorldDEM DSM in red rectangle covering town center; and (c) downscaled LiDAR DSM of red rectangle (BNG coordinate system).

In the double scattering analysis, the same edge strength, intensity ratio, and distance thresholds were used as in the Fishlake case. Figure 12 shows the accepted double scattering points for flooded and unflooded pixels for the Pontypridd urban area for the image of February 16, 2020, superimposed on the WorldDEM DSM. The S-1image was again descending pass and right-looking, so that most of the double scattering points should lie immediately to the east of buildings, which often does appear to be the case. Both the flooded and the unflooded double scatterers seem to be located in sensible places.

Fig. 12

WorldDEM DSM for Pontypridd urban area with double scattering points for descending-pass S-1 image of February 16, 2020, superimposed (height range = 46 to 138 m, lighter gray = higher, blue/red = flooded/unflooded double scatterers).

The domain used for the Pontypridd flood was $2\times 4{\mathrm{km}}^2$, as the urban areas are largely confined to the lower areas near the valley bottom [Fig. 13(a)]. For the purpose of combining the two WLO types, the domain was subdivided into four nonoverlapping rectangular subdomains of size $2\times 1{\mathrm{km}}^2$ each. The section of Pontypridd subject to flooding lay in rectangle (0, 2) [with (0, 0) being furthest north]. This subdomain had no WLOs from areas away from high DSM slopes, and the WLOs measured were all due to double scattering from buildings.

Fig. 13

(a) WorldDEM DSM of Pontypridd area ($2\times 4{\mathrm{km}}^2$, urban area visible in aerial photos masked out); (b) correspondence between SAR image of February 16, 2020, and aerial photo flood extent in urban area that is visible in aerial photos, superimposed on the WorldDEM image (lighter gray = higher; yellow, wet in SAR and aerial photos; red, wet in SAR only; and cyan, wet in aerial photos only).

From the Natural Resources Wales flood risk map,⁵⁶ the area flooded has a low risk of flooding, with an AEP of between 0.1% and 1%. Because the whole of the urban area had the same AEP, there was no need to use the flood risk maps to modify the DSM to account for high return periods in protected areas.

The aerial photos were used to construct a validation flood image at the WorldDEM DSM resolution by the method used for Fishlake. The river was not included in the flood class.

Table 4 gives the mean flood height of the double scatterers, together with that of the validation image, for the rectangular $2\times 1{\mathrm{km}}^2$ urban subdomain of the Pontypridd area at (0, 2). There were no WLOs from pixels away from high slopes in this subdomain, so that the mean flood height was estimated solely from double scattering. Unlike the Fishlake case, the slope of the regression line of the DTM heights of the double-scattering edge pixels against their intensity ratios was slightly positive, so that the mean height of the flooded double scatterers was slightly higher than that of the unflooded ones. This may be due to limitations in the DSM in this scenario. Even so, the overall weighted mean height was not significantly lower than the flood height estimated from the validation image.

Table 4

Flood heights of both WLO types and validation images, for 2×1  km2 subdomain covering central Pontypridd. Errors quoted are standard errors on the means.

Figure 13(b) shows the class correspondence between the S-1 image of February 16, 2020, and the aerial photo flood extent in the urban area that was visible in the aerial photography, superimposed on the WorldDEM image. Table 5 gives the flood detection performance measures in the urban area for February 16, 2020. At 72% accuracy, the flood detection rate can only be described as reasonable, while the Precision is reduced (63%) because there are a substantial number of false positives. These inaccuracies are partly caused by the fact that the streets in Pontypridd are so narrow that the WorldDEM DSM may overestimate the height in the streets, so that they are not classed as flooded. For example, the flooding in Taff Street has not been detected [cyan in Fig. 13(b)], though that in Sion Street has [yellow in Fig. 13(b)]. The high false-positive rate is partly due to an area of the WorldDEM DSM west of the town center being slightly low compared to the LiDAR.

Table 5

Urban flood detection accuracy.

A further difficulty with narrow streets roughly parallel to the satellite track is that the backscatter from a double scatterer wall-ground combination in one street may be affected by that from the roof of a house in the next street farther in ground range from the satellite. In this case, the return from the roof may fall into the same slant range bin as that from the double scatterer. The return from the roof is likely to be strong, though as the roof would be unflooded in the postflood image, its intensity ratio may be 1. If the double scatterer happens to be flooded, the additional signal from the roof may reduce the intensity ratio for the double scatterer.

It is clear from the above results that a DSM with higher spatial resolution than that of WorldDEM would be beneficial for detecting urban flooding for the Pontypridd flood. A higher resolution version of WorldDEM (HDEM) has been developed using the TanDEM-X mission data.⁵⁷ HDEM relies on several new acquisitions with larger baselines resulting in smaller height errors from phase noise, giving a DSM with 6-m pixel size yet similar height accuracy to WorldDEM. However, only selected areas of the globe have been processed, so that HDEM is not a publicly available global DSM. Nonlocal Interferometric SAR (InSAR) filters have also been used to generate higher resolution DSMs from TanDEM-X data, though again these are not publicly available and global.⁵⁸ An airborne InSAR 5-m DSM is available for Pontypridd instead of WorldDEM under the NEXTMap Britain program.⁵⁹ Airborne InSAR data at 5-m resolution are available at both national and regional scales, but are mainly confined to Western Europe, North America, and the Middle East, and again are not global.

We also investigated whether image deblurring could be used to improve the WorldDEM DSM prior to detecting urban flooding using it. Blind deconvolution was applied to an upscaled version of the DSM having half the pixel spacing (6 m) of the original. The iterative deconvolution method in MATLAB^® was used, which restored the image and the point spread function (PSF) simultaneously using the Richardson–Lucy algorithm.⁶⁰ Prior to deblurring, the one-dimensional (1D) PSF of the WorldDEM image was estimated at a number of sharp edges in the LiDAR DSM. As a result, the initial estimate of the 2D PSF input to the deblurring was normally distributed with a standard deviation of 9 m. The revised PSF after deblurring was very similar to this. The deblurred DSM visually appeared to have more structure in it than the original. Using the deblurred DSM to predict urban flooding produced flooding in Taff Street, but also introduced false positives elsewhere. The urban flood detection rate fell slightly from 71% to 64%, while the Precision fell from 63% to 51% because the false-positive rate rose (Table 5). Overall, deblurring of the DSM gave a worse result than the original.