Fusing Digital Elevation Models to Improve Hydrological Interpretations

Improving the accuracy of digital elevation is essential for reducing hydrotopographic derivation errors pertaining to, e.g., flow direction, basin borders, channel networks, depressions, flood forecasting, and soil drainage. This article demonstrates how a gain in this accuracy is improved through digital elevation model (DEM) fusion, and using LiDAR-derived elevation layers for conformance testing and validation. This demonstration is done for the Province of New Brunswick (NB, Canada), using five province-wide DEM sources (SRTM 90 m; SRTM 30 m; ASTER 30 m; CDED 22 m; NB-DEM 10 m) and a five-stage process that guides the re-projection of these DEMs while minimizing their elevational differences relative to LiDAR-captured bareearth DEMs, through calibration and validation. This effort decreased the resulting non-LiDAR to LiDAR elevation differences by a factor of two, reduced the minimum distance conformance between the non-LiDAR and LiDARderived flow channels to ± 10 m at 8.5 times out of 10, and dropped the nonLiDAR wet-area percentages of false positives from 59% to 49%, and of false negatives from 14% to 7%. While these reductions are modest, they are nevertheless not only consistent with already existing hydrographic data layers informing about stream and wet-area locations, they also extend these data layers across the province by comprehensively locating previously unmapped flow channels and wet areas.

In terms of acquisition and availability, DEMs of varying origins are becoming freely accessible [8] [10] [15]- [23].Some of these are listed in Table 1 [19] [20] [21] [22] [23], i.e., the Shuttle Radar Topography Mission (SRTM90 and SRTM30 DEMs) and the Advanced Spaceborne Thermal Emission and Reflectance Radiometer (ASTER DEM).These are satellite derived and global.Also listed are: the nationally available DEM for Canada, i.e., the Canadian Digital Elevation Model (CDED, generated from elevation contours and spot heights), and a provincial example, e.g., the New Brunswick DEM (NB-DEM) derived through stereo-photogrammetry.Also increasingly available are Light Detection and Ranging (LiDAR) DEMs generated from point-cloud data through air-borne laser-light scanning and pulse return classification [24].
Elevation differences between LiDAR and other DEMs (hereby referred to as In this regard, the former refer to Digital Surface Models (DSMs), while the latter refer to Digital Elevation Models (DEMs).Both are subsets of Digital Terrain Models (DTMs) [5].LIDAR point cloud data can be used to generate DSMs as well as DEMs through determining elevation differences between the first and last laser pulse returns, generally at a vertical accuracy of ± 0.15 m [24].
All DEMs can be used to generate hydro-topographic interpretations pertaining to, e.g., flow directions, flow accumulation, stream channel networks, upslope basin areas and borders, location of depressions, and extent of areas subject to flooding and well-to-poor soil drainage.These interpretations are, however, influenced by DEM accuracy [28]- [34].For example, 10 to 20 m DEMs are preferable to determine seamless flow-channel connectivities across roads, but lead to underestimating slope steepness especially along shorelines, road cuts and deeply incised stream valleys.High-resolution LiDAR DEMs can serve both purposes, by using them at their finest resolution to determine where roads potentially block channel flow and therefore need to be breached, or where the DEMs need to be re-sampled towards coarser resolutions to approximately connect flow channels across barriers without breaching.In contrast, attempts to increase the resolution of photogrammetrically-derived non-LiDAR DEMs through re-interpolation alone do not generate more information, but introduce DEM artifacts such as "ridging" [35].
Several approaches are available to reduce vertical and lateral DEM errors through fusion.These involve DEM re-projecting, re-sampling, re-interpolation, amalgamation, and hydrological enforcement (e.g., [36] [37] [38] [39] [40]).For example, the extent of "ridging" can be reduced through DEM editing by way of Tin Random Densification [22] and/or spatial filtering [41] [42].Luedeling et al. [43] applied a DEM fill technique to fill SRTM voids with ASTER data.Fusing DEMs for the purpose of DEM-error reduction was reviewed by [39] 2) using bare-earth 1m LiDAR elevation data as reference DEM; 3) nearest-distance conformance testing of non-LiDAR versus LiDAR-derived flow channels; 4) evaluating false positives and false negatives within DEM-derived cartographic depth-to-water indices (DTW [32]) for each DEM.

Methodology
Located in Eastern Canada and spanning an area of 7,282,014 ha, the Province of New Brunswick encompasses an array of diverse geomorphologies and landforms, and has province-wide non-LiDAR DEM and hydrographic network coverages available from Service New Brunswick's GeoNB data catalogue, and Li-DAR coverages for parts of the province (Figure 1, Table 1).The SRTM and ASTER DEMs were acquired through the United States Geological Survey Branch's Earth Explorer application.The CDED data were obtained from Natural Resources Canada.A semi-automated ArcGIS 10.1 five-stage process (Figure 2) was developed as follows:

Results
Elevation differences, by DEM Layer.The layer-by-layer non-LiDAR to LIDAR elevation differences are overlain on the corresponding hill-shaded DEMs in Figure 3.Among these, the contour-derived CDED differences are smoothest, the NB-DEM differences are ridged, and the ASTER differences are the most variable.Across the LiDAR-DEM coverages, the differences tend to be NBDEM-Fused 0.3NB-DEM 0.375SRTM90 0.325CDED (weights were chosen to eliminate elevation "ridging" across NBDEM-Fused), and (a, b, c, d, e refer to intercept and regression coefficients).The best-fitted regression results so produced are compiled in Table 3.In combination, the influence Hence, the SRTM, CDED and NBDEM-Fused DEMs account for most of the non-LiDAR to LiDAR elevation difference reductions.Entering the selected CDED and SRTM DEMs individually into the stepwise regression process is of further benefit, but only marginally so.Using the ASTER DEM produced no improvements.In detail, the NBDEM-Fused and NBDEM-Optimized layers matched the LiDAR-DEM with the least bias, least minimum, and maximum differences, and with about 70% (i.e., 90 th percentiles) of the elevation differences falling within the ±2 m LiDAR elevation range (Figure 4).(Figure 1), are compiled in Table 4 and Table 5.For this tile, all layers are upwardly biased, but least so for NBDEM-Optimized at 0.58 m, with standard deviation and root mean square differences also being least at 2.84 and 2.90 m, respectively.The ≤ ±2 and ±4 m percentages of the elevation differences remained about the same overall across the DEM optimization and validation extents, but dropped somewhat from 70.1% to 60.5% for ≤ ±2 m, and increased from 92.9% to 95.4% for ≤ ±4 m (compare Table 2 with Table 4).
The conformance results for the nearest flow channel distances between the non-LiDAR and LiDAR-derived DEMs in Figure 7 improved by layer as follows ASTER < NB-DEM< CDED < SRTM90 < SRTM30 <NBDEM-Fused < NBDEM-Optimized.
There is a similar performance increase from ASTER to the NBDEM-Optimized layers in terms of false positive and false negative DTW < 1 m reductions, with the optimized NBNB-DEM layer being closest to the corresponding 10 m re-sampled LiDAR DEM derivation (Table 5).
In summary, the 5-stage process of combining to the original NB DEM with the CDED and SRTM DEMs and subsequently calibrating the result with available LiDAR DEM pieces not only improved but also extended the flow-channel

Discussion
The above analysis demonstrates that the fusion of non-LiDAR DEMs can lead to systematic elevation difference reductions, which can be further enhanced through regression calibration with available LiDAR datasets.The DEM so optimized can then be used to generate province or region-wide hydrographic DEM interpretations that are similar to what can be derived from LiDAR-generated DEMs, at 10 m resolution at least.
The non-LiDAR-DEM uncertainty by way of the 5-stage process appear to be small numerically at a 20% reduction of false positives, and a 10% reduction of false negatives (Table 4).There is, however, a substantial 8 times out of 10 distance-to-flow-channel improvement from ±25 m (NB-DEM) to ±5 m (NBDEM-Optimized) (Figure 7).This, by itself and in view of the illustrations The fact that DEM fusion leads to DEM improvements in terms of vertical and lateral error reductions has been demonstrated repeatedly (e.g., [37] [38] [46] [47]), but the fusion processes pertaining to cell re-sizing, re-projection, resampling re-interpolation, DEM weighting and noise filtering all vary.For example, [40] produced "a nearly-global, void-free, multi-scale smoothed, 90 m digital elevation model" called EarthEnv-DEM90 (http://geomorphometry.org/content/earthenv-dem90).Tran et al.

Conclusions
The systematic fusion of currently available DEM layers for all of New Brunswick not only led to considerable non-LiDAR to LiDAR DEM elevation difference reductions, but also produced a closer and verifiable correspondence between the resulting flow-channels and wet-area derivations.In summary, the 5-stage process as described in this article has shown that: 1) Non-LiDAR elevation differences relative to LiDAR DEMs can be reduced through careful analysis requiring re-projecting, re-sampling, and re-interpolation, followed by selective non-LiDAR DEM amalgamation.
2) The fusion process of the SRTM, CDED and NB-DEM layers, each used at about equal weight, was effective in generating a much improved non-LiDAR-DEM coverage across New Brunswick.Using the ASTER DEM did not improve the best-fitted fusion result so obtained.
3) The fusion process removed many layer-specific artifacts and large layerto-layer elevation differences, while the non-LiDAR to LiDAR-DEM regression process reduced the NBDEM-Optimized elevation bias to less than 1 m.4) While the results are specific to and can be applied comprehensively across New Brunswick, similar non-LiDAR DEM improvements could be incurred elsewhere.

Figure 1 .Figure 2 . A 5 - 3 )
Figure 1.LiDAR DEM coverages (~11%) used for improving non-LiDAR DEMs across all of New Brunswick by way of a 5-stage process.Also shown: latest LiDAR-DEM acquisition for New Brunswick, LiDAR coverage for optimization and process validation, and scan line (green), used to represent elevation differences associated with each non-LiDAR DEM.Background: hill-shaded NB-DEM.LiDAR-DEM source: http://www.snb.ca/geonb1/e/DC/DTM.asp.

Figure 3 . 32
Figure 3. Example for non-LiDAR to LiDAR elevation differences (color-coded) draped over DEM-derived hill-shade for each non-LiDAR DEM.Bottom right: hill-shaded bare-earth LiDAR DEM.

Figure 4 .
Figure 4. Box plots for the non-LiDAR to LiDAR elevation differences for SRTM90, SRTM30, CDED, NB-DEM, NBDEM-Fused, and NBDEM-Optimized across the DEM optimization extent, showing the 10th, 25 th , 50 th , 75 th and 90 th percentiles, the points above and below the 10th and 90 th percentiles, and a reference line at 0 m.

Figure 5 .Figure 6 .
Figure 5. Flow-channel and cartographic depth-to-water patterns overlaid on the hillshaded non-LiDAR and LiDAR DEMs.
Brunswick in a systematic and comprehensive manner.This is illustrated in Figure8by way of an example within the validation tile (Figure1).

Figure 7 .
Figure 7. Cumulative frequency of nearest distances between the non-LiDAR-and Li-DAR-derived flow-channel networks, across validation extent.

Figure 8 .
Figure 8. NBDEM-Optimized (bottom left) and LiDAR-DEM (bottom right) derived flow-channel, and DTW < 1 m delineations, versus the water courses of the New Brunswick Hydrographic Network, overlain on aerial imagery and hill-shaded LiDARDEM (top right only).Note the correspondence between the DEM-derived flow channels and the riparian vegetation buffers.Location: part of the validation tile in Figure 1.
[48] fused ASTER with SRTM30 data through (i) DEM quality assessment and preprocessing, (ii) hydrologic DEM enforcement, (iii) void filling and projection shifting, (iv) DSM versus DTM bias elimination by landform, and (v) DEM denoising.The 5-stage process in this study varies from[48] by way of systematic cell size and DEM re-processing (re-projecting and re-interpolation), and using the regression process for bias removal.The reference DEMs also differ: using a DEM generated from the 1:10,000 topographic map 5 m intervals and spotheight elevation data (i.e., similar to CDED) versus using 1 m LiDAR DEM resampled at 10 m.In terms of applying the above approach to other areas with similar and/or different DEMs including LiDAR DEM coverages, it is important to examine each re-projected, re-sampled and re-interpolated DEM in reference to artifacts and hydrographic correctness.In this regard, all open water surfaces need to be S. Furze et al.DOI: 10.4236/jgis.2017.95035572 Journal of Geographic Information System rendered flat, and streams and rivers need to drop monotonously through their surrounding terrain towards their receiving shores.
et al.
DOI: 10.4236/jgis.2017.95035559 Journal of Geographic Information System surface as technology and applications of spatial modeling advance.Among these datasets are digital elevation models (DEMs), i.e., gridded datasets representing continuous elevation changes across landscapes at both local and global extents [1]

Table 1 .
Overview of open-sourced DEMs and LiDAR-DEMs utilized in this study.Note variation in coverage, resolution, and vertical error.

Table 2 .
Non-LiDAR and LiDAR DEM elevation difference comparison across the DEM optimization extent: statistical summary, in m, including increase in ≤ ±2 to ±4 m elevation difference percentages.

Table 3 .
Stepwise regression results with LiDAR-DEM as dependent variable and SRTM90, SRTM30m, CDED, and NBDEM-Fused as predictor variables: regression coefficients and related errors in m; R2 values near 1 across DEM optimization extent.
of stepwise non-LiDAR layer inclusion into the regression analysis generated the following improvement sequence:

Table 4 .
Non-LiDAR and LiDAR DEM elevation difference comparison: statistical summary for validation site, in m, including percentage of elevation differences ≤ ±2 m and ≤ ±4 m.

Table 5 .
Reduction in area (as percentage) of false positive and false negative DTW < 1 m areas relative to the 10m LiDAR-derived DTW pattern across validation extent.