**4. Results and discussion**

#### **4.1 Accuracy of elevation values**

Table 4 presents the statistics of the error maps obtained for both sites, whereas figure 2 (*a d*) shows the spatial distribution of the errors and the percentage of pixels that falls in different error ranges. It is quite evident that better results were obtained for site 1 than site 2. This is manifested in the RMSEs obtained for site 1. Although all RMSEs fall within predefined vertical accuracy specification (Slater *et al*., 2006; Fujisada *et al*., 2005), results for site 1 indicate that the products (of site 1) are three-times better than that of site 2. This could be due to the physical characteristics of site 1, which has a relatively flat terrain with a mean slope of about 0.90. It can, thus, be said that both products do better on flat and less complex terrain than would do on hilly and mountainous terrain as in site 2.


Table 4. Difference statistics of the study sites

Table 4 further reveals that, compared to the reference DEM, SRTM has a better vertical accuracy than the ASTER GDEM. In both sites, a smaller RMSE was obtained for SRTM than ASTER GDEM. This finding is in line with the pre-launch vertical accuracy of 16m for SRTM (Hensley *et al*., 2001) and 20m for ASTER GDEM (Fujisada *et al*., 2005; Slater *et al*., 2009).

Figures 2*a* and 2*b* shows the spatial distribution of errors in the ASTER GDEM for both sites. The graphs and statistics indicate that ASTER GDEM elevations are generally lower, compared to the reference DEM (i. e biased negatively). In other words, the ASTER GDEM underestimates elevation on both sites. Statistics from site 1 indicate that 74% of pixels fall below zero (0), whereas 58% of pixels fall below zero (0) in site 2. This further reveals that, though ASTER GDEM generally underestimates elevation, this underestimation is more pronounced on flat and less complex terrains (as in site 1) than in hilly and complex terrains.

Figures 2*c* and 2*d* shows that SRTM have the directly opposite characteristic – overestimates elevation. Elevation differences are positively biased, resulting in majority of pixels being greater than zero (0). Statistics from site 1 indicate that about 78% of pixels were greater than

Table 4 presents the statistics of the error maps obtained for both sites, whereas figure 2 (*a d*) shows the spatial distribution of the errors and the percentage of pixels that falls in different error ranges. It is quite evident that better results were obtained for site 1 than site 2. This is manifested in the RMSEs obtained for site 1. Although all RMSEs fall within predefined vertical accuracy specification (Slater *et al*., 2006; Fujisada *et al*., 2005), results for site 1 indicate that the products (of site 1) are three-times better than that of site 2. This could be due to the physical characteristics of site 1, which has a relatively flat terrain with a mean slope of about 0.90. It can, thus, be said that both products do better on flat and less complex

**Site 1**  *ASTER - Reference -82.92 118.01 -3.30 6.05 5.46 1.4326 20.884 SRTM - Reference -70.96 143.57 3.67 5.70 4.95 2.3606 43.820*  **Site 2**  *ASTER - Reference -245.56 233.78 -3.323 20.41 18.76 -0.4743 10.512 SRTM - Reference -229.89 204.44 2.089 16.08 14.54 -0.7992 15.054* 

Table 4 further reveals that, compared to the reference DEM, SRTM has a better vertical accuracy than the ASTER GDEM. In both sites, a smaller RMSE was obtained for SRTM than ASTER GDEM. This finding is in line with the pre-launch vertical accuracy of 16m for SRTM (Hensley *et al*., 2001) and 20m for ASTER GDEM (Fujisada *et al*., 2005; Slater *et al*., 2009).

Figures 2*a* and 2*b* shows the spatial distribution of errors in the ASTER GDEM for both sites. The graphs and statistics indicate that ASTER GDEM elevations are generally lower, compared to the reference DEM (i. e biased negatively). In other words, the ASTER GDEM underestimates elevation on both sites. Statistics from site 1 indicate that 74% of pixels fall below zero (0), whereas 58% of pixels fall below zero (0) in site 2. This further reveals that, though ASTER GDEM generally underestimates elevation, this underestimation is more pronounced on flat and less complex terrains (as in site 1) than in hilly and complex terrains. Figures 2*c* and 2*d* shows that SRTM have the directly opposite characteristic – overestimates elevation. Elevation differences are positively biased, resulting in majority of pixels being greater than zero (0). Statistics from site 1 indicate that about 78% of pixels were greater than

**deviation RMSE Skewness Kurtosis** 

classes and plotted for comparison purposes.

terrain than would do on hilly and mountainous terrain as in site 2.

**Difference Map Min Max Mean Standard** 

Table 4. Difference statistics of the study sites

**4. Results and discussion 4.1 Accuracy of elevation values** 

When using a DEM, *L* can be defined as being equal to the horizontal resolution of the DEM (Pan *et al*., 2004). In this study, the algorithm applied uses a Deterministic-8 flow direction algorithm to obtain the (specific) flow accumulation area. The continuous Topographic Index data range obtained for each of the DEMs was classified into integer zero (0), whereas about 60% was greater than zero (0) in site 2. This overestimation may be partly due to the fact that SRTM records the reflective surface and, thus, may be positively biased with respect to the bare earth when foliage is present. This under- and overestimation of ASTER GDEM and SRTM respectively has been noted in previous studies (Slater *et al*., 2009).

Fig. 2. Difference maps computed for the two study regions. (a) ASTER minus Reference (Site 1). (b) ASTER minus Reference (Site 2). (c) SRTM minus Reference (Site 1). (d) SRTM minus Reference (Site 2).

Apart from generating error maps, horizontal profiles were created on the DEMs using the 3-D analyst extension in ArcGIS®, and the data exported to excel for comparison. Figure 1 above shows the location of the profile lines, whereas figure 3 (*a* and *b*) below shows the comparison between the three (3) DEMs for both sites. The results obtained in this section further confirm the earlier finding that ASTER GDEM underestimates elevation whereas SRTM overestimates. Figure 3*a* clearly shows how bad ASTER GDEM performs on lowlands – its profile line is consistently below that of SRTM and the reference DEM. A visual inspection of figure 3 reveals that, the magnitude of overestimation of SRTM is less than the magnitude of underestimation of ASTER GDEM. In other words, SRTM is "closer" to the reference than ASTER GDEM. This further confirms that SRTM has an accuracy superior to ASTER.

Figure 4 (*a* – *d*) shows the correlation plots obtained for both sites. As stated earlier, these plots are based on a random selection of points representing different land covers. Results from site 1 indicate that both products have the same correlation coefficient with the

Comparison of SRTM and ASTER Derived Digital Elevation Models

**4.2 Accuracy of terrain derivatives** 

respectively.

overestimation of elevation.

over Two Regions in Ghana – Implications for Hydrological and Environmental Modeling 231

Results of the hydro-processing to extract catchments and drainage information, using a common outlet, from the three DEMs are shown in Table 5. The upstream catchment area extracted for a common outlet location is largest for the Reference DEM, the catchment areas of ASTER and SRTM are -1% and -0.7% respectively. Although the same flow accumulation threshold map has been used for all DEMs, larger differences appeared during the drainage extraction process. This resulted in the largest deviations with respect to the Reference DEM of the drainage length and drainage density for the SRTM DEM, +7.6% and +4.5%

**Catchment characteristics Reference ASTER SRTM** 

Area (km2) 7,189.97 7,118.36 7,140.06 Perimeter (m) 442,767.37 475,829.21 463,395.49 Total Drainage Length (m) 2,725,840.8 2,890,504 2,911,511.2

Drainage Density (m/km2) 379.12 406.06 407.77

Sinuosity 1.787 1.816 1.864

Table 5. Attribute values for extracted catchments and longest flow path

Fig. 5. Longitudinal profiles extracted from the three DEMs

Longest Flow Path Length (m) 189,275.21 194,572.84 197,697.76 Longest Drainage Length (m) 186,556 192,018.2 194,910.4

Figure 5 shows the longitudinal profiles extracted at 500 m interval along the longest flow path, with the various depression-filled DEMs as the elevation source. The graph confirms results of the absolute accuracy assessment, i.e. ASTER's underestimation and SRTM's

Horton statistics were computed using the extracted drainage data from the three DEMs. The statistical values are shown in Table 6 while Figure 6 shows the resulting Horton plot for Strahler stream orders 1 to 5. The Strahler order is plotted on the "X" axis while the

reference DEM, which is slightly different from earlier results discussed above. This could be due to the number and distribution of points selected (i. e. 6000 out of over a million points). The plot for site 2, however, indicates that SRTM is slightly better correlated to the reference than ASTER GDEM.

Fig. 3 (a). Comparison of profile lines derived from all DEMs for site 1. (b). Comparison of profile lines for site 2

Fig. 4. Correlation plots for the two study sites. (a) ASTER versus Reference (Site 1). (b) ASTER versus Reference (Site 2). (c) SRTM versus Reference (Site 1). (d) SRTM versus Reference (Site 2).

#### **4.2 Accuracy of terrain derivatives**

230 Studies on Environmental and Applied Geomorphology

reference DEM, which is slightly different from earlier results discussed above. This could be due to the number and distribution of points selected (i. e. 6000 out of over a million points). The plot for site 2, however, indicates that SRTM is slightly better correlated to the

Fig. 3 (a). Comparison of profile lines derived from all DEMs for site 1. (b). Comparison of

(a) (b)

(c) (d)

Fig. 4. Correlation plots for the two study sites. (a) ASTER versus Reference (Site 1). (b) ASTER versus Reference (Site 2). (c) SRTM versus Reference (Site 1). (d) SRTM versus

reference than ASTER GDEM.

profile lines for site 2

Reference (Site 2).

Results of the hydro-processing to extract catchments and drainage information, using a common outlet, from the three DEMs are shown in Table 5. The upstream catchment area extracted for a common outlet location is largest for the Reference DEM, the catchment areas of ASTER and SRTM are -1% and -0.7% respectively. Although the same flow accumulation threshold map has been used for all DEMs, larger differences appeared during the drainage extraction process. This resulted in the largest deviations with respect to the Reference DEM of the drainage length and drainage density for the SRTM DEM, +7.6% and +4.5% respectively.


Table 5. Attribute values for extracted catchments and longest flow path

Figure 5 shows the longitudinal profiles extracted at 500 m interval along the longest flow path, with the various depression-filled DEMs as the elevation source. The graph confirms results of the absolute accuracy assessment, i.e. ASTER's underestimation and SRTM's overestimation of elevation.

Fig. 5. Longitudinal profiles extracted from the three DEMs

Horton statistics were computed using the extracted drainage data from the three DEMs. The statistical values are shown in Table 6 while Figure 6 shows the resulting Horton plot for Strahler stream orders 1 to 5. The Strahler order is plotted on the "X" axis while the

Comparison of SRTM and ASTER Derived Digital Elevation Models

**Area (km2)** 

Ratio Reference Ratio ASTER Ratio SRTM

**4.3 Implications for hydrological and environmental modeling** 

Rb 3.55 3.61 3.64 Rl 2.22 2.26 2.28 Ra 4.55 3.99 4.6

**Length (km)** 

**Order No. of** 

**streams**

Table 6. Horton statistics

DEM or a higher accuracy DEM.

 **Reference ASTER SRTM** 

**Horton Ratio's (calculated excluding lowest and highest stream order)** 

**No. of streams**

over Two Regions in Ghana – Implications for Hydrological and Environmental Modeling 233

1 502 2.7 8.34 537 2.66 7.72 550 2.63 7.84 2 105 8.66 52.55 114 8.93 48.83 119 8.67 47.59 3 23 28.2 284.62 27 23.79 237.75 29 22.03 221.73 4 6 53.7 1146.61 7 49.48 972.54 7 47.88 975.53 5 2 77.42 3496.54 2 120.9 3540.11 2 123.14 3549.87 6 1 172.09 7190.37 1 145.98 7138.2 1 148.56 7154.38

The reported accuracies and geomorphological behavior of the studied DEMs have numerous implications for hydrological and environmental modeling in the study regions. Topography is a crucial land surface characteristic and controls many earth processes (Hutchinson, 1996). For this reason, topography needs to be adequately represented (as in the form of a DEM) to ensure that modeling results, e.g. predicting surface/ sub-surface runoff, erosion estimates, etc. are as much as possible close to observed values. The implications of using inappropriate DEMs in hydrological and environmental modeling have been amply studied and reported in the literature. For example, Datta and Schack-Kirchner (2010), in reviewing erosion studies conducted in the Indian lesser Himalayas, attributed the large variations in the range of soil loss estimates chiefly to poor description of the terrain in the form of a DEM. They compared erosion relevant topographical parameters – elevation, slope, aspect and LS factor – derived from DEMs of different source and accuracy and concluded that the choice of a DEM for soil erosion modeling has a significant impact on the relevant topographical parameters and, consequently, on the modeling results. In a related study, Rojas et al. (2008) studied the effects of DEM grid sizes – 30m, 90, 150, 210, 270 and 330 - on results of modeling upland erosion and sediment yield from natural watersheds. They found that using different resolution DEMs (30m – 330m) significantly reduces land surface slopes and channel network topology, resulting in varied upland erosion estimates. Walker and Wildgoose (1999) studied the implications of using different source DEMs – cartometric, photogrammetric and ground truth - of varying resolution and accuracy on key hydrologic statistics. They found catchment sizes and stream networks derived from the cartometric and photogrammetric DEMs to be significantly different from that of the ground truth. This was particularly the case in smaller catchments where a localized error in elevation may direct a major stream line in a wrong direction. They concluded that the use of published DEMs for determining catchment boundaries and stream networks must be done with care by comparing results with that of a ground truth

**Length (km)** 

**Area (km2)**  **No. of streams** **Length (km)** 

**Area (km2)** 

number of drainage channels, stream length and stream area are plotted on a log transformed "Y" axis. According to Horton's law the values obtained should plot along a straight line and this can be used as an indicator that the parameters used for drainage extraction are properly selected (Chow *et al*., 1988).

SRTM and ASTER have a larger number of drainage lines per Strahler order, especially for the lower order streams and therefore the stream length per order is less for SRTM and ASTER compared to the Reference DEM. The stream area shows a similar tendency. The stream lengths for the fifth and sixth order are the main deviating phenomena; smaller and larger for the Reference DEM, compared to ASTER and SRTM respectively. The Horton ratio's, calculated excluding the lowest and highest stream orders, shows that SRTM has slightly higher ratio values compared to those derived from the Reference DEM for all ratio's. ASTER derived ratio's for "Rb" and "Rl" are in between, the area ratio of ASTER is strongly deviating, only 3.99. In general the trend of the ratios as plotted in Figure 6 show a similar geomorphological structure for ASTER and SRTM and only deviates notably with respect to the Reference DEM for the Length Ratio. The "Rb", "Rl" and "Ra" values vary normally between 3 and 5 for "Rb", between 1.5 and 3.5 for "Rl" and between 3 and 6 for "Ra" (Rodrguez-Iturbe, 1993). For all DEMs the derived ratios are within the ranges given.

Fig. 6. Horton plot (Legend: Red = Reference; Blue = ASTER; Black = SRTM)


Table 6. Horton statistics

232 Studies on Environmental and Applied Geomorphology

number of drainage channels, stream length and stream area are plotted on a log transformed "Y" axis. According to Horton's law the values obtained should plot along a straight line and this can be used as an indicator that the parameters used for drainage

SRTM and ASTER have a larger number of drainage lines per Strahler order, especially for the lower order streams and therefore the stream length per order is less for SRTM and ASTER compared to the Reference DEM. The stream area shows a similar tendency. The stream lengths for the fifth and sixth order are the main deviating phenomena; smaller and larger for the Reference DEM, compared to ASTER and SRTM respectively. The Horton ratio's, calculated excluding the lowest and highest stream orders, shows that SRTM has slightly higher ratio values compared to those derived from the Reference DEM for all ratio's. ASTER derived ratio's for "Rb" and "Rl" are in between, the area ratio of ASTER is strongly deviating, only 3.99. In general the trend of the ratios as plotted in Figure 6 show a similar geomorphological structure for ASTER and SRTM and only deviates notably with respect to the Reference DEM for the Length Ratio. The "Rb", "Rl" and "Ra" values vary normally between 3 and 5 for "Rb", between 1.5 and 3.5 for "Rl" and between 3 and 6 for "Ra" (Rodrguez-Iturbe, 1993). For all DEMs the derived ratios are within the ranges given.

Rl

Ra

Fig. 6. Horton plot (Legend: Red = Reference; Blue = ASTER; Black = SRTM)

Rb

extraction are properly selected (Chow *et al*., 1988).

#### **4.3 Implications for hydrological and environmental modeling**

The reported accuracies and geomorphological behavior of the studied DEMs have numerous implications for hydrological and environmental modeling in the study regions. Topography is a crucial land surface characteristic and controls many earth processes (Hutchinson, 1996). For this reason, topography needs to be adequately represented (as in the form of a DEM) to ensure that modeling results, e.g. predicting surface/ sub-surface runoff, erosion estimates, etc. are as much as possible close to observed values. The implications of using inappropriate DEMs in hydrological and environmental modeling have been amply studied and reported in the literature. For example, Datta and Schack-Kirchner (2010), in reviewing erosion studies conducted in the Indian lesser Himalayas, attributed the large variations in the range of soil loss estimates chiefly to poor description of the terrain in the form of a DEM. They compared erosion relevant topographical parameters – elevation, slope, aspect and LS factor – derived from DEMs of different source and accuracy and concluded that the choice of a DEM for soil erosion modeling has a significant impact on the relevant topographical parameters and, consequently, on the modeling results. In a related study, Rojas et al. (2008) studied the effects of DEM grid sizes – 30m, 90, 150, 210, 270 and 330 - on results of modeling upland erosion and sediment yield from natural watersheds. They found that using different resolution DEMs (30m – 330m) significantly reduces land surface slopes and channel network topology, resulting in varied upland erosion estimates. Walker and Wildgoose (1999) studied the implications of using different source DEMs – cartometric, photogrammetric and ground truth - of varying resolution and accuracy on key hydrologic statistics. They found catchment sizes and stream networks derived from the cartometric and photogrammetric DEMs to be significantly different from that of the ground truth. This was particularly the case in smaller catchments where a localized error in elevation may direct a major stream line in a wrong direction. They concluded that the use of published DEMs for determining catchment boundaries and stream networks must be done with care by comparing results with that of a ground truth DEM or a higher accuracy DEM.

Comparison of SRTM and ASTER Derived Digital Elevation Models

Fig. 8. Comparison of Topographic Index classes for the DEM's

desired slope compared to the reference.

Schack-Kirchner (2010).

**5. Conclusions** 

employed in the comparison.

over Two Regions in Ghana – Implications for Hydrological and Environmental Modeling 235

to cause a more "rough" topography and the difference with respect to ASTER may be attributed to the resampling of the original 30m to 90m for purposes of comparison with the other DEMs. Previous studies, e.g. Rojas et al. (2008), have noted that resampling DEMs to coarser resolutions generally reduces surface slopes and changes channel topology. Slopes have also been found to be highly sensitive to varying DEM resolution and accuracy (Datta and Schack-Kirchner, 2010). Zhang and Montgomery (1994), in their investigation of the effect of grid size on TI concluded that increasing DEM grid sizes results in increased mean TI due to increased contributing area and decreased slopes. This fact was also emphasized by Wilson et al. (2000). A reasonable conclusion can, thus, be drawn that the low percentage of pixels up to 10 in ASTER, and the resultant TI curve, could be attributed to the resampling of the DEM from the original 30m to 90m. The similarity between the ASTER and SRTM curves indicate that SRTM failed to produce the

Results obtained in the GIUH and TI analysis is a clear demonstration of the effects of topography on hydrological processes and the need to select the right DEM (resolution and accuracy) for hydrological and environmental modeling. Use of a DEM that does not adequately represent the surface landforms of a catchment has the tendency of producing erroneous modeling results. With the exception of the TI, the comparison in this study consistently revealed SRTM to have a superior accuracy compared to ASTER DEM, although its resolution is coarser. This is in line with results of previous studies (Datta and

In this study, two near-global DEMs - SRTM and ASTER – are compared and validated against a reference DEM for two sites in Ghana. The reference DEM used was generated using hypsographic and hydrographic data from a 1:50 000 topographical map produced by the SDG. DEM differencing, profiling, correlation plots, extraction of catchment area and drainage network, computation of Horton statistics and GIUH are some of the methods

In light of the above, this study computed two indices - GIUH and TI – to assess the suitability of using the published elevation products under consideration in hydrological and environmental modeling. A GIUH enables the determination of the hydrological response of a catchment to rainfall by taking into consideration its geomorphology. The runoff volumes generated at the outlet of a catchment and time-to-peak are dependent on the topography of the overland regions as well as the transmission surfaces. The reliability of these parameters (runoff & time-to-peak) is, therefore, dependent on how well a catchment's terrain (landform) is represented by the underlying elevation product (DEM). A GIUH was calculated using the three DEMs and their responses compared. Apart from changing the Horton statistics for the respective DEMs, all other variables, such as the rainfall intensity and a mean holding time of 5 hours, remained constant. Result of the GIUH analysis is shown in Figure 7. The figure shows that the direct runoff hydrographs for the Reference DEM and SRTM DEM are comparable with respect to the volume as well as the timing (i.e. time to peak). The ASTER DEM, however, shows a delay in the rising limb and a higher peak discharge. Considering that Horton statistics are the only variable in the analysis (with all others remaining constant), the behavior of ASTER can be attributed to its representation of the catchment's geomorphology. Although ratios obtained in the Horton analysis fall within acceptable ranges, the stream area ratio (Ra) obtained for the ASTER DEM (3.99), which strongly deviates from that of the other two DEMs, is believed to have caused the noted delay in rising limb and higher peak discharge.

Fig. 7. Direct runoff hydrographs for the three DEMs

Figure 8 shows results of the TI analysis. Continuous Topographic Index data range obtained for each of the DEMs was classified into integer classes, and the percentage of pixels falling in each was determined and plotted. The graph shows a notable difference between the reference DEM and the two global DEMs. In order to attribute reasons for the results obtained, slope maps of the three DEMs were created and analyzed. Slope was chosen and analyzed due to the fact that TI is a function of the local slope angle acting on the pixel. The analysis revealed that, the distribution of slopes was quite different in all three DEMs. The reference DEM was found to have about 67% of its area having slopes up to 10, while for the ASTER and the SRTM DEMs, this slope class accounted for nearly 50% and slightly over 50% respectively. In the case of SRTM the radar reflective surface seems to cause a more "rough" topography and the difference with respect to ASTER may be attributed to the resampling of the original 30m to 90m for purposes of comparison with the other DEMs. Previous studies, e.g. Rojas et al. (2008), have noted that resampling DEMs to coarser resolutions generally reduces surface slopes and changes channel topology. Slopes have also been found to be highly sensitive to varying DEM resolution and accuracy (Datta and Schack-Kirchner, 2010). Zhang and Montgomery (1994), in their investigation of the effect of grid size on TI concluded that increasing DEM grid sizes results in increased mean TI due to increased contributing area and decreased slopes. This fact was also emphasized by Wilson et al. (2000). A reasonable conclusion can, thus, be drawn that the low percentage of pixels up to 10 in ASTER, and the resultant TI curve, could be attributed to the resampling of the DEM from the original 30m to 90m. The similarity between the ASTER and SRTM curves indicate that SRTM failed to produce the desired slope compared to the reference.

Results obtained in the GIUH and TI analysis is a clear demonstration of the effects of topography on hydrological processes and the need to select the right DEM (resolution and accuracy) for hydrological and environmental modeling. Use of a DEM that does not adequately represent the surface landforms of a catchment has the tendency of producing erroneous modeling results. With the exception of the TI, the comparison in this study consistently revealed SRTM to have a superior accuracy compared to ASTER DEM, although its resolution is coarser. This is in line with results of previous studies (Datta and Schack-Kirchner (2010).

Fig. 8. Comparison of Topographic Index classes for the DEM's
