**3.2 Comparison of DEMs**

Two main approaches were used to compare and validate the elevation products against the reference. These are: (1) determining the accuracy of the *elevation values* of the products (absolute accuracy) and (2) determining the accuracy of terrain derivatives of the products (relative accuracy).

#### **3.2.1 Accuracy of elevation values**

This was achieved by performing DEM differencing, profiling and correlation plots.

• **DEM differencing**: This was performed to derive elevation error maps. Root mean square error (RMSE), a common measure of quantifying vertical accuracy in DEMs, was

Comparison of SRTM and ASTER Derived Digital Elevation Models

were plotted and compared.

event for all three DEMs and compared.

over Two Regions in Ghana – Implications for Hydrological and Environmental Modeling 227

flow direction algorithm, flow accumulation and drainage maps were subsequently generated. Next, a common outlet location was used to extract an upstream catchment area from the DEMs and the attributes of the derived catchments compared. This analysis was conducted for site 1 alone due to two main reasons: (1) the location of the Volta Lake within site 2 would result in a large number of relatively small catchments that directly drain into the lake, and (2) the relief of site 1 is relatively gentle (average slope = 0.90) and for the accuracy of terrain derivatives this is critical since in steeply sloping terrain the flow direction is assigned correctly. Using statistics extracted, the following analyses and comparisons were performed.

• **Longitudinal Profiles**: these were extracted at 500m interval, along the longest flow path, with the respective depression- filled DEMs as source. Profiles of the three DEMs

• **Horton Plot:** In hydrology, the geomorphology of the watershed, or quantitative study of the surface landform, is used to arrive at measures of geometric similarity among watersheds, especially among their stream network. The quantitative study of stream networks was originated by Horton. Horton's original stream ordering was slightly modified by Strahler, and Schumm added the law of stream areas. Number of streams of successive order, the average stream length of successive order and the average catchment area of successive order is found to be relatively constant from one order to another. Graphically this can be visualized by construction of a Horton plot. The Horton plots show the relationship between Strahler order and total number of Strahler order stream segments for a given order, average length per Strahler order and average catchment area per Strahler order, as well as the bifurcation (Rb), channel length (Rl) and stream area ratio's (Ra), by means of a least square regression line. Using the extracted drainage data from the three DEMs, Horton's statistics were derived and the results graphically displayed by plotting Strahler order on the X-axis and the number of

drainage channels, stream length and stream area on a log transformed Y axis. • **Geomorphological Instantaneous Unit Hydrograph (GIUH)**: The GIUH model is based on the theory proposed by Rodriquez-Iturbe and Valdes and its subsequent generalization by Gupta. According to the theory, the unit input (unit depth of rainfall) is considered to be composed of an infinite number of small, non-interacting drops of uniform size, falling instantaneously over the entire region. The basin geomorphology plays an important role in the transition of water from the overland region to channels (streams) and also from the channels of one order to the other (Bhadra *et al*., 2008). Using extracted statistics such as Horton's ratios, length of highest order stream, maximum order, etc., a GIUH was calculated, assuming identical effective precipitation and effective holding capacity for each of the datasets. No infiltration was assumed. A user-friendly event based computerized GIUH model, "GIUH\_CAL" (Bhadra *et al*., 2008) was applied to derive the direct runoff hydrograph of an assumed uniform storm

• **Topographic Index (TI)**: TI is a topography-based concept for watershed hydrology modeling which has been widely used to study the effects of topography on hydraulic processes (Wolock and McCabe, 1995). The TI, *ln*(*a*/*tan b*), is the natural logarithm of the ratio of the specific flow accumulation area "*a"* to the ground surface slope "*tan b"*. Surface slope can be evaluated from DEMs. The specific flow accumulation area is the total flow accumulation area (or upslope area) "*A"* through a unit contour length "*L"*.

calculated for each error map. In addition, skewness and kurtosis (King and Julstrom, 1982) was calculated for each error map. Skewness is a unitless measure of asymmetry in a distribution (Shaw and Wheeler, 1985). Negative skewness indicates a longer tail to the left, while positive skewness indicates a longer tail to the right. Excess kurtosis is a unitless measure of how sharp the data peak is. A value larger than zero (0) indicates a peaked distribution, while a value less than zero (0) indicates a flat distribution. Percentage of pixels falling within different error ranges was also determined.



Table 3. Summary statistics of DEMs analysed for both sites

#### **3.2.2 Accuracy of terrain derivatives**

In this assessment, the three DEMs were first preprocessed to obtain a hydrologically consistent elevation model (filling local depressions). Flow direction, using a Deterministic-8

Percentage of pixels falling within different error ranges was also determined. • **Profiling**: Horizontal profiles were created on the DEMs and compared. Profile lengths were 35 km and 45 km for site 1 and 2 respectively. A graph of elevation against distance was produced for comparison. Figure 3 (*a* and *b*) shows profile graphs for sites

• **Correlation scatter plots**: This was performed to assess the level of correlation between the DEMs. It was difficult making a scatter plot from all the pixels in a DEM, as each DEM contained over a million pixels. For this reason, the scatter plots are based on randomly selected points/pixels. In all, about 6000 points/pixels were randomly selected from each DEM. They are an aggregation of pixels randomly selected from different landcover types identified in each site. For each site, two scatter plots were

*Reference* **Elevation** *105 463 213.0 63.2 0.45 2.3* 

*SRTM* **Elevation** *111 467 216.9 63.5 0.45 2.4* 

*Aster* **Elevation** *77 464 209.87 64.8 0.4 2.3* 

*Reference* **Elevation** *44.8 836.0 238.9 139.8 1.2481 3.8751* 

*SRTM* **Elevation** *51.7 838.3 241.0 139.7 1.2499 3.9459* 

*Aster* **Elevation** *41.3 848.7 235.6 139.6 1.2479 3.9275*  Slope *0 44.3 3.7 4.0 2.4926 10.561* 

In this assessment, the three DEMs were first preprocessed to obtain a hydrologically consistent elevation model (filling local depressions). Flow direction, using a Deterministic-8

**Site 1** 

Slope *0 30.2 0.86 0.94 9.5 183.6* 

Slope *0 31.9 0.97 0.9 11.1 240.6* 

Slope *0 29.9 1.06 0.9 9.3 182.2*  **Site 2** 

Slope *0 45.1 3.3 4.2 2.523 10.758* 

Slope *0 47.1 3.5 4.1 2.5949 11.311* 

**deviation Skewness Kurtosis** 

produced and correlation coefficient determined.

Table 3. Summary statistics of DEMs analysed for both sites

**3.2.2 Accuracy of terrain derivatives** 

Dataset **Description Min Max Mean Standard** 

1 and 2.

calculated for each error map. In addition, skewness and kurtosis (King and Julstrom, 1982) was calculated for each error map. Skewness is a unitless measure of asymmetry in a distribution (Shaw and Wheeler, 1985). Negative skewness indicates a longer tail to the left, while positive skewness indicates a longer tail to the right. Excess kurtosis is a unitless measure of how sharp the data peak is. A value larger than zero (0) indicates a peaked distribution, while a value less than zero (0) indicates a flat distribution. flow direction algorithm, flow accumulation and drainage maps were subsequently generated. Next, a common outlet location was used to extract an upstream catchment area from the DEMs and the attributes of the derived catchments compared. This analysis was conducted for site 1 alone due to two main reasons: (1) the location of the Volta Lake within site 2 would result in a large number of relatively small catchments that directly drain into the lake, and (2) the relief of site 1 is relatively gentle (average slope = 0.90) and for the accuracy of terrain derivatives this is critical since in steeply sloping terrain the flow direction is assigned correctly. Using statistics extracted, the following analyses and comparisons were performed.


Comparison of SRTM and ASTER Derived Digital Elevation Models

(Slater *et al*., 2009).

minus Reference (Site 2).

over Two Regions in Ghana – Implications for Hydrological and Environmental Modeling 229

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

(a) (b)

(c) (d) 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

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

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 classes and plotted for comparison purposes.
