The study area corresponds to a NW portion of the state of Nevada (U.S.A.) that includes the Humboldt Range, with latitude in the range 40.31458° to 40.68847° (N) and longitude in the range -118.30319° to -118.00930° (W). The Humboldt Range is formed by gently sloping mountain sides while the dichotomic drainage pattern indicates that the range is surrounded by coalescent alluvial fans [9].

NED was used as the reference DEM. NED is a digital terrain model depicting bare earth (ground) elevation in geographic co-ordinates (horizontal datum of NAD83, vertical datum of NAVD88) with spacing 1 arc second, with accuracy specification of root mean square error (RMSE) equal to 7 m [12]. The NED DEM of the study area (Figure 1a) consists of 1,346 rows and 1,058 columns. Slope (Figure 1b) and aspect, the slope pointing direction (Figure 1c) were computed on the basis of NED DEM [9]. The method that derives the topographical variables from DEMs given in geographical co-ordinates was used [17].

SRTM finished DEM of the study area (Figure 2a) is available [3] in geographic co-ordinates (horizontal datum of WGS84, vertical datum of EGM96) with 1 arc second spacing. The absolute horizontal and vertical accuracies are equal to 20 meters (circular error at 90% confidence) and 16 meter (linear error at 90% confidence) respectively [7]. The SRTM DEM presents an intrinsic random noise level of five m [18] that was visualized in Figure 2.

The vertical accuracy is actually significantly better than the 16 meters and it is closer to +/- 10 meters [7]. The elevations are provided with respect to the reflective surface (first return), which may be vegetation, human-made features, etc.

The ellipsoids (horizontal datums) GRS 80 for NAD 83 (for NED) compared to WGS 84 (for SRTM) are for all practical purposes at scales smaller than 1:5,000 identical [19], [20].

In order to conduct a realistic and consistent comparison amongst the available height data sets (vertical datum of NAVD88 for NED versus the vertical datum of EGM96 for SRTM), it was imperative that all heights refer to the same vertical datum. It was decided to perform the data comparisons in terms of ellipsoidal heights with respect to WGS84 that is consistent with the geocentric reference system employed by GPS. The difference between GPS ellipsoid height (WGS84), h, and levelled orthometric height, H, is called geoid height, N (N= h-H).

Orthometric heights (NAVD88) of NED DEM were converted (recalculation of elevation values) to WGS84 ellipsoid heights [21]. The geoid height within the study area varies from -22 to -21 m (Figure 2).

The SRTM DEM grid values are provided to users in terms of orthometric heights with respect to EGM96 [22]. Ellipsoidal heights with reference to the WGS84 ellipsoid [23] were desirable. The geoidal undulations were interpolated from the EGM96 height file [24]. The geoid heights within the study area vary from -22 to -20.9 m.

The elevation difference (NED-SRTM) per grid point was computed (Figure 3b). The visual interpretation indicated that the difference image was correlated to the aspect image (Figures 1c). An error pattern composed from dark and white regions was revealed in Figure 3b. Landsat image (Figure 4a) indicated a surface mine and a new void mask (Figure 3c) was computed.

The National Landcover Dataset (NLCD) 2001 is a Landsat based landcover database containing 21 classes of land-cover data [13]. The snow cover was interpreted from the Landsat image (Figure 3a) downloaded from the US Geological Survey data distribution system [2]. The landcover map of the study area (Figure 4b) includes eight classes (Table 1). A snow mask was applied on the landcover map of the study area (Figure 5a).

Aspect is undefined when slope is minimised [8] so a mask was created (Figure 5b) for a slope threshold equal to 2°. The slope mask was applied to the landcover map. The final landcover map that includes a snow class is given in Figure 5c. The snow cover class consists of grid points that were initially classified as forest (4.4%), shrubs (87.3%), or grass (8.2%). The occurrence (percent area extent) in the final landcover map of forest, shrubs, grass and snow cover is 5.3%, 56.9%, 23.2%, 13% respectively (the 98.5% of the non-masked grid points).

Statistics and rose diagrams per landcover class per aspect direction were used in an attempt to reveal the directional dependency of elevation differences (Figure 6).

Forest and snow presented an almost similar pattern of directional dependency. SRTM instrument seems to over-estimate elevation towards the N, NE, E directions and under-estimates it towards the W, SW, S. An analogous pattern was observed for shrub and grass but the relative elevation differences were less than those observed for forest and snow (Table 2). Table 2 indicated that the magnitude of the overall mean elevation difference per landcover class was a function of mean vegetation height as it was interpreted from Table 1. That is why elevation differences were minimized for grass (Table 2).

RMSE is maximised for NE-SE direction for snow (Figure 7, Table 2). Forest, shrubs and grass presented an almost similar directional pattern (RMSE was maximised toward the North direction). RMSE magnitude (Table 2) seemed to be landcover dependent and interpreted to be associated to mean vegetation height estimated from Table 1. RMSE was minimised for the grass class.

The elevation difference frequency distributions per aspect direction for forest and snow (Figures 8, 9) as well as the statistical data of Table 2, indicate that the absolute value of the skew is less than 0.5 and normal distribution criterion is fulfilled [5].

On the contrary, for grass and shrub landcover classes (Figures 10, 11) and for the majority of geographic directions, the absolute value of the skew exceeds 0.5 (Table 2), and so the distributions are sufficiently asymmetrical to cause concern that the dataset may not represent a normal distribution [5]. The interpretation given is that although these landcover classes were dominated by shrubs or grass, trees or man-made elevated features of greater height exist (Table 1).

The interpretation of frequency distributions (Figures 8, 9 and 10) per landcover class (the grass landcover class was excluded since the directional dependency of elevation differences was minimised) revealed that elevation difference for grid points that slopes in opposite geographic directions (Table 2) was maximized, an exception being the NW-SE direction.

A two-sample means test (Equation 2) is applied [14], the null hypotheses being that for NE and SW directions of the forest class, the mean elevation difference is statistically the same.

(2) t = X − Y S x 2 n x − 1 + S y 2 n y − 1where X and Y correspond to the means of the two populations compared, Sx and Sy, the corresponding standard deviations, nx and ny the sample size.

The mean elevation difference was proved statistically significant since the observed t-statistics equal to 61.349 that was far greater than the tabled critical value (2.326) of t (one-tailed test, for infinite degrees of freedom at the 0.01 level). So the null hypothesis was rejected.

Mean slope per geographic direction per landcover class is presented in Table 3, expressed as well as rose-diagrams (Figure 12).

The relationship between one-degree slope intervals (x) and the corresponding mean elevation difference (y) is further explored by assuming the linear regression model (Figure 13, Tables 4). Y′ corresponds to the estimated value, (y′=a*x+b).

Elevation differences are linearly correlated to the terrain slope (the steeper the slope, the greater the |error|) for the eight principal geographic directions. The eight lines that correspond to the eight geographic directions per landcover class were interpreted to intersect Y-axis at a common point that corresponds (y-coordinate) to the mean vegetation height (derived from Table 1).

For snow landcover class this point approach zero (C-band was proved to penetrate snow). The lines for the forest class were interpreted to be quite noisy (due to the complex interaction of tree canopy to the radar signal) than the corresponding lines of the shrub class (Figure 13).