Geomorphometry from LIDAR DEMs: Issues of Scale and

ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

GEOMORPHOMETRY FROM LIDAR DEMS: ISSUES OF SCALE AND COMPARISON TO CARTOGRAPHIC DEMS

Jean Hyde, Student

Peter L. Guth, Professor Department of Oceanography United States Naval Academy

572C Holloway Road Annapolis, MD 24102

[email protected] [email protected]

ABSTRACT

Digital elevation models (DEMs) provide a window to view the characteristics of the landscape. A number of point and area parameters allow quantitative description of topography from gridded DEMs. The United States has cartographic DEMs with 10-30 m spacing, combined in the seamless National Elevation Dataset (NED) with 1/3-1 arc second spacing. LIDAR DEMs are becoming increasingly available with horizontal spacing around 1 m, and NED now has limited such DEMs with about 3 m (1/9 arc second) spacing. We have investigated a range of geomorphic parameters, including elevation and slope, to determine how values computed from LIDAR DEMs compare to coarser cartographic DEMs. Because of the small horizontal spacing, accurate computation of geomorphic parameters requires that LIDAR DEMs use floating point values to store elevations. LIDAR DEMs continue the trends seen with other DEMs, with steeper computed slopes as the horizontal DEM spacing decreases. While LIDAR DEMs can improve the characterization of terrain, for many applications the differences compared to cartographic DEMs will be marginal.

INTRODUCTION The 2-dimensional cartographic information systems of previous centuries are becoming quaint historical

artifacts. The advent of computerized Geographic Information Systems (GIS) has afforded scientists the opportunity to look at landforms in 3, and even 4 dimensions; making analysis of time-spatial relationships and geological processes, geochronology, and model development possible (Bishop and Schroeder, 2004).

Advances in GIS, particularly in spatial data collection techniques and model development, have allowed scientists to construct accurate Digital Terrain Models (DTMs). Although the formatting of DTMs varies, this paper will only be concerned with spatial data stored in the form of Digital Elevation Models (DEMs), which use a regular, rectangular grid structure.

DEMs are produced in a variety of manners; and DEM quality and resolution reflect these varying production methods. As in any concentration, modelers seek to maximize quality, while minimizing costs. In this study, we will compare lower resolution cartographically generated National Elevation Dataset (NED) DEMs to high resolution Light Detection and Ranging (LIDAR) generated DEMs.

Geomorphologists use DEMs to enable geomorphometric quantification of ground surface relief and patterns (Evans 1980, 1998; Pike 1988, 2000, 2002). Many terrain parameters depend on the DEM spacing or horizontal resolution (Hodgson, 1995; Kienzle, 2004), and also on the collection method. Guth (2006) showed systematic differences between 1” DEMs created with radar interferometry from the Shuttle Radar Topography Mission and cartographically derived DEMs at the same scale, and in this paper we seek to determine whether similar differences exist in high resolution LIDAR DEMs compared to cartographic DEMs. In addition to the effects on scientific studies of geomorphometry, such differences could have practical implications for users of terrain information like slope, include military trafficability studies or viewshed analysis.


THE DEMs

The United States Geological Survey (USGS) produces DEMs as part of the National Elevation Dataset (NED), which provides seamless coverage of the continental United States (Gesch et al., 2002). NED is a living dataset and provides the best quality and most recent DEMs of United States topography. NED currently includes three different resolutions of DEMs for the contintental United States: complete coverage at 1” ( 30m), nearly complete coverage at 1/3” ( 10m), and very limited coverage at 1/9” ( 3 m). The 1” and 1/3” DEMs are cartographically generated, while the 1/9” DEMs are LIDAR generated.

To compare the differences between cartographic and LIDAR DEMs in their ability to capture the geomorphic characteristics of the topography, we selected three of the four regions with 1/9” currently available. We attempted to vary DEM geography and terrain as much as possible, and selected regions covering Lincoln, Nebraska; a region southwest of Seattle, Washington; and a portion of Applachians in West Virginia (Figure 1). The only other area with 1/9” NED currently available, around Houston, TX, proved too flat for good statistical analysis and also showed artifacts relating to building removal in the LIDAR DEMs.

Figure 1. DEMs used for analysis.

NED DEM GENERATION

In order to understand the limitations of cartographically generated DEMs and the superior nature of LIDAR generated DEMS, it is useful understand the manner in which the respective models are generated. NED provides multi-resolution, seamless raster data for the entire United States. In this study we will look at NED based DEMs in 1”, 1/3”, and 1/9” resolution. 1” and 1/3” models are generated in the same manner: UTM coordinates are digitally transformed into geographic coordinates (Gesch et al., 2002). Thereafter, the original elevation data is resampled and reviewed in an attempt to eliminate artifacts (Gesch et al., 2002). Because the elevation data used in the generation of these DEMs is derived from standard USGS DEMs, the new DEMs have great potential to inherit any artifacts present in the original DEM. As a result, the accuracy of these DEMs is in question and may vary regionally (Gesch et al., 2002).

Washington State West Virginia Lincoln, Nebraska

Center: N47.0645343° W123.130184°

Center: N37.5463844° W80.4804344°

Center: N40.7040158° W96.8167145°

Elevation range: 0-720 m Elevation range: 582-1161 m Elevation range: 36-462 m 1/9” spacing: 2.34x3.43 m 1/9” spacing: 2.72x3.43 m 1/9” spacing: 2.60x3.43 m


Unlike the 1” and 1/3” data, the 1/9” data is LIDAR generated. LIDAR is a remote sensing platform that is typically mounted to aircraft (Fowler, 2001). The platform sends out a laser signal and uses the time it takes the signal to return to calculate elevation. Collected elevation data, coupled with corresponding positional data provides superior DTMs for a number of reasons. LIDAR collects data at very high spatial resolution, and therefore, offers modelers the opportunity to construct highly detailed surface grids. Also, some sensors can record multiple returns, allowing separate first return (top of vegetation) and bare earth DEMs. In addition to multiple returns, LIDAR can further enhance generated DEMs by interpreting the intensity of returns for terrain identification and to distinguish unique surface features. As a result of LIDAR’s data collecting capabilities, it offers a superior, high resolution DEM that can be used as a standard to assess the accuracy of cartographically generated DEMs.

Although LIDAR DEMs provide a superior representation of a surface, production of is both time-consuming and costly. We seek to prove that, for most applications, the already existing 1” and 1/3” NED DEMs adequately represent the terrain. In addition, we seek to determine if analysis methods need to be modified because LIDAR DEMs might have different characteristics that would appear in geomorphometric analysis.

METHODS

Several different techniques were employed to compare the 1” and 1/3” DEMs to LIDAR generated 1/9” DEMs. All DEM processing was performed using MICRODEM GIS software that specializes in DEM analysis and geomorphometry (Guth, 2003).

In order to make a fair assessment, the 1/9” DEMs were decimated by factors of 3 and 9 in order to equate them to 1/3” and 1” DEMs, respectively. We also decimated the 1/3” DEM to 1” resolution. MICRODEM can thin a DEM in two manners: averaging the points within a neighborhood, or true decimation by removing all data postings except those at the desired locations. We chose to decimation, thereby maintaining the integrity of the original DEM’s elevation data. All elevation values in the thinned DEM have the same elevation as those in the original DEM. We thus had 6 DEMs for each of the three areas: one at 1/9” spacing, two at 1/3” spacing, and 3 at 1” spacing. At each data spacing the DEMs are independent; in particular, the 1” DEM created by thinning the 1/3” NED differs from the 1” NED, even though both are cartographically produced by USGS.

Following the decimation process, we used MICRODEM to obtain and compare terrain statistics. These statistics include elevation and slope and their first, second, and third order moments: standard deviation, skewness, and kurtosis, respectively (Tables 1-3). Slope, the rate amount of elevation change per horizontal distance and the first derivative of elevation, was analyzed as a percent. Previous work suggests that calculations in degrees would lead to very similar conclusions. Many analyses show that many slope algorithms all correlate extremely highly (Guth, 1995; Hodgson, 1998; Jones, 1998), and we used an eight equally weighted neighbors algorithm (Evans, 1998; Guth 2003) because it produces a better statistical distribution by minimizing slope quantization. We do not report here on the second derivative of elevation, profile and plan curvature, which like the higher moments, tends to suffer from noise in the DEMs.

Standard deviation of elevation correlates extremely highly with slope. Standard deviation of slope identifies and quantifies surface curvature (Evans, 1998). We employed standard deviation primarily to quantitatively compare the 1” and 1/3” NED to the corresponding thinned 1/9” DEMs. Skewness and kurtosis also served as values for quantitative comparison. Skewness, fundamentally a measure of symmetry, characterizes the extent of convexity versus concavity of the terrain surface (Evans, 1998). Kurtosis indicates the peakedness or flatness of the tails in the data distribution. Third and fourth order moments are often unreliable statistics due to noise.

In addition to quantitative moment statistics, MICRODEM also generates slope and elevation histograms (Figure 2). The histograms indicate the normalized concentration of points in a histogram bin. Because the 1/9” DEM contains 9 times as many points as the 1/3” DEM, and 81 times as many points as the 1” DEM, plotting the number of points leads to histograms where the 1” DEMs cannot be interpreted. In the normalized histograms, a concentration of 1 would have all bins with the same number of points and a totally uniform distribution of slopes or elevations in the DEM.

The moment statistics in Tables 1-3 show the DEMs in the following order: 1/9”, 1/9” decimated to 1/3”, 1/3”, 1/9” decimated to 1”, 1/3” decimated to 1”, and 1”. Assuming higher spatial resolution makes a more accurate DEM, this order arranges the DEMs in order of declining quality.

MICRODEM can create graphs that plot elevation versus slope (as a percent) and indicate the elevations (in


meters) at which steeper or flatter terrain exist (Figure 3).

Table 1. Slope and Elevation Moments, Washington State DEMs

WA 1/9" WA 1/9" WA 1/3" WA 1/9" WA 1/3" WA 1" ELEVATION thin 1/3" thin 1" thin 1" Average 211.16 211.18 218.92 211.48 218.81 218.7 Average dev 118.79 118.78 118.99 118.84 119.1 119.09 Standard dev 143.38 143.36 143.08 143.42 143.22 143.21 Skewness 0.6144 0.6143 0.5844 0.6122 0.5824 0.5826 Kurtosis -0.4097 -0.4095 -0.4758 -0.4116 -0.4758 -0.4763 n=2497288 n=2495806 n=2458609 n=276984 n=273425 n=274458 SLOPE Average 24.87 23.78 22.55 21.87 21.66 21.59 Average dev 14.44 13.76 12.36 12.32 11.55 11.43 Standard dev 17.52 16.59 15.3 14.82 14.1 13.95 Skewness 0.7246 0.5935 0.7121 0.5021 0.5266 0.5259 Kurtosis 0.5847 -0.2531 0.365 -0.5293 -0.2351 -0.2329

n=2460436 n=2463301 n=2446041 n=271371 n=269728 n=269972

Table 2. Slope and Elevation Moments, West Virginia DEMs

WV 1/9" WV 1/9" WV 1/3" WV 1/9" WV 1/3" WV 1" ELEVATION thin 1/3" thin 1" thin 1" Average 761.02 761.06 760.99 761.1 760.99 761.22 Average dev 66.28 66.29 66.23 66.36 66.28 66.37 Standard dev 89.29 89.31 89.23 89.4 89.3 89.39 Skewness 1.3801 1.3793 1.3813 1.3781 1.381 1.3774 Kurtosis 2.3905 2.3873 2.3937 2.3835 2.3929 2.3569 n=1965965 n=1964248 n=1967682 n=217932 n=218504 n=219459 SLOPE Average 24.15 23.41 23.38 21.2 21.16 21.05 Average dev 12.22 11.83 11.81 10.79 10.78 10.73 Standard dev 14.98 14.45 14.42 13.18 13.16 13.1 Skewness 0.7467 0.6939 0.6941 0.7141 0.7149 0.7168 Kurtosis 0.4814 0.0565 0.0572 -0.0066 -0.0062 0.0064

n=1958863 n=1951730 n=1954810 n=214134 n=214695 n=215642


Table 3. Slope and Elevation Moments, Nebraska DEMs

NB 1/9" NB 1/9" NB 1/3" NB 1/9" NB 1/3" NB 1" ELEVATION thin 1/3" thin 1" thin 1" Average 405.58 405.58 405.52 405.68 405.6 405.45 Average dev 15.32 15.32 15.31 15.32 15.31 15.32 Standard dev 18.44 18.44 18.43 18.44 18.44 18.44 Skewness -0.0175 -0.0175 -0.0114 -0.0219 -0.014 -0.0064 Kurtosis -0.7208 -0.7208 -0.705 -0.7189 -0.7032 -0.7074 n=1200320 n=1200320 n=1201746 n=132990 n=133393 n=134128 SLOPE Average 6.51 5.83 5.79 4.99 5.12 5.1 Average dev 3.3 2.45 2.57 1.89 2 2 Standard dev 5.1 3.47 3.47 2.47 2.62 2.62 Skewness 3.2531 1.8183 1.5173 0.6425 0.8613 0.8757 Kurtosis 19.5373 7.9783 4.6321 1.4478 1.5568 1.6044

n=1196449 n=1190903 n=1183071 n=130058 n=129703 n=130435

Derivative slope grids were created for all 6 DEM resolutions in each area, showing the percent slope at each point. We plotted the slopes and elevations from each pair of DEMs, for each of the three areas. This created 15 graphs for each area, for both slope and elevation. Figure 4 shows 4 of the 45 graphs for elevation, and Figure 5 shows 4 of the 45 graphs for slope. As a way to compare the results, Tables 4-6 show correlation matrices for each area showing how the correlation coefficients for each pair of DEMs. The matrices are symmetrical. Figure 6 shows slope maps for a small area in the Washington State DEM, which allows assessment of the overall success of slope computations from these DEMs.


Figure 2. Elevation and slope histograms, normalized to remove the effect of DEM spacing. (a) and (b) show the 6 Washington state DEM, (c) and (d) the West Virginia DEMs, and (e) and (f) the Nebraska DEMs.


Figure 3. Elevation slope plots. (a)Washington State, (b)West Virginia, (c) Nebraska

Figure 4. Graphs showing elevations from the 1” DEMs compared to the elevations at the same location in the 1/3”

and 1/9” DEMs. (a) and (b) show the Nebraska DEMs, and (c) and (d) the Washington state DEMs. Note the extremely high correlation coefficients shown on each graph.


Figure 5. Graphs showing slopes from the 1” DEMs compared to the slopes at the same location in the 1/3” and

1/9” DEMs. (a) and (b) show the Nebraska DEMs, and (c) and (d) the Washington state DEMs.

RESULTS

Elevation Distributions

For all three areas, the elevation moments show in Tables 1-3 show almost no change across the 6 DEMs we consider. The representative scatter plots shown in Figure 4 demonstrate that while the different DEMs are not identical, they correlate extremely highly. The differences probably reflect the level of detail captured as the resolution increases, and varying effects of vegetation. The elevation histograms in Figure 2 also demonstrate that at the range of resolutions considered, LIDAR and cartographic DEMs provide essentially identical slope distributions. The only exception to this generalization occurs in the Nebraska DEM shown in Figure 2e, which displays an oscillating sawtooth pattern to the elevation distribution. The distribution has a period of about 3 m , and may reflect a ghost 10 foot contour interval in the USGS topographic maps used to create the DEMs (Guth, 1999).

The slope distributions in Figure 2 show several trends. As the DEM grid spacing increases from 1/9” to 1”, there are fewer steep slopes. Figures 2b, 2d, and 2f all have crossover points: for steeper slopes the 1/9”has the largest concentration, and for gentler slopes the 1” DEM has the largest concentration.

Unlike the elevation moment statistics, the slope statistics differed among the DEMs. In general, as resolution decreases, the average slope and standard deviation decrease, in line with previous findings (e.g. Guth, 1995). There was one exception this overall trend, the Nebraska 1/9” thinned to 1” DEM has the lowest slope and standard deviation values of all of the Nebraska DEMs. This difference may not be significant, and probably relates to the characteristics of this DEM. As seen in Figure 3c, the 1/9” LIDAR DEM has extreme slopes at the lowest elevations, several times larger than in the thinned versions or any of the cartographic DEMs. These high average slopes result from a small stream channel, which has several meter elevation drops over the approximately 3 meter grid spacing. With larger grid spacings these extreme slopes disappear, and the Nebraska LIDAR DEMs more closely resemble the cartographic


DEMs. In addition, the contour line ghosts in the cartographic DEMs exert an influence on the slope distribution by elevation (Figure 3c).

Figure 6. Slope maps showing for the same area in Washington state, from the 1” DEM (a), the 1/3” DEM (b), and the 1/9” DEM (c). (a) to (c) are at the same scale, which shows all the data points in the 1” DEM. (d) blows up the

1/3” DEM to show all its points, and (e) blows up the 1/9” DEM to show all its points.

The results for slope skewness and kurtosis were less consistent, but clearly show that the different DEMs do not capture the same details of the slope distribution. The slope skewness values for the Washington and West Virginia DEMs differed slightly, perhaps not significantly (Tables 1 and 2), but slope skewness varies dramatically among the Nebraska DEMs, from 3.25 to 0.64 (Table 3). Skewness is highest for the 1/9” DEM, and then decreases for the 1/3”DEMs, both of which are similar, and decreases again for the 1/9” DEMs. This follows the average slope trends, where large spacing averages out slope changes and removes the larges slopes from the distribution (Figure 2f). Slope kurtosis was so variable for these DEMs that there might be no signal amid the noise. For the Nebraska DEM, kurtosis ranged from 19.5 to 1.4 (Table 3), while for the Washington state and West Virginia DEMs kurtosis did not even have a consistent sign (Tables 1 and 2).

The elevation slope plots for each of the three regions analyzed are available in Figure 3. There was an overall trend in slopes, similar to that observed in the moment statistics. In general, the 1/9” LIDAR DEMs had greater slopes than the rest of the DEMs. As resolution decreased, so did the average slope at each elevation. The West Virginia and Washington State had slope elevation profiles that exhibited a similar shape for different resolutions. However, at certain elevations there were exceptions. For example, at 650 m elevation for the Washington state DEMs the 1/3” and 1/3” decimated to 1” appear to contain artifacts, as it exhibits a spike in slope where none of the other DEMs do. Less than 0.15% of the points in the LIDAR DEM occur on the two peaks above 650 m, making any statistics there suspect and not statistically valid. In addition the 1/9” West Virginia LIDAR DEM picked up a spike in slope at 1160 m that the cartographically generated DEMs did not, but only 13 of 17 million points in the LIDAR DEM fall into this elevation range, so the statistics are based on miniscule sample sizes. In general the elevation-slope plots provide a great deal of information once outliers have been identified.


Table 4. Correlations of slopes computed from different DEMs, Washington State DEMs

Washington 1/9" 1/9" thin

1/3" 1/3" 1/9" thin 1" 1/3" thin

1" 1" 1/9" 1.000 0.940 0.480 0.762 0.518 0.504

1/9" thin 1/3" 0.940 1.000 0.566 0.872 0.614 0.595 1/3" 0.480 0.566 1.000 0.677 0.932 0.901

1/9" thin 1" 0.762 0.872 0.677 1.000 0.757 0.741 1/3" thin 1" 0.518 0.614 0.932 0.757 1.000 0.965

1" 0.504 0.518 0.901 0.741 0.965 1.000

Table 5. Correlations of slopes computed from different DEMs, West Virginia DEMs

West Virginia 1/9" 1/9" thin

1/3" 1/3" 1/9" thin 1" 1/3" thin

1" 1" 1/9" 1.000 0.962 0.838 0.822 0.786 0.751

1/9" thin 1/3" 0.962 1.000 0.874 0.897 0.854 0.811 1/3" 0.838 0.874 1.000 0.853 0.899 0.873

1/9" thin 1" 0.822 0.897 0.853 1.000 0.956 0.894 1/3" thin 1" 0.786 0.854 0.899 0.956 1.000 0.961

1" 0.751 0.811 0.873 0.894 0.961 1.000

Table 6. Correlations of slopes computed from different DEMs, Nebraska DEMs

Nebraska 1/9" 1/9" thin

1/3" 1/3" 1/9" thin 1" 1/3" thin

1" 1" 1/9" 1.000 0.606 0.200 0.208 0.178 0.175

1/9" thin 1/3" 0.606 1.000 0.398 0.523 0.420 0.390 1/3" 0.200 0.398 1.000 0.484 0.730 0.573

1/9" thin 1" 0.208 0.523 0.484 1.000 0.708 0.653 1/3" thin 1" 0.178 0.420 0.730 0.708 1.000 0.816

1" 0.175 0.390 0.573 0.653 0.816 1.000

DISCUSSION AND CONCLUSIONS

For all three of our areas, the 6 DEMs produce essentially identical elevation distributions. The only significant differences that we see result from the contour line “ghosts” present in both the 1” and 1/3” NED for the Nebraska area. This is the flattest of the three areas, but despite the visible anomalies, the overall elevation moment statistics actually match the thinned LIDAR very closely. The Nebraska data makes a strong case for the superiority of LIDAR DEM data where it exists, and supports the assertion of Maune et al. (2001a,b) that the quality of cartographic generation varies regionally. Our results also confirm the findings of Hodgson et al. (2003) that LIDAR and Level 2 USGS DEMs produce very similar, small elevation errors compared to surveyed reference points.

Over the range of DEMs considered, from 1/9” (about 3 m) to 1” (about 30 m), we see a decrease in computed slope as resolution decreases. This to be expected due to the data averaging that must occur in order to consolidate the elevation information. Lower resolution models smooth the data, consequently smoothing the terrain. However, there is still a distinct difference between the lower resolution LIDAR generated DEMs and the lower resolution cartographically generated DEMs. Aside from the anomaly in the Nebraska dataset, the decimated 1/9” DEMs had greater slopes than their cartographic counterparts. They do a better job preserving the higher slopes present in the


“best” DEM, the 1/9” models. However, the higher resolution DEMs have a noisier slope map (Figure 6) that may not be useful. Users of slope data must decide whether they want noisy depictions of micro-relief, or whether smoothing produces a more useful product even though it removes many of isolated steepest slopes. Albani et al. (2004) discussed the tradeoffs in topographic detail versus reduction in propagated errors for derived terrain parameters like slope. While their DEMs had grid spacing of 75-100 m, this work shows that the same principles apply to DEMs with an order of magnitude higher resolution.

Our results suggest that skewness and kurtosis for slope distributions do not correlate well as DEM resolution and collect method vary. Guth (2006) compared 1” NED to 1” Shuttle Radar Topography Mission (SRTM) DEMs, and found very low correlations for slope skewness and kurtosis. The correlations improved if only slopes greater than 5% were included, and if the 1” SRTM was compared to 2” decimated NED. If slope skewness and curtosis are to be used (Evans, 1988), perhaps they can only be applied and compared among DEMs with the same resolution and production methods.

NED LIDAR generated DEMs provide a better model of the surface than the cartographically generated DEMs. However, for many purposes the standard NED 1/3” and 1” are nearly comparable to decimated 1/9” LIDAR DEMs. As more LIDAR regions become available, a better alternative could be to use LIDAR generated models in their high resolution and decimated forms. Until that happens, 1/3” and 1” NED DEMs provide an acceptable substitute for less sensitive operations as long as the user understands their limitations.

REFERENCES CITED Albani, M, Klinkenberg, B., Andison, D.W.,and Kimmins J.P. (2004). The choice of window size in approximating

topographic surfaces from Digital Elevation Models: International Journal of Geographical Information Science: 18(6):577-593.

Bishop, B.P. and Shroder, J.F., Jr. (2004). An introduction in Geographic Information Science and Mountain Geomorphology: Praxis Publishing Ltd, Chichester, p.4.

Evans, I.S. (1980). An integrated system of terrain analysis and slope mapping: Zeitschrift für Geomorphologie N.F. Supplementband 36, 274-295.

Evans, I.S. (1998). What do terrain statistics really mean? in Lane, S.N., Richards, K.S., and Chandler, J.H., eds.,Landform monitoring, modelling and analysis, J.Wiley, Chichester, pp.119-138.

Fowler, R. ( 2001). Topographic lidar in Maune, D.F., ed., Digital elevation model technologies and applications: the DEM users manual: The American Society for Photogrammetry and Remote Sensing, Bethesda., pp. 207-236.

Gesch, D.B., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., and Tyler, D. (2002). The national elevation dataset: Photogrammetric Engineering & Remote Sensing, 68(1):5-11.

Guth, P.L. (2003). Terrain organization Calculated From Digital Elevation Models in Evans, I.S., Dikau, R., Tokunaga, E., Ohmori, H., and Hirano, M., eds., Concepts and Modelling in Geomorphology: International Perspectives: Terrapub Publishers, Tokyo, pp.199-220.

Guth, P.L. (1995). Slope and aspect calculations on gridded digital elevation models: Examples from a geomorphometric toolbox for personal computers: Zeitschrift für Geomorphologie N.F. Supplementband 101, pp.31-52.

Guth, P.L. (1999). Contour line “ghosts” in USGS Level 2 DEMs: Photogrammetric Engineering & Remote Sensing, 65(3):289-296.

Guth, P.L. (2006), Geomorphometry from SRTM: Comparison to NED: Photogrammetric Engineering & Remote Sensing, 72(3), in press.

Hodgson, M.E. (1998). Comparison of angles from surface slope/aspect algorithms: Cartography and Geographic Information Systems, 25(3):173-185.

Hodgson, M.E., Jensen, J.R., Schmidt, L., Schill, S., and Davis, B. (2003). An evaluation of LIDAR- and IFSAR-derived digital elevation models in leaf-on conditions with USGS Level 1 and Level 2 DEMs: Remote Sensing of Environment, 84:295-308.

Jones, K.H. (1998). A comparison of algorithms used to compute hill slope as a property of the DEM: Computers & Geosciences, 24(4):315-324.


Maune, D.F., Huff, L.C., and Guenther, G.C. (2001a). DEM user applications in Maune, D.F., ed., Digital elevation model technologies and applications: the DEM users manual: The American Society for Photogrammetry and Remote Sensing, Bethesda. pp 367-394.

Maune, D.F., Kopp, S.M., Crawford, C.A., and Zervas, C.E. (2001b). An Introduction in Maune, D.F., ed., Digital elevation model technologies and applications: the DEM users manual: The American Society for Photogrammetry and Remote Sensing, Bethesda, pp. 1-34.

Pike, R.J. (1988). The geometric signature: quantifying landslide-terrain types from digital elevation models: Mathematical Geology, 20(5):491-512.

Pike, R.J. (2000). Geomorphometry--diversity in quantitative surface analysis: Progress in Physical Geography, 24(1):1-20.

Pike, R.J. (2002). A bibliography of terrain modeling (geomorphometry), the quantitative representation of topography--Supplement 4.0: U.S. Geological Survey Open File Report 02-465, 157 p.

Documents

Geomorphometry from LIDAR DEMs: Issues of Scale and