Effects of DEM horizontal resolution and methods on

Catena 87 (2011) 368–375

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Catena j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c a t e n a

Effects of DEM horizontal resolution and methods on calculating the slope length factor in gently rolling landscapes Honghu Liu a, b, Jens Kiesel b, Georg Hörmann b, Nicola Fohrer b,⁎ a b

Changjiang River Scientific Research Institute, Wuhan 430010, PR China Department of Hydrology and Water Resources Management, Institute of the Conservation of Natural Resources, Kiel University, Germany

a r t i c l e

i n f o

Article history: Received 7 August 2010 Received in revised form 3 July 2011 Accepted 10 July 2011 Keywords: Slope length factor Grid cumulating method Contributing area method DEM USLE Northern Germany

a b s t r a c t The USLE is used world-wide to predict soil loss on the field scale from sheet and rill erosion. The slope length (L) factor is derived as its topographical factor. The accuracy of L factor determines the precision of soil loss estimation with USLE. Uncertainties on L factor are caused by DEM resolution and the choice of the processing algorithm. In the present study we made two comparisons to evaluate the effects of DEM horizontal resolution and processing algorithm on the accuracy of the L factor in gently sloped landscapes: one is between the grid cumulating method (GC) and the contributing area method (CA) using D8 flow-routing algorithm, the other is among single (D8, Rho8) and multiple (FD8, FRho8 and DEMON) flow-routing algorithms for processing the contributing area method. In two comparisons, 5 m, 10 m, 25 m, 50 m and 100 m DEM of a 0.88 km2 catchment in the lowland of Northern Germany were applied. The results indicate that L factor calculated with any of the six methods is sensitive to horizontal resolution, which strongly affects the accuracy. With decreasing resolution, correlations of LCA_Rho8 and LCA_D8, LCA_FD8 and LCA_D8, LCA_FD8 and LCA_Rho8 increase while those between DEMON and the other flow-routing algorithms do not change significantly. With decreasing resolution, the difference between LGC_D8 and LCA_D8 is enlarged, while differences between any two flow algorithms using CA did not change significantly. The L factor variation between any two methods is larger on the upslope than the flat valley for the 5 m and 10 m DEM while terrain characteristics are not visible on the 25 m, 50 m and 100 m DEM. The L factor also depends on the computation method. LGC_D8 is approximately half of LCA. It is concluded that DEM horizontal resolution is very important for L factor calculation. The most suitable calculation method is LGC_D8 for gently rolling landscapes. This study can be used for selecting a suitable method and DEM resolution for accurate calculation of L factor and soil loss in gently rolling landscapes. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Topography influences the movement of water, sediment and other constituents within a landscape (Moore et al., 1991; Wilson et al., 2007). Thus, topography is very fundamental to predict soil loss using soil erosion models such as the USLE (Wischmeier and Smith, 1978). The slope length factor (L) is derived as the topographical factor of USLE, which is the ratio of soil loss from the field slope length to soil loss from a 72.6-ft design length under identical conditions (Wischmeier and Smith, 1978). Slope length is defined as the distance from the point of origin of overland flow to either: (1) the point where the slope decreases to the extent where deposition begins or (2) the point where runoff enters a well-defined channel that may be part of a drainage network or a constructed channel such as a terrace or diversion (Wischmeier and Smith, 1978). ⁎ Corresponding author. Tel.: +49 431 8801276; fax: +49 431 8804607. E-mail addresses: [email protected] (H. Liu), [email protected] (N. Fohrer). 0341-8162/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.catena.2011.07.003

Digital elevation models (DEMs) are very convenient to represent the continuously varying topographic surface of the Earth (Thompson et al., 2001). Advances in GIS systems make it possible to compute the L factor on the watershed scale from DEMs (Hickey et al., 1994; Winchell et al., 2008). To obtain an accurate output for soil loss, more attention must be paid to the accuracy of the L factor on the watershed scale. The accuracy of the L factor depends on DEM accuracy and the precision of different calculation methods (Thompson et al., 2001). DEM accuracy is very sensitive to horizontal resolution, vertical precision and the density of sample points as well as the source of the elevation data. As horizontal resolution decreases, slope gradient decreases (Chang and Tsai, 1991; Thieken et al., 1999; Wolock and Price, 1994; Zhang and Montgomery, 1994); the total flow length and drainage density also have a decreasing trend (Thieken et al., 1999; Wang and Yin, 1998; Yin and Wang, 1999) and the specific catchment area increases (Quinn et al., 1991; Wolock and Price, 1994; Zhang and Montgomery, 1994). As vertical precision decreases, the overall distribution of slope gradient and contributing area for large catchments do not change (Gyasi-Agyei et al., 1995). As the density

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of DEM sample points increases, slope gradient increases and specific catchment area decreases (Bolstad and Stowe, 1994; Sasowski et al., 1992; Wolock and Price, 1994). Thus, horizontal resolution and the density of sample points affect total flow length. Slope gradient and contributing area will have effects on the L factor. However, few studies have examined how the L factor is affected by horizontal resolution, which will be discussed in this paper. The precision of L factor processing is very sensitive to the chosen calculation method and the primary attributes derived from DEMs which are mentioned above. Four methods for quantifying the L factor from DEMs are available, including the unit stream power theory method (Moore and Wilson, 1992), the network triangulation techniques (Cowen, 1993), the grid cumulating method (GC) (Hickey, 2000) and the contributing area method (CA) (Desmet and Govers, 1996a). The unit stream power theory is used to create a simplified equation for calculating the L factor over two-dimensional terrain. The equation is implemented in the GIS software GRASS (Winchell et al., 2008). The network triangulation techniques provide an approach to derive the L factor from triangulated irregular networks (TIN) (Cowen, 1993), which is a vector based representation of the physical land surface or sea bottom, made up of irregularly distributed nodes and lines with three dimensional coordinates (x, y, and z) that are arranged in a network of nonoverlapping triangles. The GC first determines the maximum downhill slope gradient from the depressionless raster grid utilizing the D8 (Deterministic eightnode) flow-routing algorithm (Hickey et al., 1994). Then the cumulative slope length is summed based on the flow direction and grid cell size and the L factor is computed. GC explicitly addresses deposition issues by evaluating changes in slope (Winchell et al., 2008). CA is convenient to use and implemented based on the contributing area, grid cell size and the ‘m’ value of the USLE (Desmet and Govers, 1996a, McCool et al., 1987). Thus, for the CA method, the contributing area and ‘m’ must be derived before the L factor is computed. As the GC and CA are the most frequently applied methods, we use them for this study. Additionally, the flow-routing algorithms D8, Rho8 (Random eight-node), FD8 (Finite deterministic eight-node), FRho8 (Finite random eight-node) and DEMON (Digital elevation model network) (Zhou and Liu, 2002) can be used in the CA method to delineate the catchment area (Desmet and Govers, 1996b). Wilson et al. (2007) describe these flow-routing algorithms in detail. DEMON avoids computational inconsistencies by ensuring that: (1) flow which originates over a two dimensional pixel is treated as a point source and is projected downslope by a line, and (2) the flow direction in each pixel is restricted to eight possibilities (Costa-Cabral and Burges, 1994). It can represent varying flow width over nonplanar topography. The following three dependences of L factor calculation are assessed in this paper: (1) The dependence of GC and CA - L factor calculation algorithms on DEM horizontal resolution is assessed. (2) Flat and sloping areas of the study catchment are used to determine the impact of terrain characteristics on L factor calculations. (3) Different types of flow-routing algorithms within CA in regard to their impact on the L factor are investigated. The three dependences are investigated for the horizontal DEM resolutions of 5 m, 10 m, 25 m, 50 m and 100 m.

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2.2. The DEM database Elevation data was surveyed along north–south oriented transects by light detection and ranging (LiDAR) data recorded in 2007 (LVA, 2008). The grid points are derived from approximately four LiDAR points per m². The vertical precision is 0.2 m and the influence of vegetation height was already removed from the data set. An Inverse Distance Weighted Interpolation (IDW) within ARC/INFO (Environmental Systems Research Institute, 1987) was used to interpolate 2.9 × 10 6 points into a 1 m DEM. Twelve nearest neighboring points and a power of two were used in the IDW operation. The 5 m, 10 m, 25 m, 50 m and 100 m DEM were derived by resampling the 1 m DEM. Thus, the DEM values represent mean values for each grid, while the recorded vertical error is identical for all DEMs. 2.3. Calculation of the L factor We evaluate the dependence of methods on calculating the L factor for different horizontal resolutions using the 5 m, 10 m, 25 m, 50 m and 100 m DEM. The depressions in these DEMs were eliminated using an AML program within the ArcGIS workstation (Hickey et al., 1994). The calculations are carried out with the grid cumulating method (GC) and the D8 flow-routing algorithm as well as with the contributing area method (CA) and D8, Rho8, FD8, FRho8 and DEMON flow-routing algorithms. GC_D8 was implemented using Hickey's AML program (Hickey et al., 1994). The slope length of every grid cell was calculated based on the D8 flowrouting algorithm (Hickey et al., 1994). It must be noted that slope length of every grid cell is different if flow direction is either cardinal or diagonal. The point of origin of the water flow was extracted at the beginning point of cumulative slope length. This was achieved by simply summing the noncumulative slope lengths along flow direction beginning at the high points (Hickey et al., 1994). The L cutoff factor (Hickey et al., 1994) was introduced as the end point of cumulative slope length and thus was used to delineate the border of the erosion-deposition belt. The end point of the L factor is the boundary of erosion and deposition and thus expresses that erosion ceases and deposition may occur. It is also the end point of the slope length and equal to the “cutoff-point”. In general, the end point is located in the lower part of the slope. The cumulative slope length is the sum of grid cells from the uppermost point in direction to the lower-most point. The ‘m’ value, which originates from the USLE, was calculated based on the maximum downhill slope gradient. According to the L factor Eqs. (1)–(3) by McCool et al. (1987), the L factor was computed for every grid cell:
L=

λ 22:13

m

ð1Þ

m = β = ð1 + βÞ

ð2Þ

h i 0:8 β = ð sin θ = 0:0896Þ = 3:0ð sin θÞ + 0:56

ð3Þ

2. Materials and methods 2.1. The study area The study area is a small catchment located in the state of Schleswig-Holstein in Northern Germany (Fig. 1). With a drainage area of 0.88 km 2 it is part of the Kielstau catchment, which is one of the headstreams of the river Treene. The river Treene is the largest tributary of the river Eider. The study site has an elevation range from 34.7 m to 51.7 m and thus, a vertical relief of 17 m (Fig. 1). It has an average slope of 3.67°.

Where L is the slope length (L) factor, 22.13 is the USLE unit plot length in meter, λ is the cumulative slope length, m is a variable slopelength exponent, β is the ratio of rill to interrill erosion for conditions when the soil is moderately susceptible to both rill and interrill erosion, and θ is the slope angle. The contributing area method (CA) was implemented in the following steps: First, the contributing area and aspect direction using D8 single-flow direction algorithm, Rho8 single-flow direction algorithm, FRho8 multiple-flow direction algorithm, FD8 multipleflow direction algorithm and DEMON multiple-flow direction

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Fig. 1. The location (right) and 1 m DEM (left) of the study site.

algorithm were computed using the TAPS-G software (Gallant and Wilson, 1996). The difference between single-flow direction algorithm and multiple-flow direction algorithm is that all flow directs to one (single) or more (multiple) of these neighboring cells after identifying all the downslope neighboring cells and calculating the slope gradients in each of these directions. Wilson et al. (2007) describe these flow-routing algorithms in detail. Second, based on another study (Liu et al., 2009), maximum slope gradients from 5 m DEM to 100 m DEM were used to compute the ‘m’ value. Third, the contributing area method by Desmet and Govers (1996a) was implemented with the model tool of the ARC/INFO toolbox. This equation is based on the contributing area of each grid cell and is written as Eq. (4).

Li;j =

 m + 1 + 1 Ai;jin + D2 −Am j;jin m D m + 2 × xm i;j × ð22:13Þ

ð4Þ

Where Li,j is the L factor for grid cell (i,j); Ai,j-in is the contributing area at the inlet of a grid cell with the coordinates (i,j) [m 2]; D is the grid cell size [m]; xi,j stands for (| sinαi,j| + | cosαi, j|) with αi,j being the aspect direction for the grid cell with the coordinates (i,j) (original equation modified) and m is the L exponent of the USLE-L factor. 2.4. Statistics McCool et al. (1987) suggested that the L factor should be calculated from contour maps having 0.7 m (2 ft) contour intervals. This infers that deriving the L factor from a 0.7 m contour map would be close to the true value. Hickey (2000) stated that the GC_D8 basically reflects the actual calculating process of the USLE L factor and is used to obtain the most accurate L factor for predicting soil loss with the USLE. Therefore, when DEM resolution is higher than or close to 0.7 m, the L factor using the GC_D8 is considered to be close to the real value. The L factor from the 1 m DEM calculated with the GC_D8 is thus used as the reference value in this study. The accuracy of the L factors calculated on the different resolution DEMs with the different

algorithms is evaluated by determining the root-mean-square-error (RMSE) of the residuals:

RMSE =

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u u ∑ ðLi −li Þ ti = 1 n

ð5Þ

Where n is the number of checked grid cells; Li is the computed L factor at the checked grid cell i; li is the reference L factor from the corresponding grid cell calculated with the 1 m DEM. 2.5. Evaluation procedure The L factors calculated by the described algorithms for the 5 m, 10 m, 25 m, 50 m and 100 m DEM are analyzed according to the following methodology (Fig. 2): First, the dependence of all L factor calculation algorithms on DEM horizontal resolution is assessed using a statistical evaluation. Therefore, we computed RMSE against the 1 m DEM LGC_D8, mean, standard deviation (SD) and maximum of LGC_D8, LCA_D8, LCA_Rho8, LCA_FD8, LCA_Frho8, LCA_DEMON for the study area. The statistical values are then plotted against all DEM resolutions to investigate if algorithms respond similarly to different resolutions. Thereafter, the analysis is split and carried out for two algorithm groups separately: In group one, the algorithm from the grid cumulating method (GC_D8) and a representative algorithm from the contributing area method (CA_D8) are compared. In group two, different flow-routing algorithms within CA (CA_D8, CA_Rho8, CA_FD8, CA_FRho8, CA_DEMON) are investigated. The analysis for each group is carried out using linear regression analysis between the calculated L factors on all five DEMs ([I] and [III]). If there is a high similarity between these L factors, the coefficient of determination approaches one (R² ≈ 1). By doing this, it is evaluated if the algorithms generally do or do not produce similar results for the same resolution and terrain. After that, the spatial distribution of L factor ratios is plotted ([II] and [IV]). In [IV] the single flow-routing algorithms (LCA_D8 with LCA_Rho8) and the

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5m

10m

25m

50m

371

100m

3.1 Statistical evaluation (RMSE, mean, SD, max) of LGC_D8, LCA_D8, LCA_Rho8, LCA_FD8, LCA_Frho8, LCA_DEMON 3.2 Comparison of algorithms: GC_D8 and CA_D8

3.3 Comparison of flow routing algorithms: CA_D8, CA_Rho8, CA_FD8, CA_FRho8, CA_DEMON

[I] [II] Linear Spatial distribution regression of LGC_D8 / LCA_D8

[III] [IV] Linear Spatial distribution regression of LCA_Rho8 / LCA_D8 & LCA_DEMON/LGC_D8

Fig. 2. Methodology of L factor algorithm tests.

single and multiple flow-routing algorithms (LCA_D8 with LCA_DEMON) are compared. It is analyzed which terrain characteristics are responsible for possible differences in L factors. This is achieved by calculating the L-factor ratio for each cell. If the ratio is close to 1.0, L factor similarity is high; if the ratio is close to 0.0, L factor difference is high. The ratio is then displayed on the map of the study area to

show the spatial distribution of the L factor differences. Areas with similar ratios can then be analyzed according to their underlying terrain characteristics. Using this methodology, it is possible to deduce recommendations toward the application of L factor and flow-routing algorithms at different DEM resolutions and terrain characteristics.

Fig. 3. RMSE (a), Mean (b), SD (c) and Maximum (d) of the L factor computed with the six methods and five different horizontal DEM resolutions.

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3. Results and discussion 3.1. Statistical evaluation RMSE, mean, standard deviation (SD) and maximum of the L factor are plotted in Fig. 3 to reveal the sensitivity of the calculation methods to DEM horizontal resolution: Several main findings result from Fig. 3: First, RMSE (Fig. 3a) of the L factor rises with decreasing horizontal resolution for any method. Second, RMSE of the six methods is different for all resolutions. The difference of RMSE between GC_D8 and the CA methods increases as DEM horizontal resolution decreases while RMSE difference within the CA methods increases initially, followed by a decrease. Third, mean (Fig. 3b) and SD (Fig. 3c) of the L factor increase as horizontal resolution decreases. This is contrary to the statement that the total flow length has a decreasing trend as horizontal resolution decreases (Thieken et al., 1999; Wang and Yin, 1998; Yin and Wang, 1999). Fourth, maximum L factor (Fig. 3d) has a decreasing trend as horizontal resolution decreases, which is opposite the trend of mean L factor. In the study site, few long slopes and many short slopes exist. The larger grid smooths the rolling relief and changes short slopes into longer slopes, but cut long slopes become relatively shorter. Thus, as DEM horizontal resolution decreases, slope gradient becomes smaller and length of many long slopes becomes relatively shorter, but mean slope length becomes bigger. These findings reveal the strong relationship between DEM horizontal resolution and L factor accuracy. RMSE rises progressively as resolution decreases for any given algorithm, which is due to the fact that the approximation of the L factor from a grid DEM is more accurate for smaller grid cell sizes. This is supported by Mitasova et al. (1996) who found that a 1:24 000 topographic map is more suitable for erosion and deposition modeling than a 30-m DEM and thus concluded that DEM horizontal resolution affects the accuracy of the L factor. The results show that the six methods can be classified into two groups. The first group only includes GC_D8, the second group the remaining methods. It can be seen that RMSE and SD of the L factor using CA algorithms are much higher than for GC_D8 (Fig. 3a and c). Fig. 3b and d shows that CA algorithms produce higher values than GC_D8. To investigate the reasons of the differences between the two groups, we compare GC_D8 and CA_D8 as the representative algorithm for the second group in more detail in the following section.

3.2. Comparison of GC_D8 and CA_D8 In this section, the L factor calculated by GC_D8 and CA_D8 is compared in more detail to investigate the reasons for the differences between the GC and CA method. First, the linear regression analysis is interpreted (Fig. 2 [I]) to reveal general similarities or differences between the algorithm groups depending on DEM resolution. The results of this analysis are listed in Table 1. Low R² values show that L factors of the corresponding grid cells using CA_D8 and GC_D8 have a poor correlation. This correlation decreases further as horizontal resolution decreases and reaches almost zero for the 100 m DEM. The low slope and the high intercept of the linear regression analysis mean that different L factors are calculated for similar terrain

Table 1 Linear regression analysis between LGC (Y) and LCA (X). DEM resolution (m)

Intercept

Slope

R2

5 10 25 50 100

0.67 0.76 0.91 0.96 1.30

0.14 0.13 0.04 0.07 0.03

0.19 0.21 0.09 0.10 0.03

characteristics, which have an even higher deviation for lower DEM resolutions. Fig. 4 supports this statement: The L factor ratio of LGC_D8/LCA_D8 was calculated on each cell and reclassified into five groups. It shows the frequency distribution, represented by the sum of the relative area in percent of each class. The higher the diagram column, the larger is the area (number of grid cells) in the corresponding ratio-class. From Fig. 4 it can be concluded that: First, with decreasing resolution, the mean ratio decreases from 0.70 with 5 m DEM to 0.48 with 100 m DEM. It can be seen, that the ratio between 0.8 and 1.0 decreases from 29.5% to 0% area while the ratio between 0.0 and 0.4 increases from 5.0% to 21.9% as grid cell size increases from 5 m to 100 m. The maximum area is in the 0.6–0.8 ratio-class for the 5 m, 10 m and 25 m DEM while it is in the 0.4–0.6 class for the 50 m and 100 m DEM. This means that the differences between GC_D8 and CA_D8 become larger as resolution decreases and thus, infers that the higher the DEM resolution, the better is the fit between the GC_D8 and CA_D8 calculations, which is in coherence with the result from the linear regression analysis. Fig. 5 is used to visualize and investigate this dependency on different terrain characteristics. To show the differences between the GC_D8 L factor and CA_D8 L factor for the same grid cell, the five ratioclasses of LGC_D8/LCA_D8 are displayed spatially distributed over the study area for each grid cell (Fig. 2 [II]). Thus, it can be seen there, how different terrain characteristics affect the two L factor calculation methods. For the 5 m and 10 m DEM, the terrain characteristics are visible in Fig. 5. It is obvious, that the L factor ratio on the upslope (b0.8) is generally lower than in the flat valley (N0.8). On the 25 m, 50 m and 100 m DEM however, the terrain cannot be distinguished. It has to be emphasized that the ratio of the L factor for 50 m and 100 m DEM has non valid (null) values (Fig. 3). CA_D8 was producing those invalid values which caused the null values of the ratio. This might be a shortcoming to compute the L factor on a regional scale using GC_D8. 3.3. Comparison of CA flow-routing algorithms Within CA, two single (D8, Rho8) and three multiple flow-routing algorithms (FD8, FRho8, DEMON) were classified (Desmet and Govers, 1996b) and used here. Referring to Fig. 3a and considering the CA methods only, it can be seen that RMSE of the single flowrouting algorithms is slightly below multiple flow-routing algorithms for most resolutions (5 m, 25 m and 50 m). Mean L factor from the single flow-routing algorithm is lower than the mean of the multiple flow-routing algorithms (Fig. 3b). Standard deviation (SD) of the L factor using single flow-routing algorithms is slightly larger than that of the multiple flow-routing algorithms. For any flow-routing algorithm, as DEM horizontal resolution decreases, mean of the L factor increases, while the maximum of the L factor decreases. An exception is the 100 m DEM, where the maximum L factor is higher than that of the 50 m DEM, except for the DEMON algorithm. Table 2 lists the results of the linear regression analysis of the L factor for the corresponding grid cells that has been carried out for all possible flow-routing algorithm combinations (Fig. 2 [III]). Because FD8 and FRho8 basically give the same results, the regression analysis of the L factor between FRho8 and the other flow-routing algorithms is omitted in the following investigation. The different slope and intercept of the linear regression analysis prove that the algorithms produce different L values at corresponding grid cells and terrain characteristics. Two trends can be noticed: the correlation coefficient of the bold marked algorithms increases with decreasing resolution. For the other flow algorithms correlated with DEMON it can be observed that R² does not change significantly from 5 m to 50 m while it gets considerably smaller for the 100 m DEM. In general, DEMON has a low correlation with both single and multiple flow-routing algorithms.

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Fig. 4. Spatial distributions of the ratio of LGC_D8/LCA_D8.

The ratio LCA_Rho8/LCA_D8 is displayed in Fig. 6 to reveal the spatial difference of the L factor between the two single flow-routing algorithms (Fig. 2 [IV]). For any given resolution, mean of the ratio for almost all grid cells is approximately 1.0. The overwhelming majority ranges between 0.5 and 1.5. The area for the 0.5–1.0 ratioclass increases from 5 m to 25 m DEM and then decreases from 25 m DEM onwards while this is vice versa for the range between 1.0 and 1.5. For the 5 m and 10 m DEM, the ratio of the L factor is relatively low for the plains while the ratio of the L factor is relatively large on the hillslopes. For the 25 m, 50 m and 100 m DEM the influence of the terrain characteristics on the L factor ratio is not visible anymore. The ratio of LCA_DEMON and LCA_D8 is shown in Fig. 7 as an example of the difference between multiple and single flow-routing algorithms (Fig. 2 [IV]). The majority of the ratio also varies from 0.5 to 1.5. Mean of LCA_DEMON/LCA_D8 decreases as grid cell size increases. For the 5 m DEM, the mean of the ratio of the L factor is 1.16 while it is 1.08 for the 100 m DEM. For the 5 m, 10 m and 25 m DEM, LCA_DEMON/LCA_D8 is relatively high for the hillslopes, while for the plains, the ratio of

Fig. 5. Frequency distribution of the ratio of LGC_D8/LCA_D8.

LCA_DEMON and LCA_D8 is relatively low. Again, for the 50 m and 100 m DEM, the terrain characteristics are not visible in the spatial distribution of the ratio of the L factor. Table 2 The linear regression analysis on the L factor using the five flow-routing algorithms. Resolution (m)

No

Y

X

Intercept

Slope

R2

5 5 5 5 5 5 5 10 10 10 10 10 10 10 25 25 25 25 25 25 25 50 50 50 50 50 50 50 100 100 100 100 100 100 100

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

DEMON Rho8 FD8 Rho8 FD8 FD8 FD8 DEMON Rho8 FD8 Rho8 FD8 FD8 FD8 DEMON Rho8 FD8 Rho8 FD8 FD8 FD8 DEMON Rho8 FD8 Rho8 FD8 FD8 FD8 DEMON Rho8 FD8 Rho8 FD8 FD8 FD8

D8 D8 D8 DEMON DEMON Rho8 FRho8 D8 D8 D8 DEMON DEMON Rho8 FRho8 D8 D8 D8 DEMON DEMON Rho8 FRho8 D8 D8 D8 DEMON DEMON Rho8 FRho8 D8 D8 D8 DEMON DEMON Rho8 FRho8

0.44 0.35 0.57 0.25 0.28 0.68 0 0.60 0.24 0.47 0.20 0.28 0.55 0 0.68 0.07 0.46 0.04 0.14 0.47 − 0.01 0.61 0.10 0.45 0.24 0.35 0.50 0 1.46 − 0.02 0.34 0.44 0.66 0.48 0.08

0.78 0.72 0.68 0.71 0.80 0.59 1 0.72 0.84 0.80 0.79 0.84 0.75 1 0.73 0.97 0.88 0.92 0.97 0.87 1 0.81 0.95 0.87 0.83 0.85 0.85 1 0.51 1.01 0.91 0.82 0.76 0.85 1

0.63 0.47 0.54 0.45 0.73 0.45 1 0.61 0.67 0.71 0.51 0.67 0.66 1 0.68 0.94 0.76 0.67 0.74 0.75 1 0.68 0.9 0.84 0.65 0.77 0.82 1 0.38 0.92 0.94 0.4 0.44 0.92 0.99

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Fig. 6. Spatial distribution of the ratio of LCA_Rho8/LCA_D8.

4. Conclusions The purpose of this study is to evaluate the effects of different calculation algorithms and DEM horizontal resolution on the L factor in gently rolling landscapes. The statistical evaluation showed that the CA algorithms yield higher errors and higher L factors than the GC algorithm, which is also found by Yitayew et al. (1999). This is probably due to the fact that the L cutoff factor in GC, which is not

integrated in CA, restricts the end point of the L factor. As DEM resolutions decreases, the deviation between CA and GC increases further. This is caused by an enlarged contributing area for lower horizontal resolution DEMs which increases the L factor. It can thus be concluded that GC is superior to CA methods, especially for lower DEM resolutions, and should be applied if possible. The linear regression (Fig. 2 [I], Table 1) and the frequency distribution (Fig. 4) carried out for GC_D8 and CA_D8 showed that the

Fig. 7. Spatial distribution of the ratio of LCA_DEMON/LCA_D8.

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differences between the calculated L factors become larger for lower DEM resolutions. This leads to the conclusion that for high resolution DEMs, the selection of L factor calculation methods tends to be not as important as for low resolution DEMs. The spatial distribution plots (Fig. 2 [II], Fig. 5) reveal a dependence of LGC_D8 and LCA_D8 on terrain characteristics, showing higher deviations in hilly than in flat areas. This infers that, if the terrain is clearly represented on the DEM, the selection of the L factor calculation method is less important in flat regions, while for hilly regions, the calculation method has a higher impact on the L factor. The linear regression (Fig. 2 [III], Table 2) carried out for the five CA flow-routing algorithms shows that the correlation coefficient of the L factor between all flow-routing algorithms increases as horizontal resolution decreases, except where DEMON is involved. This means that with decreasing DEM resolution, the choice of flow-routing algorithm becomes less important. They tend to give more similar results for DEMs with larger cell size. DEMON however, gives L factor results that have a higher deviation from the other algorithms regardless of DEM resolution. The spatial comparison (Fig. 2 [IV], Fig. 6) between the single flow-routing algorithms shows, that CA_Rho8 obtains higher L factors than CA_D8 in areas of steeper slopes. As soon as the terrain characteristics and slopes are not depicted well by the DEM, this effect lessens. From the spatial comparison (Fig. 2 [IV], Fig. 7) between the single and multiple flowrouting algorithms it can be deduced that the multiple flow-routing algorithm DEMON yields higher L factors for steep slopes — if these slopes are depicted on the DEM. Thus, the difference of the L factor using single and multiple flow-algorithms is higher on the upslope than flat areas. However, the mean L factor using the five flow-routing algorithms is nearly the same and thus, in practical terms, algorithm choice within CA impacts the statistical parameters not as extensive as DEM cell size or the usage of GC. All tests showed, that DEMs which are not able to properly depict the terrain, should not be used for L factor calculations as high uncertainties are introduced into the calculations. The most suitable calculation method is LGC_D8 for gently rolling landscapes as GC differentiates the zones of erosion and deposition. Application of standard implemented L factor calculation methods in GIS software should be taken with care when applied for erosion studies on the river basin level with coarse DEMs. Acknowledgement This project was funded by the EU Seventh Framework Programme (No. 243857). References Bolstad, P.V., Stowe, T., 1994. An evaluation of DEM accuracy: elevation, slope, and aspect. Photogramm. Eng. Remote. Sens. 60, 1327–1332. Chang, K.T., Tsai, B.W., 1991. The effect of DEM resolution on slope and aspect mapping. Cartogr. Geogr. Inf. Syst. 18, 69–77. Costa-Cabral, M., Burges, S.J., 1994. Digital Elevation Model Networks (DEMON): a model of flow over hillslopes for computation of contributing and dispersal areas. Water Resour. Res. 30 (6), 1681–1692.

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Cowen, J., 1993. A Proposed Method for Calculating the LS Factor for Use with the USLE in a Grid-Based Environment: Proceedings of the Thirteenth Annual ESRI User Conference, pp. 65–74. Desmet, P.J.J., Govers, G., 1996a. A GIS procedure for automatically calculating the USLE LS factor on topographically complex landscape units. J. Soil Water Conserv. 51, 427–433. Desmet, P.J.J., Govers, G., 1996b. Comparison of routing algorithms for digital elevation models and their implications for predicting ephemeral gullies. Int. J. Geogr. Inf. Syst. 10 (3), 311–331. Environmental Systems Research Institute, 1987. ARC/INFO Users Guide. Environmental Systems Research Institute, Redlands, CA. Gallant, J.C., Wilson, J.P., 1996. Tapes-G: a grid-based terrain analysis program for the environmental science. Comput. Geosci. 22, 713–722. Gyasi-Agyei, Y., Willgoose, G., de Troch, F.P., 1995. Effects of vertical resolution and map scale of digital elevation models on geomorphological parameters used in hydrology. In: Kalma, J.D., Sivapalan, M. (Eds.), Scale Issues in Hydrological Modeling. Wiley, New York, pp. 121–140. Hickey, R., 2000. Slope angle and L solutions for GIS. Cartography 29 (1), 1–8. Hickey, R., Smith, A., Jankowski, P., 1994. Slope length calculations from a DEM within ARC/INFO GRID. Comput. Environ. Urban Syst. 18 (5), 365–380. Liu, H., Fohrer, N., Hörmann, G., Kiesel, J., 2009. Suitability of S factor algorithms for soil loss estimation at gently sloped landscapes. Catena 77 (3), 248–255. LVA, 2008. Land Survey Office Schleswig-Holstein, Kiel, 2008. ATKIS©-DGM2 — Grid Size 1 m × 1 m. McCool, D.K., Brown, L.C., Foster, G.R., Mutchler, C.K., Meyer, L.D., 1987. Revised slope steepness factor for the universal soil loss equation. Trans. ASAE 30, 1387–1396. Mitasova, H., Hofierka, J., Zlocha, M., Iverson, L.R., 1996. Modeling topographic potential for erosion and deposition using GIS. Int. J. Geogr. Inf. Syst. 10, 629–641. Moore, I.D., Wilson, J.P., 1992. Length-slope factors for the revised universal soil loss equation: simplified method of estimation. J Soil Water Conserv. 47 (5), 423–428. Moore, I.D., Grayson, R.B., Ladson, A.R., 1991. Digital terrain modeling: a review of hydrological, geomorphological and biological applications. Hydrol. Proc. 5, 3–30. Quinn, P., Beven, K., Chevallier, P., Planchon, O., 1991. The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models. Hydrol. Proc. 5, 59–79. Sasowski, K.C., Petersen, G.W., Evans, B.M., 1992. Accuracy of SPOT digital elevation model and derivatives: utility for Alaska's north slope. Photogramm. Eng. Remote. Sens. 58, 815–824. Thieken, A.H., Lucke, A., Diekkruger, B., Richter, O., 1999. Scaling input data by GIS for hydrological modeling. Hydrol. Proc. 13, 611–630. Thompson, J.A., Bell, J.C., Butler, C.A., 2001. Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling. Geoderma 100, 67–89. Wang, X., Yin, Z.Y., 1998. A comparison of drainage networks derived from digital elevation models at two scales. J. Hydrol. 210, 221–241. Wilson, J.P., Lam, C.S., Deng, Y.X., 2007. Comparison of the performance of flow-routing algorithms used in GIS-based hydrologic analysis. Hydrol. Proc. 21, 1026–1044. Winchell, M.F., Jackson, S.H., Wadley, A.M., Srinivasan, R., 2008. Extension and validation of a geographic information system-based method for calculating the Revised Universal Soil Loss Equation length-slope factor for erosion risk assessments in large watersheds. J. Soil Water Conserv. 63 (3), 105–111. Wischmeier, W.H., Smith, D.D., 1978. Predicting Rainfall Erosion Losses—A Guide to Conservation Planning. USDA Handb. 537. U.S. Government Printing Office, Washington, D.C. Wolock, D.M., Price, C.V., 1994. Effects of digital elevation model map scale and data resolution on a topography based watershed model. Water Resour. Res. 30, 3041–3052. Yin, Z.Y., Wang, X., 1999. A cross-scale comparison of drainage basin characteristics derived from digital elevation models. Earth Surf. Processes Landforms 24, 557–562. Yitayew, M., Pokrzywka, S.J., Renard, K.G., 1999. Using GIS for facilitating erosion estimation. Appl. Eng. Agric. 15 (4), 295–301. Zhang, W., Montgomery, D.R., 1994. Digital elevation model grid size, landscape representation, and hydrological simulations. Water Resour. Res. 30, 1019–1028. Zhou, Q., Liu, X., 2002. Error assessment of grid-based flowrouting algorithms used in hydrological models. Int. J. Geogr. Inf. Sci. 16 (8), 819–842.