**3. Results and Discussion**

#### **3.1. Performance of LiDAR data with D∞ and D8 Flow Direction Models**

Logistic regression models and statistical tests are given in Table 2. The topographic wetness index, length-slope, and plan curvature values were all highly significant in the models. The discretized output of the LiDAR D8 (Figure 3) and D∞ (Figure 4) models indicated a high correspondence between the eroded waterway boundaries and the black shaded areas (i.e., areas with probability of concentrated flow erosion > 0.5 and ≤ 1.0). The average of the com‐ bined type 1 and type 2 error rates across the five fields was 8% for D8 and 9% for D∞ (Table 2). This data can be interpreted using Table 1 provided in the methods section.

The LiDAR predictions with D8 and D∞ were excellent (Figure 3 and 4). Interestingly, the D8 approach differentiated between the eroded and non eroded areas in the lower central portion of Field A (Figure 3). In this area, an eroded feature that appears to be an island can be observed by examining the polygon boundaries. The water flowing across this island area disappeared underground and reemerged in the waterway below. The terrain model‐ ing predicted high upslope contributing area and therefore high topographic wetness and length-slope index indices below this island area; however, plan curvature values did not have large negative values (indicating concavity) because there was no erosion area as deter‐ mined during field observations with the NRCS conservationist. The D8 model differentiat‐ ed this area because most of the prediction weight from this model came from plan curvature values. This was apparent from the Wald Chi Square statistic which was much greater for the D8 (180) than D∞ (71) analyses.


**Table 2.** Logistic regression model parameters and tests for the LiDAR data analyses for the TauDEM D8 and D∞ flow direction models.

#### **3.2. Impact of data cleaning**

We considered what would have been the result if we had not contoured and rasterized the data. The average combined type-1 and type-2 error rate for D8 and D∞ was 8% for the smoothed data (Table 2) and 12% for the unsmoothed data. The logistic regression analyses did not differentiate as clearly eroded and non-eroded areas when the data were not smoothed. This is very apparent when comparing the unsmoothed analyses of Fields D and E (Figure 5) with smoothed analyses (Figure 3).

**Figure 3.** Discretized erosion probability maps derived from LiDAR measurements overlain by the boundaries of the observed concentrated flow pathways. Terrain attributes were calculated with TauDEM using the D 8 flow direction

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algorithm.

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areas with probability of concentrated flow erosion > 0.5 and ≤ 1.0). The average of the com‐ bined type 1 and type 2 error rates across the five fields was 8% for D8 and 9% for D∞ (Table

The LiDAR predictions with D8 and D∞ were excellent (Figure 3 and 4). Interestingly, the D8 approach differentiated between the eroded and non eroded areas in the lower central portion of Field A (Figure 3). In this area, an eroded feature that appears to be an island can be observed by examining the polygon boundaries. The water flowing across this island area disappeared underground and reemerged in the waterway below. The terrain model‐ ing predicted high upslope contributing area and therefore high topographic wetness and length-slope index indices below this island area; however, plan curvature values did not have large negative values (indicating concavity) because there was no erosion area as deter‐ mined during field observations with the NRCS conservationist. The D8 model differentiat‐ ed this area because most of the prediction weight from this model came from plan curvature values. This was apparent from the Wald Chi Square statistic which was much

2). This data can be interpreted using Table 1 provided in the methods section.

**Variable**

D8 Intercept -3.58 68 \*\*

D∞ Intercept -5.97 111 \*\*

**Table 2.** Logistic regression model parameters and tests for the LiDAR data analyses for the TauDEM D8 and D∞ flow

We considered what would have been the result if we had not contoured and rasterized the data. The average combined type-1 and type-2 error rate for D8 and D∞ was 8% for the smoothed data (Table 2) and 12% for the unsmoothed data. The logistic regression analyses did not differentiate as clearly eroded and non-eroded areas when the data were not smoothed. This is very apparent when comparing the unsmoothed analyses of Fields D and

Topographic Wetness Index 0.303 24 \*\* Length-Slope 0.758 45 \*\* Plan Curvature -6.81 180 \*\*

Topographic Wetness Index 0.573 59 \*\* Length-Slope 1.06 75 \*\* Plan Curvature -4.75 71 \*\*

**Parameter Estimate**

**Wald Chi Square**

greater for the D8 (180) than D∞ (71) analyses.

**Flow Direction Method**

direction models.

52 Research on Soil Erosion Soil Erosion

**3.2. Impact of data cleaning**

E (Figure 5) with smoothed analyses (Figure 3).

**Figure 3.** Discretized erosion probability maps derived from LiDAR measurements overlain by the boundaries of the observed concentrated flow pathways. Terrain attributes were calculated with TauDEM using the D 8 flow direction algorithm.

**Flow Direction Algorithm D8 FD8**

**Field Actual Field Status NE E Ne E** A NE 81 16 80 17

B NE 83 11 81 13

C NE 79 18 79 18

D NE 78 10 76 13

F NE 75 17 73 18

**Table 3.** Confusion table for the TauDEM D8 and D∞ flow direction models. The values are given in percentages of the total observations from each field. This table can be interpreted using the guide presented in Table 1.

**Figure 5.** Discretized erosion probability maps derived from unsmoothed LiDAR data overlain by field boundaries. Ter‐

rain attributes were calculated with TauDEM using the D ∞ flow direction algorithm.

**Predicted**

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E 1 3 1 3

Terrain Analysis for Locating Erosion Channels: Assessing LiDAR Data and Flow Direction Algorithm

E 1 5 2 5

E 0 2 0 2

E 4 7 4 8

E 3 6 3 6

**Figure 4.** Discretized erosion probability maps derived from LiDAR measurements overlain by the boundaries of the observed concentrated flow pathways. Terrain attributes were calculated with TauDEM using the D ∞ flow direction algorithm.

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**Table 3.** Confusion table for the TauDEM D8 and D∞ flow direction models. The values are given in percentages of the total observations from each field. This table can be interpreted using the guide presented in Table 1.

**Figure 5.** Discretized erosion probability maps derived from unsmoothed LiDAR data overlain by field boundaries. Ter‐ rain attributes were calculated with TauDEM using the D ∞ flow direction algorithm.

**Figure 4.** Discretized erosion probability maps derived from LiDAR measurements overlain by the boundaries of the observed concentrated flow pathways. Terrain attributes were calculated with TauDEM using the D ∞ flow direction

algorithm.

54 Research on Soil Erosion Soil Erosion

One problem with LiDAR data is that it contains systematic artifacts resulting from differen‐ tial plant stubble heights in the direction perpendicular to crop rows associated with the di‐ rection of movement of farm machinery. With terrain modeling, they can create artificial flow lines along pathways of farm equipment. These lines are apparent in the unsmoothed but not smoothed LiDAR slope data (Figure 6). Unfortunately, the method of smoothing presented in this chapter introduced new artifacts along the contours because the procedure involved

**3.4. Impact of Flow Direction Algorithm**

similar to the one used in this study.

**Flow Direction Method**

models.

The FD8 and DEMON methods were not used with the LiDAR data because TAPES no lon‐ ger works with the latest version of ArcGIS (i.e., version 10.0). The regression parameters and Wald Chi Square test for the RTK (Table 4) and USGS (Table 5) analyses could be com‐ pared with those for the LiDAR models (Table 2). All of the parameters were statistically significant except for plan curvature in the USGS FD8 analyses (Table 5) which was consis‐ tent with [6]. The concentrated flow prediction models can be tested in other areas across the country with the same data source (RTK, LiDAR, and USGS) and flow direction (D8, D∞, FD8, and DEMON). The users should note that use of these may only be valid when similar smoothing techniques and DEM resolutions are used. In our case, all of our analyses were made with 4 by 4-m rasters. Grid scale is a very important factor to consider because at a small scale, there may be no relationship between land forms and curvature values; howev‐ er, at a large increment, landscapes could have a profoundly large impact on an analysis

Terrain Analysis for Locating Erosion Channels: Assessing LiDAR Data and Flow Direction Algorithm

**Variable**

D8 Intercept -3.14 57 \*\*

D∞ Intercept -6.17 119 \*\*

FD8 Intercept -9.88 161 \*\*

DEMON Intercept -5.94 79 \*\*

**Table 4.** Logistic regression parameters for the RTK dataset using the D8, D∞, FD8, and DEMON flow direction

Topographic Wetness Index 0.251 18 \*\* Length-Slope 0.681 42 \*\* Plan Curvature -7.979 188 \*\*

Topographic Wetness Index 0.603 65 \*\* Length-Slope 1.01 77 \*\* Plan Curvature -5.73 82 \*\*

Topographic Wetness Index 0.882 88 \*\* Length-Slope 1.88 137 \*\* Plan Curvature -5.54 39 \*\*

Topographic Wetness Index 8.510 34 \*\* Length-Slope 1.06 70 \*\* Plan Curvature -10.1 161 \*\*

**Parameter Estimate**

**Wald Chi Square**

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This smoothing is very computationally resource intensive, and potentially problematic for professional conservation planners. It may be necessary for GIS experts to smooth the Li‐ DAR data during preprocessing and make the analyses available to planners. More compu‐ tationally efficient smoothing techniques should be considered that minimize new artifacts.

**Figure 6.** Comparison of unsmoothed and smoothed LiDAR slope data for Field D.

### **3.3. Comparison of LiDAR with RTK and USGS**

The type-1 and -2 average misclassification errors for TauDEM D8 and D∞ output for Li‐ DAR (8%) were similar in size as errors for the RTK (8%) dataset and lower than those for the USGS data (12%). The predictions were not very different for any of the datasets as shown in Figure 7. In many areas throughout the United States, LiDAR is being purchased for various applications (e.g., agriculture, soil mapping, transportation, land use planning). In those situations, it would be advantageous to use the LiDAR data for identifying eroded waterways. In areas where LiDAR is not available, USGS 10-m grids may be adequate for conservation planning [6].

#### **3.4. Impact of Flow Direction Algorithm**

One problem with LiDAR data is that it contains systematic artifacts resulting from differen‐ tial plant stubble heights in the direction perpendicular to crop rows associated with the di‐ rection of movement of farm machinery. With terrain modeling, they can create artificial flow lines along pathways of farm equipment. These lines are apparent in the unsmoothed but not smoothed LiDAR slope data (Figure 6). Unfortunately, the method of smoothing presented in this chapter introduced new artifacts along the contours because the procedure

This smoothing is very computationally resource intensive, and potentially problematic for professional conservation planners. It may be necessary for GIS experts to smooth the Li‐ DAR data during preprocessing and make the analyses available to planners. More compu‐ tationally efficient smoothing techniques should be considered that minimize new artifacts.

The type-1 and -2 average misclassification errors for TauDEM D8 and D∞ output for Li‐ DAR (8%) were similar in size as errors for the RTK (8%) dataset and lower than those for the USGS data (12%). The predictions were not very different for any of the datasets as shown in Figure 7. In many areas throughout the United States, LiDAR is being purchased for various applications (e.g., agriculture, soil mapping, transportation, land use planning). In those situations, it would be advantageous to use the LiDAR data for identifying eroded waterways. In areas where LiDAR is not available, USGS 10-m grids may be adequate for

involved

56 Research on Soil Erosion Soil Erosion

**1.** calculating contours from DEMs and

**Figure 6.** Comparison of unsmoothed and smoothed LiDAR slope data for Field D.

**3.3. Comparison of LiDAR with RTK and USGS**

conservation planning [6].

**2.** rasterizing the contours.

The FD8 and DEMON methods were not used with the LiDAR data because TAPES no lon‐ ger works with the latest version of ArcGIS (i.e., version 10.0). The regression parameters and Wald Chi Square test for the RTK (Table 4) and USGS (Table 5) analyses could be com‐ pared with those for the LiDAR models (Table 2). All of the parameters were statistically significant except for plan curvature in the USGS FD8 analyses (Table 5) which was consis‐ tent with [6]. The concentrated flow prediction models can be tested in other areas across the country with the same data source (RTK, LiDAR, and USGS) and flow direction (D8, D∞, FD8, and DEMON). The users should note that use of these may only be valid when similar smoothing techniques and DEM resolutions are used. In our case, all of our analyses were made with 4 by 4-m rasters. Grid scale is a very important factor to consider because at a small scale, there may be no relationship between land forms and curvature values; howev‐ er, at a large increment, landscapes could have a profoundly large impact on an analysis similar to the one used in this study.


**Table 4.** Logistic regression parameters for the RTK dataset using the D8, D∞, FD8, and DEMON flow direction models.

The average Type 1 and Type 2 error rates for the RTK dataset were ranked in the follow order (from lowest to highest): FD8 (6%), DEMON (7%), D8 (9%), and D∞(11%). The differ‐ ences were smaller for the USGS dataset but procedures were ranked in a similar order: FD8 (10%), DEMON (10%), D∞(11%), D8 (12%). The map analysis for the RTK data (Figure 8) demonstrates that differences between methods were small with the FD8 model showing

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**Figure 8.** Discretized erosion probability maps for the logistic regression analysis of the RTK dataset comparing the

The findings of this study indicate that LiDAR data can be used to clearly identify eroded features in agricultural landscapes with a level of accuracy that is similar to RTK GPS and better than USGS DEMs. It is critical that LiDAR data are smoothed prior to modeling ero‐

least noise in the southern part of the field.

D8, D∞, FD8, and DEMON flow direction algorithm.

**4. Conclusion and Recommendations**

**Figure 7.** Discretized erosion probability maps for the logistic regression analysis of the LiDAR, RTK, and USGS datasets using the D∞ flow direction algorithm.


**Table 5.** Logistic regression parameters for the USGS dataset using the D8, D∞, FD8, and DEMON flow direction models.

The average Type 1 and Type 2 error rates for the RTK dataset were ranked in the follow order (from lowest to highest): FD8 (6%), DEMON (7%), D8 (9%), and D∞(11%). The differ‐ ences were smaller for the USGS dataset but procedures were ranked in a similar order: FD8 (10%), DEMON (10%), D∞(11%), D8 (12%). The map analysis for the RTK data (Figure 8) demonstrates that differences between methods were small with the FD8 model showing least noise in the southern part of the field.

**Figure 8.** Discretized erosion probability maps for the logistic regression analysis of the RTK dataset comparing the D8, D∞, FD8, and DEMON flow direction algorithm.
