**1. Introduction**

optimal solutions visualises much better the character and behaviour of the designed system in reactions to modifications of the input conditions and requirements and thus enables to

A great advantage of the model lies in the general formulation of its components – partial models of conservation measures at individual sites of the experimental locality, water‐ course and reservoir. This should enable its problem-free application for optimization de‐

Brno University of Technology, Faculty of Civil Engineering, Department of Landscape Wa‐

[1] Benedini, M. (1988). Developments and possibilities of optimisation models. *Agric.*

[2] Dumbrovský, M., et al. (2003). Optimisation of the system of soil and water conserva‐ tion for runoff minimizing in certain watershed in the process of land consolidation

[4] Korsuň, S., et al. (2002). Creating and verification of the model for optimisation of soil and water conservation (in Czech). *Final research report, A01-NAZV-QC1292*,

[5] Kos, Z. (1992). Water management systems and their mathematical models during

[6] Major, D. C., Lenton, R. L., et al. (1979). Applied water resource systems planning. .

[7] Onta, P. R., Gupta, A. D., & Harboe, R. (1991). Multistep planning model for conjunc‐ tive use of surface and groundwater resources. *Jour. Water Res. Plan. Manag.*, 6,

[8] Patera, A., Váška, J., Zezulák, J., Eliáš, V., Korsuň, S., et al. (2002). Floods: prognosis,

water streams and landscape (in Czech). *ČVUT / ČVVS*, Praha.

[3] Charamza, P., et al. (1993). Modelling system GAMS (in Czech). MFF UK, Praha.

(in Czech). *Final research report, NAZV-QC1292*, VÚMOP, Praha.

climate changes (in Czech). *Vod. Hosp.*, 7, 211-216.

Prentice- Hall Inter., Inc., London.

improve significantly the process of making decisions about the design final shape.

sign of integrated territory protection under any conditions and at any site

and Svatopluk Korsuň

\*Address all correspondence to: dumbrovsky.m@fce.vutbr.cz

**Author details**

44 Research on Soil Erosion Soil Erosion

**References**

Miroslav Dumbrovsky\*

ter Management, Czech Republic

*Water Manag.*, 13, 329-358.

FAST VUT, Brno.

662-678.

Terrain analysis can be used to locate concentrated flow erosion (e.g., ephemeral gully ero‐ sion) across landscapes. For example, studies have found that ephemeral gullies were likely to occur when field specific thresholds were exceeded for the following terrain attributes: the product of upslope area, slope, and plan curvatures [1]; topographic wetness index, up‐ slope area, and slope [2]; and the topographic wetness index and the product of the upslope area and slope [3]. Another study used a cartographic classification and threshold procedure for erosion channel identification [4].

An alternative approach utilized logistic regression and artificial neural network procedures to predict where erosion channels would appear in agricultural fields based on digital ter‐ rain attributes [5]. With leave-one-field-out validation, it was determined that the more sim‐ ple logistic regression was more appropriate because it performed as well as the non-linear neural network procedure. In a follow up study, erosion channels predicted from terrain at‐ tributes derived from 10-m US Geological Survey (USGS) digital elevation models (DEMs) were compared to those derived from DEMs created with survey-grade real-time kinematic (RTK) Global Positioning System (GPS) data [6]. The USGS models identified most eroded features but the RTK analyses delineated them more clearly. The authors concluded that the USGS predictions were adequate for many agricultural applications because creating DEMs with RTK was relatively costly while USGS data was freely available on the Internet for most of the United States. A graphical representation illustrates how the logistic regression analysis [5,6] can be fit (step 1) and then applied (step 2) in Figure 1.

© 2012 Pike et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Pike et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In another study, the model from reference [5] predicted where eroded waterways would occur 223 km away in a different physiograpic region of Kentucky where there were marked textural and parent material differences between the soils [7]. The locations of the Outer Bluegrass [6,7] and Western Coal Fields studies are shown in Figure 2.

This usually involves setting up one RTK receiver as a base station, to broadcast via radio corrections to a mobile receiver, which calculates elevation on-the-fly. Elevation data can al‐ so be obtained with light detecting and ranging (LiDAR) systems mounted at the bottom of airplanes with a pulsing laser scanning rapidly from side to side. Detectors determine the time required for laser pulses to bounce back in order to calculate the distance between the aircraft and the ground surface. With simultaneous in-flight RTK GPS measurements, esti‐ mates of ground elevation are obtained at a high spatial intensity (e.g., several points per square meter). In one study [8], RMSEs for LIDAR were determined to be 33.3 cm in short grass. The USGS National Elevation Dataset (NED) includes Level-2 DEMs for most of the United States, which in many cases were reinterpolated from USGS topographic contours. These contour maps were originally created by the USGS using stereo orthophotogramme‐ try. Level-2 DEMs have an accuracy of one-half the contour width (e.g., the contour width

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

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47

Of the three elevation datasources discussed, RTK GPS is one of the most accurate methods for creating ground surveys. Unfortunately, these systems are relatively expensive and ob‐ taining ground measurements and data processing may be labor intensive. USGS DEMs are an attractive option because they are free; however, they do not identify erosion pathways as clearly as the RTK data [6]. Elevation data obtained with LiDAR is relatively inexpensive on a per area basis and are currently being obtained by various government agencies not necessarily associated with agriculture, but urban planning, transportation, and geophysics applications. LiDAR has a great potential to aid in the identification of concentrated flow

Terrain attributes (e.g., length–slope, topographic wetness index) require estimates of the upslope contributing area for each cell in the DEM. This necessitates the calculation of single or multiple flow direction for each cell in the DEM. The most common single direction flow model is the deterministic eight-neighbor (D8) procedure. Multiple direction flow models include fractional deterministic eight-neighbor (FD8), digital elevation model networks (DE‐ MON), and deterministic infinity (D∞). There are a number of software programs that can calculate terrain attributes, including ArcGIS, Grid-Based Terrain Analysis Programs for the Environmental Sciences (TAPES-G), and Terrain Analysis Using Digital Elevation Models (TauDEM). ArcGIS, TauDEM, and TAPES-G predict D8 single direction flow. The TAPES-G program can also estimate multidirectional flow with FD8 and DEMON while TauDEM pro‐

O'Callaghan and Mark [11] developed the D8 model that routs flow from each cell to one of its single eight neighbors in the cardinal or diagonal direction with the steepest grade. How‐ ever, the D8 method does not accurately model divergent flow in ridge areas and it produ‐ ces unrealistic parallel flow lines [12]. The FD8 multidirection method [13] allows flow to be routed to more than one of its eight neighbors in an amount proportional to the slope gradi‐ ent between the center cell and the adjacent eight neighbors. Once the upslope contributing

was for the studies in [5,6] was 304 cm).

pathways [9,10].

**1.2. Flow Direction Algorithm**

gram can estimate flow with D∞.

#### **1.1. RTK GPS, LiDAR, and USGS DEM Accuracy**

The performance of terrain analysis applications depends on the source and quality of the elevation information. Very accurate elevation measurements can be obtained with surveygrade RTK GPS (e.g., horizontal rmse < 2.2 cm).

**Figure 1.** Description of the basic two-step logistic regression analysis procedure used in references [5,6]. The first step involves fitting a model with field observations of soil erosion as a function of terrain attributes. The second step in‐ volves applying the model. In this example, the model was applied to the same field as it was fit. However, references [5,6] used a leave one-field out validation and fit the model to four fields and applied it in a fifth. See equation 3 in methods section for a mathematical definition of the Length-Slope terrain attribute.

**Figure 2.** Locations of the Pike et al. (2009 and 2010) [5,6] and Luck et al. (2010) [7] studies. The Kentucky Physio‐ graphic regions are labelled and colored.

This usually involves setting up one RTK receiver as a base station, to broadcast via radio corrections to a mobile receiver, which calculates elevation on-the-fly. Elevation data can al‐ so be obtained with light detecting and ranging (LiDAR) systems mounted at the bottom of airplanes with a pulsing laser scanning rapidly from side to side. Detectors determine the time required for laser pulses to bounce back in order to calculate the distance between the aircraft and the ground surface. With simultaneous in-flight RTK GPS measurements, esti‐ mates of ground elevation are obtained at a high spatial intensity (e.g., several points per square meter). In one study [8], RMSEs for LIDAR were determined to be 33.3 cm in short grass. The USGS National Elevation Dataset (NED) includes Level-2 DEMs for most of the United States, which in many cases were reinterpolated from USGS topographic contours. These contour maps were originally created by the USGS using stereo orthophotogramme‐ try. Level-2 DEMs have an accuracy of one-half the contour width (e.g., the contour width was for the studies in [5,6] was 304 cm).

Of the three elevation datasources discussed, RTK GPS is one of the most accurate methods for creating ground surveys. Unfortunately, these systems are relatively expensive and ob‐ taining ground measurements and data processing may be labor intensive. USGS DEMs are an attractive option because they are free; however, they do not identify erosion pathways as clearly as the RTK data [6]. Elevation data obtained with LiDAR is relatively inexpensive on a per area basis and are currently being obtained by various government agencies not necessarily associated with agriculture, but urban planning, transportation, and geophysics applications. LiDAR has a great potential to aid in the identification of concentrated flow pathways [9,10].

#### **1.2. Flow Direction Algorithm**

In another study, the model from reference [5] predicted where eroded waterways would occur 223 km away in a different physiograpic region of Kentucky where there were marked textural and parent material differences between the soils [7]. The locations of the Outer

The performance of terrain analysis applications depends on the source and quality of the elevation information. Very accurate elevation measurements can be obtained with survey-

**Figure 1.** Description of the basic two-step logistic regression analysis procedure used in references [5,6]. The first step involves fitting a model with field observations of soil erosion as a function of terrain attributes. The second step in‐ volves applying the model. In this example, the model was applied to the same field as it was fit. However, references [5,6] used a leave one-field out validation and fit the model to four fields and applied it in a fifth. See equation 3 in

**Figure 2.** Locations of the Pike et al. (2009 and 2010) [5,6] and Luck et al. (2010) [7] studies. The Kentucky Physio‐

methods section for a mathematical definition of the Length-Slope terrain attribute.

graphic regions are labelled and colored.

Bluegrass [6,7] and Western Coal Fields studies are shown in Figure 2.

**1.1. RTK GPS, LiDAR, and USGS DEM Accuracy**

46 Research on Soil Erosion Soil Erosion

grade RTK GPS (e.g., horizontal rmse < 2.2 cm).

Terrain attributes (e.g., length–slope, topographic wetness index) require estimates of the upslope contributing area for each cell in the DEM. This necessitates the calculation of single or multiple flow direction for each cell in the DEM. The most common single direction flow model is the deterministic eight-neighbor (D8) procedure. Multiple direction flow models include fractional deterministic eight-neighbor (FD8), digital elevation model networks (DE‐ MON), and deterministic infinity (D∞). There are a number of software programs that can calculate terrain attributes, including ArcGIS, Grid-Based Terrain Analysis Programs for the Environmental Sciences (TAPES-G), and Terrain Analysis Using Digital Elevation Models (TauDEM). ArcGIS, TauDEM, and TAPES-G predict D8 single direction flow. The TAPES-G program can also estimate multidirectional flow with FD8 and DEMON while TauDEM pro‐ gram can estimate flow with D∞.

O'Callaghan and Mark [11] developed the D8 model that routs flow from each cell to one of its single eight neighbors in the cardinal or diagonal direction with the steepest grade. How‐ ever, the D8 method does not accurately model divergent flow in ridge areas and it produ‐ ces unrealistic parallel flow lines [12]. The FD8 multidirection method [13] allows flow to be routed to more than one of its eight neighbors in an amount proportional to the slope gradi‐ ent between the center cell and the adjacent eight neighbors. Once the upslope contributing area for each cell exceeds a threshold (i.e., maximum cross grading area), the FD8 procedure switches to D8 flow, allowing the modeling of both divergent and convergent flow [12]. Lea [14] developed an aspect driven kinematic routing algorithm that was no longer restricted to the eight nearest neighbors (i.e., cardinal and diagonal directions). This algorithm inspired both the D∞ and DEMON methods. The DEMON stream tube method developed by Costa-Cabral and Burges [15] is computationally intensive and involves routing flow downstream along tubes that expand and contract in a way where the tubes do not necessarily coincide with the cell boundaries [12]. The D∞ algorithm first calculates flow direction from the infin‐ ite set of possible flow directions around each cell, not just in the 8 cardinal directions.

**2. Materials and Methods**

**2.1. Field observations**

sented in this chapter difficult or impossible to interpret.

CRP program if they did not already have waterways installed.

**2.2. Acquisition of Elevation Data, DEM Creation, and Terrain Analysis**

This study was conducted in five fields in Shelby County located in the Outer Bluegrass physiographic region of Kentucky. Field A (38°17´ N, 85°9´ W), B (38°18´ N, 85°11´ W), C (38°20´ N, 85°12´ W), D (38°20´ N, 85°11´ W), and Field E (38°20´ N, 85°14´ W), were 23, 36, 11, 57, and 33 ha in size, respectively. The fields had been in a no-till, corn (Zea mays L.), wheat (Triticum aestivum L.), and double-crop soybean [Glycine max (L.) Merr.] or cornwheat rotation for more than 20 yr. Soils in this region developed primarily from limestone residuum overlain with pedisediment from limestone weathered materials and loess [22].

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One of the co-owners of the Worth and Dee Ellis Farms was trained by the NRCS to identify eroded zones from concentrated water flow. The farmer delineated and mapped the eroded ephemeral gullies in the five study fields using a DGPS system. Subsequently, the farmer in‐ stalled grassed waterways in these areas but did not reshape them as is typically the case when installing these conservation structures. This is an important distinction because re‐ shaping these locations would have changed the terrain attributes, making the analyses pre‐

Because these field observations were conducted by the farmer, we asked the NRCS district conservationist to validate the erosion delineations in the field. The conservationist visited the fields in 2008 and examined 42% of the eroded channels delineated by the farmer in the five study fields. He determined that all the channels would have been eligible for cost sup‐ port for grassed waterways through the continuous USDA Conservation Reserve Program

Survey grade RTK GPS equipment was used to collect elevation data from Field D in 2000 [23], Fields E and B in 2004 [24], and in Fields A and C in 2007 [5]. Dual frequency Trimble AgGPS 214 (base station) and Trimble 5800 (rover) RTK receivers were used to create sur‐ veys in Fields A, B, C, and E. The survey for Field D was created with two single-frequency Trimble 4600 receivers and elevation was determined during post processing. The surveys were created at varying intensities with elevation measurements spaced approximately ev‐ ery 3 (Field D) and 4 m (Fields A, B, C, and E) along the direction of travel during the sur‐ vey. There were 7.5 (Field D) and 12 m (Fields A, B, C, and E) between survey passes. According to the Trimble data specifications, vertical errors for all receivers were expected to be <2.2 cm because the baselines were <1200m [25,26]. The LiDAR survey was created (courtesy of Photo Science) in November of 2009 after harvest with soybean residue and stubble on the ground. The airplane height above ground was 1.219 km and speed was 185 km hr-1. The estimated horizontal and vertical accuracies were 16 and 11 cm, respectively. The average elevation point density was 2.82 points m-2. PhotoScience converted the raw Li‐ DAR data into a triangulated irregular network (TIN). Then they converted the TIN into a 1 m raster file using natural neighbor interpolation. After the 1-m LiDAR DEM was delivered

The terrain attributes in references [5-7] were calculated with TAPES-G utilizing the FD8 method. TAPES-G still exists but it is no longer being supported and updated by the devel‐ opers. The Windows installation only works on legacy versions of ArcGIS. The preferred ap‐ proach for terrain analysis today has become TauDEM with the D∞ flow direction algorithm.

#### **1.3. Concentrated Flow Erosion, Grassed Waterways and The Environment**

Agriculture contributes 80% of the excessive phosphorus (P) flowing to the Gulf of Mexico from the Mississippi River Basin. Among the states contributing to this environmental im‐ pact, Kentucky is the sixth largest contributor of nitrogen and phosphorus to the Mississippi River Basin [16]. Sediment is the leading cause of impairment of Kentucky's rivers and streams, impacting over 4,329 linear km with agriculture being the primary contributing source [17]. The problem of sedimentation, often underestimated, is enormous. It not only adversely impacts aquatic life [18] and impaires ecological and economic functioning of drainage systems, wetlands, streams, and rivers but also increases the risk of flooding and the need for water treatment. Properly constructed grassed waterways (NRCS Code 412), with appropriately sized vegetative filters on either side reduce considerable runoff, nu‐ trient, and sediment delivery to surface waters. Specifically, they reduce ephemeral gully erosion, which is a substantial but often overlooked problem that accounts for about 40% of all erosion in agricultural fields [19]. In one study, the installation of grassed waterways led to reductions of 39 and 82% in runoff and sediment, respectively [20]. In another study, grassed waterways reduced dissolved reactive phosphorus losses by factors ranging be‐ tween 4 to 7 and particulate phosphorus by factors ranging between 4 and 10 [21]. Because grassed waterways are so effective, the USDA Conservation Reserve Program (CRP) and Environmental Quality Incentives Program (EQIP) provide funding for this and other con‐ servation practices.

#### **1.4. Research Objective**

The objective of this study was to compare how predictions of concentrated flow erosion performed with LiDAR, survey grade RTK GPS, and 10-m USGS DEMs, and using the D8, FD8, DEMON, and D∞ flow direction models.
