Using digital photogrammetry to monitor soil erosion under conditions of simulated rainfall and wind.
Abstract: We investigated a method to measure sheet erosion by characterising the soil erosion of an upland field in a dryland environment. Digital photogrammetry was used to measure the erosion rates of soil surfaces packed to different densities under simulated rainfall or wind conditions. The photogrammetry system consisted of 2 digital cameras, a rainfall simulator, a wind tunnel, and a computer program for 3-dimensional algorithm analysis. First, we assessed the accuracy of our method by comparing conventionally measured data to photogrammetric data under conditions of either no rainfall or no wind application. Two statistical parameters were used to evaluate the soil surface evolution: the mean absolute error (MAE) and the mean relative error (MRE). Their values were 0.21 mm and 15.8%, respectively. We then assessed the precision of our system under simulated rainfall conditions using 3 different dry bulk densities for the packed saturated soil surface. At densities of 0.91, 0.98, and 1.09 g/[cm.sup.3], the MAE (MRE) values were 2.21 mm (392.5%), 1.07 mm (126.4%), and 0.59 mm (57.6%), respectively. It was possible to monitor and evaluate both the amount of eroded soil and the erosion mechanism in a specific area. Moreover, this system could be applied to measuring wind erosion with an MAE accuracy as high as 0.21 mm. The digital elevation models (DEMs) allowed for detailed analyses of soil surface evolution, and it was also possible to monitor sheet erosion with high spatial and temporal resolutions.

Additional keywords: soil erosion, photogrammetry, precision, bulk density.
Article Type: Report
Subject: Photogrammetry (Methods)
Soil erosion (Observations)
Authors: Moritani, S.
Yamamoto, T.
Andry, H.
Inoue, M.
Kaneuchi, T.
Pub Date: 02/01/2010
Publication: Name: Australian Journal of Soil Research Publisher: CSIRO Publishing Audience: Academic Format: Magazine/Journal Subject: Agricultural industry; Earth sciences Copyright: COPYRIGHT 2010 CSIRO Publishing ISSN: 0004-9573
Issue: Date: Feb, 2010 Source Volume: 48 Source Issue: 1
Product: Product Code: 3811370 Photogrammetric & Geodetic Instr NAICS Code: 334516 Analytical Laboratory Instrument Manufacturing SIC Code: 7336 Commercial art and graphic design; 7389 Business services, not elsewhere classified
Geographic: Geographic Scope: Australia Geographic Code: 8AUST Australia
Accession Number: 222313805
Full Text: Introduction

Soil degradation resulting from accelerated water- and wind-induced erosion is a serious problem in drylands, and will remain so throughout this century. The detachment and transport of soil particles degrade the fertility of agricultural land and reduce its productivity. Soil erosion causes the siltation of ditches, and runoff material from eroding surfaces is a major constituent of non point-source pollutants that accumulate in surface water bodies. Many of the particles involved in soil erosion processes, such as raindrops, soil aggregates, and sediment, have characteristic dimensions on the millimeter scale (Huang 1998). The modeling and quantification of such processes require detailed measurements of the physical, chemical, and biological properties of soils (Soil Conservation Service 1976). However, these measurements are too slow, tedious, and expensive for routine or regular monitoring.

Several researchers have already used aerial photography to assess soil erosion. A precise form of this photography, photogrammetry, has the advantage of very efficiently and cost-effectively providing detailed information about a large area. Together with aerial photography, the use of remotely sensed data forms the basis for land use mapping and change detection (Pellikka et al. 2004). In particular, for inaccessible areas, photogrammetry is far superior to traditional ground surveys. The subsequent convergence in recent years of photogrammetry and digital imaging technology has led to an increase in the use of digital elevation models (DEMs) in modem studies involving the monitoring of landscape changes (Prosser and Aberneathy 1996; DeRose et al. 1998).

The areas measured experimentally in microtopographical studies of soil erosion range from 1 to ~20 [m.sup.2]. In general, the DEMs used for analysis have grid resolutions of 1-15 mm (Elliot et al. 1997; Darboux and Huang 2003). A variety of instruments and methods are used by soil scientists to acquire measurement coordinates, including mechanical point gauges (Elliot et al. 1997) that make contact with the soil surface, optoelectronic measurement devices such as laser scanners (Huang et al. 1988; Darboux and Huang 2003), and image processing techniques (Abd Elbasit et al. 2008). Point gauges have been widely replaced by laser scanners, because the former make contact with the soil and can thus disturb it or sink into it (Romkens et al. 1988). While laser scanners have proven their usefulness in many experiments, a photogrammetric system is more advanced, comparatively cheaper, and provides images and morphological properties simultaneously (Chandler et al. 2005; Hodge et al. 2009).

Automated digital photogrammetry allows DEMs to be generated with sufficient resolution for microtopographical analysis. Jeschke (1990) applied correlation matching to softcopy images taken by a Zeiss SMK 40 camera to analyze soil microtopography. Recent advances in digital image processing and camera calibration techniques make it possible to use the digitised images taken by consumer-grade analogue cameras to automate the generation of DEMs (Brasington and Smart 2003; Abd Elbasit et al. 2009). Some researchers, e.g. Chandler et al. (2002) and Lascelles et al. (2002), have calibrated consumer-grade cameras and employed the images taken with them to generate DEMs automatically on digital photogrammetric workstations, which are becoming increasingly accessible to non-photogrammetrists.

Analytical photogrammetry has often been used in geomorphological studies of gully and rill formation (Elliot et al. 1997; Pyle and Richards 1997; DeRose et al. 1998; Helming et al. 1998; Pellikka et al. 2004; Rieke-Zapp and Nearing 2005). In these previous studies, the DEM resolutions were generally produced from photographs taken under a no-rainfall condition, i.e. the photographs were taken just before and after the rainfall events (Rieke-Zapp and Nearing 2005). Moreover, studies reporting this method to monitor sheet erosion, which predominates in drylands, are relatively few. It is necessary to evaluate the reliability of the DEM produced using a camera during the rainfall event to quantify the sheet erosion at the laboratory scale before field scale application.

The purpose of this study was to generate DEMs with high spatial and temporal resolutions from soil surfaces that developed sheet erosion. Digital photogrammetry was used to measure the erosion rates and evolution of a sheet erosion network under laboratory simulated conditions.

Materials and methods

Overview of the photogrammetry system

In order to study in 3 dimensions the soil surface evolution that results from water erosion, a new automated photogrammetry system was developed by Tottori University's Arid Land Research Center (ALRC), in collaboration with Asia Air Survey Co. Ltd. Figure 1 shows a flow chart of this photogrammetry system (Moritani et al. 2006).

[FIGURE 1 OMITTED]

Two Nikon D2H digital cameras were focused on the centre of the target object, as shown in Fig. 2. A focus length of 50 mm was used. The CCD sensor had a matrix of 2464 x 1632 picture elements (pixels). The distance between 2 pixel centers, [[delta].sub.CCD], was 0.094 mm. The memory card used was capable of storing ~60 images of 7.9 MB, allowing the analysis to be performed on uncompressed tagged image file format (TIFF) images. A PC software program was used to analyse the pictures taken by the D2H cameras. The inner orientation factor was obtained from a calibration factor called the calibration field (CF), as shown in Fig. 3.

It is well known that even 2 cameras of the same type do not have exactly equal characteristics such as the shape of the lens and the spatial arrangement of the CCD and lens (Weng et al. 1992). This made inner orientation calibration necessary for each camera to obtain more accurate DEM data. As shown in Fig. 4, the camera calibration was performed using a 3-dimensional CF with 32 well-distributed control points, known with an accuracy of 0.2 mm. This CF was equipped with 20 square poles with 3 different lengths, and 12 points on the planar table (which was placed between the square poles by 3 horizontal lines). Pictures of the CF were taken by each camera from a fixed distance, H (camera pair to object), of approximately 3.0m. During this photography process, the camera position was shifted parallel with the CF board to capture 6 multiple images of the entire area of the image plane, including every corner of the image plane, where there were large amounts of radial distortion. The least-square of the bundle adjustment among these images was then used to determine the inner orientation parameters, lens focus length, principal point offsets, and radial distortion, as listed in Table 1 (Huang and Mitchell 1995; Rieke-Zapp et al. 2001; Abd Elbasit et al. 2008).

The gradient of the pair of pictures was adjusted to minimise the parallax, and then the relative orientation was determined with the resulting points fixed on the x-axis. The result of this process is called a rectified photograph. The relative orientation yielding the rectified images was determined by a complicated equation based on a geometric consideration of the coplanar condition (Fig. 3), in which the image points P and P' always lay on the epipolar lines l and l', respectively (Huang and Mitchell 1995; Heipke 1997). The rectification required that both image planes used the same coordinate system ([X.sub.3], [Y.sub.3]) and that the y-axes of P and P' were at the same position ([bar.P] and [bar.P']). This reduced the search space for P and P' from 2 dimensions to 1, and thus increased the speed and reliability of the matching (Jeong et al. 2004).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The 3-dimensional calculation consisted of 2 methods: point measurement and surface measurement. Point measurement was used for visual matching to acquire a limited number of DEMs, while surface measurement was used to automatically calculate an enormous number of dense DEMs such as for the contour line of a surface. In the point measurement, as illustrated in Fig. 5, the cursor (shown as a star) was first moved onto a reference pixel point selected in the left rectified picture. The corresponding cursor in the fight picture automatically followed along the y-axis to a position that matched that on the left. Then, the cursor in the fight picture was moved along the x-axis (epipolar line) to the same corresponding point. Three-dimensional data were calculated based on the absolute orientation from the [x.sub.1] [y.sub.1] and [x.sub.2] [Y.sub.2] coordinates of the image points (Fig. 3). In the case of surface measurement, a quadrangular analytical frame was placed in each of the rectified images. These frames were aligned as closely as possible to cover and represent the same image area to reduce the matching error. Finally, ~16 000 pixels (shown as circles) were calculated and automatically matched in a few seconds to acquire DEMs, based on a coarse-to-fine matching strategy using multi-resolution representations, with a Laplacian of Gaussian filter (Cruz et al. 1995; Kim et al. 1997).

Accuracy of the DEM

The accuracy of this inner orientation was examined using the known DEM values of the CF board. The positions of the 2 D2H cameras were oriented to the CF board to include the 32 ground control points (GCPs). The CF was photographed at 5 different positions, ranging from a distance H of 2.0 to 6.0 m, and with a base length B (between the cameras) of 1.0m. The point measurement process was used for the 3-dimensional measurements of the 32 points on the CF, and the precision of the system was determined by comparing the results after the inner orientation against those without calibration.

The accuracy of the photogrammetry system was also evaluated under a no-rainfall condition using a soil box with a width, length, and height of 0.30, 0.50, and 0.10m, respectively. Sandy soil was packed into the soil box and 20 nails were inserted into the soil surface to be used as "unknown" measurement points, with an 'x' mark made on the top of each nail. The measured values, Mp (mm), on the z-axis were obtained using the point gauge method similar to that described by Abd Elbasit et al. (2009), which consists of vertical pins, with wooden supporter, sitting on the nails put on the soil surface. A micrometer caliper was used to record the elevation of the soil surface by measuring the length of each pin with accuracy in the order of [+ or -] 0.01 mm (Model 19971, Shinwa Rules Co. Ltd).

[FIGURE 5 OMITTED]

Point measurement was used to determine the photogrammetric value [A.sub.p] (mm) on the z-axis, with 10 marks on the frame of the soil box used as the ground control points (GCPs). The object was then photographed from 11 different positions, with H values ranging from 2.4 to 4.7 m and B values ranging from 0.3 to 1.0 m. Then the simulated depth of the soil erosion was evaluated after removing 50 mg (36 mL) of the air-dried sandy soil from the soil surface. This process was repeated 16 times until ~800mL of soil was collected. The surface measurement process was used to calculate the DEM of the soil surface in each image. The average depth of the eroded soil, [A.sub.s] (mm), was calculated from the average value of the DEMs on the z-axis, while the value of [M.sub.s] (mm) was calculated based on the amount of collected soil (g), the bulk density (g/[cm.sup.3]), and the measured area ([cm.sup.2]).

Accuracy of the DEM under the rainfall and wind application

A water erosion experiment was conducted using the rainfall simulator at ALRC. Three soil bulk densities (0.91, 0.98, and 1.09 g/[cm.sup.3]) were prepared from soil taken from a paddy field in Tottori prefecture, Japan. The physicochemical characteristics of this soil are shown in Table 2. The soil was saturated from the bottom of the soil box with tap water, and then gravimetrically drained for 1 day to obtain a condition similar to the soil's field capacity. Simulated rain was delivered from a tower 12 m high. The rainfall distribution uniformity, which was calculated from the equation of uniformity coefficient developed by Christiansen, was set at 80%, and about 85% of the drops had a diameter <2mm (Andry et al. 2007). A rainfall intensity of 60 mm/h, developing an energy of 27.1 J/[m.sup.2].mm (van Dijk et al. 2002; Andry et al. 2008), was applied for 1 h to the soil box under a 10[degrees] slope. The runoff and splashed soil samples were collected every 5 or 10min, just after taking pictures at H = 2.7 and B=0.8. The two D2H cameras were controlled with a cable release in order to simultaneously capture a pair of images and suppress the camera shake from clicking the shutter. This helped to shorten the time for the photogrammetry since the GCP points in each image were represented by the same pixels. A high optimal image quality was attained by using an aperture setting of f/5.6 and a 1/250 s exposure time, which was sufficiently rapid to follow the flow of the runoff water on the soil surface. The splashed soil was collected on a sheet that was placed under the soil box. This sheet also helped to reduce the effect of halation in the images as a result of direct sunlight on the soil surface. The surface measurement process was used to obtain the value of [A.sub.s] (mm). The measurement area for the DEM was reduced to 80% of the entire soil surface, because the shade produced by the sides of the soil box, as seen in the images, was removed from the study. The value of the eroded soil depth, [M.sub.s] (mm), was calculated from the amount of soil loss obtained after oven-drying at 105[degrees]C for 48 h each initial soil bulk density and soil surface area.

A wind erosion experiment was carried out in the straight-line puff wind tunnel at ALRC. The working section of this wind tunnel is 2.0m long, 0.45m wide, and 0.55m high. A 20mm depth of air-dried sandy soil was placed in the wind tunnel and subjected to wind at a velocity of 4.5 m/s for 45 min. The soil surface was photographed using a selected target object at a distance of 0.6 m, using a base length of 0.3 m, before and after the wind events. The DEM soil surface data were obtained using the surface measurement process. The accuracy of the photogrammetry system was evaluated using the DEM values for 20 nails on the z-axis, i.e. comprising the [M.sub.p] (mm) values measured from the soil surface with a point gauge against the [A.sub.p] values from the point measuring method.

Results and discussion

Influence of inner orientation on the DEM accuracy

The accuracy of the DEM along the z-axis, which is the soil depth [[delta].sub.z], was affected by (1) the resolution of the camera, [[delta].sub.CCD] (mm); (2) the distance between the camera and object, H (m); (3) the base distance between the pair of cameras, B (m); and (4) the focus length [f.sub.C] (mm) (Fig. 2). The relationships between these 4 factors can be expressed as shown in Eqn 1 (Moritani et al. 2006):

[[delta].sub.z] = H/f H/B [[delta].sub.CCD] (1)

Accuracy was also influenced by (5) the declinations in the principal coordinate points of the lenses in the longitudinal and horizontal directions, and (6) the distortion of the lenses. However, factors (5) and (6) can be compensated for by calculating the inner orientation of each camera.

The precision along the z-axis was evaluated using the mean absolute error (MAE) and the mean relative error (MRE) (%), shown, respectively, in Eqns 2 and 3:

MAE = 1/N [N.summation over (i=1)[absolute value of [M.sub.(p,s)i] - [A.sub.(p,s)i]] (2)

MRE = 1/N [N.summation over (i=1)[absolute value of [M.sub.(p,s)i] - [A.sub.(p,s)i]]/[M.sub.(p,s)i] x 100% (3)

where N is the number of samples. The inner orientation was calculated for each camera. The factors for a pair of D2H cameras are shown in Table 1. Here, [[delta].sub.z] is proportional to [H.sup.2]/B as described in the Eqn 1, which highlights the importance of the positional relation for precision, although few clear reports are available in the literature. Therefore, integrating the value of L into these positional lengths was introduced to indicate the precision, as shown in Eqn 4:

[[delta].sub.Z] = L x [[delta].sub.CCD]/f (4)

where L is [H.sup.2]/B.

Thus, the precision is proportional to the factor of L. In fact, a precision comparison under different conditions was performed based on the correlation value of the relationship between L and MAE from the equation MAE = a x L.

In a case where the inner orientation was not accounted for, the value of a was 0.74, which represents a low precision compared to a [[delta].sub.z] of 0.19 (Fig. 6). However, when the inner orientation was applied, the value of a was 0.057, indicating a higher precision compared with the [[delta].sub.z] of 0.19. This is because the [[delta].sub.z] value calculated from Eqn 1 indicates the variation along the z-axis when 2 points in the rectified pair of images were located 1 pixel apart in the relative vicinity of matching points. However, in a matching process such as point measurement, these 2 points were effectively converged into a single pixel. It was found that this photogrammetry system with the inner orientation was 4.5 times as accurate as the results of Rieke-Zapp and Nearing (2005) at the same distance, L, due to the use of a lower focus length of 19 mm. Based on its performance, the application of this photogrammetry system in a research field such as wind and/or water erosion could be helpful in reducing the necessary time and labour. However, the interference effects of rainfall and the physical properties of soil on the system have to be tested in a laboratory before any large field-scale application.

[FIGURE 6 OMITTED]

Accuracy of the DEM without the application of rainfall and wind

The accuracy of the DEM was determined using point and surface measurements with inner orientation. In the point measurement, the value of a was 0.049, which was a higher precision than the value of 0.057 obtained by the same methods, as previously discussed. This better value was the result of using a closer camera-to-object distance, which produced clearer images. The maximum H was 4.7 m, compared to 7 m for the above experiment, although the same range was used for L (5-35 m).

In the surface measurement, the value of a was 0.030, or 63% higher than for the point measurement; this was because the matching process was conducted automatically based on multi-resolution representations (Cruz et al. 1995; Kim et al. 1997). The DEM value for the cumulative eroded depth was proportional to the measured value. When this proportionality was given as b, this value differed from 1.0 according to the increase in L, although the coefficient of determination in every case was >0.97. It was also found that the equilateral was significantly correlated at a 1% level when the number of samples ranged from 13 to 18.

Effect of soil bulk density on DEM accuracy

In the field water-capacity procedure, soil samples with 3 different bulk densities (0.91, 0.98, and 1.09g/[cm.sup.3]) were subjected to a rainfall intensity of 60 mm/h. Figure 7 shows the amount of soil erosion, as determined by the sampling and photogrammetry methods. As the soil bulk density increases to 1.09g/[cm.sup.3], the relationship between the sampling and photogrammetry values approaches a slope of 1.0 with a high correlation coefficient. The MAE (MRE) values for densities of 1.09, 0.98, and 0.91g/[cm.sup.3] were 0.59mm (57.6%), 1.07mm (126.4%), and 2.21 mm (392.5%), respectively. The accuracy of the DEM was improved considerably when the bulk density increased from 0.91 to 1.09 g/[cm.sup.3]. This could have been because of the additional compacting of the soil by the rainfall, which likely had less of a compaction effect on the soil surfaces with higher bulk densities. The influence of soil consolidation on the accuracy was also confirmed under different soil conditions, and also with laser scanners under different monitoring capabilities (Moritani et al. 2007; Scholl et al. 2007). The lower accuracy was also confirmed using dry soil subjected to rainfall even under the higher bulk density, since the soil was swelled during wetting process, and on the other hand, the soil surface was easily disturbed by drops of rain, especially at the first stage of the experiment as reported in the studies of Moritani et al. (2006). This study shows that the accuracy of DEM under the rainfall could be improved when the additional parameters such as antecedent moisture and hardness condition of the soil surface were investigated.

[FIGURE 7 OMITTED]

Possible additional applications of photogrammetry in soil erosion studies

In the rainfall simulation, 80% of the soil surface was divided into 2 regions, upstream and downstream, along the slope. The results show that the quantity of soil eroded in the upstream region was 0.49mm greater than in the downstream region (Fig. 8). This observation implies that it is possible to evaluate the amount of soil eroded in a specific area, and monitor the erosion mechanisms. When L was 9.1 m, the characterising factors for accuracy, b, MAE, and MRE, were 1.06, 0.21 mm, and 15.8%, respectively.

Figure 9 shows the shapes of the wind ripples. Here, the MAE value for data obtained by the point gauge photogrammetry methods was 0.21 mm. This high precision was obtained because the images were taken before and after the wind events. Monitoring the soil surface under the condition of wind application involves some difficulties such as unclear soil displacement--settlement and dust interference during the photographic process. Therefore, a determination of the photogrammetry system precision during a wind erosion application is needed for further application in soil erosion studies. This research focused on the accuracy of photogrammetry when used to measure soil erosion. However, a more specific investigation of soil surfaces in relation to the spatial coherence of erosion/deposition patterns should be performed.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

Conclusion

Soil erosion was estimated by a digital photogrammetry system that used 2 cameras. This study primarily focused on the precision of photogrammetry. It was found that the accuracy was influenced by declinations in the principal coordinate points of the lenses and the distortion of the lenses. However, these factors could be compensated for by calculating the inner orientation of each camera. The value of the cumulative eroded depth determined by photogrammetry under a no-rainfall condition was significantly proportional to the measured value at the 1% level, although the accuracy under rainfall was influenced by the soil compaction as a result of the raindrop impact. Therefore, because of its high accuracy, this system could be applied when monitoring the changes in soil surface shapes under water and wind erosion, or when measuring the amount of eroded soil in the case of soil with a high bulk density.

10.1071/SR09058

Manuscript received 2 April 2009, accepted 20 October 2009

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S. Moritani (A,C), T. Yamamoto (A), H. Andry (A), M. Inoue (A), and T. Kaneuchi (B)

(A) Arid Land Research Center, Tottori University, Tottori, Japan.

(B) Tokyu Construction Co., Ltd, Tokyo, Japan.

(C) Corresponding author. Email: hatshige01@alrc.tottori-u.ac.jp
Table 1. Specifications of the Nikon D2H camera and the calibration
information for the left and right cameras

              Focus         CCD          CCD        Corrected
            length f       size       pixel size   focus length
Camera        (mm)       (pixels)     SCCD (mm)        (mm)

Left           50       2464 x 1632     0.094          51.4
Right          50       2464 x 1632     0.094          51.5

            Corrected principal point
            of lens (mm)
Camera      Longitudinal              Horizontal

Left        -2.2 x [10.sup.-3]        -7.7 x [10.sup.-3]
Right       3.8 x [10.sup.-3]         7.9 x [10.sup.-3]

            Radial distortion
            parameters
Camera         K1                     K2

Left        7.6 x [10.sup.-6]         2.0 x [10.sup.-8]
Right       1.3 x [10.sup.-6]         2.2 x [10.sup.-8]

Table 2. Physical and chemical properties of the soil used
for the rainfall experiment

           Fraction (%)
                                                     Bulk
Gravel     Sand          Silt            Clay        density
>2.0 mm    2.0-0.02 mm   0.02-0.002 mm   <0.0002 mm  (g/[cm.sup.3])

3.0        22.0          19/0            56.0        1.09

                         [MATHEMATICAL
                         EXPRESSION NOT
           Sat. hyd.     REPRODUCIBLE    EC
Porosity   conduct.      IN ASCII]       1:5         CEC
(%)        (cm/s)        1:2.5           (dS/m)      (cmol(+)/kg)

58.7       6.7 x         6.7             0.70        11.4
           [10.sup.-5]
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