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Assessment of soil roughness after tillage using spectral analysis
Soil & Tillage Research 159 (2016) 73–82
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Assessment of soil roughness after tillage using spectral analysis T. Bo¨gel, P. Osinenko *, Th. Herlitzius Institute of Processing Machines and Mobile Machinery, P.O. Box: 01069, Technische Universita¨t Dresden (TU Dresden), Dresden, Germany
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 July 2015 Received in revised form 28 January 2016 Accepted 7 February 2016 Available online 16 February 2016
Tillage is one of the most important and expensive operations in agriculture. A crucial measure in soil protection and tillage quality is assessment of soil roughness. The objective of the current study is to utilize spectral analysis while investigating the effects of tillage with a heavy duty tine at work depths of 5, 10, 15, 20 cm and speeds of 4, 7, 10, 13 km h1 on the soil cross-section. In order to pick a practically appropriate longitudinal step size, a high-resolution measurement was performed. The conditions of this measurement included 4 km h1 speed with 10 cm working depth. Spectral analysis of selected soil cross-section parameters was performed to assess a cutting frequency below which the significant spectral contents were located. Such an analysis led to the conclusion on a practical longitudinal resolution of 5 cm. This measure is more reliable than picking several cross-section measurements at random. Influence of different tillage depths and speeds on selected soil cross-section parameters was investigated. It was observed that the volumes of disturbed and loosened soil were mainly influenced by the tillage depth while the furrow was more affected by the work speed. ß 2016 Published by Elsevier B.V.
Keywords: Soil roughness Tillage Power spectrum
1. Introduction Soil roughness quality after tillage is mainly influenced by soil conditions, e.g., moisture and soil type, and tillage system parameters including implements, tools, work speed, depth, etc. Tillage implements are often designed for minimizing draft force and power requirements and not for optimal tillage results which define the yield. For evaluation of tillage operations, objective criteria are necessary. One widely used criterion is the soil crosssection (see Fig. 1). It allows describing the effects of the tillage implement and also mainly defines the wind and water erosion resistance properties. For soil conservation against wind and water erosion, the soil cross-section assessment after tillage is crucial. The so-called soil surface roughness eventually defines the effects of hydraulic and erosion processes on the field (Hagen, 1988; Potter et al., 1990). Soil factors like clod size and clod distribution are influenced by tillage operation and affect crop yield (Anken et al., 1997). Common devices for surface cross-section measurement range from mechanical solutions, such as pin meter or a chain ruler (Saleh, 1993) and optical devices like laser scanner and, cameras (Rieke-Zapp et al., 2001; Bretar et al., 2013) to acoustic devices
* Corresponding author. E-mail addresses: [email protected] (T. Bo¨gel), [email protected] (P. Osinenko), [email protected] (T. Herlitzius). http://dx.doi.org/10.1016/j.still.2016.02.004 0167-1987/ß 2016 Published by Elsevier B.V.
(Oelze et al., 2003). They include stationary and mobile solutions such as a portable tillage profiler with a computer (Raper et al., 2004). In the stationary case, measurements are usually performed in a special soil bin. Fig. 2 illustrates some devices. Besides these, complex technical solutions are found in the literature such as Remotely Piloted Aircraft Systems (RPAS) equipped with a polarimetric radar (Klein et al., 2014). In this section, selected methods are briefly reviewed. For a general review of analysis and measurement methods, refer to Bhushan (2001). A more recent review can be found in Thomsen et al. (2015). Liu (2005) presented a soil cross-section model after tillage with a single sweep. Five sections in the furrow, picked at random positions, were measured. The results showed a significant increase of the soil distribution width with the increase of operating speed. The maximal relative error of the model predictions about cross-section geometric parameters have not exceeded 16%. Hasimu and Chen (2014) investigated the influence of several different seed openers on soil. In particular, the furrow cross-section was measured by a profiler with multiple plastic pins freely lowered into the furrow. The pin placement was then recorded on graphic paper. The cross-section was calculated relative to the cross-section before tillage. Three cross-sections were measured at random positions in the furrow. The statistical analysis was performed by analysis of variance (ANOVA). Shinde et al. (2011) used a soil profilometer to investigate the influence of the tool shape, working depth and speed on soil conditions after tillage. In this study, the resolution along the soil bin had been fixed at 2 cm.
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Fig. 1. Soil cross-section.
Jester and Klik (2005) performed soil surface measurements using contact and contactless methods. The contact methods have included a pin meter set parallel to the soil surface. The distance between two adjacent pins was 5 mm. The pin readings were recorded on graph paper and entered in a computer. The crosssection length was measured by means of a chain ruler. The contactless measurement was performed via a laser scanner placed on a two-dimensional traversing frame controlled by a computer. In the cross-section analysis, outliers exceeding the specified tolerance were removed and substituted with interpolated values. In this study, the cross-section spacing in contact measurements was 25 mm and 2 mm in contactless measurements. The laser scanner provided the most detailed soil surface measurements. A laser profiler was applied in Zhixiong et al. (2005) for soil roughness assessment. The soil cross-sections were measured at three different angles relative to the direction of tillage. Zhixiong et al. (2005) have concluded that soil roughness should be characterized not only by the tillage operating conditions (indicated as a single-scale process), but also by the field topography. A fine-scale roughness index for assessment and prediction of soil porosity was suggested by Sun et al. (2009). They used a mobile laser profiler to measure the soil cross-section with a vertical resolution of 1 mm, and longitudinal and lateral resolutions of 20 mm. Garcı´a Moreno et al. (2010) compared a so-called shadow analysis to chain ruler and pin meter methods to assess soil
[(Fig._2)TD$IG]
roughness. The pin meter had a resolution of 20 mm between adjacent pins. The same resolution was assumed between two section measurements. The statistical indices, used to investigate correlations between shadow analysis and the two reference methods, i.e., the chain ruler and the pin meter, included the standard deviation of the cross-section compared to the line parallel to the direction of tillage. The results showed significant correlation between shadow analysis and the reference methods. Sandri et al. (1998) investigated correlations between different roughness estimation methods, including image analysis and cross-section standard deviation obtained via a laser scanner. The study was focused on the amount of clods on the soil surface after tillage. The results were compared to the sieve method (Carter and Gregorich, 2007). The distance between two laser scans of the cross-section was fixed at 10 mm. The coefficient of determination was estimated at 81% for the amount of clods index obtained via the image analysis and sieve method, and 63% for the amount of clods index and cross-section standard deviation obtained via the laser scanner. A multi-stereo reconstruction method was presented by Petitpas et al. (2010) to assess ground roughness in which a three-dimensional plots were reconstructed from a collection of photos. This technique has certain advantages compared to laser scanning and mechanical methods, such as pin meter, since it is not restricted to cross-section measurements only. However, it requires complex image processing methods and corresponding software. Also, it is subject to inaccuracies related to numeric procedures of three-dimensional plot reconstruction which are not present in direct cross-section measurements. An approach to three-dimensional mapping using stereo vision was suggested by Riegler et al. (2014). Marzahn et al. (2012) also suggested threedimensional soil roughness assessment using a photogrammetric acquisition system. Solhjou et al. (2012, 2013) assessed the effect of rake angles and blade face geometry, single side and double side chamfers in particular, on soil movement in tillage. Soil cross-section measurements were performed via so-called cubic tracers placed in the soil following a homogeneous reference grid before tillage.
Fig. 2. Different surface measurement methods: a chain ruler (a) and a pin meter (b) (Jester and Klik, 2005), a portable tillage profiler (c) (Oelze et al., 2003), setup with seed openers in a soil bin (d) (Hasimu and Chen, 2014).
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After tillage, the tracers were shifted and their locations were measured in turn. In this study, the grid had an equal resolution in all three directions of 1 cm. Some authors focused on developing mathematical models of the soil surface in order to predict its roughness. Vannier et al. (2014) studied large aggregates in tilled soil and suggested a model for generation of a surface with half-ellipsoid clods. For their automatic detection, wavelet and contour-based methods were used. To summarize, two major concerns are to be addressed in soil roughness assessment based on cross-section analysis: accuracy of cross-section parameter measurement on one hand, and performance of the measurement procedure on the other. In simple terms, balancing these two factors amounts to choosing the quantity and periodicity of cross-sections to be measured. The above described methodologies can be roughly classified into two categories: the ones that use fewer cross-sections measured at random positions, and the ones that use numerous cross-sections measured with a high lateral resolution chosen heuristically. The first approach might lead to accuracy loss while the second might be unreasonably time-consuming and labor intensive. The goal of the present work is to choose a resolution along tillage direction using analysis of frequency components of the respective soil cross-section parameters, i.e., how the parameters behave along the tillage direction. The objective of such a spectral analysis is to determine a resolution that captures the most significant frequencies while dropping the higher ones to reduce labor intensity. First, the soil bin is described, where the experiments were performed. Measurement devices and methods, and the cross-section characteristics calculation routines as well as the cross-section spectral analysis procedure were then explained. The results and discussion section describes the high-resolution measurement results followed by the results of further measurements and their statistical analysis. 2. Materials and methods 2.1. Furrow cross-section measurement and tillage tool A 28 m long and 2.5 m wide soil bin is available at the Chair of Agricultural Systems and Technology of the TU Dresden where different implements and measurement devices can be mounted onto two three-point-hitches. It allows in-door experiments independent from weather conditions. The soil type used in the experiments was classified as loamy sand. The experiments were conducted at 10% gravimetric soil water content. Fig. 3 illustrates the soil bin along with the used coordinate system.
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Fig. 4. Heavy duty tine used for tillage.
A heavy duty tine, which is typically used for soil loosening operations, was applied for tillage. The tine had a width of 6.5 cm and a length of 47 cm (see Fig. 4). A laser scanner was used to measure the soil cross-section (see Fig. 5). The scanner was a non-contact laser relief meter, and was mounted on a sled which was moved manually. A laser sensor OptoNCDT 1700 from Micro-Epsilon was used for height measurement. The horizontal position of the laser was measured with a rope position sensor WS17KT from ASM. Both sensors worked with a sampling frequency of 100 Hz. To scan the soil cross-section, the laser profilometer was placed over the soil bin. The sled with the laser was pulled over the complete width of the soil bin. For the following scans, the laser profilometer was moved manually to the next position. A lateral length of 2 m was used for soil cross-section measurement truncating the sides where the soil was undisturbed. With the lateral resolution of 5 mm, a total number of 40 crosssection points were measured in lateral direction. For more details, refer to Section 2.2. The cross-section measurements were performed over a longitudinal distance of 1 m where approximately constant speed and draft force are achieved. After each test, the entire soil bin was re-tilled. To ensure the same conditions for a subsequent test, the soil was loosened by a rotary tillage machine followed by flattening and compaction measures with a compaction roller. Soil samples were taken to check the soil moisture content and soil density. 2.2. Soil cross-section parameters In the soil cross-section assessment, the following parameters
(Fig._5)TD$IG][were considered (Manuwa and Ogunlami, 2010): ridge-to-ridge
Fig. 3. Soil bin and the coordinate system used in surface assessment.
Fig. 5. Soil cross-section measurement setup with a laser scanner.
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(ACF). There exist several methods of estimating the PSD. In particular, one can first estimate ACF using the following formula: Nlþ1 X 1 Rxx ½l ¼ x kDt x xðk þ lÞDtx ; ˆ ¯ ¯ ðNlÞs2x
l ¼ 1; . . .; L;
(1)
k¼1
Fig. 6. Diagram of the cross-section parameters. Direction of tillage.
distance, RRD; maximum width of soil throw, MWT; maximum width of soil cut Wf; ridge height, RH (also left RHL and right RHR); furrow height, FH; tool width Wt; tillage depth, d; and areas Af (remaining loosened soil in the furrow), Ar(distributed loosed soil) and Aa (removed soil from the furrow) as indicated in Fig. 6. From this set of parameters, the FH, RH, RRD, MWT, Af, Ar and Aa were the subject of the present study. The disturbed soil surface is the surface right after tillage while the compacted soil surface is the surface after removal of the ridges and loose parts, such as clods, from the furrow. This removal was necessary to estimate the parameter Af which characterizes the difference between the loose and compacted soil. The data analysis was performed in MATLAB R2013a and Microsoft Excel 2010. A set of MATLAB-programs was developed in order to compute the soil cross-section parameters, plot the cross-sections and the parameters as well as to save the data in Microsoft Excel spreadsheets. In each experiment, a set of soil cross-sections was measured along with two additional cross-sections: cross-section before tillage and after removing loose parts of soil, i.e., compacted soil cross-section. The former was used as the pivot for computation of the parameters. Each cross-section consisted of an array of measured vertical coordinates. The furrow height FH was computed as the minimum element of the array. The ridge heights were computed as the two maximum elements of the array. To estimate the MWT, a script was programmed which has tried to detect the first rise of the disturbed soil cross-section before the first ridge. The operation was mirrored from left to right to detect the starting point of the right ridge accordingly. The lateral coordinates of the ridge heights were used to compute the RRD. The areas were estimated via Riemann sums. The lateral length of the cross-section measurement was set at 2 m. The sled with the laser scanner was moved in lateral direction at approximately constant speed to achieve a lateral resolution of 5 mm. This resolution was chosen to be sufficiently high to capture the significant soil surface details. Finally, the cross-section scans were performed in the region of the soil bin where approximately constant speed and draft force were achieved. 2.3. Power spectrum estimation and analysis Power spectral density (PSD) is an important and informative [(Fig._7)TD$IG] stochastic signal characteristic besides the autocorrelation function
where l is the lag index, N is the number of samples in data, L < N is the maximal lag index, x is the data point, t is the independent variable (for example, time), Dt is the sample step size, and x; sx are ¯ the sample mean and standard deviation, respectively. Eq. (1) describes ACF estimation of a discrete signal x sampled at (times) kDt, k = 1, 2, . . .. Using Wiener–Khinchin theorem, one can compute the PSD and therefore the ACF and PSD are interchangeable. However practically, usage of Eq. (1) is restricted to relatively small lags. Instead, one can start with estimating the PSD directly from all data points. Usually, this is performed by computing periodograms as follows: 2 N 1 X jX ½nj2 ¼ pffiffiffiffiffiffiffi xðt k Þeikn=N ; 2pN k¼1
n ¼ 1; . . .; N:
(2)
The PSD at the index n = 1 corresponds to the zero frequency while at n = N, it corresponds to the Nyquist frequency fN = (1/2Dt) which is half the sampling frequency. The Nyquist frequency is the maximal frequency that a PSD estimate covers. To estimate the spectra at higher frequencies, the signal must be measured at higher sampling rates. Smoothed estimates can be obtained by averaging and windowing. In this case, realizations xðt k Þ; k ¼ 1; . . .; N are divided into segments which can be, in general, overlapped. Each segment is multiplied by a so-called window function which is usually used to ‘‘amplify’’ the segment ‘‘in the middle’’ and to ‘‘weaken on tails’’ (since overlapping is used). For these purposes, several methods exist with different window functions. In the present work, the widely-used Welch’s method (Welch, 1967) was applied. The PSD estimates allow assessing a cutting frequency below which significant spectral components are situated. For the high-resolution cross-section measurements in the current study, 200 scans with a longitudinal resolution of 5 mm were performed in the region of the soil bin where approximately constant speed and draft force were achieved. 3. Results and discussion 3.1. Determining longitudinal resolution A sample of cross-sections was obtained with a longitudinal resolution of 5 mm to assess a suitable resolution for further measurements. Fig. 7 illustrates the soil cross-sections. Selected soil cross-section parameters, as they behave along the longitudinal coordinate, are illustrated in Fig. 8. Notice that the estimate of the distance between the two highest points (RRD) has a few rectangle-shaped peaks (Fig. 8C). These are artifacts of automatic detection of ridge tops. Since the cross-section measurement fluctuates, the exact lateral positions
Fig. 7. Soil cross-section measurements with 5 mm longitudinal resolution and its 3D-map. The cross-sections are shown in a lateral range of 1300 mm for clarity since the soil surface outside of this range was not disturbed by tillage.
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Fig. 8. Soil cross-section parameters with 5 mm longitudinal resolution as the behave along the direction of tillage.
of the two maximal cross-section heights (ridges) vary. In general, it is difficult to unambiguously detect the ridge tops especially if the soil surface is highly disturbed and therefore an automatic RRD estimation has certain limitations. On the other hand, manual estimation may be cumbersome if the data set is large.
Fig. 9 illustrates the normalized estimates of PSD. These have the following interpretation. Consider, for example, the PSD estimate of the furrow height (Fig. 9A). It has two characteristic peaks – at the frequency of approximately 0.004 mm1 and 0.01 mm1. These peaks reveal two frequency components of the
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Fig. 9. PSD estimates of the soil cross-section parameters with 5 mm longitudinal resolution. A 90%-confidence bound is shown with dash-dot lines.
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furrow height with periods 250 mm and 100 mm, respectively. Four oscillations with a period of 100 mm may be recognized in Fig. 8A in the range from zero to approximately 400 mm. It can be also recognized that oscillations with this period are higher in magnitude than oscillations with smaller periods. Suppose that one estimates the mean furrow height by picking three random cross-sections: at the longitudinal coordinate 50 mm, 300 mm and 800 mm. The respective furrow heights would be 42.4 mm, 30.44 mm and 27.43 mm, respectively. Their mean is 33.42 mm. The mean, calculated from all cross-sections measured, is 24.9 mm which is more accurate since it accounts for all the significant frequency components. If cross-sections were taken at longitudinal resolution of 50 mm, the mean furrow height would be 25.2 mm which is close to 24.9 mm. It is assumed that the longitudinal resolution of 50 mm would suffice to estimate the mean furrow height by avoiding superfluous cross-sections measurements. The same observation is made from analysis of the other PSD estimates. The frequency of 0.02 mm1, which corresponds to the longitudinal resolution of 50 mm, would suffice for soil cross-section parameter assessment. The only PSD estimate, that did fall off this pattern, was the PSD estimate of the ridge-to-ridge distance. It had more significant frequency components, than the above described PSD estimates, also above the frequency of 0.02 mm1. However, these components reflect the presence of rectangle-shaped peaks in the RRD (see Fig. 8D) which are the result of automatic ridge top detection, and not of the physical process. The RRD and MWT, that is even harder to estimate due to the reasons mentioned in Section 2.2, were not selected for spectral analysis. From the analysis of the PSD estimates of the furrow height, ridge heights and areas Af and Ar, a longitudinal resolution of 50 mm was chosen for [(Fig._10)TD$IG] the successive measurements.
Fig. 10 illustrates the respective ACF estimates. All cross-section parameters reveal a correlation length of approximately 300 mm which is within the total length of measurement. All ACF estimates have low-frequency components as reflected in the respective PSD estimates. The estimate of the ridge-to-ridge distance ACF (Fig. 10D) contains high-frequency components related to imperfections of the calculation procedure as discussed above. To conclude, a longitudinal measurement distance of 1 m with a distance between subsequent cross-sections measurements of 50 mm was a practically reasonable experimental setting that allows for satisfactory cross-section parameter estimation accuracy and avoids excessive experimental efforts. 3.2. Effect of working depth and speed on selected cross-section parameters This section is concerned with the regression analysis of selected soil-cross section parameters with the work speed and depth as independent factors. All cross-section measurements were performed with a longitudinal resolution of 50 mm according to the procedure described in Section 3.1. The tillage was performed at 5, 10, 15, 20 cm work depths and 4, 7, 10, 13 km h1 1 speeds. Due to presence of autocorrelation in soil cross-section parameter samples, confidence intervals of the sample mean were computed following the methodology of effective number of observations (Zie˛ba and Ramza, 2011). The effective number of observations is a quantity that reflects the effect of autocorrelation on confidence bounds, and depends on the sample ACF and number of observations n as follows: n neff ¼ P c ; (3) 1 þ 2 nk¼1 ð1ðk=nÞÞRxx ½k ˆ
Fig. 10. ACF estimates of the soil cross-section parameters with 5 mm longitudinal resolution.
T. Bo¨gel et al. / Soil & Tillage Research 159 (2016) 73–82
where Rxx ½k is the kth value of the ACF estimate, nc is the index of ˆ Rxx where it first crosses zero. The sample dispersion s2 is estimated ˆ ˆ by: n X neff s2 ¼ ðx xÞ; ˆ nðneff 1Þ k¼1 k ¯
(4)
where xk is the kth measurement of a soil cross-section parameter x, and x is the sample mean. Consequently, Student t-distribution ¯ with neff degrees of freedom at a significance level of 5% was used to compute confidence intervals. The ridge heights were averaged to one parameter RH. Fig. 11 illustrates the effects of the work speed and depth on the selected soil cross-section parameters. To quantitatively assess the influence of the work speed and depth on soil roughness after tillage with a heavy duty tine, the selected soil cross-section parameters were approximated with different models up to the second order including interaction terms. All models been tested with F-test with a significance level of [(Fig._1)TD$IG] 5%. The models were compared in terms of correlation with the
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measured data and model complexity, i.e., the number of model parameters. The R2-coefficient was at least 80%. Higher-order terms were dropped if satisfactory correlation could be achieved without them. For furrow height FH, maximal width of soil throw MWT, and ridge-to-ridge distance RRD was achieved with a linear model with one interaction term: Mðv; dÞ ¼ p0 þ pv v þ pd d þ pvd vd;
(5)
where v denotes the work speed, d denotes the work depth and p0 ; pv ; pd ; pvd are the model parameters. In the regression models for the area parameters Af, Ar, and Aa, as well as ridge height RH, satisfactory correlation was obtained without the interaction term pvd vd. All regression coefficients were tested using t-test with a significance level of 5%. Fig. 12 illustrates modeling accuracy of the selected soil cross-section parameters along with the R2-coefficients. In Table 1, the model parameters are summarized. Coefficients with p-values less than 0.05 are marked bold. Notice that constant
Fig. 11. Effect of working speed and depth on soil cross-section parameters FH, RH, RRD, MWT, Af, Ar, Aa. Error bars indicate 95%-confidence bounds. Trend lines are displayed for visibility.
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Fig. 12. Soil cross-section parameter approximation along with the R2-coefficients.
Table 1 Soil cross-section parameter models. The coefficients are given along with 95%confidence bounds (in parentheses). Significant coefficients are marked bold. FH
RH
p0 pd pv pdv
0.41 (0.56, 0.26) 0.05 (0.06, 0.04) 0.82 (0.80, 0.84) 0.016 (0.01, 0.017)
2.12 (1.39, 2.86) 0.24 (0.21, 0.28) 0.10 (0.16, 0.04)
RRD
MWT
p0 pd pv pdv
7.77 (27.58, 12.04) 1.39 (0.06, 2.84) 6.28 (4.12, 8.45) 0.16 (0.31, 0)
2.15 (32.28, 36.57) 1.71 (0.80, 4.23) 9.83 (6.06, 13.59) 0.01 (0.29, 0.26)
p0 pd pv
Af
Ar
18.95 (102.03, 64.12) 16.50 (12.29, 20.72) 5.29 (12.32, 1.73)
70.53 (114.12, 26.95) 10.58 (8.37, 12.79) 11.82 (8.13, 15.51)
Aa p0 pd pv
35.65 (62.79, 8.52) 2.21 (0.83, 3.58) 7.62 (5.33, 9.92)
terms highlight the effects that were not captured by the experiment. The following conclusions were made from the analysis of the results and modeling. The furrow height FH weakly correlates with the set up tillage depth as expected while the effect of the speed is stronger. At higher speeds, the furrow height became larger and this effect increases when the tillage depth is higher. Increase of the furrow height with increase of the tillage depth and speed was also observed for shovel and sweep tools (Shinde et al., 2011). An opposite effect was observed for the ridge height RH. There is a weak correlation between RH and the work speed in comparison to the effect of the set up depth. Indeed, larger tillage depths lead to larger volumes of soil being displaced by the tool. The soil disturbance, as characterized by the ridge-to-ridge distance RRD and the maximal width of soil throw MWT, was greater at higher speed while the effect of the set up depth stayed minor. Physically, the volume of soil being displaced by the tool increased with the work depth. This led to different ridge heights at different depths. The distance between the ridges RRD and the maximum width of soil throw MWT, on the other hand, are more sensitive to the different work speeds. The ridges stayed practically uninfluenced
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Table 2 Sample mean of selected soil cross-section parameters obtained with longitudinal resolution of 50 mm. The work depth and speed are in cm and km h1 respectively. The parameters furrow height FH, left ridge height RHL, right ridge height RHR, ridge-to-ridge distance RRD, width of soil throw MWT are in cm, and the areas Af, Ar, Aa – in cm2. Depth
Speed
FH
RH
RRD
MWT
Af
Ar
Aa
5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20
4 4 4 4 7 7 7 7 10 10 10 10 13 13 13 13
2.6 2.3 2.5 3.5 4.1 5.0 5.0 4.3 4.6 7.7 6.5 6.4 4.8 7.4 8.5 7.3
2.9 3.5 5.6 6.4 2.9 4.0 5.6 6.0 2.1 4.2 5.2 5.6 1.8 3.0 4.2 6.0
23.3 31.7 30.3 30.9 32.2 36.4 41.0 41.4 43.9 56.5 59.5 45.8 72.3 73.0 68.8 57.6
48.4 59.2 68.1 70.4 78.5 91.9 97.0 101.9 92.1 118.2 147.7 120.0 137.9 148.9 154.9 154.2
57.5 75.9 233.6 350.4 23.5 96.5 156.7 274.3 29.4 48.9 143.1 258.2 76.0 67.1 96.2 290.1
49.9 75.5 137.8 167.2 75.6 122.0 189.2 186.6 77.8 181.7 232.3 252.7 102.9 177.1 243.3 322.7
17.5 13.7 19.5 31.6 34.3 51.1 54.3 38.4 42.8 84.9 81.2 91.6 46.5 78.7 105.3 115.9
by the working depth and shifted to the sides as the working speed increased. This was also observed from the behavior of the areas Af, Ar and Aa. The furrow area Af had stronger correlation with the working depth than with the speed which is physically evident. Distribution of the loosened soil to the sides from the furrow is characterized by Ar. It is affected by both the working depth and work speed. The working depth influenced the amount of compacted soil that is eventually loosened. Increased working speeds led to a wider distribution of soil out of the furrow to the sides. This correlation was found in the regression model for Af and the corresponding in Aa as well. The observed increase of RRD and MWT, as the working speed increased, correlates with the results by Liu (2005) for a sweep tool. Hasimu and Chen (2014) observed similar behaviors of RH, MWT and Af as work depth increased, with seed openers as the tool. The general conclusion can be drawn that the volume of distributed soil is mainly influenced by working depth and speed. It was also indicated by Shinde et al. (2011) for a shovel tool. Table 2 gives numeric values of the sample mean of the selected soil cross-section parameters corresponding to different tillage conditions. 3.3. Discussion on spectral analysis The current study was limited to one soil type, and a practically satisfactory longitudinal resolution was the subject of spectral analysis. It should be pointed out that choosing a frequency that captures all significant frequency components of a physical process is subjective in general. Eventually, it is up to the user to find a compromise between capturing possibly many soil surface details and saving time and labor resources. PSD estimates should help understand the physical process in question better than such metrics as mean and standard deviation alone. One possible automation routine may involve computing a resolution based on PSD threshold or PSD integral threshold. Another subject, that needs further investigation, is spectral analysis of cross-sections of different soil types under different moisture condition and after different tillage implements. Characterizing soil roughness by PSD estimates of cross-section parameters may be also an interesting topic in its own right. 4. Conclusions In this study, analysis of power spectral density estimates was suggested in order to choose an appropriate cross-section measurement resolution along the tillage direction and to avoid inaccuracies of picking several cross-sections at random positions
on one hand, and reduce efforts of experimental routines on the other. The experiments were performed with a heavy duty tine at 5, 10, 15, 20 cm working depths and 4, 7, 10, 13 km h1 speeds with a longitudinal resolution of 50 mm. Selected soil cross-section parameters were modeled with the working speed and depth as regressors and the R2-coefficients yielded at least about 80%. The results have shown that the volumes of disturbed and loosened soil were mainly influenced by the work depth while the furrow was more affected by the work speed. Acknowledgements The research was funded by the German Research Foundation (DFG), project reference number: HE 5738/2-1. References Anken, T., Hilfiker, T., Bollhalder, H., Sandri, R., Satori, L., 1997. Digital image analysis and profile meter for defining seedbed fineness. Agrarforsch. Schweiz 4 (1), 13–16. Bhushan, B., 2001. Surface roughness analysis and measurement techniques. Modern Tribol. Handb. 1, 49–119. Bretar, F., Arab-Sedze, M., Champion, J., Pierrot-Deseilligny, M., Heggy, E., Jacquemoud, S., 2013. An advanced photogrammetric method to measure surface roughness: application to volcanic terrains in the Piton de la Fournaise, Reunion Island. Rem. Sens. Environ. 135, 1–11. Carter, M., Gregorich, E., 2007. Soil Sampling and Methods of Analysis, 2nd ed. CRC Press. Garcı´a Moreno, R., Diaz Alvarez, M.C., Tarquis Alfonso, A.M., Paz Gonza´lez, A., Saa Requejo, A., 2010. Shadow analysis of soil surface roughness compared to the chain set method and direct measurement of micro-relief. Biogeosciences 7 (8), 2477–2487. Hagen, L., 1988. New wind erosion model developments in the USDA. In: 1988 Wind Erosion Conference ProceedingsTexas Tech. University, Lubbock, pp. 11–13. Hasimu, A., Chen, Y., 2014. Soil disturbance and draft force of selected seed openers. Soil Till. Res. 140, 48–54. Jester, W., Klik, A., 2005. Soil surface roughness measurement-methods, applicability, and surface representation. Catena 64 (2), 174–192. Klein, T., Kassner, J., Kulke, R., Seeger, M., 2014. A polarimetric radar for soil roughness characterization flying on small RPAS. In: Radar Conference (Radar), 2014 InternationalIEEE, , pp. 1–4. Liu, J., 2005. Study of soil profile of a single sweep tool. In: CSAE/SCGR 2005 Meeting, Winnipeg, Manitoba, June 26-29. Manuwa, S., Ogunlami, M., 2010. Soil–tool interaction modeling of parameters of soil profile produced by tillage tools. J. Eng. Appl. Sci. 5 (2), 91–95. Marzahn, P., Rieke-Zapp, D., Ludwig, R., 2012. Assessment of soil surface roughness statistics for microwave remote sensing applications using a simple photogrammetric acquisition system. ISPRS J. Photogram. Rem. Sens. 72, 80–89. Oelze, M.L., Sabatier, J.M., Raspet, R., 2003. Roughness measurements of soil surfaces by acoustic backscatter. Soil Sci. Soc. Am. J. 67 (1), 241–250. Petitpas, B., Beaudoin, L., Roux, M., Rudant, J.-P., 2010. Roughness measurement from multi-stereo reconstruction. In: ISPRS Commission III Symposium on Photogrammetry Computer Vision and Image Analysis, Paris, France. Potter, K., Zobeck, T., Hagan, L., et al., 1990. A microrelief index to estimate soil erodibility by wind. Trans. ASAE 33 (1), 151–155.
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Raper, R., Grift, T., Tekeste, M., 2004. A portable tillage profiler for measuring subsoiling disruption. Trans. ASAE 47 (1), 23–28. Riegler, T., Rechberger, C., Handler, F., Prankl, H., 2014. Image processing system for evaluation of tillage quality (in German). Landtechnik 69 (3), 125–131. Rieke-Zapp, D., Wegmann, H., Santel, F., Nearing, M., 2001. Digital photogrammetry for measuring soil surface roughness. In: Proceedings of the Year 2001 Annual Conference of the American Society for Photogrammetry & Remote Sensing ASPRS. pp. 23–27. Saleh, A., 1993. Soil roughness measurement: chain method. J. Soil Water Conserv. 48 (6), 527–529. Sandri, R., Anken, T., Hilfiker, T., Sartori, L., Bollhalder, H., 1998. Comparison of methods for determining cloddiness in seedbed preparation. Soil Till. Res. 45 (1), 75–90. Shinde, G.U., Badgujar, P.D., Kajale, S.R., 2011. Experimental analysis of tillage tool shovel geometry on soil disruption by speed and depth of operation. In: International Conference on Environmental and Agriculture Engineering, vol. 15, pp. 65–70. Solhjou, A., Desbiolles, J., Fielke, J., 2013. Soil translocation by narrow openers with various blade face geometries. Biosyst. Eng. 114 (3), 259–266.
Solhjou, A., Fielke, J., Desbiolles, J., 2012. Soil translocation by narrow openers with various rake angles. Biosyst. Eng. 112 (1), 65–73. Sun, Y., Lin, J., Lammers, P., Damerow, L., Hueging, H., Zhang, H., Sun, W., 2009. Predicting surface porosity using a fine-scale index of roughness in a cultivated field. Soil Till. Res. 103 (1), 57–64. Thomsen, L., Baartman, J., Barneveld, R., Starkloff, T., Stolte, J., 2015. Soil surface roughness: comparing old and new measuring methods and application in a soil erosion model. SOIL 1 (1), 399–410. Vannier, E., Taconet, O., Dusse´aux, R., Chimi-Chiadjeu, O., 2014. Statistical characterization of bare soil surface microrelief. Adv. Geosci. Rem. Sens.. Welch, P., 1967. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73. Zhixiong, L., Nan, C., Perdok, U., Hoogmoed, W., 2005. Characterisation of soil profile roughness. Biosyst. Eng. 91 (3), 369–377. Zie˛ba, A., Ramza, P., 2011. Standard deviation of the mean of autocorrelated observations estimated with the use of the autocorrelation function estimated from the data. Metrol. Meas. Syst. 18 (4), 529–542.
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Soil & Tillage Research journal homepage: www.elsevier.com/locate/still
Assessment of soil roughness after tillage using spectral analysis T. Bo¨gel, P. Osinenko *, Th. Herlitzius Institute of Processing Machines and Mobile Machinery, P.O. Box: 01069, Technische Universita¨t Dresden (TU Dresden), Dresden, Germany
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 July 2015 Received in revised form 28 January 2016 Accepted 7 February 2016 Available online 16 February 2016
Tillage is one of the most important and expensive operations in agriculture. A crucial measure in soil protection and tillage quality is assessment of soil roughness. The objective of the current study is to utilize spectral analysis while investigating the effects of tillage with a heavy duty tine at work depths of 5, 10, 15, 20 cm and speeds of 4, 7, 10, 13 km h1 on the soil cross-section. In order to pick a practically appropriate longitudinal step size, a high-resolution measurement was performed. The conditions of this measurement included 4 km h1 speed with 10 cm working depth. Spectral analysis of selected soil cross-section parameters was performed to assess a cutting frequency below which the significant spectral contents were located. Such an analysis led to the conclusion on a practical longitudinal resolution of 5 cm. This measure is more reliable than picking several cross-section measurements at random. Influence of different tillage depths and speeds on selected soil cross-section parameters was investigated. It was observed that the volumes of disturbed and loosened soil were mainly influenced by the tillage depth while the furrow was more affected by the work speed. ß 2016 Published by Elsevier B.V.
Keywords: Soil roughness Tillage Power spectrum
1. Introduction Soil roughness quality after tillage is mainly influenced by soil conditions, e.g., moisture and soil type, and tillage system parameters including implements, tools, work speed, depth, etc. Tillage implements are often designed for minimizing draft force and power requirements and not for optimal tillage results which define the yield. For evaluation of tillage operations, objective criteria are necessary. One widely used criterion is the soil crosssection (see Fig. 1). It allows describing the effects of the tillage implement and also mainly defines the wind and water erosion resistance properties. For soil conservation against wind and water erosion, the soil cross-section assessment after tillage is crucial. The so-called soil surface roughness eventually defines the effects of hydraulic and erosion processes on the field (Hagen, 1988; Potter et al., 1990). Soil factors like clod size and clod distribution are influenced by tillage operation and affect crop yield (Anken et al., 1997). Common devices for surface cross-section measurement range from mechanical solutions, such as pin meter or a chain ruler (Saleh, 1993) and optical devices like laser scanner and, cameras (Rieke-Zapp et al., 2001; Bretar et al., 2013) to acoustic devices
* Corresponding author. E-mail addresses: [email protected] (T. Bo¨gel), [email protected] (P. Osinenko), [email protected] (T. Herlitzius). http://dx.doi.org/10.1016/j.still.2016.02.004 0167-1987/ß 2016 Published by Elsevier B.V.
(Oelze et al., 2003). They include stationary and mobile solutions such as a portable tillage profiler with a computer (Raper et al., 2004). In the stationary case, measurements are usually performed in a special soil bin. Fig. 2 illustrates some devices. Besides these, complex technical solutions are found in the literature such as Remotely Piloted Aircraft Systems (RPAS) equipped with a polarimetric radar (Klein et al., 2014). In this section, selected methods are briefly reviewed. For a general review of analysis and measurement methods, refer to Bhushan (2001). A more recent review can be found in Thomsen et al. (2015). Liu (2005) presented a soil cross-section model after tillage with a single sweep. Five sections in the furrow, picked at random positions, were measured. The results showed a significant increase of the soil distribution width with the increase of operating speed. The maximal relative error of the model predictions about cross-section geometric parameters have not exceeded 16%. Hasimu and Chen (2014) investigated the influence of several different seed openers on soil. In particular, the furrow cross-section was measured by a profiler with multiple plastic pins freely lowered into the furrow. The pin placement was then recorded on graphic paper. The cross-section was calculated relative to the cross-section before tillage. Three cross-sections were measured at random positions in the furrow. The statistical analysis was performed by analysis of variance (ANOVA). Shinde et al. (2011) used a soil profilometer to investigate the influence of the tool shape, working depth and speed on soil conditions after tillage. In this study, the resolution along the soil bin had been fixed at 2 cm.
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Fig. 1. Soil cross-section.
Jester and Klik (2005) performed soil surface measurements using contact and contactless methods. The contact methods have included a pin meter set parallel to the soil surface. The distance between two adjacent pins was 5 mm. The pin readings were recorded on graph paper and entered in a computer. The crosssection length was measured by means of a chain ruler. The contactless measurement was performed via a laser scanner placed on a two-dimensional traversing frame controlled by a computer. In the cross-section analysis, outliers exceeding the specified tolerance were removed and substituted with interpolated values. In this study, the cross-section spacing in contact measurements was 25 mm and 2 mm in contactless measurements. The laser scanner provided the most detailed soil surface measurements. A laser profiler was applied in Zhixiong et al. (2005) for soil roughness assessment. The soil cross-sections were measured at three different angles relative to the direction of tillage. Zhixiong et al. (2005) have concluded that soil roughness should be characterized not only by the tillage operating conditions (indicated as a single-scale process), but also by the field topography. A fine-scale roughness index for assessment and prediction of soil porosity was suggested by Sun et al. (2009). They used a mobile laser profiler to measure the soil cross-section with a vertical resolution of 1 mm, and longitudinal and lateral resolutions of 20 mm. Garcı´a Moreno et al. (2010) compared a so-called shadow analysis to chain ruler and pin meter methods to assess soil
[(Fig._2)TD$IG]
roughness. The pin meter had a resolution of 20 mm between adjacent pins. The same resolution was assumed between two section measurements. The statistical indices, used to investigate correlations between shadow analysis and the two reference methods, i.e., the chain ruler and the pin meter, included the standard deviation of the cross-section compared to the line parallel to the direction of tillage. The results showed significant correlation between shadow analysis and the reference methods. Sandri et al. (1998) investigated correlations between different roughness estimation methods, including image analysis and cross-section standard deviation obtained via a laser scanner. The study was focused on the amount of clods on the soil surface after tillage. The results were compared to the sieve method (Carter and Gregorich, 2007). The distance between two laser scans of the cross-section was fixed at 10 mm. The coefficient of determination was estimated at 81% for the amount of clods index obtained via the image analysis and sieve method, and 63% for the amount of clods index and cross-section standard deviation obtained via the laser scanner. A multi-stereo reconstruction method was presented by Petitpas et al. (2010) to assess ground roughness in which a three-dimensional plots were reconstructed from a collection of photos. This technique has certain advantages compared to laser scanning and mechanical methods, such as pin meter, since it is not restricted to cross-section measurements only. However, it requires complex image processing methods and corresponding software. Also, it is subject to inaccuracies related to numeric procedures of three-dimensional plot reconstruction which are not present in direct cross-section measurements. An approach to three-dimensional mapping using stereo vision was suggested by Riegler et al. (2014). Marzahn et al. (2012) also suggested threedimensional soil roughness assessment using a photogrammetric acquisition system. Solhjou et al. (2012, 2013) assessed the effect of rake angles and blade face geometry, single side and double side chamfers in particular, on soil movement in tillage. Soil cross-section measurements were performed via so-called cubic tracers placed in the soil following a homogeneous reference grid before tillage.
Fig. 2. Different surface measurement methods: a chain ruler (a) and a pin meter (b) (Jester and Klik, 2005), a portable tillage profiler (c) (Oelze et al., 2003), setup with seed openers in a soil bin (d) (Hasimu and Chen, 2014).
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After tillage, the tracers were shifted and their locations were measured in turn. In this study, the grid had an equal resolution in all three directions of 1 cm. Some authors focused on developing mathematical models of the soil surface in order to predict its roughness. Vannier et al. (2014) studied large aggregates in tilled soil and suggested a model for generation of a surface with half-ellipsoid clods. For their automatic detection, wavelet and contour-based methods were used. To summarize, two major concerns are to be addressed in soil roughness assessment based on cross-section analysis: accuracy of cross-section parameter measurement on one hand, and performance of the measurement procedure on the other. In simple terms, balancing these two factors amounts to choosing the quantity and periodicity of cross-sections to be measured. The above described methodologies can be roughly classified into two categories: the ones that use fewer cross-sections measured at random positions, and the ones that use numerous cross-sections measured with a high lateral resolution chosen heuristically. The first approach might lead to accuracy loss while the second might be unreasonably time-consuming and labor intensive. The goal of the present work is to choose a resolution along tillage direction using analysis of frequency components of the respective soil cross-section parameters, i.e., how the parameters behave along the tillage direction. The objective of such a spectral analysis is to determine a resolution that captures the most significant frequencies while dropping the higher ones to reduce labor intensity. First, the soil bin is described, where the experiments were performed. Measurement devices and methods, and the cross-section characteristics calculation routines as well as the cross-section spectral analysis procedure were then explained. The results and discussion section describes the high-resolution measurement results followed by the results of further measurements and their statistical analysis. 2. Materials and methods 2.1. Furrow cross-section measurement and tillage tool A 28 m long and 2.5 m wide soil bin is available at the Chair of Agricultural Systems and Technology of the TU Dresden where different implements and measurement devices can be mounted onto two three-point-hitches. It allows in-door experiments independent from weather conditions. The soil type used in the experiments was classified as loamy sand. The experiments were conducted at 10% gravimetric soil water content. Fig. 3 illustrates the soil bin along with the used coordinate system.
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Fig. 4. Heavy duty tine used for tillage.
A heavy duty tine, which is typically used for soil loosening operations, was applied for tillage. The tine had a width of 6.5 cm and a length of 47 cm (see Fig. 4). A laser scanner was used to measure the soil cross-section (see Fig. 5). The scanner was a non-contact laser relief meter, and was mounted on a sled which was moved manually. A laser sensor OptoNCDT 1700 from Micro-Epsilon was used for height measurement. The horizontal position of the laser was measured with a rope position sensor WS17KT from ASM. Both sensors worked with a sampling frequency of 100 Hz. To scan the soil cross-section, the laser profilometer was placed over the soil bin. The sled with the laser was pulled over the complete width of the soil bin. For the following scans, the laser profilometer was moved manually to the next position. A lateral length of 2 m was used for soil cross-section measurement truncating the sides where the soil was undisturbed. With the lateral resolution of 5 mm, a total number of 40 crosssection points were measured in lateral direction. For more details, refer to Section 2.2. The cross-section measurements were performed over a longitudinal distance of 1 m where approximately constant speed and draft force are achieved. After each test, the entire soil bin was re-tilled. To ensure the same conditions for a subsequent test, the soil was loosened by a rotary tillage machine followed by flattening and compaction measures with a compaction roller. Soil samples were taken to check the soil moisture content and soil density. 2.2. Soil cross-section parameters In the soil cross-section assessment, the following parameters
(Fig._5)TD$IG][were considered (Manuwa and Ogunlami, 2010): ridge-to-ridge
Fig. 3. Soil bin and the coordinate system used in surface assessment.
Fig. 5. Soil cross-section measurement setup with a laser scanner.
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(ACF). There exist several methods of estimating the PSD. In particular, one can first estimate ACF using the following formula: Nlþ1 X 1 Rxx ½l ¼ x kDt x xðk þ lÞDtx ; ˆ ¯ ¯ ðNlÞs2x
l ¼ 1; . . .; L;
(1)
k¼1
Fig. 6. Diagram of the cross-section parameters. Direction of tillage.
distance, RRD; maximum width of soil throw, MWT; maximum width of soil cut Wf; ridge height, RH (also left RHL and right RHR); furrow height, FH; tool width Wt; tillage depth, d; and areas Af (remaining loosened soil in the furrow), Ar(distributed loosed soil) and Aa (removed soil from the furrow) as indicated in Fig. 6. From this set of parameters, the FH, RH, RRD, MWT, Af, Ar and Aa were the subject of the present study. The disturbed soil surface is the surface right after tillage while the compacted soil surface is the surface after removal of the ridges and loose parts, such as clods, from the furrow. This removal was necessary to estimate the parameter Af which characterizes the difference between the loose and compacted soil. The data analysis was performed in MATLAB R2013a and Microsoft Excel 2010. A set of MATLAB-programs was developed in order to compute the soil cross-section parameters, plot the cross-sections and the parameters as well as to save the data in Microsoft Excel spreadsheets. In each experiment, a set of soil cross-sections was measured along with two additional cross-sections: cross-section before tillage and after removing loose parts of soil, i.e., compacted soil cross-section. The former was used as the pivot for computation of the parameters. Each cross-section consisted of an array of measured vertical coordinates. The furrow height FH was computed as the minimum element of the array. The ridge heights were computed as the two maximum elements of the array. To estimate the MWT, a script was programmed which has tried to detect the first rise of the disturbed soil cross-section before the first ridge. The operation was mirrored from left to right to detect the starting point of the right ridge accordingly. The lateral coordinates of the ridge heights were used to compute the RRD. The areas were estimated via Riemann sums. The lateral length of the cross-section measurement was set at 2 m. The sled with the laser scanner was moved in lateral direction at approximately constant speed to achieve a lateral resolution of 5 mm. This resolution was chosen to be sufficiently high to capture the significant soil surface details. Finally, the cross-section scans were performed in the region of the soil bin where approximately constant speed and draft force were achieved. 2.3. Power spectrum estimation and analysis Power spectral density (PSD) is an important and informative [(Fig._7)TD$IG] stochastic signal characteristic besides the autocorrelation function
where l is the lag index, N is the number of samples in data, L < N is the maximal lag index, x is the data point, t is the independent variable (for example, time), Dt is the sample step size, and x; sx are ¯ the sample mean and standard deviation, respectively. Eq. (1) describes ACF estimation of a discrete signal x sampled at (times) kDt, k = 1, 2, . . .. Using Wiener–Khinchin theorem, one can compute the PSD and therefore the ACF and PSD are interchangeable. However practically, usage of Eq. (1) is restricted to relatively small lags. Instead, one can start with estimating the PSD directly from all data points. Usually, this is performed by computing periodograms as follows: 2 N 1 X jX ½nj2 ¼ pffiffiffiffiffiffiffi xðt k Þeikn=N ; 2pN k¼1
n ¼ 1; . . .; N:
(2)
The PSD at the index n = 1 corresponds to the zero frequency while at n = N, it corresponds to the Nyquist frequency fN = (1/2Dt) which is half the sampling frequency. The Nyquist frequency is the maximal frequency that a PSD estimate covers. To estimate the spectra at higher frequencies, the signal must be measured at higher sampling rates. Smoothed estimates can be obtained by averaging and windowing. In this case, realizations xðt k Þ; k ¼ 1; . . .; N are divided into segments which can be, in general, overlapped. Each segment is multiplied by a so-called window function which is usually used to ‘‘amplify’’ the segment ‘‘in the middle’’ and to ‘‘weaken on tails’’ (since overlapping is used). For these purposes, several methods exist with different window functions. In the present work, the widely-used Welch’s method (Welch, 1967) was applied. The PSD estimates allow assessing a cutting frequency below which significant spectral components are situated. For the high-resolution cross-section measurements in the current study, 200 scans with a longitudinal resolution of 5 mm were performed in the region of the soil bin where approximately constant speed and draft force were achieved. 3. Results and discussion 3.1. Determining longitudinal resolution A sample of cross-sections was obtained with a longitudinal resolution of 5 mm to assess a suitable resolution for further measurements. Fig. 7 illustrates the soil cross-sections. Selected soil cross-section parameters, as they behave along the longitudinal coordinate, are illustrated in Fig. 8. Notice that the estimate of the distance between the two highest points (RRD) has a few rectangle-shaped peaks (Fig. 8C). These are artifacts of automatic detection of ridge tops. Since the cross-section measurement fluctuates, the exact lateral positions
Fig. 7. Soil cross-section measurements with 5 mm longitudinal resolution and its 3D-map. The cross-sections are shown in a lateral range of 1300 mm for clarity since the soil surface outside of this range was not disturbed by tillage.
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Fig. 8. Soil cross-section parameters with 5 mm longitudinal resolution as the behave along the direction of tillage.
of the two maximal cross-section heights (ridges) vary. In general, it is difficult to unambiguously detect the ridge tops especially if the soil surface is highly disturbed and therefore an automatic RRD estimation has certain limitations. On the other hand, manual estimation may be cumbersome if the data set is large.
Fig. 9 illustrates the normalized estimates of PSD. These have the following interpretation. Consider, for example, the PSD estimate of the furrow height (Fig. 9A). It has two characteristic peaks – at the frequency of approximately 0.004 mm1 and 0.01 mm1. These peaks reveal two frequency components of the
[(Fig._9)TD$IG]
Fig. 9. PSD estimates of the soil cross-section parameters with 5 mm longitudinal resolution. A 90%-confidence bound is shown with dash-dot lines.
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furrow height with periods 250 mm and 100 mm, respectively. Four oscillations with a period of 100 mm may be recognized in Fig. 8A in the range from zero to approximately 400 mm. It can be also recognized that oscillations with this period are higher in magnitude than oscillations with smaller periods. Suppose that one estimates the mean furrow height by picking three random cross-sections: at the longitudinal coordinate 50 mm, 300 mm and 800 mm. The respective furrow heights would be 42.4 mm, 30.44 mm and 27.43 mm, respectively. Their mean is 33.42 mm. The mean, calculated from all cross-sections measured, is 24.9 mm which is more accurate since it accounts for all the significant frequency components. If cross-sections were taken at longitudinal resolution of 50 mm, the mean furrow height would be 25.2 mm which is close to 24.9 mm. It is assumed that the longitudinal resolution of 50 mm would suffice to estimate the mean furrow height by avoiding superfluous cross-sections measurements. The same observation is made from analysis of the other PSD estimates. The frequency of 0.02 mm1, which corresponds to the longitudinal resolution of 50 mm, would suffice for soil cross-section parameter assessment. The only PSD estimate, that did fall off this pattern, was the PSD estimate of the ridge-to-ridge distance. It had more significant frequency components, than the above described PSD estimates, also above the frequency of 0.02 mm1. However, these components reflect the presence of rectangle-shaped peaks in the RRD (see Fig. 8D) which are the result of automatic ridge top detection, and not of the physical process. The RRD and MWT, that is even harder to estimate due to the reasons mentioned in Section 2.2, were not selected for spectral analysis. From the analysis of the PSD estimates of the furrow height, ridge heights and areas Af and Ar, a longitudinal resolution of 50 mm was chosen for [(Fig._10)TD$IG] the successive measurements.
Fig. 10 illustrates the respective ACF estimates. All cross-section parameters reveal a correlation length of approximately 300 mm which is within the total length of measurement. All ACF estimates have low-frequency components as reflected in the respective PSD estimates. The estimate of the ridge-to-ridge distance ACF (Fig. 10D) contains high-frequency components related to imperfections of the calculation procedure as discussed above. To conclude, a longitudinal measurement distance of 1 m with a distance between subsequent cross-sections measurements of 50 mm was a practically reasonable experimental setting that allows for satisfactory cross-section parameter estimation accuracy and avoids excessive experimental efforts. 3.2. Effect of working depth and speed on selected cross-section parameters This section is concerned with the regression analysis of selected soil-cross section parameters with the work speed and depth as independent factors. All cross-section measurements were performed with a longitudinal resolution of 50 mm according to the procedure described in Section 3.1. The tillage was performed at 5, 10, 15, 20 cm work depths and 4, 7, 10, 13 km h1 1 speeds. Due to presence of autocorrelation in soil cross-section parameter samples, confidence intervals of the sample mean were computed following the methodology of effective number of observations (Zie˛ba and Ramza, 2011). The effective number of observations is a quantity that reflects the effect of autocorrelation on confidence bounds, and depends on the sample ACF and number of observations n as follows: n neff ¼ P c ; (3) 1 þ 2 nk¼1 ð1ðk=nÞÞRxx ½k ˆ
Fig. 10. ACF estimates of the soil cross-section parameters with 5 mm longitudinal resolution.
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where Rxx ½k is the kth value of the ACF estimate, nc is the index of ˆ Rxx where it first crosses zero. The sample dispersion s2 is estimated ˆ ˆ by: n X neff s2 ¼ ðx xÞ; ˆ nðneff 1Þ k¼1 k ¯
(4)
where xk is the kth measurement of a soil cross-section parameter x, and x is the sample mean. Consequently, Student t-distribution ¯ with neff degrees of freedom at a significance level of 5% was used to compute confidence intervals. The ridge heights were averaged to one parameter RH. Fig. 11 illustrates the effects of the work speed and depth on the selected soil cross-section parameters. To quantitatively assess the influence of the work speed and depth on soil roughness after tillage with a heavy duty tine, the selected soil cross-section parameters were approximated with different models up to the second order including interaction terms. All models been tested with F-test with a significance level of [(Fig._1)TD$IG] 5%. The models were compared in terms of correlation with the
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measured data and model complexity, i.e., the number of model parameters. The R2-coefficient was at least 80%. Higher-order terms were dropped if satisfactory correlation could be achieved without them. For furrow height FH, maximal width of soil throw MWT, and ridge-to-ridge distance RRD was achieved with a linear model with one interaction term: Mðv; dÞ ¼ p0 þ pv v þ pd d þ pvd vd;
(5)
where v denotes the work speed, d denotes the work depth and p0 ; pv ; pd ; pvd are the model parameters. In the regression models for the area parameters Af, Ar, and Aa, as well as ridge height RH, satisfactory correlation was obtained without the interaction term pvd vd. All regression coefficients were tested using t-test with a significance level of 5%. Fig. 12 illustrates modeling accuracy of the selected soil cross-section parameters along with the R2-coefficients. In Table 1, the model parameters are summarized. Coefficients with p-values less than 0.05 are marked bold. Notice that constant
Fig. 11. Effect of working speed and depth on soil cross-section parameters FH, RH, RRD, MWT, Af, Ar, Aa. Error bars indicate 95%-confidence bounds. Trend lines are displayed for visibility.
[(Fig._12)TD$IG]
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Fig. 12. Soil cross-section parameter approximation along with the R2-coefficients.
Table 1 Soil cross-section parameter models. The coefficients are given along with 95%confidence bounds (in parentheses). Significant coefficients are marked bold. FH
RH
p0 pd pv pdv
0.41 (0.56, 0.26) 0.05 (0.06, 0.04) 0.82 (0.80, 0.84) 0.016 (0.01, 0.017)
2.12 (1.39, 2.86) 0.24 (0.21, 0.28) 0.10 (0.16, 0.04)
RRD
MWT
p0 pd pv pdv
7.77 (27.58, 12.04) 1.39 (0.06, 2.84) 6.28 (4.12, 8.45) 0.16 (0.31, 0)
2.15 (32.28, 36.57) 1.71 (0.80, 4.23) 9.83 (6.06, 13.59) 0.01 (0.29, 0.26)
p0 pd pv
Af
Ar
18.95 (102.03, 64.12) 16.50 (12.29, 20.72) 5.29 (12.32, 1.73)
70.53 (114.12, 26.95) 10.58 (8.37, 12.79) 11.82 (8.13, 15.51)
Aa p0 pd pv
35.65 (62.79, 8.52) 2.21 (0.83, 3.58) 7.62 (5.33, 9.92)
terms highlight the effects that were not captured by the experiment. The following conclusions were made from the analysis of the results and modeling. The furrow height FH weakly correlates with the set up tillage depth as expected while the effect of the speed is stronger. At higher speeds, the furrow height became larger and this effect increases when the tillage depth is higher. Increase of the furrow height with increase of the tillage depth and speed was also observed for shovel and sweep tools (Shinde et al., 2011). An opposite effect was observed for the ridge height RH. There is a weak correlation between RH and the work speed in comparison to the effect of the set up depth. Indeed, larger tillage depths lead to larger volumes of soil being displaced by the tool. The soil disturbance, as characterized by the ridge-to-ridge distance RRD and the maximal width of soil throw MWT, was greater at higher speed while the effect of the set up depth stayed minor. Physically, the volume of soil being displaced by the tool increased with the work depth. This led to different ridge heights at different depths. The distance between the ridges RRD and the maximum width of soil throw MWT, on the other hand, are more sensitive to the different work speeds. The ridges stayed practically uninfluenced
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Table 2 Sample mean of selected soil cross-section parameters obtained with longitudinal resolution of 50 mm. The work depth and speed are in cm and km h1 respectively. The parameters furrow height FH, left ridge height RHL, right ridge height RHR, ridge-to-ridge distance RRD, width of soil throw MWT are in cm, and the areas Af, Ar, Aa – in cm2. Depth
Speed
FH
RH
RRD
MWT
Af
Ar
Aa
5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20
4 4 4 4 7 7 7 7 10 10 10 10 13 13 13 13
2.6 2.3 2.5 3.5 4.1 5.0 5.0 4.3 4.6 7.7 6.5 6.4 4.8 7.4 8.5 7.3
2.9 3.5 5.6 6.4 2.9 4.0 5.6 6.0 2.1 4.2 5.2 5.6 1.8 3.0 4.2 6.0
23.3 31.7 30.3 30.9 32.2 36.4 41.0 41.4 43.9 56.5 59.5 45.8 72.3 73.0 68.8 57.6
48.4 59.2 68.1 70.4 78.5 91.9 97.0 101.9 92.1 118.2 147.7 120.0 137.9 148.9 154.9 154.2
57.5 75.9 233.6 350.4 23.5 96.5 156.7 274.3 29.4 48.9 143.1 258.2 76.0 67.1 96.2 290.1
49.9 75.5 137.8 167.2 75.6 122.0 189.2 186.6 77.8 181.7 232.3 252.7 102.9 177.1 243.3 322.7
17.5 13.7 19.5 31.6 34.3 51.1 54.3 38.4 42.8 84.9 81.2 91.6 46.5 78.7 105.3 115.9
by the working depth and shifted to the sides as the working speed increased. This was also observed from the behavior of the areas Af, Ar and Aa. The furrow area Af had stronger correlation with the working depth than with the speed which is physically evident. Distribution of the loosened soil to the sides from the furrow is characterized by Ar. It is affected by both the working depth and work speed. The working depth influenced the amount of compacted soil that is eventually loosened. Increased working speeds led to a wider distribution of soil out of the furrow to the sides. This correlation was found in the regression model for Af and the corresponding in Aa as well. The observed increase of RRD and MWT, as the working speed increased, correlates with the results by Liu (2005) for a sweep tool. Hasimu and Chen (2014) observed similar behaviors of RH, MWT and Af as work depth increased, with seed openers as the tool. The general conclusion can be drawn that the volume of distributed soil is mainly influenced by working depth and speed. It was also indicated by Shinde et al. (2011) for a shovel tool. Table 2 gives numeric values of the sample mean of the selected soil cross-section parameters corresponding to different tillage conditions. 3.3. Discussion on spectral analysis The current study was limited to one soil type, and a practically satisfactory longitudinal resolution was the subject of spectral analysis. It should be pointed out that choosing a frequency that captures all significant frequency components of a physical process is subjective in general. Eventually, it is up to the user to find a compromise between capturing possibly many soil surface details and saving time and labor resources. PSD estimates should help understand the physical process in question better than such metrics as mean and standard deviation alone. One possible automation routine may involve computing a resolution based on PSD threshold or PSD integral threshold. Another subject, that needs further investigation, is spectral analysis of cross-sections of different soil types under different moisture condition and after different tillage implements. Characterizing soil roughness by PSD estimates of cross-section parameters may be also an interesting topic in its own right. 4. Conclusions In this study, analysis of power spectral density estimates was suggested in order to choose an appropriate cross-section measurement resolution along the tillage direction and to avoid inaccuracies of picking several cross-sections at random positions
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