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a Dep. of Geological Sciences, Univ. of Tennessee, Knoxville, TN 37996-1410
b Département des Sols et de Génie agro-alimentaire, Université Laval, Pavillon Comtois, Sainte-Foy, PQ, Canada G1K 7P4
* Corresponding author (eperfect{at}utk.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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), bulk density (
b) and total C (TC) in the upper 10 cm of long-term conventional-till (CT) and no-till (NT) soil management practices at Lexington, KY. The soil was a Maury silt loam (fine, mixed, semiactive, mesic Typic Paleudalf). Replicate transects were established in untracked interrows parallel to the direction of tillage in the CT practice. Each transect was 48.5 m long with 107 equally spaced sampling points. Soil spatial variability was higher under NT than under CT. Spectral analyses of variance identified significant differences between tillage treatments at frequencies <0.02 cycles m-1 for all soil properties, and at 0.18 cycles m-1 for w, 0.13, 0.31 and 0.48 cycles m-1 for , and 0.22, 0.70 and 0.90 cycles m-1 for b. Spatial variations in water content and b appeared to be related to the distribution of TC. Coherency analysis indicated relationships were strongest at frequencies <0.09 cycles m-1. For NT the relationship between w and TC was also significant at higher frequencies (1.01–1.05 cycles m-1). Gravimetric water content increased as TC increased, while and b decreased. Lagged relations for w versus TC were more frequent in CT than NT, possibly due to soil translocation during tillage operations. The opposite was true for versus TC and b versus TC, suggesting that soil aggregates form at some distance from sites of carbon deposition under NT.
Abbreviations: CT, conventional tillage soil management practice • CV, coefficient of variation • DFT, discrete Fourier transform • NT, no-till soil management practice • TC, total C content • TDR, time domain reflectometry • w, gravimetric water content • , volumetric water content • b, bulk density
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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To explain differences in crop yields when nutrient inputs are similar, researchers have often investigated tillage treatment effects on soil physical properties. Because of their residue cover, no-till soils conserve soil moisture, resulting in increased water contents early in the growing season as compared with moldboard plowed soils (Blevins et al., 1971; Zhai et al., 1990). Bulk densities often increase with depth in the surface horizons of no-till soils (Gantzer and Blake, 1978; Hill, 1990). In contrast, bulk densities under CT are relatively constant with depth, until they experience a step increase at the base of the plow layer. No-till has been shown to increase saturated hydraulic conductivity because of the presence of continuous macropores, and increase the amount of soil water that is retained at tensions greater than those required for gravity drainage (Ehlers, 1975; Hill and Cruse, 1985). Tillage-induced differences in soil mechanical (Hill, 1990) and thermal (Johnson and Lowery, 1985) properties have also been reported.
Soil physical properties that are randomly distributed can be characterized in terms of their mean and variance. Tillage studies have traditionally focused on mean effects, with differences between treatments analyzed by comparison of means using randomized block experimental designs (Hill, 1990). Soil spatial variability is often cited as a cause of nonsignificant mean differences in such studies (e.g., Bhatti et al., 1991).
Many spatially variable soil physical properties are not randomly distributed but are regionalized variables, that is, observations located close to one another tend to exhibit behavior more similar to their neighbors than those located further apart (Gajem et al., 1981; Viera et al., 1983). Because their error terms are correlated, such variables violate the assumptions of classical ANOVA and regression techniques. As a result, geostatistics and time-space series analysis have been developed specifically to handle regionalized variables (Shumway, 1988; Burrough, 1993; Goovaerts, 1999). These statistical techniques have been widely used to analyze the spatial variability of soil properties within uniformly managed fields (e.g., Nielsen et al., 1983; Shumway et al., 1989; Kachanoski et al., 1985; Timlin et al., 1998). However, relatively few studies have compared different management practices in terms of their spatial variability.
Roseburg and McCoy (1988) applied time series analysis to surface roughness measurements collected along transects oriented perpendicular to NT, minimum-till, and CT treatments. Tillage effects were inferred from valleys in the power spectra, which occurred at frequencies corresponding to the width of the imposed treatments. Tsegaye and Hill (1998) employed geostatistical methods to evaluate tillage effects on the spatial variability of particle-size distribution, bulk density, water retention, saturated hydraulic conductivity, and penetration resistance. They found that scale dependency increased with increasing soil depth and decreased with increasing tillage intensity.
Time-space series analysis provides a method, referred to as analysis of power or spectral ANOVA, for comparing the variance of transect data collected within applied treatments in the frequency domain (Brillinger, 1981; Shumway, 1988). The approach partitions the variance of each time-space series within a treatment as a function of frequency using discrete Fourier transforms, and performs treatment comparisons by analysis of the transforms obtained at different frequencies. This is very similar to polynomial contrasts in classical ANOVA, where the spatial variance within a treatment is broken down as a function of the polynomial degree, and the common error variance is partitioned into scale dependent error variance components (Rowell and Walters, 1976). In the spectral approach, however, the spatial signals are described using Fourier frequencies and the spatial variance is broken down as a function of a fitted spatial frequency instead of a fitted polynomial degree.
The frequency domain approach to ANOVA is particularly appropriate for scale- dependent processes and out of phase relationships (Tremblay, 1999). It can also be extended to investigate classical regression relationships. To our knowledge, it has not been previously applied to analyze soil physical data obtained from tillage experiments.
Collecting information on tillage-induced differences in soil spatial variability is relevant for both practical and scientific reasons. The practical reasons come mainly from an increased interest in issues of scale driven by developments in precision agriculture. Knowledge of spatial variation in yield-influencing properties can help define appropriate management scales (Sadler, 1998). For example, differences in the spatial structure of soil matric potentials might imply a modification of the positioning of tensiometers for system control in irrigated agriculture. Alternatively, it may provide useful information for assessing the risk of leaching under different cropping systems (e.g., Mallawatantri and Mulla, 1996). The scientific interest derives from a desire to identify key processes based on the variability they produce; for example, the spatial distribution of primary particles is often used to infer mechanisms involved in the transport of soil parent materials (Brady and Weil, 1999). From a statistical viewpoint, our ability to detect differences between treatments and the efficiency of future sampling strategies are improved when spatial structure is taken into account (O'Halloran et al., 1985; López and Arrúe, 1995).
The objectives of this research were to: (i) describe the spatial variability of soil water content, b, and TC under long-term CT and NT practices using time-space series analysis; (ii) employ spectral ANOVA to identify the spatial periods at which tillage-induced differences in these properties were most pronounced; and (iii) investigate the scale dependency of relations among water content, b, and TC within each tillage treatment.
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MATERIALS AND METHODS |
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Sampling for soil water content and b took place on two consecutive days in early May 1996 prior to spring tillage in the CT treatment. Linear transects were established along untracked interrows in the center of the first three replications of both tillage treatments. This resulted in six transects spaced 5.5 m apart from each other. Each transect was 48.5 m long with 107 equally spaced (0.46 m lag) sampling locations (i.e., a total of 642 points). The transects were oriented parallel to the historical pattern of tillage in the CT treatment, and passed through all of the eight fertilizer x cover crop sub-subplots.
The volumetric water content of the 0- to 10-cm soil layer was measured nondestructively at each sampling location using time domain reflectometry (TDR). Crop residues were brushed aside prior to sampling. A 10-cm long coaxial hand probe with seven 2-mm diam. rods (Heimovaara, 1994) was pushed vertically into the soil. A Tektronix 1502C metallic TDR unit (Tektronix, Inc., Beaverton, OR) connected to the hand probe was used to measure the apparent dielectric constant. The Topp et al. (1980) equation was used to convert these measurements into values of . The hand probe was then removed and a 1.8-cm diam. tube sampler was used to obtain 10-cm long soil cores from exactly the same locations where the TDR measurements were made. These disturbed samples were sealed in plastic bags and transported to the laboratory, where they were analyzed for w using the oven drying method (Gardner, 1986). Soil bulk density was calculated using the relationship b = w/w, where w is the density of water, which was assumed to be equal to 1 g cm-3.
Sampling for TC took place in mid May, immediately following primary and secondary tillage operations in the CT plots. The six transects were reestablished, crop residues were brushed aside, and soil was collected from the 0- to 10-cm layer at the same sampling locations as before using a 5.4-cm diam. core sampler. In the laboratory, samples were air-dried, subsampled and ground to pass a 250-µm sieve. The sieved soil was analyzed for TC content by the dry combustion method using a LECO automatic C analyzer (Nelson and Sommers, 1982).
Data for the individual transects were first summarized in terms of the means and variances of the tillage treatment main plots. Classical ANOVAs were then performed on the sub-subplot means using ‘PROC GLM’ (SAS Institute, 1988) with a significance level of p < 0.05. The experiment was analyzed as a split-split plot, with tillage as the main plot, cover as the subplot and fertilizer as the sub-subplot. As the subplot error did not differ statistically from the sub-subplot error, data were reanalyzed as a split plot design with tillage as the main plot and N and cover as subplots.
The soil water contents were relatively stable over time during the sampling period because of the absence of rain and low evapotranspiration rates. No significant trends (i.e., linear change in values from one end of the transect to the other) were encountered in any of the transects, so time-space series analyses were performed on the raw data. Fourier transforms (Shumway, 1988) were used to separate out the variance as a function of spatial frequency for each soil property within each transect. Power spectra were estimated using periodograms (Shumway, 1988) that were computed using ‘PROC SPECTRA’ (SAS institute, 1991). No smoothing was done. Our use of the frequency domain approach with these data was validated by the fact that all but one of the 24 individual periodograms (six transects x four soil properties) were significantly different from white noise at p < 0.05 according to Fisher-Kappa or Kolmogorov-Smirnov tests (SAS Institue, 1991). For graphical presentation the individual periodograms were arithmetically averaged for each tillage treatment.
A spectral ANOVA was performed for each variable based on the individual periodograms (Brillinger, 1981; Shumway, 1988). The input for the ANOVA was the discrete Fourier transform (DFT) of the data. A total of 53 DFTs (corresponding to 53 frequencies) were generated for each transect. Each DFT represents the contribution of a sine and cosine function of a given frequency that matches the transect data. Since these are complex numbers, the complex conjugate (the reciprocal function of the DFT) was employed in the ANOVAs. The analyses were performed for all 53 frequencies using Mathcad Release 7 (Mathsoft, Cambridge, MA). Following Shumway (1988), we computed the degrees of freedom for the Fourier transformed data as twice those for tillage and rep in the classical ANOVA's reported in Table 2.
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Lagged regression models were generated for each transect using a fast Fourier transform algorithm and transfer functions before being averaged by tillage treatment. All calculations were performed with the ASTSA program (Shumway and Stoffer, 2000). A five-point moving average process was employed (three- and seven-point moving averages gave similar spectral and transfer function estimates). The transfer function estimates were compared with those obtained by spectral analysis to verify their consistency. Confidence intervals were computed for one regression parameter at a time according to Shumway (1988). Average confidence intervals for all three replications in a tillage treatment were then used to assess the significance of the lagged regression models.
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RESULTS AND DISCUSSION |
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, and TC were consistently lower at the time of sampling under CT as compared with NT, whereas b was higher. These observations are consistent with previous studies conducted at this site (Blevins, 1971, Ismail et al., 1994). Classical ANOVAs, used for separating out mean effects, are reported in Table 2. Tillage treatment followed by rate of N-fertilizer application were the most important main factors influencing w, , and TC, whereas b was only influenced by N rate. The magnitude of the fertilizer effect on b was somewhat surprising. Tiarks et al. (1974) and Sommerfeldt and Chang (1985) reported decreasing b with increasing rate of manure application. However, we are unaware of any studies showing a similar effect for inorganic fertilizers. Type of cover crop was only marginally significant in the case of TC (Table 2).
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, p < 0.002 for b, and p < 0.040 for TC. The observation that soil spatial variability was higher under NT than under CT is consistent with the homogenizing effect of CT operations. Average periodograms for the two tillage treatments are presented in Fig. 2 . Spatial variability, as signified by larger values of the periodogram ordinates, was always greater between plots (i.e., at frequencies <0.16 cycles m-1 or spatial periods >6.25 m) than within plots. This is to be expected because of the imposed N fertilizer and cover crop treatments represented within each transect. The area under the curve of the periodogram is directly related to the variance (Shumway, 1988). This quantity was always greater for the no-till system than for the tilled system, which is consistent with our conclusions regarding the CVs. The greatest differences because of tillage history were observed for w and TC (Fig. 2a,d). For these variables, the periodogram ordinates for NT were consistently greater than those for CT regardless of frequency.
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transect length) for all four soil properties. In addition to these large-scale effects, significant differences were also found between the tillage treatments at higher frequencies in the case of w, , and b (Fig. 3). A significant difference in the spatial variability of w was found at 0.18 cycles m-1 (5.6 m). For , significant differences occurred at 0.13, 0.31, and 0.48 cycles m-1 (7.7, 3.2, and 2.1 m, respectively) while for b significant differences were observed at 0.22, 0.70, and 0.90 cycles m-1 (4.5, 1.4, and 1.1 m, respectively).
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and b are unclear, but may be related to lateral traffic patterns (caused by liming), preserved under NT and eliminated by plowing and disking in the CT transects. What are the advantages of spectral ANOVA as compared with more traditional statistical approaches? Because of spatial structures in the raw data, classical ANOVAs could only be performed on summary statistics (means and CVs). Comparison of means techniques are normally employed to identify significant differences between treatment means. However, they can also be used to compare treatment-induced differences in variability, as was done with the CVs in Table 1. Those analyses, which required all of the available observations, identified significant differences in variability between NT and CT (at p < 0.05) for three out of the four soil properties investigated; the variation in w under NT was not statistically different from that under CT using this approach. In contrast, spectral ANOVAs, based on the same number of observations, found significant differences in variability between tillage treatments (again at p < 0.05) for all four soil properties. Furthermore, this approach also identified the spatial periods at which those differences in variability were most pronounced (e.g., the transect- and plot-scales in the case of w). This additional information and the method's greater sensitivity to tillage-induced differences in soil spatial variability are strong endorsements for the spectral ANOVA approach.
Based on the periodograms (see above), the fluctuations in w, , and b observed along the transects (see Fig. 1) are not random. Instead, they are most likely the result of spatial variation in other properties with which they are correlated. Management-induced changes in soil C content are an obvious possible causal factor in this context. Therefore, coherency and lagged regression analyses were employed to investigate the nature of the relationship between soil physical properties and TC.
The averaged results of the coherency analyses are presented in Fig. 4 . Values of the squared coherency were generally only significant at low frequencies (<0.09 cycles m-1 or >11.1 m). This observation suggests that large-scale changes in soil organic matter, probably associated with the imposed fertilizer and cover crop treatments (spatial period = 6.1 m), were mainly responsible for the observed relations between TC and soil physical properties.
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versus TC (Fig. 4b) and b versus TC (Fig. 4c), the squared coherencies at low frequencies were greater for NT than for CT. This trend indicates a stronger relationship between soil physical properties and TC in the absence of plowing at the plot scale. It may be related to the movement and mixing of TC under CT as compared with NT.
The results of the lagged regression analyses are summarized in Table 3. The slope estimates for zero lag correspond to the standard linear regression case. The positive and negative slopes indicate that w increased as TC increased, while b decreased. Since = wb/w, and w is a constant, these opposing trends probably offset one another resulting in the nonsignificant relations observed between versus TC at zero lag (Table 3). The increase in w with increasing C is probably due to improved water retention. Biswas and Ali (1969) and Hudson (1994) showed that water retention is enhanced by the presence of TC regardless of matric potential. The negative relationship between b versus TC is also well known (e.g., Curtis and Post, 1964; Adams, 1973), and can be attributed to a combination of increased aggregation and decreased b (because of the lower density of organic matter relative to mineral particles) with the addition of TC.
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(Table 3). These relations suggest that longitudinal variations in TC because of differences in N-fertilizer rate and cover crop were much greater than any vertical trends (i.e., C was relatively uniformly distributed with depth under CT).
Lagged relations for w versus TC were more frequent in CT than in NT (Table 3); soil movement during plowing and disking may explain this observation. In contrast, lagging was more important in NT than in CT for b versus TC and versus TC. However, the slopes were generally greater for CT relative to NT indicating greater sensitivity of b and to changes in TC within the tilled plots. The lagged relations for b versus TC under NT indicate that changes in bulk density can occur at some distance from sites of soil C accumulation. This observation favors increased soil aggregation (associated with mobile water soluble organic compounds) over decreased b (because of the lower density of organic matter relative to mineral particles) as the most likely explanation of the inverse relationship between b and TC.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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, b, and TC, were much greater under NT relative to CT. The coefficients of variation for these properties were up to 2.6 times higher for the NT transects as compared with the CT transects. This observation is consistent with the homogenizing effect of CT, and suggests that more samples will be needed to identify mean effects in long-term NT soils than in CT soils.
Periodograms indicated that large-scale sources of variability (driven by the randomized N-fertilizer rate and cover crop treatments represented within each transect) were more important than small-scale variations (i.e., fluctuations within the plots). As a result, spectral ANOVAs identified significant differences in spatial variability between CT and NT at frequencies <0.02 cycles m-1 (periods transect length) for all of the soil properties investigated. Significant differences in spatial variability were also found between the tillage treatments at higher frequencies in the case of w, , and b. These differences could be related to the plot spacing or to the presence of antecedent traffic patterns in NT.
Coherency and lagged regression analyses indicated that fluctuations in water content and b were related to the spatial variation in TC along the transects. Squared coherencies were generally highest at the transect scale, although the relationship between w and TC under NT was also significant at a spatial period 1 m. The later observation suggests that small-scale fluctuations in TC, possibly related to the patchy distribution of crop residues, may be important in determining the spatial distribution of w under NT. Gravimetric water content increased as TC increased, while and b decreased. Lagged relationships for w versus TC were more frequent in CT than NT, possibly because of soil translocation by plowing and disking. The opposite was true for versus TC and b versus TC, suggesting that changes in soil b occur at some distance from sites of TC deposition under NT.
Our results demonstrate the benefits of using time-space series analysis to study the variance and covariance structure in transect data. Significant spatial periodicities and lagged relationships were clearly identified for all of the soil properties investigated. The present study is limited in that only a single-sampling time was considered. Thus, the spatial relationships observed might be more or less pronounced when sampled at other times. This possibility invites further research into the temporal stability of tillage-induced differences in soil spatial variability.
Received for publication June 4, 2001.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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