Starr 2005

Agricultural Water Management 72 (2005) 223–243 www.elsevier.com/locate/agwat

Assessing temporal stability and spatial variability of soil water patterns with implications for precision water management$ G.C. Starr* USDA-ARS-NEPSWL University of Maine, Orono, ME 04469, USA Accepted 3 September 2004

Abstract The temporal stability of soil water content patterns may have profound implications for precision agriculture in general and water management in particular. Spatio-temporal variability in soil water was assessed over four fields in a two-year potato (Solanum tuberosum L.) and barley (Hordeum vulgare L.) rotation to determine the potato yield implications and the potential for precision water management based on a stable spatial pattern of soil water. A hammer-driven time domain reflectometry probe was used to measure soil water content repeatedly along 10 transects. Irrigated, un-irrigated, and late irrigated treatments were employed. The temporally stable soil water pattern was mapped and compared with elevation and soil particle size classifications. A temporal stability model explained 47% of the observed variability in soil water content. An additional 20% of the variability was attributed to random measurement error. Calibrated in 2002, the model predicted water content (root mean square error of 0.05 m3 m
3) along transects in 2003 from a single measurement at the field edge. Field-scale trends and extended (>100 m) wet and dry segments were observed along transects. Coarser particle size class soils were generally drier. Potato yield increased linearly with water content in un-irrigated areas. Yield was comparatively high in the drier areas for the irrigated treatment but was highly variable and frequently poor in the wetter areas. For the late-irrigated treatment, a strong yield response to added water was evident in the dry areas; however, the yield response was neutral to negative in the wetter areas. Knowledge

$ Mention of trade names or commercial products in this article is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture. * Tel.: +1 207 581 3304; fax: +1 207 866 0464. E-mail address: [email protected].

0378-3774/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.agwat.2004.09.020

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of the underlying stable soil water distribution could provide a useful basis for precision water management. Published by Elsevier B.V. Keywords: Soil; Water; Potato; Irrigation; Variability; Precision agriculture

1. Introduction It is well established that soil water content in a field varies over time and location. It is often the case that the pattern of spatial variability is much more stable in time than would be expected from random processes (Vachaud et al., 1985; Kachanoski and De Jong, 1988; Jaynes and Hunsaker, 1989; Zhai et al., 1990; Goovaerts and Chiang, 1993; Comegna and Basile, 1994; Tomer and Anderson, 1995; Pires da Silva et al., 2001). The stable pattern of spatial variability has been correlated with relatively stable properties such as topography and soil particle size class. Vachaud et al. (1985) pointed to the role of soil particle size in explaining the first reported observation of soil water temporal stability. Tomer and Anderson (1995) found that 51–77% of spatial variability in soil water content could be explained by a combination of elevation, slope, and curvature in a sandy hill slope. Pires da Silva et al. (2001) found that clay content, C content, and tillage method influenced soil water storage patterns. Temporal stability has been widely reported on a field scale where vegetation and tillage methods are consistent. However, several processes can disrupt temporal stability. The relevant processes depend on the spatial and temporal scale of the observations. On a small scale, such as a crop row cross-section, temporal instability over a wet to dry cycle can be expected because of such processes as stem flow, canopy interception, compaction, and uneven drying rates (Van Wesenbeeck and Kachanoski, 1988; Saffigna et al., 1976). On an intermediate scale, runoff events and uneven infiltration can disrupt temporal stability during wet periods. Kachanoski and De Jong (1988) found that spatial variability in soil water was induced during recharge rather than drying. Western et al. (1998) documented a seasonal evolution of soil water patterns that was related to lateral redistribution of moisture during the wet season. Lateral redistribution tends to increase spatial variability so that wet periods with runoff events have higher variability than dry periods (Famiglietti et al., 1998; Western et al., 1998). On a larger scale in a semi-arid environment, changes in vegetation lead to temporal instability (Gomez-Plaza et al., 2004). Particularly at larger scales, the intensive sampling required to adequately characterize spatio-temporal variability (Famiglietti et al., 1998; Western et al., 1998) has hindered many research studies. Soil water content and matric potential measurements have long been used for scheduling irrigation in virtually all crops including potato. Spatial variability of soil water presents a significant challenge for irrigation scheduling because of the difficulty in obtaining measurements representative of the field average (Van Pelt and Wierenga, 2001). Effective site-specific management of soil water through irrigation is possible provided an adequate yield response can be demonstrated and the zones of management are comparable in size to the correlation distance of soil water variability (Wheelan and McBratney, 2000). Although this implies that a fairly high-spatial resolution soil water survey will be required, temporal stability means that the soil water pattern may be determined with very few sample dates.

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It is anticipated that soil water storage will vary dramatically across the rolling landscapes of the potato-producing region in north-central Maine, but that the pattern will be consistent over time. If a uniform pattern of irrigation water is applied to meet the requirements of the driest part of a field, excess water will be applied to the wetter areas. This will be particularly problematic in a humid region such as Maine where excess rainfall can lead to potato yield reduction (Benoit and Grant, 1985). Potato producers in the region frequently need to circumnavigate field areas that are too wet to be cropped. Farmers in the process of implementing irrigation systems are faced with the question of which fields and areas to irrigate given limited water resources. Using the temporally stable pattern of soil water content as a basis for precision farm management is an approach that has received little attention in the literature. It is conceivable that a spatially variable but temporally stable irrigation water application pattern can be prescribed (given the fixed soil water pattern) leading to savings in energy, water, equipment cost, labor, and improved production efficiency. Therefore, the objective of this study was to characterize the spatiotemporal variability of soil water content during the growing season and evaluate the potato yield implications of the temporally stable pattern. Particular emphasis was placed on evaluating the potential for precision water management.

2. Materials and methods The study site was located near Houlton, Maine (longitude
67.898, latitude 46.168) on a commercial potato farm. It is characterized by gently rolling terrain and gravelly sandy loam (Sandy-skeletal, mixed, frigid Typic Haplorthod), gravelly loam (Coarse-loamy, mixed, frigid Typic Haplorthod), shaly silt loam (Loamy-skeletal, mixed frigid Typic Haplorthod), and silt loam (Coarse-loamy, mixed, frigid Aquic Haplorthod) soils. An overhead photo overlain with an elevation contour map (Fig. 1a) shows the partitioning of the study area into four fields with 10 transects. The elevation data were obtained from the Maine office of geographic information systems (GIS), Augusta, Maine, USA. These fields are farmed in a potato-barley 2-year rotation. In the first year of the study (2002), fields A and B were cropped to potato, fields C and D to barley. Within each field, local topography is evident, but there is a gradual trend of decreasing elevation from west to east over the study area, particularly fields B and C. The same photo overlain with the soil classifications (Fig. 1b) depicts the different soil types occurring in each field. The dominant soil in field A is Caribou gravelly loam with lesser amounts of Conant, Monarda, and Burnham silt loams and Mapleton shaly silt loam. Fields B and C were almost entirely silt loam, dominated by Mapleton shaly silt loam with lesser amounts of Conant silt loam. Field D has about equal amounts of Caribou gravelly loam and Coulton gravelly sandy loam, with lesser amounts of Conant, Monarda, and Burnham silt loams. The irrigation system used is a mobile gun and reel design whereby the gun is pulled across a field by a hose that is taken up by a reel. Varying irrigation rates along transects traversed by the gun would be quite feasible; however, for this study uniform applications were used. The system, although commonly used in the region, is not highly efficient and is laborious to move. Thus, farmers tend to use infrequent irrigation schedules with relatively heavy applications. Three water management regimes were employed. The first (termed

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Fig. 1. Study site located on a commercial potato farm near Houlton, Maine showing: (a) elevations, sampling points, and fields; (b) soil classifications.

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irrigated) had irrigation applications throughout the growing season (roughly 2.5 cm of water applied on four dates in 2002 and on a single date in 2003). The second (termed lateirrigated) had applications toward the end of the growing season (late August and early September, 2.5 cm applied on three dates in 2002 and one date in 2003). The third treatment was no irrigation (termed un-irrigated). Barley was un-irrigated in both years. The potato transects in 2002 (T1–T6) were cropped to either Russet Burbank (T2–T6) or Red Norland (T1) variety potatoes. In 2002, T1–T2 were irrigated, T5–T6 were lateirrigated, and all other transects were un-irrigated. In 2003, T7 and T8 were cropped to Frito Lay 1533 variety and late-irrigated, T9 and T10 to Red Norland and irrigated. Yield samples were collected for each sample point for the Russet Burbank and Frito Lay 1533 varieties but not the Red Norland. Following windrowing of four rows of potatoes, yield samples were collected by hand from the equivalent of 3 m of row and total yield determined by first washing, then weighing the sample. Soil water content was measured using the time domain reflectometry (TDR) method (Topp et al., 1980) and a hammer-driven probe (obtained from Soil Moisture Equipment Corp., Santa Barbara, CA). The basic measurement is similar to that of other large-scale studies (Western et al., 1998; Green and Erskine, 2004). The probe was driven vertically 30 cm through the center of potato hills or through the soil surface in barley. Transects were laid out parallel to the potato rows and parallel to the travel of the irrigation unit. Making measurements at the same point repeatedly might not be representative of the management area because some rows experience more compaction from wheel traffic than others. For this reason, a random number between
6 and +6 was chosen prior to each sample date and the sample row was offset by that number of rows from a central sample point (row separation was 0.9 m). Transects were sampled at 30 m intervals repeatedly throughout the growing season of 2002. The number of 30 m samplings varied between 5 and 9 per transect in 2002. A smaller number of 30 m samplings (3–4) were obtained for the potato transects in 2003. In 2003, three transects in potato (T7, the eastern half of T8, and T9) were sampled with a single high-resolution (6 m) survey. The measurement process was time consuming and laborious, and needed to be completed before the soil dried appreciably for the sampling to be representative of a single point in time. A single transect (30 m survey) could be measured in about an hour. Thus, analysis of temporal stability and spatial variability was undertaken for each transect, separately. Yields were plotted against season average water content to determine what, if any, influence the water pattern had on yield. The implications of increasing or decreasing water content via precision irrigation were then inferred by assessing the yield effect of a shift along the water content axis for the various treatments for a given potato cultivar. 3. Assessing temporal stability and spatial variability Vachaud et al. (1985) scaled the deviations from the field mean or expected water storage at a point, j, on each sample date as: dt ðjÞ ¼

St ðjÞ
hSt ðjÞi hSt ðjÞi

(1)

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where dt(j) is the scaled deviation at time, t. St(j) is the observed value of cumulative water storage, and hSt ðjÞi is the expected or mean value of soil water storage. When the deviations were scaled by the mean, they were found to be roughly constant for each point over time (hence the term temporal stability). An issue with applying the aforementioned approach in our experiments is that the soil water storage to a given depth is not particularly well defined. A probe was driven in vertically through the center of a potato hill to 30 cm and that does not translate into 30 cm of water storage across the field because the field was not flat. Therefore, it was decided to reformulate the problem using the volumetric water content, uv, and its scaled values. For a given study area with a perfectly stable water pattern that varies temporally only by scaling the means, one can deduce: uðt; jÞ ¼ rðjÞ huðt; jÞij

(2)

where u(t, j) is the measured value at time t and position j, r(j) is a time independent scaling factor defined for each point j, and huðt; jÞij is the mean value of water content at a given time averaged over locations. A value of r(j) greater than one indicates a relatively wet point, less than one is relatively dry, and equal to one is the mean. Eq. (2) describes the spatial variability in a field with perfect temporal stability in the sense defined by Vachaud et al. (1985). However, this perfect stability can be upset by a wide variety of processes that require an extra term in the equation to fit a more general situation: ut ðjÞ ¼ rðjÞ þ eðt; jÞ ¼ sðt; jÞ hut ðjÞij

(3)

where s(t, j) is the scaled value (depending on both time and location), and e(t, j) is an additional term that accounts for random measurement errors, random sampling variability, and any true deviations from time stability. The e(t, j) could depend on the field average water content; however, it will be useful to assume that it does not depend on the constant coefficients r(j). The variance in s(t, j) over space at any given time, gj2[s(t, j)], can then be expressed as: g 2j ½sðt; jÞ ¼ g 2j ½rðjÞ þ g 2j ½eðt; jÞ

(4)

where gj2[r(j)] is the variance in r(j) over location, and gj2[e(t, j)] is the variance in e(t, j) over location. The best estimate of the variances in Eq. (4) is obtained by averaging the calculated variances for each time of observation. The fraction of the variance assessed over location that is explained by the temporal stability model (Eq. (1)) can be expressed as: g 2j ½rðjÞ hg 2j ½sðt; jÞ it

¼ R2s

(5)

where R2s is the average spatial coefficient of determination, and hg 2j ½sðt; jÞ it is the spatial variance averaged over time. In order to calculate R2s , it is necessary to know the r(j) coefficients. To calculate these, it was assumed that e(t, j) has an average value of zero

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(there is an equal probability of a positive or negative value) over time, so that r(j) can be approximated by time average of s(t, j): hsðt; jÞit ¼ rðjÞ

(6)

The r(j) coefficients can then be used to calculate the model prediction of volumetric water content at any point, i, from any other point, j, by the formula: uðt; iÞ ¼

uðt; jÞrðiÞ rðjÞ

(7)

The formula (7) can be used to calculate water content at all spatial points in the study area with a measurement at a single point. This is a useful theoretical result for precision agriculture because a convenient location can be selected for monitoring water content, then water content over entire fields can be estimated. If a spatially biased water application is used that reflects the underlying soil water distribution, this will disrupt the stable pattern of soil water. The water application should be calculated to reduce the spatial variability by applying more water to the drier areas of the field than the wetter areas. The R2s approaches 1 for a pattern of spatial variability that is completely described by Eq. (2), assuming there is no measurement error and no noise signal generated because the measurements were not at exactly the same place each time. The R2s approaches zero when there is no spatial variability explained by the temporal stability model. The R2s is not, however, a good measure of how stable a water content pattern is. Consider a field that is uniform (r(j) = 1, for all j) and completely stable in time. In this case, the R2s will be zero because there is no variance in r(j). Clearly, there is a need for another measure to assess the degree of temporal stability. Consider the variance in s(t, j), gt2[s(t, j)], assessed over time at a given point: g 2t ½sðt; jÞ ¼ g 2t ½eðt; jÞ

(8)

None of this variance is explained by the temporal stability model that has s(t, j) = r(j), a constant over time. However, it is possible to define for each point a coefficient of variability in s(t, j) over time. If this coefficient of variability is averaged for all points, it gives an overall indication of how stable s(t, j) is over time:   s t ½sðt; jÞ CVt ¼ 100 (9) hsðt; jÞit j where CVt is the temporal coefficient of variability expressed as a percentage, st[s(t, j)] is the standard deviation in s(t, j) over time at a point j, hsðt; jÞit is the average in time of s(t, j), and hs t ½sðt; jÞ =hsðt; jÞit ij is the average over spatial locations. The CVt approaches zero for a temporally stable pattern with zero measurement error and no noise signal generated by not measuring at exactly the same place each time. The expected measurement error in this experiment of 0.02 m3 m
3 volumetric water content is not negligible. The measurements were made within the same management location; however, they were deliberately not made at exactly the same point. There is expected to be a non-negligible noise signal from spatial variability on a small scale within the management unit. Thus, it is not expected that Rs will approach 1 or that CVt will approach zero even if the spatial distribution were 100% stable on the scale of interest. The propagation of these errors and their probable affect on Rs and CVt will be discussed in a later section. The scaled volumetric water content

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coefficients, r(j), were calculated from repeated 30 m samplings along transects throughout the growing season of 2002. Based upon the 2002 data, Rs and CVt were evaluated for each transect. A limited number of 30 m surveys were conducted in 2003 and these data were used to validate the model. As a final test of temporal stability, the 2003 trends measured with the 6 m surveys were compared with the trends measured the previous year. Our interest was not only in determining how stable the water content patterns were, but also determining what the underlying pattern of spatial variability was and examining that spatial variability in the context of precision agricultural management. To accomplish this, trends in r(j) were assessed along each transect using standard regression methods. Polynomial trends were shown as significant only when they were significantly (p < 0.05) better than the next lower order polynomial, based on analysis of variance. The variogram, a plot of the semivariance of a pair of data points versus their distance of separation (McBratney and Pringle, 1986) can be used to assess the adequacy of a spatial sampling design for precision agriculture purposes. We had insufficient data for variogram analysis on individual transects with the 30 m samplings. However, the season average water content in 2002 was assessed for each of the 158 sample points and these data were subjected to variogram analysis. Soil water maps were generated using the ordinary Kriging technique and compared with maps of soil type and elevation within fields.

4. Results and discussion A table of summary statistics (Table 1) for 2002 shows that season average water contents for transects ranged from 0.17 to 0.21 m3 m
3 with standard errors averaging 0.006 m3 m
3. As a result of variation in the number of spatial points and number of sample dates, the total number of data points collected in 2002 ranged from a minimum of 24 for T9 to a maximum of 198 for T2. The temporal stability model fit some transects better than others. The percentage of variability explained by the model (calculated as Table 1 Statistical summary of soil water across transects, crops, and irrigation treatments in 2002 Transect

Crop

Irrigation treatment

Soil water average (m3 m
3)

CV (%)

Number sample points

Number sample dates

R2s

CVt (%)

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

Red Norland Russet Burbank Russet Burbank Russet Burbank Russet Burbank Russet Burbank Barley Barley Barley Barley

Irrigated Irrigated Un-irrigated Un-irrigated Irrigated-late Irrigated-late Un-irrigated Un-irrigated Un-irrigated Un-irrigated

0.195 0.176 0.175 0.179 0.197 0.191 0.209 0.204 0.172 0.186

26 32 30 30 30 34 31 27 34 27

20 22 15 9 20 19 19 20 4 7

9 9 7 7 9 8 8 7 6 5

0.36 0.60 0.38 0.26 0.39 0.42 0.31 0.61 0.76 0.60

15 16 18 17 13 18 15 11 17 15

The R2s indicates the fraction of variability explained by the temporal stability model, and CVt indicates the temporal variability of scaled soil water.

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100R2s ) was 26% at the minimum for T4 and a maximum of 76% for T9. On average, the model explained 47% of the observed variability in the data. A random measurement error of 0.02 m3 m
3 for single measurement of water content would explain much of the variance that is not explained by the temporal stability model. Propagation of error analysis can be applied to Eqs. (3) through (5) using the overall season average water content (0.191 m3 m
3) of the study area for the scaling factor in Eq. (3) and the average transect spatial variance (0.056) in scaled values for the denominator in Eq. (5). It is thereby estimated that measurement error would explain around 20% of the observed variability. Thus, between 46 and 96% of the variability in the scaled water content data can be explained by a combination of measurement error and a temporally stable pattern of spatial variability. The temporal coefficient of variability, CVt, in the scaled values was in a range of 11– 18%, with an average of 16%. Propagation of errors for Eqs. (8) and (9) can be used to show that a random measurement error of 0.02 m3 m
3 would give rise to a CVt of 10%. Random error in the measurements undoubtedly contributed heavily to the observed variability. The coefficient of variability in volumetric water content, CV, averaged over all transects was 30%. The process of scaling the means and applying a temporal stability model reduced the CV to 16%. Thus, it may be concluded that the temporal stability model fit the data quite well and the pattern of spatial variability changed little over time. Graphs of the scaled average water content, r(j), versus distance (Fig. 2) show that trends were evident in two of these three transects (Fig. 2b and c). It would be a straightforward process to program the irrigation system to apply water reflecting this pattern. Although the transect T2 showed no long-range trend (Fig. 2a), it exhibited a wet segment of four consecutive above average readings followed by a dry segment with six consecutive below average readings. These wet and dry segments could easily be irrigated differently. Adjacent to the dry segment is a segment with very high-spatial variability. To adequately manage water in a highly variable segment might be possible, but a higher resolution soil water survey would be advantageous to more completely characterize the spatial variability. Data for model validation was collected in 2003 for the four transects T7, T8, T9, and T10 that were cropped to potato (Table 2). The season average water contents were lower than the previous year and the coefficients of variability were comparable or somewhat lower. Average soil water content ranged from 0.172 to 0.209 in T7–T10 in 2002, while in 2003, they ranged from 0.157 to 0.181. The high-resolution surveys in 2003 were conducted on three potato transects (T7, the easterly half of T8, and T9) that were cropped to barley in 2002. The observed trends along transects in 2003 (Fig. 3) were very similar to those measured in 2002 when barley was cropped. There was greater scatter in the single measurement data points for the high-resolution surveys (Fig. 3) than were evident in the season average values for 2002 (Fig. 2). Thus, the coefficients of determination are generally somewhat lower. This is particularly evident in transect T8 where the 2003 trend was so scattered as to be statistically non-significant; however, the regression line was nearly identical to 2002. Transects T7 and T9 showed quadratic trends in both years that were very similar in shape with deviations between the two years being greatest at the ends of the transects where the confidence level in the fitted functions will be at its minimum.

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Fig. 2. Spatial patterns of soil water variability along three transects in 2002 showing: (a) no trend; (b) linear trend; (c) quadratic trend. The error bars indicate standard error approximations calculated for each point using all sample dates.

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Fig. 2. (Continued ).

The similarity in trends for 2002 and 2003 suggest that the temporal stability in the data extend beyond 1 year and the r(j) were substantially the same regardless of whether barley or potato was cropped along a transect. Once known, these trends could certainly be managed by applying more/less water to the dry/wet segments. However, it is not obvious that a polynomial trend is the best model of spatial variability. The residuals in transect T7 (Fig. 2c and Fig. 3a) between 100 and 300 m show a segment below trend followed by a segment above trend suggesting that the actual water content variability was much steeper than the quadratic trend. There is no a priori reason why the pattern should follow longrange polynomial trends. Therefore, the best approach to precision irrigation on a transect scale may be to break transects into segments of manageable size and use an appropriate model for each segment. The 30 m surveys of 2003 were used for validation of the model Eq. (7) that predicts water content at all points along a transect from measurements at a single point. The end of Table 2 Summary statistics for potato transects in 2003 including the number of high-resolution (6 m) and low-resolution (30 m) samplings conducted Transect

Crop

Irrigation treatment

Soil water average (m3 m
3)

CV (%)

30 m surveys

6 m surveys

T7 T8 T9 T10

Frito Lay 1533 Frito Lay 1533 Red Norland Red Norland

Irrigated-late Irrigated-late Irrigated Irrigated

0.181 0.171 0.157 0.166

19.4 24.6 27.9 27.4

3 3 4 4

1 1 1 0

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Fig. 3. Comparison of 2002 trends with 2003 high-resolution survey of spatial variability in scaled water content for: (a) transect T7; (b) transect T8; (c) transect T9.

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Fig. 3. (Continued ).

the row is the most convenient to access so this point was used to predict others along each transect. These predictions will naturally be subject to considerable scatter because of the 0.02 m3 m
3 measurement error. A plot of measured versus modeled water content (Fig. 4) shows that the data were grouped around the line Y = X as would be expected. The regression line through the origin (Y = 1.03X) had a root mean square error (RMSE) of 0.049 and was very close to Y = X. Random measurement error enters both the predicted (based on a single measurement) and the measured (single measurement) axis. Thus, much of the observed scatter would be present even if the model perfectly predicted water content. The model accuracy would be improved if several measurements were made rather than just one. Clearly, the model retains its validity from one year to the next despite the change in crop. Robinson et al. (2002) and literature cited therein shows that the TDR method is insensitive to water held in soil when it is air dry (termed hygroscopic or bound water). Soil-specific calibrations, relative to oven dry gravimetric standards and determination of percent available water, were not attempted nor could they be easily obtained given the intensive sampling requirements. Because hygroscopic water is always present in the field and is unavailable to plants, the application of a generalized calibration equation that is insensitive to hygroscopic water could be advantageous when trying to explain agronomic response to water and irrigation requirements. However, future research is needed to address issues of plant availability of water measured using this method. Both irrigation treatments experienced periods of excess water in 2002 from irrigation applications prior to unpredictably heavy rains. Yield data for 2002 suggest that the effect of season average water content on yield varied with treatment (Fig. 5). Irrigated 2002 Russet Burbank yield versus water content (Fig. 5a) data exhibited relatively consistent and

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Fig. 4. Graph of measured vs. model predicted volumetric water content in 2003. Model predictions are based on a single measurement at the edge of the field.

high yields in the drier parts of the field (below 0.16 m3 m
3) as opposed to the wetter areas. Above 0.16 m3 m
3 the results were very mixed. Fully 58% (seven data points) of the wetter soil data showed yields lower than any data at the dry end. However, three data points in the wet soil yielded comparatively well. The regression line (suggesting a decline in yield with water content) was statistically non-significant, largely because of the highyield variability in the wetter areas. The un-irrigated 2002 Russet Burbank (Fig. 5b) treatment showed a significant linear trend of increasing yield with increasing water content. Although not highly explanatory of the yield variability (R2 = 0.13), the trend was fairly steep with about a 30% yield increase from driest to wettest. The late-irrigated treatment exhibited a quadratic trend (R2 = 0.21) with yield increasing dramatically from around 25 Mg ha
1, peaking around 38 Mg ha
1, and then declining substantially at the high end of the water content range. The data (Fig. 5b) suggest a classic yield–response curve to water management with the point of negative returns for adding more water being around 0.18 m3 m
3. The amount of water required to reach the optimum yield level is greater when the average water content is less. The season average water content in these graphs (Fig. 5) was measured by repeated sampling in 2002 and these data were used to calculate the r(j). They represent the best estimate of the relative stable water pattern throughout the study site, and it was shown that the pattern persisted into 2003. Because of the limited sampling done in 2003, there was insufficient data to accurately establish season average water content. Therefore, the scaled results for 2002 were used in a graph for late-irrigated treatment in 2003 (Fig. 6), which

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Fig. 5. Russet Burbank yield in 2002 vs. season average water content for: (a) irrigated treatment; (b) lateirrigated and un-irrigated treatments. Trends are significant at the p = 0.05 level unless otherwise indicated.

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Fig. 6. Frito Lay 1533 yield in 2003 vs. scaled water content for late-irrigated treatment with significant (p = 0.05) linear trend.

behaved similarly to the un-irrigated 2002 data, probably in part because it received very little irrigation water (only 2.5 cm at the beginning of September). Yield increased sharply and significantly from around 27 to 38 Mg ha
1 across most of the water content range. The wettest point in the field was well below the trend. It was expected from the previous analysis that the wettest end of the water content curve would not fit the same linear trend as the drier areas. One can estimate how much water storage needs to be increased to reach the optimum level for production based on these results. For instance, if the rooting zone of potato is taken to be 20 cm and an increase of water content of 0.04 m3 m
3 is needed to reach the peak, this is achieved by increasing water storage by 0.8 cm. The yield data suggest that the driest part of the fields will respond best to irrigation and require the most water. Irrigating the wetter areas showed mixed results and may even decrease yield. These results suggest that applying a varying amount of water, depending on the relative water content of the area, would have yield advantages. A variogram of season average water content in 2002 (Fig. 7) shows a linear fit to the data for lag distances ranging from 30 to 550 m. The Y intercept of the line (termed the nugget) was over forty percent of the maximum semivariance. A high-nugget value such as this suggests that a substantial portion of the variability is caused by a combination of measurement errors and variability on a scale shorter than the minimum sample interval. The semivariance rises steadily from its minimum at the Y-axis suggesting that much of the large-scale spatial variability will be adequately characterized using our sampling protocol.

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Fig. 7. Variogram of 2002 season average soil water content for the entire study area with linear fitted function.

Maps of spatial variability in season average soil water were generated using the ordinary Kriging technique for each field. The root mean square errors in the prediction maps were: 0.027 for field A (Fig. 8a); 0.020 for field B (Fig. 8b); 0.026 for field C (Fig. 8c); and 0.048 for field D. Field D (Fig. 8d) had the greatest errors because of the comparatively few spatial points and high-spatial variability. By comparing Figs. 1 and 8 it can be seen that for transects crossing major particle size class boundaries (T1, T2, T3, T4, T9, T10), the coarser textural class was relatively dry. In field A, the transition was between silt loam (season average water content of 0.197 with a standard error of 0.006) and gravelly loam (season average water content of 0.177 with a standard error of 0.007). In field D, there were transitions between silt loam, gravelly loam, and gravelly sandy loam, but too few spatial samplings for statistical calculations. Transects in fields B and C did not cross major textural classes (T5, T6, T7, T8). Although there was a wet area in the middle of T7, the overall trend in water content (from high to low traveling west to east) coincided with a gradual decrease in elevation (Fig. 1). The drier soils were generally found at the lower end of fields B and C. The relatively wet section in the middle of transects T2 and T3 of field A coincided with a relative low point or surface drainage way in the landscape.

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Soil water content maps could be used to design an irrigation management plan to treat the drier areas with more water than the wetter areas. Our data and analysis suggest that this would be highly advantageous from the standpoint of saving water and probably improving yield. Alternatively, the water maps could be used to design drainage improvements or targeted fungicide applications in the wet areas. Organic matter and

Fig. 8. Maps of 2002 season average soil water content (m3 m
3) using ordinary Kriging for: (a) field A; (b) field B; (c) field C; (d) field D.

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Fig. 8. (Continued ).

tillage management to conserve water could be targeted to the drier areas of the field. Although yield decreases caused by excess water will be more problematic in humid regions under water sensitive crops, the models used here are theoretically applicable in drier regions as well. It would be an interesting course of future study to test the generality of these results across climatic regions and crops. Many possibilities exist for improving precision agriculture when a parameter with a profound effect on production

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such as soil water is found to have a stable distribution. The temporal stability obviates frequent sampling of spatial variability and makes practical a form of precision agriculture that is also stable in time.

5. Conclusions The soils of the study site exhibited a high degree of temporal stability in their soil water content spatial patterns. Half of the observed variability (R2 = 0.47) in water content measurements made at the scale appropriate for precision irrigation management can be explained by a temporally stable pattern of spatial variability. Another 20% of the variability can be explained by random measurement error. Along field transects, the stable soil water pattern often exhibited field-long trends or extended segments (>100 m) of consistently wet or dry soil. These trends persisted from one year to the next despite the fact that a different crop was grown. The high-resolution surveys in 2003 exhibited very similar trends as 2002. The 30 m surveys of 2003 were used to further validate the model calibration of 2002. Observed versus predicted water content data were grouped around the expected regression through the origin with a RMSE of 0.049. Yield relationships with season average water content depended on treatment and year. Un-irrigated (Russet Burbank) yields in 2002 increased linearly with increasing water content. The irrigated (Russet Burbank) treatment in 2002 showed uniformly high yields in drier soil, but highly variable yields in the wetter soil. More than half of the 2002 irrigated yield data in wetter soil was lower than any of the yields in the irrigated dry soil. The lateirrigated treatment showed a classic yield curve in 2002 (Russet Burbank) with yield increasing dramatically at the drier areas up to a maximum yield and then decreasing at highwater contents. In 2003, the late-irrigated (Frito Lay 1533) treatment showed sharp yield increases as a function of water content over most of the range of field conditions except at the wettest point. Coarser particle size classes were generally drier than adjacent finer particle size class soil. In fields and areas where there was no evident particle size class change, elevation appeared to play a role. The drier areas were, somewhat surprisingly, located at the lower end of the two fields with uniform particle size class. Localized low points coinciding with surface drainage pathways were relatively wet. The observation that particle size and elevation appear to play a role in explaining the stable water distribution is not surprising as these properties change little with time. Maps of the stable water distributions may prove to be valuable tools for precision agriculture management in general and water management in particular. The yield data suggest that the drier parts of a field will respond very well to irrigation but the wetter parts of the field may experience a yield decrease caused by excessive water.

Acknowledgements Thanks go to Mr. Donald Fitzpatrick for making his farm available to us for this research and for diligently managing the crops under study and to Ms. Peggy Pinette for her tireless efforts in field data collection and GIS mapping.

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References Benoit, G.R., Grant, W.J., 1985. Excess and deficient water stress effects on 30 years of Aroostok county potato yields. Am. Potato J. 62, 49–55. Comegna, V., Basile, A., 1994. Temporal stability of spatial patterns of soil water storage in a cultivated Vesuvian soil. Geoderma 62, 299–310. Famiglietti, J.S., Rudnicki, J.W., Rodell, M., 1998. Variability in surface moisture content along a hillslope transect: rattlesnake hill. Tex. J. Hydrol. 210, 259–281. Gomez-Plaza, A., Alvarez-Rogel, J., Albaladejo, J., Castillo, V.M., 2004. Spatial patterns and temporal stability of soil moisture across a range of scales in a semi-arid environment. Hydrol. Process. 14, 1261–1277. Goovaerts, P., Chiang, C.N., 1993. Temporal persistence of spatial patterns for mineralizable nitrogen and selected soil properties. Soil Sci. Soc. Am. J. 57, 372–381. Green, T.R., Erskine, R.H., 2004. Measurement, scaling, and topographic analyses of spatial crop yield and soil water content. Hydrol. Process. 18, 1447–1465. Jaynes, D.B., Hunsaker, D.J., 1989. Spatial and temporal variability of water content and infiltration on a flood irrigated field. Trans. ASAE 32 (4), 1229–1238. Kachanoski, R.J., De Jong, E., 1988. Scale dependence and the temporal persistence of spatial patterns of soil water storage. Water Resour. Res. 24, 85–91. McBratney, A.B., Pringle, M.J., 1986. Estimating average and proportional variograms of soil properties and their potential use in precision agriculture. Prec. Agric. 1, 125–152. Pires da Silva, A., Nadler, A., Kay, B.D., 2001. Factors contributing to temporal stability in spatial patterns of water content in the tillage zone. Soil Tillage Res. 58, 207–218. Robinson, D.A., Cooper, J.D., Gardner, C.M.K., 2002. Modelling the relative permittivity of soils using soil hygroscopic water content. J. Hydrol. 25, 39–49. Saffigna, P.G., Tanner, C.B., Keeney, D.R., 1976. Non-uniform infiltration under potato canopies caused by interception, stemflow, and hilling. Agron. J. 68, 337–342. Tomer, M.D., Anderson, J.L., 1995. Variation of soil water storage across a sand plain hill slope. Soil Sci. Soc. Am. J. 59, 1091–1100. Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res. 16, 574–582. Vachaud, G., Passerat De Silans, A., Balabanis, P., Vauclin, M., 1985. Temporal stability of spatially measured soil water probability density functions. Soil Sci. Soc. Am. J. 49, 822–828. Van Pelt, R.S., Wierenga, P.J., 2001. Temporal stability of spatially measured soil matric potential probability density function. Soil Sci. Soc. Am. J. 65, 668–677. Van Wesenbeeck, I.J., Kachanoski, R.G., 1988. Spatial and temporal distribution of soil water in the tilled layer under a corn crop. Soil Sci. Soc. Am. J. 52, 363–368. Western, A.W., Gunter, B., Grayson, R.B., 1998. Geostatistical characterisation of soil moisture patterns in the Tarrawara catchment. J. Hydrol. 205, 20–37. Wheelan, B.M., McBratney, A.B., 2000. The ‘‘null hypothesis’’ of precision agriculture management. Prec. Agric. 2, 265–279. Zhai, R., Kachanoski, R.G., Voroney, R.P., 1990. Tillage effects on the spatial and temporal variations of soil water. Soil Sci. Soc. Am. J. 54, 186–192.