We investigate an experiment using controlled drainage water management and assess its impact on corn [Zea mays L.] yields at the field level in Indiana. Controlled drainage restricts outflow during periods of the year when equipment operations are not required in the field. This may increase yields as well as reduce the losses of nutrients with negative environmental externalities. Specifically, we analyze yield monitor data over space and time, using Geographical Information Systems (GIS) and spatial panel econometric methods. The use of panel data methods controlling simultaneously for spatial and temporal heterogeneity and dependence as well as potential omitted variable bias provides precision agriculture researchers with a powerful framework to model crop sensor data over space and time. It allows us to evaluate the impact of alternative management practices on crop yields and attain a better understanding of the complex agronomic phenomena underlying yield response. We find that on average over the period 2005-2009, controlled drainage outperforms free-flow systems by up to 1.37 Mg/ha near the control structure. However, these aggregate results mask substantial year-to-year and field-to-field variations.
This paper investigates an experiment using controlled drainage technology and assesses its impact on corn yields at the field level in the state of Indiana, USA. Although water is a vital component for plant development, both excess and lack of water at critical stages of growth can result in irreversible crop damages and consequently yield losses. There is a direct cause-effect relationship between drought and plant stress, which can be managed through irrigation systems. Overly wet conditions may affect yields through various indirect channels. Excess water may render the ground untrafficable for machinery, and force critical field operations such as planting, spraying pesticides or applying fertilizers and harvesting to be performed at suboptimal dates. The later a crop is planted, the more likely it is not to reach its potential maximum yield by harvest time. Failure to apply pesticides on time may facilitate the spread of diseases; failure to supply nutrients when needed may slow down plant growth. Alternatively, standing water may cause root asphyxia or accelerate fungus proliferation, particularly during early stages of crop development. Regions or fields prone to flooding are typically equipped with surface or subsurface drainage systems, which collect and evacuate excess water to the nearest natural streams. Conventional drainage targets the water table depth at a specific level all year round, regardless of weather conditions. Temperate climates are characterized by seasonal patterns creating alternating periods of "wetter" (during the winter) and "dryer" (during the summer) conditions determined primarily by the contradictory effects of precipitation and evapotranspiration. Although free drainage is well suited to deal with excess water, it may actually result in harmful overdrainage in a situation of water scarcity. In response to this drawback, controlled drainage was developed to allow for adjustments of the water table depth by means of "logs" (i.e. barriers) inserted in control structures in the tile network. By adjusting the height of the tile outlet, outflow can be intensified to permit field operations, while more water can be retained to increase crop water availability during the growing season. By giving more flexibility to the farmer in terms of water management, controlled drainage is expected to improve yields over conventional drainage (Evans et al., 1996). Using empirical evidence to test this hypothesis for cornfields in Indiana is the primary objective of the present paper.
Policy makers have shown increasing interest in water table management systems because of environmental considerations. There have been growing concerns that abnormal concentrations of nutrients from anthropogenic sources in rivers foster algal production in coastal ecosystems, eventually causing eutrophication. Fingers are pointed at free-flow drainage systems, which are thought to be responsible for facilitating and accelerating the downstream transport of soluble chemicals used in agriculture, primarily nitrates. For instance, nitrate load from subsurface tile drainage, which constitutes the bulk of the total nitrogen load from the Mississippi River Basin to the Gulf of Mexico, has increased 300% since 1970 (Goolsby et al., 2001). This is the source of negative environmental externalities (Burkhart and James, 1999). As a result, the Gulf of Mexico hypoxic zone is now the second largest area of oxygen depleted waters in the world and appears to be growing (Rablais et al., 2002). Numerous studies have investigated the effects of controlled water management on nutrient losses, starting in the early 1970s. A review by Evans and Skaggs (1996) concludes that nutrient concentrations are for the most part unaffected within the tile network, but that regulating water outflow successfully reduces downstream pollution (see also Wesström et al., 2001; Ma et al., 2007). Given the well-documented environmental benefits, there is an incentive for public authorities to stimulate farmers to invest in drainage water management, which translates into subsidized programs such as the United States Department of Agriculture (USDA) Environmental Quality Incentives Program (EQIP) or the cost-share assistance under the North Carolina Agricultural Cost Share Program (NCACSP). Existing incentive programs such as the EQIP require quantitative information on practice efficacy and on private benefits. This paper provides part of the required information in the form of yield premiums associated with controlled drainage. Water quality and soil quality effects of this project are presented by Adeuya (2009) and Utt (2010). The assessment of environmental benefits will be left aside in the remainder of this paper because our objective is limited to determining the yield effects of controlled drainage.
Farmers are economic agents and are hypothesized to maximize profits among other objectives. The motivation behind this paper is the recognition that voluntary adoption of drainage water management by growers depends on the size of the yield increase (Evans et al., 1996). Indeed farmers will decide not to invest in more expensive technologies unless installation costs outweigh the discounted stream of expected additional revenues, which are in turn directly linked to the expected change in yields. A full cost-benefit analysis using estimates of the yield premium is needed to make a case in favor of controlled water management to farmers. To our knowledge, Brown (2006) and Nistor (2007) are the only examples of such an analysis in the literature. In particular, Nistor (2007) showed that a 2 to 4 percent average yield increase would be sufficient to make controlled drainage profitable without subsidies.
The 1996-2002 USDA Agricultural Resource Management Surveys (ARMS) found that adoption of precision agriculture continues to grow. They also show that yield monitors are the most common precision agriculture technology used on major field crops, especially by corn [Zea mays L.] and soybean [Glycine max L. (Merr.)] producers. As more combine harvesters are equipped with yield monitors and hence data become available, there is a growing need to determine how these data can be used to best help farmers make management decisions. Griffin et al. (2005) point out that precision agriculture has renewed farmers' interest in on-farm planned comparisons. Yield monitor data can be collected on-the-go while harvesting, and analyzed without interfering with crop production when appropriate precision technologies are used.
There are only a few studies of the effect of drainage management on crop yields. Sipp et al. (1986), Cooper et al. (1991), Drury et al. (1997), Fisher et al. (1999), and Ng et al. (2002), among others, document yield increases with subirrigation, but results are less clear-cut without subirrigation, which is the relevant benchmark for the present paper. Evans and Skaggs (1996) state that in the long run, controlled drainage generates average yield increases of 2 to 5 percent above yields with a conventional drainage system for a crop such as corn in North Carolina. Tan et al. (1998) present a study for Ontario, Canada, which shows that controlled drainage increases average soybean yields 12 to 14 percent above free-flow drainage in a conventional tillage system, but decreases yields in no-tillage systems. Nine out of 15 farmers involved in a central Illinois drainage management project report higher yields with drainage water management (Pitts, 2003). However, not all studies show yield benefits from controlled drainage. Sipp et al. (1986) in Illinois, Grigg et al. (2003) in Louisiana, and Fausey et al. (2004) in Ohio do not find any significant difference in crop yield between controlled and conventional drainage. Sipp et al. (1986) note that this result is particularly relevant as long as drainage is allowed to occur (i.e., water is not completely held back).
All of the above studies use small-plot or whole-field data with the crop transferred from the combine harvester to a weigh wagon, and subsequent analysis based on comparing treatment trials or performing an analysis of variance. Effectively, this implies that it is a priori assumed that the distribution of yields across the field is homogenous and independent of location. Geo-referenced yield monitor data allow for relaxation of this assumption by forming a direct tie between a yield measure and a location in the field. Some of the earliest studies using yield monitor data have estimated and compared site-specific crop response functions using multivariate regression analysis (e.g., Malzer et al., 1996; Wendroth et al., 1999; Nielsen et al., 1999). These applications rely on linear regressions estimated with ordinary least squares (OLS) and therefore implicitly assume independent and identically distributed errors (Kessler and Lowenberg-DeBoer, 1999; Bakhsh et al., 2000). However Kessler and Lowenberg-DeBoer (1999), Lambert et al. (2004) and Anselin et al. (2004) among others show that this is an erroneous assumption and that yield monitor data are typically heterogeneous and spatially dependent in nature. The field of spatial econometrics was developed to deal directly with these issues and a number of studies have estimated such models to investigate crop response to nitrogen application (Lambert et al., 2003; Bongiovanni and Lowenberg-DeBoer, 2000, 2002; Liu et al., 2006). Bullock and Lowenberg-DeBoer (2007) provide a recent review of studies using spatial econometric analysis techniques applied to precision agriculture data. To our knowledge, only two studies have previously explicitly attempted to model the impact of controlled drainage on crop yields, focusing specifically on corn (Brown, 2006; Nistor, 2007).
Brown (2006) applies spatial econometric techniques to cross-section yield monitor data from 2005 for four farms located in White, Montgomery and Randolph Counties in Indiana in order to study the economic feasibility of controlled drainage in the Cornbelt. Using spatial error regression models for the estimation of yields as a function of linear, quadratic and interaction terms including elevation, slope, distance to the nearest tile line and infrared soil color, Brown (2006) finds that controlled drainage impacts yield in the range of 0.5 megagram per hectare (Mg.ha-1) to 1.82 Mg.ha-1. Nistor (2007) proposes a framework to model crop sensor data over time by using spatial fixed and random effects panel data models, with an application focused on estimating the controlled drainage impact on farm profitability in the Cornbelt. She finds the decision to invest in controlled drainage technology to be supported for three out of four experimental farms, both with and without subsidy.
The use of spatial modeling techniques for replicated yield measurements over time is motivated by the fact that precision agriculture data are measured at such a low level of spatial aggregation that spatial clustering is endemic. In addition, the precision agriculture literature shows that yield response can vary substantially from year to year (Cooper et al., 1991; Mejia, 2000). Yield response functions are therefore perfectly suited to be analyzed utilizing spatial panel datasets, allowing for rather involved spatially clustered error patterns as well as appropriate parameter variation over time.
A panel data set consists of a sequence of observations repeated through time, on a set of units (e.g., fields, farms, or countries). Traditional panel data models used in applied research are the fixed effects (FE) and the random effects (RE) models (Baltagi, 2005). A panel data regression is different from a time-series or cross-section regression in that it considers both the temporal and the cross-sectional dimensions. Panel data offer researchers extended modeling possibilities as compared to purely cross-sectional or time-series data, because they contain more information, more variability, less collinearity among variables, more degrees of freedom, and hence the estimators are likely to be more efficient. Panel data can also reduce the effect of omitted variable bias by controlling for (unobserved) individual heterogeneity. Time-series and cross-section studies not controlling for this heterogeneity run the risk of obtaining biased results (Moulton, 1986).
MATERIALS AND METHODS
Experimental design
This interdisciplinary project is designed as a split field experiment on four different farms in Indiana (see Frankenberger et al., 2005, for a general description of the project). The general idea is to compare two areas similar in characteristics and management except for a specific treatment of interest, here controlled drainage. This paper is concerned with yield monitor data sampled from the Davis Purdue Agricultural Center (DPAC), field W, located in Randolph County, Indiana. Data collection started in 1996 on the DPAC farm and the "calibration" period lasted until 2004. The controlled water management system was installed for the 2005 growing season and thereafter. Our panel data approach allows the inclusion of both the calibration data and the experiment data in a common econometric framework and therefore makes use of the maximum information available.
Until 2004, field W on the DPAC farm was cultivated under a corn-soybeans rotation but 2005 marked a transition into corn monoculture. As a result, corn was harvested in 1996, 1998 and from 2005 until 2009 on both sides of the field. In addition, data was collected in 2000 [2] and 2002 for the East side and 2001 and 2003 for the West side. The difference in farming practices and cultivation history motivates the separate analysis of the two sides, henceforth East and West. Following the split field approach, only the northern half of the West side and the southern half of the East side of the field are setup for controlled drainage.
Data collection and treatment
Yield data are collected "on-the-go" during harvest, with a yield monitor linked to a global positioning system (GPS) mounted in the combine. The "raw" yield data are exported as a map on which each point, characterized by its coordinates (longitude and latitude), represents the measured yield over a small surface surrounding each point. Anselin et al. (2004) provide a more complete description of the composition of the yield files and Griffin et al. (2005) elaborate on the nature of this particular type of spatial data. The "raw" yield values are computed by an algorithm combining, among others, information on grain flow in the machine, grain moisture, combine speed, and swath width. Measurement errors linked to these "combine dynamics" are frequent and jeopardize subsequent quantitative analysis. For a detailed treatment of combine dynamics and yield monitor data analysis we refer the reader to Lark and Wheeler (2003).
The USDA-ARS Cropping Systems and Water Quality Unit designed the Yield Editor software for the very purpose of removing questionable observations based on criteria such as start or end of pass delay, grain flow delay, and minimum and maximum combine speed or yield.
Because the points of the raw yield data are closer inside the row than between rows, datasets for each site are constructed by aggregating the data points into squares with a width approximately equal to the average combine pass. In effect, this creates a dataset that is spatially balanced in all directions. Previous applications of this methodology can be found in Mamo et al. (2003), and Anselin et al. (2004). Over the time period of the experiment, we determine the average combine pass to be approximately equal to five meters. The grid thus created is overlaid on the yield points after rotation by the corresponding field angle in order for the row of cells to follow the combine harvester passes through the field and avoid mixing data from multiple passes. Each cell value represents the average yield of all points contained within that square. Cleaning and aggregating results in a smoothing of the data as the extreme yield values and hence the variability shrinks from one step to the next in the data preparation.
< Figure 1 about here >
Figure 1 illustrates each of these steps for the 2008 harvest on field W. Figure 1a is a map of the raw yield data points as exported from the combine computer. Figure 1b represents the outcome of the data cleaning process during which many data points are removed, in particular at the end rows. Figure 1c is obtained after aggregating the data points from Figure 1b into the 5-by-5-meter grid. We perform this process using the same grid each year, which enables us to compare yields for different years in the "same" location. Because of cleaning the data in this fashion, some grid cells wind up not intersecting with any yield point for certain years. We remove these cells from the grid and as a consequence some data is lost for the remaining years. The balanced design thus obtained, allows for a spatial econometric approach using a weighting scheme (Anselin et al., 2004). Moreover, since the prediction error for the average values of yields within grids is smaller than the prediction error for any yield point prediction, the precision of the average yield estimator is higher than that of the point estimator (Haining, 2003). However, this procedure also introduces heteroskedasticity as will be detailed in a later section.
We can see from Tables 1 and 2 that mean corn yield is fairly stable over time, except for 1996 (weed problems), 2002 (severe drought), and 2007. Examining figures during the calibration period (i.e., before 2005) may give an indication of inherent yield potential differences between conventional and controlled portions of each side of field W. With only three years of data for the East side, there is no discernable pattern. For the West however, the portion of the field which is set up for drainage water management exhibits higher yields three out of the four calibration years. A similar comparison of yields under controlled and conventional drainage after 2005 for both sides does not lead to conclusive evidence, although it seems to have a tendency to still be higher.
< Tables 1 and 2 about here >
Simple comparisons based on average yield may be misleading because they do not take into account other factors that may affect yield, such as elevation, soil type and microclimate, as well as any potential interaction between these factors and the drainage system. These grid cells' individual characteristics are the source of what we refer to as spatial heterogeneity. What can be concluded from examining yield maps is the apparent clustering of yields in zones of high and low yields, which leads us to suspect the presence of positive spatial autocorrelation in the data (see Figure 1c for 2008). Essentially, this indicates that a cell's yield is similar to the yield in neighboring grid cells. However, spatial autocorrelation is not the only possible diagnosis when spatial clustering patterns are visible. It could just as well stem from groups of cells for which the yield distribution has a different mean or variance, which is indicative of spatial heterogeneity. This "observational equivalence" between spatial correlation and spatial heterogeneity demonstrates the need to go beyond exploratory analyses and utilize a spatial econometric quantitative method.
Empirical model
Heady and Dillon (1961) provide a review of algebraic functional forms for crop response estimation. The selection of variables and the specification of the crop yield functional form, which are both reviewed by, for instance, Nistor (2007) and Voortman (2010), are difficult due to the complexity of the yield response (Swanson, 1963; Florax et al., 2002; Anselin et al., 2004). For this application we choose a simple linear form with interaction variables, because we have data only on a limited number of variables. For on-farm yield trials, elevation and rainfall are the most commonly available variables. We have yearly precipitation data for the DPAC farm but it does not vary within the field. Hence rainfall cannot be used directly for purpose of estimation as it is perfectly collinear with the yearly dummies included to control for temporal heterogeneity. We will interpret the time dummies as capturing primarily climate factors, and specifically rainfall. Data that vary over time and space (e.g., annual soil tests, remotely sensed biomass information) are sometimes available on research farms, but rarely for commercial fields like those used for the drainage trials.
Elevation point data with reference to the sea level, collected by topographic surveys performed by contractors for the farm, are interpolated using the Inverse Distance Weighted (IDW) power 1 method, so that a point data set is obtained with elevation across the whole field. Each grid cell is assigned the average of the elevation points that fall within its boundaries and is converted with reference to the lowest elevation level in each side of the field (henceforth elevfld). The resulting relative elevation map is represented in Figure 2.
< Figure 2 about here >
Inspection of this map reveals a general northwest-southeast upward slope for the East side as well as the West side. This is confirmed by Tables 1 and 2, which give summary statistics for the elevfld variable. The southern half is on average 0.58 m and 0.34 m higher than its northern counterpart for the West and the East side, respectively. Installing the controlled drainage system under the lowest part of the field on one side (West) and the highest part of the field on the other side (East) is part of the experimental design.
Pivotal characteristics of the specification we use are as follows. First, we allow for elevfld to have a nonlinear effect on yields by letting elevation enter the model as a logarithmic term. This is motivated by the idea that low spots in a field are commonly wet and hence detrimental to plant growth. As elevation increases natural drainage occurs and roots get some breathing room fostering plant development. However, beyond a certain level, the water table gets harder and harder for the roots to reach and yields are expected to start decreasing because the plant is unable to fulfill its water needs. Such a profile of the effect of elevation on yields would ideally call for a monotonically increasing function that eventually reaches a plateau. Using such a nonlinear functional form would render estimation unfeasible given our econometric framework. We therefore rely on a logarithmic transformation of elevation, which behaves in a similar fashion (see below).
Second, the controlled drainage treatment is incorporated in the model as a dummy variable that takes the value one for cells where the control system is in place in a specific year. Given this construct, the advantages or disadvantages of managed drainage are measured in comparison to the "benchmark" free-flow drainage. This dummy is interacted with the time dummies to account for likely differential impacts of controlled drainage across years. In other words, we expect the controlled drainage setup to either benefit, hurt or have no effect on yields in response to varying environmental conditions.
Finally, we anticipate the elevation above the soil surface at the control structure (henceforth elevstr) to be a critical factor in the impact of managed drainage on yields. As an illustration, assume that the water table is set 12 inches below the surface in the control box. For corn plants located two feet higher in elevation, roots have to grow 36 inches deep to reach moisture. There is a threshold beyond which the performance gap between conventional and controlled drainage narrows down to zero. This threshold is not fixed and depends on water availability and log height. This is why we further expect the response of controlled drainage to this variable to vary from one year to another. This calls for a three-way interaction between the drainage dummy, the year dummies, and elevstr. Our hypothesis is that in relatively dryer years controlled drainage allows the retention of more water than conventional drainage and hence favors plant development at points close to the control structure. We suspect this advantage to deteriorate as elevation increases until it eventually evens out. Alternatively, controlled drainage may lead to drowning the root system at low elevations above the control structure in comparatively wetter years, in which case free-flow drainage would have more satisfactory results. The "real" story is likely to be more complex than this clear-cut wet/dry distinction because not only the quantity but also the timing of precipitation matters and controlled water management allows the farmer to fine tune the water table level in response to field and weather conditions. The nonlinearity of the relationship between elevstr and the controlled drainage dummy is captured by using the logarithm of this variable (see below).
With the inclusion of these interaction variables, the model to be estimated reads as:
(1)
where yieldt is average yield per grid cell in year t, yeart is the time dummy for year t, drain is the controlled drainage dummy, elevfld is elevation above the lowest point in field W, elevstr is the distance between the control structure and the soil surface, and εt is an error term. The use of dummies conveniently leads to a three-factor interpretation of this model. The intercept captures the yield potential inherent to the focus field for a specific reference year under conventional drainage. Each year dummy represents the yield premium or loss resulting from the conditions in which the crop is cultivated during a particular year. The drainage dummy and the related interaction terms further refine the yield response decomposition by quantifying the benefits of controlled water management over free-flow drainage. Strictly speaking this dummy "absorbs" everything that is specific to the controlled portion of each field over the course of the project.
In view of the data aggregation procedure based on calculating average yields for data points contained in each grid cell, the left-hand side variable is average or expected yield rather than actual yield. This implies that the model in equation (1) is inherently heteroskedastic because the variance of the mean varies over grid cells. We therefore scale the left- and right-hand side of equation (1) by the standard error of the mean yield for each grid cell. When only a single data point falls into a grid cell the standard error of the mean for that cell does not exist. Therefore we replace it by the average of all standard errors of the mean for the corresponding year.
Spatial panel model
Contemporaneous spatial clustering between observations at each point in time and spatial heterogeneity (i.e., parameter variation over space) may arise when panel data include a locational component (Anselin, 1988; Elhorst, 2009). We control for spatial clustering by estimating a spatial version of panel models that allows for spatially autocorrelated errors. Anselin et al. (2008) provide an overview of specifications and estimators available for spatial panel data. There are three different specifications that fit our purpose: the models developed by Anselin (1988), Kapoor et al. (2007) and Baltagi et al. (2007). These models build upon each other, starting from the more restrictive form of Anselin (1998) who considers a random effects model in which only the innovations are spatially correlated. Kapoor et al. (2007) extend this form to allow for the unit-specific time-invariant random effects to be correlated over space with the restriction that the spatial correlation parameter be equal between the two error components. Baltagi et al. (2007) relax this restriction. We carefully test for the most appropriate model for each of our panel datasets (East and West side) using the Lagrange Multiplier (LM) and Likelihood Ratio (LR) tests derived by Baltagi et al. (2007). Results from these tests point to most general of the three models, namely Baltagi et al. (2007). Estimation and testing were performed with the open-source statistical software R using self-programmed scripts [3] . Spatial panel techniques allow for temporal and spatial heterogeneity as well as spatial dependence to be incorporated and hence they permit isolation of the effect of controlled drainage on yields.
RESULTS AND DISCUSSION
In this section we focus on calculating and discussing how controlled drainage impacts yields as compared to free-flow systems. The full set of estimation results for both sides of the field is presented in Table 3. A quick glance at this table reveals that all but a few coefficients are significant.
< Table 3 about here >
With the presence of interaction terms for each of our explanatory variables, interpretation of estimated coefficients as marginal effects is complicated. Regression coefficients are however meaningful by themselves. For instance the estimates on the yearly dummies are interpreted as the yield advantage (or disadvantage) for the conventionally drained part of the field due to unobserved parameters specific to each year using 1996 as a reference. The estimated coefficients corroborate the yield summary statistics presented in Tables 1 and 2. Table 1 shows that 1996 was the worst year for the West side of field W which is captured by all yearly dummies showing positive coefficients, the largest of all being for 2008. The situation for the East side of the field is identical except for the drought year 2002 which translates into a negative coefficient on the corresponding dummy variable.
The effect of controlled drainage water management on corn yields is, however, the result of a combination of factors that we accounted for by adding interaction terms with the elevstr variable. Additional steps are necessary to obtain appropriate marginal yield effects with associated statistical tests. Because the controlled drainage variable is a dummy variable, the marginal effects for year t are calculated as follows:
(2)
By averaging the and coefficients and plugging in each cell's elevation above the surface on the control structure (elevstr), we obtain the mean marginal effects of controlled drainage over the period 2005-2009. Equation (2) highlights the fact that these marginal effects need not be interpreted as absolute but in comparison to the experimental benchmark, namely free-flow drainage. From this point on, this will be implied when we refer to the "marginal effects of controlled drainage." Table 4 summarizes the marginal effects for all five years, individually as well as for the total period, at three different elevations (minimum and two arbitrarily chosen intermediate values) in the controlled area of each side of the field. By design we do not anticipate to observe any notable differences between controlled and free-flow drainage 0.6 meters above the control structure. We report 95-percent confidence intervals for each marginal effect. [$] Interpretation of these confidence intervals is two-fold. First, they indicate whether the marginal effect is statistically different from zero. If insignificant, we can conclude that controlled drainage did not make a difference over free-flow systems at the specific corresponding time/elevation combination. Second, confidence intervals provide an indication of the margin of error made on each marginal effect calculation.
< Table 4 about here >
The results presented in Table 4 deliver two key messages. First, on average over the period 2005-2009, controlled drainage yields outperformed free-flow drainage on both sides of the field. We estimate that corn yields improved by 1.19 Mg/ha (1.37 Mg/ha) close to the control structure on the West (East) side of the field which corresponds to a 12 (13.3)-percent premium over average free-flow yields. These benefits decrease as elevstr rises which is in line with our expectations. Note that this is consistently what can be observed across all years except for the East side of the field in 2005. Second, the break down by year reveals substantial temporal heterogeneity of the impacts of controlled drainage on average yields. However, the bottom line is that controlled drainage is almost always at least as good as conventional drainage. The relationship between elevstr and the marginal effects of controlled drainage is illustrated on Figure 4 where the marginal effects are laid down on the grid map. We want to emphasize that the negative values reported in Table 4 and on Figure 4 result from the particular functional form that was imposed on the link between elevstr and the marginal effects and are therefore interpreted as estimation artifacts. Note that negative marginal effects are relatively rare and occur primarily at values of elevstr beyond the threshold at which we consider conventional and controlled drainage to be equivalent.
Year-to-year and field-to-field variation in impact of controlled drainage on yields is a result of many factors, many of which are beyond the scope of this study. We can, however, identify some key elements in that year-to-year variability, including:
- The amount and timing of precipitation is the key factor in year to year variability. If little rain falls after logs are installed, then control drainage cannot retain water in the root zone and hence cannot improve yields. For example, in 2005, the first year of the project, corn was planted early around April 20. The logs were set in place on June 21. Little precipitation fell in late June and July keeping the water level in the tiles low until mid-August, and hence during pollination (see Figure 2). This is why controlled drainage made little difference over conventional drainage that year. In 2009 logs were put in place soon after planting and accumulated sufficient rainfall from the late spring to carry the corn crop through pollination resulting in a substantial yield benefit for controlled drainage despite the dry summer.
- Tile system design affects field to field differences. For example, in the controlled part of the West side the main tile outlet is too small for the amount of water that accumulates. This makes the controlled section of the West side prone to flooding and this tendency is accentuated when the drainage control logs are in place. These tile system design issues are part of the reason why controlled drainage benefits are smaller and more variable on the West Side.
- Year-to-year differences are also affected by how intensively the water table was managed. The first three years of the trial, the farmer installed the logs in late spring and pulled them out shortly before harvest. In 2008 the logs were managed more intensively. They were inserted and removed several times during the summer in response to field conditions. For instance, in case of a heavy rain on already saturated soil, logs may be lowered to accelerate tile outflow. The yield improvement linked to controlled drainage was positive and statistically significant up to 0.5 meters elevation above the control structure on both East and West Sides in 2008.
SUMMARY AND CONCLUSIONS
Controlled drainage systems are designed to provide farmers better water management possibilities than with conventional free-flow drainage. Because of the ability to raise the level of the water table during periods requiring no machine operations, controlled drainage may boost corn yields. With yield monitor data collected from an experiment designed at the Davis Purdue Agricultural Center from 1996 to 2009, this paper uses spatial panel data techniques to determine whether controlled drainage outperforms conventional drainage in terms of yields. The use of spatial panel data methods provides precision agriculture researchers with a powerful framework to model crop sensor data over space and time. We find the following results:
- The impact of controlled drainage varies greatly over space and over time. In our model, variation over space is closely tied to elevation, and we suggest that differences in rainfall and drainage management are responsible for year-to-year variations.
- On average over the period 2005-2009, we find that controlled drainage improved corn yields when compared to conventional drainage at all relevant elevation above the control structure. The estimated yield premium was as high as 1.37 Mg/ha (or 13.3 percent) and benefits decrease as elevation above the surface at the control structure increases. Furthermore we find that controlled water management does always at least as well as free-flow drainage near the control structure. We interpret the few significant negative marginal effects as artifacts stemming from the logarithmic functional form imposed on the model.
- More intensive management of the logs leads to the best performance. In addition to facilitating machinery access to the fields for planting and harvesting, controlled drainage provides farmers with means to react to unpredictable climate events. In particular we observe that it can play a crucial role in ensuring that enough moisture is available to crops during critical growth periods.
These results provide valuable insights for farmers to decide whether to install drainage water management systems. However it also shows that each farm and within each farm, each field needs to be considered on a case-by-case basis. Based on the findings by Nistor (2007) that a yield gain of 2 to 4% would be sufficient to make controlled drainage profitable without subsidies, and considering our own results that on average over our period of study controlled drainage improved yields by at least 7.9 percents (0.78 Mg/ha), we recommend farmers to consider this option seriously. A farm specific cost-benefit analysis at current crop and input prices should be done before making the final investment decision.
In addition to specific yield estimates for controlled drainage, this study provides an example of how farmers, agricultural business and agronomists can make use of the data from combine yield monitors to statistically test the impact of production practices like drainage that are difficult to test in a small plot situation. Spatial panel econometric methods explicitly model the spatial autocorrelation inherent in combine yield monitor data and allow unbiased inferential statistics. Spatial panel methods also provide a robust methodology for summarizing yield monitor data over time, eliminating the need for "normalizing" or other ad hoc methods used by some analysts with multiple years of yield maps.
