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Department of Environmental Sciences, University of California, Riverside, CA 92521
* Corresponding author (David.Crohn{at}ucr.edu)
Received for publication April 22, 2005.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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Abbreviations: +30%, management plan that for each planning period applies a total N amount equal to the crop N target need plus 30% • 1Wtr, management plan determined through deterministic optimization with 10-d summer application schedule and one winter application • d°, temperature-adjusted day unit • DOpt, management plan determined through deterministic optimization with 10-d year-round application schedule • PAN, plant-available nitrogen (kg ha–1) • SOpt, management plan determined through stochastic optimization with 10-d year-round application schedule • TAT, temperature-adjusted time
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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California has been the largest dairy producing state since 1993, when it passed Wisconsin. In 2002, 2153 farms, averaging 776 cows per farm, produced about one-fifth of the nation's milk and cheese (California Department of Food and Agriculture, 2003), along with an estimated 120 million m3 yr–1 of liquid dairy manure (Harter et al., 2002). The San Joaquin Valley is one of three dairy basins located in the California's Central Valley. Dairies in the region generate large amounts of liquid manure when water is used to wash feedlots and milking areas. Some large solids are removed from the washwater with various degrees of efficiency, and the remaining effluent composed of dissolved and particulate manure is stored in lagoons. Water from these lagoons is later mixed with irrigation water and applied to cropland through surface irrigation. Harter et al. (2002) have shown that land application of manures to crops in the area has significantly contaminated area ground water with nitrate (Harter et al., 2002). Dilution and rapid infiltration tends to control ammonia losses from these applications, but the sandy loam to sand soils typical of the regions also tend to transmit water rapidly so that irrigation can also serve to quickly leach nutrients below the root zone of growing plants (Harter et al., 2002).
A variety of state and regional regulatory agencies are currently developing rule and training programs that may affect Central Valley manure disposal (Meyer et al., 2005). Although there has been activity in assisting dairy farmers with manure management generally (Cabrera et al., 2005; De et al., 2004; Hess et al., 2001) little guidance is currently available for designing land application rates over time for lagoon water or other organic N fertilizers in California. In detailed simulation studies of the region, Feng et al. (2005) concluded that limiting applications to 120 to 140% of crop demand can assure reasonable crop growth while restricting leaching. It should be noted that when some organic fertilizers, such as manures and biosolids, are applied at these rates, phosphorus (P) accumulation can become of environmental concern (Pierzynski and Gehl, 2005). Phosphorus management is a critical issue in much of the United States but, in the Central Valley, N, rather than P, typically limits application rates. Regional regulators are considering a strategy that will limit total N applications to the crop N removal rate plus an acceptable loss factor, but farmers will need assistance in scheduling applications to optimize yields under such a constraint (Marsha Campbell-Matthews, personal communication, 2005). Inefficient application schedules may result in underfertilization of crops and excessive nitrate leaching. The objective of this study was to develop a simple linear optimization model that identifies an optimal and sustainable application schedule expected to meet plant-available nitrogen (PAN) needs while minimizing the potential for losses to ground water.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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Nitrogen Mineralization
The approach to be developed here for scheduling the organic fertilizer applications concerns itself with the release of introduced N. Nitrogen mineralization from applied organic fertilizers is widely represented as a first-order process (Benbi and Richter, 2002; Fortuna et al., 2003; Gilmour et al., 2003). Under field conditions, however, the decay rates vary with temperature. This normally requires a numerical solution:
 | [1] |
 | [2] |
2 (Andrén and Paustian, 1986; Lloyd and Taylor, 1994).
Temperature-Adjusted Time
When the Arrhenius equation is substituted into Eq. [1], the decay rate can be brought outside of the integral and the solution can be written in terms of temperature-adjusted time (TAT), t°, which has an SI unit of d but to which is assigned a more informative unit here of d° to indicate days adjusted for temperature (Crohn and Valenzuela-Solano, 2003). Equation [1] can then be written as:
 | [3] |
 | [4] |
i are ordered points in time and an exact solution to Eq. [3] is found as i 
. This procedure effectively expands time in the warmth of summer and contracts it appropriately during cooler months while keeping the decay rate constant. A TAT stream can be calculated easily with a computer and maintained along with temperature and growing degree-days data.
If it is assumed that all mineralizable organic fertilizer N is released at a uniform rate, then the organic N remaining at the end of a particular year of applications can be predicted as:
 | [5] |
Steady-State Condition
At steady state, fertilizer organic N in the soil at the beginning of each annual cycle, Sto (kg ha–1), can be estimated directly from the annual application schedule by setting Stf = Sto and solving for Sto:
 | [6] |
Of course, steady state is never actually reached. It is approached asymptotically. After Y (yr°) temperature-adjusted years, the initial soil organic N concentration of a newly amended field, So (kg ha–1) will rise to an N concentration of StY (ha ha–1):
 | [7] |
Since StY = Sto at steady state, the number of temperature-adjusted years, Y, required to reach steady state from an initial condition, So, may be considered in terms of a fraction, pss, of the true steady-state value. Variable Y is then defined as the integer value where soil organic N just exceeds the pre-selected fraction of steady-state organic N:
 | [8] |
A closed-form solution to this expression can be derived by substituting Eq. [6] into Eq. [8] and solving for Y:
 | [9] |
Often it is easier to conceptualize decomposition in terms of half-lives, t1/2 (d°), rather than decay rates. Time to steady state can also be considered using half-lives. In the case of a newly manured field where So = 0, pss < 1, and Eq. [9] reduces to:
 | [10] |
Optimization Model
The approach divides the year into a number of planning periods. Fertilization can only occur at the beginning of a planning period. Applications are scheduled such that target crop N demand during the planning period is met by PAN derived from the inorganic N applied at the beginning of the period and from the mineralization of freshly applied and residual soil organic N reserves. The model depends on the user to predetermine application times, although solutions may assign application rates of 0 kg ha–1 to some possible application dates. In general, the N made available to plants (PAN) between two applications can be determined as:
 | [11] |
 | [12] |
A linear optimization model may now be constructed to minimize N losses while guaranteeing the crop N demands. Let Cj (kg ha–1) be the crop N demand during a planning period j. Where significant, denitrification losses can be accounted for by increasing Cj appropriately (Crohn, 1996; Meisinger and Randall, 1991). Assuming n applications per year, the amount and timing of each application, Aj, can be made so that crop N needs are met while minimizing the total N applied:
 | [13] |
Because this model is linear, it can be solved quickly and precisely using an optimization algorithm that includes a simplex method option, such as Microsoft Excel's Solver (Microsoft Corporation, 2000).
In some cases it may be appropriate to allow PAN from one planning period to be available to one or more subsequent periods. This is particularly useful when a single application before planting must supply all of the needs for that crop. One approach is to assign the entire growing season to a single planning period. This approach has a rather limited resolution, however, and may result in crop N deficits since it assumes that N mineralized late in the season, when crop uptake is low, can be used to meet peak crop N demands, which occur earlier in the season before the N is actually available. As an alternative, Eq. [13] can be modified so that sharing between some consecutive planning periods is possible. Mathematically, this can be done by grouping the planning periods into ordered sets, 
x. Each set may contain one or more planning periods and different sets may contain different numbers of elements. Application rates are normally fixed at 0 kg N ha–1 for all but the first planning period contained in a set, though sharing between different applications may be considered by allowing for multiple applications. Solutions are constrained by the assurance that for each planning period, 
, contained within each set x, cumulative crop N demands are supplied by the PAN applied or mineralized during that period or by previous periods, j 
, contained within x. This constraint may be expressed as:
 | [14] |
The model may now be expressed as:
 | [15] |
is the set of planning periods that include potential application dates.
Equations [13] and [15] require known values for Q10 and k, but for many organic fertilizers there will be uncertainty associated with these parameters. It is possible to incorporate parameter uncertainty into the linear model by adding additional N-release constraints associated with equally probable permutations of k, Q10, or, if desired, other variables of interest. For example, if the distributions associated with k and Q10 are broken into quintiles of equal (20%) probability, and these quintiles are represented by their midpoint probabilities, such that Pr[X kp (or Q10p)] = p: p 
{0.1, 0.3, 0.5, 0.7, 0.9}, a total of 25 constraint scenarios may be considered, each with a 4% probability of occurrence. If, as a subscript, p represents each of these permutations, the deterministic model represented by Eq. [13] can be rewritten stochastically:
 | [16] |
This stochastic linear model assures that crop N demands are met for all planning periods, j, regardless of the probability permutation, p. A similar stochastic expression could be derived for Eq. [15] but is not considered here.
Crop Nitrogen Demand
Crop demand is often represented with a logistic expression. A highly generalizable form is:
 | [17] |
Example Application
The example considers dairy manure lagoon water from a hypothetical farming operation located in Stanislaus County, California. Two forage crops are grown in rotation: summer forage maize and winter triticale. Forage maize is grown from 14 May through 11 September and triticale from 16 October through 14 April. Crop N-demand parameter values associated with Eq. [17] (tP, C, B, M, D, tH) were, respectively, 135 d, 280 kg ha–1, –0.0958 d–1, 39.04 d, 0.316, 120 d for maize and, respectively, 290 d, 224 kg ha–1, –0.0652 d–1, 84.76 d, 1.131, 180 d for triticale. The curves were derived from data supplied by a local University of California Cooperative Extension agronomist (Marsha Campbell-Matthews, personal communication, 2004). To evaluate the deterministic models represented by Eq. [13] and [15], a 283 d° half-life (Tr = 298 K, Q10 = 2) was selected for this example as representative of dairy manure materials under laboratory and field conditions (Feng et al., 2005). This has an associated decay rate of k = 0.00245 d°–1. Although actual values can vary considerably (Van Kessel and Reeves, 2002), these values are used by local experts for planning purposes (Feng et al., 2005).
The stochastic model represented by Eq. [16] requires some understanding of the distributions underlying Q10 and k. The example case considers dairy lagoon water. Pettygrove et al. (2003) incubated samples (22°C) from 10 anaerobic dairy storage lagoons in the San Joaquin Valley of California. Two unusually dilute samples (1.2% solids) were predominately composed of inorganic N, and were not included in this analysis. The difference technique used in the mathematical procedures made these samples particularly prone to experimental error due to the difficulty in reliably measuring small amounts of mineralized N in the presence of high background levels of inorganic N. Because these two samples were responsible for both the highest and the lowest reported mineralization rates, their exclusion does not bias the result in a singular direction. Decay rates, determined after 77 d of digestion, were fitted to a lognormal distribution, which could not be rejected with a Shapiro–Wilk test (
= 0.05) using SPSS 11.0 software (Noru
is, 2002). Log-transformed decay rate statistics were –5.86 ± 0.64 (mean ± 1 standard deviation). These transformed statistics were associated with an expected decay rate value of k = 0.00286 d°–1 or t1/2 = 242 d°. The 242 d° half-life for this data set is statistically indistinguishable from the 283 d° period (k = 0.00245 d°–1) considered by area experts.
There is relatively little N mineralization data available to assess uncertainty associated with Q10 for organic fertilizers. More, however, is available for soil organic N mineralization. Kätterer et al. (1998) normalized and fitted data from 25 N mineralization temperature response experiments to several models, including the Arrhenius equation. Fitted parameters corresponded to Q10 values of 2.03 ± 0.35. The data were consistent with a normal distribution (Shapiro–Wilk test, = 0.05). These results are consistent with the previous conclusion of others such as Stanford et al. (1973) who also suggested 2 as a Q10 value for soil nitrogen mineralization, as well as with Vigil and Kissel (1995) who studied N release from crop residues.
For illustrative purposes, four cases are considered. Three cases consider a rotation scheduled to receive year-round side-dressings at 10-d intervals. The term "side-dressing" is used somewhat loosely here since liquid manures are applied broadly with the irrigation water rather than specifically to the root area of growing plants. The planning year begins 1 May and the 10-d application cycle initiates 4 May. Feng et al. (2005) used these values for detailed simulation models to conclude that crops supplied with 20 to 40% more N than their annual uptake would present acceptable yields while avoiding excessive impacts on ground water quality. For comparison purposes, a reference schedule is included in which application rates are set at 1.3Cj (+30%) for each planning period. A deterministic optimized schedule (DOpt) is then derived using Eq. [13]. Mineralization parameter values for the +30% and DOpt examples conform to local conventions (k = 0.00245 d°–1, Q10 = 2). A stochastically optimized solution (SOpt) is also presented using Eq. [16] and the distributions for k and Q10 derived from the literature. Because winter forage crops in Stanislaus County generally receive their water through natural precipitation, operating dairies often apply winter crop manure as a single application before planting and summer manure with surface irrigation. The fourth case uses Eq. [15] to address this scenario (1Wtr). For the purposes of the examples, all manure N is assumed to be 50% organic and 50% inorganic (aj = 0.5 
j) (Feng et al., 2005) except for the single winter manure application, which is assumed to be 90% organic and 10% inorganic as might occur with an aged manure (Hartz et al., 2000). In practice the ratio of organic to inorganic N varies somewhat both between lagoons and at different locations within a particular lagoon (Pettygrove et al., 2003). Volatilization and denitrification losses after land application, which are low in the Stanislaus County area (Harter et al., 2002), are not included in these examples.
Monte Carlo Simulations
Two sets of Monte Carlo simulations were completed to consider the uncertainty associated with the linear optimization approach. All simulations used Crystal Ball 2000 software (Wainwright, 2001) to generate 10 000 trials per experiment. The first set considered the uncertainty associated with k and Q10 under steady-state conditions (Eq. [12]). Solutions for +30%, DOpt, and SOpt were considered using Eq. [13] while Eq. [15] was used for 1Wtr. Parameters k and Q10 were varied and statistics were collected on total annual surplus N, total annual deficit N, annual maize deficit N, and annual triticale deficit N. As in the solution for SOpt, parameter k was assumed lognormally distributed with log-transformed data parameters –5.86 ± 0.64. Parameter Q10 was assumed normally distributed with parameters 2.03 ± 0.35.
The second set of simulations collected similar statistics on an aggrading soil in its tenth year of applications. Initial soil amendment N was assumed to be 0, and applications were performed according to the SOpt and +30% schedules. Soil organic N accumulation and mineralization were determined with Eq. [4], [5], and [11]. Throughout an experiment, each mineralizing organic N application event maintained a unique k value. The values of Q10 were varied for each trial but were consistent between applications to reflect the influence of the soil and its associated microbial ecology on this parameter. In addition, these simulations varied the amendment organic N fraction (a) and soil temperatures. Soil temperatures during each 10-d planning period were assumed to be normally distributed. Parameters were estimated from CIMIS measurement data (California Irrigation Management Information System) collected in Modesto, CA, representing the period from 1988–2004 (Eching et al., 1995). Values for a were assumed to vary uniformly between 0.25 and 0.75, a range consistent with measurements in the area (Marsha Campbell-Matthews, personal communication, 2005).
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RESULTS |
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{0.00126, 0.00204, 0.00285, 0.00399, 0.00648} d°–1 and Q10 {1.58, 1.85, 2.03, 2.21, 2.48}. Annual application rates in Fig. 3 totaled 633 kg ha–1 yr–1, an increase of 25 kg ha–1 over the DOpt solution, but 22 kg ha–1 less than the +30% approach. Annual leachate was estimated to be 129 kg ha–1. Application schedules for +30%, DOpt, and SOpt are compared in Fig. 4.
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Single Winter Applications
When winter manure is applied as a single application and Eq. [15] is employed such that the period between application on 11 October and harvest on 10 April is grouped into a single set, and the rest of the year with independent 10-d planning periods, a total of 145 kg N ha–1 is applied during the summer and an additional 551 kg ha–1 is applied before the planting of winter triticale. This pattern results in no N deficit for summer maize (Fig. 5), but a total potential deficit of 123 kg ha–1 between 10 December and 28 February for winter triticale. This is the deficit that would occur if there were, for example, a large leaching event on 10 December, the date when the rate of crop N demand begins to exceed the organic N mineralization rate. The potential 123 kg ha–1 deficit also equals the total potential excess N occurring between the 11 October application and 10 December. If no losses occur, then there is no N deficit and the annual surplus N is 192 kg ha–1. Including the entire potential deficit increases annual N losses to 316 kg ha–1 representing 45% of the total 696 kg ha–1 applied annually.
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Stochastic optimization increased surplus N to 131.0 ± 4.1 kg ha–1. Surplus N fell between 128 and 129 kg ha–1 in 71% of all trials and in other trials exceeded this amount. Total annual N deficits were reduced to 1.7 ± 4.1 kg ha–1. No N deficit occurred in 77% of trials for maize and in 91% of trials for triticale.
Results for 1Wtr, derived using Eq. [15], are also presented in Table 1. Surplus N (Fig. 6) for 1Wtr was 182.0 ± 10.3 kg ha–1. The assumptions for this approach permit N sharing between planning periods. Nitrogen deficit values for 1Wtr are, therefore, less conservative and not directly comparable to results from Eq. [13] and [16]. Total deficits were 10.3 ± 5.0 kg ha–1. Maize and triticale N deficits were 3.1 ± 0.7 and 7.2 ± 12.5 kg ha–1, respectively.
When SOpt and +30% solutions were tested over time in an aggrading system while varying soil temperatures and manure a parameters as well as k and Q10, annual surplus N variables were 127.9 ± 18.8 and 180.0 ± 17.7 kg ha–1, respectively (Fig. 7). Total annual deficits were 9.1 ± 6.1 and 38.9 ± 6.5 kg ha–1, respectively. Maize deficits were slightly lower and less variable for + 30% (5.1 ± 4.6 kg ha–1) than for SOpt (7.4 ± 6.0 kg ha–1), but +30% triticale deficits were much greater at 33.8 ± 6.9 kg ha–1 compared to 1.7 ± 0.9 kg ha–1 for SOpt.
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DISCUSSION |
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Differences are still more pronounced when uncertainty is considered. Stochastic optimization increases summer and winter applications by an additional 1.7 and 6.2% over DOpt, respectively. Incorporating the uncertainty associated with k and Q10 into designs (SOpt) increases surplus N well above DOpt, but reduces deficit N (Fig. 6).
The parameters of most concern for the management approach under discussion are k and Q10, which control N mineralization. Parameter estimates for k can be determined from the literature data for many materials including biosolids, soil organic N, and manures (Crohn and Valenzuela-Solano, 2003; Gilmour et al., 2003; Sullivan et al., 2004; Van Kessel and Reeves, 2002). Several factors confound accurate predictions of net N mineralization from organic fertilizers over time under temperature-varying conditions. Organic N mineralization rates are measured indirectly as the appearance of inorganic species, but inorganic N may be lost to leaching or atmospheric volatilization (Calderón et al., 2004). Efforts to minimize such losses corrupt results by affecting the processes being measured. Environmental variability is substantial in the field, but laboratory results designed to constrain such variability are not fully reliable indicators of field kinetics. Organic amendments may temporarily immobilize N, but the rates and duration of immobilization are not easily predicted. The influence of environmental factors such as temperature, moisture, and soil texture are not truly separable but their relation may be soil- and substrate-specific (Griffin et al., 2002). The chemical properties of organic fertilizers can also affect mineralization rates, but the predictive power of analytical tests and computer simulations seems promising for particular materials (Gilmour et al., 1996; Gilmour and Skinner, 1999; Qafoku et al., 2001; Sullivan et al., 2004; Pierzynski and Gehl, 2005). No universally effective approach is yet available (Van Kessel and Reeves, 2002). For these reasons, there is relatively little scientific literature reflecting the influence of heat on the mineralization of organic N fertilizers and efforts to fill this gap have not been completely successful (Griffin and Honeycutt, 2000). Estimates should, therefore, be considered approximations of actual mineralization rates. In general, fertilizers that are thoroughly processed and homogenous, such as digested biosolids from a particular water treatment plant, would be expected to mineralize more consistently than materials from many diverse sources or unstabilized materials that may immobilize N to some degree. Uncertainty associated with k must, therefore, be considered on a case-by-case basis. In the case of dairy manures generally, considerable uncertainty exists. For example, when Van Kessel and Reeves (2002) incubated 107 dairy manures for 56 d at 25°C they found that net N mineralization averaged 12.8% but ranged from –29.2 to 54.9% and could not be predicted from chemical parameters.
Fortunately, the model is not highly sensitive to moderate changes in k. Sensitivity analysis shows that optimal application schedules do not vary a great deal when mineralization rates are varied. Figure 8 considers what happens when the half-life of a material varies from its design specification. For the wheat–triticale rotation under consideration, if a material is applied according to the DOpt schedule, but varies from the 283 d° design fertilizer organic N half-life by ±2/3, the resulting PAN patterns are reasonably similar. Assuming such an application schedule, materials with half-lives of 94, 283, and 424 d° will have respective cumulative crop N deficits of 3.8, 0, and 1.9 kg ha–1, respectively. Excess N will be 108, 104, and 106 kg ha–1. The associated variation is minor in the context of the many other environmental factors determining PAN availability and crop development that are not considered in the model. An exact determination of mineralization rates is, therefore, not necessary and a certain amount of variation in the properties of applied materials is tolerable.
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Adding soil temperature and organic N fraction (a) variability has a more profound influence on results. Expected crop deficits in the SOpt case increase from 0.0 to 7.4 ± 6.1 kg ha–1 for maize and to 1.7 ± 0.9 kg ha–1 for winter triticale. Temperature variability affects PAN more in the summer than in the winter because more fertilizer is applied during that season and the inorganic component these applications is not affected by soil temperature variability. Summer PAN depends to a greater extent on the temperature-sensitive mineralization of residual organic N from previous applications. When the relative influence of soil temperatures and a fractions were compared by holding one constant and varying the other, soil temperature had a greater influence on variability (data not shown). The effect of temperature on losses may be overstated to a certain extent in these simulations, however, because the crop target N used to determine deficit and surplus N remained constant for all trials. It is likely that the same temperatures will also affect crop development so that, to a certain extent, under warm conditions crops will assimilate additional N, while cool conditions themselves may limit growth reducing the limiting effects of lowered PAN.
Single Winter Applications
Natural precipitation is used to irrigate winter crops. Because, in some locations, no irrigation water is available to deliver manure during the winter growing season, winter manure may be applied in a single application before planting. In this case, side-dressing continues during the summer. Sharing between planning periods must be assumed when a single application made before plant establishment is considered. Surplus N is allowed to accumulate in the soil during early stages of plant development to be drawn on later when demand increases. Of course, this entails a risk that a large rainfall event will leach PAN from the soil denying N to the crop and delivering nitrate to ground water. Applying single applications of materials with mostly organic N also results in an unbalanced schedule in which relatively little annual N is applied during the summer. For the situation depicted in Fig. 5, only 26% of the total applied N was applied during the summer. This increases the risk of summer N deficits if mineralization is faster than expected. To help control these problems, an organic fertilizer containing more inorganic N could be applied. Had the winter fertilizer contained 50% inorganic N (ai = 0.5), the winter application rate would have been 283 kg N ha–1. This would have represented 49% of the 578 kg N ha–1 added annually. However, higher inorganic N concentrations leave the system more vulnerable to unexpected leaching events. Growers can also consider one or more supplemental inorganic N fertilizer applications during the growing season since inorganic fertilizers can be easier to apply to established crops. An inorganic application could be included in the model as an amendment containing only inorganic N (ai = 0). Supplementation with an inorganic fertilizer may make particular sense when P rather than N limits the application of the organic fertilizer so that less organic fertilizer can be applied thus reducing the overall P load.
The effects of uncertainty are increased when amendments are applied infrequently. Higher than expected mineralization rates result in an abundance of PAN during the winter and a shortage during the following summer. The opposite is true for a slower mineralization rate. When a single winter application (Eq. [15]) is designed by assuming a 283 d° half-life and the resulting PAN is completely conserved in the soil during the winter (11 November–18 February), a 94 d° half-life results in a summer crop N deficit of 10.4 kg ha–1 and a winter crop surplus of 45.0 kg ha–1. An opposite pattern occurs when decay rates increase. A 424 d° half-life results in a summer crop N surplus of 1.3 kg ha–1 and a winter crop deficit of 7.2 kg ha–1. Assuming that no substantial leaching occurs due to heavy precipitation during the time of the winter crop, the environmental impact of the different half-lives is similar. According to leaching assumptions for the 1Wtr approach and Eq. [14], the 94, 283, and 424 d° half-lives will leach 203, 192, and 199 kg ha–1, respectively, if materials are all applied according to the optimized 283 d° half-life. If fertilizers are applied according to schedules optimized using their correct half-lives, then the deterministically predicted leaching losses are 130, 192, and 206 kg ha–1 with no crop deficits. More labile materials, therefore, have two advantages. First, because they mineralize more quickly, they can be utilized more efficiently. Second, systems relying on labile materials arrive at steady state more rapidly.
Time to Steady State
The optimization model assumes that the system is already at steady state. If the approach taken here is applied to a newly installed field, time will be needed for organic N to accumulate to a steady-state condition. The example condition has a time to approximate steady state of 7 yr, but times will be greater in cooler regions. Conditions similar to newly installed fields are likely to be common for farms transitioning to organic agriculture and applications above steady-state rates can be reasonable under such circumstances. Fields with histories of receiving significant organic N applications, such as those serving the needs of livestock operations, are likely to have organic N concentrations approaching or exceeding steady-state levels. In such cases upward adjustments are inappropriate.
Multiple Compartment Approaches
Mineralization is often represented using two or more linear compartments. An additional compartment can also be used to incorporate immobilization. Because the underlying model is linear, the approaches represented by Eq. [13] and [15] may be easily modified to permit multiple linear compartments. Such a procedure would require supplementary terms within the crop N constraint. A variation on this would occur if materials with different decay rates were applied. The decomposition of each could be included as separate terms within the model. Such approaches merit more study.
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CONCLUSIONS |
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When organic fertilizers can be applied regularly, solutions are only moderately sensitive to errors with respect to mineralization rate or Q10 estimates. Monte Carlo simulations suggest that soil temperature variations affect accuracy more strongly, but optimization remains a preferred approach for determining application rates given that soil temperature cannot be determined in advance of applications. Although an explicit simulation of the movement of N to ground water is not necessary to design application rates, the linear optimization approaches developed here could be further improved by allowing the option of partial rather than complete leaching of N between consecutive planning periods. Additional research is needed to develop appropriate partial leaching parameters.
The models can be solved easily using computer spreadsheets. Results indicate that side-dressing, when feasible, provides more reliable and efficient N delivery than single applications before crop establishment. Single wintertime treatments demand disproportionately large applications before planting because cool weather retards mineralization reducing the PAN available to winter crops. This effect was magnified in the case considered here by the use of an aged manure containing relatively little ammonium. A material richer in inorganic N could be applied at lower rates permitting increased applications during the summer.
Optimized schedules will be more accurate with relatively labile amendments such as processed organic fertilizers, labile manures, lagoon water N, and biosolids. This is because net mineralization rates from materials that first immobilize N, as occurs with some manures and incompletely cured composts, can be difficult to predict (Calderón et al., 2004; Hartz et al., 2000). In their present form, the approaches developed here are not suitable for materials that immobilize N for significant lengths of time. A true steady-state condition may not be reached if organic fertilizer properties change over time or if there is a need to significantly change cropping patterns. If the fertilizers and crops are relatively similar so that a consistent pool of fertilizer organic N has accumulated in the soil, a reasonable approach would be to optimize the application schedule to reflect conditions as they change. To account for the additional uncertainty this imposes, a SOpt can be used or crop target N levels can be increased. Additional stochastic variables could be added to Eq. [16] although each would add an additional dimension making solutions more computationally intensive so that specialized software is needed. Safety factors can also be introduced to anticipate denitrification losses where appropriate. Research is needed as to the reasonableness and economic significance of such safety factors.
The linear programming approaches developed here could be easily incorporated into more comprehensive manure management software packages to assist farmers in developing sustainable practices. They would also be useful for designing application schedules for other organics residuals, such as those resulting from food processing and wastewater treatment.
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APPENDIX |
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ACKNOWLEDGMENTS |
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REFERENCES |
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is, M.J. 2002. SPSS 11.0: Guide to data analysis. Prentice Hall, Upper Saddle River, NJ.
