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Journal of Environmental Quality - Article



This article in JEQ

  1. Vol. 39 No. 5, p. 1699-1710
    unlockOPEN ACCESS
    Received: Sept 3, 2009

    * Corresponding author(s): david.nash@dpi.vic.gov.au
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A Bayesian Network for Comparing Dissolved Nitrogen Exports from High Rainfall Cropping in Southeastern Australia

  1. David Nash *a,
  2. Murray Hannaha,
  3. Fiona Robertsonb and
  4. Penny Rifkinb
  1. a Victorian Dep. of Primary Industries–Ellinbank, RMB 2460 Hazeldean Road, Ellinbank, Victoria 3821, Australia
    b Victorian Dep. of Primary Industries–Hamilton, Private Bag 105 Hamilton VIC 3300, Australia. Assigned to Associate Editor Robert Hubbard


Best management practices are often used to mitigate nutrient exports from agricultural systems. The eff ectiveness of these measures can vary depending on the natural attributes of the land in question (e.g., soil type, slope, and drainage class). In this paper we use a Bayesian Network to combine experiential data (expert opinion) and experimental data to compare farmscale management for different high-rainfall cropping farms in the Hamilton region of southern Australia. In the absence of appropriate data for calibration, the network was tested against various scenarios in a predictive and in a diagnostic way. In general, the network suggests that transport factors related to total surface water (i.e., surface and near surface interfl ow) runoff, which are largely unrelated to Site Variables, have the biggest effect on N exports. Source factors, especially those related to fertilizer applications at planting, also appear to be important. However, the effects of fertilizer depend on when runoff occurs, and, of the major factors under management control, only the Fertilizer Rate at Sowing had a notable effect. When used in a predictive capacity, the network suggests that, compared with other scenarios, high N loads are likely when fertilizer applications at sowing and runoff coincide. In this paper we have used a Bayesian Network to describe many of the dependencies between some of the major factors affecting N exports from high rainfall cropping. This relatively simple approach has been shown to be a useful tool for comparing management practices in data-poor environments.

Nutrient exports from agriculture adversely affect water resources in many parts of the world (European Union, 2000; Granlund et al., 2005; USEPA, 1996). Nitrogen (N) and phosphorus (P) exported from agricultural catchments can accelerate the natural ageing of water bodies (Sharpley et al., 2003a), promote algal blooms, and degrade water quality. Over the last two decades, research has focused on developing agricultural systems that are environmentally and economically sustainable (Cannell and Hawes, 1994; Di Pietro, 2001). In southeastern Australia, these studies have generally targeted pasture-based dairying (Nash et al., 2005; Nash and Halliwell, 1999; Nash et al., 2007). However, in this region nutrient exports from high rainfall (>550 mm) cropping are increasingly of concern (Mathers et al., 2007).

As a result of a downturn in world markets for meat and wool, extensive grazing land in southeastern Australia is being converted to broad-acre cropping. For example, in the Glenelg and Hopkins Rivers catchments (Fig. 1 ), cropping increased from 62,000 to 205,000 ha between 1992 and 2002 (Holmes, 2002) and is estimated to exceed 250,000 ha (Mark McDonald, Southern Farming Systems, personal communication, 2009), with 30% of the land under barley, 35% under canola, and the remainder under wheat (Gerrard Bibby, Graincorp Operations Ltd., personal communication, 2009). In an area where stream N and P concentrations are already unacceptably high (Commissioner for Environmental Sustainability, 2008), this land use change has probably increased nutrient exports, especially N exports (Johnston, 2006), with adverse financial consequences for the region (Read Sturgess and Associates, 1999).

Fig. 1.
Fig. 1.

Map of the Glenelg and Hopkins rivers management regions in southeastern Australia.


Modern cropping systems using minimal or no tillage and retention of plant residues have been designed to minimize the export of sediment-bound nutrients (Holland, 2004). Consequently, dissolved nutrients often form a larger proportion of total exports when such systems are compared with conventional systems using deep cultivation (>250 mm) (Kimmell et al., 2001). The higher proportions of dissolved nutrients from conservation tillage systems may, at least in part, be the result of better soil structure and improved infiltration (Mathers and Nash, 2009; Sharpley and Smith, 1994).

Deterministic models such as SWAT (Drury et al., 2009), LEACHMN (Sogbedji et al., 2001), EPIC (Gassman et al., 2004), and DRAINMOD (Salazar et al., 2009) have been used to simulate N exported from cropping systems. However, linking crop management to N exports at the paddock (<100 ha) or farm scales remains difficult where rainfall variability is high and soil types, crops, fertilizer rates, sowing times, and crop residue management vary. This is especially true in southeastern Australia where there are few empirical relationships on which to base a deterministic model of N exports from cropping and where there is a general lack of parametric information describing interactions between different management practices (Mathers et al., 2007).

Bayesian Networks have been used extensively in natural resource sciences to examine complex relationships in data-poor environments (Pearl, 1988) and for investigating multifactor problems such as those associated with resource management (Ames, 2002; Ames and Neilson, 2001; Varis, 1997; Varis and Kuikka, 1999). Despite the word “Bayesian” in the title, Bayesian Networks do not necessarily imply a commitment to Bayesian inference. Their operation is built on well established rules of conditional probability. Non-Bayesian methods are often used to estimate the conditional probability distributions that define such networks. Nonetheless, a Bayesian framework can usefully relax the rules for defining which quantities may be considered “random” and hence incorporated, with probability distributions, into such networks.

In the context of analyzing the effects of management on water quality, Bayesian Networks (i) can combine subjective and objective information into models that are conceptually sound, even where empirical data are limited and factors are complex; (ii) allow uncertainty to be built into all components of the network, from uncertainty in input data to uncertainty in assumptions describing biophysical processes; and (iii) provide a transparent and logical linking of cause and effect that is easy to understand and communicate and in which all assumptions are explicit.

Conversely, Bayesian Networks (i) reflect current knowledge on how fixed attributes and management interact to affect water quality in a qualitative rather than quantitative way, and output, being represented by probability distributions, is less definitive than many traditional physically based modeling approaches; (ii) are difficult to validate when there are limited empirical data on which to independently assess the model; and (iii) often require categorization (classification), which may not adequately capture the nature of continuous, quantitative relationships, especially where nonlinear relationships exist, and can lessen the sensitivity of findings to factors further from the terminal node.

Bayesian Networks are well reviewed elsewhere (Jensen and Nielsen, 2007; Korb and Nicholson, 2004; Pourret et al., 2008). In summary, Bayesian Networks provide a graphical representation of cause-and-effect relationships with the strength of the interdependencies (causal links) represented as conditional probabilities. The nodes represent variables (discrete or continuous), and directed links (also called “arcs,” which pass from the parent node to the child node) are used to represent dependencies between variables. Dependencies are quantified by conditional probability distributions that are associated with each node. The conditional probability of each child node value is specified given each combination consisting of one value selected from each parent node (also called an “instantiation of the parent set”). For discrete nodes, the conditional probability distributions are represented as tables that can be populated using techniques including (i) direct data analyses/tabulation of observed frequencies (e.g., for probability of rainfall); (ii) elicitation of expert opinion; (iii) Monte Carlo simulations where deterministic relationships are known (points drawn from distributions for inputs); and, where sufficient data are available, (iv) machine learning techniques. Once all instantiations are considered, a probability distribution is established for each node. These distributions are referred to as “prior probabilities.” As evidence of state values is received for specific nodes and added into the network, the prior probability distributions are conditioned, and the posterior probability distributions for the remaining nodes in the network, in particular, for a set of query nodes, are computed based on basic laws of probability. Consequently, as evidence is added to a network in the form of node values, the possible outcomes that the network represents do not change; only the relative probabilities of those outcomes change.

In this study we develop and test a simple Bayesian Network relating cropping management to N exports to surface waters from the Hamilton region of southeastern Victoria (Fig. 1). The aims of the study were (i) to combine deterministic equations and experiential data into a Bayesian Network representing N exports from high rainfall cropping, which incorporates landholder decision-making and the episodic nature of rainfall runoff, and (ii) to use that network to predict and diagnostically examine likely differences in N exports between crops and tillage systems used in the high rainfall zone of southeastern Australia.

The Network Development Process

The process for developing the Bayesian Network is presented in Fig. 2 The network development process drew heavily on the processes used for developing a similar network for the dairy industry (McDowell et al., 2009). To constrain intra-annual variation, the network was conceptualized using an annual time step and applied at the “paddock scale” where a paddock is defined as an area with similar physical attributes (i.e., soil type, slope) that is treated by the landholder as a single management unit. In the Hamilton region, fields (paddocks) can range in size from 10 to >100 ha.

Fig. 2.
Fig. 2.

Conceptual representation of methodology for development of a Bayesian Network to describe farm-scale N exports.


Where possible, the network was developed using empirical data and deterministic relationships. In some cases, the deterministic relationships were inferred from other industries or model studies. Information from a variety of data types and sources was collected using a knowledge-gathering framework based on five variable types. “Site Variables” were the physical attributes of the site in question and over which the manager has little or no control (i.e., inherent soil properties). “Year Variables” depended on chance events, most often rainfall characteristics, and changed annually. “Management Variables” were those that were under land manager control, most notably Crop Type and Fertilizer Type and Rate and Depth of placement. “Intermediate Variables” were defined as factors that combine the effects of Site, Year, and Management variables to describe aspects of N exports (e.g., Fertilizer Source Factor). The Outcome Variable (Dissolved N Export Factor) describes the range of dissolved N exports that may be expected from paddocks (Fig. 3 ).

Fig. 3.
Fig. 3.

Bayesian Network of high rainfall cropping in southeastern Australia.


Research data were initially collected through an extensive review of relevant literature relating to N mobilization and transport processes (Mathers et al., 2007). Whereas Mathers et al. (2007) focused on published reports, journal articles and scientific textbooks, unpublished reports and other information sources such as Victorian Resources Online (http://www.dpi.vic.gov.au/vro) were also used for network development. Experiential knowledge was initially gathered through a survey of 189 cropping farmers who manage an estimated 215,000 ha of farm land in southwestern Victoria (Nicholson and Alexander, 2005). This information was augmented by interviews with six technical specialists and a similar number of farmers familiar within the Hamilton region. The methodology used for interviews has been described previously (Gillham, 2000; Gillham, 2005; Patton, 1988; Patton, 2002).

Using the research and experiential data, a preliminary “cause-and-effect” diagram was created to describe the key N sources and processes. NETICA, version 4.08 (Norsys Software Corp., Vancouver, Canada) software, which used forward Monte Carlo simulations to generate the probability distribution for the query nodes (i.e., Dissolved N Export Factor), was used for the entire model development and interrogation process. Continuous variables were discretized (i.e., the range was divided into a number of intervals with specified thresholds), and all variables represented by Nodes (with States defining the possible values of the node) and causation were represented as linkages between Nodes.

To test the veracity of the cause-and-effect diagram, it was presented to a specially convened half-day workshop involving 14 farmers and farm advisors. The workshop commenced with an introduction to cause-and-effect relationships and progressed to examine cropping. The cause-and-effect diagram was presented, and each Node and Link was examined in sequence and in detail. This examination comprised a two-step process: (i) determining the appropriateness or otherwise of the network structure (or cause-and-effect diagram) and (ii) collecting information regarding node values and relationships. The workshop was professionally facilitated, and all discussions were recorded on an audio tape and by a designated minute secretary. In addition, notes were collected from each participant. Although there were some cosmetic changes to the cause-and-effect diagram, two areas were subject to major changes. The workshop participants indicated that soil cracking that occurred over summer was particularly important for drainage in the Hamilton region. A node relating to soil cracking was added to the cause-and-effect diagram. Far more importantly, the workshop participants believed that the node representing the timing of sowing, while approximately correct, inadequately considered farmer decision-making and behavior. Timing of sowing was a critical factor if deterministic equations relating dissolved N in runoff to time elapsed since fertilizing (at sowing) were to be used. This was represented in the initial network as a uniform distribution between optimum sowing dates for a particular crop.

The cause-and-effect diagram was modified to reflect comments from farmers and farm advisors and presented at a specialists' workshop attended by four crop researchers who were familiar with the Hamilton region. Feedback from this researcher workshop again resulted in changes to the network structure, primarily relating to the calculation of water exports.

In the final cause-and-effect diagram, there were five main components: two transport factors (Surface Drainage and Sub-Surface Drainage) and three source factors (Soil, Plant, and Fertilizer) (Fig. 3). Using the NETICA software, the State descriptor for each Node and the probabilities of each State are represented numerically and by the horizontal column graph. For continuous distributions, a mean estimate for that node, calculated as the sum of products of the midpoints of the ranges and probabilities, is presented below the column graph along with the standard deviation (Fig. 3).

The first step in quantifying the network was to define the States. A full description of each Node, its States, and the sources of data used for compiling or calculating the conditional probability tables are presented in the online Supplemental Material. For some Nodes, States were represented as ranges rather than discrete numbers, which allowed uncertainty of the impact of that node to be included in the analyses. In other Nodes where no data were available, States were described qualitatively using subjective descriptions.

The relationships between parent (independent) and child (dependent) nodes and their states were then documented in the conditional probability tables that underpin the Bayesian Network structure (i.e., Given each set of conditions in the parent nodes, what are the chances of each condition occurring in the child node?) (Cain, 2001). Where possible, quantitative data (i.e., rainfall and runoff records) and deterministic equations (i.e., derived from experimental data relating management variables and N loads) were used. Deterministic equations were converted by the NETICA software to conditional probability tables. Uncertainty due to the sampling was not used in developing conditional probability tables because most of the relationships between nodes were based on the “conservation of mass.” The major deterministic equation not based on the conservation of mass (i.e., relating to the time between fertilizer application and N concentrations) was structured to incorporate the upper and lower 95% confidence estimates for the equation parameters in parent nodes. In cases where objective information was not available, conditional probabilities tables were generated by expert opinion.

An artifact of the NETICA software was that where deterministic equations were used to derive conditional probability tables, the numerical ranges assigned to States potentially distorted subsequent probability distributions. For example, the software assumed that all values within a State (defined by upper and lower values) were equally likely to occur when in fact for nonlinear equations values closer to the overall mean for that Node had a higher probability of occurrence. To accommodate the extensive use of nonlinear deterministic equations, the number of States was often expanded in child nodes and the numerical ranges assigned to States were not uniform. The number of States and numerical ranges assigned to them depended on the forms of the equations (i.e., log-normal) and the effects of the ranges on the estimated mean for the node.

When using expert opinion to compile conditional probability tables for child nodes, each combination of states of parent nodes was ranked from greatest positive effect on the child node to greatest negative effect on the child node. Ranking was always based on general principles and assumptions made during the model development process. Once the ranking was ordered in this way, conditional probabilities were assigned to selected combinations based on knowledge collected in previous stages of the project (i.e., literature and interviews), and general rules of thumb were developed for interpolation of the remaining conditional probabilities, using the method suggested by Cain (2001)

Once conditional probability tables for the network were constructed, the network was considered to be functional. Because there was no comprehensive data set that could be used for formal validation, the network was assessed by examining a limited number of case studies and comparing the network output with the expectations of experts familiar with these systems. The mean estimate of the “Dissolved N Export Factor” provides a useful indication of the performance of different systems. For comparison purposes, a small change was considered to have occurred if the Dissolved N Export Factor changed by >1 unit and >10%, a medium change was considered to have occurred if the Dissolved N Export Factor changed by >2 units and >20%, and a large change was considered to have occurred if the Dissolved N Export Factor changed by >3 units and >25%. With this method, the change measure considered the absolute and relative magnitudes of changed management predicted effects. The change measure and the “Sensitivity to Findings” function of the NETICA software were used extensively as part of this quasi-validation process to examine specific relationships within the network and to compare those relationships with observed data and the assumptions used in their development (Korb and Nicholson, 2004).

The Network Structure

The Bayesian Network was conceptualized as having transport and source factors similar to phosphorus (P) indices (DeLaune et al., 2004; Elliott et al., 2006; Hooda et al., 2000; Sharpley et al., 2003b). Like indices, where data are limited, additive, multiplicative or additive-multiplicative approaches were used to develop relationships (Buczko and Kuchenbuch, 2007). However, unlike index systems, Bayesian Networks facilitate the incorporation of more complex cause and effect relationships.

The transport component of the Bayesian Network was initially based on conservation of mass and conceptualized using Eq. [1]:

[1] D s = P ET Plant ET Soil D d
where Ds is drainage to surface water, P is annual precipitation, ETPlant is the plant evapotranspiration based on pan evaporation, ETSoil is innate soil evapotranspiration, and Dd is drainage to deep water tables (deep drainage). The equation assumes similar soil water storage from year to year.

Although there were few if any data for the high rainfall zone, it was the consensus from the specialists' workshop that the APSIM crop model (McCown et al., 1996) provided the best estimates of crop water use. The APSIM modeling provided a deterministic relationship that could also be used to estimate deep drainage. The network was modified to calculate drainage using Eq. [2]:

[2] D s = P −( YId/PWU )− D d
where Ds is drainage to surface water, P is annual precipitation, Yld is crop yield (kg), PWU is plant water use (kg grain mm−1) estimated by APSIM, and Dd is drainage to deep water tables (deep drainage).

In the network, drainage to surface water (Ds) is assumed to have surface and subsurface (i.e., fast and slow) flow components. The surface flow is assumed to be overland flow, and the slow flow is assumed to be interflow (Nash et al., 2002).

In developing the source components of the network, it was assumed that N was mobilized independently from the different sources (i.e., the plants, soil, and fertilizer applied in that year). This assumption has been used elsewhere for P (Nash et al., 2005; Pierson et al., 2001). Crops in the Hamilton region are often grown on soils with low slopes and therefore low erosion potential. Not surprisingly, under such circumstances, total dissolved N (TDN) comprises 46 to 98% of total N (Johnston, 2006), and nitrate/nitrite can comprise >95% of TN (T. Johnson, personal communication). Although there are clear relationships between plant, soil, and fertilizer N, given the solubility of nitrate the assumption of independent mobilization would seem reasonable for cropping systems in the Hamilton region.

The fertilizer source factor was the subject of major changes during network development. Nutrient exports from recently applied fertilizers depend on the time between application and runoff, which was estimated from the Week of Sowing and the Monthly Runoff Probability Nodes. In the original conceptualization, it was assumed that sowing date was uniformly distributed between the earliest and latest sowing dates based on, among other things, degree days (as a determinant of crop development), frost risk, and drought risk. The farmer and consultant workshop participants believed sowing time was determined by rainfall. Moreover, once significant rainfall occurred, sowing did not commence immediately. Seedbed preparation necessitated a delay between rainfall and sowing that depended on the size of the area being planted and the availability of machinery. The workshop participants indicated that, after rainfall, the likelihood that a particular tract of land would be planted increased for about 12 d and gradually declined thereafter until 25 d after rainfall when sowing ceased. The cause-and-effect diagram combines a uniform and a triangular probability distribution to better reflect farmer behavior.

Application and Analyses of the Network

As a first step to examining the network, three sites with contrasting physical characteristics were used to investigate the sensitivity of the output node (Dissolved N Export Factor) to site variables. Two of the sites had been instrumented to measure sample runoff (Hamilton and Cressy runoff sites). The characteristics of the sites are presented in Table 1 The primary measure used to compare the sensitivity of the output node to site variables was Variance Reduction. The output node (Dissolved N Export Factor) is quantitative and has an initial distribution. When information is supplied about the state of a parent (e.g., site) node, this may shrink the output node distribution toward more probable values, reducing its variance. The variance reduction then is simply the difference between the variances of the output node distribution computed before and after information was supplied. A second metric, Belief Variance, was also used. Belief Variance measures the expected squared change in class probabilities in the output node distribution. The Variance Reduction and Belief Variance are each averaged appropriately over the range of the parent node values. Both these metrics can be automatically computed from within the NETICA software (Pearl, 1988).

View Full Table | Close Full ViewTable 1.

Site attributes used in for investigating the cropping network.

Attribute Case study 1 Case study 2 Case study 3
Site† Hamilton runoff site Cressy runoff site Hamilton research station
Soil type (Isbell, 2002) brown chromosol grey sodosol black vertosol
Soil type (Soil Survey Staff, 2006) mollic haploxeralf vertic natrixeralf xeric endoaquerts.
Subsurface soil texture clay sodic clay sodic clay
Surface cracking–facilitated drainage moderate weak strong
Surface slope high low low
Sealing topsoil yes yes yes
Surface soil texture fine sandy clay loam fine sandy loam clay
For additional detail of soil types, refer to http://www.dpi.vic.gov.au/dpi/vro/glenregn.nsf/pages/glenelg_soil_surveys_hri

The results of the sensitivity analyses are presented in Table 2 For the purposes of these analyses it was assumed that: (i) the crop was canola, (ii) it was a medium rainfall year, (iii) the field had been under continuous cropping, and (iv) the field had been under conventional cultivation. These assumptions affect the sensitivity analyses, as does the discretization of node states and the associated probabilities. Further, where findings are combined into Intermediate Variables, especially those with a limited number of states, sensitivity diminishes the further a node is away from the Target Node.

View Full Table | Close Full ViewTable 2.

Sensitivity analyses of Dissolved Nitrogen Export Factor using the Bayesian Network for high rainfall cropping in south eastern Australia (assuming that the crop was canola, it was a medium rainfall year, and the field had been under continuous cropping and would be conventionally tilled).

Variance node Hamilton site Cressy site Hamilton research farm
Variance reduction Belief variance Variance reduction Belief variance Variance reduction Belief variance
Dissolved N export factor 13.8 0.519 14.0 0.519 13.97 0.519
Surface water 5.9 0.161 6.0 0.163 6.0 0.164
Total runoff 5.9 0.195 5.9 0.195 5.9 0.195
Subsurface water 4.8 0.142 4.8 0.142 4.9 0.142
Crop yield 4.0 0.125 4.0 0.125 4.0 0.125
Sowing fertilizer source factor 2.1 <0.001 2.2 <0.001 2.2 <0.001
Sowing fertilizer nitrogen 0.7 <0.001 0.7 <0.001 0.7 <0.001
Days between sowing and runoff 0.7 <0.001 0.7 <0.001 0.7 <0.001
Soil source factor 0.2 0.002 0.2 0.002 0.2 0.001
Fertilizer rate at sowing 0.2 <0.001 0.2 <0.001 0.2 <0.001
Estimated mineral nitrogen 0.1 0.001 0.1 0.001 0.1 0.001

The drought conditions prevalent in southern Australia did not allow a meaningful comparison between actual and measured N exports. However, for all three sites, the Dissolved N Export Factor of 2.2, which loosely equates to N load, is consistent with local expectations and modeling (0.63–1.83 kg N ha−1) (Holmes, 2002). There was very little difference in the sensitivity of the Dissolved N Export Factor from findings at the nodes representing Site Variables. Intermediate nodes (i.e., computed from a series of parent nodes) associated with transport processes, Surface Water, Total Runoff, Sub-Surface Water, and Crop Yield accounted for most of the Variance Reduction. A similar categorization could be achieved by sequentially changing child node findings and comparing changes in the target node, and the results are again consistent with expectations. Given that Annual Rainfall was assumed to be “medium” and there was a greater probability of high flow through surface pathways, it was not surprising that the Variance Reduction due to Surface Runoff was similar to Total Runoff and higher than Sub-Surface Runoff and Crop Yield. The importance of crop yield in a transport context stems from its influence on Total Runoff.

Source-related factors accounted for most of the remaining Variance Reduction. The most important were the intermediate nodes Sowing Fertilizer Source Factor, Sowing Fertilizer Nitrogen, Days Between Sowing and Runoff, and Soil Source Factor, followed by the Fertilizer Rate at Sowing and Estimated Mineral Nitrogen. The relative importance of the transport and source nodes in explaining the Variance Reduction was particularly sensitive to nodes, such as the Fertilizer Rate at Sowing, that were effectively scaling factors in the model that changed the probability distributions and the maximal value a node could take (data not shown).

The relationships measured by differences in the variance reduction were not replicated in the Belief Variance, which examines changes in probabilities of the target node rather than its estimated value. For example, the Sowing Fertilizer Source Factor accounted for approximately 15% of the variance reduction and only approximately 0.005% of the Belief Variance. Factors associated with transport capacity (i.e., Total Runoff, Surface Water, Sub-Surface Water, and Crop Yield) had the highest Belief Variance. Because the value of the target node is the metric used for assessing outcomes in this application, it follows that Variance Reduction is probably the better estimate of sensitivity, as one would expect for a quantitative factor such as the Dissolved N Load Factor. However, the apparent sensitivity of Variance Reduction to multipliers in deterministic relationships suggests that both measures are useful.

The network was subsequently used to compare a series of different management options (Table 3 ). The first comparison was between surface- and subsurface-dominated flow for midseason wheat, canola, and barley. The network suggests that, in general, surface and subsurface pathways have only a minor effect on N exports, in keeping with a solute that does not interact strongly with soil after mobilization. The Network suggests that, all else being equal, there will be a small increase in N exported from canola compared with wheat (approximately +1.3) and a large increase (approximately +4) in N exported from barley. This is a direct result of the method used to estimate transport potential, as indicated by the increased estimates of the Surface and Sub-Surface Water nodes, and agrees with anecdotal evidence provided by farmers not involved with the model development who suggested that surface drainage was more likely to occur in a canola crop than in wheat.

View Full Table | Close Full ViewTable 3.

Results of interrogating the cropping Bayesian Network.

Node settings Node values
Transport conditions Crop Rainfall Yield Pasture/ley rotation Tillage practices Estimated mineral N Fertilizer rate at sowing Fertilizer type at sowing Surface water Subsurface water Soil source factor Plant source factor Sowing fertilizer source factor Dissolved N load factor
Surface-dominant flow midseason wheat medium default default default default default default 33.3 4.5 5.4 0.2 2.2 1.0
Subsurface-dominant flow midseason wheat medium default default default default default default 6.6 29.1 5.5 0.2 2.2 1.0
Surface-dominant flow canola medium default default default default default default 74.4 9.3 5.4 0.4 2.2 2.3
Subsurface-dominant flow canola medium default default default default default default 12.8 71.4 5.5 0.4 2.2 2.2
Surface dominant-flow barley medium default default default default default default 351.0 34.2 5.4 0.2 2.4 6.5
Subsurface-dominant flow barley medium default default default default default default 51.9 319.0 5.5 0.2 2.4 6.0
Surface-dominant flow canola medium high default default default default default 0.0 0.0 5.4 0.4 2.2 0.0
Surface-dominant flow canola medium medium default default default default default 51.9 9.5 5.4 0.4 2.2 3.3
Surface-dominant flow canola medium low default default default default default 484.0 45.2 5.4 0.4 2.2 6.7
Subsurf-ce dominant flow canola medium high default default default default default 0.0 0.0 5.4 0.4 2.2 0.0
Subsurface-dominant flow canola medium medium default default default default default 15.3 49.9 5.4 0.4 2.2 3.2
Subsurface-dominant flow canola medium low default default default default default 51.9 470.0 5.4 0.4 2.2 6.3
Surface-dominant flow canola medium medium default default high default default 51.9 9.5 6.8 0.4 2.2 3.7
Surface-dominant flow canola medium medium default default low default default 51.9 9.5 1.5 0.4 2.2 2.0
Subsurface-dominant flow canola medium medium default default high default default 15.3 48.8 6.9 0.4 2.2 3.8
Subsurface-dominant flow canola medium medium default default low default default 15.3 48.8 1.5 0.4 2.2 1.7
Surface-dominant flow canola medium medium continuous cropping no tillage default default default 51.9 9.5 4.9 0.4 3.1 3.4
Surface-dominant flow canola medium medium continuous cropping conventional cultivation default default default 51.9 9.5 5.9 0.4 3.1 3.1
Default default default default default default default high MAP† 163 29.4 5.4 0.27 4.4 4.5
Default default default default default default default nil MAP 163 29.4 5.4 0.27 0 2.6
Default default default default default default default high urea 163 29.4 5.4 0.27 3.6 4.1
Default default default default default default default nil urea 163 29.4 5.4 0.27 0 2.6
MAP, mono-ammonium phosphate.

The effects of crop yield were investigated assuming a canola crop was grown in a medium rainfall year. Crop Yield had a large effect (+6.7) on N exports, expressed again through the water-related transport nodes. A medium rainfall year in the high rainfall cropping zone of southern Australia is most often associated with higher crop yields because neither moisture limitation nor water logging adversely affect plant growth. On the basis of the data from the network, it could be argued that optimizing crop performance and ensuring high yields will benefit the environment. In some cases, farmers may need to use additional fertilizer to achieve higher yields, and the network provides a mechanism for comparing the likely outcome of such a strategy. For example, the network suggests that in a system with low fertilizer inputs and for a N-limited crop, increasing crop yields could effectively eliminate N exports (data not shown).

The effects of Estimated Mineral N on the Dissolved N Load Factor were investigated for surface and subsurface dominant flow. In both cases there was a small to medium (approximately +2) increase in the Dissolved N Export Factor when moving from low to high Estimated Mineral N. However, if low Estimated Mineral N increased the probability of crop failure or the need for remedial higher fertilizer applications, these interacting effects may negate the benefits of low mineral N in terms of N exports.

The final comparisons were between conventional cultivation and no tillage in a continuous cropping system and fertilizer strategies using the default network values. The network suggests that the different tillage systems have little if any overall impact on N exports. The slight increase in the Soil Source Factor reflects the overall higher N content under no-till systems and the increase in nutrients near the soil surface (Mathers and Nash, 2009). Fertilizer management, on the other hand, had a small to medium effect on the Dissolved N Export Factor. The slightly higher exports with monoammonium phosphate rather than urea are largely inconsequential.

A major advantage of Bayesian Networks over alternative approaches is their ability to be diagnostic as well as predictive. In this case the network was used to investigate the conditions under which very high N exports, based on the Dissolved N Load Factor (i.e., Very High for the query node, Dissolved N Export Factor, approximates a load of 20–25 kg N ha−1) could be expected for the Hamilton runoff site in years of medium annual rainfall. Nitrogen exports approaching approximately 30 kg ha−1 annually have been measured in a field study in the region for which the network was developed (Johnston, 2006). The network (Fig. 4 ) suggests that such N exports are likely to occur in years when the majority of the rainfall coincided with sowing of Canola or Barley and resulted in a medium to high Sowing Fertilizer Source Factor (i.e., above-average rainfall years when crop production is poor and when sowing precedes heavy rainfall). This is consistent with field experiments (Johnston, 2006).

Fig. 4.
Fig. 4.

A Bayesian Network of high rainfall cropping in which there is a “very high” Dissolved Nitrogen Load Factor in a medium rainfall year at a site with the following characteristics: Clay- Sub-Surface Soil Texture, Clay; Surface Cracking Facilitated Drainage, Moderate; Surface Slope, High; Sealing Topsoil (Yes); and Surface Soil Texture, Loam.



When asked “What is the best management practice to reduce N exports from high rainfall cropping?” the answer is often “Well it depends!” Conditional dependency can be difficult to reproduce in conventional modeling systems, especially where data are limited. In this case, using the collective knowledge of practitioners (farmers), consultants, and researchers, we have created a cause-and-effect diagram in the form of a Bayesian Network describing N exports from high rainfall cropping in southeastern Victoria. These same stakeholders were sufficiently conversant with the technology to help us quantify the network and examine its properties.

Investigation of the Bayesian Network suggests that the most important management factor affecting N exports is probably fertilizer application. The importance of fertilizer, applied at sowing, on N exports is somewhat surprising, though understandable. Soil inorganic N stores can be in excess of 100 kg N ha−1, whereas only 15 to 30 kg N ha−1 would be considered a medium-high fertilizer application rate at sowing. The Network assumes that fertilizer, which is commonly drilled in a row below the seed (for urea) or planted with the seed (for diammonium phosphate or monoammonium phosphate P) at sowing can be more easily mobilized than inorganic N, which is distributed through the upper 300 mm of the soil profile. The equation used to estimate urea mobilization was based on surface application and adjusted for depth. This may overestimate fertilizer N fertilizer availability. Conversely, the 0.75 attenuation factor used to compensate for decreased mobilization of soil inorganic N is extremely conservative.

Given the importance of soil N in determining the optimum fertilizer application rate for crop production targets and contributing directly to N exports, especially through subsurface pathways, better defining the relationships between inorganic soil N, fertilizer application rates, and yield for different growing season conditions (i.e., rainfall and soil properties) are important. For example, incorporating data from a crop model such as Yield Prophet (http://www.yieldprophet.com.au), which is based on APSIM (McCown et al., 1996), into the network may enable the development of guidelines that draw more heavily on site-specific characteristics (e.g., soil type) to optimize N retention. Equally important is better defining the mobilization of soil N to ensure that the relative weightings of N mobilized from fertilizer and soil are appropriate under differing soil conditions. How best to acquire these data over a range of soil types and flow conditions (i.e., matrix versus macropore flow; Nash et al. [2002]) is problematic. Better information on the relative importance of soil and fertilizer N is likely to assist in the development of more site-specific guidelines for N retention.

In the high rainfall zone of southeastern Australia, water logging is common in wet years. Denitrification, which may accompany water logging, was not considered to be a significant omission from the network when it was tested with farmers, consultants, or researchers. Water logging can be related to soil type and may warrant investigation if the resolution of the source terms in the network are refined.

Because it was assumed in developing the Network that N mobilization from soil and fertilizer were only marginally affected by whether water was moving through or over the soil, the network also suggests that the predominant transport pathway (i.e., surface or subsurface) has minimal effect on N exports. This is probably a reasonable simplification given that N (especially in the form of nitrate) is relatively mobile, when compared with inorganic P, for example, but results in a site's soil physical characteristics having only a minor influence on estimated N exports. It is more likely that if the comparative relationships between soil N and fertilizer N were refined that the predominant transport pathway would be of greater importance.

From a regulatory standpoint, the network provides some interesting insights. The Dissolved N Load Factor was very sensitive to the transport factors associated with drainage volumes, which in turn are affected by crop yield. Is there an argument for more flexible cropping systems where the trade-offs between source and transport factors are optimized? The Network suggests that, all else being equal, maximizing crop yield minimizes N exports. What about using minimum sowing fertilizer N and then optimizing crop yields and water use through additional fertilizer applications during the season? Can additional fertilizer applications be justified on economic and environmental grounds?

Minimizing sowing fertilizer minimizes N availability. In a dry year, water may limit crop yield, and N exports are unlikely to be significant. In a wet year, water logging is likely to limit crop yields, and denitrification is likely to limit the effectiveness of fertilizer N additions at sowing. Moreover, in wet years it is not possible to traverse fields. In a medium year, however, strategic N applications may be environmentally justified because the increased availability of N from fertilizer is offset by higher crop water use. Testing such a strategy is possible but would require significant modifications to the current network that assumes there are no within-season N applications.

In summary, this study has used a Bayesian Network to investigate N exports from high rainfall cropping in southeastern Victoria. The cumulative uncertainties associated with this approach are significant, as indicated by the standard deviations provided with the estimates of node means (Fig. 3). As part of this study, we have identified areas in which the network could be improved. The complexity of these changes may require the use of a different software platform. Farming systems, in this case high rainfall cropping, leak nutrients. This study suggests that despite their deficiencies, Bayesian Networks provide a useful way of defining the complex relationships that exist within these systems and investigating and communicating the likely effects of changed management.


The authors would like to acknowledge the assistance of Southern Farming Systems, especially Mark McDonald and Cameron Nicholson, in completing this work. This work was sponsored by the Grains Research and Development Corporation (DAV 00059) and the Victorian Government through the Department of Primary Industries (CMI 100127). The authors thank Roger Armstrong, Tim Johnston, Gary O'Leary, Malcolm McCaskill, Peter Dixon, Rob Harris, and Peter Moate of DPI; Gerrard Bibby of GrainCorp Operations limited; and Dr. Ann Nicholson from Bayesian Intelligence who reviewed this manuscript.




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