COST-DP – Cost Effective Diffuse Pollution Mitigation

Development and Application of the ‘Cost-Cube’ Methodology

for Diffuse Pollutant Cost-curve Calculation

Cost-Cube

27th April, 2005

prepared as part fullfillment of defra project eso121 ‘cost-dp: cost effective diffuse pollution management’.

Anthony, S.1,Granger, S.2, Haygarth, P.2, Chadwick, D.2, Chambers, B.3, Smith, K.2 and Harris, D.3

1ADAS, Wolverhampton, Woodthorne, Wolverhampton, WV6 8TQ.

2Institute of Grassland and Environmental Research (IGER), North Wyke Research Station, Okehampton, Devon, EX20 4LR.

3ADAS, Gleadthorpe, Meden Vale, Mansfield, Notts, NG20 9PF.

1

COST-DP

1 Modelling Approach

1.1Introduction

The objective of this part of the COST-DP project was to develop a model framework capable of estimating the diffuse pollutant losses from model farm systems representative of UK practices. The pollutants to be considered were nitrite, ammonium, pathogens and biochemical oxygen demand (BOD). The framework was to be measure centric. By this, we mean having an explicit representation of the functional behaviour of pollutants and of the processes and pathways that can be affected by remediation measures. These dimensions of diffuse pollution can be summarised as pollutant source, mobilisation and transport (see, for example, RPA, 2003). The approach taken was based on the export coefficient approach (see, for example, Johnes, 1996) but extended to provide explicit fractions of the total pollutant loss by unique aspects of the source, mobilisation and transport dimensions. The approach taken is first illustrated with empirical data for diffuse phosphorus pollution for which these concepts are more developed (Leinweber et al., 2002). For example, the mobilisation dimension is sub-divided into the processes of solubilisation, physical detachment and incidental transfers, which are estimated to contribute 20%, 60% and 20% of total phosphorus losses, respectively (Defra, 2002). The partitioned export coefficient is prepared for a reference crop-soil-climate environment based upon empirical data and expert interpretation, and extrapolated to other environments by scaling pollutant loads in proportion to the magnitude of the pollutant vectors (soil drainage and eroded soil) estimated by simple conceptual models. Critical to this model is the recognition that the vector magnitude, and hence measure effectiveness, will vary considerably between soil types and with regional climate and land management practices. This approach with its explicit representation of the three dimensions of diffuse pollution is named the Cost-Cube export model and provides for explicit calculation of the cost and benefit of mitigation measures, and derivation of the cost curve. The methodology as implemented makes the critical assumption that pollutant losses are not source limited.

1.2Cost-Cube Export Model

The consortium was invited to develop a measure centric approach to the prioritisation of diffuse pollution mitigation measures. Measures have been previously characterised as targeting management of one of source, mobilisation or the transport of a diffuse pollutant (RPA, 2003; Dampney et al., 2002). For example, source control might involve reduction of potential pollutant applications to agricultural land; mobilisation control might involve timing of applications to avoid periods of saturated soils and rainfall; and transport control might involve the placement of riparian areas to trap and filter pollutants in over land flow. These dimensions of diffuse pollutant control can be expanded further by consideration of the primary sources and functional behaviour of pollutants against which a measure might be effective. For example, the mobilisation dimension can be separated into the processes of solubilisation, detachment and contingent losses (Haygarth and Jarvis, 1999). A remediation measure that is effective in reducing soil detachment will be effective against a strongly adsorped pollutant (phosphorus) but ineffective against a highly soluble pollutant (nitrate). The dimensions of diffuse pollution have therefore each been divided into three aspects, defined fully in Section 1.4, which distinguish between the source and behaviours of different diffuse pollutants:

  • Source Control – Internal, External, and Recycled;
  • Mobilisation Control – Solubilisation, Detachment, and Contingent;
  • Transport Control – Surface, Preferential, and Through;

The three dimensions and aspects of diffuse pollution are represented by the Cost-Cube. The Cost-Cube is an explicit representation of the proportions of the total pollutant loss due to aspects of the source, mobilisation and transport dimensions of diffuse pollution. The volume of the Cost-Cube is in proportion to the total loss for a specific crop-soil-climate condition. Each dimension of the cube represents one of the source, mobilisation or transport dimensions. Each dimension is sub-divided into three aspects, presenting type of source, process of mobilisation, and path of transport. If each combination is equally important in contributing to the observed pollutant loss, the Cost-Cube is made up of 27 equally sized cubes (Figure 1.1).

Figure 1.1 Dimensions and aspects of the Cost-Cube export model.

The Cost-Cube can be considered an extension of the export coefficient modelling approach (Johnes, 1996). This

This is a semi-distributed modelling approach, applied at the catchment scale, that calculates total pollutant losses as a fixed rate per unit area of cropping or as a percentage of pollutant output by livestock. The model is calibrated against field scale experiments and observed long-term changes in river water quality and the management of a catchment. It is recognised that the export coefficient is sensitive to the relative importance of pollutant pathways that vary geographically. For example, Johnes and Hodgkinson (1998) estimate export coefficients separately for surface and drain flow from arable land at ADAS Rosemaund, and Johnes (2003) reports nutrient export coefficients that differ between geo-climatic regions. The scaling of the export coefficients developed for a reference crop-soil-climate condition in proportion to the volumes of surface and drain flow potentially allows for improved estimation of pollutant losses at other sites.

1.2.2 Model Parameterisation

Application of the Cost-Cube model requires estimation of a parameter set describing the total pollutant loss and the relative contributions of the aspect combinations. The data required can be summarised by the following questions:

  • What is the total pollutant loss ?
  • What are the proportions of the total pollutant loss due to internal, external

and recycled sources of pollutant ?

  • What are the proportions of the internal, external and recycled sources of

pollutant that are lost due to detachment, solubilisation or contingent

mobilisation ?

  • What are the proportions of the detachment, solubilisation and contingent

losses of pollutant that are lost by surface, preferential or through flow transport ?

Figure 1.2 Cost-Cube parameterisation form for crop-soil-climate condition.

The answers to these questions are recorded on a form like that in Figure 1.2. In this cartoon example, total phosphorus losses from a dairy system have been estimated to derive primarily from internal sources, mobilised by detachment processes and lost by surface flow. The data given in Figure 1.2 can be used to divide the Cost-Cube.

The model parameters might be estimated by the running of a sophisticated deterministic model that represents all of the pollutant sources, methods of mobilisation and transport pathways. Example models include ANIMO and MACRO (Schoumans and Groenendijk, 2000; McGechan and Vinten, 2004). However, these models do not describe the complete range of pollutants and to set these models up for all of the model farms was beyond the available resource for this project.

1.2.2.1Expert Consultation

The simplest means of model parameterisation is to invite experts to estimate the total quantity of pollutant lost and the relative importance of the source, mobilisation and transport aspects. This can be informed by empirical measurements of pollutant losses at the plot and field scale, providing the experimental set-up is capable of separating the contributions made by the different pollutant vectors.

As an example, members of this project were presented with a scenario concerning the loss of phosphorus associated with the maintenance of a dairy farm system for a year. The members were asked to consider the losses that would occur due to runoff from manure storage and hard standings, the spreading of manures onto arable land and the direct excretion onto grassland whilst at grazing. Table 1.1 summarises the range of parameters reported. There was generally good agreement on the relative importance of the transport and mobilisation types, but agreement was poor for the source types. This reflected uncertainty in the definition of the internal or soil contribution to the total pollutant loss. The range of parameter values given by the group members could be used in an uncertainty analysis.

Table 1.1 Estimates of the relative importance of diffuse pollution control aspects in the delivery of phosphorus to river waters from a dairy farm system. Table values are the proportion of the total pollutant loss due to each aspect of a cost cube dimension.

External / Internal / Recycled
Source : / 0.10 to 0.30 / 0.05 to 0.60 / 0.30 to 0.85
Detachment / Solubilisation / Contingent
Mobilisation : / 0.25 to 0.55 / 0.05 to 0.10 / 0.35 to 0.75
Surface / Preferential / Through
Transport : / 0.75 to 0.90 / 0.05 to 0.25 / 0.05 to 0.25

1.2.2.2 Model Extrapolation

It was apparent from the above exercise that to estimate the pollutant loss and aspect contributions would be a significant task if required for every location in England and Wales, with differing weather and soil hydrology. A strategy was therefore developed whereby expert consultation was used to define the model parameters for a reference condition and simple conceptual models of the principal pollutant vectors (soil drainage and erosion) would be used to interpolate the results to other environments.

The principal adopted was that of the Event Mean Concentration (EMC). The estimated quantity of pollutant lost by each pathway at the reference condition was diluted with a modelled volume of drainage to give an EMC. The EMC was multiplied by modelled drainage volumes to give the pollutant loss for other environments. This linear dependency assumed that the environment was rich in pollutant and would not be eluted out by increasing volumes of drainage. For pathogens and BOD, monitored losses are a small percentage of the source due to adsorption. For nitrate and ammonia, the source is regularly replenished due to the transient nature of these species in the nitrogen cycle.

The magnitude of the pollutant vectors are calculated by a conceptual model of soil drainage and erosion (see Section 1.5).

For example, the reference condition defined by Figure 1.2 might be for a clay-loam soil, under permanent grass, in the east of England with an annual rainfall of 650mm. The Cost-Cube form indicates that 0.65kg (43%) of the total phosphorus loss is by detachment of soil particles in over land flow. The vector model estimates that 50kg soil are lost by this pathway each year under these conditions. Assuming that the source strength remains constant (i.e. grazing intensity, manure and fertiliser inputs do not change), the vector model estimates that 172kg of soil would be lost for the same soil in the south-west of England with an annual rainfall of 1,100mm. Hence, the phosphorus loss by detachment and over land flow would be increased to 1.48kg. Contingent losses in over land flow make up the bulk of the remainder of reference loss at 0.44kg (29%) of the total phosphorus loss, and are assumed to scale in proportion to the volume of over land flow. This is calculated to be 12mm in the east and 44mm in the south west, resulting in a trebling of the phosphorus loss.

For comparison, Johnes (2003) calculates a phosphorus export coefficient of 0.03 for permanent grass in the south west, and only 0.002 for the east of England. Similarly, the export coefficient for cattle reduces from 0.0285 to 0.017. The contrast is similar to that calculated by scaling in proportion to the results of the vector model.

1.2.2.2Source Magnitude

For the scaling of results from the reference to other conditions:

  • Incidental – Surface : Volume of over land flow
  • Incidental – Preferential : Volume of preferential land flow
  • Detachment – Surface : Sediment in over land flow
  • Detachment – Preferential : Sediment in preferential flow
  • Solubilisation – Surface : Volume of over land flow
  • Solubilisation – Preferential : Volume of preferential flow
  • Solubilisation – Through : Volume of through flow

It is assumed that appropriate scalars can be found for the source strengths. For example, the external source may be proportional to the total quantity of fertiliser applied. The internal source may be proportional to the quantity of nitrogen mineralised each year.

1.2.3Measure Implementation

Pollutant loss is an ordered sequence of source, mobilisation and transport. Pollutants may be input to receiving waters (surface and ground) indirectly as solute and in suspension in waters draining from agricultural land or from hard-standings, and directly by the failure of storage systems or drift during manure and fertiliser handling operations.

The magnitude of a source is measured at the source area. Therefore, pathogens in spread manure are the source, not pathogens in excreta at livestock houses. Reduction of the pollutant source is carried through the model to reduce the pollutant mobilisation and transport, but measures that reduce transport do not have an impact on source, i.e. the model calculation is directed.

Measures can affect any combination of dimension or aspect in the Cost-Cube. For example, dietary manipulation may reduce the quantity of phosphorus in the source-recycled aspect (excreta), and hence also reduce pollutant loss by all aspects of the mobilisation and transport dimensions. In contrast, the implementation of a riparian area would affect only the transport-surface aspect (over land flow).

Implementation of a measure reduces the pollutant loss at the target aspect in proportion to the percentage efficiency of the measure.

If a cost of measure implementation can be provided, a cost-curve can be calculated that prioritises the order of implementation of the available measures. A cost-curve is defined as the relationship between emission abatement and marginal cost. The function is continuous and has a positive gradient, i.e. the marginal cost always increases with increasing emission reduction, thereby satisfying the law of diminishing returns.

Measures are defined by their efficiency, applicability (percentage uptake) and cost. Cost-curve optimisation is a numerically intensive calculation that scales exponentially with the number of potential measures. The ideal or optimal cost-curve can be determined only by simulating all possible orders of measure implementation, as the marginal cost is dependent on the measures already implemented. For this work, we have adopted the algorithms used by the NARSES model (Webb et al., 2002) that adopts a pragmatic approach in which the model iteratively selects and implements the measure with the least cost-benefit ratio at each cost-step. At each step, each measure from the pool of currently unimplemented measures is implemented separately and the cost-benefit of implementation calculated. The measure with the least ratio of cost and emission reduction is implemented. Under the traditional method of calculating a cost-curve, this measure now has priority of implementation. Mutually exclusive measures that are implemented at subsequent cost-steps will have their implementation reduced in proportion to the measure overlap. It is important to note that implementation of a measure can change the cost-benefit ratio of measures at subsequent cost-steps. For this work, we have assumed that all measures are applicable to 100% of the farm landscape.

1.3 Example Calculation

A scenario was described in which fresh farm yard manure was applied to a clay loam soil under arable cultivation, located in East Anglia, with an annual rainfall of 650mm. The only source of pathogens is in excreta and manure. Hence, 100% of the total pathogen loss was due to the source-recycled aspect.

The expert on pathogen diffuse pollution was asked to complete a standard Cost-Cube form for their assessment of the relative importance of the Cost-Cube dimensions and aspects to the total pollutant loss (Tables 1.2 and 1.3).

Table 1.2 Expert assessment of the percentage contribution of mobilisation aspects to total pathogen loss for the East Anglia reference condition.

Mobilisation Aspect / Percentage
Detachment / 15
Solubilisation / 5
Contingent / 80
*What percentage of the total pathogen loss is due to detachment, solubilisation and incidental mobilisation ?

Table 1.3 Expert assessment of the percentage contribution of transport aspects to the total pathogen loss for the East Anglia reference condition.

Transport Aspect
/
Mobilisation Aspect
Detachment / Solubilisation / Contingent
Surface / 50 / 40 / 50
Preferential / 50 / 50 / 50
Through / 0 / 10 / 0
*What percentage of the total pathogen losses due to detachment, solubilisation and incidental mobilisation occur in surface, preferential and through flow ?

The Cost-Cube vector model was used to calculate the volumes of over land (12mm), preferential (69mm) and through flow (122mm) for the reference condition, and the quantities of sediment lost in over land (50kg ha-1) and preferential flow (171kg ha-1).

The consequences of the expert assessment for the relative concentrations of pollutant in surface, preferential and through flow were calculated (Table 1.2). It was calculated that pathogen concentrations would decrease significantly with depth of drainage, reflecting the likelihood of physical filtering and adsorption of the pathogens to the soil matrix. It was estimated that pollutant concentrations in preferential flow were reduced to less than half those in over land flow due to adsorption and filtration.

The resultant Cost-Cube parameter form is shown by Figure 1.3. Summary statistics indicated that 80% of the total loss was contingent, and that surface (50%) and preferential (50%) flow accounted for the whole of the pollutant transport.

To illustrate the general methodology, the vector model was then used to calculate soil drainage and sediment losses for a location in the south west, with a mean annual rainfall of 1,100mm. Soil type, slope and land use were held constant. Drainage and erosion increased significantly. Over land flow was 45mm, preferential flow was 219mm and through flow was 322mm. Surface sediment loss was 1069kg ha-1 and preferential sediment loss was 1351kg ha-1. As a consequence, the total pathogen export was estimated to be 5.1 times that for the reference cube, and detachment had increased in importance as a means of mobilisation relative to contingent losses (Figure 1.4). As a consequence, measures that mitigate against soil erosion would be more cost-effective than they would in East Anglia. The same calculation but for grassland at the new site, gives a total pathogen loss of 3.1 times that at the reference condition.