Appendix 1 to the final report to Defra on Project Number ES0107
Quantifying uncertainty in the MEASURES framework
Adrian Williams, Daniel Sandars and Eric Audsley
Biomathematics Group, Silsoe Research Institute, Wrest Park, Silsoe, Bedford, MK45 4HS.
1. Introduction
1.1 Objectives
The main objective was to quantify the uncertainty in the MEASURES framework and present it. The individual objectives follow.
1. To identify the different forms of uncertainty in the MEASURES framework.
2. To quantify the different forms of uncertainty in the MEASURES framework.
3. To program the MEASURES framework so that the uncertainty is produced along with predicted mean values.
4. To use this knowledge to highlight areas of particular concern where scientific results used to inform Defra policy decisions may be misleading because of the absence of quantified uncertainty.
5. To suggest areas of work need to resolve such matters.
6. To hold a workshop on multiple environmental interactions in which the model with uncertainty will be demonstrated.
1.3 The original MEASURES project (WA0801)
The project produced the MEASURES (Multiple Environmental outcomes from Agricultural Systems) framework to integrate multiple environmental impacts and sustainable farm profitability and initiated an active forum where stakeholders of environmental impacts of farming systems could shape, review and discuss the insights of this project. An important feature is that the framework predicts how farming systems will adapt to maintain profit, given changed restrictions or constraints. Environmental relationships were associated with many individual farming activities, e.g. growing crops, housing livestock and spreading manure. Equations describing these were derived from several sources, including mechanistic process models and the UK national inventories. Data sources required careful interpretation as they generally apply to short term experimental work, while the underlying philosophy of MEASURES is long term and steady state. MEASURES calculates environmental burdens (i.e. quantities of materials that adversely affect the environment) rather than impacts (i.e. the response of the environment to those materials, e.g. eutrophication from nitrate). The environmental burdens are: ammonia volatilisation, nitrate leaching, nitrous oxide emissions, methane emissions and soil erosion. It also calculates soil phosphate balance.
1.2 How MEASURES works and what it does
MEASURES takes the definition of a whole farm, which is described in a set of equations and information in databases, and calculates the most profitable cropping rotation for that farm. It also calculates a variety of environmental burdens from that farm as well as indicators, such as the soil phosphate balance (Figure 1). The farm may be arable only or mixed and the animal enterprise can be housed-only livestock (e.g. finishing pigs) or grazing animals with forage requirements.
A farm is principally described in terms of area, soil texture (one only per farm), rainfall and animal types and numbers (as developed in the Silsoe Whole Farm Model). The user can specify a selection of crops, each of which has a set of time-bound cultivation requirements that require inputs of labour, machinery, fertilisers, pesticides etc. Each crop is defined by a growth equation, which links yield to the input of N fertiliser and soil texture. Yield and /or cost penalties are applied if a crop is established too late or too early and if crops are grown in successive years. Various rules determine the level of penalty and some crop successions are prohibited to minimise disease transfer. If grazing livestock are included, part of the farm must provide the forage component of their diet. Manure from all livestock is applied to the land and nutrients contained therein are accounted for within the estimation of fertiliser requirements.
The model finds the optimum plan by maximising the whole farm net profit (all farm income minus the costs of inputs, labour and machinery – it does not include general farm overheads or rent). All costs, whether machinery (ploughs, tractors, slurry stores etc), labour, chemical inputs or crop income are considered as annual values to make them comparable. Machinery costs are annualised using discounted cash flow analysis (Audsley and Wheeler, 1978), which requires values for interest rates, inflation, machinery life, machinery price and resale value and maintenance costs. Within this process, it assimilates the costs of all inputs for the possible crops, the timings and time taken for each operation together with yields as affected by non-optimal activities. This process also calculates the actual equipment inventory and labour needed for the whole farm. The optimisation is achieved with linear programming.
1.31 The long term
MEASURES, like the Silsoe Whole Farm Model, analyses farm with a long term view, which requires operating in a steady state manner. This is manifested, for example, by the N balance being maintained over a whole rotation, although variations in soil N status may be inferred within a rotation. An implication of this is that we oblige all N losses to reach the environment, rather than being locked up in short or medium term soil pools. This can cause emissions like nitrate leaching to be somewhat larger than is normally expected. The philosophy behind this is that organic N (e.g. from crop debris or manure) will eventually be mineralised and partitioned between useful crop offtake and wastage by denitrification or leaching (Appendix 2).
1.32 Soil, rain and crop interactions.
Crop yields depend on soil texture and, in the case of grass, on rainfall. Soil texture is defined by a numerical index (0.5 to 2.5) representing the range of textures from sandy to heavy clay and yields increase with the soil index, because the water retentiveness increases, so supporting better growth in the summer. Working heavier soils, however, require more effort in terms of time and fuel than lighter ones. The hours that a soil is workable decreases as soil index and rainfall increases. The extra flexibility and economy in cultivation given by a lighter soil is thus offset by lower revenue from reduced yields.
1.33 Optimal timing
There is an optimally profitable time to establish a crop (Figure 2a). Premature establishment reduces yield
Figures 2a and 2b. Effects of timing of establishment on costs, margin and yield and typical distribution of timing crop establishment in fortnight periods.
by disease and late establishment reduces yield through a shortage of light and growing time (and possibly poorer germination in winter crops). Establishing all of a crop at the ideal time for maximum yield requires a large input of labour and machinery and so would increase the cost, while spreading out the time of establishment will reduce both yield and cost and this usually provides the optimum approach (Figure 2b). Most operations are time-bound within seasonal windows and some must fit into particular sequences, e.g. drilling cannot precede cultivation. Additional constraints, like NVZ regulations, can impose restrictions on the timings or duration or extent of operations, e.g. manure spreading. Since these operations are time-bound, the constraints will impose a stress on the whole farm system. A consequence is likely to be a change in the crop rotation to accommodate the constraint. This is a particular strength of the whole farm approach, as apparently counter-intuitive responses can result from it with good reason.
1.34 Mixed farms
Housed animals add an extra dimension, mainly though manure. It is assumed for simplicity that all non-forage feed is bought into the farm, while all arable products are exported. The animal enterprise thus contributes a profit, the plant nutrients in manure, the effort needed to spread manure, as well as gaseous emissions from the animal house and manure management. There are also losses of N by leaching and N taken into crop yield to consider. Manure management requires extra operations and a variety of constraints, e.g. limits in the application rates and timing. Grazing animals incur these as well as the need to calculate a forage-based ration, with a consequent need for grass (and optionally maize for silage). The forage crops and the operations they require must, of course, fit in with the overall farm cropping plan.
1.35 The N cycle, P and K
The N cycle is crucial to the agronomic aspect of the model as well as the calculation of environmental burdens. A foundation of the model is that it analyses a farm in steady state, so that the flows of N, P and K into the farm (feed and hence manure, atmospheric deposition and mineral fertilisation) equal those leaving in crop and animal offtakes and environmental burdens for a whole rotation. The model will balance N and K almost exactly, although P may float for reasons described later.
MEASURES is not a simulation model, although much of the underlying structure is mechanistic. Fertiliser requirements (NF) are calculated on the basis of an expected yield and soil index, typically in the following form, where I is the soil index, Y the yield and Greek characters are coefficients.
(Eqn1)
Assumptions are made about reasonable yield expectations in order to predict fertiliser and manure application rates and these are effectively used as “seed values” in the optimisation. The actual yield calculated by the model depends also on penalties for non-ideal establishment, or harvesting and disease losses. The primary yield (grain, tuber etc) is based on a linear-exponential equation of the following form (England, 1986). Again, Greek characters are coefficients.
(Eqn2)
N offtake is simply derived from this and the N concentration of the crop (NC). There are similar expressions for straw or haulm. These terms are modified according to how much is directly ploughed in.
The equations for grass yield are slightly different, including a term for rainfall (R). It was derived from data on productivity, fertilisation and site class (Halley & Soffe, 1988)
Y = a + b I +g R + d NF (Eqn3)
Also, the N content of grass is given by a linear equation (Scholefield et al., 1991):
N C = a + b N F (Eqn4)
The N balance for a crop is given by:
N F + N M + N A + NS = NO + NW + N¯S (Eqn5)
where the subscripts represent manure N (M), atmospheric deposition (A), rotational soil N supply (S), offtake (O), losses or wastage (W) and rotational return to soil (¯S). The balance for a rotation is the sum of those from all the crops and the sum of all inputs must equal the sum of all outputs. N fixed by legumes is included as a part of atmospheric deposition.
1.36 Rotational N transfers
At the start of crop growth, some N will be supplied from the soil pools of mineral and organic N. At the end, some will return to soil from unused fertiliser or fixed N or decaying debris. The values for these were derived for crops from RB209 (7th edition) and from NFixCycle for rotational grassland and depend on crop type, rainfall and soil index. The values derived ensure that a balance is obtained over the whole crop rotation and form a plank of good practice within MEASURES in that we assume that the rotational transfers are accounted for.
1.37 N losses
The N losses are calculated from the difference between all the other input and output terms. The N wasted is partitioned into three streams:
N W = N L + N D + N S (Eqn6)
where the subscripts refer to leaching (L), total denitrification (D) and senescence (S). Loss through senescence is a process that has not yet been modelled well so that it was regarded as a real contribution to the N balance but was fixed for all crops at 2kgha-1 and was assumed to be NH3-N. The partition between leaching and total denitrification was achieved with the use of the SUNDIAL simulation model for arable crops and NFixCycle for grassland. In its earliest form, MEASURES partitioned N loses for each crop as:
N L / N W = a + (b * R) - (g * I) (Eqn7)
in which R is annual rainfall. Subsequent work suggested that this type of equation was not valid for all crops and it was subsequently simplified for arable crops to:
N L / (N D + N L) = a (Eqn8)
For grassland, leached N was related to soil index and total losses by:
NL = NW * (.954 - .125 * I)*.7 (Eqn9
Total denitrification includes losses of benign N2 and the powerful greenhouse gas N2O (together with traces of other nitrogen oxides that we have not quantified). The N2O-N was calculated from the Bouwman equation in which NA is the sum of all applied (mineral or manurial) or fixed N.
N2O-N = 1 + 0.0125 * (N A) (Eqn10)
Benign N2 can thus be calculated by difference. The constant, with value of 1kgN2ONha1, represents emissions from unfertilised fields (subject to atmospheric deposition), which we assumed applies to set aside. The slope term thus applies independently to applied N.
1.38 The overall balance
For a whole rotation on an all-arable farm, the losses are thus derived from the difference between the achieved yield, hence N offtake, and total N inputs, which highlights the importance of a high N utilisation efficiency (NUE). The partition of losses depends mainly on characteristics of each crop.
1.39 P & K
K generally balances well, although fertiliser requirements require substantial adjusting for manurial K. The P balance cannot always be maintained because of manurial inputs and the supra-responsive application rates that are suggested for potatoes, even by RB209. This means that an excess on mineral P can still give a crop response, but will not remove it all, so a P surplus can be created. In practice, a build-up of soil P over time can be prevented (if there are not too many animals) by frequent soil analysis and hence adjusting P application rates.
1.40 Summary of how MEASURES works
At the crop level, MEASURES calculates the work, operations and inputs needed to grow a crop, together with the associated costs and income from the useful offtake. It also calculates the environmental burdens of that crop in terms of N losses and any possible P surplus together with the rotational transfer of N for the next crop.
At the rotational level, MEASURES calculates all the work and inputs needed for the complete crop cycle and ensures that N inputs and outputs balance. It also aggregates environmental losses associated with crop growth and manure application, together with the income and costs of the whole rotation. This represents the whole farm, if it is all arable.