Tutorial handout — Monte Carlo and carbon accounting
Overview
You are a team of environmental modellers who have been assigned the task of assessing the
ongoing greenhouse gas (GHG) mitigation potential and cost of alterations to typical arable
crop rotations. The simulation has already been part completed, so your task is to a) complete the
model and b) use Monte Carlo simulation to run a full uncertainty and sensitivity analysis on the
results.
The measure in brief
Most management systems for crop farms consist of rotations 4—6 years in duration. A rotation,
in this context, means that the crop grown is changed every year in a cycle which repeats every
4—6 years. Crops are rotated in this way to make the best use of soil nutrients; however, these
rotations are typically designed to maximise profit in the short term, but risk depleting the soil
of nutrients and organic matter over time. This risks negative economic and environmental
impacts, most notably a) loss of crop yield, and b) release of stored soil carbon to the
atmosphere as CO2.
To combat this, one prominent suggestion is that each rotation should be adjusted to contain a
mix of crops and grassland. The presence of grassland acts to improve soil structure and quality,
and increases nutrient input back into the soil. Most farmers don’t include grass leys in their
rotations, as it’s typically not profitable over the short term. However, long-term benefits to the
soil may improve the performance of the system over time, and offset these costs in the long run.
Your assignment is to compare the profitability and GHG emissions from two comparable arable
systems — one using traditional 4-year arable-only rotations, and one using the suggested
approach of following 3 years of arable crops with 1 year of grass.
Some GHG accounting terminology
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CO2 equivalent, usually shortened to CO2-eq, is a way of summarising emissions of
different gases (e.g. CH4, N2O) into one metric based on their global warming potential
over 100 years (GWP100). Typical assumptions are that methane has 25× and N2O 296×
the GWP100 of CO2. So 1 kg N2O is equal to 296 kg CO2-eq.
An emission factor is a term for the factor used to estimate the amount of GHG
emissions arising from a particular source. For example, if 1 litre of fuel produces 0.3 kg
of CO2-eq when burnt, we might say that this fuel has an emission factor of 0.3 kg CO2eq per litre. Emission factors can refer to either direct or embedded emissions.
Embedded emissions are emissions associated with the production of a certain
commodity. We normally want to account for this if such commodities are used in our
scenario. So, for example, we might say that 1 kg of fertiliser has 7 kg CO2-eq associated
with its production, and as such, the “embedded” emissions we’d associate with using
that fertiliser are 7 kg CO2-eq per kg.
Direct emissions are emissions which occur at the point of use of a particular commodity,
such as CO2 released from fuel burning or N2O from application of nitrogen fertiliser.
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Marginal abatement cost (MAC) is a term used to describe the cost of reducing
(abating) GHG emissions. So, if a particular activity has a marginal abatement cost of £50
per tonne of CO2-equivalent, that’s telling you that every tonne of CO2-eq that is abated
by that activity will cost £50 to achieve. Sometimes, MACs might be negative, showing
that an activity will both reduce GHGs and save money. It’s a very useful way of helping
governments and decision-makers decide which measures to reduce emissions are worth
supporting.
Task 1
Once you open the spreadsheet model, spend a good five minutes exploring. Don’t change
anything (yet) — just search through the sheets, examine the formulae, and start to form an
understanding of how the model works. Think about:
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Where does the input data go?
How does the model process this input data?
What outputs does it generate?
When you’re ready, input the following data into the control sheet to complete the static
simulation:
1. The Farm Management Handbook (SAC, 2017) estimates the following values for crops:
a. Oilseed Rape: £325 tonne-1
b. Winter wheat: £165 tonne-1
c. Oats: £155 tonne-1
2. DairyCo Grass+ (AHDB Dairy, 2011) estimates the value of for grass silage at £89 tonne1
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3. SAC (2017) estimate the following costs (in £ ha-1) for crop and silage production
(including establishment of the grass sward in the case of silage):
Best
estimate
Oilseed rape
366
Winter wheat
466
Oats
299
Silage
775
4. Using a process-based model of crop production, Prade et al. (2017) estimate that the net
sequestration resulting from implementation of a grass ley in an arable rotation is 1789 kg
CO2 ha-1 year-1. No sequestration can be assumed for an arable-only rotation.
5. Using the same model, the authors estimate that crop yields are likely to increase by an
annual increment of between 0.16% and 0.32% where a grass ley is present.
6. In addition, Prade et al. (2017) estimate that, where a grass ley is present in the rotation,
the GHG emissions associated with producing other arable crops will reduce by 13—17%
as a result of increased soil carbon uptaking available N and mitigating direct N2O
emissions.
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7. A life-cycle analysis of grass production shows that implementation of a grass ley is
likely to result in the release of 1,200 kg CO2-eq ha-1. An estimated standard deviation for
this value is ± 50 kg CO2-eq.
Task 2
Where you have uncertainties in the data present in the model Control Sheet, use ModelRisk’s
Select Distribution function to select an appropriate distribution and input it into the column
labelled Estimate used in model. Remember to think about the following:
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What parameters do you have available? How might they fit the distribution?
Is your distribution both-bounded, left-bounded, or unbounded? Is this appropriate for
your data?
Is the distribution skewed or unskewed? Is this appropriate for your data?
Implement the following further information using ModelRisk distributions:
1. The authors who modelled soil carbon sequestration estimate a standard deviation for
their calculations of ± 230 kg CO2-eq.
2. The life cycle assessment which estimated GHG emissions for cultivation of the arable
crops estimated an uncertainty of -10% — +25% in this calculation.
3. It is not clear whether yields in the arable-only rotation are likely to decline over the
timescale, but anecdotal evidence suggests this may be the case. To assess this,
implement a distribution which assumes a maximum annual yield impact of 0% and a
minimum yield impact of -0.2%.
Consider using the data presented in the worksheet Agricultural price indices to assess
uncertainty in the reported crop prices and cultivation costs. Price indices are time-series of
commodity prices which are standardised for inflation. In this case they have been
standardised such that 2017—your base year—is equal to 100. So, if a price index in the year
2000 is 48.9, that shows that the inflation-adjusted price of that commodity was 49.9% of the
2017 value. For the purposes of looking at price uncertainty, we want to remove inflation from
the equation because it's a confounding variable — so these indices are a very useful place to
start.
Task 3
Use the model you have created to run a full Monte Carlo simulation which can answer the
following questions:
1. What is the average cost (in £ ha-1 year-1), GHG abatement (in kg CO2-eq ha-1 year-1) and
marginal abatement cost (in £ tonne CO2-eq) of implementing grass leys in arable
rotations?
2. What is the uncertainty surrounding these modelled outputs?
3. What are the most influential model inputs influencing the marginal abatement cost of
this measure?
Remember to think about:
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Making sure you have all of your Monte Carlo inputs linked into the model calculations
— if not, they won’t have any effect on the output.
What model inputs and outputs you want to include in the Monte Carlo simulation
(remember to use ModelRisk’s Mark Input/Output option to specify these).
How many simulation runs you want to complete to ensure you have a representative
sample.
What kind of statistics and plots you might want to use to assess a) uncertainty in your
outputs, and b) sensitivity of your model to variability in inputs.
When in doubt, refer to the Monte Carlo Simulation Tutorial Booklet. It’s far from the last word
on Monte Carlo, but it’s a useful (and hopefully not too heavy) reference text which will answer
the majority of your questions on MCS.
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