Contraction and Convergence, C&C,
is a scheme to provide a framework for a smooth transition to a low level of
CO2 emissions from human activity. It can either follow or replace the Kyoto
protocol. The first step in C&C, 'Contraction', is based on agreeing a safe
target concentration level and the determination of global annual emissions
levels into the which should take the atmosphere to that target. We assume that
what is 'safe' would be determined by an international agreement, probably by
the UNFCCC acting under guidance from the IPCC. A profile of plausible annual
emissions levels can be set by GCI's CCOptions model. We project forward to
2200.
Having defined a global budget, the second step, 'convergence' defines allocations
to each country. CCOptions assumes that each country is assigned annual allowances
which vary, per capita, linearly, starting from actuals in 2000 and converging
to a common level of per-capita emissions in a target year. This target year
need not be the same as the contraction target year and is a likely topic for
political negotiation.
A cap year can be set so that population growth after that year does not accrue
additional emissions rights.
The C&C package is expected to be completed with an emissions-trading mechanism
and with a governance framework including penalties for non-compliance.
The model is built round tables of population and CO2 emissions by country for as far as possible all countries.
2.1 Countries.
There is a challenge to decide precisely which countries to use: we aimed to
use those listed by CDIAC in its emissions tables and which are functioning
as nation-states in 2003. UN population data is available for all from this
list apart from Taiwan. To tabulate past emissions for these countries one has
then to cope with the numerous political changes of countries splitting and
merging, as well as with the numerous gaps and inconsistencies in the CDIAC
tables.
2.2 Emissions.
These were sourced from CDIAC in
2003, but much interpolation, extrapolation and other manipulation was necessary
to convert that into the required tabular form. The computation process has
been stored in another spreadsheet, obtainable from GCI on request. The country
called 'other' contains the difference between CDIAC's estimate of the global
total emissions and the sum of their estimates for each country. The data goes
from 1800 to 1999. Emissions for 2000 have been extrapolated from each country's
trend for 1995-1999.
2.3 Population
This is taken from UN median projections as of 2003. As well as the countries listed by CDIAC it includes 20-odd others, mostly small islands. The latter have been grouped together into 'other', as well as, again, a discrepancy between the quoted global total and the sum of the country totals. This 'other' probabably bears little relationship to the CO2-data 'other'; but both are fairly small and serve to get the global totals as right as possible. The population data runs from 1950 to 2050, and interpolation has been necessary as the UN do not quote data for every year.
2.4 Damages
Data on climate induced damages are taken from Munich Re [6]. They quote uninsured+ insured global damage totals for each decade from the 1950s through the 1990s. The extrapolations we illustrate are not, unlike the other charts, based on results from full-scale models and should not be taken too seriously.
CC Options contains a number of built-in scenarios, as well as the facility for the user to easily create more, either from scratch or by amending those that are there. It is recommended that the first time user looks at some of the r350 - r750 scenarios, aimed at CO2 concentration stabilisation, a BAU scenario and t1.5 to t3 scenarios which have global mean temperature reaching the indicated value in 2200 (but not yet stabilised). Note that it doesn't seem feasible to construct a scenario that gets the concentration down to 350ppmv by 2200, so our "r350" scenario only brings it back down to 380 ppmv.
Currently the model makes no allowance for conformance or otherwise to the Kyoto protocol, and starts projecting forward from 2001.
A quartic formula is used to calculate the results from the start year of 2000 to a user-definable contraction target year, which can be any year between 2001 and 2100. It is of the form
Et = k+lt+mt2+nt3+pt4
where Et is the total global industrial CO2 emissions; t is the year and the parameters k,l,m,n and p are jointly determined by the following five conditions:
i: E is set to be the known value of emissions in the start year.
ii: E is set at a contraction target value for the transition year.
iii: dE/dt, the rate of increase in emissions, is set to a target overall emissions decline rate for the contraction year.
iv: dE/dt is set to the actual value in the start year.
v: The area under the curve between
1990 and 2100, calculated by integration of the above formula, corresponding
to the total global industrial CO2 emissions over the 110-year period, is set
by the user. The values in the r350-r750 scenarios may be used as a guide to
plausible values. In earlier versions of CCOptions these 110-year integrals,
based on IPCC numbers (from [1]&[2]) were taken as the key determinant of
the stabilisation level. The research published by the Hadley Centre in 2002-3
[4],[5], are taken by GCI as superseding this - mainly by taking much fuller
account of biosphere feedbacks, the integrals are retained in CCOptions for
historical comparisons.
These conditions yield a set of 5 simultaneous linear equations which are solved to compute the actual values of k,l,m,n, and p.
Note (1) that an allowance of 50GTC
in total has been made for deforestation emissions. As even the present annual
emissions rate appears to be uncertain to within at least 50% or so; and the
total amount of carbon in global forests is orders of magnitude less than that
in unburnt fossil fuels, we think it both justifiable and politically helpful
to make this very crude approximation. The actual figure of 50GTC is towards
the optimistic end of the range (30GTC to 90GTC) used in the six IS92a-f scenarios
which were set out in IPCC WG1's 1992 report [3]. 'Bunker fuels' – fuel
used in international civil air and sea transport, which are not allocated to
countries and have been excluded from most calculations up to now - really need
to be added in also, perhaps as a world overhead.
Note (2) that the percentages relate to global emissions in 1990, which has
been used as a base year for all the negotiations so far.
Note (3) ppmv = parts per million by volume, the normal measure of trace gas
concentrations in the atmosphere, though occasionally parts by mass are used
to confuse us.
Note (4) Emissions are always measured in tonnes of carbon in this business,
the weight of the carbon atoms in the CO2 molecules. It is 12/44 of the weight
of the carbon dioxide. The use of this unit causes endless confusion, but since
everyone uses it we're stuck with it. Hence GTC = gigatonnes carbon.
A separate option should be available to enter a preset profile of global emissions from 2000 to 2100 as a set of numbers. This then replaces the contraction part of stage 1, the convergence part is unchanged. This can be deferred to v2.2, but needs to be borne in mind. One use of this feature should be to make available a Business-as-Usual comparison scenario based on a growth rate of emissions extrapolated from past actuals since 1975 (this is roughly 1.5% per annum).
Contraction is continued after the contraction target year to 2200 on a much simpler basis.We posit exponential convergence towards a limit value taken originally from reference[1] (p63) and modified by assessing the impact of the Hadley research in [4]&[5]. This limiting value is not reached of course. The formula is Et+1=(1-alpha)Et + (alpha)E2200.
This is the process to allocate percentage shares of global emissions to all the worlds' countries. Each country's emissions in the start year are known or computed as described above. Their emissions in the convergence year are simply the global emissions for that year divided up according to their respective populations, possibly capped as described in section 5 below. In between country emissions in year t are just interpolated, i.e.
St = (St(Y-t) + SY(t-y))/(Y-y)
where St is the emissions share of a country in year t, Y is the convergence year, y is the start year
Earlier versions of CC Options included an alternative more complex option of exponential convergnce. This has been dropped as experience suggests it is more likely to cause confusion than to help.
The formula used to compute atmospheric CO2 concentrations is:
Ct = Ct-1 + A0 +A1t +A2Et + A3(Ct-25)2
where Ct is the
concentration in year t, Et is the global emissions in year
t, and Ai for i=0,1,2,3 are constants determined
by a least squares minimisation process similar to a regression.
It should be noted the the formula is based on a very simple model, and has validity only within the time-period up to 2200 and only for ppmv values up to 750, though any forecast for ppmvs above 750 can only be mainly guesswork as conditions are too far away from those known to permit any credible validation of models. The formula was chosen to reproduce as closely as possible the concentrations/emissions relationships in the Hadley papers[4-5] over the time-period 1990-2200 These show a much steeper rise of concentrations than the IPCC WG1 reports[1-3], which were used in earlier versions of CCOptions, due mainly to better modelling of biosphere/atmosphere interactions and feedbacks.
The previous formula showing the
rises expected according to the IPCC WG1 reports is also retained for comparison.
A separate worst-case calculation is made of what would happen if the ocean
& biosphere sinks for CO2 stopped working entirely, by assuming that all
the CO2 emitted stays in the atmosphere.
The formulae used to compute global mean temperature rises are as follows: firstly to allow for the lagging in effect of the concentrations, a smoothed concentrations curve My is computed, the smoothing constant k being chosen (as 0.3) to give the best fit in the end:
Mt = kCt + (1-k)Mt-25
then the temperature rise Tt is computed as:
Tt = B0 + B1t +B2Ct + B3(sqrt(Ct)) + B4Mt + B5(sqrt(Mt))
where again the Bi are
constants determined by a least-squares minimisation to fit the data reported
by WG1 and Hadley. This formula also only has validity between 1990 and 2200
and for the 350-750 range of ppmv.
The results of applying the formula to the old pre-feedback expected concentration
rises are shown as well as the current best guess.
The actual industrial CO2 emissions allocations are made by multiplying the global total value derived from the contraction process by each country's shares derived from the convergence process.
These are computed by dividing each country's total annual emissions by that country's population, subject to possible capping as per section 5.
Weather-related damage figures have been estimated by Munich Re[6] for the period 1950-2000. In CCOptions they are modelled by fitting the following curves to the Munich Re figures. For damages Dt in year t, with temperature Tt:
Dt = K1 + K2t + K3Tt + K4Tt2 and by Dt = K1 + K2t + K3Tt + K4Tt1.5 - both fit the data equally well and give a some sort of feel for the uncertainty about future damage costs. Note that the log scale used to display damages makes the two alternatives look much closer than they really are.
There arguably needs to be a 'cap' on population growth for the purposes of allocation of emissions rights, otherwise countries are given an incentive to expand their populations. This is done by notionally freezing populations for years beyond a 'population cutoff year' at the values for that year. Note there is no assumption being made about what populations will or should be beyond the cutoff year; merely that population growth after that year should not accrue additional emissions rights, to avoid giving governments a possible incentive to encourage population growth.
This feature also has the advantage for us that we do not need to include forecasts for expected population growth so far into the future, so the program requires a population cap year no later than the population data figures that it has (2050).
If the set of parameters chosen leads to emissions declining and then rising again, a block of red Xs is displayed on the control page to show that the solution is impractical, as there is usually no point in requiring reductions only then to let emissions increase again.
[1]CLIMATE CHANGE 1994 Radiative Forcing of Climate Change and An Evaluation of the IPCC IS92 Emission Scenarios. Cambridge University Press for the IPCC. 1995
[2]CLIMATE CHANGE 1995 The Science of Climate Change, Summary for Policymakers and Technical Summary of the Working Group I report. IPCC. 1996.
[3]CLIMATE CHANGE The IPCC 1990 and 1992 Assessments. WMO/UNEP June 1992.
[4] Stabilisation and Commitment
to Future Climate Change. Hadley Centre 2002:
http://www.met-office.gov.uk/research/hadleycentre/pubs/brochures/B2002/global.pdf
[5] Results from carbon cycle experiments
- Predictions of accelerated climate change. Hadley Centre 2003:
http://www.met-office.gov.uk/research/hadleycentre/models/carbon_cycle/results_trans.html
[6]
Munich Re: Topics 2000 - Natural catastrophes - the current position: http://www.munichre.com/pdf/topics_SH2000_e.pdf