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As modelled in CBAT, the C&C Principle embraces 4 sequenced DOMAINS: -

  1. Contraction and Concentrations [Science, Logic, Risk] - governs . . .
  2. Contraction and Convergence [Global Constitutional Politics and Diplomacy]
  3. Contraction and Conversion [Green Growth]
  4. Growth and Damages [we cause the problem faster than the solution - we must reverse this].

A summary overview of these domains is shown here at three rates
Acceptable [C1] Dangerous [C2] Impossible [C3]

An article for UNEP 'Climate Action' based on this schematic is here


UNFCCC Compliance means being compliant with the objective of the UNFCCC.

To this end, there is a strong case that this sequence of Domains [from 1 to 4] is 'ordinal'. In other words it is the order in which the Carbon Budget Accounting in CBAT needs to be analysed, if it is to be strategically policy-relevant to UNFCCC-compliance.

The objective of the UNFCCC is achieving stable and safe GHG concentrations in the global atmosphere. So policy, if it is to be relevant at all, is fundamentally governed by that global objective and the need to achieve it.

The Principles of the UNFCCC are Precaution and Equity. When nations agreeing to become a Party to the UNFCCC, it means being party to a collective and strategic commitment to achieving UNFCCC-compliance.

Ideological and Constitutional issues of Contraction and Convergence arising in Domain Two are governed by UNFCCC-compliance. Logically therefore, a reckoning of Domain One issues needs to precede any reckoning of the issues arising in Domain Two, Domain Three and Domain Four.


NOTE When the CBAT Domain Two 'file-image' in the left-hand column of the GUI is mouse-touched, Domain Two goes centre screen and Domain One retires to the top position in the left-hand column where it continues to be 'active'.

The same will be true for Domains Three and Four.


Mouse-touch-click each little DOMAIN PANEL in LEFT-HAND margin to
'SWAP' to CENTRE-SCREEN position & see how full animation will work

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When Domain Two is fully operational, it will have a 'Table' floating on-screen, as in the next still-image [below]. This table will be reading off: -

  • values arising in Gt C for the globe divided into 6 regions as follows: -

  1. USA [grey]
  2. OECD minus the USA [green]
  3. Former Soviet Union [FSU in white]
  4. China [yellow]
  5. India [orange]
  6. Rest of World [ROW in dark blue]
  • for periods: -

  1. before convergence starts [2010 to start-date - here 2015]
  2. while convergence lasts [from start-date to end-date - here 2030]
  3. after convergence ends [from end-date to 2110]
  • from any user-choices made from Slider-use, that will look like this: -


. . . where the user-choices for any: -

  1. 'Carbon-Budget' using 'Budget Buttons' & the Vertical Slider for Domain One &
  2. 'Convergence-Window' using the Horzontal Slider 'pair' [<>] in Domain Two

. . . result in the Table of values shown in the image above for all values arising adjusting the values to read [in Gt C] any Domain One/Domain Two combination chosen by the CBAT-user.

In other words Contraction and Convergence 'commute' . . .
[as they need to for UNFCCC-Compliance]

That means that for any relevant rate of Contraction with any rate of Convergence-Window arising, CBAT will instantly calculate and display charts and table-values in Gt C from any of the: -

  1. Three Carbon Budgets, [three buttons, LOW, MEDIUM, HIGH, top right] multiplied by
  2. 80 positions each [from +40 to -40, on the VERTICAL SLIDER] multiplied by
  3. Any convergence start-date [2010-2110 - on the HORIZONTAL SLIDER] multiplied by
  4. Any convergence end-date [2010-2110 or 100 years - on the HORIZONTAL SLIDER]

. . . to give in all a 'suite' of 2.4 million 'C&C' Carbon-Budget user-options, where 'Contraction and Convergence' TOTALS in the Vertical Slider Clock on the right and in the on-screen Table bottom right [column 5 row 8] are the same value [see here]. In other words, as they need to for UNFCCC-Compliance, they 'commute'.

However the budget size and the regional shares in it may vary, the 'Budget-Total-Clock' on the Vertical Slider and the 'Budget-Total' in the Table will always show the same quantity of Gigatonnes of Carbon [Gt C] in the same path-integrals [shape and weight of budgets] in Gt C, no matter which user-positions the sliders are pushed to.


The essence of this is to establish that the relevant non-random 'numeraire' [unit of measurement] for UNFCCC-compliance is the '100% of: -

  1. tonnes-of-carbon per-limit ['precaution'] *before* it embraces the derivatives of
  2. tonnes-of-carbon-per-person ['equity'] and then, and only then, when the ratio of
  3. dollars-per-tonne-of-carbon ['efficiency' & marginal 'carbon-spot-pricing' & 'damage-trend-costing'] in Domains 3 & 4 have been subordinated to UNFCCC-compliance, do they become relevant [where, "the economy is a wholly-owned subsidiary of the environment"].

When complete, CBAT Domain 1 [Contraction and Concentrations] & Domain 2 [Contraction and Convergence] will give users 240 different rates of contraction and 10,000 different rates of convergence within those.

Moreover, subject to its 4-Domain organising structure, the CBAT model is easily reprogrammed to calculate and graphically demonstrate virtually an infinity of such options.



Much of the favourable response to classic 'C&C' over the past twenty years has been due to the perceived 'ethical' content of a proposal to share 'equally' a global resource on which we all depend [the atmosphere and its presently 'unequal use'] between all people who do depend on it.

Indeed GCI agrees with this 'ethic' and continues to do so.

However, the issue of 'measuring' this ethic also requires a 'logic' that in fact precedes the ideological constructions that are put upon this matter.

It is mathematically self-evident that overall a future global Emissions-Convergence of some sort will have to occur, if the global Emissions-Contraction needed for UNFCCC-compliance is to occur.

So subject to answers pursued logically and arrived at consequentially in Domain One, the questions arising in Domain Two are also logical as much as ethical: -

[1] Will this 'convergence' just occur spontaneously?
[2] If it won't, what inclusive, non-conflict-based and non-random template might be proposed to guide the full international political negotiations to UNFCCC-compliance?
[3] With such a template, how best might negotiators pursue and generate a global consensus that is UNFCCC-compliant?

The answers to these question that GCI has suggested since 1990 are: -

[1] 'No', it won't occur spontaneously, it needs an organisational principle.
[2] The only inclusive, non-conflict-based and non-random template is globally equal rights to emit GHG to the global atmosphere per capita.
[3] Propose Convergence to equal shares at a rate to be agreed under the Contraction rate determined in Domain One.

GCI has a very detailed 'Contraction and Convergence' [C&C] model available for all countries and for all regional groupings that will calculate 'classic' 'Contraction & Convergence', at any carbon-budget size, with any convergence year within that and also with any year set as a population 'base-year' if so desired.

So far however, it has proved too complex to animate this full 'C&C model' for CBAT.

So the simpler six-region world shown below is being animated here.

This will have clock-values in Gt C for the 'shares' arising for all three of the CBAT carbon-budgets already programmed in via xml data-sheets. Note: - any such sheet for any such budget can be inserted as a formatted xml-data-sheet and CBAT will calculate it.

As a first-order argument, CBAT Domain Two quantifies the integration of International Convergence with Global Contraction at fifty different rates of convergence [for each year from 2010 to 2060] for each of the three Budget Rates Low, Medium and High, as set out in Domain One.

The Horizontal Slider [shown below] will give users control over the rate of convergence. This will be control over the 'start-date' and the 'end-date' for the 'convergence-window' [see example below]. Clocks, when ready, will show the carbon-weights for the the global sharing resulting from exercising these choices.

When complete, Domain Two will analyse all three budgets [Low Medium & High] and the 'on-screen' budget will change if and when the LOW, MEDIUM, HIGH budget buttons are used.



'Start Convergence' in the year 2015 and 'End Convergence' in the year 2020.


'Instant Convergence' in the year 2030.

'Start Convergence' in the year 2015 and 'End Convergence' in the year 2020.

'Start Convergence' in the year 2020 and 'End Convergence' in the year 2035.

MOCK-UP ONLY of Domains ONE, TWO, THREE & FOUR set at CBAT LOW Budget

DOMAIN ONE EXAMPLE - Segregated Feedback, Medium Sensitivity, Slider at '0'
DOMAIN TWO EXAMPLE - Convergence Start 2015 & Convergence End 2020
DOMAIN THREE EXAMPLE - rates for Conversion to Renewable Techniques
DOMAIN FOUR EXAMPLE - as DOMAIN ONE goes higher so do Damages

DOMAIN ONE controls are visbly active regardless of which DOMAIN is screen-centre.
UK Climate Act Switch is 'On' showing budget outline as "too weak" [Hansen].

CBAT GUI - FULL 4 DOMAIN MOCK-UP animations not working yet



Some Responses to CBAT so far


This is to demonstrate a basis for the rational and basic political compromise that is a necessary part of achieving an all-party commitment to UNFCCC-compliance. Over twenty years, this C&C 'analogue' has attracted much support.


CBAT will also analyse some of the variants of this procedure. For the moment these are briefly compared in Chapters 8 & 9 of the the animation here and prefigured in the frozen imagery and the animation shown below.


From years gone by, some widely used C&C images are: -

Both examples show an international convergence of 'shares' by 2030 inside global emissions contraction-events that were considered [during the period 1995-2005] roughly consistent with a stable 450 PPMV atmosphere concentration by 2100.

A previous simpler attempt to integrate and animate rates of: -

  1. Contraction and Concentrations with
  2. Contraction and Convergence

is here or in the example below: -

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