To successfully limit global warming,we need to stay within a remaining global CO2 budget.
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Reference values to NDCs resp. NDC calculators
Short introduction
Core question: distribution of a global CO2 budget
CO2 affect the climate for a long time. Therefore, remaining global CO2 budgets correspond to certain limits of global warming. Here are key statements from the IPCC's Sixth Assessment Report on remaining CO2 budgets.
Which concrete global budget we want to orientate, however, must ultimately be decided politically on the basis of the current state of scientific knowledge.
Such a global budget raises the question of how it can be distributed amongst the countries in a fair and economically reasonable way. Such a distribution should be an important guidance of the ratchet up mechanism (ambition mechanism) of the Paris Agreement with Nationally Determined Contributions (NDCs).
Here, two models including tools are presented that involve distributing a global budget and determining national paths:
- the Regensburg Model (RM) and
- the Extended Smooth Pathway Model (ESPM)
Tools based on the RM Scenario Types are also offered for the determination of emission paths that are compatible with a predefined budget.
Basic idea behind the Regensburg Model Scenario Types RM 1 - 6 (here is a short description)
With the help of the Regensburg Model Scenario Types, global or national emission paths can be determined that meet a given budget. The scenario types differ in the assumption about the property of the annual reductions. The emission paths are therefore indirectly determined essentially via the annual reductions. This approach is particularly useful when it comes to making political decisions about emission paths.
Publication: Zenodo, Mathematical Description of the Regensburg Model Scenario Types RM 1 – 6 
Basic idea behind the Regensburg Model (RM)
- Global paths: Global emission paths are determined that are compatible with a global CO2 budget to be specified. For this purpose, the RM tool provides the Regensburg Model Scenario Types RM 1 - 6 (see above).
- National paths: National emission paths are derived from this global paths with the Regensburg Formula, which leads to the convergence of per capita emissions (see mathematical description: ).
Publication: Journal "Climate Policy", 2016, The Regensburg Model: reference values for the (I)NDCs based on converging per capita emissions
Basic idea behind the Extended Smooth Pathway Model (ESPM; inspired by Raupach et al.; brief background )
- National budgets: A predefined global CO2 budget is distributed to countries. The ESPM tool offers the use of a weighted distribution key that includes the 'population' and the 'emissions' in a base year (here: 2019).
- National paths: The ESPM tool offers the Regensburg Model Scenario Types RM 1 - 6 (see above) to derive plausible national paths that adhere to a national budget.
Publications:
- Wirtschaftsdienst, 2/2021, Berechnung Paris-kompatibler Emissionspfade mit dem ESP-Modell am Beispiel der EU, ;
update published on Zenodo - Zeitschrift für Umweltpolitik & Umweltrecht (ZfU), 9/2021, Calculation of Paris-compatible emission targets for the six largest emitters;
update published on Zenodo in English
Download tools
Calculation of national emission paths and targets for all countries in the world that are compatible with a specified global CO2 budget 2020 - 2100
Regensburg Model (RM) |
Extended Smooth Pathway Model (ESPM) |
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| version of the tool | 40.0 |
60.0 |
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| instruction for the tool | |
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| published on Zenodo | ||||
| method | national paths are derived from a global path using the Regensburg Formula | national paths are derived that adhere to a given national budget | ||
| allocation approach | converging per capita emissions | weighted distribution key for a global budget with "emissions" and "population" as factors to be weighted | ||
selectable parameter to map climate justice |
convergence level | weighting population | ||
| emission paths | The Regensburg Model Scenario Types (RM 1 - 6) are used to derive paths that are compatible with a specified budget. ► see mathematical description of the RM Scenario Types: . |
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| scenario types RM 1 - 6 are used to determine global emission paths | scenario types RM 1 - 6 are used to determine national emission paths | |||
| data base | EDGAR - is provided by the EU Commission: CO2 fossil and industrial processes. For the handling of LUC and ISA emissions in the tools, see this paper: |
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| exemplary results | global CO2 budget 2020 - 2100 |
Here you will find results in the ESPM with different framework data:
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400 Gt |
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550 Gt |
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650 Gt |
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| further here specified parameters: | ||||
| minimum global emission in Gt | 0 |
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| convergence level in t/capita | 0.5 |
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| relationship between ESPM and RM |
Depending on the chosen global path and the chosen convergence level, there is an implicit weighting of the population in the resulting national budgets across all countries in the RM (see proof in the mathematical description). The use of this implicit weighting as an explicit weighting in the ESPM leads to very similar results as in the RM. The results in the RM can therefore also be generated in the ESPM if the weighting of the population is specified accordingly. The implicit weighting can be calculated in the RM tool and is given above in the examplary results in the RM for all countries in the world. | |||
| last publication | Journal "Climate Policy" published online 2016: The Regensburg Model: reference values for the (I)NDCs based on converging per capita emissions |
Calculation of Paris-compatible emission targets for the six largest emitters |
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Determination of emission paths that adhere to a given buget using the Regensburg Model Scenario Types
ESPM approach: Set budget and determine emission paths |
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determine global paths Tool_global_paths |
determine global or national paths Tool_Paths_RM_ST |
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| donwload tool | |
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| version of the tool | 23.0 |
39.0 |
| preview ot the tool in the browser | ||
| instruction for the tool | |
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| published on Zenodo | ||
| background | In determining plausible global emission paths, the challenge before which we aside is particularly evident. Therfore we have decoupled determining smooth global paths in a separate tool. |
With this simple tool, global or national emission paths can be derived that meet a specified budget. This tool is particularly suitable if
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| additional feature | Contains the illustrative IPCC SR1.5 paths P1 - P4 (LED, S1, S2, S5). | A temporary corona effect can be taken into account. |
| data base | Global Carbon Project; IPCC SR1.5 | Data for the EU, Germany and globally from various sources are offered. For EU and Germany, it is offered to calculate a budget with our ESPM on the basis of data from the European Environment Agency (EEA). |
| exemplary results | Here you will find some results for the EU and Germany with different framework data. Especially on the basis of the framework data from the German Advisory Council on the Environment (SRU). | |
| method | The tools uses the Regensburg Model Scenario Types (RM 1 - 6) to determine emission paths that are compatible with a given budget. These sceanrio types differ in the assumption about the property of the annual changes (see mathematical description: ). |
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| last publication | Berechnung Paris-kompatibler Emissionspfade mit dem ESPM am Beispiel der EU ; published on Zenodo |
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| web apps | EU: eu.climate-calculator.info |
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universally applicable app: espm.climate-calculator.info |
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Calculation of the implicit weighting of the population
With this tool (preview), you can determine the implicit weighting of the population (IWP) based on a national CO2 budget that you specify, if a global CO2 budget that you also specify were to be distributed to countries using a weighted distribution key. The weighted distribution key takes into account the share of the global population and the share of global emissions of the selected country in 2019. The national budget can be derived from an NDC, for example. The IWP thus offers an additional helpful assessment criterion for NDCs. The tool contains a database on the emissions and population figures of all countries in the world in 2019.
Easy access to results of the models based on framework data specified by you
- Here you will find results in the ESPM with different framework data:
- weighting population:
100, 85, 70, 50, 30, 15 or 0% - global budgets 2020 - 2100: 400, 550, 650 or 700 Gt
- Szenario Types: RM 3 - 6
- weighting population:
- Here a web app for the EU based on the ESPM:
eu.climate-calculator.info - Here a universal web app based on the ESPM approach:
espm.climate-calculator.info - Overview web apps
Comparison similar approaches (Resource Sharing Models)
Resource sharing models directly address the allocation of a remaining global budget. This article will therefore give an overview of the properties of resource sharing models that, in principle, use current emissions and population as a distribution key. The following models are compared: Regensburg Model (Regensburg Formula), Contraction & Convergence (C&C), Smooth Pathway Models (Smooth Pathway Formula from Raupach and Extended Smooth Pathway Model), Chakravarty et al. (cap per capita emissions), Höhne et al. (common but differentiated convergence; CDC).
- Comparison Resource Sharing Models published on the Zenodo platform
- Comparison Resource Sharing Models.xlsm (Preview of the tool in the browser here)
- Resource Sharing Models - A Mathematical Description
Remark on the tools
The Excel tools include macros. On request, the tools can be provided without macros and the macros as text or bas files for self-integration. Please contact us: save-the-climate@online.ms (mail to). You can also remove the macros by saving the downloaded xlsm file as an xlsx file. The main function of the macros is to determine the free parameters in the scenario types so that the specified budget is adhered to. You then have to do this individually for each scenario type in the sheet "goal seek" using the target value search (goal seek) integrated in Excel.
Mathematical papers
- Resource Sharing Models - A Mathematical Description - published on the Zenodo platform
This paper shines the spotlight on the mathematical formulae of resource sharing models. It contributes to greater transparency and comparability through a uniform mathematical representation, by showing generalisations and mergers as well as similarities and differences between currently used models. It also contains mathematical proofs for specified properties of the models.
In Chapter 2 we consider models with a limited convergence period, at the end of which global emissions are allocated to countries according to population only (C&C, LIMITS, Regensburg Formula, CDC). The Smooth Pathway Models in Chapter 3 calculates national paths starting from allocated remaining national budgets. The Emission Probability Model in Chapter 4 determines country specific emission density functions and caps the emissions of individuals. - Regensburg Model Scenario Types (RM 1 - 6)
The Regensburg Model Scenario Types are used to derive plausible emission paths that meet a certain budget.- Comprehensive mathematical description: - published on the Zenodo platform
- Schort description:
- Comprehensive mathematical description:
