To successfully limit global warming,
we need fair global cooperation andCO2 must get an effective price.DOWNLOADS
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 (more information here).
Which concrete global budget we want to orientate by 2100, 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 and
- the Extended Smooth Pathway Model.
Tools based only on the Regensburg Model Scenario Types are also offered
- for determining global paths that are compatible with a given global budget
- for determining paths that are compatible with a given budget.
With these tools, we make a contribution to operationalizing the goals of the Paris Agreement.
In addition, resource sharing models are compared.
Basic idea behind the Regensburg Model Scenario Types RM 1 - 6 (here is a mathematical 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.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.
Basic idea behind the Extended Smooth Pathway Model (ESPM; inspired by Raupach et al.)
- 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.
Download tools and papers
National reference vlaues that are compatible with a given global CO2 budget 2018 - 2100: Tools RM and ESPM
Regensburg Model (RM) |
Extended Smooth Pathway Model (ESPM) |
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| version of the tool | 34.0 |
38.0 |
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| preview ot the tool in the browser | ||||
| instruction for the tool |  |
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| 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 |
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| paper | Journal "Climate Policy" published online on 14 June 2016:
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working paper:
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| exemplary results | global CO2 budget 2018 - 2100 |
EU27 2030 vs. 1990 (RM-5) |
Here you will find results in the ESPM with different framework data:
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420 Gt |
-64% |
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570 Gt |
-58% |
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680 Gt |
-54% |
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| further here specified parameters: | ||||
| minimum global emission in Gt | -3.67 |
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| convergence level in t/capita | 0.25 |
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Notes on the 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 in the RM. 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 tool or is indicated above in the exemplary results. |
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| web app |  eu.climate-calculator.info |
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Determination of emission paths that adhere to a given buget using the RM Scenario Types
determine global paths Tool_global_paths |
determine global or national paths Tool_Paths_Regensburg_Model_Scenario_Types |
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| donwload tool | |
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| version of the tool | 15.0 |
18.0 |
| preview ot the tool in the browser | ||
| instruction for the tool | |
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| 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
The basic approach corresponds to the ESPM. |
| additional feature | Contains the illustrative IPCC SR1.5 paths P1 - P4 (LED, S1, S2, S5). | Here a "corona effect" can be taken into account. Sample data for the EU and global are offered. |
| exemplary results | Here you will find some results for the EU with different framework data. | |
| 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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| paper | working paper:
Application of the ESPM to the EU objectives: Is the EU 2030 target compatible with the Paris Agreement? (in German) |
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| web app | eu.climate-calculator.info |
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Results of the models based on the framework data specified by you
- There is the option of making the results of the tools available as PDFs based on the framework data you specified. Here you can download a form for a request .
- Current: We are making a web application for ESPM available for the EU:
eu.climate-calculator.info
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
- 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. If the target value search does not find a solution, you can change the default values in this sheet and try again.The "Paths_Regensburg_Model_Scenario_Types" tool is ideal for this because of its simple structure.
Mathematical papers
- Resource Sharing Models - A Mathematical Description
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. - Mathematical Description of the Regensburg Model Scenario Types (RM 1 - 6)
The Regensburg Model Scenario Types are used to derive plausible emission paths that meet a certain budget.
