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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 Regensburg Model 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 (here are exemplary courses). This approach is particularly useful when it comes to making political decisions about emission paths.

Web app: http://paths.climate-calculator.info

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: ; exemplary course of per capita emissions here).

Web app: http://RM.climate-calculator.info

Publications:

Journal "Climate Policy", 2016, The Regensburg Model: reference values for the (I)NDCs based on converging per capita emissions
Zenodo, 2022, Calculation of Paris-compatible Emission Targets for the Six Largest Emitters with the Regensburg Model

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.

Web apps

Publications:

Wirtschaftsdienst, 2/2021, Berechnung Paris-kompatibler Emissionspfade mit dem ESPM am Beispiel der EU,
- Update published on Zenodo (with exemplary reference values for the EU and Germany), 2022
Zeitschrift für Umweltpolitik & Umweltrecht (ZfU), 9/2021, Calculation of Paris-compatible emission targets for the six largest emitters
- Update published on Zenodo, 2022

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)
download Excel tool from Zenodo platform	here			here
preview ot the tool in the browser	here			here
instruction for the tool
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 (example)			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: ; exemplary courses
	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: With this database, the EU provides the emissions of all countries in the world due to the use of fos-sil fuels (excluding international shipping and aviation; ISA) and cement production. For the handling of land-use change emissions (LUC) in the tools, see this paper:
exemplary results	global CO2 budget 2020 - 2100	all countries		Here you will find results in the ESPM with different framework data: weighting population: 100, 85, 70, 50, 30, 15 or 0% different global budgets Szenario Types: RM 3 - 6
	400 Gt
	550 Gt
	650 Gt
	further here specified parameters:
	minimum global emission in Gt		-0.7
	convergence level in t/capita		0.5
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	Calculation of Paris-compatible emission targets for the six largest emitters
	- published on Zenodo			- published on Zenodo
web apps	RM.climate-calculator.info			national-budgets.climate-calculator.info
				paths.climate-calculator.info

Determination of emission paths that adhere to a given buget using the Regensburg Model Scenario Types

	ESPM approach: Set budget and determine emission paths
	determine global paths	determine global or national paths
download Excel tool from Zenodo platform	here	here
preview ot the tool in the browser	here	here
instruction for the tool
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 a global or national budget is already known and the first interest is in compatible emission paths, the focus is on getting to know the RM Scenario Types or a database other than EDGAR is to be used.
additional feature	Contains the illustrative IPCC SR1.5 paths P1 - P4 (LED, S1, S2, S5).
data base	Global Carbon Project IPCC SR1.5	The tool does not contain any data. The required data for all countries in the world can be provided with the following tools: web app: http://national-budgets.climate-calculator.info Excel tool: https://doi.org/10.5281/zenodo.5837866
exemplary results		Here you will find some results for the EU and Germany 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: ; exemplary courses).
last publication		Berechnung Paris-kompatibler Emissionspfade mit dem ESPM am Beispiel Deutschlands und der EU ; published on Zenodo
web app	http://paths.climate-calculator.info

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
Here a web app for the EU based on the ESPM:
eu.climate-calculator.info
Here a web app to calculate Paris-compatible CO2 budgets for all countries of the world:
national-budgets.climate-calculator.info
Here a universal web app to calculate emission paths that adhere to a predefined budget:
paths.climate-calculator.info
Here a web app based on the Regensburg Model (for furhter exemplary results in the RM, see table above):
RM.climate-calculator.info
Overview web apps
Here you can request the results for a country according to the RM or the ESPM via a Google form. Here is a request for all Excel tools as a PDF.

Implicit and explicit weighting of the population in the allocation of a global CO2 budget

Implicit and explicit weighting population vs. emissions - Download Excel tool from Zenodo (preview) .
- Determine the implicit weighting of the population (IWP) based on a national CO2 budget.
- Paris-compatible national CO2 budgets can be calculated based on an explicit weighting of population against emissions for all countries in the world.
Web app - Paris-compatible CO2 budgets for all countries of the world: http://national-budgets.climate-calculator.info
Here is a tool for deriving an implicit CO2 budget from the German Climate Protection Act.

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

Notes on macros in Excel tools

Some Excel tools contain macros. You can remove the macros by saving the downloaded xlsm file as an xlsx file. The key macro "Goal Seek" has the function of determining the free parameters in the scenario types in such a way 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.

On request, the macros can be provided as text or bas files for self-integration. Please contact us: save-the-climate@online.ms (mail to).

We have published the code of the macro "Goal Seek" and the corresponding bas file on Zenodo: https://doi.org/10.5281/zenodo.7494168.

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:
- exemplary courses