Tool for the Calculation of Paris-compatible National Emission Paths with the Regensburg Model

DOI 10.5281/zenodo.5846043 Instructions to the Excel tool for the Regensburg Model Calculation of Paris-compatible national emission paths and budgets based on converging per capita emissions www.save-the-climate.info [email protected] (mail to) Download Excel tool from the zenodo platform (Wolfsteiner & Wittmann, 2025a): https://doi.org/10.5281/zenodo.5846043 Web application for the Regensburg Model: http://RM.climate-calculator.info Version instructions: 23/11/2025 Instructions for the Excel tool for the Regensburg Model page 2 of 15 Contents 1 Brief introduction to the Regensburg Model ............................................................................... 3 2 Brief introduction to the Excel tool for the Regensburg Model .................................................. 4 3 Global framework data - entries in the sheet “base data” ............................................................ 5 4 Determination of global emission paths ....................................................................................... 7 4.1 Entries in the sheet “goal seek” .............................................................................................. 7 4.2 Where and how the global paths are determined .................................................................... 7 4.3 Actual emissions after the base year 2019 .............................................................................. 7 4.4 RM Scenario Types 1 – 6 ....................................................................................................... 7 4.5 Macro in the sheet “goal seek” ............................................................................................... 7 5 Determination of national emission paths .................................................................................... 9 5.1 The Regensburg Formula ....................................................................................................... 9 5.2 Deviations from the Regensburg Formula in the Regensburg Model .................................. 10 5.2.1 Consideration of increasing global emissions post 2019 ...................................... 10 5.2.2 After the convergence year ................................................................................... 10 5.2.3 Actual emissions after the base year 2019 ............................................................ 10 5.3 Formulas to determine national paths in the Regensburg Model ......................................... 11 6 Reference values for every country in the world ....................................................................... 12 7 Implicit Weighting Population (IWP) ........................................................................................ 13 8 Macro security............................................................................................................................ 14 References ..................................................................................................................................... 15 List of Figures Figure 1: Exemplary course of per capita emissions in the Regensburg Model .................................. 3 Figure 2: Exemplary emission paths and annual change rates of the RM Scenario Types ................. 3 Instructions for the Excel tool for the Regensburg Model page 3 of 15 1 Brief introduction to the Regensburg Model Our future cumulative CO2 emissions are a decisive factor in whether we will be able to meet a given target for limiting global warming [cf. (IPCC, 2021) and (Wolfsteiner, 2025)]. The crucial question is therefore who gets or takes how much of a remaining global CO2 budget. On the general question of the distribution of a global budget, see the corresponding excursus in: (Sargl, et al., 2025b). For a comparison of resource sharing models, see: (Sargl, et al., 2024a). The Regensburg Model makes it possible to determine national CO2 budgets that comply with a predefined global CO2 budget, with per capita emissions converging [cf. (Sargl, et al., 2017), (Sargl, et al., 2024b) and (Wolfsteiner & Wittmann, 2024b)]. For this purpose, a global emission path is distributed among the countries using the Regensburg Formula (cf. Wittmann & Wolfsteiner, 2023). Figure 1: Exemplary course of per capita emissions in the Regensburg Model 1 This tool offers the RM Scenario Types 1 – 6 for converting a global CO2 budget 2020 – 2100 into plausible global emission paths (cf. Wolfsteiner & Wittmann, 2024a). Figure 2 shows graphically the differences in the scenario types: Figure 2: Exemplary emission paths and annual change rates of the RM Scenario Types 1 In the sheet "convergence", any three countries and the scenario type can be selected to show the course of per capita emissions in the Regensburg Model and the convergence of per capita emissions. Instructions for the Excel tool for the Regensburg Model page 4 of 15 2 Brief introduction to the Excel tool for the Regensburg Model Go to the sheet “graphs country” in the tool and select a country from those offered in the dropdown list. The tool calculates the national emission paths based on six scenario types for the global paths (RM 1 - 6). The RM Scenario Types differ primarily in the shape of the curve for annual global change rates (see Figure 2). The free parameter in the scenario type is determined with a macro in the sheet “goal seek”. If you change input data, you have to run this macro. Important input values in the sheet “base data”: • global CO2 budget 2020 – 2100 • minimum emissions 2100 (potential global net negative emissions) • convergence level: This means that the national emission paths are calculated using the Regensburg Formula in such a way that at the point in time at which this value is reached on the global path (convergence year) the per capita emissions of every country are at the same level. In the sheet “dashboard” you get an overview of current input values and important results. Instructions for the Excel tool for the Regensburg Model page 5 of 15 3 Global framework data - entries in the sheet “base data” I. Entry of data to determine global emission paths from 2020 - 2100 I. a) Global CO2 budget 2020 – 2100 as a basis for national reference values Input global CO2 budget 2020 - 2100 based for example on the IPCC AR6 WG I. I. c) Global budget 2020 – 2100 without LUC and ISA Since, among other things, it is difficult to find national figures for CO2 emissions caused by land use changes (LUC), these emissions are not included here and must therefore be deducted from the global budget. Enter the LUC budget 2020 – 2100 in Gt. You can find our separate paper on this topic here (Wolfsteiner & Wittmann, 2025b). Emissions from international shipping and aviation (ISA) also have to be deducted, since attributing them to countries is difficult. The current share of global ISA emissions is given for information. LUC and ISA are not included in the national data used (EDGAR, 2024). I. d) Global budget 2020 – 2100 to distribute in this tool A certain value is calculated from the data entered. You may however also enter your own budget. You can select the value to be used in the tool from the drop-down menu. In this case, please make sure that the budget does not include LUC and ISA. I. d) Emissions 2100 (potential for net negative emissions) For the emissions for 2100, you set a minimum value (Emin) which may not be undercut. In doing so, a negative value is also possible, standing for global negative emissions (net negative emissions). The specification is made by entering a percentage that will be applied to global emissions in 2019. See also our separate paper on this topic for downloading in the sheet (Wolfsteiner & Wittmann, 2025b). II. Initial values for national emission paths Convergence level Using the Regensburg Formula, national emission paths in which the per capita emissions converge are deduced from a global path. At this point you can set the convergence level at which the per capita emissions should converge. Depending on the global path the smallest value is then sought which is greater than or the same as the convergence level set. This value then constitutes the convergence year of the global path. The convergence level in the case of the concrete global path will generally be somewhat higher than the value set here (see sheet “dashboard”). Population Since the Regensburg Formula is designed to include converging per capita emissions, the choice of population figures in the convergence year on which the calculations are based is crucial. We offer two options: (1) Freeze the population figures at those of the base year, 2019. (2) Take today’s population forecasts into consideration. Instructions for the Excel tool for the Regensburg Model page 6 of 15 If option (1) is chosen, the population figures according to the sheet "EDGAR-P" are used. If option (2) is chosen, the figures in the sheet "UN-P" are used (data status 2019), which also include an estimate for the future. III. Increasing global emissions: See page 10. Instructions for the Excel tool for the Regensburg Model page 7 of 15 4 Determination of global emission paths 4.1 Entries in the sheet “goal seek” • RM 2 – 5: rates of change for 2020 (RR20) The actual RR20 cannot be used because of the temporary corona effect. Instead, a value should be used that would probably have been set without corona. The rates of change of the last few years are given as an indication. • Different thresholds (TV) für RM 1 und RM 2 – 5 In the scenarios RM 1 - 5, a constant reduction amount is applied from this threshold values for the transition to net negative emissions. From the TV onwards, there is therefore a linear emission path. The potential for net negative emissions specified in the ‘base data’ sheet is generally used as TV (as a positive value). This means that the higher the potential for net negative emissions, the earlier a switch to a linear emissions path occurs. You can increase this value by a supplement. Plausible values are pre-set for this, but these can be changed. Minimum values must still be specified for TV. 3.5% for RM 2 - 5 and 4.5% for RM-1 have proven to be suitable. 4.2 Where and how the global paths are determined The global emission paths are calculated in the sheet “RM”. The results are transferred to the sheet “country”. In the sheet “graphs global” you can see the graphical results. The global emission paths are determined using the Regensburg Model Scenario Types 1 – 6 (see Chapter 4.4). In the sheet “goal seek” the free parameter of the respective scenario is determined so that the global budget 2020 - 2100 is adhered to. The macro 'goal seek' in this sheet uses the target value search integrated in Excel (see Chapter 4.5). 4.3 Actual emissions after the base year 2019 Already known actual CO2 emissions after the base year 2019 are not taken into account in the emission paths, as the primary aim here is to determine the national CO2 budgets that result in the Regensburg Model in the case of a distribution of a global CO2 budget from 2020. These national CO2 budgets or the implicit weighting of the population (see Chapter 7) can be the basis for deriving plausible national emission paths in our Extended Smooth Pathway Model (ESPM), which also take actual emissions after 2019 into account [cf. (Sargl, et al., 2025b), (Sargl, et al., 2025a) and http://short.national-budgets.climate-calculator.info]. 4.4 RM Scenario Types 1 – 6 See Figure 2 for a graphical representation of the scenario types. Here is a brief description. For a comprehensive description, we refer to our paper ‘Mathematical Description of the Regensburg Model Scenario Types RM 1 – 6’ published on zenodo (Wolfsteiner & Wittmann, 2024a). 4.5 Macro in the sheet “goal seek” The macro 'goal seek' tries to determine the free parameter in the scenario (row 12 or 13) so that the budget (row 16) is adhered to (► row 15 = row 16). Instructions for the Excel tool for the Regensburg Model page 8 of 15 If this does not succeed at first go, the macro tries to find a solution with a different rate of change for 2020 in the scenario types RM 2 - 5. The initial value you specify is changed by a maximum of 2.5 percentage points in both directions in 0.01 steps. The start value you specified will therefore be changed. If a solution cannot be found either, the macro will inform you and advise you to change the start value for 2020 more significantly. In the RM-1 scenario, the macro increases the threshold value (TV) if necessary to find a solution. The macro also tries in scenario RM-1 that the minimum value (Emin) specified in the sheet 'base data' is reached (► row 18 = row 19). If this does not succeed straight away, the macro increases the threshold value (TV) in the RM-1. If E_min can still not be reached, the original TV will be reset. Instructions for the Excel tool for the Regensburg Model page 9 of 15 5 Determination of national emission paths 5.1 The Regensburg Formula For a comprehensive mathematical description see: (Wittmann & Wolfsteiner, 2023). The national emission paths are calculated in the sheet "country". By using the Regensburg Formula, national emission paths are derived from a global path. The national emission paths yield converging per capita emissions in the convergence period. In the "convergence" sheet, convergence is shown graphically using three selectable countries (see also Figure 1). The Regensburg Formula: 𝑬𝒕 𝒊= (𝟏 − 𝑪𝒕)∗𝑬𝑩𝒀 𝒊 + 𝑪𝒕∗ 𝑬𝑪𝒀 𝒊 where: 𝐶𝑡= 𝐸𝐵𝑌 −𝐸𝑡 𝐸𝐵𝑌 −𝐸𝐶𝑌 and 𝐸𝐶𝑌 𝑖=𝐸𝐶𝑌 𝑃𝐶𝑌 ∗𝑃𝐶𝑌 𝑖 Note: CBY = 0; CCY = 1 CY = convergence year; BY = base year = 2019 in the tool; P = population Was does the Regensburg Formula do? The allocation based on the emissions in the base year will be gradually replaced by an allocation based on equal emissions per capita. The globally necessary ambition is thereby transposed to each country. In this way we can be sure that the global path is adhered to, and every country reaches its target quantity in the convergence year. Convergence year The convergence year in the respective global path results from the convergence level which you can determine in the sheet "base data". Thus, also the emissions in the convergence year (𝐸𝐶𝑌 𝑎𝑛𝑑 𝐸𝐶𝑌 𝑖) are determined. Summary of the properties of the Regensburg Formula: • converging per capita emissions; same per capita emissions in each country in the convergence year • a global monotonic path leads to national monotonic paths o countries that start with per capita emissions below the convergence level will never exceed this convergence level (no "hot air" for developing countries) o countries that start above the convergence level with per capita emissions must reduce their emissions from the outset (including emerging countries) • reference values on this basis therefore represent a kind of “moral lower limit” for industrialised countries if the convergence level is chosen relatively low