DOI 10.5281/zenodo.4568839
Ve sion o he ins uc ions: 20/11/2025
Ins uc ions o he Tool:
Calcula ion o Emission Pa hs Using
he Regensbu g Model Scena io Types
And eas Wol s eine ● www.sa e- he-clima e.in o ● sa e- he-clima [email protected] (mail o)
The la es e sion o he ool can be downloaded a he pla o m zenodo:
h ps://doi.o g/10.5281/zenodo.4568839.
The da a equi ed o his ool can be e ie ed om he ollowing ools, o example:
• De ailed Excel ool (Wol s eine & Wi mann, 2025): h ps://doi.o g/10.5281/zenodo.5837866
• Web app: h p://na ional-budge s.clima e-calcula o .in o
O e iew ou ools: h ps://clima e-calcula o .in o.
Rela ed publica ions:
(Wiegand, e al., 2021; Sa gl, e al., 2021; Sa gl, e al., 2025a; Sa gl, e al., 2025b)
Tool ‘Regensbu g Model Scena io Types” page 2 o 7
Con en s
1 Basic idea o his ool ................................................................................................................... 3
2 En ies in he ‘base da a’ shee ..................................................................................................... 3
3 Da a and budge s o all coun ies in he wo ld ........................................................................... 3
4 De e mina ion o emission pa hs .................................................................................................. 4
4.1 En ies in he ‘goal seek’ shee ............................................................................................... 4
4.2 Whe e and how he pa hs a e de e mined ............................................................................... 4
4.3 RM Scena io Types 1 – 6 ....................................................................................................... 4
4.4 Mac os in he ‘goal seek’ shee ............................................................................................... 5
4.4.1 Mac o ‘goal seek’ .................................................................................................... 5
4.4.2 Mac os inding budge ............................................................................................ 5
4.4.3 Mac o secu i y ......................................................................................................... 6
5 Pa hs and e e ence alues ........................................................................................................... 6
Re e ences ....................................................................................................................................... 7
Tool ‘Regensbu g Model Scena io Types” page 3 o 7
1 Basic idea o his ool
Wi h his ool, wi h he help o he Regensbu g Model Scena io Types (RM 1 - 6), global o na ional
emission pa hs can be de i ed ha mee a speci ied budge 2020 - 2100 (c . Wol s eine &
Wi mann, 2024).
Basically, only he budge and he cu en annual emissions ha e o be speci ied.
2 En ies in he ‘base da a’ shee
The da a o a coun y, global da a o o he uni can be speci ied he e.
• Wha do he igu es e e o? Fo example: EU.
• Speci y he uni o he emission da a. Fo example: G .
• Budge 2020 – 2100: He e you speci y he budge ha he pa hs should adhe e o.
• Annual emissions:
o En e he ac ual emissions in he base yea 2019.
You can also speci y he emissions in 2018 and 1990 also. This allows e e ence
alues o be calcula ed in compa ison o emissions in 1990. Emissions in 2018 can
be help ul in de e mining he s a change a e in he ‘goal seek’ shee (see Chap e
4.1).
o En e he ac ual emissions a e 2019 i a ailable.
• Minimum emissions (Emin)
He e you can speci y which minimum he pa hs can achie e in 2100. I you speci y a nega-
i e alue, his means ne nega i e emissions. The speci ica ion is made by en e ing a pe -
cen age ha will be applied o emissions in 2019.
I ne nega i e emissions a e allowed, he budge may be empo a ily exceeded. This o e -
shoo will hen be o se by ne nega i e emissions by 2100.
3 Da a and budge s o all coun ies in he wo ld
We o e an Excel ool ha con ains he emission da a o all coun ies in he wo ld (Wol s eine &
Wi mann, 2025). He e we also o e a simpli ied web app o i : h p://na ional-budge s.clima e-
calcula o .in o. To de i e na ional budge s om a global budge , hese ools o e a weigh ed dis-
ibu ion key ha akes in o accoun a coun y's sha e o global emissions and i s sha e o he wo ld
popula ion in a base yea (usually 2019).
The da a equi ed o he EU, Ge many and globally is p o ided in he ool in co esponding shee s
(sou ce: (Wol s eine & Wi mann, 2025)). This can be copied in o he ‘base da a’ and ‘goal seek’
shee s using a mac o.
In he ‘base da a’ shee , he ields o be en e ed can be linked locally o he co esponding cells in
his Excel ool (Wol s eine & Wi mann, 2025). This allows he ields o be illed au oma ically
wi h he da a o all coun ies in he wo ld.
Tool ‘Regensbu g Model Scena io Types” page 4 o 7
4 De e mina ion o emission pa hs
4.1 En ies in he ‘goal seek’ shee
• RM 2 – 5: S a ing a e o change in he s a yea (RRSY)
The s a change a e mus be speci ied in hese scena io ypes. This makes i possible o
de e mine i on he basis o a ealis ic assessmen . Howe e , since he change a es o he
en i e budge pe iod a e de e mined based on his, a no malised alue (wi hou , o exam-
ple, a empo a y e ec om he co ona pandemic o he wa in Uk aine) mus be used. The
s a yea is he i s yea wi hou a ailable ac ual emissions.
• Di e en h esholds (TV) o RM 1 and RM 2 – 5
In he scena ios RM 1 - 5, he las cons an educ ion amoun is applied om his h eshold
alues o he ansi ion o ne nega i e emissions. F om he TVs onwa ds, he e is he e o e
a linea emission pa h.
To achie e a nega i e alue o E_min mo e quickly, i may be use ul o de ine he TVs
depending on he po en ial o ne nega i e emissions (NNE). You can choose whe he you
wan o p oceed in his way. In his case, he NNE speci ied in he ‘base da a’ shee is gen-
e ally used as TV (as a posi i e alue). This means ha he highe he po en ial o ne neg-
a i e emissions, he ea lie a swi ch o a linea emissions pa h occu s. You can inc ease his
alue by a supplemen . Plausible alues a e p e-se o his, bu hese can be changed.
Minimum alues mus s ill be speci ied o TVs. 3.5% o RM 2 - 5 and 4.5% o RM-1 ha e
p o en o be sui able. These alues a e also used i you do no wan o de ine he TVs de-
pending on NNE.
4.2 Whe e and how he pa hs a e de e mined
The pa hs a e calcula ed in he ‘calcula ion’ shee .
Emission pa hs a e be de e mined using he Regensbu g Model Scena io Types RM 1 – 6 (see Chap-
e 4.3). The pa hs a e essen ially de e mined by speci ying he annual a es o change (RM 1 - 5)
o he annual cons an educ ion amoun (RM-6). F om he speci ied h eshold alue (TV), a con-
s an educ ion amoun is used un il he emissions each he p ede ined minimum alue (E_min).
This usually leads o he ollowing h ee phases o de e mining he pa hs:
1. Applica ion o he annual educ ion a es (RM 1 - 5) o he annual educ ion amoun (RM-6).
2. Annual emissions less han o equal o TV: The las annual absolu e educ ion is con inued.
3. Minimum o he annual emissions (Emin) ha you speci y in he ‘base da a’ shee will be ap-
plied un il 2100.
In he ‘goal seek’ shee he ee pa ame e o he espec i e scena io is de e mined o each scena io
ype using an i e a i e solu ion me hod so ha he budge is adhe ed o. The ‘goal seek’ mac o in
his shee uses he a ge alue sea ch in eg a ed in Excel o his pu pose (see Chap e 4.4.1).
4.3 RM Scena io Types 1 – 6
Fo a comp ehensi e ma hema ical desc ip ion, we e e o ou pape ‘Ma hema ical Desc ip ion o
he Regensbu g Model Scena io Types RM 1 - 6’published on Zenodo (Wol s eine & Wi mann,
2024).
Tool ‘Regensbu g Model Scena io Types” page 5 o 7
4.4 Mac os in he ‘goal seek’ shee
4.4.1 Mac o ‘goal seek’
The ‘goal seek’ mak o ies o de e mine he ee pa ame e in he scena io ( ow 12 o 13) so ha
he budge ( ow 16) is adhe ed o (► ow 15 = ow 16). The mac o also ensu es ha he cons ain s
o he ee pa ame e a e me .
I his does no succeed a i s go, he mac o ies o ind a solu ion wi h a di e en a e o change
o 2020 in he scena io ypes RM 2 - 5. The ini ial alue you speci y is changed by a maximum o
2.5 pe cen age poin s in bo h di ec ions in 0.01 s eps. The s a alue you speci ied will he e o e
be changed. I a solu ion canno be ound ei he , he mac o will in o m you and ad ise you o change
he s a alue mo e signi ican ly.
In he RM-1 scena io, he mac o inc eases he h eshold alue (TV) i necessa y o ind a solu ion.
The mac o also ies in scena io RM-1 ha he minimum alue (Emin) speci ied in he 'base da a'
shee is eached (► ow 18 = ow 19). I his does no succeed s aigh away, he mac o inc eases
he h eshold alue (TV) in he RM-1. I E_min can s ill no be eached, he o iginal TV will be ese .
4.4.2 Mac os inding budge
Mac o ‘ a ge 2030’
Wi h his mac o you can se he emissions a ge o a ce ain scena io ype o 2030 compa ed o
1990 and sea ch o he app op ia e budge . The 2030 emissions a ge o be speci ied mus be
less ambi ious han he solu ion al eady ound.
The use o his mac o is pa icula ly use ul i a coun y speci ies a lowe le el o ambi ion o 2030
in i s NDC han would be necessa y wi h he gi en amewo k da a. This shows which budge NDC
o 2030 co esponds o wi h o he wise he same amewo k da a.
The scena io ypes RM-2, RM-4 and RM-6 a e pa icula ly sui able o his analysis. The scena io
ypes RM-3 and RM-5 a e less sui able i a coun y is no e y ambi ious when i comes o he 2030
emissions a ge , since in hese scena io ypes a ela i ely apid inc ease in he annual educ ion
a es is implemen ed igh om he s a . This cha ac e is ic does no come in o play due o he less
ambi ious 2030 a ge . Howe e , he la e inc ease in he educ ion a es is only possible o a limi ed
ex en wi h hese scena io ypes. The e o e, a less ambi ious a ge o 2030 equi es a ela i ely
high budge o hese scena io ypes.
Be o e his mac o can be execu ed, he no mal a ge alue sea ch o he scena io ypes RM 2 - 6
mus ha e been ca ied ou success ully.
Mac o ‘yea emissions neu ali y’
Wi h his mac o you can se he yea o emissions neu ali y o a ce ain scena io ype and sea ch
o he app op ia e budge . The yea o emissions neu ali y o be speci ied mus be less ambi ious
han he solu ion al eady ound.
The use o his mac o is pa icula ly use ul i a coun y speci ies a lowe le el o ambi ion in i s
NDC han would be necessa y wi h he gi en amewo k da a. This shows which budge NDC co -
esponds o wi h o he wise he same amewo k da a.
Be o e his mac o can be execu ed, he no mal a ge alue sea ch o he scena io ypes RM 2 - 6
mus ha e been ca ied ou success ully.
Tool ‘Regensbu g Model Scena io Types” page 6 o 7
4.4.3 Mac o secu i y
Please use Mic oso 's ins uc ions o allow mac os i hey ha e been blocked.
I you do no wan o use he buil -in mac os, you can sa e he ile as an xlsx ile. This will emo e
all mac os.
We ha e published he code o he key mac o 'goal seek' he e:
h ps://doi.o g/10.5281/zenodo.7494168
This gi es you he op ion o in eg a ing he mac o in o you Excel ile you sel . Please use a ian
2 he e.
5 Pa hs and e e ence alues
The esul ing emission pa hs, e e ence alues and sum o he ne nega i e emissions (o e shoo s)
a e shown in he ‘ esul s’ shee .
Abo e his shee you will see whe he he a ge alue sea ch mus be ca ied ou in he ‘goal seek’
shee .
Tool ‘Regensbu g Model Scena io Types” page 7 o 7
Re e ences
Sa gl, M., Wiegand, D., Wi mann, G. & Wol s eine , A., 2021. Be echnung Pa is-kompa ible
Emissionsziele ü die sechs g öß en Emi en en mi dem ESPM. Zei sch i ü Umwel poli ik &
Umwel ech , Issue 3/2021, pp. 269 - 286.
Sa gl, M., Wiegand, D., Wi mann, G. & Wol s eine , A., 2025a. Be echnung Pa is-kompa ible
Emissionsp ade mi dem ESPM am Beispiel Deu schlands und de EU. [Online]
A ailable a : h ps://doi.o g/10.5281/zenodo.5678717
Sa gl, M., Wiegand, D., Wi mann, G. & Wol s eine , A., 2025b. Calcula ion o Pa is-compa ible
emission a ge s o he six la ges emi e s wi h he ESPM. [Online]
A ailable a : h ps://doi.o g/10.5281/zenodo.4764408
Wiegand, D. e al., 2021. Be echnung Pa is-kompa ible Emissionsp ade mi dem ESP-Modell am
Beispiel de EU. Wi scha sdiens , 2, pp. 127 - 133.
Wol s eine , A. & Wi mann, G., 2024. Ma hema ical Desc ip ion o he Regensbu g Model
Scena io Types RM 1 – 6. [Online]
A ailable a : h ps://doi.o g/10.5281/zenodo.4540475
Wol s eine , A. & Wi mann, G., 2025. Tool: Implici and explici weigh ing o he popula ion in
he alloca ion o a global CO2 budge . [Online]
A ailable a : h ps://doi.o g/10.5281/zenodo.5837866
