DOI 10.5281/zenodo.5846043
Ins uc ions
o he Excel ool o he
Regensbu g Model
Calcula ion o Pa is-compa ible na ional emission pa hs and
budge s based on con e ging pe capi a emissions
www.sa e- he-clima e.in o
[email p o ec ed] (mail o)
Download Excel ool om he zenodo pla o m (Wol s eine & Wi mann, 2025a):
h ps://doi.o g/10.5281/zenodo.5846043
Web applica ion o he Regensbu g Model: h p://RM.clima e-calcula o .in o
Ve sion ins uc ions: 23/11/2025
Ins uc ions o he Excel ool o he Regensbu g Model page 2 o 15
Con en s
1 B ie in oduc ion o he Regensbu g Model ............................................................................... 3
2 B ie in oduc ion o he Excel ool o he Regensbu g Model .................................................. 4
3 Global amewo k da a - en ies in he shee “base da a” ............................................................ 5
4 De e mina ion o global emission pa hs ....................................................................................... 7
4.1 En ies in he shee “goal seek” .............................................................................................. 7
4.2 Whe e and how he global pa hs a e de e mined .................................................................... 7
4.3 Ac ual emissions a e he base yea 2019 .............................................................................. 7
4.4 RM Scena io Types 1 – 6 ....................................................................................................... 7
4.5 Mac o in he shee “goal seek” ............................................................................................... 7
5 De e mina ion o na ional emission pa hs .................................................................................... 9
5.1 The Regensbu g Fo mula ....................................................................................................... 9
5.2 De ia ions om he Regensbu g Fo mula in he Regensbu g Model .................................. 10
5.2.1 Conside a ion o inc easing global emissions pos 2019 ...................................... 10
5.2.2 A e he con e gence yea ................................................................................... 10
5.2.3 Ac ual emissions a e he base yea 2019 ............................................................ 10
5.3 Fo mulas o de e mine na ional pa hs in he Regensbu g Model ......................................... 11
6 Re e ence alues o e e y coun y in he wo ld ....................................................................... 12
7 Implici Weigh ing Popula ion (IWP) ........................................................................................ 13
8 Mac o secu i y............................................................................................................................ 14
Re e ences ..................................................................................................................................... 15
Lis o Figu es
Figu e 1: Exempla y cou se o pe capi a emissions in he Regensbu g Model .................................. 3
Figu e 2: Exempla y emission pa hs and annual change a es o he RM Scena io Types ................. 3
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1 B ie in oduc ion o he Regensbu g Model
Ou u u e cumula i e CO2 emissions a e a decisi e ac o in whe he we will be able o mee a gi en
a ge o limi ing global wa ming [c . (IPCC, 2021) and (Wol s eine , 2025)].
The c ucial ques ion is he e o e who ge s o akes how much o a emaining global CO2 budge .
On he gene al ques ion o he dis ibu ion o a global budge , see he co esponding excu sus in:
(Sa gl, e al., 2025b). Fo a compa ison o esou ce sha ing models, see: (Sa gl, e al., 2024a).
The Regensbu g Model makes i possible o de e mine na ional CO2 budge s ha comply wi h a
p ede ined global CO2 budge , wi h pe capi a emissions con e ging [c . (Sa gl, e al., 2017), (Sa gl,
e al., 2024b) and (Wol s eine & Wi mann, 2024b)]. Fo his pu pose, a global emission pa h is
dis ibu ed among he coun ies using he Regensbu g Fo mula (c . Wi mann & Wol s eine , 2023).
Figu e 1: Exempla y cou se o pe capi a emissions in he Regensbu g Model
1
This ool o e s he RM Scena io Types 1 – 6 o con e ing a global CO2 budge 2020 – 2100 in o
plausible global emission pa hs (c . Wol s eine & Wi mann, 2024a). Figu e 2 shows g aphically
he di e ences in he scena io ypes:
Figu e 2: Exempla y emission pa hs and annual change a es o he RM Scena io Types
1
In he shee "con e gence", any h ee coun ies and he scena io ype can be selec ed o show he cou se o pe capi a
emissions in he Regensbu g Model and he con e gence o pe capi a emissions.
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2 B ie in oduc ion o he Excel ool o he Regensbu g Model
Go o he shee “g aphs coun y” in he ool and selec a coun y om hose o e ed in he d op-
down lis .
The ool calcula es he na ional emission pa hs based on six scena io ypes o he global pa hs (RM
1 - 6). The RM Scena io Types di e p ima ily in he shape o he cu e o annual global change
a es (see Figu e 2). The ee pa ame e in he scena io ype is de e mined wi h a mac o in he shee
“goal seek”. I you change inpu da a, you ha e o un his mac o.
Impo an inpu alues in he shee “base da a”:
• global CO2 budge 2020 – 2100
• minimum emissions 2100 (po en ial global ne nega i e emissions)
• con e gence le el:
This means ha he na ional emission pa hs a e calcula ed using he Regensbu g Fo mula in such
a way ha a he poin in ime a which his alue is eached on he global pa h (con e gence yea )
he pe capi a emissions o e e y coun y a e a he same le el.
In he shee “dashboa d” you ge an o e iew o cu en inpu alues and impo an esul s.
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3 Global amewo k da a - en ies in he shee “base da a”
I. En y o da a o de e mine global emission pa hs om 2020 - 2100
I. a) Global CO2 budge 2020 – 2100 as a basis o na ional e e ence alues
Inpu global CO2 budge 2020 - 2100 based o example on he IPCC AR6 WG I.
I. c) Global budge 2020 – 2100 wi hou LUC and ISA
Since, among o he hings, i is di icul o ind na ional igu es o CO2 emissions caused by land use
changes (LUC), hese emissions a e no included he e and mus he e o e be deduc ed om he global
budge .
En e he LUC budge 2020 – 2100 in G . You can ind ou sepa a e pape on his opic he e
(Wol s eine & Wi mann, 2025b).
Emissions om in e na ional shipping and a ia ion (ISA) also ha e o be deduc ed, since a ibu ing
hem o coun ies is di icul . The cu en sha e o global ISA emissions is gi en o in o ma ion.
LUC and ISA a e no included in he na ional da a used (EDGAR, 2024).
I. d) Global budge 2020 – 2100 o dis ibu e in his ool
A ce ain alue is calcula ed om he da a en e ed. You may howe e also en e you own budge .
You can selec he alue o be used in he ool om he d op-down menu. In his case, please make
su e ha he budge does no include LUC and ISA.
I. d) Emissions 2100 (po en ial o ne nega i e emissions)
Fo he emissions o 2100, you se a minimum alue (Emin) which may no be unde cu . In doing so,
a nega i e alue is also possible, s anding o global nega i e emissions (ne nega i e emissions).
The speci ica ion is made by en e ing a pe cen age ha will be applied o global emissions in 2019.
See also ou sepa a e pape on his opic o downloading in he shee (Wol s eine & Wi mann,
2025b).
II. Ini ial alues o na ional emission pa hs
Con e gence le el
Using he Regensbu g Fo mula, na ional emission pa hs in which he pe capi a emissions con e ge
a e deduced om a global pa h. A his poin you can se he con e gence le el a which he pe
capi a emissions should con e ge. Depending on he global pa h he smalles alue is hen sough
which is g ea e han o he same as he con e gence le el se . This alue hen cons i u es he con-
e gence yea o he global pa h. The con e gence le el in he case o he conc e e global pa h will
gene ally be somewha highe han he alue se he e (see shee “dashboa d”).
Popula ion
Since he Regensbu g Fo mula is designed o include con e ging pe capi a emissions, he choice o
popula ion igu es in he con e gence yea on which he calcula ions a e based is c ucial.
We o e wo op ions:
(1) F eeze he popula ion igu es a hose o he base yea , 2019.
(2) Take oday’s popula ion o ecas s in o conside a ion.
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I op ion (1) is chosen, he popula ion igu es acco ding o he shee "EDGAR-P" a e used. I op ion
(2) is chosen, he igu es in he shee "UN-P" a e used (da a s a us 2019), which also include an
es ima e o he u u e.
III. Inc easing global emissions: See page 10.
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4 De e mina ion o global emission pa hs
4.1 En ies in he shee “goal seek”
• RM 2 – 5: a es o change o 2020 (RR20)
The ac ual RR20 canno be used because o he empo a y co ona e ec . Ins ead, a alue should
be used ha would p obably ha e been se wi hou co ona. The a es o change o he las ew
yea s a e gi en as an indica ion.
• Di e en h esholds (TV) ü RM 1 und RM 2 – 5
In he scena ios RM 1 - 5, a 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 TV onwa ds, he e is he e o e a linea
emission pa h.
The po en ial o ne nega i e emissions speci ied in he ‘base da a’ shee is gene ally used as
TV (as a posi i e alue). This means ha he highe he po en ial o ne nega 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 supple-
men . Plausible alues a e p e-se o his, bu hese can be changed. Minimum alues mus
s ill be speci ied o TV. 3.5% o RM 2 - 5 and 4.5% o RM-1 ha e p o en o be sui able.
4.2 Whe e and how he global pa hs a e de e mined
The global emission pa hs a e calcula ed in he shee “RM”. The esul s a e ans e ed o he shee
“coun y”. In he shee “g aphs global” you can see he g aphical esul s.
The global emission pa hs a e de e mined using he Regensbu g Model Scena io Types 1 – 6 (see
Chap e 4.4).
In he shee “goal seek” he ee pa ame e o he espec i e scena io is de e mined so ha he
global budge 2020 - 2100 is adhe ed o. The mac o 'goal seek' in his shee uses he a ge alue
sea ch in eg a ed in Excel (see Chap e 4.5).
4.3 Ac ual emissions a e he base yea 2019
Al eady known ac ual CO2 emissions a e he base yea 2019 a e no aken in o accoun in he emis-
sion pa hs, as he p ima y aim he e is o de e mine he na ional CO2 budge s ha esul in he Re-
gensbu g Model in he case o a dis ibu ion o a global CO2 budge om 2020.
These na ional CO2 budge s o he implici weigh ing o he popula ion (see Chap e 7) can be he
basis o de i ing plausible na ional emission pa hs in ou Ex ended Smoo h Pa hway Model (ESPM),
which also ake ac ual emissions a e 2019 in o accoun [c . (Sa gl, e al., 2025b), (Sa gl, e al.,
2025a) and h p://sho .na ional-budge s.clima e-calcula o .in o].
4.4 RM Scena io Types 1 – 6
See Figu e 2 o a g aphical ep esen a ion o he scena io ypes. He e is a b ie desc ip ion.
Fo a comp ehensi e 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, 2024a).
4.5 Mac o in he shee “goal seek”
The mac o 'goal seek' 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).
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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 o 2020 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 shee 'base da a'
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 .
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5 De e mina ion o na ional emission pa hs
5.1 The Regensbu g Fo mula
Fo a comp ehensi e ma hema ical desc ip ion see: (Wi mann & Wol s eine , 2023).
The na ional emission pa hs a e calcula ed in he shee "coun y".
By using he Regensbu g Fo mula, na ional emission pa hs a e de i ed om a global pa h. The na-
ional emission pa hs yield con e ging pe capi a emissions in he con e gence pe iod. In he "con-
e gence" shee , con e gence is shown g aphically using h ee selec able coun ies (see also Figu e
1).
The Regensbu g Fo mula:
𝑬𝒕
𝒊= (𝟏 − 𝑪𝒕)∗𝑬𝑩𝒀
𝒊 + 𝑪𝒕∗ 𝑬𝑪𝒀
𝒊
whe e:
𝐶𝑡= 𝐸𝐵𝑌 −𝐸𝑡
𝐸𝐵𝑌 −𝐸𝐶𝑌 and 𝐸𝐶𝑌
𝑖=𝐸𝐶𝑌
𝑃𝐶𝑌 ∗𝑃𝐶𝑌
𝑖
No e: CBY = 0; CCY = 1
CY = con e gence yea ; BY = base yea = 2019 in he ool; P = popula ion
Was does he Regensbu g Fo mula do?
The alloca ion based on he emissions in he base yea will be g adually eplaced by an alloca ion
based on equal emissions pe capi a. The globally necessa y ambi ion is he eby ansposed o each
coun y. In his way we can be su e ha he global pa h is adhe ed o, and e e y coun y eaches i s
a ge quan i y in he con e gence yea .
Con e gence yea
The con e gence yea in he espec i e global pa h esul s om he con e gence le el which you can
de e mine in he shee "base da a". Thus, also he emissions in he con e gence yea (𝐸𝐶𝑌 𝑎𝑛𝑑 𝐸𝐶𝑌
𝑖)
a e de e mined.
Summa y o he p ope ies o he Regensbu g Fo mula:
• con e ging pe capi a emissions; same pe capi a emissions in each coun y in he con e -
gence yea
• a global mono onic pa h leads o na ional mono onic pa hs
o coun ies ha s a wi h pe capi a emissions below he con e gence le el will ne e
exceed his con e gence le el (no "ho ai " o de eloping coun ies)
o coun ies ha s a abo e he con e gence le el wi h pe capi a emissions mus educe
hei emissions om he ou se (including eme ging coun ies)
• e e ence alues on his basis he e o e ep esen a kind o “mo al lowe limi ” o indus ial-
ised coun ies i he con e gence le el is chosen ela i ely low
