| ALbedo (1) |
AL |
ISCEGA |
ALIS ALGAV GLSU |
TRHGS |
0.3094 |
\(\mathtt{AL}\left(t\right)=\frac{\mathtt{ALGAV}\cdot\left(\mathtt{GLSU}-\mathtt{ISCEGA}\left(t\right)\right)+\mathtt{ALIS}\cdot\mathtt{ISCEGA}\left(t\right)}{\mathtt{GLSU}}\) |
| Cost of air capture GDollar/y |
CAC |
DACCO2 |
CCCSt |
CE |
|
\(\mathtt{CAC}\left(t\right)=\mathtt{CCCSt}\cdot\mathtt{DACCO2}\left(t\right)\) |
| CH4 in Atmosphere GtCH4 |
CH4A |
CH4BD CH4E |
|
CH4BD CH4CA |
2.5 |
\(\frac{\mathrm{d}\mathtt{CH4A}\left(t\right)}{\mathrm{d}t}=-\mathtt{CH4BD}\left(t\right)+\mathtt{CH4E}\left(t\right)\) |
| CH4 BreakDown GtCH4/y |
CH4BD |
CH4A |
LCH4A |
CH4A CO2FCH4 |
|
\(\mathtt{CH4BD}\left(t\right)=\frac{\mathtt{CH4A}\left(t\right)}{\mathtt{LCH4A}}\) |
| CH4 concentration in atm ppm |
CH4CA |
CH4A |
GCH4PP |
FCH4 |
|
\(\mathtt{CH4CA}\left(t\right)=\frac{\mathtt{CH4A}\left(t\right)}{\mathtt{GCH4PP}}\) |
| CH4 emissions GtCH4/y |
CH4E |
MMCH4E NCH4E |
|
CH4A GHGE |
|
\(\mathtt{CH4E}\left(t\right)=\mathtt{MMCH4E}\left(t\right)+\mathtt{NCH4E}\left(t\right)\) |
| CH4 forcing per ppm W/m2/ppm |
CH4FPP |
|
|
FCH4 |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.82), (2000.0, 0.94), (2020.0, 1.01), (2100.0, 1.1)])\) |
| CO2 in Atmosphere GtCO2 |
CO2A |
CO2FCH4 CO2AB CO2E |
|
CO2AB CO2CA |
2600.0 |
\(\frac{\mathrm{d}\mathtt{CO2A}\left(t\right)}{\mathrm{d}t}=-\mathtt{CO2AB}\left(t\right)+2\cdot\mathtt{CO2FCH4}\left(t\right)+\mathtt{CO2E}\left(t\right)\) |
| CO2 absorption GtCO2/y |
CO2AB |
LECO2A CO2A |
CO2A1850 |
CO2A |
|
\(\mathtt{CO2AB}\left(t\right)=\frac{-\mathtt{CO2A1850}+\mathtt{CO2A}\left(t\right)}{\mathtt{LECO2A}\left(t\right)}\) |
| CO2 concentration in atm ppm |
CO2CA |
CO2A |
GCO2PP |
FCO2 CO2ELY |
|
\(\mathtt{CO2CA}\left(t\right)=\frac{\mathtt{CO2A}\left(t\right)}{\mathtt{GCO2PP}}\) |
| CO2 emissions GtCO2/y |
CO2E |
CO2ELULUC DACCO2 CO2EI |
|
CO2A CO2GDP GHGE |
|
\(\mathtt{CO2E}\left(t\right)=-\mathtt{DACCO2}\left(t\right)+\mathtt{CO2EI}\left(t\right)+\mathtt{CO2ELULUC}\left(t\right)\) |
| CO2 from CH4 GtCO2/y |
CO2FCH4 |
CH4BD |
TCO2PTCH4 |
CO2A |
|
\(\mathtt{CO2FCH4}\left(t\right)=\mathtt{TCO2PTCH4}\cdot\mathtt{CH4BD}\left(t\right)\) |
| CO2 forcing per ppm W/m2/ppm |
CO2FPP |
|
|
FCO2 |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.0032), (1990.0, 0.0041), (2000.0, 0.0046), (2020.0, 0.0051), (2100.0, 0.006)])\) |
| CO2 per GDP (kgCO2/Dollar) |
CO2GDP |
GDP CO2E |
|
|
|
\(\mathtt{CO2GDP}\left(t\right)=\frac{1000\cdot\mathtt{CO2E}\left(t\right)}{\mathtt{GDP}\left(t\right)}\) |
| Direct Air Capture of CO2 GtCO2/y |
DACCO2 |
IPP |
DACCO22100 |
CO2E CAC |
|
\(\mathtt{DACCO2}\left(t\right)=\mathtt{ifelse}\left(\left(t>2000\right),\mathtt{ramp}\left(t,\frac{\mathtt{DACCO22100}}{\mathtt{IPP}\left(t\right)},2000,2000+\mathtt{IPP}\left(t\right)\right),0\right)\) |
| Extra cooling from ice melt ZJ/y |
ECIM |
MRDI |
HRMI AI1980 TPM3I |
EHS |
|
\(\mathtt{ECIM}\left(t\right)=\mathtt{AI1980}\cdot\mathtt{HRMI}\cdot\mathtt{TPM3I}\cdot\mathtt{MRDI}\left(t\right)\) |
| Extra heat in surface ZJ |
EHS |
HDO ECIM EWFF HTS |
|
HTS OW HDO |
0.0 |
\(\frac{\mathrm{d}\mathtt{EHS}\left(t\right)}{\mathrm{d}t}=-\mathtt{ECIM}\left(t\right)-\mathtt{HDO}\left(t\right)-\mathtt{HTS}\left(t\right)+\mathtt{EWFF}\left(t\right)\) |
| Extra Warming from forcing ZJ/y |
EWFF |
TMMF |
GLSU |
EHS |
|
\(\mathtt{EWFF}\left(t\right)=0.032\cdot\mathtt{GLSU}\cdot\mathtt{TMMF}\left(t\right)\) |
| Forcing from CH4 W/m2 |
FCH4 |
CH4CA CH4FPP |
|
MMF |
|
\(\mathtt{FCH4}\left(t\right)=\mathtt{CH4CA}\left(t\right)\cdot\mathtt{CH4FPP}\left(t\right)\) |
| Forcing from CO2 W/m2 |
FCO2 |
CO2CA CO2FPP |
|
MMF |
|
\(\mathtt{FCO2}\left(t\right)=\mathtt{CO2CA}\left(t\right)\cdot\mathtt{CO2FPP}\left(t\right)\) |
| Forcing from N2O W/m2 |
FN2O |
N2OFPP N2OCA |
|
MMF |
|
\(\mathtt{FN2O}\left(t\right)=\mathtt{N2OCA}\left(t\right)\cdot\mathtt{N2OFPP}\left(t\right)\) |
| Forcing from other gases W/m2 |
FOG |
|
|
MMF |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.18), (2000.0, 0.36), (2020.0, 0.39), (2050.0, 0.37), (2100.0, 0.0)])\) |
| GHG emissions GtCO2e/y |
GHGE |
N2OE CH4E CO2E |
TCO2ETN2O TCO2ETCH4 TCO2ETCO2 |
|
|
\(\mathtt{GHGE}\left(t\right)=\mathtt{TCO2ETCH4}\cdot\mathtt{CH4E}\left(t\right)+\mathtt{TCO2ETCO2}\cdot\mathtt{CO2E}\left(t\right)+\mathtt{TCO2ETN2O}\cdot\mathtt{N2OE}\left(t\right)\) |
| Heat to deep ocean ZJ/y |
HDO |
EHS TRHGA |
|
EHS |
|
\(\mathtt{HDO}\left(t\right)=\mathtt{EHS}\left(t\right)\cdot\mathtt{TRHGA}\left(t\right)\) |
| Heat to space ZJ/y |
HTS |
EHS TRHGS |
|
EHS |
|
\(\mathtt{HTS}\left(t\right)=\mathtt{EHS}\left(t\right)\cdot\mathtt{TRHGS}\left(t\right)\) |
| Ice and snow cover Mha |
ISC |
ISCEGA |
|
|
|
\(\mathtt{ISC}\left(t\right)=100\cdot\mathtt{ISCEGA}\left(t\right)\) |
| Ice and snow cover excl G&A Mkm2 |
ISCEGA |
MEL |
|
AL MEL ISC |
12.0 |
\(\frac{\mathrm{d}\mathtt{ISCEGA}\left(t\right)}{\mathrm{d}t}=-\mathtt{MEL}\left(t\right)\) |
| kg CH4 emission per kg crop |
KCH4EKC |
|
ERDCH4KC2022 KCH4KC1980 RDCH4KC |
MMCH4E |
|
\(\mathtt{KCH4EKC}\left(t\right)=\mathtt{KCH4KC1980}\cdot e^{-\mathtt{RDCH4KC}\cdot\left(-2000+t\right)}\cdot\mathtt{ifelse}\left(\left(t>2000\right),e^{-\mathtt{E\mathtt{RDCH4KC}2022}\cdot\left(-2000+t\right)},1\right)\) |
| kg N2O emission per kg fertiliser |
KN2OEKF |
|
RDN2OKF KN2OKF1980 ERDN2OKF2022 |
MMN2OE |
|
\(\mathtt{KN2OEKF}\left(t\right)=\mathtt{KN2OKF1980}\cdot e^{-\mathtt{RDN2OKF}\cdot\left(-1980+t\right)}\cdot\mathtt{ifelse}\left(\left(t>2022\right),e^{-\mathtt{ERDN2OKF2022}\cdot\left(-2022+t\right)},1\right)\) |
| Life of extra CO2 in atm y |
LECO2A |
OWLCO2 |
LECO2A1980 |
CO2AB |
|
\(\mathtt{LECO2A}\left(t\right)=\mathtt{LECO2A1980}\cdot\mathtt{OWLCO2}\left(t\right)\) |
| Melting Mha/y |
MEL |
ISCEGA MRS |
|
ISCEGA |
|
\(\mathtt{MEL}\left(t\right)=\mathtt{ISCEGA}\left(t\right)\cdot\mathtt{MRS}\left(t\right)\) |
| Man-made CH4 emissions GtCH4/y |
MMCH4E |
KCH4EKC CRSU |
|
CH4E |
|
\(\mathtt{MMCH4E}\left(t\right)=\frac{1}{1000}\cdot\mathtt{CRSU}\left(t\right)\cdot\mathtt{KCH4EKC}\left(t\right)\) |
| Man-made Forcing W/m2 |
MMF |
FN2O FCO2 FCH4 FOG |
|
TMMF |
|
\(\mathtt{MMF}\left(t\right)=\mathtt{FCH4}\left(t\right)+\mathtt{FCO2}\left(t\right)+\mathtt{FN2O}\left(t\right)+\mathtt{FOG}\left(t\right)\) |
| Man-made N2O emissions GtN2O/y |
MMN2OE |
KN2OEKF FEUS |
|
N2OE |
|
\(\mathtt{MMN2OE}\left(t\right)=\frac{1}{1000}\cdot\mathtt{FEUS}\left(t\right)\cdot\mathtt{KN2OEKF}\left(t\right)\) |
| Melting rate deep ice 1/y |
MRDI |
MRS |
SVDR |
ECIM |
|
\(\mathtt{MRDI}\left(t\right)=\frac{\mathtt{MRS}\left(t\right)}{\mathtt{SVDR}}\) |
| Melting rate surface 1/y |
MRS |
OW |
MRS1980 WA1980 |
MRDI MEL |
|
\(\mathtt{MRS}\left(t\right)=\frac{\mathtt{MRS1980}\cdot\mathtt{OW}\left(t\right)}{\mathtt{WA1980}}\) |
| N2O in Atmosphere GtN2O |
N2OA |
N2OE N2OBD |
|
N2OBD N2OCA |
1.052 |
\(\frac{\mathrm{d}\mathtt{N2OA}\left(t\right)}{\mathrm{d}t}=-\mathtt{N2OBD}\left(t\right)+\mathtt{N2OE}\left(t\right)\) |
| N2O BreakDown GtN2O/y |
N2OBD |
N2OA |
LN2OA |
N2OA |
|
\(\mathtt{N2OBD}\left(t\right)=\frac{\mathtt{N2OA}\left(t\right)}{\mathtt{LN2OA}}\) |
| N2O concentration in atm ppm |
N2OCA |
N2OA |
GN2OPP |
FN2O |
|
\(\mathtt{N2OCA}\left(t\right)=\frac{\mathtt{N2OA}\left(t\right)}{\mathtt{GN2OPP}}\) |
| N2O emissions GtN2O/y |
N2OE |
NN2OE MMN2OE |
|
N2OA GHGE |
|
\(\mathtt{N2OE}\left(t\right)=\mathtt{MMN2OE}\left(t\right)+\mathtt{NN2OE}\left(t\right)\) |
| N2O forcing per ppm W/m2/ppm |
N2OFPP |
|
|
FN2O |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.43), (2000.0, 0.64), (2010.0, 0.73), (2020.0, 0.8), (2100.0, 1.0)])\) |
| Natural CH4 emissions GtCH4/y |
NCH4E |
|
|
CH4E |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.19), (2020.0, 0.19), (2100.0, 0.19)])\) |
| Natural N2O emissions GtN2O/y |
NN2OE |
|
|
N2OE |
|
\(\mathtt{withlookup}(t, [(1980.0, 0.009), (2020.0, 0.009), (2099.27, 0.0)])\) |
| OBserved WArming deg C |
OW |
EHS |
WFEH EH1980 WA1980 |
PWA OWLCO2 TRHGS MRS WVC REHE TRHGA WELY OWECC OWELC WELE OWTFP |
|
\(\mathtt{OW}\left(t\right)=\mathtt{WA1980}+\mathtt{WFEH}\cdot\left(-\mathtt{EH1980}+\mathtt{EHS}\left(t\right)\right)\) |
| OWeoLoCO2 |
OWLCO2 |
OW |
OBWA2022 SOWLCO2 |
LECO2A |
|
\(\mathtt{OWLCO2}\left(t\right)=\mathtt{ifelse}\left(\left(t>2000\right),1+\mathtt{SOWLCO2}\cdot\left(-1+\frac{\mathtt{OW}\left(t\right)}{\mathtt{OBWA2022}}\right),1\right)\) |
| Perceived WArming deg C |
PWA |
PWA OW |
PD |
PWA AWBGW |
0.4 |
\(\frac{\mathrm{d}\mathtt{PWA}\left(t\right)}{\mathrm{d}t}=\frac{-\mathtt{PWA}\left(t\right)+\mathtt{OW}\left(t\right)}{\mathtt{PD}}\) |
| Risk of extreme heat event (1) |
REHE |
OW |
|
|
|
\(\mathtt{withlookup}(\mathtt{OW}(t), [(0.0, 1.0), (1.2, 4.8), (2.0, 8.6), (2.9, 14.0), (5.2, 40.0)])\) |
| Total man-made forcing W/m2 |
TMMF |
WVF MMF |
|
EWFF |
|
\(\mathtt{TMMF}\left(t\right)=\mathtt{MMF}\left(t\right)+\mathtt{WVF}\left(t\right)\) |
| Transfer rate for heat going to abyss 1/y |
TRHGA |
OW |
TRSA1980 |
HDO |
|
\(\mathtt{TRHGA}\left(t\right)=\frac{1}{290}\cdot\mathtt{TRSA1980}\cdot\left(290+\mathtt{OW}\left(t\right)\right)\) |
| Transfer rate for heat going to space 1/y |
TRHGS |
OW AL |
TRSS1980 |
HTS |
|
\(\mathtt{TRHGS}\left(t\right)=0.011\cdot\mathtt{TRSS1980}\cdot\left(300+\mathtt{OW}\left(t\right)\right)\cdot\mathtt{AL}\left(t\right)\) |
| Water Vapor Concentration g/kg |
WVC |
OW |
WVC1980 WA1980 OWWV |
WVF |
|
\(\mathtt{WVC}\left(t\right)=\mathtt{WVC1980}\cdot\left(1+\mathtt{OWWV}\cdot\left(-1+\frac{\mathtt{OW}\left(t\right)}{\mathtt{WA1980}}\right)\right)\) |
| Water Vapour Feedback W/m2 |
WVF |
WVC |
WVC1980 WVF1980 WVWVF |
TMMF |
|
\(\mathtt{WVF}\left(t\right)=\mathtt{WVF1980}\cdot\left(1+\mathtt{WVWVF}\cdot\left(-1+\frac{\mathtt{WVC}\left(t\right)}{\mathtt{WVC1980}}\right)\right)\) |