The series, one by one
Reference CO₂ series
Atmospheric concentration in ppm. The 1900–1958 segment is a Law Dome ice-core reconstruction based on measured trapped air; from 1959 onward, the series uses instrumental observations — NOAA's global annual mean wherever it exists (1979 onwards), with Mauna Loa filling only the 1959–1978 gap.
The ice core is smoothed by gas diffusion in the firn, so year-to-year variability before 1958 is damped and not comparable with the instrumental part.
You can switch which record the model is scored against. Each one starts the comparison at its own first year, so the baseline moves with it: NOAA global mean from 1979, Mauna Loa from 1959, and the spliced series from 1900. Mauna Loa is one Northern-Hemisphere station and reads above the global mean by a margin that grows over time (+0.75 ppm in 2000, +1.8 ppm in 2024).
Predicted CO₂ — computed here
The only series we calculate. Each year's global emissions are treated as a pulse, multiplied by the Bern impulse-response function, and accumulated on top of the baseline year: C(T) = C(base) + Σ E(t)·IRF(T−t), where IRF(Δt) = a₀ + Σ aᵢ·e^(−Δt/τᵢ). It is recomputed in your browser whenever you change the observed record, baseline, or coefficients.
“Bern” names the impulse-response model family; “Joos 2013” names the published parameter set selected by default. Choose whether the inputs include fossil fuels and flaring alone, cement, and/or land-use change. Components come from Our World in Data, converted using 1 ppm = 2.124 GtC.
Deviations — predicted minus observed
The gap between the two series above, calculated as predicted minus observed. Positive values mean the prediction overshoots reality; negative values mean it underestimates. This is where the finding lives.
Year-over-year change
Annual deltas for both series. Useful because a model can land on the right level for the wrong reason: the deltas show whether it is absorbing too fast or too slow in a given decade.
Emissions and the two conversions
Emissions come from the Global Carbon Budget via Our World in Data. The three choices are: fossil fuels and flaring excluding cement; those sources plus cement; or those sources plus cement and net land-use change. They arrive as mass of CO₂ and are converted twice before entering the model.
MtCO₂ → GtC, factor 12/44. The sinks retain the carbon atom, not the whole molecule, so we keep the carbon fraction of CO₂ by molar mass.
GtC → ppm, factor 2.124. The atmosphere weighs about 5.135·10¹⁸ kg, so one part per million by volume holds roughly 2.124 gigatonnes of carbon. Same value used by the Global Carbon Budget and IPCC AR6.
The coefficients, and what they are not
Joos 2013 (AR5) is the multi-model fit adopted by IPCC AR5: a₀ = 0.2173, then 0.2240/394.4 yr, 0.2824/36.54 yr and 0.2763/4.304 yr.
Forster 2007 (AR4) is the previous IPCC reference, taken from the single Bern2.5CC carbon-cycle-climate model on a 378 ppm background: a₀ = 0.217, then 0.259/172.9 yr, 0.338/18.51 yr and 0.186/1.186 yr. Same functional form, different calibration — a shorter leading timescale and more weight on the fast term. Switching between the two shows how much of the deviation is a parameter choice rather than a measurement.
Both parameter sets have four weights summing to 1.0 — a pulse starts out entirely in the atmosphere.
«Short decay» and «Long decay» are exploratory. Their weights are normalised to 1.0 but come from no paper; they are there to move the parameters by hand, not as published alternatives.
What this model leaves out
The Bern coefficients are calibrated for a single pulse on a given background. Applying them to the whole emissions trajectory from a fixed baseline ignores that sink capacity depends on the state of the system.
This is a model with declared assumptions, not a measurement.