Table 1.

Prior distributions for components of the state vector

Model input	Distribution	$𝐚$	$𝐛$	$𝝁$	$𝝈$	$\tau$, y
Annual components (emissions, isotopic compositions, and anomalies)
NH ${\mathrm{CH}}_4$, Tg/y	${\mathcal{N}}_B$	300	500	412.5	20	5
SH ${\mathrm{CH}}_4$, Tg/y	${\mathcal{N}}_B$	100	250	137.5	20	5
NH ${\delta }^{13}{\mathrm{CH}}_4$, ‰	$\mathcal{U}$	−60.0	−45.0	—	—	—
SH ${\delta }^{13}{\mathrm{CH}}_4$, ‰	$\mathcal{U}$	−60.0	−45.0	—	—	—
NH MCF, Gg/y	${\mathcal{N}}_B$	−1.0	$\beta$	$\alpha$	$\gamma$	3
SH MCF, Gg/y	$\mathcal{U}$	−1.0	1.0	—	—	—
NH OH, %	${\mathcal{N}}_B$	−20	20	0	10	3
SH OH, %	${\mathcal{N}}_B$	−20	20	0	10	3
Initial conditions (IC)
NH ${\mathrm{CH}}_4$, ppb	$\mathcal{U}$	1,540	1,620	—	—	—
SH ${\mathrm{CH}}_4$, ppb	$\mathcal{U}$	1,480	1,580	—	—	—
NH ${\delta }^{13}{\mathrm{CH}}_4$, ‰	$\mathcal{U}$	−48.2	−46.6	—	—	—
SH ${\delta }^{13}{\mathrm{CH}}_4$, ‰	$\mathcal{U}$	−48.2	−46.6	—	—	—
NH MCF, ppt	$\mathcal{U}$	15	135	—	—	—
SH MCF, ppt	$\mathcal{U}$	15	135	—	—	—

α is the updated annual MCF emissions from Prinn et al. (39), β =max ([1:0 Gg=y, 2α]), and γ=max ([0:2α, 1:5 Gg=y]). ppb, parts per billion; ppt, parts per trillion.