Clouds, Not Carbon Dioxide: Where the Uncertainty in Climate Sensitivity Lives — Epoche C2
A common impression is that the range of projected warming reflects disagreement about the warming power of carbon dioxide itself. It does not, and the arithmetic that shows this is short. This review follows the causal chain from the forcing through the feedbacks to the assessed range, and identifies where the residual uncertainty actually sits. Units are strict SI throughout, as in the climate literature: radiative fluxes in W m$^{-2}$, temperatures in K, concentrations in ppm. 1. The forcing is the well-known part Doubling atmospheric CO$_2$ produces an effective radiative forcing $F_{2\times} = 3.93$ W m$^{-2}$ in the current assessment. The underlying radiative transfer — absorption line strengths and shapes integrated through a modelled atmosphere — is checked between independent line-by-line codes and agrees at the level of a few per cent. Two per cent of 3.93 is 0.08 W m$^{-2}$. The response with no feedbacks follows from the Stefan-Boltzmann law. A planet radiating as a blackbody at its effective emission temperature $T_e = 255$ K increases its outgoing radiation at a rate $4\sigma T_e^3$, with $\sigma = 5.67\times10^{-8}$ W m$^{-2}$ K$^{-4}$; that gives $4\times5.67\times10^{-8}\times1.66\times10^{7} = 3.76$ W m$^{-2}$ K$^{-1}$. The real atmosphere does not emit from a single level, and the same quantity computed with radiative kernels — which track how the top-of-atmosphere flux responds to a warming applied layer by layer — is $\lambda_{\mathrm{Planck}} = -3.22$ W m$^{-2}$ K$^{-1}$. Dividing, the no-feedback warming for a doubling is $3.93/3.22 = 1.2$ K. Nothing in this paragraph is contested. 2. Where the spread enters Equilibrium climate sensitivity is $S = F_{2\times}/|\lambda|$, where $\lambda$ is the sum of feedback parameters. The assessed values, with the uncertainties that matter here, are: feedback $\lambda$ (W m$^{-2}$ K$^{-1}$) uncertainty Planck $-3.22$ $\pm0.10$ water vapour and lapse rate $+1.30$ $\pm0.15$ surface albedo $+0.35$ $\pm0.10$ clouds $+0.42$ $\pm0.35$ total $-1.15$ $\pm0.41$ The four terms sum to $-1.15$ W m$^{-2}$ K$^{-1}$, and AR6 assesses the total as $-1.16$ once a small biogeophysical term is included, giving $S = 3.93/1.16 = 3.4$ K. That is the process-understanding estimate on its own, and it sits above the 3.0 K reached by combining it with the historical and palaeoclimate lines. The combined uncertainty is $\sqrt{0.10^2+0.15^2+0.10^2+0.35^2} = 0.41$ W m$^{-2}$ K$^{-1}$, of which the cloud term supplies $0.35^2/0.41^2 = 74\%$ of the variance. Water vapour and lapse rate are grouped because their errors are strongly anticorrelated: a moister atmosphere is also one whose temperature falls more slowly with height, and the two effects partly cancel, which is why the pair is better constrained than either alone. Propagating the uncertainty is instructive because $S$ is a reciprocal. Taking $|\lambda| = 1.16 \mp 0.41$ gives $3.93/0.75 = 5.2$ K and $3.93/1.57 = 2.5$ K. The interval is asymmetric, with a long upper tail, and that asymmetry is not a statistical artefact — it is what happens when a roughly symmetric uncertainty in a denominator approaches zero. Set beside this, the assessed $\pm0.47$ W m$^{-2}$ on the forcing contributes about $0.12\times3.4 = 0.41$ K. The cloud term is worth roughly a kelvin; the carbon dioxide term about four tenths of one, and part of even that is cloud adjustment rather than radiative transfer. 3. Why clouds behave this way The cause is that the cloud feedback is a small difference between large quantities of opposite sign. Satellite radiometry gives the present-day cloud radiative effect as approximately $-45$ W m$^{-2}$ in the shortwave, because clouds reflect sunlight, and $+27$ W m$^{-2}$ in the longwave, because they emit to space from a colder level than the surface would. The net is about $-18$ W m$^{-2}$: a residual two and a half times smaller than its shortwave component. Warming perturbs three properties at once, and they do not act together. Amount. Marine low clouds — the stratocumulus decks over the eastern subtropical oceans — appear to thin and retreat as the boundary layer warms and deepens. Less reflection means more absorbed sunlight: positive. Altitude. High tropical anvils rise as the troposphere deepens, and observations support the fixed-anvil-temperature idea that they stay near the same emission temperature. Their longwave emission to space therefore does not increase with surface warming: positive. Optical depth. In the mid and high latitudes, warming converts cloud ice to liquid, producing more and smaller droplets and a brighter cloud for the same water content: negative. The assessed net, $+0.42$ W m$^{-2}$ K$^{-1}$, corresponds over 3 K of warming to $0.42\times3.0 = 1.26$ W m$^{-2}$ — a change of $1.26/45 = 2.8\%$ in the shortwave cloud effect. A quantity of that relative size cannot be obtained by subtracting two terms each carrying a 10% error. 4. Why resolution alone does not fix it The second cause is structural. A typical global climate model integrates on a horizontal grid of about 100 km. Stratocumulus is maintained by turbulent entrainment at cloud top on scales of tens to hundreds of metres — three orders of magnitude smaller, comparing $10^5$ m with $10^2$ m. Everything that sets the sign of the low-cloud feedback therefore happens inside one grid box and must be represented by a parameterisation: a formula relating grid-mean quantities to the unresolved process, with coefficients chosen rather than derived. The cost of removing the problem by brute force can be stated exactly. Refining from 100 km to 1 km multiplies the number of columns by $10^4$ and, through the stability condition on the time step, the number of steps by $10^2$: a factor of $10^6$. Refining to 100 m gives $10^6\times10^3 = 10^9$. Global storm-resolving models now run at a few kilometres, and they genuinely resolve deep convection. They do not resolve boundary-layer turbulence, which is still an order of