 Solution

For a small fractional change $ϵ=\Delta N_d/N_d$, use $\Delta A\simeq A(1-A)ϵ/3$. With $ϵ=0.1$ the changes areThus the respective albedos become approximately 0.5083 and 0.7070 in the first-order calculation. These are increases of 0.83 and 0.70 percentage points, not 0.83% and 0.70% relative changes. Relative to the initial albedos, the increases are about 1.67% and 1.00%.

The exact finite-change version of the stipulated optical model is $A^{\prime }=sA/(1-A+sA)$ with $s=(1.1{)}^{1/3}$, giving $A_{\mathrm{marine}}^{\prime }=0.50794$ and $A_{\mathrm{continental}}^{\prime }=0.70663$. Its slightly smaller changes are consistent with curvature neglected in the differential approximation. For equal fractional number increases, the cleaner, intermediate-albedo marine cloud is somewhat more susceptible; for equal absolute number increases its susceptibility would be much greater because of the extra $1/N_d$ factor. The two starting albedos are treated as the supplied separate baselines, not as an exact common-proportionality calibration of the approximate optical-depth law.