In their letter, Taboada and Anadón (1) use an integral form of the sea-level formula that we have proposed (2), obtained simply by integrating our equation over time (Eq. 1):Because Eq. 1 is equivalent to our equation, these authors, not surprisingly, obtain the same result as we do, with parameter values differing only insignificantly from ours as we verified using (Eq. 2)

and t₁₂₀ − t₀ = 120 years (Table 1).

However, the authors' discussion of the parameter fit relating to their figures 1 and 2 is simply wrong (1). In figure 1, they show a regression of sea level H vs. the integral over temperature T only—relative to an arbitrary reference level, which is the mean over 1951–1980—when the equation contains the integral over the difference (T − T₀); i.e., the second term in our Eq. (1) above. It is only the latter expression, with T₀ designating preindustrial equilibrium sea level, that is nonarbitrary and makes physical sense.

Regressing the full sea-level H against T in figure 2 is similarly wrong (1). In Eq. 1, the b coefficient indeed expresses a proportionality between temperature and sea level, but in figure 2, this dependence is drowned out by the much larger contribution of the terms in a, which our equation models as a dependence between temperature and the rate of sea-level rise (dH/dt).

Only the sum of contributions as modeled by our equation correlates well with sea level; partial regressions like this do not work. Hence, neither of the graphs presented makes sense.