A discussion on sea level rise, rate ad acceleration. Venice as a case study

The paper discusses the equations used to represent the sea level rise, and in particular the second-order polynomial, generally preferred because its second-order coefficient is related to acceleration. The long series of the sea level rise in Venice offers a particularly useful case study from 1350 to 2016, because it may be equally represented, at the same level of explained variance, by an exponential or a quadratic best-fit equation. The first-order and the second-order derivatives, respectively, represent the rate and the acceleration of sea level rise. The derivatives obtained from the second-order polynomial representation generate a linear rate and a constant acceleration, while those derived from an exponential preserve the exponential character. The two rates (i.e. from the quadratic and the exponential equations), and the two accelerations are characterized by different equations and different plots, but their average values are the same. The second-order polynomial with constant acceleration is in line with a climate with constant forcing factors; the exponential with a dynamic condition with increasing forcing factors and acceleration. Mathematical formulae and physical consequences are discussed in the framework of different scenarios. Finally, the trend-forecast extrapolation is discussed and applied to the case study of Venice. It is shown that, in the most optimistic assumption of forcing increasing at unchanged rate, the sea level in Venice will rise by 33.8 ± 4 cm over this century. This extrapolation is compared to the most recent projections of the Intergovernmental Panel on Climate Change (IPCC).