Ocean Acidification

That equation sums the contributions from the simultaneous change (Δ) in each of the 4 input variables, with each Δ being multiplied by a partial derivative (sensitivity) so that each term on the right has same units as the total change term on the left.

If results don’t add up (i.e., the right side does not equal the left), there are three potential causes:

1. the Δ are not accurate enough, e.g., from imprecise measurements,
2. the Δ are too large and the system is nonlinear, or
3. the sensitivities are inaccurate.

In models, the first concern is not an issue because the $\Delta$s are internally consistent. The second concern might also be neglected based on results from a recent model study. Kwiatkowski and Orr (2018) deconvolved modeled seasonal amplitudes of CO₂ system variables, i.e., where the $\Delta$s are typically quite large, but in all cases their results added up precisely. Their success appears to stem from the internal consistency and presumably the accuracy of their calculated sensitivities, an issue that has not received enough attention.

Sometimes sensitivities have been approximated by neglecting some terms to get at a straightforward analytical approximation. These approximations are useful to help understand the system. But their accuracy also matters when performing a Taylor series decomposition because there is a delicate balance between terms in some regions. Even minor imprecisions in the sensitivities of say 10% can lead to things not adding up and thus to the wrong conclusions. So if your deconvolution terms don’t add up, stop and check your sensitivities. Make sure that they are accurate.

Fortunately, it is now easy to avoid approximated sensitivities. Accurate sensitivities are provided as part of the set of new routines that were released along with the publication describing the OA-ICC-funded effort to provide uncertainty propagation add-ons in several public software packages that compute CO₂ system variables (Orr et al., 2018). These packages include CO2SYS-MATLAB, seacarb, and mocsy. Clicking on those links will lead you directly to the archive where each package can be downloaded, on CRAN for seacarb and on GitHub for the other 2 packages.

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James Orr, 23 November 2018. Blog.