Deducing acidification rates based on short-term time series

We show that, statistically, the simple linear regression (SLR)-determined rate of temporal change in seawater pH ($β$pH), the so-called acidification rate, can be expressed as a linear combination of a constant (the estimated rate of temporal change in pH) and SLR-determined rates of temporal changes in other variables (deviation largely due to various sampling distributions), despite complications due to different observation durations and temporal sampling distributions. Observations show that five time series data sets worldwide, with observation times from 9 to 23 years, have yielded $β$pH values that vary from 1.61 × 10−3 to −2.5 × 10−3 pH unit yr−1. After correcting for the deviation, these data now all yield an acidification rate similar to what is expected under the air-sea CO2 equilibrium (−1.6 × 10−3 ̃ −1.8 × 10−3 pH unit yr−1). Although long-term time series stations may have evenly distributed datasets, shorter time series may suffer large errors which are correctable by this method.