3.3 Tidal anomaly correlations (TAC)

Tidal range changes are quantified using tidal anomaly correlations (TACs), the relationships of detrended short-term tidal variability to detrended short-term MSL fluctuations. These are used to determine the sensitivity of individual constituents to a sea-level perturbation, and the result is expressed as a millimeter change in constituent amplitude per meter change in sea-level. The M2, S2, K1, and O1 tidal constituents are first considered separately, and later in combination as a proxy for the change in the highest astronomical tide (δ-HAT). We assume that the interannual variability captured by TACs can be extrapolated to the longer time scales, subject to the qualification that the changes remain "small-amplitude", meaning a 0.5–1 m change in MSL and a change in tidal amplitude of a few tens of cm. Thus, we report TACs in units of mm m�<sup>1</sup> . The detrended time series of A and P can each be compared to detrended MSL, but herein, only the absolute magnitudes of the A for major constituents will be considered, because of their direct role in changing high water levels. The slope of the regression between A and MSL is the definition of the TA, deemed significant if the signal to noise ratio (found from comparing the magnitude of the TAC to the 95% confidence interval (CI) of the robust fitting error) is greater than 2.0.

#### 3.4 Example of a TAC

The M2 TAC results at Honiara in the Solomon Islands exhibits one of the clearest signals in our data inventory. Figure 2 shows the M2 TAC at Honiara on the island of Guadalcanal (Solomon Islands, 9.4167°S and 159.950°E). The M2 tide amplitude is relatively small at this location (�50 mm), but the anomaly correlation is large, +58.9 � 3.7 mm m�<sup>1</sup> (118% of the local M2 amplitude), and very coherent. Since the trend is reasonably linear over such a large range (>100% in terms of tidal amplitude and �0.45 m MSL), our analysis approach is demonstrated to be valid, even in cases where the small amplitude assumption is stretched.
