Wave setup at the Minamitorishima tide gauge

Abstract

A tide gauge situated on the western shore of Minamitorishima, a small atoll in the western Pacific, has measured sea levels significantly impacted by wave setup. Evidence for this rests with (a) strong correlations between sea level anomalies and high swell and (b) sea-level differences with satellite altimetry that display near-linear dependence on offshore swell heights (regression coefficient 30 cm per meter of swell). Setup is primarily induced by swell from the northwest. We develop models of wave setup which lead to corrected sea levels better reflecting the surrounding ocean, and thus more readily useful to studies of regional sea level and practical applications such as altimetry calibration. The wave setup is also evidently affecting measurements of the tide, with suppressed tide amplitudes in winter when swell is generally largest. In February 2020 the tide gauge was relocated to the southern shore of the island, and the wave setup is now markedly reduced.

Appendices

Appendix A: Consistency of altimeter and tide-gauge data processing

The source of the satellite altimeter sea-level data used in this work is the Data Unification and Altimeter Combination System (DUACS) delayed-time (DT-2018) product, described by Taburet et al. (2019). These are gridded sea-surface height anomalies, produced daily on a 0.25$^{\circ }$ global grid and based on multiple satellite missions.

The tide gauge data are in the form of daily means, formed after hourly data were subjected to an anti-aliasing low-pass filter with cutoff about 60 hours. When these data were used in comparison with altimetry, as in Figs. 2 and 7, the daily mean values were subjected to additional low-pass filtering to account for the temporal smoothing used in the DUACS solutions. The DUACS gridding algorithm used temporal correlation scales ranging from 10 to 33 days, depending on latitude (Pujol et al. 2016); at the latitude of Minamitorishima the correlation scale was approximately 29 days, so our tide-gauge filter had approximately that cutoff. However, when used in the wave-setup analysis of Sects. 4–5, the daily means were not further filtered as the goal was to capture relatively high-frequency setup anomalies.

In all accounts, it is necessary to ensure that the tide gauge data be processed in a manner as consistent as possible with the processing of the altimetry. Thus, the tide gauge data were “corrected” for long-period tides (periods between one week and 18.6 y) and the pole tide (dominant periods at 12 and 14 months). In both cases, only the ocean components were removed from the gauge data, whereas the altimetry required both ocean and solid-earth components. The altimeter data had also been adjusted by the ocean model of Carrère et al. (2016), which is a simple isostatic inverted-barometer response to pressure loading at periods longer than 20 days and a dynamic response to both winds and pressures at shorter periods. Since the Nyquist period of Topex and Jason sampling is 20 days, the idea behind the dynamic modeling is to act as a de-aliasing correction. We subsequently used the same model to remove these effects from the tide gauge data. In principle, the tide gauge data should also be adjusted for vertical land motion, but we ignored this because the motion is thought to be small, less than 0.5 mm year$^{-1}$ based on the island GNSS data (see Appendix B).

Appendix B: Vertical land motion at Minamitorishima

Global Navigation Satellite System (GNSS) data have been collected on the island since 1995. In the international GNSS archives there are two stations, MARC and MCIL, from nearly identical locations (24.2901$^{\circ }$N, 153.9787$^{\circ }$E). The older MARC time series is short and relatively noisy. Daily estimates of vertical position as extracted by Blewitt et al. (2018) from both stations are shown in Fig. 12.

Our final time series of altimeter and tide-gauge differences (Fig. 7, lower panel) is a proxy measure for vertical position of the tide gauge (e.g. Cazenave et al. 1999). The altimeter-gauge differences are somewhat erratic during the first few years of the record, which (aside from many other errors) could be explainable by anomalous ground motion. However, the GNSS series at MARC is too noisy to shed light on the question.

The vertical rate as implied by the MCIL data is $-0.39 \pm 0.52$ mm year$^{-1}$. The corresponding rate from the altimeter-gauge differences of Fig. 7 is $0.95 \pm 1.0$ mm year$^{-1}$. The uncertainty takes account of serial correlation in the time series. Within the given uncertainties the GNSS and altimeter-gauge rates are consistent even though of different sign; both overlap with zero motion. Together, they suggest the island motion has been small over the period since 1997.

Appendix C: Altimeter estimates of seasonal M$_2$ changes

It is desirable to know how the tide as observed at Minamitorishima (Fig. 10) compares with the tide in the surrounding deep water. Altimetry can determine this, but some care is required owing to the lack of nearby satellite tracks and the inherent aliasing problems of altimetry.

Figure 13 shows four sets of repeat tracks on the primary Topex/Poseidon-Jason orbit. Estimation of subseasonal M$_2$ coefficients at the one track closest to the island yields rather noisy estimates, so we have used data from all four tracks. Combining data within the magenta rectangular region of the figure, we have estimated the mean tide and its spatial gradients, and used the latter to determine the tide at the island location. (This approach works so long as there is little curvature over the region; according to the tide chart plotted in the figure background, that is here the case.) Mean monthly M$_2$ estimates (as could be done at the tide gauge—Fig. 10) were again rather noisy, so we solved for mean quarterly (i.e., 3-month) tides. Resulting M$_2$ amplitudes are shown in Fig. 13b. There is no seasonal change comparable to the $\sim \!20$% seasonal range seen at the tide gauge, and certainly no large amplitude drop during winter months when the tide gauge gave amplitudes less than 7.5 cm. Only the tide-gauge estimates for the summer months are comparable to the altimetric tide.