Introduction

Fringing reefs, the most common reef type across the tropical ocean, are characterized by a shallow reef platform extending from the shore to the reef crest, where the seafloor slopes downward across the fore reef. Through wave breaking and friction, these reefs dissipate, on average, 97% of the incident sea-swell (‘SS’; wave periods < 25 s) wave energy (Ferrario et al. 2014), and the SS waves that translate onto the reef are constrained by the shallow depths. However, the unique morphology of fringing reefs, coupled with oceanic forcing, can generate longer-period waves (often referred to as ‘infragravity,’ ‘low frequency,’ or ‘long waves’) on the reef flat. As incident waves break on the fore reef and reef crest, the time-varying breakpoint drives corresponding low-frequency (f < 0.04 Hz) fluctuations of water levels over the shallow reef that are unbound to the SS wave groups (Pomeroy et al. 2012). Additional nonlinear interactions between waves on the reef can further cause wave energy to shift into lower frequencies (Lee and Black 1978). For many shallow reefs, low-frequency waves are a primary driver of reef water-level fluctuations, including shoreline runup and wave-driven flooding. Here, we present the first documentation of extreme low-frequency waves on the Ofu reef and show that these waves are an important feature of the Ofu reef-flat water-level variability.

Study area and methods

This study took place on Ofu, part of the Manu’a Islands of American Samoa in the South Pacific (Fig. 1). The island is surrounded by a fringing reef, ranging from 80–180 m in width. Our study sites were located on the southern reef, which is part of the National Park of American Samoa’s Ofu Unit. At our locations the reef flat is shallow (< 0.3 m) but has some small, natural pools 1–2 m deep on the middle and inner reef flat close to shore.

Fig. 1
figure 1

Map of study area, showing a location of American Samoa in southwestern Pacific Ocean; b the Islands of Ofu and Olosega with the locations of our West and East transects (orange boxes) and the SWAN model outputs (yellow box); c) the West transect with inner- and mid-reef sites, as well as the location of the thermal camera system (purple triangle); d the East transect with inner- and mid-reef sites

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In February 2020, we deployed pressure gauges along two transects: (1) a ‘West’ transect near the airport runway and (2) an ‘East’ transect about 800 m to the northeast alongshore from West (Fig. 1). The reef width at these locations is approximately 144 m (West) and 170 m (East). At both sites, the mid- to inner-reef water depth ranged from about 0.4 to 1.7 m. The original deployment included a large suite of hydrodynamic instruments and sensors, most of which were lost because of a prolonged delay in the recovery due to COVID travel restrictions. Only 4 pressure gauges were recovered: 2 from the inner reef flat and 2 from the middle reef flat of each transect. Each gauge—an RBR Virtuoso—collected 4096 pressure measurements at 2 Hz every hour during a 34-min burst. These gauges operated until their batteries ran out, resulting in a 13-month long record ( February 5, 2020, to March 10, 2021), except for the East inner reef flat sensor that only operated for 10 months (until December 1, 2020).

From each hourly burst, we subtracted the atmospheric pressure measured at the National Oceanographic and Atmospheric Administration American Samoa Observatory (https://gml.noaa.gov/obop/smo/) approximately 97 km west of the study sites. We computed reef-flat significant wave height, Hs, and peak wave period, Tp, following standard spectral techniques. We examined the energy density spectra across all four sites (Fig. 2a, b) and identified three prominent frequency ranges: (1) the short-period sea-swell band (‘SS’; Tp < 25 s) band, (2) mid-range infragravity band (‘IG’; 25 < Tp < 100 s), and (3) far infragravity or very-low frequency band (‘LF’; 100 < Tp < 1000 s). The full-burst water levels were also filtered according to these bands, using infinite impulse response anti-aliasing, set-order (Butterworth window = 3), digital filter (see Fig. 2c, d, for example).

Fig. 2
figure 2

Mean water-level spectra, Sxx, from a West transect and b East transect, showing how wave energy is partitioned according to the low-frequency (LF), infragravity (IG), and sea-swell (SS) frequency bands, from the March 19–23 large wave event (bold lines) and calm conditions (thin lines). Two example water-level bursts are shown from the c West and d East inner reef sites, showing the full instantaneous water level (blue), as well as the LF (yellow) and IG + LF (orange) fluctuations. The stars indicate the LF wave crests with the largest trough-to-peak vertical height measured at the sites. Note that c and d y-axes have the same scale but different limits

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Information about offshore wave conditions was obtained from: (1) the Pacific Islands Ocean Observing System Aunu’u buoy (https://www.ndbc.noaa.gov/station_page.php?station=51209) located about 90 km west of Ofu and (2) the Simulating Waves Nearshore (SWAN) Regional Wave Model for Manu’a, American Samoa (Cheung 2019).

An Optris IP640i infrared camera system was installed on the shoreline looking oceanward across the West reef flat at ~ 12 m above mean sea level (Fig. 1c); it collected an image every minute. Survey control was established using temporary ground control points, whose positions were measured using real-time kinematic or post-processed GPS, with corrections from a concurrently operating GPS base station located near the study area. The images were processed according to methods in Truong et al. (2017).

Results and discussion

Our observations captured a large wave event, which produced exceptional IG (> 0.5 m) and LF waves (> 1 m) at the inner reef sites (Fig. 3), including what could be the largest LF wave ever directly measured on a reef flat (Fig. 2c). This event was driven by a southerly “blue sky” swell event that occurred from 12:00 on March 19 to about 7:00 on March 23, 2020 (times in GMT), with large waves originating from a storm in the Southern Ocean near New Zealand. During the event, Hs from the offshore SWAN model reached 2.9 m but may have been as large as ~ 4.0 m (as measured by the Aunu’u wave buoy) with associated Tp ~ 14 s (Fig. 3a). This swell was directly out of the south (mean Dp = 179° ± 13°T), shore-normal to our study area.

Fig. 3
figure 3

20-day time series of wave and water levels showing the March 19-23 large wave event. a Offshore significant wave height (Hs) from the model (black) and buoy (green), with peak wave direction indicated by the gray arrows, and peak wave period (Tp) from the model (purple). Hs for the three frequency bands (sea-swell ‘SS,’ infragravity ‘IG,’ low-frequency ‘LF’) from the b West mid-reef site and c West inner reef site; the arrows indicate the timing of bursts shown in Fig. 2c and d. d Hourly averaged water levels, h, and the maximum (per hourly burst) instantaneous water levels measured at the West inner reef-flat site

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At the West inner reef flat site, the mean Hs_LF during this event was 0.7 m, reaching a maximum of 1.2 m, while the mean Hs_IG was 0.4 m, and the mean Hs_SS was 0.2 m. At the mid-reef flat sites, Hs_IG was roughly equivalent to Hs_SS, but by the inner reef sites, Hs_IG was about double Hs_SS (Fig. 3b, c). This is consistent with the spectra, which show a prominent energy peak in the IG band at the mid-reef sites that shifts to lower frequencies (longer wave periods) by the inner reef, indicating energy transfer toward lower frequencies with distance toward shore (Fig. 2a, b).

Though the spectrally derived Hs_LF reached a maximum of 1.2 m, several individual LF waves exhibited larger trough-to-peak vertical excursions. At 04:21 on March 21, a LF wave with trough-to-peak height of 1.5 m was observed at the West inner reef flat (Fig. 2c)—possibly the largest LF wave ever directly measured on a reef. The smaller IG and SS waves traveling on top of this wave led to an overall maximum vertical excursion of 2.2 m, which was reached approximately 18 s after the leading trough. The corresponding hourly averaged h during the passage of this wave was 1.9 m. Thus, these extreme LF waves nearly doubled the nearshore (within 10–20 m of the shoreline) total water levels, for time periods of several minutes. In addition to this single wave, the LF waves on the inner reef flat constituted a sizable portion of the maximum water levels (estimated as the maximum instantaneous water level per hourly burst) throughout the wave event. At the West inner reef site, Hs_LF represented, on average, 28% (± 5%) of the total water levels (19% ± 6% for East inner reef) during the wave event. In comparison, the Hs_IG were, on average, 15% (± 3%) of the maximum water levels (14% ± 2% for East), and the Hs_SS were only 8% (± 2%) of the maximum water levels (5% ± 1% for East). Using geo-referenced imagery of the West reef flat, we estimate that, during the large wave event, shoreline runup was at least 3 m in vertical extent (Fig. 4).

Fig. 4
figure 4

Imagery looking oceanward over the West reef flat during calm conditions (a, b), and during the large wave event (c, d) with representative snapshots from low and high tides. Dark colors in lower portion of images are the exposed beach, and the light colors are the water. The ruler in a indicates the approximate vertical excursion up the beach face. e Four-day time series showing water levels before and during the large wave event and the timing of the images

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In general, the LF waves at the East sites were somewhat smaller than those at the West. During the large wave event, the mean Hs_LF was 0.5 m, with a maximum of 0.9 m on the East inner reef flat. The largest LF wave observed at the East inner reef occurred at 9:24 on March 20, with a trough-to-peak height of 1.2 m (Fig. 2d). Though the LF waves were slightly smaller at East, these observations show that extreme LF waves (Hs_LF > 0.5 m) were likely occurring across the whole expanse of southern Ofu reef flat in response to this southerly wave event.

The large LF waves observed at the inner Ofu reef were likely amplified by resonance. Previous work noted the presence of multiple resonant modes on the southern Ofu reef (Maticka et al. 2022). Treating the reef like a bounded open basin, the fundamental resonance mode is given by \({T}_{0}=4L/\sqrt{gh}\), where L is the reef width, h is the reef water depth, and g is gravitational acceleration. Using the mean h across the middle and inner reef flat sites gives a mean T0 of 230 s for the West reef and 235 s for the East reef, but, with frictional effects, we would expect the actual resonant period to be slightly longer than these theoretical values. The reef-flat energy peak is, in fact, centered around T = 250 s (Fig. 2a, b), nearly equivalent to T0 estimates, indicating a strong likelihood of resonant behavior at this reef.

The March 19–23, 2020, event was not the only instance of large LF waves on the Ofu reef. Throughout the 13-month record, 17 distinct events of Hs_LF > 0.5 m occurred, the majority (n = 13) of which were during the months of February–June, when the study site is more likely to experience southerly swell generated by austral-winter storms in the Southern Ocean (Fig. 5). In total, the West inner reef flat experienced Hs_LF > 0.5 m 2% of the time. Though this is a small fraction of time, these events likely disproportionately affect shoreline runup and erosion. Indeed, the Ofu airport runway requires regular repairs due to chronic shoreline erosion from “wave attack” (USACE 2023). Even outside the most extreme events, the Ofu reef—particularly the West reef, which is closest to the runway—experiences regular exposure to moderate LF waves. At the West inner reef, Hs_LF > 0.2 m occurred nearly a quarter of the time (24% of the record), compared to Hs_SS > 0.2 m occurring only 6% of the time. At the East reef, the prevalence of moderate LF waves (Hs_LF > 0.2 m) decreases to 13% of the time, but these waves still dominate the reef wave regime, with Hs_SS reaching 0.2 m less than 0.2% of the time at this site.

Fig. 5
figure 5

13-month time series of meteorological and oceanographic conditions. a Aunu’u buoy wave conditions (3-h average): significant wave height, Hs (blue) and peak wave period, Tp (gray); the red overlay on Hs indicates when peak wave direction was oriented toward our south-facing study site (between 135 and 190 °T). Hs for the three frequency bands (sea-swell ‘SS,’ infragravity ‘IG,’ low-frequency ‘LF’) from the b West inner reef site and c East inner reef site; the dashed lines indicate the time window shown in Fig. 3

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In addition to coastal hazards, LF waves are important drivers of mass transport on reefs, which influences coral health through sediment and larvae transport, as well as exposure to nutrients and contaminants (Roberts et al. 1992). Within coral canopies, wave-driven oscillatory flows can increase turbulence (e.g., Huang 2015) and mass transfer (Lowe et al. 2005), which can enhance nutrient update by corals (e.g., Hearn et al. 2001). LF waves are also known to affect groundwater dynamics on sandy beaches (Sous et al. 2016), though this relationship remains unclear for reef environments. Thus, for the nearshore areas of the Ofu reef that are removed from the energetic, wave breaking at the reef crest, LF waves are likely an important source of oscillatory motions and turbulence, potentially providing both bottom-up and top-down benefits to the corals.