Hydrodynamic and atmospheric drivers create distinct thermal environments within a coral reef atoll

Within coral reefs, different thermal environments can be found at locations separated by less than 100 s of meters and can generate fine-scale patterns of thermal stress and subsequent bleaching. In this study, we use an 11-month record of in situ temperature measurements, coupled with oceanographic and atmospheric data to examine the role of surface and advective heat fluxes in driving spatial patterns of temperature variability across several reef zones (i.e., fore-reef, reef flat, channel and lagoon) within an individual coral reef atoll. We show that advection of heat (driven by a combination of wave and tidal flows) was dominant across all sites and surface heating was more important across shallow areas or areas of low net exchange (i.e., reef flat and lagoon zones). Tidal flows were important in driving short term variability in the transport of heat across the atoll, but their contribution to the net transport of heat (cooling vs heating) was less significant over the longer timescales (days to weeks) that are typically used to assess thermal stress experienced by coral reef communities (e.g., Degree Heating Weeks). Conversely, although the wave-driven advection of heat contributed minimally to reef temperature changes over short timescales, the net transport of heat over daily to weekly timescales had a significant influence on persistent temperature anomalies. By parameterising the mechanisms driving temperature variability across the reef flat and lagoon zones, we demonstrate how satellite measurements of sea surface temperatures can be corrected to provide robust temperature estimates at the reef scale.


Introduction
Marine heatwaves pose a growing threat to coral reefs worldwide, causing mass coral bleaching and coral mortality due to extended periods of elevated ocean temperatures. Over large spatial scales (hundreds of kilometres), regional ocean heating events (e.g., marine heatwaves) have triggered widespread mass bleaching events that are growing in frequency (Hughes et al. 2018;Skirving et al. 2019). However, temperature variability also occurs over much smaller spatial scales (tens to hundreds of meters; Gorospe and Karl 2011;Pineda et al. 2013;Zhang et al. 2013), often resulting in highly-spatially variable patterns of bleaching within reefs (Penin et al. 2007;Grimsditch et al. 2010;Green et al. 2019b). As a result, the accurate quantification of the mechanisms responsible for reef-scale temperature variability is critical to understand and quantify, not only to help target management efforts and conserve reefs (Hoegh-Guldberg et al. 2007;Hughes et al. 2017), but also to help understand how systems will acclimate and adapt under climate change (e.g., Lowe et al. 2016).
Temperature variability within reefs is broadly driven by a combination of local atmospheric conditions and oceanic processes. Atmospheric conditions, such as solar radiation, air temperature, cloud cover and wind speed, alter air-sea heat fluxes that warm or cool reef waters (McCabe et al. 2010;McGowan et al. 2010;MacKellar et al. 2013;Zhang et al. 2013). Advection of heat by oceanic flows created by tides (McCabe et al. 2010;Lowe et al. 2016), wind stresses (Nadaoka et al. 2001), internal waves (Leichter et al. 2005;Storlazzi et al. 2020;Wyatt et al. 2020) and surface waves (Davis et al. 2011;Falter et al. 2014), interact with a reef bathymetry to determine water residence times, which then regulate reef heat budgets (MacKellar et al. 2013;Zhang et al. 2013;Lowe and Falter 2015). As a result, the combination of surface and advective heat fluxes can lead to extreme temperature variability (and in turn coral bleaching) across reef scales (Leichter et al. 2005;McCabe et al. 2010;Davis et al. 2011).
To investigate the processes that govern temperature variability at the reef-scale, previous studies have often focused on specific reef zones (e.g., lagoon, reef flat; Ouillon et al. 2005;Andréfouët et al. 2006;Dumas et al. 2012;Reid et al. 2020) or the role of specific hydrodynamic drivers (e.g., internal waves; Leichter et al. 2005;Reid et al. 2019;Storlazzi et al. 2020;Davis et al. 2020 or tides;McCabe et al. 2010;Lowe et al. 2016). Yet, few studies have investigated the role of different local hydrodynamic processes in driving temperature variability in reef zones spanning the same reef system (Leichter et al. 2006;Rogers et al. 2017;Herdman et al. 2015). Developing an improved understanding of the drivers of reef-scale temperature variability is particularly useful given that satellite sea surface temperature (SST) data and regional ocean model forecasts cannot resolve the finescale spatial and temporal variability of temperature (scales of order of hundreds of meters and minutes to hours) (Sheppard 2009;Falter et al. 2014;Van Wynsberge et al. 2017 and only measure the surface skin temperature of the ocean (top ~ 0.1 mm), providing limited information of the temperature distribution through depth.
In this study, we investigate the relative importance of the dominant drivers of temperature variability within four key reef zones of a coral reef atoll (reef flat, fore-reef, channel and lagoon) located off northwestern Australia over an approximately one-year period. We first describe the oceanic and atmospheric conditions as well as the temperature variability recorded during the experiment. To gain a better understanding of the role of surface (air-sea) heat exchange versus advection of heat to temperature variability, we then apply a simple heat budget across all reef zones. Finally, we show how the simple parameterisation of these processes can be used to correct SST measurements to better reproduce in situ reef temperature measurements. We discuss the significance of our findings in the context of coral reefs worldwide, particularly how our study advances our understanding of fine-scale temperature variability within individual reef systems.

Study site
Mermaid Reef atoll is part of the Rowley Shoals, located on Australia's North West Shelf (NWS). It is composed of four main reef zones: a steeply sloping fore-reef (rising from about 500 m depth), a shallow reef flat enclosing a lagoon (50 km 2 , 20 m-deep), and a single channel (8 m-deep, 250 m-wide) on the northeast side that serves as the only continuous opening to the surrounding ocean. Since the mid-1990s, Mermaid Reef and the Rowley Shoals more broadly have maintained a high and stable coral cover and have not experienced any major coral bleaching events, contrary to most coral reefs in Western Australia and around the world (Hughes et al. 2018;Gilmour et al. 2019). However, minor bleaching was documented in 2005, 2016 and 2020 (Rosser and Gilmour 2007;Gilmour et al. 2019Gilmour et al. , 2022. To date, the fore-reef zone is characterized by the highest coral cover percentages (> 80%), especially on the eastern side of the atoll (Gilmour et al. 2022;Grimaldi et al. 2022a) with lower coral cover observed on the reef flat and in the lagoon, which largely consists of rubble apart for the occasional patch reefs found all across the lagoon.

Field experiment
An array of velocity, temperature and pressure sensors were deployed over ~ 11 months (26 Nov 2017-14 Oct 2018, to characterize the thermodynamics and hydrodynamics around the atoll ( Fig. 1a and Table 1). Hydrodynamic measurements of waves (significant wave height, H s , and mean period, T m01 ), currents and pressure were collected at S1 (fore-reef site; 13.4 m depth) using a Nortek 1 MHz AWAC. Additional current acoustic profilers were deployed at S2 (RDI Acoustic Doppler Current Profiler), S3 and S4 (Nortek Aquadopp Profilers) and pressure sensors (RBR Solo 3 D) at locations on the reef flat (S4, S6, S8), and inside the lagoon (S2) and the channel (S3) (Fig. 1a, Table 1). Fourteen temperature loggers (HOBO U22 Pro-v2, ± 0.2 °C accuracy), sampling at 10-min intervals, were deployed ~ 0.1 m above the seabed within a range of reef zones (i.e., reef flat, lagoon, channel and fore-reef) in depths varying from 1 to 14 m (mean sea level, MSL). In addition, a thermistor chain (vertical array of temperature loggers attached to a sub-surface float near the surface) was deployed in the northern centre of the lagoon (S5), with 7 loggers deployed every 2 m from the bottom (14 m depth, MSL) to the surface. The loggers were inter-compared for consistency in a room-temperature water bath for 5-day periods both before and after the deployments, with verification that all read within 0.1 °C of each other over a temperature range varying between 17 and 28 °C. Each site was assigned to a reef zone (i.e., reef flat, lagoon, channel or fore-reef) based on its location on the atoll and depth range (Table 1), and results are reported throughout as the mean and standard deviation between the sites composing each reef zone.  Atmospheric data were obtained from the fifth generation atmospheric reanalysis of the global climate from the European Center for Medium-Range Weather Forecasts (ECMWF) ERA5 dataset (Hersbach et al. 2020) available from January 1979 to present. Latent heat flux (Q L ), sensible heat flux (Q S ), longwave radiation flux (Q LW ), shortwave radiation flux (Q SW ), and the eastward and northward components of the wind velocity at 10 m above the surface (U 10 and V 10 , respectively) were extracted at the available 0.25° (~ 27 km) resolution over Mermaid Reef (119.45 to 119.75° E; − 17.25 to − 16.85° N). The incoming shortwave radiation was corrected for an additional albedo (10%), to account for reflectance of the seabed that is typical for shallow reef systems (Maritorena et al. 1994).
Finally, daily SST measurements were extracted from the Group for High Resolution Sea Surface Temperature (GHRSST) Level 4 sea surface temperature analysis, on a global 0.01° grid produced as a near-real-time dataset (one day latency) at the National Aeronautics and Space Admin- To compare the in situ and SST temperature, the daily-averaged night-time temperature (T reef ) was computed for each logger. Night-time recordings were defined as measurements from 2000 to 0400 hrs, local time, as this time range is the less affected by solar heating in the remote atolls of the North West Shelf.

Estimates of contributions to reef heat balances
The net air-sea heat flux and advection of heat play an important role in regulating rates of ocean temperature changes, especially in shallow water. For the case where a flow is aligned into a dominant stream-wise (x) direction, assuming no significant variation in temperature and velocity with depth, no vertical advective heat flux from groundwater movement and direct thermal conduction, and that horizontal diffusion is comparatively negligible relative to advection, the depth-averaged temperature (T) is governed by the 1D heat budget equation (e.g., Herdman et al. 2015, Davis et al. 2011 where ρ is the seawater density, c p is the specific heat of water, h is the water depth and q the discharge (i.e., depthaveraged stream-wise velocity u × water depth h). The term x on the left-hand side (LHS) of Eq. (1) represents the rate of temperature change (in °C h −1 ) and the first and second terms on the right-hand side (RHS) represent the surface (air-sea) heat flux and advective heat flux, respectively. The advection of heat by processes acting at subtidal scales (time scales longer than 33 h) was investigated by applying a low-pass filter using the PL64 filter with a half amplitude period of 33 h (Beardsley et al. 1983). The advection of heat by processes acting at tidal scales (time scales shorter than 33 h) was then obtained by subtracting the subtidal time series from the original advection time series. Finally, Q N is the net heat flux across the air-sea interface, calculated as the sum of the shortwave radiation flux (Q SW ), net longwave radiation flux (Q LW ), sensible heat flux (Q S ), and latent heat flux (Q L ): where Q N > 0 denotes a net heat flux into the water column. While no local in situ measurements of the net air-sea heat fluxes were available at Mermaid Reef to assess the performance of the ERA5 dataset, such measurements were available at Tallon Reef, also located in northwestern Australia, for 12 days (Lowe et al. 2016) and showed reasonable agreement with the ECMWF ERA5 dataset (Root Mean Square Deviation RMSD = 165 W m −2 , approx. ~ 18% of the average diurnal range, mainly over-estimating the night-time cooling; see Supplementary Material, Fig. S1).

Oceanic and atmospheric forcing conditions
During the study period (26 Nov 2017-14 Oct 2018), Mermaid Reef was exposed to large (meso-) tides, with a mean tidal range of 2.4 m (at S1; mean neap = 0.9 m; mean spring = 3.9 m, Fig. 2b) and a wide range of significant wave heights (H s = 0.3-3.2 m; mean = 0.9 m; Fig. 2c). The incident waves measured on the fore-reef had a wave period (T m01 ) (at S1, Fig. 2c) ranging between 2 and 14 s (averaging ~ 11 s) and a wave direction varying from 55 to 350° N, averaging ∼270°N (i.e., coming from the west, not shown). The wind speed averaged 5.3 m s −1 (Fig. 2d), with a direction predominantly from the southwest (mean direction = 200°N, not shown). The resulting hydrodynamic circulation at Mermaid Reef was investigated in detail in Grimaldi et al. 2022b, but a short summary is presented here. The residual water circulation within the atoll (arrows in Fig. 2a) was mainly driven by tides, with the occasional influence by wave forcing, and displayed a mean eastward flow from the fore-reef (S1), across the western reef flat (S4) and through the lagoon (S2) and channel (S3). Most of the current variance was dominated by flows occurring at tidal frequencies (red arrows and ellipse in Fig. 2a), with the subtidal variability represented by the small area between the red and black ellipses. Overall, the streamwise depth-averaged velocities were largest in the channel, reaching up to 2 m/s (not shown) and slowest in the lagoon, reaching up to 0.2 m/s (not shown, Grimaldi et al. 2022b). Comparison of the seabed and surface current velocities from the current profilers revealed little variations through the water column during the experiment, with mean standard deviations of 0.1 m/s (~ 10% of maximum velocity range), 0.17 m/s (~ 4%), 0.08 m/s (~ 2%), 0.14 m/s (~ 22%) m/s at S1 (fore-reef), S2 (lagoon), S3 (channel) and S4 (reefflat), respectively.
The air-sea heat flux variability was predominantly driven by variations in the positive solar energy input by shortwave radiation (Q SW ) and latent heat loss due to evaporation (Q L ). Over seasonal timescales, net heating (positive Q N ) occurred in the extended austral summer-autumn period (December 2017 through April 2018) and net cooling (negative Q N ) in the austral autumn-winter period (May through August 2018, Fig. 2e). Net longwave (Q LW ), sensible (Q S ), and latent (Q L ) heat fluxes averaged − 85, − 7, and -157 W m −2 over the study period, respectively, with the latent heat flux acting as the dominant heat loss term (Fig. 2e). Diurnal variations in Q N typically averaged from +632 Wm −2 (max. +842 Wm −2 ) during the day to 198 Wm −2 (min. of +467 Wm −2 ) at night. Clear skies likely persisted throughout most of the experiment providing consistent diurnal variations in net surface heat fluxes, apart from a couple of "stormy" conditions that led to negative net surface heat fluxes throughout the whole day (e.g., January 30, 2018; Fig. 2e).

Water temperature variability
Water temperature at Mermaid Reef varied both in space (i.e., among and within reef zones) and in time (i.e., over short (hours to days) and longer (weekly to seasonal) time scales; Fig. 1b, c, d and e). Over the study period, temperature variability was relatively consistent among . a Depthaveraged current velocities, with arrows representing the time-averaged current vectors and ellipses indicating the standard deviation of the current variability from a principal component analysis over a 11-month period. The total current velocities are plotted in black and the tidal current in red. Note the difference in scale of current velocities between the solid lines for the reef flat, fore-reef and lagoon sites (S1, S2 and S4) and the dotted lines for the channel site (S3) given the much larger velocities in the channel. b Water levels (ƞ) measured at S1; c wave height (H s , black line) and mean period (T m01 , grey line) measured at S1; both d wind velocity 10 m above the surface and e daily net (Q N ), sensible (Q S ), latent (Q L ), longwave (Q LW ) and shortwave (Q SW ) radiation fluxes were extracted from ERA5 and averaged over Mermaid Reef individual sites within a reef zone (reef flat: correlation coefficient r = 0.96 and RMSD = 0.07 °C; lagoon: r = 0.99 and RMSD = 0.06 °C, fore-reef: r = 0.67 and RMSD = 0.2 °C; channel: only one site), and hence results are reported as averages within each zone.
Over seasonal timescales, temperatures were primarily influenced by variations in net air-sea heat fluxes (Q N in Fig. 2e; R ~ 0.43 to 0.55; p < 0.01), resulting in warmer water temperatures from November through April (monthly mean of 30.6 ± 0.4 °C in April; monthly mean ± standard deviation), followed by temperatures decreasing to a minimum in August (monthly mean of 24.6 ± 0.6 °C). While there was a broad consistency across all reef zones, fore-reef temperatures were consistently colder throughout the year, while lagoon temperatures were consistently warmer (Fig. 1e and  c), with no clear seasonal trend in the thermal stratification (RMSD between bottom and surface temperatures from moorings in the north lagoon site S5 = 0.27 °C, r = 0.98, p < 0.01).
Over shorter (several days to weeks) timescales, occasional large swell generated by tropical cyclones and winter storms (Fig. 2b) coincided with sharp decreases in temperature across the reef. For example, Tropical Cyclone Marcus (Category 5, March 2018), which developed ~ 250 km away and increased significant wave heights at the reef to ~ 2 m (Fig. S2a), coincided with a decrease in mean temperatures (5-day mean temperature before/after event: fore-reef: 30.5-29.3 °C; lagoon: 30.7-29.8 °C; channel: 30.3-29.7 °C and reef flat: 30.9-29.5 °C) and dampening of hourly temperature variability at all reef zones (Fig. S2b).
Over even shorter (diurnal and higher frequencies) timescales, the shallow reef flat zone experienced the largest mean daily temperature ranges (2.4 °C) compared to the deeper lagoon sites (0.3 °C) and deeper fore-reef site (1.9 °C). The diurnal temperature ranges followed a power function relationship with depth (r = 0.67; p < 0.001; y = 2.59 x −0.49 ; Fig. S3), indicating that deeper reef zones experience less diurnal variability. This was also apparent in the lagoon along the thermistor chain, where the diurnal variability was most pronounced in the surface compared to the bottom measurements (not shown). An exception to that relationship was the deeper fore-reef site that exhibited large mean and maximum daily temperature ranges at 14 m depth (1.9 and 5.3 °C, respectively) and experienced rapid instantaneous temperature fluctuations of up to 5.6 °C in an hour (Fig. S4).

Relative importance of reef heat budget drivers
To examine the physical processes shaping such temperature variability across the reef, a simple heat budget analysis was performed. Two main mechanisms for temperature variability were considered here: surface atmospheric heating/cooling and advection of heat (Eq. 1).
First, the thermal balance of the western reef flat zone was examined (Fig. S5a) by considering the rate of temperature changes at S9, with T and q, the depth-averaged temperature and discharge measurement at S9 and the spatial temperature gradient based on the temperature difference between S8 and S4. As velocity measurements were not available at S9, q was assumed the same as at nearby location in similar regimes (i.e., S4 located 700 m away) where depth-averaged velocity measurements were collected. Comparison of the estimates of the heat budget forcing terms (RHS of Eq. 1) to the measured time rate of change of depth-averaged temperature at S9 (LHS of Eq. 1) allows the evaluation of the accuracy of our simple 1D heat budget model. The two terms showed a moderately strong relationship (r = 0.53, p-value < 0.0001, RMSD = 0.22 °C/h which represent ~ 8% of the maximum range in temperature time rate of change, Fig. S5b). Note that while the heat budget does not close exactly, the correlations provide confidence that the primary dynamics of the thermal balance can be captured and that surface and advective heat fluxes are the two main drivers of temperature change on the reef flat.
In addition, the advection of heat calculated from the in situ measurements showed a moderately strong relationship with the residual between the temperature rate of change and the air sea heat flux terms (r = 0.46, p-value < 0.0001, RMSD = 0.26 °C/h, which represent ~ 8% of the maximum range in advection of heat; Fig. S5c). As a result and because insufficient temperature measurements were collected to estimate the heat fluxes in other reef zones, the relative contribution of local atmospheric heating/cooling and heat advection was investigated by estimating the advection of heat q T x as the residual between the temperature rate of change T t and the surface heat flux Q N c p h terms (Fig. 3). Applying the one-dimensional model to the other, deeper, reef zones relies on the assumption that no significant variation in temperature and velocity occurs with depth. Even though no significant variations in current velocity profiles were observed during the field experiment at sites where current measurements were collected (S1, S2, S3 and S4; see "Oceanic and atmospheric forcing conditions" section), both temperature and flow divergence might occur depending on the atmospheric and oceanographic conditions. A more complete record of temperatures, oceanographic and atmospheric conditions could provide a means to quantify those fluxes better; however, this was not possible in the present study. Figure 3 summarizes the estimated values of the surface heat flux and advective heat flux across the four reef zones. Across the fore-reef and channel zones, the results indicate that the surface (air-sea) heat fluxes played a minor role in driving the instantaneous temperature changes (0.02 ± 0.02 °C/h and 0.04 ± 0.04 °C/h, mean ± standard deviation, respectively) compared to the magnitude of the advective fluxes (0.2 ± 0.35 °C/h and 0.13° ± 0.2 °C/h, respectively). Across the lagoon and reef flat zones, both the surface (air-sea) heat (0.02 ± 0.03 °C/h and 0.1° ± 0.12 °C/h, respectively) and advective fluxes (0.03 ± 0.05 °C/h and 0.16° ± 0.23 °C/h, respectively) contributed similarly to the temperature time rate of change.

Role of surface heat fluxes
Temperature variability induced by surface heat fluxes resulted from a combination of variable net air-sea heat fluxes (Q N ) and tidal water variations (h). Across all sites, variability in strength of this atmospheric heating/cooling occurred most strongly at diurnal timescales, i.e., was mostly positive on average during the day (indicating net heating) and negative at night (indicating net cooling), with this variability small at the deeper reef zones (channel and fore-reef) compared to the shallower reef flat and the lagoon zones (Fig. 3b, e, h and k). Although the maximum and minimum solar heating occurred around mid-day and midnight each day, the time of offshore low and high tide showed less consistency because of the 12.4 h period of the dominant M 2 tidal constituent. As a result of the phasing between maximum/minimum solar heating and tidal water levels, greater warming (cooling) can be expected when the maximum (minimum) solar heating and low water levels are in phase over shallow areas, such as the reef flat. The phasing of those two parameters was investigated by quantifying the time lag (ΔHr, in hours) between daily maximum surface heating and low tide, with a small ΔHr indicating that the two parameters are approximately in phase (Fig. 4b).
Diurnal temperature fluctuations (Fig. 4a) at the reef flat sites were slightly enhanced (by ~ 0.8 °C on average) when low tide and solar peak were in phase (small ΔHr; Fig. 4c) and both processes were correlated with daily temperature range (r = 0.55, p < 0.01). The relative importance of these tidal and solar heating interactions was not evident in the lagoon (Fig. 4a), as the tidal range is only a small fraction

Tidal and subtidal advection of heat
Advection of heat played a major role in driving temperature changes across all reef zones, rates of temperature change reaching values up to ±2 °C/h on the fore-reef. At Mermaid Reef, hydrodynamic processes such as waves and tides play a variable role in driving the circulation and their relative contribution was investigated by looking at the subtidal (including mean) and tidal timescales of the heat budget terms. Heat advection from subtidal processes showed strong correlations with offshore significant wave height at all sites (r = 0.5 to 0.77, p < 0.001; Fig. 5b, d, f and h), indicating an important role of wave-driven flows in driving low-frequency temperature variability (i.e., at time scales greater than diurnal). This subtidal (wave-driven) advection of heat was largest on the western reef flat, reaching up to − 0.2 °C/h for a 3 m significant wave height (H s ) that persisted for about 10 days (e.g., 25 Jan-04 Feb 2018) and resulted in an overall cumulative change of − 10.4 °C/week during the high wave energy event. Across the other reef zones (channel, fore-reef and lagoon), the wave-driven advection of heat contributed minimally to shorter term (shorter than diurnal) temperature variability (up to ±0.02 °C/h) but contributed up to − 2 °C/ week during that same wave event at the channel site. Conversely, the advection of heat through flows at tidal frequencies resulted in much larger temperature changes over daily timescales (Fig. 5a, c, e and g), with daily averagedheating and cooling rates of ± 2.3, 0.4, 1.6 and 1.9 °C/day on the fore-reef, lagoon, channel and reef-flat, respectively (Fig. 6a). However, due to the oscillatory nature of tidal flows, their contribution to the net transport of heat (net heating + net cooling) over longer (daily to weekly) timescales were negligible (Fig. 6b). Overall, the contribution of advection from wave-forced flows and surface heating on instantaneous temperature changes was much lower than from tidally driven flows across all reef zones, but its effect Fig. 4 a Temperature at reef flat and lagoon sites (black and grey line, respectively) (28/11/2017-23/12/2017); b Hour of day when low tide (from water level measured at S1) and peak solar irradiance (estimated from the maximum daily Q N ) occurred. Grey shading represents night-time (1800-0600 h the following day, local time, UTC + 8); c Boxplot of the mean daily temperature range (ΔT d ) on the reef flat as a function of the lag between peak solar and low tide in hours (ΔHr) from 26/11/2017 to 1/10/2018. On each boxplot, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the '+' marker symbol on cumulative heating and cooling was more important over larger (daily to weekly) timescale.

Empirical prediction of differences between reef and offshore water temperatures
As shown in the previous section, advection from waveforced flows and surface heating terms played a key role in modulating temperature variability over daily timescales. Due to such mechanisms, temperatures across the reef zones presented large deviations (up to 2.6 °C lower) from offshore remotely sensed sea surface temperatures offshore (Fig. 7a).
Here, we investigate whether those two mechanisms drove the differences in temperatures between the reef and offshore waters (ΔT SST ) during the duration of the field experiment (26 Nov 2017-14 Oct 2018) across the reef flat and lagoon sites, according to: where <> denotes daily-averaged quantities, overbar denotes low pass filtered quantities (here the wave-driven advective flux), a and b the best-fit slope and intercept computed from a linear regression of ΔT SST and the daily surface heat flux and wave driven advection term ( Eq. 1) at each reef zone ( Fig. 7a and b). ΔT SST and x were well correlated within both reef zones (r = 0.79 and 0.44 and p < 0.001 for the reef flat and lagoon zones, respectively). Based on these relationships we can then model daily Advection of heat across the reef zones. a, c, e and g Tidedriven advection of heat (in °C/h) and b, d, f and h wave-driven advection of heat (in °C/h) against the significant wave height off-shore (at S1 in m) at the a, b fore-reef, c, d lagoon, e, f channel and g, h reef flat (28/11/2017-23/12/2017) average temperatures at each reef zone (T modelled ) by empirically correcting the SST offshore data with ΔT SST calculated from Eq. (3), according to Eq. (4): The comparison between daily corrected SST offshore (T modelled ) based on the net surface heat flux and wave driven advection contribution showed improved agreement of T reef observations (from RMSD = 0.73 to 0.35 °C and from 0.51 to 0.32 °C for the reef flat and lagoon zones, respectively; Fig. 7c and d), confirming that such mechanisms are drivers of temperature differences between the reef and offshore waters. Despite the simplicity of the predictive model given by Eq. (3 and 4), accounting for the local atmospheric heat fluxes and wave-driven advection of heat substantially improve predictions of in situ temperatures from knowledge of offshore sea temperatures surrounding reefs.
Similar corrections have been applied on wave-driven reefs, where temperature variability was driven by offshore waves (Falter et al. 2014). While this approach can only be used at a site after collecting in situ measurements to effectively calibrate the semi-empirical model, this method can be used to correct hindcast and predictions of offshore SST to estimate reef temperatures. The range in temperature variability found within coral reefs highlights the value of in situ temperature measurements on coral reefs, as SSTs (4) T modelled = SST offshore + ΔT SST measurements currently do not widely resolve their finescale temporal and spatial variability (order of hundreds of meters and minutes to hours). Given that obtaining in situ temperature measurements from many reefs can be logistically difficult, downscaling prediction methods for reef temperature offer a means to develop simple corrections based on SST measurements.

Discussion and conclusions
By examining the role of surface and advective heat fluxes in driving spatial patterns of temperature variability across several reef zones (i.e., fore-reef, reef flat, channel and lagoon) of an individual coral reef atoll, we showed that advection of heat (driven by a combination of wave and tidal flows) was dominant across all sites and surface heating was more important across shallow areas or areas of low net exchange (i.e., reef flat and lagoon zones).
Net fluxes of heat across the air-sea interface varied with local meteorology (e.g., light, cloud cover, relative humidity, wind speed, air temperature, albedo, etc.), and the resulting effect on temperature primarily increased in shallower reef areas. It was also modulated by the interaction between tidal water level variations (tidal range = 1-4 m) and solar radiation, which has previously been observed on other reefs with large tidal ranges (McCabe et al. 2010;Lowe et al. 2016) and Daily-averaged net contribution from surface heating, tidal and wave driven advection. Note that the daily-averaged net tidal advection term is too small to be displayed on (b) resulted in a strong diurnal temperature signal (Davis et al. 2011;Herdman et al. 2015;Reid et al. 2019).
The advection of heat through tidal flows drove large instantaneous temperature variations (over minutes to hours), but their contribution to net transport of heat (cooling vs. heating) was less significant over longer timescales (days to weeks). Several studies have suggested that temperature fluctuations over short (hourly or shorter) timescales can expose corals to stressful temperatures for periods short enough to avoid coral mortality, but long enough to drive adaptation (McClanahan et al. 2007;Oliver and Palumbi 2011;Palumbi et al. 2014;Safaie et al. 2018;DeCarlo et al. 2019;Schoepf et al. 2022). As a result, coral populations from thermally variable environments (e.g., fore-reef and channel) are thought to be more resistant to heat stress and bleaching than corals in areas where temperatures are more stable (e.g. lagoon; Barshis et al. 2013;Rivest et al. 2017;Thomas et al. 2018;Safaie et al. 2018). The importance of tides has become increasingly documented by in situ observations of large fluctuations of temperature, nutrient concentrations, and carbonate chemistry (McCabe et al. 2010;Lowe et al. 2016;Green et al. 2019a, b).
The rapid temperature fluctuations on the fore-reef likely indicate internal bores generated by tides that produce pulses of cool water on the reef slope at roughly semi-diurnal frequencies (Leichter et al. 1996). Internal waves have been extensively observed both across Australia's NWS and its coral reef atolls (Scott Reef, located ~ 400 km from the Rowley Shoals; Rayson et al. 2018;Green et al. 2019a;Gong et al. 2021). In addition, near-surface ocean temperatures measured on the fore-reef slope at Clerke Reef, located approximately ~ 30 km SW of Mermaid Reef, also showed temperature variation from deep-ocean waters (up to 5.4 °C; Fig. S6). Coral reefs exposed to internal waves (Leichter et al. 1996;Sevadjian et al. 2012;Comfort et al. 2019;Reid et al. 2019) may contain "thermal refuges", where heat stress and coral bleaching risk is reduced (e.g., Storlazzi et al. 2020;Wyatt et al. 2020). Fig. 7 a Differences between reef and offshore daily temperatures (ΔT SST = T reef − SST offshore ), b and c indicate the daily average difference in temperature between reef and offshore waters (ΔT SST ) versus the ratio of daily average surface heat and wave-driven advection term for the period from 26/11/17 to 01/10/18 at the reef flat and lagoon sites, respectively. The grey lines represent the best-fit linear regression for each fitted regression. d and e show time series (26/11/17-20/09/18) of daily mean SST offshore from the MUR satellite data and modelled (T modelled ) and observed (T reef ) daily night-time mean temperatures at the reef flat and lagoon zones, respectively Conversely, the wave-driven advection of heat contributed minimally to reef temperature changes over short timescales, but the net transport of heat over daily to weekly timescales had a significant influence on persistent temperature anomalies within the reef flat, that are typically used to assess thermal stress experienced by coral reef communities (e.g., Degree Heating Weeks). Indeed, as waves broke on the reef flat, the resulting subtidal flows advected water from offshore waters, generally led to negative temperature changes on the atoll indicating cooling over periods of several days to weeks, suggesting that such flow could provide relief from thermal stress over longer periods of time. Surface waves are an important driver of reef circulation and have been documented as the driver of spatial patterns of water residence times, coral larvae transport, temperature and water chemistry on various reef systems (Zhang et al. 2012(Zhang et al. , 2013Falter et al. 2014;Rogers et al. 2016;Grimaldi et al. 2022a). While they can cause extensive damage to reef communities, wave-driven flows could also help decrease residence time and alleviate heat stress and subsequent coral bleaching within specific areas within a reef system.
The findings presented here based on observations at Mermaid Reef have broader relevance to other reef environments worldwide. In the context of the drivers of temperature, advection from wave-and tide-driven flows can generate substantial temperature variability with estimates of wave-and tide-dominated reefs accounting for about twothird and one-third of reefs worldwide, respectively (Lowe and Falter 2015). Yet, the relative influence of wave versus tidal advection of heat has rarely been explored within coral reef systems (Herdman et al. 2015;Rogers et al. 2016). Our findings specific to the various reef zones are also likely also relevant to many other reef systems regardless of whether they are part of an atoll reef. For example, surface waves usually break on steep fore-reef slopes on fringing and barrier reefs, driving flow over the shallow reef flat, where wave-driven advection processes can contribute to modify reef temperatures (e.g., Davis et al. 2011;Falter et al. 2014;Herdman et al. 2015;Reid et al. 2020;Zhang et al. 2013). The reef flats are also usually shallow and highly susceptible to air-sea heat exchanges (Davis et al. 2011;Zhang et al. 2013;Reid et al. 2020). Fore-reefs also commonly experience large temperature fluctuations, especially those exposed to internal waves (e.g., Reid et al. 2020;Storlazzi et al. 2020;Wyatt et al. 2020). Finally, depending on reef morphology and "openness", reef lagoons can experience a wide range of residence times that determines how temperature variability responds to atmospheric warming/cooling (e.g., Dumas et al. 2012;Van Wynsberge et al. 2020).
While the primary motivation for this study has been on applications to coral bleaching, improved predictions of fine-scale temperature variability in coral reefs (and other shallow water coastal systems) is relevant to range of other applications, including assessing thermal stresses on other marine taxa (e.g., macro-algae, seagrass, fish, etc.) and to support marine management (e.g., for aquaculture and commercial fisheries) where accurate temperature records and forecasts are required.