Observations of the thermal environment on Red Sea platform reefs: a heat budget analysis

Hydrographic measurements were collected on nine offshore reef platforms in the eastern Red Sea shelf region, north of Jeddah, Saudi Arabia. The data were analyzed for spatial and temporal patterns of temperature variation, and a simple heat budget analysis was performed with the goal of advancing our understanding of the physical processes that control temperature variability on the reef. In 2009 and 2010, temperature variability on Red Sea reef platforms was dominated by diurnal variability. The daily temperature range on the reefs, at times, exceeded 5°C—as large as the annual range of water temperature on the shelf. Additionally, our observations reveal the proximity of distinct thermal microclimates within the bounds of one reef platform. Circulation on the reef flat is largely wave driven. The greatest diurnal variation in water temperature occurs in the center of larger reef flats and on reefs protected from direct wave forcing, while smaller knolls or sites on the edges of the reef flat tend to experience less diurnal temperature variability. We found that both the temporal and spatial variability in water temperature on the reef platforms is well predicted by a heat budget model that includes the transfer of heat at the air–water interface and the advection of heat by currents flowing over the reef. Using this simple model, we predicted the temperature across three different reefs to within 0.4°C on the outer shelf using only information about bathymetry, surface heat flux, and offshore wave conditions.


Introduction
Coral reefs typically thrive in environments characterized by a high degree of thermal stability (Hoegh-Guldberg 1999). Rising sea surface temperatures due to global climate change are a severe threat to coral reefs, as reef corals live near their upper thermal limits (Goreau et al. 2000;Guinotte et al. 2003;Cantin et al. 2010). Coral bleaching is the loss of pigmentation due to the breakdown of symbiosis between reef-building corals and their symbiotic algae (zooxanthellae). Elevated temperature is the primary cause of mass coral bleaching events (Glynn 1993), but recent work also suggests that organismal response to temperature variation is complex; it can depend on other biological and physiochemical factors such as the history of thermal exposure, ability to adapt or acclimate to thermal changes, short-term temperature variability, water flow, heterotrophic feeding, and light (Nakamura and van Woesik 2001;Berkelmans 2002;Lesser et al. 2004;McClanahan et al. 2005;Sammarco et al. 2006;Palardy et al. 2008;Weller et al. 2008). These factors contribute to the high degree of spatial variability in coral bleaching observed at global, regional, and even individual reef scales (Riegl and Piller 2003;McClanahan et al. 2005).
The work presented here was inspired by observations revealing distinct thermal microclimates on table reef platforms on the Saudi coast of the Red Sea during a shelf-wide Communicated by Guest Editor Dr. Clifford Hearn circulation study from October 2008 to May 2010. Temperature variability on the Red Sea reef platforms is strongly diurnal, and as we show below, the daily temperature range can vary drastically across the reef. For example, a coral on the wave-exposed side of the reef, which is regularly flushed with water from the shelf, may experience a diurnal water temperature range of 0.5-1.5°C, while colonies of the same species in the interior or wave-protected side of the reef platform, approximately 200 m away, experience a 2-5°C diurnal range. Spatial patterns in temperature variation on reefs have been shown to influence the distribution of stresstolerant coral symbionts (Glynn et al. 2001) and, recently, much attention has focused on the potential for corals to increase their thermal tolerance through a shift to more stress-tolerant symbiont assemblages (Buddemeier and Fautin 1993;Jones et al. 2008a, b;Oliver and Palumbi 2009). The history of local environmental conditions on a reef can influence the acclimation and adaptation of corals to extreme thermal events (Riegl and Piller 2003). To improve our understanding of the role that local environmental conditions play in coral bleaching and mortality, it is crucial to have a detailed understanding of the physical processes that shape the hydrodynamic and thermal environment on reefs. Nadaoka et al. (2001) conducted a month-long observational study on a fringing reef in Okinawa and found that spatial variability in water temperature was influenced by atmospheric conditions and the horizontal advection of water from a river plume and from offshore of the reef. Similar results were found by Smith (2001) in a study of heat fluxes on a Bahamian reef during a bleaching event in July and August 1990. Smith (2001) found that anomalously high water temperature during the bleaching episode was due to a combination of low winds, which reduced evaporative cooling, and the advection of warm water onto the reef from both along-and across-shelf currents. Schiller et al. (2009) used ocean reanalysis data to examine the dynamical drivers of sea surface temperature (SST) anomalies in the Coral Sea and Great Barrier Reef. The authors found that mean horizontal advection largely controls SST in the region for most of the year, but that eddy-induced heat flux becomes important during extreme SST anomalies.
In a study of coral health and recovery after the worldwide 1998 coral bleaching event, Riegl and Piller (2003) suggested that the upwelling of cool, deep water onto reefs in the Bahamas and South Africa may be responsible for the reduced bleaching observed at these locations. Vertical mixing driven by wind stress and tidal flows around reefs can also act to cool down surface water and may be another factor responsible for the spatial variability observed in thermal stress on reefs (Bird 2005;Skirving et al. 2006).
These studies identify several mechanisms that influence the thermal environment on reefs, but observational work in this area is limited to studies with relatively short time series (Nadaoka et al. 2001;Smith 2001) or those without local meteorological measurements (Bird 2005) forcing them to rely on surface heat fluxes calculated from distant meteorological data or from model or satellite-derived products which can have large uncertainties. Here, we use a 20-month record of meteorological conditions, currents, and water temperatures to examine temporal and spatial patterns of temperature variation on Red Sea platform reefs and the surrounding shelf and to perform a simple heat budget analysis with the goal of advancing our understanding of the physical processes that shape the thermal environment on the reef. Additionally, these measurements are of value because there are few time series of oceanographic and meteorological properties in this region that can be used to characterize the physical conditions on the Red Sea reef systems.

Measurements and methodology
Field site description Hydrographic measurements were collected on offshore reef platforms in the eastern Red Sea shelf region, north of Jeddah, Saudi Arabia (Fig. 1a). The climate in this region is arid, with strong evaporation (*2 m year -1 ) and very little precipitation or river runoff (Sofianos and Johns 2002). In the northern part of the Red Sea (north of 19-20°N), winds are primarily from the northwest throughout the year (Fig. 1a), modified by a strong diurnal land-sea breeze cycle in the coastal regions and, in the winter, by a series of westward-blowing mountain gap wind jets along the Saudi Arabian coast (Jiang et al. 2009). Tidal currents in the central and northern Red Sea are mixed semi-diurnal and are weak (Sofianos and Johns 2007).
The coral reefs in the vicinity of Jeddah are classified as either fringing reefs or offshore reef platforms (Montaggioni et al. 1986). Fringing reefs line the shore and typically have a reef flat and steep reef slope area on the offshore side but can also have shallow lagoons between the reef and shore with coral knobs and patches. Farther offshore, reef platforms rise from the sandy shelf bottom (depth *20-50 m) to within a meter of the surface with reef flats composed of coral rubble and scattered live coral colonies (predominantly Stylophora pistillata) and steeply sloping flanks on all sides that are more densely populated with a diverse assemblage of corals including Pocillopora spp., Porites spp., Acropora spp., Millepora spp., and Platygyra spp. and coralline algae. The offshore reef platforms can vary in size and shape from submerged coral patches (*10 m 2 ) to coral knolls (*10 3 m 2 ) to elongate or crescentic table reefs (*10 5 -10 6 m 2 ) (Montaggioni et al. 1986). The four northern reefs instrumented in this study (Shi'b Nazar,Tahala,Al Degaig,and Abu Madafi,Fig. 1b) are best classified as table reefs, elongated in the alongshore dimension with a cross-shore scale of 100-500 m. The reefs in the Qita Dukais system are smaller, knoll-like platforms that are round or elliptical in shape and have no preferred orientation to the shoreline. Sea surface height fluctuates seasonally with wind patterns over the Red Sea . Average water depth on the reef flat during the winter is approximately 1 and 0.5 m in the summer.

Experiment
The observations presented here are part of a larger, multiyear study of coral ecology, shelf-scale circulation, and air-sea dynamics in the Red Sea. We restrict our focus to measurements of meteorological conditions, currents, and water temperatures on nine offshore reef platforms (Tahala, Shi'b Nazar, Al Degaig, Abu Madafi, and five reefs in the Qita Dukais system) and the surrounding shelf (see Temperature was measured on all reef flats, with the exception of Shi'b Nazar, using Onset Computer Corporation's HOBO U22 Water Temp Pro sensors attached to a small lead weight and placed on the bottom by a snorkler. Onset Temp Pros have a stated accuracy of 0.2°C; however, with careful calibration in the laboratory, in situ comparisons to more accurate temperature sensors have shown that accuracy can be improved to 0.02°C. Table 1 details the number of sensors distributed on each reef. On Tahala, Al Degaig, and Abu Madafi reefs, two temperature sensors were placed on the offshore or wave-exposed side of the reef flat with two further sensors on the onshore or wave-protected side. Within the Qita Dukais reef system, temperature sensors were concentrated on two of the largest coral knolls (''QD1'' and ''QD2'') and a few sensors were also placed on smaller reefs (see Fig. 6 for sensor distribution in the Qita Dukais reef system). In addition to temperature sensors, a 2-MHz Nortek AquaDopp Profiler and Seabird SBE-37 Microcat were placed on reef QD1 and later on QD2 to measure currents, temperature, and conductivity.
To characterize the environmental conditions on the shelf surrounding the reefs, vertical arrays of temperature sensors, including Seabird SBE-39s, Seabird SBE-37s, RBR-1060s, RBR-2050s (all measuring temperature to ±0.002°C), and Onset Temp Pros, were deployed on tautline moorings on the forereefs of Shi'b Nazar, Tahala, Al Degaig, and Qita Dukais and on the outer shelf at Mooring K2, at which conductivity was also measured using SBE-37s. Vertical profiles of water velocity were measured with an upward-looking Teledyne RDI Acoustic Doppler Current Profiler (ADCP) mounted on a bottom tripod at the K2 site ( Fig. 1; see mooring details in Table 1). Tidal analysis was performed using the MATLAB toolbox T_TIDE (Pawlowicz et al. 2002).
The meteorological data used in this study are taken from a surface buoy deployed in 700 m of water (about 30 km offshore of Abu Madafi) and a 9-m coastal meteorological tower located on the campus of the King Abdullah University of Science and Technology (KAUST). Both the surface buoy and tower carry improved meteorological (IMET) sensor suites for measuring wind speed and direction, air temperature, relative humidity, barometric pressure, incoming shortwave radiation, incoming longwave radiation, and precipitation, which allow for estimates of the air-sea exchange of heat, freshwater, and momentum (Hosom et al. 1995;Colbo and Weller 2009 Additionally, SST (at 0.6 m depth) and surface wave height were measured at the buoy.

Heat budget analysis
Here, we present the equations and define the coordinate system for a heat budget analysis on a reef platform. The coordinate system is aligned with the shape of the reef platform, which can be approximated as an ellipse. The temperature balance on the reef can be represented as follows: where we use the summation convention with the index i = 1-3 and a right-handed coordinate system is adopted with the principle axes defined by x i : x, aligned with the minor axis of the elliptical reef shape and positive toward the back reef, y, aligned with the major axis of the reef, and z, positive upward. u i represents the corresponding velocity components u, v, and w, and T is water temperature. Overbars denote time-averaged quantities (in the case of our calculations, 1-h averages), and primed values are the fluctuating components The terms on the left-hand side of Eq. 1 represent the rate of change of temperature and the divergence of the advective heat flux. The terms on the right-hand side represent turbulent heat flux (including unresolved heat fluxesanything with time scales of less than an hour) and sources or sinks of heat (S), respectively. Current measurements were only collected at one location on top of the reef, and For Reef Platform moorings, the location given is in the center of the reef platform and the depth represents the range of water depths in which the reef-top sensors were deployed thus we cannot directly calculate spatial gradients in the turbulent transport of heat. However, this term can be estimated from a gradient diffusion-type model: where K i is the turbulent diffusivity.
Using the parameterization in Eq. 2, K i * 0.1-1 m 2 s -1 (Sundermeyer and Ledwell 2001; Jones et al. 2008b), and an estimate of spatial gradients in temperature across the reef derived from observations on the most densely instrumented reef platforms in the Qita Dukais system, we estimate turbulent heat flux to be more than an order of magnitude smaller than the advective or surface heat flux. This is not sufficient justification for neglect of this term, especially since it seems likely that there will be times when turbulent heat flux will be of first-order importance. However, due to our inability to directly calculate turbulent heat flux, or alternatively, to have a better estimate of K i , we will not include this term in the heat budget.
Vertically averaging Eq. 1 over the water column, neglecting the turbulent flux term, and multiplying by the heat capacity per unit volume (qc p ; assumed constant and equal to 4.1 9 10 6 W s m -3°C-1 ), gives an expression for the heat balance within a volume of water of unit length and width, with the top defined by the water surface (z = h) and bottom defined by the bed (z = 0): In the derivation of Eq. 4, we assume that water temperature is vertically uniform in the water column above the reef. Over a very rough coral bed, the vertical turbulent mixing is likely to be strong enough to maintain a nearly uniform temperature under most conditions. We tested this assumption using two temperature sensors on the reef flat separated vertically by 0.5 m and horizontally by 2 m, and they typically agreed to within the calibration uncertainty of the instruments. Eq. 4 also assumes that h does not vary spatially over the unit area or in time over the period of the calculation of these terms (1 h, in this case). The left-hand side of Eq. 4 represents the rate of change of heat storage within the volume (Q T ). The terms on the right-hand side of Eq. 4 are the advection of heat through the sides of the volume (DF) and the flux of heat through the water surface and the bed, respectively, and can be written as follows: In this study, we assume that vertical advective heat flux due to groundwater movement and direct thermal conduction, Q bed , is negligible, so that Net heat flux between the ocean and atmosphere, Q N , is calculated as follows: where the terms on the right-hand side of Eq. 7 represent latent, sensible, net shortwave, and net longwave heat flux, respectively. Incoming shortwave radiation was corrected for surface reflection using an albedo that accounts for atmospheric transmittance (Payne 1972), plus an additional albedo (10%) to account for the reflectance of the coral bed in shallow water (Maritorena et al. 1994). Longwave, latent, and sensible heat fluxes were computed using a modified version 2.5 TOGA (Tropical Oceans Global Atmosphere) COARE (Coupled Ocean-Atmosphere Response Experiment) bulk algorithm (Fairall et al. 1996(Fairall et al. , 2003. Cool skin and warm layer corrections were not applied. DF is estimated from currents measured by the AquaDopp profiler on the reef flat and across-reef and along-reef temperature gradients, which are approximated by the centered difference of three reef-top temperature sensors aligned in each direction.

Results
Water temperature on the Red Sea reef platforms is spatially and temporally variable. Figure 2 illustrates the differences in water temperature on the wave-exposed and wave-protected sides of Abu Madafi reef, on the outer shelf, and Tahala reef, on the inner shelf, for a week in August 2009. This time series represents a period with some of the largest temperature variability in our observations. Water temperature on the side of the reefs protected from direct wave forcing has a larger diurnal range than on the wave-exposed side. For example, a coral on the wave-exposed side of the reef, which is regularly flushed with water from the shelf, may experience a diurnal temperature range of 0.5-1.5°C, while the same species on wave-protected side of the reef platform, approximately 200 m away, experiences a 2-5°C diurnal range. August (Fig. 3). In late fall and winter, shelf water temperature decreases and there is relatively little stratification (N 2 = 2 9 10 -5 s -2 on the forereef of Abu Madafi, where ; q is potential density, q 0 is a reference density, g represents gravitational acceleration). During a period of steady cooling, from November 2008 to January 2009 (Fig. 3), inner shelf waters at Tahala are approximately a degree cooler than middle and outer shelf waters (Qita Dukais, Abu Madafi, Shi'b Nazar). In late spring and summer, shelf waters warm, stratification strengthens (N 2 = 2 9 10 -4 s -2 ), and inner shelf waters at Tahala are warmer than middle and outer shelf waters. Periods of cooling water temperatures, 1 to 3 weeks in duration, are superimposed on the annual temperature variation at all sites and may be due to wind-forced coastal upwelling on the eastern Red Sea shelf. An empirical orthogonal function (EOF) analysis of 33-h low-pass-filtered, depth-averaged water temperature on the forereefs of Shi'b Nazar, Tahala, Abu Madafi, and Qita Dukais reveals the spatial structure of the dominant mode, accounting for 97% of temperature variance, to be approximately uniform between the sites (not shown), suggesting that sub-diurnal frequency temperature variability is generally similar across the shelf. While sub-diurnal temperature variability is fairly uniform across the shelf, diurnal oscillations in water temperature can look very different between sites. As an example, Fig. 4 presents week-long time series of water temperature at 0.6-m depth at the meteorological buoy and on the reef flat of QD1 in the Qita Dukais reef system for both winter and summer seasons. Temperatures on the reef have larger diurnal variations than surface temperature offshore. In the winter, the diurnal temperature variation on the reef can be fairly small, on the order of a 0.25-0.5°C, but in the summer, it can approach 6°C, when offshore surface waters vary only by 1.5-2°C. In the following section, we will show that there can be a significant amount of spatial variability in the thermal environment within the bounds of one reef platform.

Temperature variability on the reef platforms
The temperature of water on the reef platforms is influenced by seasonal cycles and synoptic wind-forcing events but also by small-scale circulation over and around the reef platforms, which controls the exchange of water with the surrounding shelf. Reef platforms rise sharply from the shelf to within a meter of the surface, and this inhomogeneity can lead to a high degree of spatial variability in the temperature field and the creation of thermal microclimates on the reef platform.
Circulation on the reef flat is largely wave-driven, with currents primarily to the southeast, in the direction of prevailing wind and waves. Previous studies have shown that waves break on the steeply sloping flanks of the reef, creating a spatial gradient in wave radiation stress and a superelevation of water level above the mean sea level (wave ''setup''), driving flow over the shallow reef flat, from the reef crest to the backreef (Longuet-Higgins and Stewart 1964;Tait 1972;Symonds et al. 1995;Hearn 1999;Coronado et al. 2007;Hench et al. 2008). Significant wave height measured at the meteorological buoy ranged from less than 0.1-4.5 m with mean 0.94 ± 0.54 m. Currents measured on reef QD1 in the Qita Dukais reef system had a maximum speed of 25 cm s -1 and mean 8.8 ± 5.4 cm s -1 . Cross-reef currents on the reef were strongly correlated with offshore wave height (r = 0.87, P-value \ 0.0001) but less correlated with eastward wind stress (approximately directed across the reef, r = 0.50, P-value \ 0.0001) or wind stress magnitude (r = 0.60, P-value \ 0.0001). While wave height is strongly coupled to wind stress magnitude in this region (r = 0.80, P-value \ 0.0001), direct wind forcing on the reef, estimated from a simple balance between bottom stress and total wind stress (not shown), only accounts for reef currents on the order of a few cm s -1 . The tidal amplitude of sea surface height is 5-20 cm; however, a tidal analysis of currents measured in the center of the reef demonstrates that the tide explains less than 5% of the reeftop velocity variance.
An approximate estimate of the residence time of water on the reef can be calculated as RT = V/Q, where V is the volume of water on the reef and Q is the volumetric flow rate. V was estimated by approximating the reef as a 200by 600-m rectangle with an average water depth of 1 m, and the volumetric flow rate was estimated from the velocity measured in the center of the reef (assumed to be representative of flow over the entire reef platform) and the cross-sectional area of the rectangular ''reef''. The average residence time of water on QD1 was approximately 100 min; however, depending on flow conditions, it can range from 10 min to several hours.
The simplified heat budget represented by Eq. 6 states that water temperature on the reef flat is determined by a balance between the transfer of heat at the air-water interface and the advection of heat by currents flowing over the reef. Thus, it is not surprising to find that the spatial variability of water temperature on the reef platforms, r Tspatial , calculated as the standard deviation of hour-averaged water temperature measured at all sensors on Qita Dukais at particular point in time, is related to the net surface heat flux, Q N (Fig. 5a), as well as the magnitude of currents across the reef (Fig. 5b). r T-spatial is maximized during periods of large, positive net surface heat flux and low currents. The strongest thermal gradients across the reef flat would be expected in the middle of the day during lowflow conditions, when both the surface heating potential and the residence time of water on the reef flat are maximized. While low-flow conditions are of great interest for the question of temperature variance on the reef flat, we do not include times when the flow is less than 2 cm s -1 in Fig. 5b, as this is approaching the uncertainty of the Nortek Aquadopp instrument. Moreover, we believe that in very sluggish flows, it is difficult to assume that flow measured at one point in the center of the reef is representative of flow across the entire reef platform. Figure 6 shows the daily variability in water temperature at several sensors in the Qita Dukais reef system, estimated as the standard deviation of the 33-hr high-pass-filtered water temperature from June 2009 to May 2010, denoted by r T-diurnal . The greatest diurnal variation in water temperature occurs at sensors located in the center of the larger reef flats and on reefs protected from direct wave forcing, while sensors on smaller knolls or on the edges of the reef flat tend to experience less diurnal temperature variance.
A complicating factor in considering the spatial dependence of temperature variability across the reef is the dependence of the heat budget on water depth (seen explicitly in Eq. 4). Even on the reef flat, bathymetry is spatially variable. If we consider a situation in which there is no flow over the reef, for a given amount of surface heat flux acting on a unit area, a shallow site will heat faster during the day (Q N [ 0) and cool faster at night (Q N \ 0) than a deeper site. The maximum difference between the depths of temperature sensors on the reef bed was 1.9 m. Figure 7 illustrates a clear dependence of temperature variability on water depth for sensors on Qita Dukais, where the line represents the best fit to the observations. In addition to this depth dependence, however, a positional dependence is evident. The location of each reef flat measurement site was classified as ''wave exposed'' (within approximately 50 m of the offshore edge of the reef flat), ''wave protected'' (within approximately 50 m of the onshore edge of the reef flat), or ''interior'' (sensors not included in first two categories) and is indicated with data markers in Fig. 7. ''Wave-exposed'' sites are clustered below the best-fit line, whereas sensors in the interior of the reef flat and in ''wave-protected'' locations tend to fall above the best-fit line, suggesting an additional dependence of position on the temperature variance at each sensor.

Discussion
Heat balance over a reef platform To examine the physical processes shaping the thermal environment on reef platforms in the Red Sea, a simple heat budget analysis (Eq. 6) was performed using a year of observations taken on QD1 and 8 months of data taken on QD2 in the Qita Dukais reef system (Fig. 6). Surface heat flux, estimated from Eq. 7 using meteorological observations from the offshore buoy and water temperature on the reef, is shown in Fig. 8a as a composite diurnal cycle (averaged over every hour of the day from October 2008 to October 2009, denoted as hi d ). Q N h i d peaks mid-day at over 500 W/m 2 and is negative at night. A diurnal composite of the cross-reef component of current (Fig. 8b) shows that flow is, on average, directed onshore and is greatest in the afternoons, when the onshore component of wind is strongest (sea breeze; Fig. 8c) and wave height is maximized (Fig. 8d). Figure 8e shows the diurnal composite average water temperature in the interior of reef QD1. T h i d increases just after sunrise, peaks in the early afternoon, after maximum surface heat flux, and then cools in the late afternoon and throughout the night. The last panel in Fig. 8 shows a composite average of the observed rate of temperature change ( oT=ot h i d ; black line) and the contribution to the rate of temperature change from surface heat flux, pure advection, and both terms, Figure 8e illustrates that considering only surface heat flux (Eq. 8) results in an overestimate of the rate of temperature change on the reef, predicting more heating during the day and more cooling at night than is observed. In contrast, the rate of temperature change that would result from pure advection (Eq. 9), is positive at night, when oT=ox is negative (because water on the shallow platform is cooler than the offshore water that is driven onto the reef by waves), and then becomes negative during the day, when the temperature gradient across the reef reverses (water on the reef is warmer than just offshore). The approximate balance of surface heat flux (blue) and advective (green) terms suggests that advection acts to relax the gradients in temperature set up by the surface heat flux. When both terms are used to estimate the rate of temperature change on the reef (Eq. 10), the resulting composite average has a shape very similar to the observations, explaining 93% of the variance in the diurnal composite averaged temperatures on the reef, with a residual (model minus observed) of 0.13°C h -1 . The primary disparity between Eq. 10 and the observations occurs at night-the model predicts more heat loss than is observed. In general, the simple model represented by Eq. 10 has skill representing the observations averaged over the whole year and performs similarly well on seasonally averaged data (winter or summer) (Fig. 9). Figure 9 presents a comparison of hour-averaged surface heat flux and advective terms calculated from the October 2008-October 2009 deployment on reef QD1 and the November 2009-May 2010 deployment on reef QD2 (see Fig. 6). The data shown here are restricted to times when flow on the reef was greater than 2 cm s -1 . A linear fit to the observations demonstrates a strong relationship (r = 0.83, P-value \ 0.0001) between surface heat flux and advective terms with a slope of 0.97. A simple conceptual model of the processes controlling the diurnal temperature variations over the reef is summarized in Fig. 10. Waves breaking on the steep forereef create a wave setup on the wave-exposed side of the reef. The pressure head from the wave setup drives flow over the reef from the wave-exposed side to the wave-protected side. We can imagine a parcel of water as it moves from the deep water offshore of the reef over the reef platform (from left to right in Fig. 10), in a Lagrangian reference frame. oT=ot for the water parcel goes as Q N =h (advection drops out in this reference frame); thus, as depth decreases over the shallow reef, the parcel of water heats up (or cools down) faster than over the deeper water offshore. Therefore, areas in the interior and on the protected side of the reef will experience much larger temperature extremes than areas on the forereef or wave-exposed side of the reef flat.
We can further test the skill of this simple model by predicting the temperature on reef platforms for which we do not have current measurements. From April-October 2009, temperature measurements were collected on the wave-exposed (offshore) and wave-protected (onshore) sides of Abu Madafi, Al Degaig, and Tahala reefs. Figure 11 shows an estimate of the temperature difference across each reef estimated from a simple heat budget model where h was chosen to be the spatially averaged water depth at the sensor locations on each reef as measured in October 2009, versus the observed difference in temperature between the sensors averaged over 1 h, DT obs . In Eq. 11, u is the across-reef component of flow, determined from an empirical relationship with offshore significant wave height, u ¼ 0:06H 0 ; which was derived from the current measurements on reefs QD1 and QD2 (r = 0.77, P-value \ 0.0001). The skill of the simple heat budget is fairly good at Abu Madafi (located on the outer shelf), giving a standard error of 0.2°C. However, the skill decreases toward the inner shelf (standard error of 0.4°C at Tahala), which is likely due to the fact that the empirical relationship used to estimate u was derived on a reef that is exposed to offshore waves (Qita Dukais reef system), and the wave heights measured offshore at the meteorological buoy are less representative of the waves incident on the protected reefs.

Conclusions
In 2009 and 2010, temperature variability on Red Sea reef platforms was dominated by diurnal variability. The daily temperature range on the reefs, at times, exceeded 5°C-as large as the annual range of water temperature on the shelf. The shallow topography of the reef platforms enhances the diurnal temperature cycle by concentrating the effect of surface heat flux into a small volume of water and by exposing the reef flat to direct wind and wave forcing, all of which have diurnal variability. The topographic complexity of the reefs also leads to a high degree of temperature variability at small spatial scales, with cooler temperatures on the forereef or wave-exposed side of the reef and warmer temperatures in the reef interior and on the wave-protected side of the reef. The existence of thermal microclimates on reef platforms may result in colonies with different physiology and diverse coral symbiont assemblages.
We found that the temporal (Fig. 8) and spatial (Fig. 11) variability in water temperature on the reef platforms can be fairly well predicted by a simplified heat budget, which includes the transfer of heat at the air-water interface and the advection by currents flowing over the reef. With this simple model, we predicted the temperature difference across three reefs to within 0.4°C on the outer shelf and 0.9°C on the inner shelf (95% confidence) using only information about bathymetry, surface heat flux, and offshore wave conditions, the last two of which were measured at the meteorological buoy for this study, but could be obtained from remote sensing products or coastal weather stations. The results of this work have implications for improving indices of coral bleaching, which typically have difficulty predicting the high degree of spatial variability observed at global, regional, and individual reef scales. The incorporation of a simple heat budget model into the coral bleaching indices could help to capture the effect of wave-driven circulation on the thermal environment of reefs.