Evaluation of coral reef carbonate production models at a global scale

Calcification by coral reef communities is esti- mated to account for half of all carbonate produced in shal- low water environments and more than 25 % of the total car- bonate buried in marine sediments globally. Production of calcium carbonate by coral reefs is therefore an important component of the global carbon cycle; it is also threatened by future global warming and other global change pressures. Numerical models of reefal carbonate production are needed for understanding how carbonate deposition responds to en- vironmental conditions including atmospheric CO2 concen- trations in the past and into the future. However, before any projections can be made, the basic test is to establish model skill in recreating present-day calcification rates. Here we evaluate four published model descriptions of reef carbon- ate production in terms of their predictive power, at both lo- cal and global scales. We also compile available global data on reef calcification to produce an independent observation- based data set for the model evaluation of carbonate bud- get outputs. The four calcification models are based on func- tions sensitive to combinations of light availability, arago- nite saturation (a/ and temperature and were implemented within a specifically developed global framework, the Global Reef Accretion Model (GRAM). No model was able to re- produce independent rate estimates of whole-reef calcifica- tion, and the output from the temperature-only based ap- proach was the only model to significantly correlate with coral-calcification rate observations. The absence of any pre- dictive power for whole reef systems, even when consistent at the scale of individual corals, points to the overriding impor- tance of coral cover estimates in the calculations. Our work highlights the need for an ecosystem modelling approach, accounting for population dynamics in terms of mortality and recruitment and hence calcifier abundance, in estimat- ing global reef carbonate budgets. In addition, validation of reef carbonate budgets is severely hampered by limited and inconsistent methodology in reef-scale observations.

. Schematic illustrating the coral reef carbonate budget and the modelled parameters (G reef and G coral ) used to quantify carbonate production. Carbonate framework is principally produced by scleractinian corals (G coral ) and crustose coralline algae (CCA; G algae ); the abiotic (inorganic) precipitation of carbonate cements (G i ) also occurs. Bioeroders break down the reef framework internally (e.g. worms, sponges) and externally (e.g. parrot fish, crown-of-thorns starfish). The rubble produced is incorporated back into the framework, by cementation or burial, or exported from the reef. The observational data available to test models of carbonate budget include G coral measured from coral cores, and G reef calculated from a reef community census or the total alkalinity of surrounding seawater. Kinzie, 1976;Kleypas and Langdon, 2006;Tambutté et al., 2011). As a result, it is anticipated that calcification on coral reefs is sensitive to climate change and ocean acidification (e.g. Kleypas et al., 1999;Erez et al., 2011;Hoegh-Guldberg, 2011) -in particular the reduction of a due to ocean acidification causing decreased calcification of individual corals (reviewed by Kleypas and Yates, 2009;Andersson and Gledhill, 2013) and coralline algae (e.g. Anthony et al., 2008;Johnson and Carpenter, 2012;Johnson et al., 2014), and rising sea surface temperatures causing an increase in coral bleaching frequency due to heat stress (e.g. Donner et al., 2005;Baker et al., 2008;Frieler et al., 2013).
The global reef carbonate budget (i.e. G global ) is inherently difficult to evaluate because it is impossible to empirically measure this variable; instead it must be extrapolated from reef-scale observations. Vecsei (2004) synthesized census-based measurements to produce values of reef calcification rates (G reef ; Fig. 1) -that varied both regionally and with depth -to estimate G global (0.65-0.83 Pg yr −1 ). In contrast, the earlier estimate of G global (0.9 Pg yr −1 ) from Milliman (1993) is calculated from two modal values for G reef (reefs: 0.4 g cm −2 yr −1 , lagoons: 0.08 g cm −2 yr −1 ). Opdyke and Walker (1992) found a lower estimate of reefal CaCO 3 budget of 1.4 Pg yr −1 derived from published Holocene CaCO 3 accumulation rates. Census-based methods calculate G reef by summing the calcification by each reef-calcifier, multiplied by its fractional cover of the reef substrate (Chave et al., 1972;Perry et al., 2008). The calcification by individual components of the reef community may be derived from linear extension rates or published values for representative species (Vecsei, 2004). Often it is only calcification by scleractinian corals (G coral ) and coralline algae (G algae ) that are considered, due to their dominance in CaCO 3 production (e.g. Stearn et al., 1977;Eakin, 1996;Harney and Fletcher, 2003). Calcification rates for portions of a reef (e.g. reef flat or back reef) can also be calculated from the total alkalinity change ( A T ) of seawater (e.g. Silverman et al., 2007;Shamberger et al., 2011;Albright et al., 2013). This is because precipitation of CaCO 3 decreases the total alkalinity (A T ) of seawater whereas dissolution has the opposite effect. This alkalinity anomaly technique was first used in a reef setting in the 1970s (Smith and Pesret, 1974;Smith and Kinsey, 1976) and has since been used to estimate basin-scale pelagic and coral reef calcification (Steiner et al., 2014). G reef is calculated by measuring the change in A T over a discrete time interval ( t); because the change in A T includes dissolution the calcification measured is net ecosystem calcification (NEC) or net G reef (Eq. 1; Albright et al., 2013): where p is seawater density (kg m −3 ) and z is water depth (m). G reef measured using A T accounts for inorganic precipitation (G i ; Fig. 1) and dissolution; however, unlike census-based methods for calculating G reef , it is not possible to break down the contribution of individual calcifiers in the reef community (Perry, 2011). G coral calculated from the width and density of annual bands within the colony skele- Derived from coral core (Porites sp.) measurements and temperature form the HadISST data set (Rayner et al., 2003).
Future climate simulations at reef locations provided by ReefBase b .

Scale applied
a Model output was compared to alkalinity changes measured in situ at Moorea by Gattuso et al. (1993Gattuso et al. ( , 1996Gattuso et al. ( , 1997 and Boucher et al. (1998) ton is commonly used in census-based observations of G reef ( Fig. 1; Knutson et al., 1972). Estimates of G global alone tell us little about how reefs will be affected by climate change at a global scale. Instead, if coral calcification (G coral ) and reef community calcification rates (G reef ) can be numerically modelled as a function of the ambient physicochemical environment (e.g. irradiance (E), a and temperature), then the results could be scaled up to produce an estimate of G global that could be recalculated as global environmental conditions change. Examples of this approach (Table 1) include: (1) Kleypas (1997;"ReefHab"), which is sensitive to E only and was initially developed to predict global reef calcification (G global ) and habitat area and used to estimate changes in G global since the Last Glacial Maximum; (2) Kleypas, Anthony and Gattuso (2011;"KAG"), which simulates G reef as a function of E and a and was originally developed to simulate carbonate chemistry changes in seawater on a reef transect; (3) Lough (2008; "LOUGH") which simulates G coral as a function of sea surface temperature (SST) and was derived from the strong relationship observed between SST and G coral in massive Porites sp. colonies from the Great Barrier Reef (GBR), Arabian Gulf and Papua New Guinea; and (4) Silverman, Lazar, Cao, Caldeira and Erez (2009;"SILCCE"), which simulates G reef as a function of SST and a and was used to simulate the effects of projected future SSTs and a at known reef locations globally. Although further models exist describing G coral as a function of carbonate ion concentration ([CO 2− 3 ]; Suzuki et al., 1995;Nakamura and Nakamori, 2007) these are synonymous to the a function used in KAG and SILCCE. With the exception of Kleypas et al. (2011), which included classes of non-calcifying substrate, the above models do not account for community composition. Reef calcification rates vary considerably depending on the abundance of corals and coralline algae . Therefore, successful up-scaling of G reef and G coral to estimate G global also requires, as a minimum, quantifying live coral cover (LCC).
To date it remains to be demonstrated that any of the published models reproduce present-day reef calcification rates (i.e. G reef ). Despite this, simulations of the effects of future climate scenarios have been attempted using calcification rate models. For example, McNeil et al. (2004) incorporated LOUGH with the linear relationship observed between a and calcification in the BioSphere 2 project (Langdon et al., 2000), and predicted that G reef will increase in the future. In contrast, a similar study by Silverman et al. (2009;SILCCE) concluded that coral reefs will start to dissolve. Whilst McNeil's study was criticized for its incorrect underlying assumptions (Kleypas et al., 2005), the contradictory predictions from these two models highlights the importance of comparing and fully evaluating reef calcification models, starting with their performance against present-day observations.
Here we describe a novel model framework, the global reef accretion model (GRAM), and evaluate the four previously published calcification models (ReefHab, KAG, LOUGH and SILCCE) in terms of their skill in predicting G coral and G reef . The independent evaluation data set comprises observations of G reef from census-based methods and A T experiments as well as G coral measured from coral cores. The individual model estimates of G global are discussed in comparison with previous empirical estimates. We highlight where model development is required in order to accurately simulate the effects of past and future environmental conditions on calcification rates in coral reefs.

Model description
Four calcification models were selected for evaluation in global-scale simulations: (1) ReefHab (Kleypas, 1997), (2) KAG , (3) LOUGH (Lough, 2008) and (4) SILCCE (Silverman et al., 2009; Table 2). Previous applications for these models cover a hierarchy of spatial scales (colony, LOUGH; reef, KAG and global, ReefHab and SIL-CCE) as well as representing different approaches for measuring G coral ( Fig. 1; LOUGH) and G reef ( Fig. 1; ReefHab, KAG and SILCCE). Any modifications of the models from their published form are described below, and these are only made where necessary to fit them into the same GRAM framework (Fig. 2). Kleypas (1997) developed ReefHab to predict changes in the global extent of reef habitat since the last Glacial Maximum (Kleypas, 1997). Like photosynthesis, calcification is light saturated ; as the rate of calcification increases toward a maximum value, it becomes light saturated after irradiance increases beyond a critical value. This curvilinear relationship can be described with various functions -however, hyperbolic tangent and exponential functions have been found to best describe the relation-ship (Chalker, 1981). The ReefHab model calculates vertical accretion (G reef in cm m −2 d −1 ) as a function of irradiance at the depth of the seabed (E z ) and maximum growth rate (G max = 1 cm yr −1 ). The hyperbolic tangent function uses a fixed light saturation constant (E k = 250 µmol m −2 s −1 ) to generate a scaling factor for G max (Eq. 2):

ReefHab
where E z is derived from the surface irradiance (E surf ) and the inverse exponent of the product of the light attenuation coefficient (K 490 ) and depth (z; Eq. 3). Following the methodology in Kleypas (1997), if E z is less than the minimum irradiance necessary for calcification (250 µmol m −2 s −1 ) G reef = 0 cm m −2 d −1 . TF is the topography factor (Eq. 4), which reduces G reef in areas of low topographic relief: where α is calculated from a nine-cell neighbourhood (centre index 2.2) by summing the inverse tangent of the difference between cell depths (z i,j − z 2.2 ) divided by the distance between cell centres (D i,j −2.2 ): Vertical accretion (cm m −2 d −1 ) is converted to g (CaCO 3 ) cm −2 d −1 by multiplying average carbonate density (2.89 g cm −3 ) and porosity (50 %) as defined by Kleypas (1997). Anthony et al. (2011) performed laboratory flume incubations on Acropora aspera to parameterize the relationship between (day and night) calcification rates and a , determining the reaction order (n) and maximum calcification rates (k day and k night ). The resultant model was then implemented by Kleypas et al. (2011), with the addition of an exponential light-sensitive function that accounted for light-enhanced calcification, to simulate seawater chemistry changes along a reef transect at Moorea, French Polynesia. The transect did not exceed 2 m in depth; therefore, it was appropriate to use the surface irradiance (E surf ) for the calculation of G reef . In this study G reef is calculated (Eq. 6) using E z (Eq. 3) rather than E surf because the maximum depth in the model domain is 100 m, greatly exceeding the depth of the original application:

KAG
where A c is the fractional cover of live coral (i.e. A c = 1 when coral cover is 100 %). Here E k is greater than in ReefHab (400 µmol m −2 s −1 versus 250 µmol m −2 s −1 ) following the parameterization used by Kleypas et al. (2011). G reef is calculated here in mmol m −2 d −1 and is divided into day and night rates (G max and G dark ); both are calculated as a function of a . For this study it was necessary to introduce day length (L day ; h) to Eq. (7) and Eq. (8) because of the daily time step as opposed to the hourly time step of the original model: L day was calculated using the method described by Haxeltine and Prentice (1996), which uses Julian day (J d ) and latitude (lat) as follows: where the variables u and v are calculated from lat and aa (a function of J d ; Eq. 14): CaCO 3 production in mmol m −2 d −1 was converted to g cm −2 d −1 using the molecular weight of CaCO 3 (MR = 100).

LOUGH
ReefHab and KAG were both derived from theoretical understanding of the process of calcification and parameterized by values observed in the literature or in situ. In contrast, LOUGH was derived from the observed relationship between annual calcification rates of massive Porites sp. colonies and local SST (Lough, 2008). A linear relationship (Eq. 15) was fitted to data from 49 reef sites from the Great Barrier Reef (GBR; Lough and Barnes, 2000), Arabian Gulf and Papua New Guinea (Lough, 2008), and accounted for 85 % of the variance (p < 0.001): Division by 365 days is necessary here to adapt the original model to the daily time step used in this study and results in G coral in g cm −2 d −1 .

SILCCE
Using the alkalinity anomaly technique ( A T ), Silverman et al. (2007) found a correlation between rates of inorganic precipitation (G i ) and net G reef (mmol m −2 d −1 ). Silverman et al. (2009) fitted observations to Eq. (16) to calculate G i as a function of a and SST (Eq. 17): Incorporating Eq. (17) with SST and a sensitivity of coral calcification gives where k r (38 m 2 m −2 ) and k p (1 • C −1 ) are coefficients controlling the amplitude and width of the calcification curve. T opt is the optimal temperature of calcification and is derived from summer temperatures in the WOA 2009 monthly average SST : June (in the Northern Hemisphere) and December (in the Southern Hemisphere). Again, CaCO 3 production in mmol m −2 d −1 was converted to g cm −2 d −1 using the molecular weight of CaCO 3 (MR = 100).

Global reef accretion model (GRAM) framework
The calcification production models above were implemented within our global reef accretion model (GRAM) framework. In this study, GRAM was implemented on a 0.25 • × 0.25 • global grid. Vertically, the model domain was resolved with 10 depth levels at equal 10 m intervals with the fraction, by area, of a model cell (quasi-seabed) within each 10 m layer recorded for calculating total CaCO 3 production ( Fig. 2). A physicochemical mask was imposed to limit CaCO 3 production to shallow-water tropical and subtropical areas. This mask was defined following Kleypas (1997;Kleypas et al., 1999): SST (> 18 • C), salinity (23.3-41.8) and depth (≤ 100 m). Calcification was calculated on a daily basis over the course of 1 full calendar year and according to the environmental conditions at each grid cell (described below). Table 1 lists the data used to force GRAM. Ocean bathymetry was calculated from GEBCO One Minute data set (https: //www.bodc.ac.uk/data/online_delivery/gebco/) and mapped to the model grid. Monthly values for SST  and salinity  were obtained from the World Ocean Atlas (WOA) 2009. These climatologies are reanalysis products of observations collected 1955-2009. The WOA data have a scaled vertical resolution with 24 layers, with a maximum depth of 1400 m; however, only surface values were used in this study. Daily photosynthetically available radiation (PAR), for the period 1991-1993, were obtained from Bishop's High-resolution (DX) surface solar irradiance data (Lamont-Doherty Earth Observatory, 2000) derived from the International Satellite Cloud Climatology Project (ISCCP) data (Bishop and Rossow, 1991;Bishop et al., 1997). Following Kleypas (1997), units of dW m −2 were converted to µmol m −2 s −1 by multiplying by a factor of 0.46. The monthly diffuse light attenuation coefficient of 490 nm light (K 490 ) was obtained from the Level-3 binned MODIS-Aqua products in the OceanColor database (available at: http://oceancolor.gsfc.nasa.gov). Surface a was derived from the University of Victoria's Earth System Climate Model (Schmittner et al., 2009;Turley et al., 2010) for the decade 1990-2000. All input data were converted, without interpolating, to the same resolution as the model by recording the closest data point to the coordinates of the model grid cell's centre. Missing values were extrapolated as an unweighted mean from the nearest values in the data set found in the model cell's neighbourhood (including diagonals) in an area up to 1 • from the missing data point.

Evaluation data set and methodology
An independent data set of in situ measured calcification rates (G reef and G coral ) was collated from the literature to evaluate model performance. In total, data from 11 coral core studies (Table 3; Montastrea and Porites sp.), 8 censusbased and 12 A T studies (Table 4) were assembled. This data set is not comprehensive of all studies that have measured G reef and G coral ; many older studies were excluded (e.g. Sadd, 1984) due to errors in calculation of G reef that were resolved by Hubbard et al. (1990). The studies sampled cover a representative range of SST and a conditions in which present-day reefs are found (Fig. 3). The positions of the in situ measurements were used to extract the equivalent data points from the gridded model output. Where location coordinates were not reported, Google Earth (available at: http://earth.google.com) was used to establish the longitude and latitude, accurate to the model resolution of 0.25 • . For uniformity, reported units of measurement were converted to g (CaCO 3 ) cm −2 yr −1 . The values of live coral cover (LCC) reported in the census-based and A T studies were used to convert model G coral to G reef . A global average of 30 % (Hodgson and Liebeler, 2002) was used where LCC was not reported (Table 4).
Model skill in reproducing the observed data was assessed using simple linear regression analysis preformed on observed calcification rates paired with their equivalent model value. When testing LOUGH against coral core data, values that were used in the original formulation of the model (Lough, 2008) were excluded so as to preserve the independence of the data. Similarly, when correlating SILCCE with  A T data, the Silverman et al. (2007) datum was excluded. A global average LCC of 30 % (Hodgson and Liebeler, 2002) was applied to model CaCO 3 production in model comparisons with census-based and A T G reef at a global scale. Global mean G reef and G global were calculated by applying a further 10 % reefal area to model CaCO 3 production; this follows the assumption in Kleypas (1997) that 90 % of the seabed is composed of unsuitable substrate for reef colonization and growth. Global and regional values are compared directly to the most recent estimates by Vecsei (2004), although other global estimates are also considered.

Model carbonate production rates
Globally averaged values of G reef (summarized in Table 5) vary little between ReefHab (0.65 ± 0.35 g cm −2 yr −1 ), KAG (0.51 ± 0.21 g cm −2 yr −1 ) and LOUGH (0.72 ± 0.35 g cm −2 yr −1 ), with SILCCE producing a somewhat smaller value (0.21 ± 0.11 g cm −2 yr −1 ). A consistent feature across all models is the high carbonate production in the southern Red Sea along the coast of Saudi Arabia and Yemen and, in KAG and LOUGH, the East African coast (Fig. 4). In all models, there was very low calcium carbonate production in the northern Red Sea compared to the south. There is higher calcium carbonate production in the western Pacific than in the east, and along the Central American and northern South American coastline, and this is more pronounced in KAG and LOUGH than ReefHab. In scaling up to the global scale, estimates of G global based on the models ReefHab (1.40 Pg yr −1 ) and SILCCE (1.1 Pg yr −1 ) were substantially lower than for the other model setups (3.06 Pg yr −1 for KAG and 4.32 Pg yr −1 for LOUGH). Figure 5 shows the location and magnitude of the calcification observations. Coral core (G coral ) values are higher (0.5-2.8 g cm −2 yr −1 ; full data set in the Supplement) than G reef measurements from either census-based (0.1-0.9 g cm −2 yr −1 ) or A T (0.003-0.7 g cm −2 yr −1 ; Table 4) methods. In general, coral core data show decreasing G coral with increasing latitude that is most pronounced in Hawaii and along both east and west Australian coastlines (Fig. 5). Table 4. Details of studies used for evaluating model calcification rates; observed calcification rates are for the reef community (G reef ) and are derived from census-based methods or alkalinity reduction experiments ( TA);indicates fields that were not reported. Studies are listed alphabetically by their ID. CCAcrustose coralline algae; NECnet ecosystem calcification. a The value for CCA cover is the average of the % framework reported by Eakin (1996) that is defined as the area of dead coral upon which CCA grows. b Authors note that the underlying assumptions for calculating calcification by algae may be unrealistic but make best use of the available data at the time of the study. c Median LCC values of the reported ranges were applied to model output for the regression analysis. d The LCC range reported by Gattuso et al. (1993) was assumed to be the same as in the subsequent study at Moorea (Gattuso et al., 1996). e Values reported in Suzuki et al. (1995) for study conducted in 1991 (Nakamori et al., 1992) at the same location.

Observed carbonate production rates
Table 5. Average regional and global reef calcification rates (G reef ) and global CaCO 3 budgets (G global ) and reef areas derived from the four model setups (≤ 40 m) and Vecsei (2004). Model G reef is calculated as the total CaCO 3 production multiplied by global average live coral cover (LCC) of 30 % (Hodgson and Liebeler, 2002) and 10 % seabed reefal area with the exception of ReefHab, which uses a function of seabed topographic relief to modify total CaCO 3 production to give G reef . Global reef area is 10 % of the total area accounting for inter-reefal area.
G reef ± SD (≤ 40 m; g cm −2 yr −1 ) However, G coral is not always smaller at higher latitudes. For example, the Arabian Gulf is toward the upper end of all G coral observations (1.44 ± 0.57 g cm −2 yr −1 ; full data set in online supplementary material) whereas G coral in the Gulf of Aqaba is twofold smaller (0.78 ± 0.28 g cm −1 yr −1 ) despite the similar latitude of the two locations. This result cannot be corroborated by A T or census data as there is no observation for the Arabian Gulf, however, there is agreement that calcification in the Gulf of Aqaba is toward to lower end of the observed range for A T measured G reef (0.18 ± 0.09 g cm −2 yr −1 ) and G coral measured from coral cores. In contrast, the census-based and A T measurements show no latitudinal trends. Figure 6 shows the correlation of corresponding model and observed calcification rates. With a slope of 0.97, the only significant correlation was that between LOUGH and independent coral core data (R 2 = 0.66, p < 0.0001). The G reef measured by Perry et al. (2013) in the Caribbean also fell close to a 1 : 1 line with LOUGH, but the positive trend was not significant, either when considering just this data subset (R 2 = 0.74, p = 0.14, n = 4), or all A T measured G reef (R 2 = 0.57, p = 0.14, n = 11). The average regional G reef estimated by all models showed little geographic difference (Fig. 7), which is in conflict with the conclusions of Vecsei (2004) who found that the Atlantic, including Caribbean reefs, had the highest G reef of all regions, followed by the Pacific and GBR (Table 5).

Discussion
Four coral reef carbonate production models, contrasting in terms of dependent environmental controls, were evaluated at local, regional and global scales. The results show that only the model using SST alone (LOUGH) is able to predict G coral , and to a degree G reef , with any statistical skill (Fig. 6). At the global scale, there is a large offset between the empirical and model estimates of G global (Table 5), with the LOUGH G global estimate approximately a factor of 5 greater than previous estimates by Milliman (1993) and Vecsei (2004). Although G global values from ReefHab and SIL-CCE (1.4 and 1.1 Pg yr −1 ) are significantly closer to the empirical estimates of G global than the other models, their poor performance at the local reef scale (measured by G reef and G coral ) undermines confidence in their predictive power at G global scale. Since empirical estimates of G global cannot themselves be evaluated, it is necessary to examine the fac- Global reef area is used in extrapolating G reef to G global and so may have a significant effect on both model and empirical estimates of G global . The LOUGH model achieves a global reef area of 567 × 10 3 km 2 , comparable to the reef area used by Milliman (1993) and Opdyke and Walker (1992) of 617 × 10 3 km 2 taken directly from Smith (1978). Whereas Vecsei (2004) used a revised reef area of 304-345 × 10 3 km 2 (Spalding and Grenfell, 1997) which is almost half Smith's estimate. Despite this difference in global reef area, Milliman (1993) and Vecsei (2004)  CaCO 3 product ion mg cm − 2 yr − 1 k Figure 5. Compilation of published reef carbonate production measurements. Location and magnitude of (a) coral calcification (G coral ) observed in coral cores and, reef community calcification (G reef ) measured in (b) census-based and (c) alkalinity anomaly studies (see Tables 4 and 5 for study ID keys).
G global , further confounding evaluation of modelled G global . The question of where to draw the line in terms of establishing reef boundaries is highly pertinent to modelling G global as it dictates the area considered to be "coral reef". In our analysis, all grid cells with positive CaCO 3 production (i.e. G > 0 g cm −2 yr −1 ) are considered to contain coral reef, even those that may be close to 0 g cm −2 yr −1 . Recently formed (immature) reefs with coral communities that have positive G reef but where little or no CaCO 3 framework is present do exist (Spalding et al., 2001) and are accounted for by all four models. However, these coral communities are not included in reef area reported by Spalding and Grenfell (1997) and further information about their production rates and global abundance is needed to accurately quantify their significance in estimating G global empirically. The presence of these coral communities has been correlated with marginal environmental conditions where low (highly variable) temperatures and high nutrient concentrations are seen (Couce et al., 2012). It logically follows that excluding these marginal reefs by tightening the physicochemical mask for SST to > 20 • C, as derived by Couce et al. (2012), would reduce global reef area and close the gap between empirical and model estimates of G global . Further to this is the assumption within GRAM that Figure 6. Correlation of observed coral calcification (G coral ) and reef community calcification (G reef ) to model predictions for coral core, census-based and alkalinity anomaly ( A T ) data (1 : 1 relationship shown as red dashed line). All model estimates are multiplied by the live coral cover (LCC) reported in the observation studies to give G reef , except ReefHab in which G reef is calculated using a function of topographic relief (TF). The use of TF follows the method of Kleypas (1997); it was derived from empirical observation of reef growth and was a means to scale potential calcification (G coral ) to produce G reef in the absence of global data for LCC. All significant linear regressions are plotted (p < 0.05; grey solid line) with equation and regression coefficient (R 2 ). Data used to develop a model are also plotted (open circles) but were excluded from the regression analysis to preserve data independence. the area between reef patches in a "reef" cell (i.e. a cell with G > 0 g cm −2 yr −1 ) accounts for 90 % of the cell's area, with only 10 % assumed to be composed of suitable substrate for reef formation and coral recruitment. The availability of suitable substrate has the greatest impact on the biogeography of coral reefs (Montaggioni, 2005) and so clearly needs to be evaluated to improve G global estimates. Reef area does not account for all of the disparity between estimates of G global ; attenuation of G reef with depth may also be a causal factor. In both Atlantic and Indo-Pacific reefs, there was an exponential trend, decreasing with depth (≤ 60 m), in G reef data collated by Vecsei (2001). Modelled G reef estimates should, therefore, also vary as a function of depth. In its published form, LOUGH produces the same value for G reef throughout the water column; however, we can account for this model limitation by imposing a lightsensitive correction in the form of an exponential function to the output from LOUGH so that G reef is a function of surface (G surf ) and depth (z): where k g is a constant controlling the degree of light attenuation with depth, in this estimate K 490 was used. Eq. (19) has the same form as that for calculating light availability (Eq. 3) used in both ReefHab and KAG. Following this adjustment, the LOUGH G global estimate is reduced to 2.56 Pg yr −1 , which is closer to empirical estimates. However, where light availability has been incorporated into other models no significant skill in predicting G coral or G reef was observed (ReefHab and KAG in Fig. 6). A further factor that strongly affects G reef and G global estimates is the percentage of the reef covered by calcifying organisms (generally abridged as the term "live coral cover", or LCC, although implicitly including other calcifiers). Applying the global average LCC of 30 % clearly does not account for the large spatial and temporal variation in coral cover (< 1-43 % in the data set collated here; Table 4). Indeed, only a very limited number of Pacific islands (4/46) were found to have ≥ 30 % LCC between 2000 and 2009 in the compilation of Vroom (2011). The global average of 30 % was calculated from surveys of 1107 reefs between 1997 and 2001 (Hodgson and Liebeler, 2002) and represents total hard coral cover (LCC plus recently killed coral), so is an overestimate of LCC. LOUGH has significant skill in replicating observed G coral and has some skill in predicting G reef values observed by a standardized census method (ReefBudget; Perry et al., 2012), but only when the local observed LCC is applied. If however, the global average LCC is applied to LOUGH the correlation with G reef is lost. In addition, the global average coral cover may also account for the uniformity of regional G reef values (Fig. 7), in contrast to the significant differences between regions identified by Vecsei (2004) -for example, the Atlantic reefs (including the Caribbean) having the greatest G reef (0.8 g cm −2 yr −1 ) and reefs in the Indian Ocean the smallest G reef (0.36 g cm −2 yr −1 ; Vecsei, 2004; Table 5). The pattern is reversed in terms of coral cover, with Indo-Pacific reefs having ∼ 35 % hard coral cover compared to ∼ 23 % on Atlantic reefs (Hodgson and Liebeler, 2002). Further studies have shown that Caribbean reefs have greater G reef and vertical accumulation rates than Indo-Pacific reefs, possibly due to increased competition for space on the latter (Perry et al., 2008). These issues highlight the need for coral cover to vary dynamically within models, allowing it to change spatially and temporally according to coral population demographics (mortality, growth and recruitment).
A specific example of unrealistic G reef is seen for the Gulf of Carpentaria, where there are no known currently accreting reefs (Harris et al., 2004) but projections of carbonate production according to output from the LOUGH model are particularly high (Fig. 4). At least seven submerged reefs have been discovered in the Gulf of Carpentaria and a further 50 may exist, but these reefs ceased growth ∼ 7 kyr BP when they were unable to keep up with sea level rise (Harris et al., 2008). Failure to repopulate may be due to a combination of factors including very low larval connectivity in the Gulf of Carpentaria (Wood et al., 2014) and high turbidity, due to re-suspension of bottom sediments and particulate input from rivers (Harris et al., 2008). ReefHab is the only model to predict an absence of reef accretion in the majority of the Gulf of Carpentaria (Fig. 4), indicating that model sensitivity to light attenuation is essential. This example also raises two further points: firstly, that there are certainly undiscovered reefs that are not accounted for in empirical estimates of G global and, secondly, that larval connectivity should be considered in simulations of G reef because of its role in regulating coral abundance after disturbance Jones et al., 2009).
In addition to static coral cover, growth parameters -G max , Eq. (2); E k , Eq. (2) and (6); k day , Eq. (7); k dark , Eq. (8); k r and k p Eq. (18) -did not vary geographically, having the same value in all model grid cells. This potentially affected the skill of KAG in reproducing G coral and G reef since in the original application of the model  parameters (k day , k dark and E k ) were determined for observations at the location of the reef transect that was simulated. However, when looking at the correlation of model to data it is important to acknowledge the observational variability and error. The standard deviation, where reported, for census-based and A T measured G reef is ≤ 100 % of the mean (Table 4). In addition to this variability, observational error is greater in census-based measurements of G reef than A T measurements (Vecsei, 2004). In a review of reef metabolism, G reef was shown to vary considerably (0.05-1.26 g cm −2 yr −1 ) depending on the abundance of coral and coralline algae . G reef (measured by A T ) appears to vary little across Pacific coral reefs (Smith and Kinsey, 1976) but Gattuso et al. (1998) attribute this to the similarity of these reefs in terms of community structure and composition, as well as coral cover. The apparent agreement between LOUGH and Caribbean G reef (as reported by Perry et al., 2013) suggests that a standardized experimental methodology for measuring G reef is needed and implementing this would also provide a consistent data set that would be invaluable for model evaluation. Unexpectedly, this result also suggests that LOUGH may have skill in predicting G reef in the Atlantic Ocean despite the absence of massive Porites sp. on which the LOUGH model is built. Porites is a particularly resilient genus (e.g. Barnes et al., 1970;Coles and Jokiel, 1992;Loya et al., 2001;Hendy et al., 2003;Fabricius et al., 2011) and so applicability to other reef settings, coral genera and calcifiers as a whole is surprising. G coral of a single species has been used in some census-based studies to calculate the G coral of all scleractinian corals present (Bates et al., 2010) and the LOUGH results suggest this generalization may be appropriate.
Unlike census-based and A T methodologies, G coral measured from coral cores spans multiple centuries (Lough and Barnes, 2000) and so smoothes the stochastic nature of coral growth and variations in reef accretion. G coral and G reef do vary a great deal temporally. For example, diurnal fluctuations may be up to fivefold and result in net dissolution at night (e.g. Barnes, 1970;Chalker, 1976;Barnes and Crossland, 1980;Gladfelter, 1984;Constantz, 1986;McMahon et al., 2013). The median ratio of light to dark calcification rates is 3.0; however, measurements of dissolution in individual corals are rarely reported . At in-termediate timescales (weekly-monthly) G coral may vary by a factor of 3, with a degree of seasonal chronology (Crossland, 1984;Dar and Mohammed, 2009;Albright et al., 2013). Over longer timescales (≥ 1 yr), G coral is less variable (Buddemeier and Kinzie, 1976) and both Hatcher (1997) and Perry et al. (2008) describe reef processes hierarchically according to temporal and spatial scales, finding that time spans of a year or more are required to study processes of reef accretion. The numerous observations of G coral measured from coral cores is a further advantage over the sparse census and A T determinations of G reef which are generally more costly and labour-intensive. More observations of G reef are, however, essential to improve statistical power and evaluation of model outputs. G reef is also invaluable from a monitoring perspective (reviewed by Baker et al., 2008;e.g. Ateweberhan and McClanahan, 2010) by providing an effective measure of reef health that encompasses the whole reef community and accounting for different relative compositions of corals and algae (Vroom, 2011;Bruno et al., 2014). These benefits provide impetus for future measurements of G reef , but our results demonstrate that a standardization of the methodology (as demonstrated in Perry et al., 2013) must be applied.
The four models used in this study all simplify the physiological mechanisms of calcification to predict G coral and G reef as a function of one or two external environmental variables. Calcification is principally a biologically controlled process in corals (e.g. Puverel et al., 2005); occurring at the interface between the polyp's aboral layer and the skeleton, which is separated from seawater by the coelenteron and oral layer . This compartmentalization means that the reagents for calcification (Ca 2+ and inorganic carbon species) must be transported from the seawater through the tissue of the coral polyp to the site of calcification (reviewed in Allemand et al., 2011). Active transport of Ca 2+ bicarbonate ions (HCO − 3 ) to the site of calcification and removal of protons (H + ) regulates the pH and a of the calcifying fluid (found between aboral ectoderm and skeleton) and requires energy (reviewed in . Although the precise mechanism is unknown it is thought that in light zooxanthellate corals derive this energy from the photosynthetic products (principally oxygen and glycerol) of their symbionts, which is thought to partially explain the phenomenon of light-enhanced calcification (reviewed in Gattuso et al., 1999;Allemand et al., 2011;Tambutté et al., 2011). Both the ReefHab and KAG models use this relationship with light to determine G coral . However, corals that have lost their symbionts by "bleaching" continue to show enhanced calcification in the light (Colombo-Pallotta et al., 2010). As such, irradiance alone cannot account for changes in G coral . Precipitation of aragonite from the calcifying fluid has been assumed to follow the same reaction kinetics as inorganic calcification with respect to a (Hohn and Merico, 2012), i.e. k p · ( a − 1) n (following Burton and Walter, 1987). KAG and SILCCE both use this function of N. S. Jones et al.: Evaluation of coral reef carbonate production models seawater a in calculating calcification; however, despite the logical connection between a and G coral neither model could reproduce observed G coral values. Inorganic precipitation of aragonite increases linearly with temperature (Burton and Walter, 1987) as does respiration in corals when oxygen is not limited (Colombo-Pallotta et al., 2010). This temperature dependence may explain the strong correlation found by Lough (2008) between Porites growth and SST and the skill LOUGH has shown in this study at reproducing G coral observed values.
This study has shown that it is possible to predict global variations in coral carbonate production rates (G coral ) across an environmental gradient with significant skill simply as a function SST (LOUGH). However, the LOUGH model assumes a linear relationship between SST and coral calcification (G coral ) whereas the increase in calcification as a function of increased temperature obviously stops at a certain threshold. For example, there is substantive evidence of declining coral calcification rates in recent decades coinciding with increasing temperatures (e.g. Cooper et al., 2008;De'ath et al., 2009De'ath et al., , 2013Cantin et al., 2010;Manzello, 2010;Tanzil et al., 2013). Further laboratory experiments have found a Gaussian or bell-shaped response to increasing temperature with optima between 25 and 27 • C (e.g. Clausen and Roth, 1975;Jokiel and Coles, 1977;Reynaud-Vaganay et al., 1999;Marshall and Clode, 2004). In contrast to the linear SST relationship in LOUGH, Silverman et al. (2009;SILCCE) use the Gaussian relationship found by Marshall and Clode (2004) to modulate the rate of calcification derived from inorganic calcification (G i ) calculated from a . But, the output from SILCCE is shown to be a poor predictor of G coral or G reef in this study. While using the LOUGH model alone is clearly not appropriate when applied to future temperature simulations, environmental gradients in G coral established using LOUGH could be modulated to account for the physiological effect for heat-stress using degree-heatingmonths (e.g. Donner et al., 2005;McClanahan et al., 2007) or summer SST anomaly (e.g. McWilliams et al., 2005). This approach would then account for the evidence that corals exhibit widely differing temperature optima depending on their temperature history or climatological-average temperature (Clausen and Roth, 1975).
Since none of the models evaluated in this study showed significant skill in capturing global patterns of G reef , none of the models provide a reliable estimate of G global . Successful up-scaling of carbonate production to the reef (G reef ) and global domain (G global ) will require accounting for both depth attenuation (e.g. light sensitivity) and inclusion of population demographics affecting calcifier abundance. An ecosystem modelling approach that captures demographic processes such as mortality and recruitment, together with growth, would result in a dynamically and spatially varying estimate of live coral cover. It is also clear that a standardized methodology for census-based measurements is required, as evident from the improved model-data fit in a subset of data collected using the ReefBudget methodology (Perry et al., 2012). Coral calcification rates have slowed by an estimated 30 % in the last three decades (e.g. Bruno and Selig, 2007;Cantin et al., 2010;De'ath et al., 2013;Tanzil et al., 2013) reinforcing the pessimistic prognosis for reefs into the future under climate change (e.g. Hoegh-Guldberg et al., 2007;Couce et al., 2013;Frieler et al., 2013); numerical modelling is an essential tool for validating and quantifying the severity of these trends.
The Supplement related to this article is available online at doi:10.5194/bg-12-1339-2015-supplement.