Effects of water flow and ocean acidification on oxygen and pH gradients in coral boundary layer

Reef-building corals live in highly hydrodynamic environments, where water flow largely controls the complex chemical microenvironments surrounding them—the concentration boundary layer (CBL). The CBL may be key to alleviate ocean acidification (OA) effects on coral colonies by partially isolating them. However, OA effects on coral CBL remain poorly understood, particularly under different flow velocities. Here, we investigated these effects on the reef-building corals Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica. We preconditioned corals to a control (pH 8.0) and OA (pH 7.8) treatment for four months and tested how low flow (2 cm s−1) and moderate flow (6 cm s−1) affected O2 and H+ CBL traits (thickness, surface concentrations, and flux) inside a unidirectional-flow chamber. We found that CBL traits differed between species and flow velocities. Under OA, traits remained generally stable across flows, except surface pH. In all species, the H+ CBL was thin and led to lower surface pH. Still, low flow thickened H+ CBLs and increased light elevation of surface pH. In general, our findings reveal a weak to null OA modulation of the CBL. Moreover, the OA-buffering capacity by the H+ CBL may be limited in coral species, though low flow could enhance CBL sheltering.


Supplementary Text
In our study, we followed the approach of Pacherres et al. 1 and calculated O2 flux using the upper linear gradient of the profile.Briefly, we chose this approach because all the calculations of flux of Pacherres et al. 1 are performed using Fick's first law of diffusion (i.e., based on molecular diffusion) and the diffusion coefficient based on temperature and salinity.Additionally, we followed this procedure because in their study Pacherres et al. 1 provided a first proof that the flux in the upper linear gradient of complex profiles (upper flux) is representative of the actual flux across the concentration boundary layer (CBL) of the coral.Specifically, they compared fluxes under the arrested cilia state (calculated using almost the entire profile) and under the active cilia state (calculated using the upper gradient of the profile), which revealed the same flux under both cilia states.This indicates that the flux is independent of the overall underlying transport mechanisms (diffusion vs a combination of diffusion and enhanced transport by vortical movement) across the CBL.In our study, however, we did not characterise the microscale flow conditions surrounding the measuring spot at the coral surface during profile measurement or perform additional measurements under arrested cilia activity.
Thus, we are unable to ascertain how much the approach used to derive the O2 flux of complex profiles deviates from the actual flux.However, in our data, complex profiles were few (Supplementary Table S3) and the CBL was generally thin (see the Results section), which suggests that the effect of ciliary vortices is negligible in our data.Thus, by following Pacherres et al. 1 and using only the linear section and diffusive parts to calculate fluxes we grasp the major transport process that govern the flux in our profiles.
Alternative approaches for the treatment of these complex profiles would be to exclude them from the study or to calculate O2 flux without considering their profile structure and using only the total CBL thickness and maximum O2 concentration at the coral surface (i.e., treating them as if all profiles had the same structure).However, we believe that it is important to include these profiles in our study to fully capture the variability of the CBL of the three tested species and their biological responses.
Additionally, we categorised all profiles into three main shapes (diffusive, S-shaped, and complex), as outlined in Martins et al. 2 , and did not detect extreme deviation associated with the complex profiles (Figure i).Furthermore, while the alternative calculation approach might be a valid option for studies with thick CBLs and strong cilia influence, this was not the case for our study.The limited influence of cilia activity in our data is mostly likely due to the moderately high bulk flow velocities used here, which are expected to compress surface vortices and strongly reduce the effects of cilia movement on the CBL 3 .In line with this, the O2 flux of the complex profiles derived following both approachesbased on the upper liner gradient of profiles vs based on total CBL thickness and maximum surface O2 concentration-on average differ by only 0.04 µmol h -1 cm -2 (n = 23) (Table i).Altogether, this suggests that calculating the O2 flux of the complex profiles in our study following the approach outlined by Pacherres et al. 1 provides a representative estimation of coral activity and flux.Supplementary Table S1.Details on coral species used in the experiment.

Figure i .
Figure i.Derived O2 flux values for all measured O2 concentration profiles, categorised into three main profile shapes (D, diffusive; S, S-shaped; C, complex).

Supplementary Fig. S1 .
Photographs of Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica (from left to right) during microsensor measurements.Rectangles mark representative locations of microsensor measurements across coral fragments and arrows indicate the direction of water flow.Scale bar = 1 cm approx.Supplementary Fig. S2.Visualisation of the effects of water flow and ocean acidification (OA) on the thickness of the concentration boundary layer (CBL) of Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica, with and without including complex profiles (i.e., microsensor profiles with multiple linear gradients within the CBL).Profiles were measured in light and dark combined with low flow (LF, 2 cm s -1 ) and moderate flow (MF, 6 cm s -1 ) and values are presented pooled over light conditions.No complex profiles were observed for the H + CBL.Boxes represent the first and third quartiles with lines as medians and whiskers as the minimum and maximum values or up to the 1.5 * interquartile range (IQR), whichever is reached first.Supplementary Fig. S3.Visualisation of the effect size of flow effects on the concentration boundary layer (CBL) of Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica.Cohen's d effect size between low flow (LF, 2 cm s -1 ) and moderate flow (MF, 6 cm s -1 ) for (A) O2 CBL thickness, (B) H + CBL thickness, (C) O2 concentration change at the coral surface relative to bulk seawater concentration (surface ∆O2), and (D) pH change at the coral surface relative to bulk seawater level (surface ∆pH), measured in light and dark.Values of CBL thickness are pooled over light conditions.Black vertical lines are 95% confidence intervals from nonparametric bootstrap resampling and greyshaded areas illustrate the resampled distribution of the effect size.Supplementary Fig. S4.Visualisation of the effects of water flow and ocean acidification (OA) on the O2 flux of Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica, derived from O2 concentration profiles categorised into three main profile shapes (D, diffusive; S, S-shaped; C, complex).Profiles were measured in light and dark combined with low flow (LF, 2 cm s -1 ) and moderate flow (MF, 6 cm s -1 ).Supplementary Fig. S5.Relationship between pH changes at the coral surface relative to bulk seawater pH (surface ∆pH) and O2 flux across the concentration boundary layer of Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica in the ocean acidification treatment, measured in light and dark.Measurements under low and moderate flow are pooled together.Significant Pearson correlation coefficients (r) at the level of a < 0.05 are marked in bold.Lines are linear regression fitting for significant (solid) and non-significant (dashed) correlations.

Table i .
Slope and respective fluxes of complex profiles calculated based on (1) the upper linear gradient of profiles, and (2) the total CBL thickness and the maximum O2 concentration at the coral surface.Values of slopes and fluxes are presented in µmol cm -2 h -1 .Acy, Acropora cytherea; Pve, Pocillopora verrucosa; Pcy, Porites cylindrica; OA, ocean acidification.Flux 1 Slope 2 Flux 2

Table S2 .
Brands of artificial-seawater salt used alternately during the acclimation and experimental period in the 'Ocean2100' experimental facility.
Supplementary TableS3.Number of complex profiles measured in Acropora cytherea, Pocillopora verrucosa, and Porites cylindrica in the control and ocean acidification (OA) treatments and under low flow (2 cm s -1 ) and moderate flow (6 cm s -1 ).

Table S4 .
Numerical output of linear mixed-effects models (LMMs) of concentration boundary layer (CBL) thickness of O2 and H + gradients (pooled over light conditions).Global models were constructed with species (3 levels: Acropora cytherea [Acy], Pocillopora verrucosa [Pve], and Porites cylindrica [Pcy]) as a fixed factor.The global model of H + CBL thickness was computed using corals only from the ocean acidification (OA) treatment (see Materials and Methods).Models of O2 CBL thickness of individual species and the model of H + CBL thickness of A. cytherea were constructed with flow (2 levels: low and moderate) and treatment (2 levels: control and OA) as fixed factors in a fully crossed design.Models of H + CBL thickness of P. verrucosa and P. cylindrica were constructed with the same structure, but without the treatment factor.All models were constructed with coral fragment identity (ID), colony, day of measurement (Day), and tank as random factors, except when the factor had near-zero variance, and treatment was additionally incorporated into global models as a random factor following the same guideline.Model formulas are specified.Logtransformation was applied to O2 CBL thickness (global model) to meet model assumptions.σ 2 , residual variance; τ00, random intercept variance; ICC, intra-class correlation coefficient; N, number of levels of random effects groups; Marginal R 2 , variance explained by the fixed effects; Conditional R 2 , variance explained by the entire model

Table S5 .
Numerical output of linear mixed-effects models (LMMs) of change in O2 concentration (surface ∆O2) and pH (surface ∆pH) at the coral surface relative to bulk seawater, and of O2 flux across the concentration boundary layer, measured in light and dark.Global models were constructed with species (3 levels: Acropora cytherea [Acy], Pocillopora verrucosa [Pve], and Porites cylindrica [Pcy]) as a fixed factor.Global models of surface ∆pH were computed using corals only from the ocean acidification (OA) treatment (see Materials and Methods).Models of surface ∆O2 and O2 flux of individual species and the model of surface ∆pH of A. cytherea were constructed with flow (2 levels: low and moderate) and treatment (2 levels: control and OA) as fixed factors in a fully crossed design.Models of surface ∆pH of P. verrucosa and P. cylindrica were constructed with the same structure, but without the treatment factor.All models were constructed with coral fragment identity (ID), colony, day of measurement (Day), and tank as random factors, except when the factor had near-zero variance, and treatment was additionally incorporated into global models as a random factor following the same guideline.Model formulas are specified.Square-root transformation was applied to dark surface ∆pH of P. cylindrica to meet model assumptions.σ 2 , residual variance; τ00, random intercept variance; ICC, intra-class correlation coefficient; N, number of levels of random effects groups; Marginal R 2 , variance explained by the fixed effects; Conditional R 2 , variance explained by the entire model

Table S6 .
Summary of the complete recording of temperature and pH during the experiment.Values are expressed as mean ± 1 SD with measurement replication (n).pHT, pH on the total scale

Table S7 .
Results of ANOVAs testing differences between treatments in seawater carbonate parameters, from linear mixed-effects models (LMMs).Significant effects at the level of a < 0.05 are marked in bold.ƒCO2, fugacity of CO2; DIC, dissolved inorganic carbon; Ωar, aragonite saturation; Ωca, calcite saturation