The supplementary section contains additional model details and an additional figure presenting model results.

Transcription

1 1 1. Supplementary materials The supplementary section contains additional model details and an additional figure presenting model results Carbon chemistry implementations The OCMIP carbon chemistry that is used in global ocean models is used in this study to calculate aragonite saturation and ph from C T and A T. One alteration from the standard global implementation of the OCMIP scheme is to increase the search space for the iterative scheme from ±.5 ph units (appropriate for the stable open ocean carbon system) to ±2.5. With this change, the OCMIP scheme converges over a broad range of DIC and A T values (Munhoven, 213). Gas exchange is calculated using a cubic relationship between wind speed (Wanninkhof and McGillis, 1999), the saturation state of the gas (described below) and the Schmidt number of the gas (Wanninkhof, 1992). The transfer coefficient, k, is given by: k = u3 1 (Sc/66) 1/2 (1) where.283 cm hr 1 is an empirically-determined constant (Wanninkhof and McGillis, 1999), u 3 1 is the short-term steady wind at 1 m above the sea surface, the Schmidt number, Sc, is the ratio of the diffusivity of momentum and that of the exchanging gas, and is given by a cubic temperature relationship (Wanninkhof, 1992). Finally, a conversion factor of 36 m s 1 (cm hr 1 ) 1 is used. In practice the hydrodynamic model can contain thin surface layers as the surface elevation moves between z-levels. Further, physical processes of advection and diffusion and gas fluxes are done sequentially, allowing concentrations to build up through a single time step. To avoid unrealistic changes in the concentration of gases in thin surface layers, the shallowest layer thicker than 2 cm receives all the surface fluxes. The change in DIC concentration due to a sea-air flux (+ from sea to air) of carbon is given by: DIC = K H k CO2 ([pco t 2 ] atm [pco 2 ]) /h wc (2) where k CO2 the transfer coefficient for carbon dioxide (Eq. 1), [pco 2 ] is the partial pressure of dissolved inorganic carbon in the surface waters determined from DIC and A T using the carbon chemistry equilibria calculations described above, [pco 2 ] atm is the partial pressure of carbon dioxide in the atmosphere, and h wc is the thickness of the surface layer of the model into which the sea-air flux flows, K H is the solubility constant of carbon dioxide gas. There is a small change in total alkalinity concentration, A T, associated with photosynthetic processes due to nutrient uptake, but we will restrict our consideration to changes A T due to changes in DIC that have the greatest impact on Ω. Note the carbon dioxide flux is not determined by the gradient in DIC, but the gradient in [CO 2 ]. At ph values around 8, [CO 2 ] makes up only approximately 1/2th of DIC in seawater, significantly reducing the air-sea exchange. Counteracting this reduced gradient, note that changing DIC results in an approximately 1 fold change in [CO 2 ] (quantified by the Revelle factor (Zeebe and Wolf-Gladrow, 21)). Thus, the gas exchange of CO 2 is approximately 1/2 1 = 1/2 of the oxygen flux for

2 the same proportional perturbation in DIC and oxygen. At a Sc number of 524 (25 C seawater) and a wind speed of 12 m s 1, 1 m of water equilibrates with air with an e-folding timescale of approximately 1 day Seaweed growth model Seaweed growth and respiration The seaweed growth model considers the diffusion-limited supply of dissolved inorganic nutrients (N and P) and the absorption of light, delivering N, P and fixed C respectively. The seaweed has a fixed stoichiometry that can be specified as: 55CO 2 +3NO 3 +PO H 55 photons 2O (CH 2 O) 55 (NH 3 ) 3 H 3 PO O 2 (3) where the stoichiometry is based on Atkinson and Smith (1983) (see also Baird and Middleton (24); Hadley et al. (214)). First we will consider the maximum nutrient uptake and light absorption, and then compare them to determine the realised growth rate Light capture The calculation of light capture by seaweed involves estimating the fraction of light that is incident upon the leaves, and the fraction that is absorbed. The rate of photon capture is given by: ( 1 9 hc ) 1 k I = E d,λ (1 exp ( A L,λ ω B B)) λdλ (4) A V where h, c and A V are fundamental constants, 1 9 nm m 1 accounts for the typical representation of wavelength, λ, in nm, and A L,λ is the spectrally-resolved absorbance of the leaf (Table 3). The term 1 exp ( ω B B) gives the effective projected area fraction of the community. In the case of light absorption of seaweed, the exponent is multiplied by the leaf absorbance, A L,λ, to account for the transparency of the leaves. At low seaweed biomass, absorption at wavelength λ is equal to E d,λ A L,λ ω B B, increasing linearly with biomass as all leaves are exposed to full light (i.e. there is no self-shading). At high biomass, the absorption by the community asymptotes to E d,λ, at which point increasing biomass does not increase the absorption as all light is already absorbed Growth The growth rate combines nutrient, light and maximum organic matter synthesis following: [ ] µ B = min µ max 3 B, 55 14k I B, (5) and the production of seaweed is given by µ B B. Note the maximum growth rates sits within the minimum operator. This allows the growth of seaweed to be independent of temperature at low light, but still have an exponential dependence as growth approaches the maximum growth rate. 2

3 3 Variable Symbol Units Downwelling irradiance E d W m 2 PAR irradiance E P AR W m 2 Seaweed biomass B g N m 2 Seaweed harvest rate H g N m 2 d 1 Water column detritus, C:N:P = 55:3:1 D Atk g N m 3 Effective projected area of seaweed A eff m 2 m 2 Leaf absorbance A L,λ - Bottom shear stress τ sh N m 2 Wavelength λ nm Water layer thickness h wc m Table 1. State and derived variables for the seaweed model. DIC = t 3 14 µ BB/h wc (6) B = µ B B φ B B H (7) t D Atk = φ B B/h wc (8) t [ ] µ B = min µ max 3 B, 55 14k I (9) B ( 1 9 hc ) 1 k I = E d,λ (1 exp ( A L,λ Ω B B)) λdλ (1) A V Table 2. Equations for the seaweed model. Other constants and parameters are defined in Table g N mol N 1 ; 12 g C mol C 1 ; 31 g P mol P 1 ; 32 g O mol O 1 2.

4 Symbol Value Units Parameters Maximum growth rate of seaweed µ max B.2 d 1 (Valiela et al., 1997) Nitrogen-specific area of seaweed Ω B 2. (g N m 2 ) 1 a Leaf absorbance A L,λ.7 - Mortality rate φ B.1 d 1 (Marba et al., 27) Speed of light c m s 1 Planck constant h J s 1 Avagadro constant A V mol 1 Atmospheric CO 2 concentration [CO 2 ] 38.6 ppmv Table 3. Constants and parameter values used in the model. a Spectrally-resolved values 4

5 REFERENCES 5 Relative Frequency Histogram of Omega change entire reef Relative Frequency Histogram of Omega change bommies Relative Frequency Histogram of Omega change reef slope.4.25 Relative Frequency Histogram of Omega change reef flat Relative Frequency Histogram of Omega change sand & rubble Figure 1. histogram of the mean change in Ω for different regions within the reef (whole reef and 3 locations as defined in Figure 6). References Atkinson, M. J., Smith, S. V., C:N:P ratios of benthic marine plants. Limnol. Oceanogr. 28, Baird, M. E., Middleton, J. H., 24. On relating physical limits to the carbon: nitrogen ratio of unicellular algae and benthic plants. J. Mar. Sys. 49, Hadley, S., Wild-Allen, K. A., Johnson, C., Macleod, C., 214. Modeling macroalgae growth and nutrient dynamics for integrated multi-trophic aquaculture. J. Appl. Phycol. DOI 17/s y. Marba, N., Duarte, C. M., Agusti, S., 27. Allometric scaling of plant life history. Proceedings Of The National Academy Of Sciences Of The United States Of America 14 (4), Munhoven, G., 213. Mathematics of the total alkalinity-ph equation pathway - to

6 REFERENCES 6 robust and universal solution algorithms: the SolveSAPHE package v1.. Geosci. Model Dev. 6, Valiela, I., McClelland, J., Hauxwell, J., Behr, P., Hersh, D., Foreman, K., Macroalgal blooms in shallow estuaries: Controls and ecophysiological and ecosystem consequences. Limnology And Oceanography 42 (5, 2), Wanninkhof, R., Relationship between wind speed and gas exchange over the ocean. J. Geophys. Res. 97 (C5), Wanninkhof, R., McGillis, W. R., A cubic relationship between air-sea CO 2 exchange and wind speed. Geophys. Res. Letts. 26, Zeebe, R. E., Wolf-Gladrow, D., 21. CO 2 in seawater: equilibrium, kinetics isotopes. Elsevier.