Mass-transfer-limited nitrate uptake on a coral reef flat, Warraber Island, Torres Strait, Australia


Previous research has identified a relationship between the rate of dissipation of turbulent kinetic energy, ε , and the mass-transfer-limited rate of uptake by a surface, herein called the ε 1/4 law, and suggests this law may be applicable to nutrient uptake on coral reefs. To test this suggestion, nitrate uptake rate and gravitational potential energy loss have been measured for a section of Warraber Island reef flat, Torres Strait, northern Australia. The reef flat section is 3 km long, with a 3 m tidal range, and on the days measured, subject to 6 m s−1 tradewinds. The measured nitrate uptake coefficient, S , on two consecutive days during the rising tide was 1.23±0.28 and 1.42±0.52×10−4 m s−1. The measured loss of gravitational potential energy across the reef flat, ΔGPE , on the same rising tides over a 178 m section was 208±24 and 161±20 kg m−1 s−2. Assuming the ΔGPE is dissipated as turbulent kinetic energy in the water column, and using the ε 1/4 law, the mass-transfer-limited nitrate uptake coefficient, S MTL , on the two days was 1.57±0.03 and 1.45±0.04×10−4 m s−1. Nitrate uptake on Warraber Island reef flat is close to the mass-transfer limit, and is determined by oceanographic nitrate concentrations and energy climate.

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  1. Atkinson MJ (1987) Rates of phosphate uptake by coral flat communities. Limnol Oceanogr 32:426–435

    CAS  Google Scholar 

  2. Atkinson MJ (1992) Productivity of Enewetak Atoll reef flats predicted from mass-transfer relationships. Cont Shelf Res 12:799–807

    Article  Google Scholar 

  3. Atkinson MJ, Bilger RW (1992) Effects of water velocity on phosphate uptake in coral reef-flat communities. Limnol Oceanogr 37:273–279

    CAS  Google Scholar 

  4. Atkinson MJ, Falter JL, Hearn CJ (2001) Nutrient dynamics in the Biosphere2 coral reef mesocosm: water velocity control NH4 and PO4 uptake. Coral Reefs 20:341–346

    Article  Google Scholar 

  5. Atkinson MJ, Smith DF (1987) Slow uptake of 32P over a barrier reef flat. Limnol Oceanogr 32:436–441

    CAS  Google Scholar 

  6. Baird ME, Atkinson MJ (1997) Measurement and prediction of mass transfer to experimental coral reef communities. Limnol Oceanogr 42:1685–1693

    Google Scholar 

  7. Batchelor GK (1959) Small-scale variations of convected quantities like temperature in turbulent fluid. J Fluid Mech 5:113–133

    Google Scholar 

  8. Bilger RW, Atkinson MJ (1992) Anomalous mass transfer of phosphate on coral reef flats. Limnol Oceanogr 37:261–272

    CAS  Google Scholar 

  9. Bode L, Mason LB, Middleton JH (1997) Reef parameterisation schemes with applications to tidal modelling. Prog Oceanogr 40:285–324

    Article  Google Scholar 

  10. Cowley R, Critchley G, Eriksen R, Latham V, Plaschke R, Rayner M, Terhell D—CSIRO Marine Laboratories Report 236 – Hydrochemistry Operations Manual. CSIRO Marine Laboratories Hobart

  11. Dipprey DF, Sabersky DH (1963) Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers. Int J Heat Mass Transfer 6:329:353

  12. Hatcher BG (1988) Coral reef primary productivity: a beggar’s banquet. Trends Ecol Evol 3:106–111

    Article  Google Scholar 

  13. Hatcher BG (1990) Coral reef primary productivity: a hierarchy of pattern and process. Trends Ecol Evol 5:149–155

    Article  Google Scholar 

  14. Hearn CJ (1999) Wave-breaking hydrodynamics within coral reef systems and the effects of changing relative sea level. J Geophys Res 104:30007–30019

    Article  Google Scholar 

  15. Hearn CJ, Atkinson MJ, Falter JL (2001) A physical derivation of nutrient-uptake rates in coral reefs: effects of roughness and waves. Coral Reefs 20:347–356

    Article  Google Scholar 

  16. Li YH, Gregory S (1974) Diffusion of ions in seawater and deep-sea sediments. Geochim Cosmochim Acta 38:703–714

    Article  CAS  Google Scholar 

  17. Nikuradse J (1933) Laws for flow in rough pipes. Forsch Arb Ing-Wes, Nr. 361

  18. Odum HT, Odum EP (1955) Trophic structure and productivity of a windward coral reef community of Eniwetok Atoll Ecol Monogr 25:291–320

    Google Scholar 

  19. Richardson LF (1922) Weather prediction by numerical processes. Cambridge University Press, Cambridge

  20. Sargent MC, Austin TS (1949) Organic productivity of an atoll. Trans Am Geophys Union 30:245–249

    Google Scholar 

  21. Smith SD, Anderson RJ, Oost WA, Kraan C, Maat N, DeCosmo J, Katsaros KB, Davidson KL, Bumke K, Hasse L, Chadwick HM (1992) Sea surface wind stress and drag coefficients: the HEXOS results. J Boundary-Layer Meteorol 60:109–142

  22. Smith SV (1973) Carbon dioxide dynamics: a record of organic carbon production, respiration, and calcification in the Eniwetok reef flat community. Limnol Oceanogr 18:106–120

    CAS  Google Scholar 

  23. Tennekes H, Lumley JL (1972) A first course in turbulence. The Massachusetts Institute of Technology

  24. Thomas FIM, Atkinson MJ (1997) Ammonia uptake by coral reefs: effects of water velocity and surface roughness on mass transfer. Limnol Oceanogr 42:81–88

    CAS  Google Scholar 

  25. Woodroffe CD, Kennedy DM, Hopley D, Rasmussen CE, Smithers SG (2000) Holocene reef growth in Torres Strait. Mar Geol 170:331–346

    Article  Google Scholar 

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The generous support of the School of Mathematics, UNSW through the University Research Support Program and School travel funds is gratefully acknowledged. The authors greatly appreciated the hospitality of the Warraber people, in particular Clara Tamu and Bogo Billy, and Bill and Bev Stephens. We would like to thank Douglas Jacobs of the Torres Strait Regional Council for coordinating the project with the Warraber Council, David Terhill at CSIRO Marine Research who generously undertook the nutrient analysis, and Jean Rueger, UNSW, for the loan of surveying equipment. We would also like to acknowledge the generous help with theoretical aspects provide by Cliff Hearn and Eric Schulz, and Marlin Atkinson for inspiring this work. MB was funded by an Australian Research Council Postdoctoral Fellowship, and RB by a UNSW Goldstar grant.

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Correspondence to Mark E. Baird.

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Communicated by B.C. Hatcher

Appendix A

Appendix A

The one-dimensional equation for depth-averaged flow across the reef flat may be written as:

$$ \frac{{\partial U}} {{\partial t}} + U\frac{{\partial U}} {{\partial x}} = g\frac{{\partial \eta }} {{\partial x}} + \frac{{\tau _{w} }} {{\rho d}} - \frac{{\tau _{b} }} {{\rho d}} $$

where U is the velocity across the reef flat, g is the gravitational acceleration, η is the sea level elevation, d is the depth, ρ is the density of water, τ w is the wind stress in the x-direction, and τ b is the bottom stress as a result of friction. A common relationship for the bottom stress is:

$$\tau _{{\text{b}}} = \rho C_{{\text{D}}} U^{2} $$

where the coefficient of drag, C D, depends on the roughness of the reef flat. The wind stress may be written in the same form:

$$\tau _{{\text{w}}} = \rho _{{\text{a}}} C_{{\text{a}}} w^{2} $$

where ρ a is the air density (~1.2 kg m-3), C a is the drag coefficient of airflow over the ocean surface, and w is the wind speed. C a depends on the roughness of the sea surface. A value of C a=1.0×10−3 from offshore measurements in small seas (Smith et al. 1992) has been used.

With values typical of Warraber Island reef flat of U ~0.2 m s−1, d ~ 0.8 m, ∂η/∂x~10−4 and w ~5 m s−1, a scaling analysis of Eq. (A1) shows that the two acceleration terms are of order 10−5, the wind stress terms is of order 5×10−5, and the pressure gradient term is of order 10−3. Thus to within 5%, the balance between pressure gradient and bottom friction terms reflects a steady-state flow in which acceleration and wind stress terms play no significant role.

The balance can be written in the form:

$$gU\frac{{\partial \eta }} {{\partial x}} = \frac{{C_{{\text{D}}} U^{3} }} {d} = \varepsilon $$

in which the left term represents the loss of gravitational potential energy and the right term the energy dissipation rate, where ε is the dissipation rate of TKE. Equation A4 can be used to obtain a value for C D.

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Baird, M.E., Roughan, M., Brander, R.W. et al. Mass-transfer-limited nitrate uptake on a coral reef flat, Warraber Island, Torres Strait, Australia. Coral Reefs 23, 386–396 (2004).

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  • Coral reefs
  • Friction
  • Nutrient uptake
  • Hydrodynamics
  • Torres Strait
  • Great Barrier Reef