Measurement and prediction of mass transfer to experimental coral reef communities

The uptake of nutrients (N and P) into coral reef communities is proposed to be limited by diffusion through concentration-depleted boundary layers between the water and organisms, or what is termed “mass transfer limitation.” The mass transfer rate is a physical limit to the rate of nutrient uptake. Maximum uptake rates by highly rough biological surfaces have not yet been evaluated. Engineering correlations indicate that increased surface roughness should increase mass transfer, although it has been difficult to quantify roughness of living corals. In this paper, the effects of highly rough coral surfaces on mass transfer were investigated by using dissolution of gypsum (Plaster-of-Paris) from flat smooth surfaces and coral skeletons. The gypsum dissolution rates were mcasurcd as an increase in concentration of calcium ions in freshwater recirculating over experimental surfaces. Stanton numbers (St,,,, a dimensionless number giving the ratio of uptake rate per unit area to the rate of advection of the substance past the uptake surface) of experimental smooth surfaces ranged from 2.6 to 3.5 X lo-’ and were the same as values in the engineering literature for smooth surfaces. St,,, for coral-shaped surfaces ranged from 70 X 10. ’ at 0.03 m s-l to 17 X 10 5 at velocities up to 0.50 m s-l and were in general 9 & 1 times that of smooth surfaces. The measured St,,, for each coral-shaped surface was the same as the predicted St,,, (+ 10%) calculated from measured friction and roughness using a correlation of heat transfer. St,,, for ammonia uptake on living coral reef communities show the same relationship between mass transfer, friction, and roughness as the coral-shaped gypsum surfaces. The transport rates of nutrients to reef surfaces are controlled by large-scale roughness, typically associated with coral heads, and not small-scale roughness elements on the organisms, nor biological alterations of diffusive boundary layers. Nutrient uptake and possibly other metabolic exchange rates arc governed by concentration, water velocity, and friction dissipated over the reef, denoting that coral reef community metabolism is physically forced. Uptake rates of nutrients (PO,, NH,) to assemblages of coral-reef benthos are positively correlated with the velocity of water flowing over the assemblage (Atkinson and Bilger 1992; Atkinson et al. 1994; Bilger and Atkinson 1995; Thomas and Atkinson 1997). These authors explained this observation by hypothesizing that the rate-limiting step for nutrient uptake is diffusion of nutrient ions through nutrientdepleted diffusive boundary layers adjacent to the surface of the benthos, termed mass-transfer limitation (Bilger and Atkinson 1992). Nutrient-uptake rate of coral-reef benthos, m,, (mol m-* s-l, where m-* is the projected planar area of the bottom), is described as a first-order rate reaction with respect to the concentration gradient through the boundary layer: