Primary production by phytoplankton : analytic solutions for daily rates per unit area of water surface

Abstract

An exact (analytic) solution is presented for the daily integral of photosynthesis by phytoplankton in a vertically homogeneous water column. The photosynthesis-light curve on which the results are based is sufficiently flexible to accommodate the effects of photoinhibition. A comparison of the available methods for the description of diurnal variation in surface irradiance reveals that for long days at high latitudes a second-order sinusoid is preferable to the conventional first-order sine function. Previously published geometrical approximations to the instantaneous and daily integrals of water-column photosynthesis are examined and explained. The impact of photoinhibition on daily primary production is quantified and discussed. A polynomial approximation is given to the exact solution for the daily integral of photosynthesis. This function is, for all practical purposes, free from error in estimation, and will decrease computation time by a factor of about 3 $\times $ 10$^{5}$ compared with a numerical integration. For maximum generality, the solutions and discussion are framed in terms of dimensionless quantities: the results are also tabulated in this form so that they can be applied where computation facilities are lacking. The solutions can be used at all hierarchical levels in the analysis of aquatic systems, including the interpretation of results from discrete stations (local scale), the use of remotely sensed data on ocean colour (regional scale) and modelling biogeochemical fluxes for climatic research (basin and global scales).