The theoretical basis is explained for some commonly used estimators of daily primary production in a vertically uniform water column. These models are recast into a canonical form, with dimensionless arguments, to facilitate comparison with each other and with an analytic solution. The limitations of each model are examined. The values of the photoadaptation parameter Ik observed in the ocean are analyzed, and Ik is used as a scale to normalize the surface irradiance. The range of this scaled irradiance is presented. An equation is given for estimation of Ik from recent light history. It is shown how the models for water column production can be adapted for estimation of the production in finite layers. The distinctions between model formulation, model implementation, and model evaluation are discussed. Recommendations are given on the choice of algorithm for computation of daily production according to the degree of approximation acceptable in the result. ¿ American Geophysical Union 1993