JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. C8, PAGES 14,561-14,576, AUGUST 15, 1993 Estimators of Primary Production for Interpretation of Remotely Sensed Data on OceanColor TREVOR PLATT Bedford Instituteof Oceanography, Dartmouth,Nova Scotia, Canada SHUBHASATHYENDRANATH 1 Department of Oceanography, Dalhousie Universi.ty, Halifax, Nova Scotia, Canada The theoretical basisis explained for somecommonly usedestimators of daily primary production in a verticallyuniformwatercolumn. Thesemodels are recast into a canonical form, with dimensionless arguments, to facilitate comparison with each other and with ananalytic solution. The limitations of each model areexamined. The values of the photoadaptation parameter b, observed in the oceanare analyzed, and I•, is usedas a scale to normalize the surface irradiance.The rangeof this scaled irradiance is presented. An equation is given for estimation of b, from recentlight history. It is shown how the modelsfor water columnproduction can be adapted for estimation of the production in finite layers. The distinctions between model formulation, model implementation andmodelevaluation 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. 1. INTRODUCTION By virtueof theirbroad, synoptic coverage, remotely sensed im- ages of ocean color areseen as important tools for thespatial extrap- olationof local datacollected from ships in ocean biogeochemical studies. Oneof theprincipal applications of theimages is theestima- tion of ocean primary production atlarge geographical scale. Various methods have been proposed to convert pigment fields derived from ocean color images intomaps of primary production. These models differ in complexity and therefore in the computing time and the amount of information required to implement them. It is natural and proper to ask how these models compare with each other, and how the essence of the morecomplex models can be captured with the least computation time. Models to compute daily water column primary production as a function of available lightand biomass werepublished more than 35 years ago [Ryther,1956; Tailing, 1957]. Othermodels have been proposed since then,andnew models are still under development. It is often not easy to discern how the various models arerelated to each other. Our objectives in thispaper are therefore to outline a systematic procedure by which the models available for estimation of primary production can be compared; to analyze the differentmodels using this procedure; to point outimportant relationships between themod- els andamong the underlying parameters; andto discuss the issues that arise when the models are implemented in a remote sensing context. We deal mainly with nonspectral models for a vertically uniform water column. Thenature of ouranalysis issuch that it leads to robust results with- out the need to invokeany data. Beforeembarking on the analysis proper, it will beuseful to clarifysome fundamental points. 2. VARIABLES AND PARAMETERS It is essential first to distinguish between variables and parame- ters. Any equation (or "model") maycontain variables, parameters andconstants. The dependent variable is usually the entity on the •Also at Biological Oceanography Division, Bedford Institute ofOceanog- raphy, Dartmouth, Nova Scotia, Canada. Copyright 1993 by theAmerican Geophysical Union. Paper number 93JC01001. 0148-0227/93/93JC-01001 $05.00. left-hand side of the equation. The independent, or forcing, vari- ablesappearon the fight, together with constants and parameters. Constants may be quantities such as rr, whose value is fixed for all time, or quantities such as the speed of light, which for all practical purposes may be considered as universal. It is crucial to recognizethat when an equationis written out in terms of variables and parameters it describes not just one line on a graph,but an entire family of thein. The different members of the family are distinguished from one another by the particular values of theirparameter sets. One should notconfuse variables and parameters. Althoughone sees many examples to the contrary, the word "parameters" should only be used to signifythe properties that make a curve uniquecompared to othermembers of the family of curves with the same general equation in common.As an example, for a circlecentered at the origin, the only parameter required is the radius. To specify the radiusis sufficient to isolateone particular circle from all the possible circlesthat could be drawn with their centers at the origin. Changing theparameter magnitudes does notchange theunderly- ing model. The model has a life of its own independent from, and much morefundamental than,the particular parameter setthatmay be applied to it. The assignment of particular values to the parame- tersof a given modelis an issue of modelimplementation, not model formulation. The two issues should be kept clearly separate from eachother. Use of poorly chosen parameters couldlead to spurious conclusions about theperformance of a modelif thisdistinction were not maintained. Models that can be shownto be equivalent to each other, either by transformation of variables or parameters, arenot dissimilar from each other. Sometimes, models are written in termsof parameters that are not observables: in suchcases, it can be advantageous to recast them.For example, at present thequantum yield of photosyn- thesis is not a direct observable of the pelagicecosystem. A model so parameterized may be recast in termsof the initial slopeof the photosynthesis-light curve, which is a directobservable in routine field work. But the underlying model will not have changed, any more thanthe volume of a sphere would change if it werecalculated froin the diameter rather than the radius. Finally,oneshould not overlook the possibility thatstatistical re- gression models might be equivalent to existing analyticmodels. Thisis especially likely for linear models, where fitting a regression 14,561