A consumer’s guide to phytoplankton primary productivity models

We describe a classification system for daily phytoplankton primary productivity models based on four implicit levels of mathematical integration. Depth-integrated productivity models have appeared in the literature on average once every 2 years over the past four decades. All of these models can be related to a single formulation equating depth-integrated primary production (2 PP) to surface phytoplankton biomass (C,,,J, a photoadaptive variable (PhO,,), euphotic depth (Z,,), an irradiance-dependent function (F), and daylength (DL). The primary difference between models is the description of F, yet we found that irradiance has a relatively minor effect on variability in X PP. We also found that only a small fraction of variability in 2 PP can be attributed to vertical variability in phytoplankton biomass or variability in the light-limited slope for photosynthesis. Our results indicate that (1) differences between or within any model category have the potential to improve estimates of X PP by <lo%, so long as equivalent parameterizations are used for C\“,., and PhOpt, and (2) differences in estimates of global annual primary production are due almost entirely to differences in input biomass fields and estimates of the photoadaptive variable, PhOpt, not to fundamental differences between model constructs. Models of daily phytoplankton carbon fixation are based on either idealized relationships between net photosynthesis and irradiance or measurements of net primary production. Net photosynthesis is estimated from the rate of 0, evolution or 14C uptake (Dring and Jewson 1982; Geider and Osborne 1992) measured during short (<2-h) incubations under a range of constant light intensities. The photosynthesis-irradiance relationships derived from these measurements can be used to estimate net primary production by calculating photosynthetic rates corresponding to changes in solar irradiance, integrating these photosynthetic rates over a photoperiod, and subtracting the daily respiratory costs associated with cell maintenance and growth. Alternatively, net primary production can be estimated directly from models based on measurements of 14C uptake during 24-h incubations under variable solar irradiance. By definition, net primary production is the amount of photosynthetically fixed carbon available to the first heterotrophic level and, as such, is the relevant metric for addressing environmental questions ranging from trophic energy transfer to the influence of biological processes on carbon Acknowledgments We thank Creighton Wirick, Richard Barber, and an anonymous reviewer for helpful recommendations and discussions, and Avril Woodhead and Claire Lamberti for editorial comments. This research was supported by the U.S. National Aeronautics and Space Administration under grant UPN161-35-05-08 and the U.S. Department of Energy under contract DE-AC02-76CHOOO 16. cycling (Lindeman 1942). Accordingly, many primary productivity models have been described. Unfortunately, the fundamental similarities and significant differences between models have been obscured by a tremendous diversity of variable names and parameterizations. Here we examine relationships between productivity models and identify where improvements are most needed to enhance model performance. A coherent discussion of productivity models requires an organizational system for distinguishing between basic model categories, yet such a system does not exist. Thus, we begin our discussion by defining a classification scheme based on inherent levels of mathematical integration. Categorization of productivity models As a point of reference, we may consider the estimation of daily phytoplankton carbon fixation within the euphotic zone (2,” = penetration depth of 1% surface irradiance) per unit of ocean surface (2 PP) as a common application for all primary productivity models. Extant models that can be used for such estimates range from simple relationships between surface chlorophyll concentration and 2 PP, to irradiance-dependent models of net photosynthesis integrated over time and based on fundamental photosynthetic parameters, such as functional absorption cross sections (gPsII) and electron turnover times (7) for photosystem II. This wide spectrum of productivity models is often delineated into