Review of PAR parameterizations in ocean ecosystem models

Commonly-used empirical equations for calculating downward 'photosynthetically available radiation' or PAR were reviewed in order to identify a more theoretically-sound parameterization for application to ocean biogeochemical models. Three different forms of broadband PAR parameterization are currently employed in biogeochemical models, each of them originating from the downward irradiance formulations normally applied to ocean circulation models, which produce poor attenuation estimates for PAR. Two of the PAR formulations, a single-exponential function and a double-exponential function, are parameterized by multiplying surface irradiance by a coefficient determining the portion of underwater PAR. The third formulation uses the second term of the double-exponential function. After elucidating the theoretical problems of modeling PAR using these parameterizations, we suggest an improved, R-modified double-exponential PAR formulation, including Paulson and Simpson's (1977) parameter values. We also newly estimate PAR penetration via least-squares fitting of values digitized from Jerlov's (1976) observations in different oceanic water types, and compare this PAR-observation derived parameterization with our new, theoretical, R-modified parameterization. Finally, we discuss a universal limitation inherent in current theoretical approaches to PAR parameterization.