Determination of Irradiation and Primary Production Using a Time-Dependent Attenuation Coefficient

Abstract

A time-dependent vertical irradiance attenuation coefficient k v(θ r) is utilized in conjunction with the Vollenweider-Fee primary production model to determine the effect of the diurnal variation of solar zenith angle on estimations of primary production and irradiation. Such effects are considered as a function of both geographic latitude (northern hemisphere) and time of year. It is shown that the effect of solar zenith angle dependence of the vertical irradiance attenuation coefficient on the determination of daily primary production is small (< ± 15%) for any latitude or time of year. The effect of solar zenith angle dependence of the vertical irradiance attenuation coefficient on the determination of irradiation at a given depth, however, can be quite significant. Examples of this impact on irradiation determinations in Lakes Superior, Ontario, and Erie are presented, as is the fact that such inaccuracies in both irradiation and primary production estimates may be dramatically minimized by a judicious selection of solar zenith angle at which to determine a single value of k v. For the Great Lakes latitudes, this solar zenith angle range is 36°–70° depending upon location and time of year.