The lognormal distribution as a model for bio-optical variability in the sea

The lognormal distribution is presented as a useful model for bio-optical variability at a variety of spatial and temporal scales. A parametric statistical framework is presented for using the lognormal model to assess the effects of heterogeneity and scale on closure. Variability at small scales affects but is unresolved by large-scale measurements. An assumed lognormal distribution allows one to integrate over small-scale variability to predict large-scale measurements. Examples are presented to demonstrate how knowledge of the variance can be incorporated into models to relate measurements made at different scales.