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

Abstract

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. 1. 13,237 13,238 CAMPBELL: LOGNORMAL VARIABILITY IN BIO-OPTICS area, and volume), and even some of the more difficult to measure properties, such as the quantum yields of photosynthesis and fluorescence, all seem to have lognormal distributions within certain sampling domains. Why is this so? There are several processes that might explain why a variable is lognormally distributed [Shimizu and Crow, , 1957] which is an analogue to the additive central limit theorem for normal or Gaussian random variables. According to the central limit theorem, a random variable will be normally distributed if it can be represented as the sum of independent random variables. The larger the number of independent variables in the sum, the closer their sum is to being normal or Gaussian. However, the independent variables being summed need not be Gaussian. 1988]. Perhaps the most relevant to bio-optical processes is the "law of proportionate effect" [Aitchison and BrownThe lognormal analogue to this is as follows: a random variable will be lognormally distributed if it can be expressed as the product of independent random variables. By taking its logarithm, the product is transformed to a sum, and the sum is normally distributed according to the central limit theorem.

Amplified Arctic warming by phytoplankton under greenhouse warming

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Factors challenging our ability to detect long-term trends in ocean chlorophyll

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Imprint of Southern Ocean eddies on chlorophyll

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