A Poisson-Pareto model of Chl-a fluorescence signals in marine environments

Stephen Woodcock, Bojana Manojlovic, Mark Baird, Peter Ralph


Because of its central role in the global carbon cycle, quantifying the biomass of photosynthetic microalgae in the oceans is crucial to our ability to estimate the oceans’ carbon drawdown. Many traditional methods of primary production assessment have proven to be extremely time consuming and, consequently, have handled only very small sample sizes. The recent advent of in situ bio-optical sensors, such as the water quality monitor (WQM), is now providing lower cost and higher throughput data on these crucial biological communities. These WQMs, however, only quantify the total fluorescence of all individual cells within their optical sample windows, irrespective of size. In this paper, we further develop an established model, based on Pareto random variables, of the size structure of the microalgae community to understand the effect of the WQMs’ sampling and data pooling on their estimates of algal biomass. Unfortunately, evaluating sums of Pareto variables is a notoriously difficult problem. Here, we utilize an approximation for the right-tail of the resulting distribution to derive parameter estimates for the underlying size structure of the microalgae community.



Poisson–Pareto random variables; shifted Hill’s estimators

DOI: http://dx.doi.org/10.21914/anziamj.v56i0.7528

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.