Determination of thorium and particulate matter cycling parameters at station P: A reanalysis and comparison of least squares techniques

Abstract

This reanalysis of data from weather station P in the North Pacific provides least squares estimates of thorium and particle cycling rate constants and of the concentration of sinking large particles. The estimated rate constants are for a particle model that includes a suspended small‐particle class and a sinking large‐particle class and for an analogous thorium model that includes a dissolved class, a suspended small‐particle class, and a sinking large‐particle class. Steady state, one‐dimensional conditions are usually considered reasonable approximations for the deep North Pacific. These assumptions lead to estimated rate constants and concentrations of large particles (PL) that are inconsistent with independent observations. A solution consistent with all observations is found by using lognormal probability distributions for the initial estimates of the rates and PL, by using a cost function that includes all imprecisely known terms, and by allowing for deviations from steady state, one‐dimensional conditions. Estimates of the mean and standard deviation for the rates and PL are k1 = 0.7 ± 0.4 y−1 for thorium adsorption, k−1 = 1.7 ± 0.9 y−1 for thorium desorption, β2 = 0.8 ± 0.9 y−1 for particle aggregation, β−2 = 400 ± 10000 y−1 for particle disaggregation, and PL = 2 ± 60 × 10−6 kg m−3. All the means and standard deviations are for lognormal probability distributions. The results suggest that estimated PL and particle aggregation and disaggregation rate constants have the greatest consistency when deviations from steady state and one‐dimensional conditions, positivity constraints (based on lognormal probability distributions), and measurement uncertainty are incorporated into a solution.