This paper reviews recent progress in the measurement and modelling of stochastic electromagnetic fields, focusing on propagation approaches based on Wigner functions and the method of moments technique. The respective propagation methods are exemplified by application to measurements of electromagnetic emissions from a stirred, cavity-backed aperture. We discuss early elements of statistical electromagnetics in Heaviside's papers, driven mainly by an analogy of electromagnetic wave propagation with heat transfer. These ideas include concepts of momentum and directionality in the realm of propagation through confined media with irregular boundaries. We then review and extend concepts using Wigner functions to propagate the statistical properties of electromagnetic fields. We discuss in particular how to include polarization in this formalism leading to a Wigner tensor formulation and a relation to an averaged Poynting vector.This article is part of the theme issue 'Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory''.
Atmospheric aerosols are the dominant source of Pb to the modern marine environment, and as a result, in most regions of the ocean the Pb isotopic composition of dissolved Pb in the surface ocean (and in corals) matches that of the regional aerosols. In the Singapore Strait, however, there is a large offset between seawater dissolved and coral Pb isotopes and that of the regional aerosols. We propose that this difference results from isotope exchange between dissolved Pb supplied by anthropogenic aerosol deposition and adsorbed natural crustal Pb on weathered particles delivered to the ocean by coastal rivers. To investigate this issue, Pb isotope exchange was assessed through a closed-system exchange experiment using estuarine waters collected at the Johor River mouth (which discharges to the Singapore Strait). During the experiment, a known amount of dissolved Pb with the isotopic composition of NBS-981 (206Pb/207Pb = 1.093) was spiked into the unfiltered Johor water (dissolved and particulate 206Pb/207Pb = 1.199) and the changing isotopic composition of the dissolved Pb was monitored. The mixing ratio of the estuarine and spike Pb should have produced a dissolved 206Pb/207Pb isotopic composition of 1.161, but within a week, the 206Pb/207Pb in the water increased to 1.190 and continued to increase to 1.197 during the next two months without significant changes of the dissolved Pb concentration. The kinetics of isotope exchange was assessed using a simple Kd model, which assumes multiple sub-reservoirs within the particulate matter with different exchange rate constants. The Kd model reproduced 56% of the observed Pb isotope variance. Both the closed-system experiment and field measurements imply that isotope exchange can be an important mechanism for controlling Pb and Pb isotopes in coastal waters. A similar process may occur for other trace elements.This article is part of the themed issue 'Biological and climatic impacts of ocean trace element chemistry'.