Current areas of research
1. The Monte Carlo procedure applied to the calculation of radiative transfer in the ocean and other aquatic systems
The Monte Carlo procedure, originally developed within nuclear physics for calculating by computer modelling the behaviour of populations of subatomic particles, is equally well suited to the calculation of what happens to solar photons within the ocean. It has been used extensively for this purpose by myself and other workers over the years. I was requested to give a course on Monte Carlo modelling of radiative transfer in the ocean at the Ocean Optics XVII conference in Fremantle, Western Australia, October 2004. The complete set of course notes, including Monte Carlo codes (Fortran), together with the accompanying set of Powerpoint slides may be accessed here.
Monte Carlo course - Powerpoint slides
[I assert the moral right to be identified as the author of these notes, but explicitly permit multiplication and distribution for non-commercial educational purposes. Naturally I would like appropriate acknowledgement to be made.]a
2. The relationships between the inherent and the apparent optical properties of the ocean
The important apparent optical properties (AOP) of the ocean, such as reflectance (R), or the vertical attenuation coefficients (Kd, Ku, KE, Ko etc.)for the various kinds of irradiance, or the average cosines (μ, μd, μu etc.), are all functions of the inherent optical properties (IOP) (absorption and scattering coefficients, scattering phase function) of the seawater. The values that the IOP have at any particular location in the ocean are in turn determined by the nature and concentration of the optically significant constituents of the water (coloured dissolved organic matter[CDOM, gelbstoff, gilvin], phytoplankton, suspended inanimate particles etc.) at that location. The quantitative relationships governing the dependence of the AOP on the IOP are of great practical significance in understanding the ways in which the underwater light field is determined by the seawater composition, as well as being of considerable theoretical interest. This is a topic to which I have given substantial attention in the time I have been studying radiative transfer in the sea: the results so far may be found in my published papers. Two recent publications in this area -
The vertical attenuation of irradiance as a function of the optical properties of the water
Light field around a point light source in the ocean
- are appended as pdf files. In a related study, also available as a pdf file -
I have examined the fate of photons emitted within, or entering into, the water not as a continuous stream but as quasi-instantaneous pulses. After any given time interval, Δt, a proportion of the photons, determined by the value of the absorption coefficient, a, will have been absorbed. I have derived an expression for the average depth traversed by those photons which, having been emitted from a thin layer of the ocean at depth z, have not been absorbed after time interval Δt, as a function of the scattering coefficient (b), the asymmetry factor (μs) of the scattering phase function, the average cosine ( μ[z]) of the light field at depth z, and Δt.
3. Measurement of the absorption coefficients of natural waters
In principle the absorption coefficient of a water sample is determined simply by measuring the extent to which the intensity of a beam of light passing through the sample is reduced by absorption within a certain defined pathlength. With clear, strongly absorbing, liquids this is readily achieved in the laboratory with a spectrophotometer. In natural waters, however, it is invariably the case that the light is scattered by suspended particles to an extent at least of the same order as that to which it is absorbed, so that the contribution of absorption per se to attenuation of the measuring beam becomes uncertain. In marine, and most fresh, waters there is the additional problem that the absorption coefficient is very low so that inconveniently long pathlengths have to be used to achieve a useful diminution of the signal. Both these problems are simultaneously solved in the integrating cavity absorption meter (ICAM) developed by Fry, Kattawar & Pope (Applied Optics 31[1992]2055-65). In this instrument a diffuse light field is set up within a cavity that has a diffusely reflective wall, and is filled with the liquid under study. From the measured effect of the liquid on the light field the value of its absorption coefficient can be determined. Because the light field is already totally diffuse, it cannot be made more diffuse by scattering within the liquid. Thus, measurement of absorption is not affected by scattering. Furthermore, as they undergo multiple reflections at the cavity wall the photons can traverse long distances before they are finally absorbed, so that the instrument effectively has a long pathlength and can be used to measure very low values of absorption coefficient.
The Fry et al. ICAM has a cavity with a shape that is essentially cylindrical with rounded ends. It can be shown (Kirk, Applied Optics 34[1995]4397-4408) that if the cavity is spherical then it is possible to derive explicit expressions for the probability of photon survival (Ps) in transit across the cavity, the average number of collisions with the wall per photon (CF), and the average pathlength per photon (lF), in terms of the absorption coefficient of the medium (a), the diameter of the cavity (2r), and the reflectivity of the cavity wall (ρ). For any integrating cavity absorption meter to work, a uniform diffuse light field must be established within the cavity. An advantage of a spherical cavity is that this can be achieved relatively simply by having a point light source located at the centre of the sphere. On this basis the point source integrating cavity absorption meter (PSICAM) was proposed, and the equations describing photon behaviour within it were derived (Kirk, Applied Optics 36[1997]6123-28). A number of prototype PSICAMs have now been built in various laboratories and have proved useful for measuring the absorption coefficients of ocean and other natural waters. There remains a good deal of scope for improving the performance of the PSICAM, notably the creation of a satisfactory point light source.