Estimating Effective Light Exposure by Property-Tracking Tracers

A numerical approach to estimating the mean exposure of a tracer to a scalar property is applied to predict the light exposure of sinking phytoplankton. In our application, effective light exposure is defined as the time integral of a light limitation factor commonly used in phytoplankton models. Solutions from an adjoint approach have previously been published for a set of one-dimensional sinking phytoplankton scenarios. We illustrate that a simple extension to a standard advection–diffusion model produces similar results. Specifically, we present numerical solutions using property tracking in a one-dimensional advection–diffusion model for multiple tracers. Solutions are calculated for a range of eddy diffusivity distributions and compared with the published solutions. The consistency of the numerical solutions with the published solutions provides validation of the property-tracking approach. While the adjoint method solution is much less computationally intensive for the test cases, the property-tracking approach can be applied in multidimensional time-varying applications with an arbitrary distribution of sinking speed, diffusivity, and turbidity for which an adjoint solution has not been developed. Our intention is for this example application and corroboration of the “property-tracking” approach to inspire readers to envision additional applications for this approach.