A schematic of the modelled silicon and phosphorus cycles.

The article provides answers to the questions posed in the silicon-phosphorus model worksheet.

## Contents

1. Try starting the model with: (a) deep P 10-fold lower, all else the same; (b) deep Si 10-fold lower, all else the same; (c) deep Si 10-fold higher, all else the same; and see whether/how the model converges to steady state.

The model always returns to the same steady-state. When there is less PO4 then there is less burial of P, so levels recover. Likewise with silicon and opal burial. When there is excess silicic acid then burial increases until Si comes back down.

2. Change the following parameters by +/- 25% and see if the model still converges to a similar steady-state: Rorg, the ideal Si:P ratio in diatoms; SR, the surface remineralisation fraction of organic phosphorus; SRs, the surface remineralisation fraction of biogenic silica; SFs, the fraction of biogenic silica that is buried; RS, the riverine input of silicic acid.

Always converges, although not always to the same steady-state.

3. Change the following parameters by +/- 25% and see if the model still converges to a similar steady-state: μD, diatom maximum growth rate; μO, other algae maximum growth rate; and M, phytoplankton mortality rate.

The model does not converge when: (1) M is increased, (2) μD is decreased, (3) μO is either increased or decreased.

4. How quickly will the ocean rid itself of excess silicic acid? Test this timescale by initialising the model with 1200 mmol Si m-3 (this is the threshold above which inorganic silica spontaneously precipitates out of seawater) and examine the model results to see how long it takes for the increased silica burial rate to return the ocean to near steady-state.

5. Make a ten-fold reduction in the initial concentration of deep silicate. How long does it take the deep silicate concentration to return to equilibrium? (calculate this as the time until 95% of the original perturbation is removed)

6. First double and then halve the deep silicate concentration, while leaving all other variables at their default values. Save the data and then examine the burial fluxes of solid silica shortly after the alterations. How do they compare?

When deep silicic acid is doubled, after about 20 years the opal burial flux is 13 Tmol y-1. When it is halved, it is around 3.4 Tmol y-1 after about 20 years.