APPENDIX A.
Model 3.
Model 3 is described by the equations provided in 2006jc003852-fs01.tiff. The state variables and functional relationships as well as parameter values are defined in this same file. Both nu_m and r_e are calculated using the Arrhenius equation with a reference temperature of 30¡C and the activation energy are also given in 2006jc003852-fs01.tiff.
Model 4.
Model 4 is described by the equations provided in 2006jc003852-fs02.tiff. The state variables, functional relationships and parameter values are defined in 2006jc003852-fs03.tiff.
Model 5.
Model 5 is based on Schartau et al. (2007) but neglects distinctions within the pool of DOM. The differential equations for dissolved organic carbon and nitrogen are provided in 2006jc003852-fs04.tiff, where PhyN = Phytoplankton nitrogen biomass, PhyC = Phytoplankton carbon biomass, DetN = Detrital nitrogen, DetC = Detrital carbon, DOC= labile and semilabile dissolved organic carbon, DON= labile and semilabile dissolved organic nitrogen, and Tf=Arrhenius relation (temperature dependence). Apart from phytoplankton growth parameters, a priori parameter values are first estimates, expressing the expected order of magnitude of the respective processes. Biomass specific remineralization rates for carbon and nitrogen are set equal: gamma_C = gamma_N = omega_C = rho_C = rho_N = 0.1 d-1. Other parameter values that differ from those used in Schartau et al. (2007) include: carbon specific maximum photosynthetic rate ((mu_C = 4.5 d-1), half saturation loss to herbivory ((epsilon = 0.1 mmol N2 m-6), nitrogen specific maximum grazing rate (gm = 0.1 d-1), degradation rate for chlorophyll a (gamma_Chl = 0.01 d-1), nitrogen specific remineralization rate (omega_N = 0.1 d-1) and the rate of phytoplankton-detritus particle aggregation ((Phi_PD = 10.0 m6 mmol N-2 d-1).
Model 8.
In this implementation, only two equations (given in 2006jc003852-fs05.tiff) were modified from Chai et al. (2002). Parameter and function definitions/values are given in Chai et al. (2002), except for a few parameters whose values have been modified and are also listed in 2006jc003852-fs05.tiff.
Model 9.
The forward (prognostic) version of the Laws et al. (2000) model (see 2006jc003852-fs06.tiff) was created by adding light dependent growth to both the large (X_2L) and small phytoplankton (X_2S) size classes so that their growth rate is modulated by both nutrient and light availability, and by incorporating explicit sinking of particulate organic matter (POM) with the remineralization products recycling directly back to the inorganic nutrient compartment. The nutrient (X1) equation (1) in Laws et al. (2000) was adjusted to include the loading term L which is now supplied via the 1-dimensional framework of the testbed through diffusion, entrainment and advection, and POM is remineralized back to the inorganic nutrient pool with the rate specified by the fractional POM loss rate D.
The growth rate term F_2S is both light and nutrient controlled, where rlt represents the PAR flux at depth and Ik_2S (Ik_2L) is the inflection point of the light saturation curve for small (large) phytoplankton. An explicit sinking term was also added to the POM equation (9) in Laws et al. (2000), where w_s is the sinking rate of POM and dPOM/dz is the vertical POM gradient. All of the other equations in the model are identical to those described in Laws et al. (2000), and all of the other terms and parameters that are not defined here are defined there.
Model 10.
Equations for Model 10 can be found in Fujii et al. (2002). Parameter values that differ from those listed in Fujii et al. (2002) are included in 2006jc003852-fs07.tiff.
Model 11.
This model is described by the equations given in 2006jc003852-fs08.tiff. State variables and functions appearing in these equations are defined in 2006jc003852-fs09.tiff. Parameter values are provided in 2006jc003852-fs10.tiff.