4.9. Biogeochemistry Tutorial

(in directory: verification/tutorial_global_oce_biogeo/)

4.9.1. Overview

This model overlays the dissolved inorganic carbon biogeochemistry model (pkg/dic) over a 2.8o global physical model. The physical model has 15 levels, and is forced with a climatological annual cycle of surface wind stresses (Trenberth et al. 1989 [trenberth:89], surface heat and freshwater fluxes (Jiang et al. 1999 [jiang:99]) with additional relaxation toward climatological sea surface temperature and salinity (Levitus and Boyer (1994a,b) [levitus:94a][levitus:94b]). It uses the Gent and McWilliams (1990) [gen-mcw:90] eddy parameterization scheme, has an implicit free-surface, implicit vertical diffusion and uses the convective adjustment scheme.

The biogeochemical model considers the coupled cycles of carbon, oxygen, phosphorus and alkalinity. A simplified parameterization of biological production is used, limited by the availability of light and phosphate. A fraction of this productivity enters the dissolved organic pool pool, which has an e-folding timescale for remineralization of 6 months (following Yamanaka and Tajika 1997 [yamanaka:97]). The remaining fraction of this productivity is instantaneously exported as particulate to depth (Yamanaka and Tajika 1997 [yamanaka:97]) where it is remineralized according to the empirical power law relationship determined by Martin et al. (1987]) [martin:87]. The fate of carbon is linked to that of phosphorus by the Redfield ratio. Carbonate chemistry is explicitly solved (see Follow et al. 2006) [follows:06]) and the air-sea exchange of CO2 is parameterized with a uniform gas transfer coefficient following Wanninkhof (1992) [wannink:92]. Oxygen is also linked to phosphorus by the Redfield ratio, and oxygen air-sea exchange also follows Wanninkhof (1992) [wannink:92]. For more details see Dutkiewicz et al. (2005) [dutkiewicz:05].

The example setup described here shows the physical model after 5900 years of spin-up and the biogeochemistry after 2900 years of spin-up. The biogeochemistry is at a pre-industrial steady-state (atmospheric ppmv is kept at 278). Five tracers are resolved: dissolved inorganic carbon (\(DIC\)), alkalinity (\(ALK\)), phosphate (\(PO4\)), dissolved organic phosphorus (\(DOP\)) and dissolved oxygen (\(O2\)).

Modeled annual mean air-sea CO2

Figure 4.32 Modeled annual mean air-sea CO2 flux (mol C m-2 y-1) for pre-industrial steady-state. Positive indicates flux of CO2 from ocean to the atmosphere (out-gassing), contour interval is 1 mol C m-2 y-1.

4.9.2. Equations Solved

The physical ocean model velocity and diffusivities are used to redistribute the 5 tracers within the ocean. Additional redistribution comes from chemical and biological sources and sinks. For any tracer \(A\):

\[\frac{\partial A}{\partial t}=-\nabla \cdot (\vec{u^{*}} A)+\nabla \cdot (\mathbf{K}\nabla A)+S_A \nonumber\]

where \(\vec{u^{*}}\) is the transformed Eulerian mean circulation (which includes Eulerian and eddy-induced advection), \(\mathbf{K}\) is the mixing tensor, and \(S_A\) are the sources and sinks due to biological and chemical processes.

The sources and sinks are:

\[\begin{split}\begin{aligned} S_{DIC} & = & F_{CO_2} + V_{CO_2} + r_{C:P} S_{PO_4} + J_{Ca} \\ S_{ALK} & = & V_{ALK}-r_{N:P} S_{PO_4} + 2 J_{Ca} \\ S_{PO_4}& = & -f_{DOP} J_{prod} - \frac{\partial F_P}{\partial z} + \kappa_{remin} [DOP]\\ S_{DOP} & = & f_{DOP} J_{prod} -\kappa_{remin} [DOP] \\ S_{O_2} & = & \left\{ \begin{array}{ll} -r_{O:P} S_{PO_4} & \mbox{if $O_2>O_{2crit}$} \\ 0 & \mbox{if $O_2<O_{2crit}$} \end{array} \right. \end{aligned}\end{split}\]

where:

  • \(F_{CO_2}\) is the flux of CO2 from the ocean to the atmosphere
  • \(V_{CO_2}\) is “virtual flux” due to changes in \(DIC\) due to the surface freshwater fluxes
  • \(r_{C:P}\) is Redfield ratio of carbon to phosphorus
  • \(J_{Ca}\) includes carbon removed from surface due to calcium carbonate formation and subsequent cumulation of the downward flux of CaCO\(_3\)
  • \(V_{ALK}\) is “virtual flux” due to changes in alkalinity due to the surface freshwater fluxes
  • \(r_{N:P}\) Redfield ratio is nitrogen to phosphorus
  • \(f_{DOP}\) is fraction of productivity that remains suspended in the water column as dissolved organic phosphorus
  • \(J_{prod}\) is the net community productivity
  • \(\frac{\partial F_P}{\partial z}\) is the accumulation of remineralized phosphorus with depth
  • \(\kappa_{remin}\) is rate with which \(DOP\) remineralizes back to \(PO_4\)
  • \(F_{O_2}\) is air-sea flux of oxygen
  • \(r_{O:P}\) is Redfield ratio of oxygen to phosphorus
  • \(O_{2crit}\) is a critical level below which oxygen consumption if halted

These terms (for the first four tracers) are described more in Dutkiewicz et al. (2005) [dutkiewicz:05] and by McKinley et al. (2004) [mckinley:04] for the terms relating to oxygen.

4.9.3. Code configuration

The modifications to the code (in verification/tutorial_global_oce_biogeo/code) are:

  • code/SIZE.h: which dictates the size of the model domain (128x64x15).
  • code/PTRACERS_SIZE.h: which dictates how many tracers to assign how many tracers will be used (here, 5).
  • code/DIAGNOSTICS_SIZE.h: assigns size information for the diagnostics package.
  • code/packages.conf: which dictates which packages will be compiled in this version of the model - among the many that are used for the physical part of the model, this also includes pkg/ptracers, pkg/gchem, and pkg/dic which allow the biogeochemical part of this setup to function.

The input fields needed for this run (in verification/tutorial_global_oce_biogeo/input) are:

  • input/data: specifies the main parameters for the experiment. Some parameters that may be useful to know: nTimeSteps number timesteps model will run, change to 720 to run for a year taveFreq frequency with which time averages are done, change to 31104000 for annual averages.
  • input/data.diagnostics: specifies details of diagnostic pkg output
  • input/data.gchem: specifies details needed in the biogeochemistry model run
  • input/data.gmredi: specifies details for the GM parameterization
  • input/data.pkg: set true or false for various packages to be used
  • input/data.ptracers: details of the tracers to be used, including makes, diffusivity information and (if needed) initial files. Of particular importance is the PTRACERS_numInUse which states how many tracers are used, and PTRACERS_Iter0 which states at which timestep the biogeochemistry model tracers were initialized.
  • depth_g77.bin: bathymetry data file
  • input/eedata: This file uses standard default values and does not contain customizations for this experiment.
  • fice.bin: ice data file, needed for the biogeochemistry
  • lev_monthly_salt.bin: SSS values which model relaxes toward
  • lev_monthly_temp.bin: SST values which model relaxes toward
  • pickup.0005184000.data: variable and tendency values need to restart the physical part of the model
  • pickup_cd.0005184000.data: variable and tendency values need to restart the cd pkg
  • pickup_ptracers.0005184000.data: variable and tendency values need to restart the the biogeochemistry part of the model
  • shi_empmr_year.bin: freshwater forcing data file
  • shi_qnet.bin: heat flux forcing data file
  • sillev1.bin: silica data file, need for the biogeochemistry
  • tren_speed.bin: wind speed data file, needed for the biogeochemistry
  • tren_taux.bin: meridional wind stress data file
  • tren_tauy.bin: zonal wind stress data file

4.9.4. Running the example

As the model is set up to run in the verification experiment, it only runs for 4 timesteps (2 days) and outputs data at the end of this short run. For a more informative run, you will need to run longer. As set up, this model starts from a pre-spun up state and initializes physical fields and the biogeochemical tracers from the pickup files.

Physical data (e.g., S,T, velocities etc) will be output as for any regular ocean run. The biogeochemical output are:

  • tracer snapshots: look in input/data.ptracers to see which number matches which type of tracer (e.g., ptracer01 is DIC).
  • tracer time averages
  • specific DIC diagnostics: these are averaged over taveFreq (set in input/data) and are specific to pkg/dic (currently are only available in binary format):
    • DIC_Biotave: 3-D biological community productivity (mol P m-3 s-1)
    • DIC_Cartave: 3-D tendencies due to calcium carbonate cycle (mol C m-3 s-1)
    • DIC_fluxCO2ave: 2-D air-sea flux of CO2 (mol C m-2 s-1)
    • DIC_pCO2tave: 2-D partial pressure of CO2 in surface layer
    • DIC_pHtave: 2-D pH in surface layer
    • DIC_SurOtave: 2-D tendency due to air-sea flux of O2 (mol O m-3 s-1)
    • DIC_Surtave: 2-D surface tendency of DIC due to air-sea flux and virtual flux (mol C m-3 s-1)