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This HOWTO describes some useful ferret commands for calculating inventories and fluxes from model output.

Ocean Carbon Integral in PgC:

This calculation is complicated by three things: the free surface which varies with time (hdt), partial bottem cells which do not vary with time (hdt), and the tri-polar grid (area_t). Currently, Ferret does not automatically account for any of these factors such that the ocean_grid and ocean_bgc files must have same output frequency to get precise integrals.
set memory/size=100
use 00020401.ocean_grid.nc
use 00020401.ocean_bgc.nc
let CO2_xyz_iint=((nsm+nlg+ndi+sdon+ldon)*117/16+dic)*dht[d=1]*area_t[d=1]
list CO2_xyz_iint[i=@sum,j=@sum,k=@sum]*12/1e15

Alternatively, the integral can be achieved with the following variable that takes into account the partial cells and variable free surface:
set memory/size=100
use 00020401.ocean_grid.nc
use 00020401.ocean_bgc.nc
let CO2_xyz_iint = carbon_tot_vert_int*area_t[d=1]
list CO2_xyz_iint[i=@sum,j=@sum,k=@sum]*12/1e15

Atmos-Ocean CO2 fluxes:

Changes in this integral over the simulation period approximated by:
list (CO2_xyz_iint[i=@sum,j=@sum,k=@sum,l=3]-CO2_xyz_iint[i=@sum,j=@sum,k=@sum,l=1])*12/1e15
should closely match the net gas exchange across the air-sea interface over this period:
let atmos_ocean_co2_flux = sfc_flux_co2*area_t[d=1]
list atmos_ocean_co2_flux[i=@sum,j=@sum,t=15-APR-0002:15-JUN-0002@din]*12/1e15
Though the comparison will not be exact do to the different averaging periods... in this case, it would be better to use snapshots of inventory spanning the flux averaging period, but those are not normally calculated. Also not the necessity aof accounting for the tripolar grid with area_t

Atmospheric Carbon Integral in PgC:

Since we are using an atmospheric model with a hybrid vertical coordinate, this calculation is a bit tricky. The gradient in pressure as determined by combining the the temporally fixed (i.e. hydrostatic) absolute pressure (PK) component and temproally variable sigma (PS*BK) coordinate at grid boundaries to get the overall mass in each layer using gravity (g = 9.80 m/s2 everywhere in the model). This mass is then converted into PgC using the molecular weights of air (assumed to be 28.96440 g/mol) and carbon (assumed to be 12 g/mol).
use 00020401.atmos_month.nc
let co2mass= co2*(PK[k=2:25]-PK[k=1:24]+PS*(BK[K=2:25]-BK[K=1:24]))/9.8*1000/28.96440*12/1e15
list co2mass[i=@din,j=@din,k=@sum]

Land-Atmos and Ocean-Atmos CO2 fluxes: This calculation is relatively simple, as it is based on a regular grid. The Ocean-Atmos CO2 flux calcualted here should be equivalent to -1 x the ocean-based atmos-ocean fluxes.

use 00020401.atmos_month.nc
let land_co2_flux = co2_flux*land_mask
list land_co2_flux[i=@din,j=@din,k=@sum,l=@ave]*86400*365*12/1e15
let ocean_co2_flux = co2_flux*(1-land_mask)
list ocean_co2_flux[i=@din,j=@din,k=@sum,l=@ave]*86400*365*12/1e15

Land Carbon Integral in PgC:

This just involves summing up vegetation and soil compartments all given in Kg/m2.
use 00020401.atmos_month.nc
use 00020401.veg_month.nc
let terrbio = (bl+br+blv+bsw+bwood+fsc+ssc)*land_mask[d=1]
list terrbio[i=@din,j=@din]/1e12

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