## 2.21.7. Final Decomposition Fluxes[¶](#final-decomposition-fluxes "Permalink to this headline")
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With \\({f}\_{immob\\\_demand}\\) known, final decomposition fluxes can be calculated. Actual carbon fluxes leaving the individual litter and SOM pools, again for the example of the CLM-CN pool structure (the CENTURY structure will be similar but, again without the different terminal step), are calculated as:

(2.21.31)[¶](#equation-21-32 "Permalink to this equation")\\\[\\begin{split}CF\_{Lit1} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, Lit1} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit1\\to SOM1} >0} \\\\ {CF\_{pot,\\, Lit1} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit1\\to SOM1} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.32)[¶](#equation-21-33 "Permalink to this equation")\\\[\\begin{split}CF\_{Lit2} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, Lit2} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit2\\to SOM2} >0} \\\\ {CF\_{pot,\\, Lit2} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit2\\to SOM2} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.33)[¶](#equation-21-34 "Permalink to this equation")\\\[\\begin{split}CF\_{Lit3} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, Lit3} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit3\\to SOM3} >0} \\\\ {CF\_{pot,\\, Lit3} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit3\\to SOM3} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.34)[¶](#equation-21-35 "Permalink to this equation")\\\[\\begin{split}CF\_{SOM1} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, SOM1} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM1\\to SOM2} >0} \\\\ {CF\_{pot,\\, SOM1} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM1\\to SOM2} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.35)[¶](#equation-21-36 "Permalink to this equation")\\\[\\begin{split}CF\_{SOM2} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, SOM2} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM2\\to SOM3} >0} \\\\ {CF\_{pot,\\, SOM2} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM2\\to SOM3} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.36)[¶](#equation-21-37 "Permalink to this equation")\\\[\\begin{split}CF\_{SOM3} =\\left\\{\\begin{array}{l} {CF\_{pot,\\, SOM3} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM3\\to SOM4} >0} \\\\ {CF\_{pot,\\, SOM3} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM3\\to SOM4} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.37)[¶](#equation-21-38 "Permalink to this equation")\\\[CF\_{SOM4} =CF\_{pot,\\, SOM4}\\\]

Heterotrophic respiration fluxes (losses of carbon as CO2 to the atmosphere) are:

(2.21.38)[¶](#equation-21-39 "Permalink to this equation")\\\[CF\_{Lit1,\\, HR} =CF\_{Lit1} rf\_{Lit1}\\\]

(2.21.39)[¶](#equation-21-40 "Permalink to this equation")\\\[CF\_{Lit2,\\, HR} =CF\_{Lit2} rf\_{Lit2}\\\]

(2.21.40)[¶](#equation-21-41 "Permalink to this equation")\\\[CF\_{Lit3,\\, HR} =CF\_{Lit3} rf\_{Lit3}\\\]

(2.21.41)[¶](#equation-21-42 "Permalink to this equation")\\\[CF\_{SOM1,\\, HR} =CF\_{SOM1} rf\_{SOM1}\\\]

(2.21.42)[¶](#equation-21-43 "Permalink to this equation")\\\[CF\_{SOM2,\\, HR} =CF\_{SOM2} rf\_{SOM2}\\\]

(2.21.43)[¶](#equation-21-44 "Permalink to this equation")\\\[CF\_{SOM3,\\, HR} =CF\_{SOM3} rf\_{SOM3}\\\]

(2.21.44)[¶](#equation-21-45 "Permalink to this equation")\\\[CF\_{SOM4,\\, HR} =CF\_{SOM4} rf\_{SOM4}\\\]

Transfers of carbon from upstream to downstream pools in the decomposition cascade are given as:

(2.21.45)[¶](#equation-21-46 "Permalink to this equation")\\\[CF\_{Lit1,\\, SOM1} =CF\_{Lit1} \\left(1-rf\_{Lit1} \\right)\\\]

(2.21.46)[¶](#equation-21-47 "Permalink to this equation")\\\[CF\_{Lit2,\\, SOM2} =CF\_{Lit2} \\left(1-rf\_{Lit2} \\right)\\\]

(2.21.47)[¶](#equation-21-48 "Permalink to this equation")\\\[CF\_{Lit3,\\, SOM3} =CF\_{Lit3} \\left(1-rf\_{Lit3} \\right)\\\]

(2.21.48)[¶](#equation-21-49 "Permalink to this equation")\\\[CF\_{SOM1,\\, SOM2} =CF\_{SOM1} \\left(1-rf\_{SOM1} \\right)\\\]

(2.21.49)[¶](#equation-21-50 "Permalink to this equation")\\\[CF\_{SOM2,\\, SOM3} =CF\_{SOM2} \\left(1-rf\_{SOM2} \\right)\\\]

(2.21.50)[¶](#equation-21-51 "Permalink to this equation")\\\[CF\_{SOM3,\\, SOM4} =CF\_{SOM3} \\left(1-rf\_{SOM3} \\right)\\\]

In accounting for the fluxes of nitrogen between pools in the decomposition cascade and associated fluxes to or from the soil mineral nitrogen pool, the model first calculates a flux of nitrogen from an upstream pool to a downstream pool, then calculates a flux either from the soil mineral nitrogen pool to the downstream pool (immobilization or from the downstream pool to the soil mineral nitrogen pool (mineralization). Transfers of nitrogen from upstream to downstream pools in the decomposition cascade are given as:

(2.21.51)[¶](#equation-21-52 "Permalink to this equation")\\\[NF\_{Lit1,\\, SOM1} ={CF\_{Lit1} \\mathord{\\left/ {\\vphantom {CF\_{Lit1} CN\_{Lit1} }} \\right.} CN\_{Lit1} }\\\]

(2.21.52)[¶](#equation-21-53 "Permalink to this equation")\\\[NF\_{Lit2,\\, SOM2} ={CF\_{Lit2} \\mathord{\\left/ {\\vphantom {CF\_{Lit2} CN\_{Lit2} }} \\right.} CN\_{Lit2} }\\\]

(2.21.53)[¶](#equation-21-54 "Permalink to this equation")\\\[NF\_{Lit3,\\, SOM3} ={CF\_{Lit3} \\mathord{\\left/ {\\vphantom {CF\_{Lit3} CN\_{Lit3} }} \\right.} CN\_{Lit3} }\\\]

(2.21.54)[¶](#equation-21-55 "Permalink to this equation")\\\[NF\_{SOM1,\\, SOM2} ={CF\_{SOM1} \\mathord{\\left/ {\\vphantom {CF\_{SOM1} CN\_{SOM1} }} \\right.} CN\_{SOM1} }\\\]

(2.21.55)[¶](#equation-21-56 "Permalink to this equation")\\\[NF\_{SOM2,\\, SOM3} ={CF\_{SOM2} \\mathord{\\left/ {\\vphantom {CF\_{SOM2} CN\_{SOM2} }} \\right.} CN\_{SOM2} }\\\]

(2.21.56)[¶](#equation-21-57 "Permalink to this equation")\\\[NF\_{SOM3,\\, SOM4} ={CF\_{SOM3} \\mathord{\\left/ {\\vphantom {CF\_{SOM3} CN\_{SOM3} }} \\right.} CN\_{SOM3} }\\\]

Corresponding fluxes to or from the soil mineral nitrogen pool depend on whether the decomposition step is an immobilization flux or a mineralization flux:

(2.21.57)[¶](#equation-21-58 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,\\, Lit1\\to SOM1} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, Lit1\\to SOM1} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit1\\to SOM1} >0} \\\\ {NF\_{pot\\\_ min,\\, Lit1\\to SOM1} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit1\\to SOM1} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.58)[¶](#equation-21-59 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,\\, Lit2\\to SOM2} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, Lit2\\to SOM2} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit2\\to SOM2} >0} \\\\ {NF\_{pot\\\_ min,\\, Lit2\\to SOM2} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit2\\to SOM2} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.59)[¶](#equation-21-60 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,\\, Lit3\\to SOM3} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, Lit3\\to SOM3} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit3\\to SOM3} >0} \\\\ {NF\_{pot\\\_ min,\\, Lit3\\to SOM3} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, Lit3\\to SOM3} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.60)[¶](#equation-21-61 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,SOM1\\to SOM2} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, SOM1\\to SOM2} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM1\\to SOM2} >0} \\\\ {NF\_{pot\\\_ min,\\, SOM1\\to SOM2} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM1\\to SOM2} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.61)[¶](#equation-21-62 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,SOM2\\to SOM3} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, SOM2\\to SOM3} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM2\\to SOM3} >0} \\\\ {NF\_{pot\\\_ min,\\, SOM2\\to SOM3} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM2\\to SOM3} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.62)[¶](#equation-21-63 "Permalink to this equation")\\\[\\begin{split}NF\_{sminn,SOM3\\to SOM4} =\\left\\{\\begin{array}{l} {NF\_{pot\\\_ min,\\, SOM3\\to SOM4} f\_{immob\\\_ demand} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM3\\to SOM4} >0} \\\\ {NF\_{pot\\\_ min,\\, SOM3\\to SOM4} \\qquad {\\rm for\\; }NF\_{pot\\\_ min,\\, SOM3\\to SOM4} \\le 0} \\end{array}\\right\\}\\end{split}\\\]

(2.21.63)[¶](#equation-21-64 "Permalink to this equation")\\\[NF\_{sminn,\\, SOM4} =NF\_{pot\\\_ min,\\, SOM4}\\\]