## 2.21.5. N-limitation of Decomposition Fluxes[¶](#n-limitation-of-decomposition-fluxes "Permalink to this headline")
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Decomposition rates can also be limited by the availability of mineral nitrogen, but calculation of this limitation depends on first estimating the potential rates of decomposition, assuming an unlimited mineral nitrogen supply. The general case is described here first, referring to a generic decomposition flux from an “upstream” pool (_u_) to a “downstream” pool (_d_), with an intervening loss due to respiration The potential carbon flux out of the upstream pool (\\({CF}\_{pot,u}\\), gC m\-2 s\-1) is:

(2.21.10)[¶](#equation-21-11 "Permalink to this equation")\\\[CF\_{pot,\\, u} =CS\_{u} k\_{u}\\\]

where \\({CS}\_{u}\\) (gC m\-2) is the initial mass in the upstream pool and \\({k}\_{u}\\) is the decay rate constant (s\-1) for the upstream pool, adjusted for temperature and moisture conditions. Depending on the C:N ratios of the upstream and downstream pools and the amount of carbon lost in the transformation due to respiration (the respiration fraction), the execution of this potential carbon flux can generate either a source or a sink of new mineral nitrogen (\\({NF}\_{pot\\\_min,u}\\)\\({}\_{\\rightarrow}\\)\\({}\_{d}\\), gN m\-2 s\-1). The governing equation (Thornton and Rosenbloom, 2005) is:

(2.21.11)[¶](#equation-21-12 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, u\\to d} =\\frac{CF\_{pot,\\, u} \\left(1-rf\_{u} -\\frac{CN\_{d} }{CN\_{u} } \\right)}{CN\_{d} }\\\]

where \\({rf}\_{u}\\) is the respiration fraction for fluxes leaving the upstream pool, \\({CN}\_{u}\\) and \\({CN}\_{d}\\) are the C:N ratios for upstream and downstream pools, respectively Negative values of \\({NF}\_{pot\\\_min,u}\\)\\({}\_{\\rightarrow}\\)\\({}\_{d}\\) indicate that the decomposition flux results in a source of new mineral nitrogen, while positive values indicate that the potential decomposition flux results in a sink (demand) for mineral nitrogen.

Following from the general case, potential carbon fluxes leaving individual pools in the decomposition cascade, for the example of the CLM-CN pool structure, are given as:

(2.21.12)[¶](#equation-21-13 "Permalink to this equation")\\\[CF\_{pot,\\, Lit1} ={CS\_{Lit1} k\_{Lit1} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{Lit1} k\_{Lit1} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.13)[¶](#equation-21-14 "Permalink to this equation")\\\[CF\_{pot,\\, Lit2} ={CS\_{Lit2} k\_{Lit2} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{Lit2} k\_{Lit2} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.14)[¶](#equation-21-15 "Permalink to this equation")\\\[CF\_{pot,\\, Lit3} ={CS\_{Lit3} k\_{Lit3} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{Lit3} k\_{Lit3} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.15)[¶](#equation-21-16 "Permalink to this equation")\\\[CF\_{pot,\\, SOM1} ={CS\_{SOM1} k\_{SOM1} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{SOM1} k\_{SOM1} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.16)[¶](#equation-21-17 "Permalink to this equation")\\\[CF\_{pot,\\, SOM2} ={CS\_{SOM2} k\_{SOM2} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{SOM2} k\_{SOM2} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.17)[¶](#equation-21-18 "Permalink to this equation")\\\[CF\_{pot,\\, SOM3} ={CS\_{SOM3} k\_{SOM3} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{SOM3} k\_{SOM3} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

(2.21.18)[¶](#equation-21-19 "Permalink to this equation")\\\[CF\_{pot,\\, SOM4} ={CS\_{SOM4} k\_{SOM4} r\_{total} \\mathord{\\left/ {\\vphantom {CS\_{SOM4} k\_{SOM4} r\_{total} \\Delta t}} \\right.} \\Delta t}\\\]

where the factor (1/\\(\\Delta\\)_t_) is included because the rate constant is calculated for the entire timestep (Eqs. and ), but the convention is to express all fluxes on a per-second basis. Potential mineral nitrogen fluxes associated with these decomposition steps are, again for the example of the CLM-CN pool structure (the CENTURY structure will be similar but without the different terminal step):

(2.21.19)[¶](#equation-zeqnnum934998 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, Lit1\\to SOM1} ={CF\_{pot,\\, Lit1} \\left(1-rf\_{Lit1} -\\frac{CN\_{SOM1} }{CN\_{Lit1} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, Lit1} \\left(1-rf\_{Lit1} -\\frac{CN\_{SOM1} }{CN\_{Lit1} } \\right) CN\_{SOM1} }} \\right.} CN\_{SOM1} }\\\]

(2.21.20)[¶](#equation-21-21 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, Lit2\\to SOM2} ={CF\_{pot,\\, Lit2} \\left(1-rf\_{Lit2} -\\frac{CN\_{SOM2} }{CN\_{Lit2} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, Lit2} \\left(1-rf\_{Lit2} -\\frac{CN\_{SOM2} }{CN\_{Lit2} } \\right) CN\_{SOM2} }} \\right.} CN\_{SOM2} }\\\]

(2.21.21)[¶](#equation-21-22 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, Lit3\\to SOM3} ={CF\_{pot,\\, Lit3} \\left(1-rf\_{Lit3} -\\frac{CN\_{SOM3} }{CN\_{Lit3} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, Lit3} \\left(1-rf\_{Lit3} -\\frac{CN\_{SOM3} }{CN\_{Lit3} } \\right) CN\_{SOM3} }} \\right.} CN\_{SOM3} }\\\]

(2.21.22)[¶](#equation-21-23 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, SOM1\\to SOM2} ={CF\_{pot,\\, SOM1} \\left(1-rf\_{SOM1} -\\frac{CN\_{SOM2} }{CN\_{SOM1} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, SOM1} \\left(1-rf\_{SOM1} -\\frac{CN\_{SOM2} }{CN\_{SOM1} } \\right) CN\_{SOM2} }} \\right.} CN\_{SOM2} }\\\]

(2.21.23)[¶](#equation-21-24 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, SOM2\\to SOM3} ={CF\_{pot,\\, SOM2} \\left(1-rf\_{SOM2} -\\frac{CN\_{SOM3} }{CN\_{SOM2} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, SOM2} \\left(1-rf\_{SOM2} -\\frac{CN\_{SOM3} }{CN\_{SOM2} } \\right) CN\_{SOM3} }} \\right.} CN\_{SOM3} }\\\]

(2.21.24)[¶](#equation-21-25 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, SOM3\\to SOM4} ={CF\_{pot,\\, SOM3} \\left(1-rf\_{SOM3} -\\frac{CN\_{SOM4} }{CN\_{SOM3} } \\right)\\mathord{\\left/ {\\vphantom {CF\_{pot,\\, SOM3} \\left(1-rf\_{SOM3} -\\frac{CN\_{SOM4} }{CN\_{SOM3} } \\right) CN\_{SOM4} }} \\right.} CN\_{SOM4} }\\\]

(2.21.25)[¶](#equation-zeqnnum473594 "Permalink to this equation")\\\[NF\_{pot\\\_ min,\\, SOM4} =-{CF\_{pot,\\, SOM4} \\mathord{\\left/ {\\vphantom {CF\_{pot,\\, SOM4} CN\_{SOM4} }} \\right.} CN\_{SOM4} }\\\]

where the special form of Eq. arises because there is no SOM pool downstream of SOM4 in the converging cascade: all carbon fluxes leaving that pool are assumed to be in the form of respired CO2, and all nitrogen fluxes leaving that pool are assumed to be sources of new mineral nitrogen.

Steps in the decomposition cascade that result in release of new mineral nitrogen (mineralization fluxes) are allowed to proceed at their potential rates, without modification for nitrogen availability. Steps that result in an uptake of mineral nitrogen (immobilization fluxes) are subject to rate limitation, depending on the availability of mineral nitrogen, the total immobilization demand, and the total demand for soil mineral nitrogen to support new plant growth. The potential mineral nitrogen fluxes from Eqs. - are evaluated, summing all the positive fluxes to generate the total potential nitrogen immobilization flux (\\({NF}\_{immob\\\_demand}\\), gN m\-2 s\-1), and summing absolute values of all the negative fluxes to generate the total nitrogen mineralization flux (\\({NF}\_{gross\\\_nmin}\\), gN m\-2 s\-1). Since \\({NF}\_{griss\\\_nmin}\\) is a source of new mineral nitrogen to the soil mineral nitrogen pool it is not limited by the availability of soil mineral nitrogen, and is therefore an actual as opposed to a potential flux.