### 2.20.1.2. 14.1.2 Offset Periods[¶](#offset-periods "Permalink to this headline")

The deciduous phenology algorithms also specify the occurrence of litterfall during offset periods. In contrast to the onset periods, only leaf and fine root state variables are subject to litterfall fluxes. Carbon fluxes from display pools into litter are calculated during these periods as:

(2.20.14)[¶](#equation-20-14 "Permalink to this equation")\\\[\\begin{split}CF\_{leaf,litter}^{n} =\\left\\{\\begin{array}{l} {CF\_{leaf,litter}^{n-1} + r\_{xfer\\\_ off} \\left(CS\_{leaf} -CF\_{leaf,litter}^{n-1} {\\kern 1pt} t\_{offset} \\right)\\qquad {\\rm for\\; }t\_{offset} \\ne \\Delta t} \\\\ {\\left({CS\_{leaf} \\mathord{\\left/ {\\vphantom {CS\_{leaf} \\Delta t}} \\right.} \\Delta t} \\right) \\left( 1-biofuel\\\_harvfrac \\right) +CF\_{alloc,leaf} \\qquad {\\rm for\\; }t\_{offset} =\\Delta t} \\end{array}\\right.\\end{split}\\\]

(2.20.15)[¶](#equation-20-15 "Permalink to this equation")\\\[\\begin{split}CF\_{froot,litter}^{n} =\\left\\{\\begin{array}{l} {CF\_{froot,litter}^{n-1} + r\_{xfer\\\_ off} \\left(CS\_{froot} -CF\_{froot,litter}^{n-1} {\\kern 1pt} t\_{offset} \\right)\\qquad {\\rm for\\; }t\_{offset} \\ne \\Delta t} \\\\ {\\left({CS\_{froot} \\mathord{\\left/ {\\vphantom {CS\_{froot} \\Delta t}} \\right.} \\Delta t} \\right)+CF\_{alloc,\\, froot} \\qquad \\qquad \\qquad {\\rm for\\; }t\_{offset} =\\Delta t} \\end{array}\\right.\\end{split}\\\]

(2.20.16)[¶](#equation-20-16 "Permalink to this equation")\\\[r\_{xfer\\\_ off} =\\frac{2\\Delta t}{t\_{offset} ^{2} }\\\]

where superscripts _n_ and _n-1_ refer to fluxes on the current and previous timesteps, respectively. The rate coefficient \\({r}\_{xfer\\\_off}\\) varies with time to produce a linearly increasing litterfall rate throughout the offset period. The \\(biofuel\\\_harvfrac\\) ([2.26.2.4.4](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Crop_Irrigation/CLM50_Tech_Note_Crop_Irrigation.html#harvest-to-food-and-seed)) is the harvested fraction of aboveground biomass (leaf & livestem) for bioenergy crops. The special case for fluxes in the final litterfall timestep (\\({t}\_{offset}\\) = \\(\\Delta t\\)) ensures that all of the displayed growth is sent to the litter pools or biofuel feedstock pools. The fraction (\\(biofuel\\\_harvfrac\\)) of leaf biomass going to the biofuel feedstock pools (Equation [(2.26.9)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Crop_Irrigation/CLM50_Tech_Note_Crop_Irrigation.html#equation-25-9)) is defined in Table 26.3 and is only non-zero for prognostic crops. The remaining fraction of leaf biomass (\\(1-biofuel\\\_harvfrac\\)) for deciduous plant types is sent to the litter pools. Similar modifications made for livestem carbon pools for prognostic crops can be found in section [2.26.2.4.4](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Crop_Irrigation/CLM50_Tech_Note_Crop_Irrigation.html#harvest-to-food-and-seed) in Equations [(2.26.9)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Crop_Irrigation/CLM50_Tech_Note_Crop_Irrigation.html#equation-25-9)\-[(2.26.14)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Crop_Irrigation/CLM50_Tech_Note_Crop_Irrigation.html#equation-25-14).

Corresponding nitrogen fluxes during litterfall take into account retranslocation of nitrogen out of the displayed leaf pool prior to litterfall (\\({NF}\_{leaf,retrans}\\), gN m\-2 s\-1). Retranslocation of nitrogen out of fine roots is assumed to be negligible. The fluxes are:

(2.20.17)[¶](#equation-20-17 "Permalink to this equation")\\\[NF\_{leaf,litter} ={CF\_{leaf,litter} \\mathord{\\left/ {\\vphantom {CF\_{leaf,litter} CN\_{leaf\\\_ litter} }} \\right.} CN\_{leaf\\\_ litter} }\\\]

(2.20.18)[¶](#equation-20-18 "Permalink to this equation")\\\[NF\_{froot,litter} ={CF\_{leaf,litter} \\mathord{\\left/ {\\vphantom {CF\_{leaf,litter} CN\_{froot} }} \\right.} CN\_{froot} }\\\]

(2.20.19)[¶](#equation-20-19 "Permalink to this equation")\\\[NF\_{leaf,retrans} =\\left({CF\_{leaf,litter} \\mathord{\\left/ {\\vphantom {CF\_{leaf,litter} CN\_{leaf} }} \\right.} CN\_{leaf} } \\right)-NF\_{leaf,litter} .\\\]

where CN is C:N.

