### 2.18.4.2. Paid-for Retranslocation[¶](#paid-for-retranslocation "Permalink to this headline")

The remaining calculations conduct an iterative calculation to determine the degree to which N retranslocation from leaves is paid for as C:N ratios and thus cost increase as N is extracted. The iteration continues until either

1.  The cost of retranslocation (\\(cost\_{retrans}\\) increases beyond the cost of acquiring N from alternative pathways (\\(N\_{cost,tot}\\)).
    
2.  \\(CN\_{fallingleaf}\\) rises to a maximum level, after which no more extraction is possible (representing unavoidable N loss) or
    
3.  There is no more carbon left to pay for extraction.
    

First we calculate the cost of extraction (\\(cost\_{retrans}\\), gC/gN) for the current leaf C:N ratio as

> \\\[cost\_{retrans}= k\_{retrans} / (1/CN\_{fallingleaf})^{1.3}\\\]

where \\(k\_{retrans}\\) is a parameter controlling the overall cost of resorption, which also increases exponentially as the C:N ratio increases

Next, we calculate the amount of C needed to be spent to increase the falling leaf C:N ratio by 1.0 in this iteration \\(i\\) (\\(C\_{retrans\_spent,i}\\), gC m\-2) as:

\\\[C\_{retrans,spent,i} = cost\_{retrans}.(N\_{fallingleaf} - C\_{fallingleaf}/ (CN\_{fallingleaf} + 1.0))\\\]

(wherein the retranslocation cost is assumed to not change over the increment of 1.0 in C:N ratio). Next, we calculate whether this is larger than the remaining C available to spend.

> \\\[C\_{retrans,spent,i} = min(C\_{retrans,spent,i}, C\_{avail,retrans,i})\\\]

The amount of N retranslocated from the leaf in this iteration (\\(N\_{retrans\_paid,i}\\), gN m\-2) is calculated, checking that it does not fall below zero:

> \\\[N\_{retrans,paid,i} = min(N\_{fallingleaf},C\_{retrans,spent,i} / cost\_{retrans})\\\]

The next step calculates the growth C which is accounted for by this amount of N extraction in this iteration (\\(C\_{retrans,accounted,i}\\)). This is calculated using the current plant C:N ratio, and also for the additional C which will need to be spent on growth respiration to build this amount of new tissue.

> \\\[C\_{retrans,accounted,i} = N\_{retrans,paid,i} . CN\_{plant} . (1.0 + gr\_{frac})\\\]

Then the falling leaf N is updated:

> \\\[N\_{fallingleaf} = N\_{fallingleaf} - N\_{ret,i}\\\]

and the \\(CN\_{fallingleaf}\\) and cost\_{retrans} are updated. The amount of available carbon that is either unspent on N acquisition nor accounted for by N uptake is updated:

> \\\[C\_{avail,retrans,i+1} = C\_{avail,retrans,i} - C\_{retrans,spent,i} - C\_{retrans,accounted,i}\\\]

