# 198: System and pool age for compartment models In SoilR: Models of Soil Organic Matter Decomposition

## Description

Computes the density distribution and mean for the system and pool ages of a SoilR model or a matrix representation of a compartmental model

## Usage

 `1` ```systemAge(A, u, a = seq(0, 100)) ```

## Arguments

 `A` A compartmental linear square matrix with cycling rates in the diagonal and transfer rates in the off-diagonal. `u` A one-column matrix defining the amount of inputs per compartment. `a` A sequence of ages to calculate density functions

## Value

A list with 4 objects: mean system age, system age distribution, mean pool-age, and pool-age distribution.

## Author(s)

Carlos A. Sierra, Markus Mueller

`transitTime`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```# Gaudinski model ks = c(kr = 1/1.5, koi = 1/1.5, koeal = 1/4, koeah = 1/80, kA1 = 1/3, kA2 = 1/75, kM = 1/110) A = -abs(diag(ks)) A[3, 2] = ks[2] * (98/(3 + 98 + 51)) A[4, 3] = ks[3] * (4/(94 + 4)) A[6, 5] = ks[5] * (24/(6 + 24)) A[7, 6] = ks[6] * (3/(22 + 3)) A[7, 2] = ks[2] * (3/(3 + 98 + 51)) A[4, 1] = ks[1] * (35/(35 + 190 + 30)) A[5, 1] = ks[1] * (30/(35 + 190 + 30)) LI = 150 #Litter inputs RI = 255 #Root inputs In=matrix(nrow = 7, ncol = 1, c(RI, LI, 0, 0, 0, 0, 0)) ages=seq(0,200) ga=systemAge(A=A, u=In, a=ages) plot(ages, ga\$systemAgeDensity, type="l") abline(v=ga\$meanSystemAge, lty=2) legend("topright",c("System Age density", paste("Mean system age = ",ga\$meanSystemAge)), lty=1:2, bty="n") pools=c("Roots", "Oi", "Oe/a L", "Oe/a H", "A, LF (>80 um)", "A, LF (< 80 um)", "Min. Ass.") par(mfrow=c(3,2)) for(i in 2:7){ plot(ages,ga\$poolAgeDensity[,i],type="l", main=pools[i], ylab="Probability density", xlab="Age", bty="n") } par(mfrow=c(1,1)) ```