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

# System and pool age for compartment models

### 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 |

### 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

### See Also

`transitTime`

### Examples

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))
``` |

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- 1: Converts from Delta14C to Absolute Fraction Modern
- 10: ~~ Methods for Function 'availableParticleProperties' ~~
- 100: ~~ Methods for Function 'getAccumulatedRelease' ~~
- 101: Calculates the accumulated carbon release from the pools as a...
- 102: getC14 method Model 14
- 103: ~~ Methods for Function 'getC14' ~~
- 104: Calculates the mass of radiocarbon (14C fraction times C...
- 105: getC method Model
- 106: ~~ Methods for Function 'getC' ~~
- 107: Calculates the C content of the pools
- 108: ~~ Methods for Function 'getCumulativeC' ~~
- 109: ~~ Methods for Function 'getDecompOp' ~~
- 11: ~~ Methods for Function 'availableParticleSets' ~~
- 110: ~~ Methods for Function 'getDotOut' ~~
- 111: read access to the models F14C variable
- 112: ~~ Methods for Function 'getF14C' ~~
- 113: Calculates the average radiocarbon fraction weighted by the...
- 114: radiocarbon
- 115: ~~ Methods for Function 'getF14' ~~
- 116: Calculates the 14C fraction of all pools
- 117: average radiocarbon fraction weighted by carbonrelease
- 118: ~~ Methods for Function 'getF14R' ~~
- 119: Calculates the average radiocarbon fraction weighted by the...
- 12: ~~ Methods for Function 'availableResidentSets' ~~
- 120: extract the format string
- 121: ~~ Methods for Function 'getFormat' ~~
- 122: creates a constant timedependent function and returns it
- 123: getFunctionDefinition method DecompositionOperator
- 124: ~~ Methods for Function 'getFunctionDefinition' ~~
- 125: getFunctionDefinition method TimeMap
- 126: getFunctionDefinition
- 127: ~~ Methods for Function 'getInFluxes' ~~
- 128: ~~ Methods for Function 'getInitialValues' ~~
- 129: compute the mean transit time
- 13: Implementation of the microbial model AWB (Allison,...
- 130: ~~ Methods for Function 'getMeanTransitTime' ~~
- 131: Access to the mean transit time
- 132: ~~ Methods for Function 'getNumberOfPools' ~~
- 133: ~~ Methods for Function 'getOutputFluxes' ~~
- 134: ~~ Methods for Function 'getOutputReceivers' ~~
- 135: ~~ Methods for Function 'getParticleMonteCarloSimulator' ~~
- 136: 14C respiration rate for all pools
- 137: ~~ Methods for Function 'getReleaseFlux14' ~~
- 138: Calculates the mass of radiocarbon in the release flux (14C...
- 139: get the release rate for all pools
- 14: Implementation of the microbial model Bacwave (bacterial...
- 140: ~~ Methods for Function 'getReleaseFlux' ~~
- 141: Calculates the release of C from each pool
- 142: return an (infinite) time range since the operator is...
- 143: ask for the boundaries of the underlying time interval
- 144: ~~ Methods for Function 'getTimeRange' ~~
- 145: ask for the boundaries of the underlying time interval
- 146: getTimeRange
- 147: getTimes method Model
- 148: ~~ Methods for Function 'getTimes' ~~
- 149: Extracts the times argument
- 15: Binding of pre- and post-bomb Delta14C curves
- 150: ~~ Methods for Function 'getTransferCoefficients' ~~
- 151: ~~ Methods for Function 'getTransferMatrix' ~~
- 152: compute the TransitTimeDistributionDensity
- 153: ~~ Methods for Function 'getTransitTimeDistributionDensity'...
- 154: methods for transit time distributions
- 155: ~~ Methods for Function 'getValues' ~~
- 156: Delta14C in soil CO2 efflux from Harvard Forest
- 157: Atmospheric radiocarbon for the period 1950-2010 from Hua et...
- 158: Implementation of the Introductory Carbon Balance Model...
- 159: Class '"InFlux"'
- 16: Class '"BoundFc"'
- 160: pass through constructor
- 161: ~~ Methods for Function 'InFlux' ~~
- 162: create a BoundInFlux from a TimeMap object
- 163: internal constructor (new)
- 164: internal constructor
- 165: initialize called by (new)
- 166: An internal constructor for 'Model_14' objects not...
- 167: internal constructor for Model objects
- 168: ~~ Methods for Function 'initialize' ~~
- 169: initialize called by (new)
- 17: constructor
- 170: Northern Hemisphere atmospheric radiocarbon for the pre-bomb...
- 171: Atmospheric radiocarbon for the 0-50,000 yr BP period
- 172: Add lines with the output of 'getC14', 'getC', or...
- 173: Class '"Model_14"'
- 174: ~~ Methods for Function 'Model_14' ~~
- 175: A general constructor
- 176: Class '"Model"'
- 177: general constructor for class Model
- 178: ~~ Methods for Function 'Model' ~~
- 179: A general constructor
- 18: constructor
- 180: Implementation of a one-pool C14 model
- 181: Implementation of a one pool model
- 182: ParallelModel
- 183: Plots the output of 'getF14' for each pool over time
- 184: Plots the output of 'getC' or 'getReleaseFlux' for each pool...
- 185: not yet implemented method to plot an overview of several...
- 186: ~~ Methods for Function 'plot' ~~
- 187: not yet implemented method to print an overview of several...
- 188: ~~ Methods for Function 'print' ~~
- 189: helper function to compute respiration coefficients
- 19: constructor
- 190: Implementation of the RothCModel
- 191: General m-pool linear C14 model with series structure
- 192: General m-pool linear model with series structure
- 193: show method Model
- 194: ~~ Methods for Function 'show' ~~
- 195: \Sexpr[results=rd,stage=build]{tools:::Rd_package_title("SoilR")}
- 196: summary method Model
- 197: ~~ Methods for Function 'summary' ~~
- 198: System and pool age for compartment models
- 199: Implementation of a 6-pool Michaelis-Menten model
- 2: Converts from Delta14C to Absolute Fraction Modern
- 20: constructor
- 200: Implementation of a three-pool C14 model with feedback...
- 201: Implementation of a three pool model with feedback structure
- 202: Implementation of a three-pool C14 model with parallel...
- 203: Implementation of a three pool model with parallel structure
- 204: Implementation of a three-pool C14 model with series...
- 205: Implementation of a three pool model with series structure
- 206: Class '"TimeMap"'
- 207: TimeMap from Dataframe
- 208: constructor
- 209: constructor
- 21: constructor
- 210: ~~ Methods for Function 'TimeMap' ~~
- 211: deprecated constructor of the class TimeMap.
- 212: generic constructor
- 213: Transit times for compartment models
- 214: Estimation of the turnover time from a soil radiocarbon...
- 215: Implementation of a two-pool C14 model with feedback...
- 216: Implementation of a two pool model with feedback structure
- 217: Implementation of a two-pool Michaelis-Menten model
- 218: Implementation of a two-pool C14 model with parallel...
- 219: Implementation of a linear two pool model with parallel...
- 22: constructor
- 220: Implementation of a two-pool C14 model with series structure
- 221: Implementation of a two pool model with series structure
- 222: Implementation of the Yasso07 model
- 223: Implementation of the Yasso model.
- 224: (experimenta) partially overload [ ] for models
- 225: ~~ Methods for Function '[' ~~
- 226: ~~ Methods for Function '[[<-' ~~
- 227: ~~ Methods for Function '[[' ~~
- 228: ~~ Methods for Function '$' ~~
- 23: ~~ Methods for Function 'BoundFc' ~~
- 24: generic constructor
- 25: Class '"BoundInFlux"'
- 26: constructor
- 27: constructor
- 28: constructor
- 29: constructor
- 3: ~~ Methods for Function...
- 30: ~~ Methods for Function 'BoundInFlux' ~~
- 31: convert to BoundInFlux
- 32: generic constructor
- 33: Class '"BoundLinDecompOp"'
- 34: convert a ConstLinDecompOp to a BoundLinDecompOp
- 35: a constructor
- 36: a constructor
- 37: ~~ Methods for Function 'BoundLinDecompOp' ~~
- 38: create a BoundLinDecompOp from a TimeMap
- 39: Generic constructor
- 4: Converts its argument to an Absolute Fraction Modern...
- 40: Post-bomb atmospheric 14C fraction
- 41: Atmospheric 14C fraction
- 42: Implementation of the Century model
- 43: ~~ Methods for Function 'computeResults' ~~
- 44: creates an object containing the initial values for the 14C...
- 45: Class '"ConstLinDecompOp"'
- 46: construct from matric
- 47: ~~ Methods for Function 'ConstLinDecompOp' ~~
- 48: Generic constructor
- 49: Class '"DecompOp"'
- 5: convert to Absolute Fraction Normal values
- 50: pass through constructor
- 51: creates a ConstanDecompOp from a matrix
- 52: ~~ Methods for Function 'DecompOp' ~~
- 53: creates a BoundLinDecompOp from a TimeMap object
- 54: Class '"DecompositionOperator"'
- 55: Converts Absolute Fraction Modern values to Delta14C
- 56: Converts to Delta14C format
- 57: ~~ Methods for Function...
- 58: Converts its argument from an Absolute Fraction Modern to a...
- 59: convert to Absolute Fraction Normal values
- 6: ~~ Methods for Function 'AbsoluteFractionModern' ~~
- 60: ~~ Methods for Function 'Delta14C' ~~
- 61: deSolve lsoda wrapper
- 62: Soil CO2 efflux from an incubation experiment
- 63: ~~ Methods for Function 'fromDataFrame' ~~
- 64: assemble the objects components
- 65: Effects of temperature on decomposition rates according the...
- 66: Effects of temperature on decomposition rates according the...
- 67: Effects of temperature on decomposition rates according the...
- 68: Effects of temperature on decomposition rates according to...
- 69: Effects of temperature on decomposition rates according to...
- 7: ~~ Methods for Function 'as.character' ~~
- 70: Effects of temperature on decomposition rates according to...
- 71: Effects of temperature on decomposition rates according to a...
- 72: Effects of temperature on decomposition rates according to a...
- 73: Effects of temperature on decomposition rates according to a...
- 74: Effects of temperature on decomposition rates according to a...
- 75: Effects of temperature on decomposition rates according to...
- 76: Effects of temperature on decomposition rates according to...
- 77: Effects of moisture on decomposition rates according to the...
- 78: Effects of moisture on decomposition rates according to the...
- 79: Effects of moisture on decomposition rates according to the...
- 8: convert TimeMap Objects to something printable.
- 80: Effects of moisture on decomposition rates according to the...
- 81: Effects of moisture on decomposition rates according to the...
- 82: Effects of moisture on decomposition rates according to the...
- 83: Effects of moisture on decomposition rates according to the...
- 84: Effects of moisture on decomposition rates according to the...
- 85: Effects of moisture on decomposition rates according to the...
- 86: Effects of moisture on decomposition rates according to the...
- 87: Implementation of a the six-pool C14 model proposed by...
- 88: a constructor for class Model
- 89: a constructor for class Model_14
- 9: creates a character representation of the object in question
- 90: a constructor for class Model <- 14
- 91: a constructor for class Model_ 14
- 92: a constructor for class Model
- 93: a constructor for class Model
- 94: ~~ Methods for Function 'GeneralModel_14' ~~
- 95: A general constructor
- 96: a constructor for class Model
- 97: ~~ Methods for Function 'GeneralModel' ~~
- 98: A general constructor
- 99: time integrals of release fluxes per pool
- manMan/as.character: creates a character representation of the object in question
- manMan/C14Atm: Atmospheric 14C fraction
- manMan/C14Atm_NH: Post-bomb atmospheric 14C fraction
- manMan/eCO2: Soil CO2 efflux from an incubation experiment
- manMan/HarvardForest14CO2: Delta14C in soil CO2 efflux from Harvard Forest
- manMan/Hua2013: Atmospheric radiocarbon for the period 1950-2010 from Hua et...
- manMan/IntCal09: Northern Hemisphere atmospheric radiocarbon for the pre-bomb...
- manMan/IntCal13: Atmospheric radiocarbon for the 0-50,000 yr BP period