131: Access to the mean transit time
In SoilR: Models of Soil Organic Matter Decomposition

Description Usage Arguments Details Author(s) References

This generic function assembles methods to compute mean transit times. The nature of the results can change considerably depending on the arguments of the function. For an argument of class model it means something different than for an object of class DecompOp To interpret them correctly refer also to the documentation of the methods.

1	getMeanTransitTime(object, inputDistribution)

`object`	a DecompOp Object.
`inputDistribution`	a vector of length equal to the number of pools. The entries are weights, which must sum to 1.

The concept of mean transit time also known as mean residence time can be used to describe compartment models. In particular it is very frequently used to characterize linear time invariant compartment models in steady state. 1, 2, 3, 4. It is very important to note that SoilR is not limited to those. To integrate the concept into the more general context therefor requires some care. This starts with the definition. Assuming a time invariant system in steady state described by the (constant) distribution of inputs to the pools and constant decomposition and transfer rates one can define the mean transit time as the average time a package of carbon spends in the system from entry to exit. From SoilRs general perspective this defintion is ambigous with regard to several points.

It does not take into account that the mean transfer time may change itself with time. For time invariant models in steady state this does not matter since the mean transit time turns out to be time invariant also but for a general model in SoilR input fluxes and decomposition coefficients can be time dependent and the system as a whole far from steady state.
It does not specify the set of particles contributing to the mean value. If the system is forever in a steady state it is possible to think of the average transit time of all particles but if the system changes with time such a definition would not be to usefull. To be able to compare time dependent models with real measurements the set of particles leaving the system at a certain point in time is a more natural choice

To incorporate the concept of transit times into SoilR we need to address these ambiguities. We also would like the new definition to agree with the old one in the special but often studied case of linear systems in steady state. We suggest the following Definition:
Given a system described by the complete history of inputs \mathbf{I}(t) for t\in (t_{start},t_0) to all pools until time t_0 and the cumulative output O(t_0) of all pools at time t_0 the mean transit time \bar T_{t_0} of the system at time t_0 is the average of the transit times of all particles leaving the system at time t_0 Remark:
For a system with several output channels one could define the mean transit time of particles leaving by this specific channel. Remark:
In future versions of SoilR it will be possible to compute a dynamic, time dependent mean transit time for objects of class Model There is also a method that constructs a time invariant mean transit time by creting a time invariant model in steady state from an input flux distribution and a constant decompostion operators. This emphasizes that different methods for this function really answer different questions.

Carlos A. Sierra, Markus Mueller

Manzoni, S., G.G. Katul, and A. Porporato. 2009. Analysis of soil carbon transit times and age distributions using network theories. Journal of Geophysical Research-Biogeosciences 114, DOI: 10.1029/2009JG001070.

Thompson, M.~V. and Randerson, J.~T.: Impulse response functions of terrestrial carbon cycle models: method and application, Global Change Biology, 5, 371–394, 10.1046/j.1365-2486.1999.00235.x, 1999.

Bolin, B. and Rodhe, H.: A note on the concepts of age distribution and transit time in natural reservoirs, Tellus, 25, 58–62, 1973.

Eriksson, E.: Compartment Models and Reservoir Theory, Annual Review of Ecology and Systematics, 2, 67–84, 1971.

SoilR documentation built on May 4, 2017, 9:08 p.m.