model
it means something different than for an object of class
DecompOp
To interpret them correctly refer also to the documentation
of the methods.getMeanTransitTime(object, inputDistribution)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.
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.