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Example: Modeling mass
loss due to decomposition
A new decomposition model representing litter mass remaining after
time t is developed. The new decomposition model was derived by
evaluating the assumptions and limitations of the commonly used simple
exponential decay model to derive a powerlaw generalization as a
nonlinear di erential equation. A closed form or integrated solution
of the new model is also derived for completeness. The powerlaw model
is shown to perform better than the simple exponential decay model for
long term projections, and it performed as well as a two compartment,
double exponential decay decomposition model representing fast and
slow decomposition fractions without the need to assume a second
compartment. A draft of the paper is
available. Please see the paper for model formulations and
parameter descriptions.
Needle litter decomposition data
plotted with fitted models: the power law model, simple
exponential decay, and the two compartment double exponential
decay model. 

For a single category of decomposable material, e.g., leaves,
needles, small twigs, etc., it seems unlikely that there are
identifiable fast and slow decomposition compartments over the
relevant time scale of months to years. This, then, begs the question
of whether the better fit of the double exponential, fast/slow model
is due solely to a regression effect, that is overfitting, by using a
sum of two simple exponential decay models. To address this question a
series of estimation problems was considered using simulated data sets
spanning time intervals of different lengths, 2.5 years to 10 years in
2.5 year increments. For each time interval simulated data were
generated from a base decomposition profile created using the power
law model estiamted from the needle litter data. Models were fit to
the simulated data and to the simulated data with 5% noise added.
Figures for each time span are presented below as well as tables of
the estimated parameter values and 95% confidence intervals for the
values.
Description 
No noise 
Noise added 
Projecting a 10 year trajectory for
each model using parameter values estimated from 2.5 years of
data with no noise and with 5% noise. 


Projecting a 10 year trajectory for
each model using parameter values estimated from 5 years of
data with no noise and with 5% noise. 


Projecting a 10 year trajectory for
each model using parameter values estimated from 7.5 years of
data with no noise and with 5% noise. 


Projecting a 10 year trajectory for
each model using parameter values estimated from 10 years of
data with no noise and with 5% noise. 


Tables of estimated parameter values
with 95% confidence intervals for each model and data set. See
the paper for parameter descriptions. 
Parameter
estimates without noise 
Parameter
estimates with noise 
