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Inverse method for estimating respiration rates from decay time series

D. Forney,D. Rothman

Published 2012 in Unknown venue

ABSTRACT

Long-term organic matter decomposition exper- iments typically measure the mass lost from decaying or- ganic matter as a function of time. These experiments can provide information about the dynamics of carbon dioxide input to the atmosphere and controls on natural respiration processes. Decay slows down with time, suggesting that or- ganic matter is composed of components (pools) with varied lability. Yet it is unclear how the appropriate rates, sizes, and number of pools vary with organic matter type, climate, and ecosystem. To better understand these relations, it is neces- sary to properly extract the decay rates from decomposition data. Here we present a regularized inverse method to iden- tify an optimally-fitting distribution of decay rates associ- ated with a decay time series. We motivate our study by first evaluating a standard, direct inversion of the data. The di- rect inversion identifies a discrete distribution of decay rates, where mass is concentrated in just a small number of dis- crete pools. It is consistent with identifying the best fitting "multi-pool" model, without prior assumption of the number of pools. However we find these multi-pool solutions are not robust to noise and are over-parametrized. We therefore in- troduce a method of regularized inversion, which identifies the solution which best fits the data but not the noise. This method shows that the data are described by a continuous distribution of rates, which we find is well approximated by a lognormal distribution, and consistent with the idea that de- composition results from a continuum of processes at differ- ent rates. The ubiquity of the lognormal distribution suggest that decay may be simply described by just two parameters: a mean and a variance of log rates. We conclude by describ- ing a procedure that estimates these two lognormal parame- ters from decay data. Matlab codes for all numerical methods and procedures are provided.

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