ARCHIEs JUN 28 2012 LIBRARIES

206 Pages·2012·27.58 MB·English

Emergent Properties of Heterogeneous Decomposition Networks
by
David C. Forney III
B.S. Mechanical Engineering, University of Delaware (2003)
S.M. Mechanical Engineering, MIT (2007)
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of ARCHIEs
Doctor of Philosophy in Mechanical Engineering MASSACHUSETTS INST E
OF TECHNOLOGy
at the
JUN 28 2012
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
June 2012
@ Massachusetts Institute of Technology 2012. All rights reserved.
x
A u th o r .... ......................... ........................... -
Department of Mechanical Engineering
May 8, 2012
4 /
Certified by. . . . . .. .. . . . . . ...
Daniel H. Rothman
Professor, EAPS
Thesis Supervisor
Certified by....... . ... ........
Anette Hosoi
Professor, ME
Thesis Chair
A ccep ted by ............ ................................................................
David E. Hardt
Chairman, Department Committee on Graduate Students
2
Emergent Properties of Heterogeneous Decomposition Networks
by
David C. Forney III
Submitted to the Department of Mechanical Engineering
on May 8, 2012, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Mechanical Engineering
Abstract
Organic matter respiration in natural ecosystems is controlled by a network of biologically, physi-
cally, and chemically driven processes. Often it is important to estimate total carbon flux from a
degradation system or the decay of mass in the system as a function of time. Historically, mass dy-
namics are predicted by a compartmental model consisting of various degradation processes. This
approach provides a complete picture of mass in the model system, but includes extra information
unnecessary for modeling overall mass dynamics. Furthermore, these models quickly become highly
parameterized and are kept tangible by reducing the number of processes and system states. This
thesis suggests a different approach. I allow the degradation system to be inherently complex, but
only consider a simple projection of the system necessary to characterize mass dynamics. Because
decomposing organic matter is often described as a heterogeneous continuum which transforms
and degrades over a wide range of rates, I model degradation as a network consisting of a large,
quasi-continuum of states. The retention of carbon in the network is then estimated by using an
eigenvalue projection to calculate the impulse response of the degradation system. For a continuous
network, the impulse response can be expressed as a Laplace transform of an "exit rate function." I
then pose and solve an inverse problem in order to identify the rates of exit of carbon from decom-
posing plant matter from across North America. Analysis of the calculated exit rate functions and
their associated decay data suggest that plant matter decomposition can often be mathematically
approximated by a continuum of parallel processes. Within this approximation, the solution of
the inverse problem yields the discovery that exit rate functions are on average lognormal. This
result suggests that the overall mass dynamics of complex decay networks often collapse to just two
parameters: the mean and the variance of the order of magnitude of exit rates from the network.
These parameters are then used to assess the effects of climate and litter chemistry on organic
carbon turnover and on rate heterogeneity. I also use observed patterns to explain the effect of
natural selection in microbial communities on degradation network kinetics.
Thesis Supervisor: Daniel H. Rothman
Title: Professor, EAPS
Thesis Chair: Anette Hosoi
Title: Professor, ME
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Acknowledgments
I first thank my parents for their support and for always providing me with the means to achieve
my dreams. They maintained a home and environment which gave me full access to knowledge
and information about the world. Anything was indeed possible in such an environment and I will
carry those feelings with me for life.
I thank my advisor Dan for providing me with the right tools, approach, and way of thinking for
tackling such a difficult, complex and unknown scientific problem. Journeys into problems like this
remind me of the journeys the great physicists Copernicus, Kepler, Newton, Heisenberg, Einstein,
and many others took over the last centuries. Attacking such problems theoretically with limited
information is not for the faint of heart. Finding and accepting success in such endeavors takes a
well-groomed mind. I also thank Dan for his continued support. Obtaining funding and a project
was THE hardest thing I had to overcome during grad school. Not even thesis writing or paper
publishing compared to jumping that difficult hurdle. I'm grateful to have had a home in the
Rothman lab where I could just think about science and not about my next meal.
I need to thank the members of the LIDET team for providing me with a huge and easy to
use data-set that I extensively used in this thesis. It is an extremely important data-set which will
provide futher understanding of ecosystems, ecology, and carbon cycling over the next few decades.
I am extremely grateful for the effort, organization and thought that they put into this study.
There have been a few heros in my life. However none of them compare to Rebecca J Hemenway.
Her ability to stay in touch with whats most important during our many orbits around the sun
amidst the numerous hurdles, walls, and bombs that come her way, and her courage to always rise
up to meet the next challenge face to face is absolutely inspiring. Her great sense of play as well
as her comprehensive approach to and perspective on issues dear to her and many others makes
the achievements here appear as mere goosebumps. No matter what happens in the future, your
efforts and passions that I have gotten to know over the recent few years will always inspire me
and catalyze similar efforts and passions that reside in me as well.
I also need to thank Chris Follett, for great discussions, especially in the months prior to the
submission of this thesis. His integrity, intuition, ability, and calm are exactly what is required to
excel at a place like MIT. He is also a hero and has been a great scientific peer and mentor for
others as well. Truly both a beauty and a geek.
I thank everyone else who has collaborated and inspired me during my time here in the Rothman
group: Yonatan, Alex P, Olivier, Hansjoerg, and Hyman, all of you have a great sense of humor
as well as an outstanding approach to science, I wish we collaborated more. Danny, Alex L, Mika,
Vid, all of you brought amazing backgrounds, tools, abilities and ways of thinking to the lab. I
wish I learned more from you all. Alex L, thanks for teaching me the wonders of the command line.
Mike A, and Robert, our time was short but you are both extremely able and fantastic. I'm sure
you will be successful. Keep your integrity and keep your nose to the grindstone. Just do what is
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right; you may make a few or many mistakes along the way but thats OK, success will come if you
persist.
I thank Prof. David Parks for offering me a position to teach 2.002, Mechanics of materials,
during my first semester. Without that gesture, I may not have attended MIT. I also thank him
for a research opportunity in his lab, which would have placed me in an exiting but also entirely
different place right now.
I thank Martin Polz and Peko for taking time out of their schedules to to discuss basic questions
with me and offer their honest insight during this past year. Your success at the institute and
positive attitudes are also very inspiring.
Finally, I need to thank the numerous waves of friends I've had here. Friendships in Boston are
constantly in flux as that is the nature of this city. Starting from the original snowriders crew, Joe
and Nici, and of course Alvin and Svea, to thirsty folks Craig, DQ, et al., to Khanh and Marcio,
and finally to my Euro-Bios for making the last few years here so fun and memorable. Boston is
a totally different place with you guys. Some of you remain, but most are gone as your journeys
take you elsewhere in this ever-changing and exciting world. Alas, it is now my turn to exit. I will
always remember and keep you in mind.
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Contents
1 Introduction 13
1.1 Overview of Thesis Results . . . . . . . . . . . . . . . . . . . . 14
1.2 Overview of Organic Carbon Degradation . . . . . . . . . . . . 15
1.3 A Common Kinetic Decay Pattern . . . . . . . . . . . . . . . . 17
1.4 A Different Approach to Decomposition Modeling . . . . . . . 17
1.5 A pplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.6 Types of Decay Systems Investigated . . . . . . . . . . . . . . . 24
1.6.1 D ata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.2 Role of litter in the carbon cycle . . . . . . . . . . . . . 25
1.7 O utline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Common Structure in the Heterogeneity of Plant-Matter Decay1 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Disordered Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1
2.2.2 Inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2
2.3 Rates are Distributed Lognormally . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Controls on the Lognormal Parameters . . . . . . . . . . . . . . . . . . . . . . . . 3 5
2.4.1 The mean p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 The variance o. . . . . . . . . ...... .. . . . . . . . . . . . . . . 36
2.4.3 Further trends . . . . . . . . . . . . . . . . . . . . 38 .
2.5 Scaling Up to the Carbon Cycle . . . . . . . . . . . . . . . . 39
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . - - - 41 .
2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7.1 Data screening . . . . . . . . . . . . . . . . . . . 43 .
2.7.2 Regularized inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.7.3 Unaveraged parameter analysis . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.7.4 Comparison of the lognormal and gamma distributions . . . . . . . . . . . . . 49
2.7.5 LIDET site descriptions . . . . . . . . . . . . . . . . . . . . . . . . . 51
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3 Inverse Method for Estimating Respiration Rates from Decay Time Series 53
3.1 Introduction . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 5 4
3.2 The Parallel Model of Decay ............. 56
3.3 Direct Inversion with Constraints ......... 57
3.3.1 Calculating the constrained direct inverse 57
3.3.2 Analysis of the multi-pool solutions . . . 60
3.3.3 Sensitivity to noise . . . . . . . . . . . . . 61
3.4 Regularized Inversion Method . . . . . . . . . . . 62
3.4.1 The L-Curve . . . . . . . . . . . . . . . . 62
3.4.2 Results of regularization . . . . . . . . . . 65
3.5 Fitting Lognormal Parameters to Decay Data . . 65
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . 68
4 Carbon Transit through Degradation Networks 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Degradation as a Network of Transformations . . . . . . . . 72
4.2.1 Two-state example . . . . . . . . . . . . . . . . . . . 73
4.2.2 A continuum of transformations . . . . . . . . . . . 74
4.3 Obtaining the Exit Rate Function r(k) from a Network . . 78
4.4 Example Systems . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.1 Calculating r(k) from a network with heterogeneous states and distributed
rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.2 Serial pools . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.3 Feedback processes . . . . . . . . . . . . . . . . . . . 80
4.5 Assembling Compartmental Models with Distributed Rates 83
4.5.1 Exit rates from the CENTURY model . . . . . . . . 83
4.6 Amorphous Networks . . . . . . . . . . . . . . . . . . . . . 85
4.7 Analyzing LIDET Data . . . . . . . . . . . . . . . . . . . . 86
4.7.1 Inversion of a LIDET dataset . . . . . . . . . . . . . 87
4.7.2 Inversion of 232 LIDET datasets . . . . . . . . . . . 89
4.8 Comparing the Exit Rate Function v(ln k) to a Distribution of Rates p(l n k) . . . 91
4.9 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.10 A ppendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.10.1 Solution to the two-state example problem . . . . . 96
4.10.2 Solving a linear system . . . . . . . . . . . . . . . . 98
4.10.3 Expressing mass loss in a network as a sum of exponentials 100
4.10.4 Im pulse response . . . . . . . . . . . . . . . . . . . . . . . . 101
4.10.5 Extrapolating the network to the continuum . . . . . . . . 102
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4.10.6 Calculating r(k) from a network with heterogeneous states and distributed
ra tes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103
4.10.7 Proof that constraints on q are sufficient to guarantee dg/dt <= 0...... . 103
4.10.8 Transfer function of the decomposition network . . . . . . . . . . . . . . . . . 107
5 Effect of Natural Selection on Degradation Kinetics 109
5.1 Estimating the Homefield Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2 Accounting for Substrate and Location Bias . . . . . . . . . . . . . . . . . . . . . . . 110
5.3 Significance of a Homefield Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6 Litter Decay with Climatic Fluctuations 115
6.1 Effect of Climate on Homogeneous Decay . . . . . . . . . . . . . . . . . . . . . . . . 115
6.1.1 Periodic T (t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1.2 Rescaling rates: averaging over seasonal variations . . . . . . . . . . . . . . . 116
6.2 Continuum of Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2.1 R escaling tim e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.2 Periodic temperature fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.3 Predicting seasonal or monthly decay . . . . . . . . . . . . . . . . . . . . . . 117
6.3 Random Temperature Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.1 Single rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.2 Reactive continuum with random temperatures . . . . . . . . . . . . . . . . . 118
6.3.3 Interpreting fitted values of p . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.4 Effect of Increasing Temperature . . . . . . . . . . . . . . . . . . . . . . . . . ... . 119
6.5 Interpreting the Effect of Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.6 Extension to the Exit Rate Function v(ln k) . . . . . . . . . . . . . . . . . . . . . . . 120
6.7 Effect of Temperature on o Agrees with Arrhenius . . . . . . . . . . . . . . . . . . . 120
6.8 Step Response of Carbon Stores from Changes in Climate . . . . . . . . . . . . . . . 121
6.9 Incorporating Time-Varying Decay Systems in Carbon Cycle Simulations . . . . . . 124
7 Conclusions 127
Appendix A Residence Times, Ages, and Turnover of Mass in Linear Time-Invariant
Systems 129
A.1 Impulse Response Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.2 Residence Time Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.3 Flux Out and Turnover Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.4 Age Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.5 Case of Random Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
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A.5.1 Mass with distributed rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.5.2 Outfluxes and turnover times associated with distributed rates . . . . . . . . 133
A.5.3 Residence times with distributed rates . . . . . . . . . . . . . . . . . . . . . . 134
A.5.4 Age distribution associated with distributed rates . . . . . . . . . . . . . . . . 134
A.5.5 Linear time invariant properties of a lognormal distribution of k . . . . . . . 134
A .6 Sum m ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.7 Predicting Soil Carbon Stores and Age in Field Experiments . . . . . . . . . . . . . 135
Appendix B Lognormally Distributed Rates and their Approximation 139
B.1 Decay Model Fits LIDET Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.2 Asymptotic Approximations of Lognormal Decay . . . . . . . . . . . . . . . . . . . . 140
B.3 Analytical Solutions to the Laplace Transform of the Lognormal Distribution . . . . 142
B .4 Loguniform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.4.1 Relations between lognormal and loguniform parameters . . . . . . . . . . . . 143
B.4.2 Comparing the Laplace transforms of the lognormal and loguniform distribu-
tion s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Appendix C Approximation of the Laplace Transform of the Lognormal: Moment
Closure 149
C.1 M otivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9
C.2 Standard Moment Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9
C.2.1 Set of raw moment equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 0
C.2.2 Set of central moment equations . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 1
C.2.3 Closing the moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 1
C.3 Modified Moment Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2
C.3.1 A partial closure method . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.3.2 A full closure method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
C.3.3 f(A) = -exp(A) . . . . . . . . . . . . . . . . . . . 154
C.4 Other Approximations to the Laplace Transform of the Lognormal . . . . . . . . . . 161
C.4.1 o- > 1 approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
C .4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Appendix D Instantaneous Reaction Rate K(t) 163
D.1 K(t) of Lognormally Distributed Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 163
D.2 Scaling K(t) from Multiple Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 166
D.2.1 Effect of o- and sampling time on pre-factor A . . . . . . . . . . . . . . . . . . 166
D.2.2 Characteristic values of a predict K(t) . . . . . . . . . . . . . . . . . . . . . . 168
D.3 Mass Scaling of Heterogeneous Substrates . . . . . . . . . . . . . . . . . . . . . . . . 168
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