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PhD thesis models. 
Benjamin Mills, updated Febuary 2013. email: b.mills@uea.ac.uk or benjaminmills@live.com.

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i. General

These models were developed as part of my PhD project, the versions included are those used to generate the figures in 
the thesis. There are 3 models in this package, all of which are based on the simple box representations of the long term carbon cycle 
described in 'GEOCARB' (Berner 1991,1994,2006,2009, Berner and Kothavala, 2001) and 'COPSE' (Bergman, 2003, Bergman et al. 2004).
For full description of the model derivation and construction, and application to Earth history problems, see the accompanying PhD thesis (Mills, 2012).
Please get in touch if you have any queries.



ii. Archive contents

This package contains 6 m-files comprising 3 models. Each model consists of a frontend file and an equations file.



iii. Running the models


The models run in MATLAB and output figure (.fig) files on request, the output matrix Y is generated, containing all model variables and should be saved 
seperately. 
All output figures are labeled, the more complicated figures contain additional labels when viewed within the MATLAB plot browser. For all figures 
the x-axis shows time (t) in years and counts forward, t=0 corresponds to 4.5Ga and t=4.5e9 corresponds to the present day. Note, some shortening of figure
labels in the frontend files may be necessary to allow easy viewing of output on small computer screens.

For each model, the 'frontend' file is used to define parameters and to specify the solving method (as default the MATLAB inbuilt solver ode15s is used).
The 'equations' file contains the flux equations and reservoir calculations.

Each file has a 'user panel' included, which contains the majority of useful model alterations. The user panel in the frontend
files allows for chopice of parameters and solving methods. The user panel in the equations file is used to change the model forcing
functions or process equations.

The models can be run by activating the appropiate frontend script from the MATLAB command window or editor, 'current directory' must be set to the 
folder containing the frontend and equations scripts. 


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1. 'Minimal Model'

Contents: 	minimal_frontend.m 
		minimal_equations.m

A direct simplification of the methods employed in the GEOCARB and COPSE models, allowing reasonable 
replication of the Phanerozoic predictions from the original models. Options in the frontend file allow user to choose how the model 
approximates organic carbon and pyrite sulphur burial, following either the GEOCARB or COPSE methods. This model is derived and 
used in chapters 3 and 4.   

Running the model as set up here produces a reconstruction of Phanerozoic climate under the reduced forcing set (see thesis section 3.4).
To run the COPSE nutrient system, set isotopeforcing = 0 in the user panel. To run the GEOCARB isotope mass balance system, set isotopeforcing = 1.
Many of the experiments from the thesis can be conducted using this framework and changing the forcing functions.


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2. 'Snowball Model'

Contents: 	snowball_frontend.m 
		snowball_equations.m

The Snowball Model is designed specifically to analyze the dynamics of the long term carbon cycle over snowball Earth periods (Mills et al. (2011), 
thesis chapter 5). It is a simplification of the Minimal Model and is derived fully in the paper/thesis. Most model 
parameters are fixed at values for 650Ma.

This version has been updated to include CO2 removal via ocean crust carbonatization (see chapter 6) and supercedes the version
used in the paper. To remove the ocean crust carbonatization flux, set its present day rate ('Kocc' in the code) to zero.

Running the model as set up here will produce an analogue of figure 4 from Mills et al. (2011). Increasing the maximum transport-limited global
weathering rate ('tlimit' in the frontend user panel) can be seen to dramatically alter the timscale for system stabilisation between snowball events. 
The other figures from the paper can be viewed by adjusting parameters in the user panel and conducting ensemble runs.



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3. 'Mantle Model'


Contents: 	mantle_frontend.m 
		mantle_equations.m
	


The Mantle Model is an extension of the Minimal model documented in chapter 5 of the accompanying PhD thesis. New fluxes are added to represent
interaction of the surface system with the mantle, this radically changes predictions for atmospheric oxygen over the Proterozoic when
compared to the Minimal model.

Running the model as it is set up here produces predictions for climate over the last 2Ga. The default setup assumes alpha=0.23 and does not
include additional forcings PW1 and PW2 (see chap 5), changing the value of alpha (user panel, frontend) can be seen to dramatically alter 
the O2 predictions. Predictions for CO2 and temperature are affected greatly by additional forcings, these can be changed in the equations file
user panel.

	


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Bibliography


N.M. Bergman. COPSE: A New Biogeochemical Earth System Model for The
Phanerozoic. PhD thesis, University of East Anglia, (2003).

N.M. Bergman, T.M. Lenton, and A.J. Watson. COPSE: A new model
of biogeochemical cycling over Phanerozoic time. American Journal of
Science, 304(May), 397-437, (2004).

R.A. Berner. A model for atmospheric CO2 over Phanerozoic time. American
Journal of Science, 291, 339-376, (1991).

R.A. Berner. Geocarb II: A revised model of atmospheric CO2 over phanero-
zoic time. American Journal of Science, 294, 56-91, (1994).

R.A. Berner and Z. Kothavala. Geocarb III: A revised model of atmospheric
CO2 over Phanerozoic time. American Journal of Science, 301, 182-204 (2001).

R.A. Berner. GEOCARBSULF: A combined model for phanerozoic atmo-
spheric O2 and CO2. Geochimica et Cosmochimica Acta, 70, 5653-5664,
(2006).

R.A. Berner. Phanerozoic atmospheric oxygen: new results using the GEO-
CARBSULF model. American Journal of Science, 309, 603-603 (2009).

B. Mills, A.J. Watson, C. Goldblatt, R. Boyle, and T.M. Lenton. Timing of
Neoproterozoic glaciations linked to transport-limited global weathering.
Nature Geoscience, 4, 861-864, (2011).

B. Mills. Weathering pathways and limitations in biogeochemical models: Application to Earth
system evolution. PhD thesis, University of East Anglia, (2012).




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