MATLAB Code for CO2 Estimates from Leaf Stomatal Index 
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               World Data Center for Paleoclimatology, Boulder
                                  and
                     NOAA Paleoclimatology Program
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NOTE: PLEASE CITE ORIGINAL REFERENCE WHEN USING THIS DATA!!!!!


NAME OF DATA SET: MATLAB Code for CO2 Estimates from Leaf Stomatal Index 
LAST UPDATE: 7/2010  Addition of smooth_monotone.m function 
See Description below for details. Original receipt by WDC Paleo 1/2010 
CONTRIBUTORS: Beerling, D.J., A. Fox, and C.W. Anderson  
IGBP PAGES/WDCA CONTRIBUTION SERIES NUMBER: 2010-013 

WDC PALEO CONTRIBUTION SERIES CITATION: 
Beerling, D.J., et al. 2010. 
MATLAB Code for CO2 Estimates from Leaf Stomatal Index. 
IGBP PAGES/World Data Center for Paleoclimatology 
Data Contribution Series # 2010-013. 
NOAA/NCDC Paleoclimatology Program, Boulder CO, USA.


ORIGINAL REFERENCE: 
Beerling, D.J., A. Fox, and C.W. Anderson. 2009. 
Quantitative uncertainty analyses of ancient atmospheric 
CO2 estimates from fossil leaves. 
American Journal of Science, Vol. 309, pp. 775787, November 2009. 
doi:10.2475/09.2009.01  

ABSTRACT:  
The relationship between atmospheric CO2 and ancient climate is of
fundamental importance for gauging the climate sensitivity of the 
Earth system to a changing CO2 regime. One of the most widely adopted 
paleobiological CO2 proxies for reconstructing Earth's atmospheric CO2 
history exploits the inverse relationship between leaf stomatal index, 
the fraction of leaf epidermal cells that are stomatal structures, 
and atmospheric CO2. However, fossil leaf-based CO2 reconstructions
make a priori assumptions about the form of the empirical relationship 
between SI and CO2 required for transfer functions and have failed to 
correctly propagate error terms. These effects can translate into 
erroneous interpretations that undermine the value of the proxy. 
Here we report the development and application of a rigorous 
generalized statistical framework overcoming these limitations 
that generates probability density functions for each atmospheric 
CO2 estimate. The utility of our statistical tools is demonstrated 
by showing how they revise earlier atmospheric CO2 estimates from 
fossil cuticles of Ginkgo and Metasequoia trees during the early 
Eocene and middle Miocene warm periods upwards by +150 to 250 ppm 
to 450 to 700 ppm. The revised CO2 reconstructions therefore help 
to resolve the paradox of warm Paleogene and Neogene "greenhouse" 
climates co-existing with near present-day levels of CO2 and support 
the emerging view from independent paleoclimate studies for a high
climate sensitivity of the Earth system. The statistical tools 
presented are sufficiently versatile to permit their use in other 
investigations of paleoCO2 estimates from fossil leaves.


GEOGRAPHIC REGION: Global 
PERIOD OF RECORD:  N/A

FUNDING SOURCES:  
Leverhulme Trust award, Royal Society-Wolfson Research Merit Award 
(to DJB)


DESCRIPTION:   
Instructions for using the MATLAB programs simple_mono_smoother, 
obs_inverter and figure_plotter: AMF 08 04 2009

These programs rely completely upon that which accompanies 
Ramsey and Silverman (2002) Applied Data Analysis: Methods 
and case studies, in particular Chapter 6.

Their MATLAB code is available from 
ftp://ego.psych.mcgill.ca/pub/ramsay/FDAfuns/Matlab

First download this and install using the installation instructions there. 

1. It should then be relatively simple to first run the simple_mono_smoother 
   program, edited to read in your input file, ginkgo_data.csv is included 
   here as an example input file. Check the comments in this program and 
   make alterations as required in your case. The output from this program 
   is a MATLAB file (simple_out_g_030409.mat in this example) which contains 
   the evaluation of the 2000 fitted functions. 
   
   This uses the function smooth_monotone.m, which is included. Note that this
   is an earlier version of that which you will find in the FDA functions from 
   the above ftp site. The latest version of that function is not compatible 
   with our program, therefore we provide a copy of the earlier version. If you
   place this smooth_monotone.m in the same location as the other code provided 
   here then the simple_mono_smoother program will use that instead of the one 
   in the FDA functions.

2. Second, the obs_inverter program will then take the fossil leaf data 
   (ginkgo_foss_data_22.csv is provided as example) and invert these SI 
   values to give CO2. The output is another MATLAB file, 
   CO2_SI_statistics_060409.mat in this example, which contains the 
   statistics of the output PDFs and the data required to plot them.

3. Finally, the figure_plotter program uses both output .mat files to 
   produce figures like those in the AJS paper. It also contains the 
   code to calculate changes in global temperature (deltaT) on the 
   basis of CO2. The figures are not formatted in anyway for publication, 
   but they display the original data, the fitted curves, example PDFs 
   and plots of CO2 and deltaT against age. For these figures to look 
   their best, you also need the modified errorbar.m, errorbarxy.m 
   and errobargrey.m files which are included.