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<h1 class="title toc-ignore">Analysis of GPWGv3 Data Using R</h1>
</div>
<div id="TOC">
<ul>
<li><a href="#introduction" id="toc-introduction">Introduction</a></li>
<li><a href="#data" id="toc-data">Data</a></li>
<li><a href="#analysis-steps" id="toc-analysis-steps">Analysis steps</a>
<ul>
<li><a href="#query-and-site-.csv-files"
id="toc-query-and-site-.csv-files">1 Query and site .csv files</a></li>
<li><a href="#transformation-and-standardizationanomalization"
id="toc-transformation-and-standardizationanomalization">2
Transformation and standardization/anomalization</a></li>
<li><a href="#presamplingprebinning" id="toc-presamplingprebinning">3
Presampling/prebinning</a></li>
<li><a href="#composite-i.e.-smooth-curves-and-bootstrap-c.i.s"
id="toc-composite-i.e.-smooth-curves-and-bootstrap-c.i.s">4 Composite
(i.e. smooth) curves and bootstrap C.I.’s</a></li>
</ul></li>
</ul>
</div>
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>This is a set of web pages that describe the development of a
composite curve of charcoal data drawn from the Global Charcoal Database
version 3, (GCDv3) using a set of R scripts. The intention here is to
explicitly document the analysis steps that were developed originally as
a set of Fortran programs, and which are now implemented in the R
<code>paleofire</code> package. The R scripts described here can also be
used as a point of departure for the development of new analysis
approaches.</p>
<p>The data source for these examples is a Microsoft Access
(<code>.mdb</code>) database, downloaded from <a
href="http:https://www.gpwg.paleofire.org/">[http:https://www.gpwg.paleofire.org/]</a>,
e.g., <code>GCDv03_Marlon_et_al_2015.mdb</code>. In the example here,
the scripts aim to reproduce the “Globe” curve in Fig. 6 of Marlon et
al. (2016).</p>
</div>
<div id="data" class="section level1">
<h1>Data</h1>
<p>The data used in this example are contained in two queries, saved as
“database” views or internal tables in the Microsoft Access database
named <code>GCDv03_Marlon_et_al_2015.mdb</code>, downloadable from the
Global Charcoal Database <a
href="http:https://paleofire.org/">[http:https://paleofire.org/]</a> by exporting
the full database. The queries are named (for historical reasons)
<code>ALL_BART_SITES</code> and <code>ALL_BART_DATA</code> and reside in
the Access database as “view”. <code>ALL_BART_SITES</code> contains a
list of sites, their names and locations, the depositional environment,
and the units of measurement (i.e. influx, concentration, etc.) while
<code>ALL_BART_DATA</code> contains the id, age, depth and quantity of
charcoal in each sample.</p>
<p>For the examples here, the following folder structure for the data
was used:</p>
<pre><code> /Projects/GPWG/GPWGv3/GCDv3Data/v3i/
v3i_curves/
v3i_debug/
v3i_mdb/
v3i_presamp_csv/
v3i_query/
v3i_sitelists/
v3i_sites_csv/
v3i_stats/
v3i_trans_csv/</code></pre>
<p>The the root folder and <code>v3i-mdb/</code> (into which the
database should be copied) are created by the user, and the others are
created during the analyses.</p>
</div>
<div id="analysis-steps" class="section level1">
<h1>Analysis steps</h1>
<p>There are four steps in the analysis:</p>
<ol style="list-style-type: decimal">
<li>reading the query results from the data base and making individual
“site” .csv files</li>
<li>transforming and standardizing or normalizing (i.e. converting to
anomalies) the individual records</li>
<li>implementing the presampling/prebinning step</li>
<li>composite-curve fitting using the R locfit() function, or via
binning, and estimating uncertainties via bootstrapping</li>
</ol>
<div id="query-and-site-.csv-files" class="section level2">
<h2>1 Query and site .csv files</h2>
<p>(<code>mdb-to-csv.R</code>)</p>
<p>The first step in the analysis approach here involves examining the
two query tables, checking for obvious issues in the data for individual
sites, converting all charcoal data to both influx and concentration
values, and finally extracting individual .csv files for each site. All
of the scripts here begin by setting appropriate path and folder names.
In the example script, the Access database files are read directly using
the <code>RODBC</code> package. (Note that on Windows, compiled versions
of this package exist, and a the appropriate database drivers are built
into the operating system. On OS X, a third-party database driver must
be used, and the <code>RODBC</code> package compiled from source. There
is a separate script, <code>mdb-to-csv_osx.R</code> that illustrates
this.</p>
<p>The main part of the script loops over the individual sites that are
specified in the site query, and does various checks and calculations,
including</p>
<ul>
<li>calculation of sedimentation rates and deposition times</li>
<li>checking for age or depth reversals, or other data issues</li>
<li>calculation of alternative quantities (e.g. influx, given
concentrations)</li>
<li>writing out a .csv file for each site</li>
</ul>
<p>The calculation of sedimentation rates and deposition times is
required for the conversion of concentration values to influx values and
vice-versa. Various checks for age reversals, zero sedimentation rates,
missing data are done. Typically, when a number of sites are added to
the database, there will be issues, which are flagged by this step and
resolved. In the example, such is not the case, but the script
illustrates those checks in any case. The last part of this analysis
step involves writing out one “site data” .csv file for each site
(e.g. <code>0001_data.csv</code>), plus a single “sitelist” file
(e.g. <code>v3i_all.csv</code>), which can be edited to control the
particular selection of sites that are analyzed.</p>
<p>New data not included in the database can be added to the analysis by
creating by hand a “site data” .csv file with the same format as those
created by <code>mdb-to-csv.R</code> and adding a line to the sitelist
file.</p>
</div>
<div id="transformation-and-standardizationanomalization"
class="section level2">
<h2>2 Transformation and standardization/anomalization</h2>
<p>(<code>trans-and-zscore.R</code> &
<code>trans-and-norman.R</code>)</p>
<p>Charcoal data are reported in units that range over thirteen orders
of magnitude, and charcoal records typically have “long-tailed”
distributions (Power et al., 2010). In order to compare or combine
records, the data must therefore be transformed to approach normality
(to reduce the impacts of non-constant variance) and rescaled to some
common basis or range. In one example here
(<code>trans-and-zcore.R</code>), we apply the variance-stabilzing
Box-Cox transformation, and rescale the data to “z-scores”. (For
historical reasons, the transformed data are also rescaled using the
“minimax” transformation so that all values lie between 0 and 1. This
reduces astonishment over transformed charcoal-influx or concentration
values that may wind up being negative after transformation.) This
approach also requires the specification of a base period or time
interval over which the transformation parameters are estimated and the
mean and standard deviation used for calculating z-scores are
calculated. Further discussion of this approach can be found in Power et
al. (2010) and Daniau et al. (2012).</p>
<p>A second example (<code>trans-and-norman.R</code>), illustrates the
use of “normalized” anomalies, in which the deviations of the
transformed charcoal influx values from a base period mean value are
divided by that mean value, to produce a relative deviation, scaled by
the overall level of the data. This approach is useful for
last-millennium type analyses, where records with few samples can
produce standard deviations that are not robust, and hence z-scores that
vary dramatically.</p>
<p>The specific tasks implemented by the script include, for each
site:</p>
<ul>
<li>censoring of samples with missing ages or ages after 2020 CE</li>
<li>maximum likelihood estimation of of the Box-Cox transformation
parameter <code>lambda</code></li>
<li>Box-Cox transformation of data</li>
<li>minimax rescaling of the transformed data<code>tall</code></li>
<li>calculation z-scores <code>ztrans</code> or normalized anomalies
<code>normans</code></li>
<li>writing out the transformed data for this site as a .csv file.</li>
</ul>
</div>
<div id="presamplingprebinning" class="section level2">
<h2>3 Presampling/prebinning</h2>
<p>(<code>presample-bin.R</code>)</p>
<p>Charcoal data are available at all kinds of “native” resolutions,
from samples that represent decades or centuries (or longer) to those
that represent annual deposition. Further, some records have been
interpolated to pseudo-annual time steps. In developing composite
curves, those records with higher resolutions will contribute
disproportionately to the curve. There are two general approaches for
dealing with this: 1) weighting individual charcoal (influx or
concentration) values according to their resolution, with
lower-resolution records receiving higher weights, and vice-versa, or 2)
reducing the sampling frequency of the records to some common interval
(without interpolating or creating pseudo data). We adopted the latter
approach for its simplicity and transparency.</p>
<p>The binning is done by establishing a set of evenly spaced target
points or bins, and then for each charcoal record, binning the
individual observations. If more that one observation falls in the same
bin, the average (of he transformed and standardized data) is taken as
the binned value. No effort is made to interpolate between observations,
to avoid pseudo-replication. A .csv file is written out for each
site.</p>
</div>
<div id="composite-i.e.-smooth-curves-and-bootstrap-c.i.s"
class="section level2">
<h2>4 Composite (i.e. smooth) curves and bootstrap C.I.’s</h2>
<p>(<code>smooth-curve.R</code> & <code>bin-boot.R</code>)</p>
<p>The first script (<code>smooth-curve.R</code>) uses
<code>locfit()</code> to get a (smooth) composite curve of the
(presampled/binned) charcoal z-scores or normans for a set of sites
specified by an input “sitelist” (ultimately based on all or a subset of
the sites listed in the <code>ALL_BART_SITES</code> query). The
smoothness of the curve is determined by the width of the smoothing
window, customarily specified by the “half-width” (<code>hw</code>).
First, a “global” curve (in the sense of using all of the data from a
particular list of sites is determined, and the number of sites with
samples (<code>ndec_tot</code>, for historical reasons) and the number
of samples that contribute to each fitted value
(<code>ninwin_tot</code>) are also calculated.</p>
<p>Then, over <code>nreps</code> replications, the data are sampled by
site (with replacement) to calculate bootstrap confidence intervals, and
the upper and lower 95th-percentile confidence intervals are determined.
In the example here, the curves produced by individual bootstrap samples
are plotted (in transparent gray), and the “global” curve is overplotted
in red to give a visual indication of the uncertainty in the composite
curve arising from the particular sample of sites.</p>
<p>The second script (<code>bin-boot.R</code>) creates a composite
“curve” by directly binning each charcoal influx value in
non-overlapping bins, and then calculating a simple average of the
values in each bin. This approach can be used over the past few
millennia, where the median sample density is generally less than 20
years, with an appropriate bin width, also around 20 years. This
approach yields a composite curve that is more temporally variable than
that provided by the local regression approach.</p>
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