SOES6047 - Global Climate Cycles
SOES 6047
Global Climate Cycles L8:
Calibrating proxy data sets
Dr. Heiko Pälike
heiko@noc.soton.ac.uk
Ext. 23638, Rm. 164/34
SOES6047 - Global Climate Cycles
๏ Biological proxies a very powerful tool to record environmental
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conditions that are not otherwise available
Transfer function methods attempt to empirically match the
correlation of present-day T°C, SSS and productivity
conditions with species and morphometric properties
Different versions of transfer functions exist, all methods have
in common certain questionable short-comings
If calibration with present-day data is required, we are limited
how far back in time we can go before evolutionary aspects
prevent analogue methods to work
Best to treat biological proxy results as only semi-quantitative
Yet, some novel applications are being developed, including
palaeo-salinity proxies
L8 Calibrating proxy data sets
recap from last “proxy” lecture:
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๏ A hands-on approach to calibrating proxy data to a set of
“calibration” data
L8 Calibrating proxy data sets
Objectives & learning outcomes
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๏ In general, we want to describe a set of proxy variable
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measurements to fit a set of observation or calibration data
The functional relationship could be linear,
or more complicated (exponential, polynomial, logarithmic etc.)
Very simple regression techniques are
available in Excel, and you can quite
easily add your own with “Macros”
L8 Calibrating proxy data sets
Principles of calibration
๏ have to learn to be confident and
find by yourself what is
needed to get the job done
๏ Here we will work through
a simple example
exponential fit in real data
is shown in link
linear fit
Link to real data plot: Rosenthal, Y., Boyle, E.A., Slowey, N., (1997) Temperature control on the
incorporation of magnesium, strontium, fluorine, and cadmium into benthic foraminiferal shells from Little
Bahama Bank: Prospects for thermocline paleoceanography.Geochimica et Cosmochimica Acta, v. 61,
no. 17, p. 3633-3643.
From: Lyle, M., Wilson, P.A., Janecek, T.R., et al.,
2002. Site 1218. Proceedings of the Ocean Drilling
Program, Initial Reports v. 199
SOES6047 - Global Climate Cycles
๏ ForKsome proxies, such as
U37 alkenone data and water
temperatures, one can achieve
fairly simple regression
calculations. This can be done in
specialist tools such as SPSS, or
even in Excel (Linear regression)
Reproduced with permission of American Chemistry Society:
Rosell-Melé, A., Carter, J. F., Parry, A. T., and Eglinton, G.
(1995). Determination of the UK37 Index in Geological Samples.
Analytical Chemistry, v. 67, p. 1283-1289. Copyright [1995]
American Chemistry Society.
L8 Calibrating proxy data sets
Regression techniques
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๏ as a “hands-on” example, consider the typical situation where a
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low-resolution data set of calibration data exists, together with a
much higher resolution data set of proxy measurements
calibration data were obtained by coulometry, and ICP-AES
(which is already a indirectly calibrated measurement)
From: Lyle, M., Wilson, P.A., Janecek, T.R., et al.,
2002. Site 1218. Proceedings of the Ocean Drilling
Program, Initial Reports v. 199
ODP Site 1218, Shipboard Sci. Party 2001
L8 Calibrating proxy data sets
Case study: CaCO3 calibration
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๏ shipboard analysis showed that proxy measurements that covary with %CaCO3 content include
๏ magnetic susceptibility (anti-correlation)
๏ colour reflectance (lightness)
๏ bulk density
๏ The aim is now to relate the calibration data to the proxy data in
a mathematical sense
๏ Initial approach: use one proxy variable at a time, let’s start with
bulk density, which reflects the relative proportion of carbonate,
opal, and clays
L8 Calibrating proxy data sets
Proxy data for %CaCO3 calculation:
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laboratory measurements of wet and bulk density (circles on
plot).
From: Lyle, M., Wilson, P.A., Janecek, T.R., et al.,
2002. Site 1218. Proceedings of the Ocean Drilling
Program, Initial Reports v. 199
L8 Calibrating proxy data sets
๏ The GRA bulk density measurements are also calibrated to
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๏ visual comparison of directly measured carbonate content and
GRA bulk density shows an interval from ~50-220 mbsf (~50245mcd) of high
carbonate, high density,
low magnetic
susceptibility, and bright
colour reflectance
๏ AIM: do a regression fit
with GRA bulk density
From: Lyle, M., Wilson, P.A., Janecek, T.R., et al.,
2002. Site 1218. Proceedings of the Ocean Drilling
Program, Initial Reports v. 199
L8 Calibrating proxy data sets
GRA bulk density record 1218
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๏ First step: acquire all of the necessary data:
๏ direct CaCO3 measurements
๏ GRA bulk density data
L8 Calibrating proxy data sets
Procedure
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SOES6047 - Global Climate Cycles
๏ First step: acquire all of the necessary data:
๏ direct CaCO3 measurements
๏ GRA bulk density data
L8 Calibrating proxy data sets
Procedure
SOES6047 - Global Climate Cycles
๏ Having assembled the data, we now need to plot one variable
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against the other, in order to estimate whether the fit is linear
(straight line), some form of polynomial, exponential etc.
To do this, we need to INTERPOLATE the higher-resolution
GRA data at the depths at which the CaCO3 measurements
were taken!
To do this, we will use a self-programmed macro function that
does a Gaussian interpolation for us. You can find the example
spreadsheet on Blackboard, and investigate the code inside the
“Visual Basic” Macro editor of Excel
L8 Calibrating proxy data sets
Interpolating GRA data
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๏ Use macro “gint”, which requires you to
๏ define the range of cells that give the source data
(the GRA density data) by selecting the cell range,
and choose the menu “Insert->Name->Define”, and giving it
a memorable name like gra_data
L8 Calibrating proxy data sets
Procedure:
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๏ If the interpolation macro is installed, after defining the name
range for the GRA data, we can calculate the interpolated
values with “gint” as a function:
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Entering the interpolation formula
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๏ For depths where there are not sufficient data around the point
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to be interpolated, gint will return -9999
Can either widen the gaussian window (here 0.1 m), or replace
-9999 values with “=na()” (“Not a Number”)
L8 Calibrating proxy data sets
Cleaning the interpolated values
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๏ Need to do this for entire column, can use Excel’s “Autofilter”
function:
L8 Calibrating proxy data sets
Cleaning the interpolated values
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๏ Need to do this for entire column, can use Excel’s “Autofilter”
function:
L8 Calibrating proxy data sets
Cleaning the interpolated values
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๏ We can now simply replace the -9999 values by replacing
the first one with “=na()”, and filling down across the rest
L8 Calibrating proxy data sets
Replacing NULL values
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๏ We can now simply replace the -9999 values by replacing
the first one with “=na()”, and filling down across the rest
๏ after unchecking the
“Autofilter” menu, we have
now what we want:
for each measured CaCO3
value we have exactly
one interpolated GRA value
L8 Calibrating proxy data sets
Replacing NULL values
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๏ We can now create a simple X-Y plot, and interpret our result
๏ we observe a general positive correlation, which we can
quantify with Excel’s “Add Trendline” function .....
L8 Calibrating proxy data sets
Plotting the first results
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๏ we observe a general positive correlation, which we can
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quantify with Excel’s “Fit Trendline” function .....
but the fit is relatively poor ....
nevertheless, let’s see how well we can calibrate our proxy
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This is the formula
we can now apply
to all GRA values
L8 Calibrating proxy data sets
Simple! linear regression
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๏ For every single GRA density value, we can now calculate the
estimated %CaCO3 value in a new column
L8 Calibrating proxy data sets
Evaluating the fit
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๏ Rather than relying on the regression options that Excel offers
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you, a much more general method is to fit a function that you
design yourself to some data ... This could be a more
complicated function, and might involve more than one proxy
variable.
You can do this by using the Excel Tool “Solver”, which tries to
adjust the value in a certain cell (or cells) until a certain fit is
obtained.
๏ This general “function” fitting is numerical, and requires some
trial and error.
๏ Available in Excel menu “Tools->Solver”, if installed properly
L8 Calibrating proxy data sets
advanced methods: “Solver”
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๏ calculate an arbitrary function from your proxy data, in this case
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%CaCO3 = a*GRA^2+b*GRA+c
Evaluate misfit between calculated and observed %CaCO3
minimise misfit with “Solver” by adjusting a,b,c
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more Solver ...
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๏ calculate an arbitrary function from your proxy data, in this case
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%CaCO3 = a*GRA^2+b*GRA+c
Evaluate misfit between calculated and observed %CaCO3
minimise misfit with “Solver” by adjusting a,b,c
L8 Calibrating proxy data sets
more Solver ...
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๏ open “Visual Basic”
Editor to see and
modify methods ...
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Looking at the code ...
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๏ Proxy calibration involves fitting a presumably known function
to a set of “calibration” measurements
๏ This often requires interpolation of data
๏ Often used statistical methods such as linear regression
๏ While dedicated packages exist, you can do most of these
calculations yourself within, e.g., a programme like Excel
๏ Example spreadsheet available on Blackboard or
http://heiko.paelike.de/SOES6047 server ...
L8 Calibrating proxy data sets
Key point summary
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L8 Calibrating proxy data sets
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