SOES6047 - Global Climate Cycles SOES 6047 Global Climate Cycles L8: Calibrating proxy data sets Dr....

SOES6047 - Global Climate Cycles


SOES 6047Global Climate Cycles L8:

Calibrating proxy data sets

SOES 6047Global Climate Cycles L8:

Calibrating proxy data sets

Dr. Heiko Pä[email protected]. 23638, Rm. 164/34

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22SOES6047 - Global Climate Cycles


recap from last “proxy” lecture:

recap from last “proxy” lecture:

๏ Biological proxies a very powerful tool to record environmental 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, includingpalaeo-salinity proxies

๏ Biological proxies a very powerful tool to record environmental 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, includingpalaeo-salinity proxies

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SOES6047 - Global Climate CyclesObjectives & learning

outcomesObjectives & learning

outcomes

๏ A hands-on approach to calibrating proxy data to a set of “calibration” data

๏ A hands-on approach to calibrating proxy data to a set of “calibration” data

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Principles of calibrationPrinciples of calibration๏ In general, we want to describe a set of proxy variable

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”

๏ have to learn to be confident and find by yourself what is needed to get the job done

๏ Here we will work througha simple example

๏ In general, we want to describe a set of proxy variable 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”

๏ have to learn to be confident and find by yourself what is needed to get the job done

๏ Here we will work througha simple example

exponential fit in real datais shown in link

linear fitLink 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

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Regression techniquesRegression techniques๏ For some proxies, such as

U37K alkenone data and water

temperatures, one can achievefairly simple regression calculations. This can be done in specialist tools such as SPSS, oreven in Excel (Linear regression)

๏ For some proxies, such as U37

K alkenone data and watertemperatures, one can achievefairly simple regression calculations. This can be done in specialist tools such as SPSS, oreven 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.

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๏ as a “hands-on” example, consider the typical situation where a 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)

๏ as a “hands-on” example, consider the typical situation where a 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)

Case study: CaCO3 calibrationCase study: CaCO3 calibration

ODP Site 1218, Shipboard Sci. Party ODP Site 1218, Shipboard Sci. Party 20012001


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Proxy data for %CaCO3 calculation:Proxy data for %CaCO3 calculation:๏ shipboard analysis showed that proxy measurements

that co-vary 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

๏ shipboard analysis showed that proxy measurements that co-vary 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

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๏ The GRA bulk density measurements are also calibrated to laboratory measurements of wet and bulk density (circles on plot).

๏ The GRA bulk density measurements are also calibrated to laboratory measurements of wet and bulk density (circles on plot).


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GRA bulk density record 1218GRA bulk density record 1218๏ visual comparison of directly measured carbonate

content and GRA bulk density shows an interval from ~50-220 mbsf (~50-245mcd) of high carbonate, high density, low magnetic susceptibility, and brightcolour reflectance

๏ AIM: do a regression fitwith GRA bulk density

๏ visual comparison of directly measured carbonate content and GRA bulk density shows an interval from ~50-220 mbsf (~50-245mcd) of high carbonate, high density, low magnetic susceptibility, and brightcolour reflectance

๏ AIM: do a regression fitwith GRA bulk density


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ProcedureProcedure๏ First step: acquire all of the necessary data:

๏ direct CaCO3 measurements๏ GRA bulk density data

๏ First step: acquire all of the necessary data:๏ direct CaCO3 measurements๏ GRA bulk density data

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ProcedureProcedure๏ First step: acquire all of the necessary data:

๏ direct CaCO3 measurements๏ GRA bulk density data

๏ First step: acquire all of the necessary data:๏ direct CaCO3 measurements๏ GRA bulk density data

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Interpolating GRA dataInterpolating GRA data๏ Having assembled the data, we now need to plot one

variable 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

๏ Having assembled the data, we now need to plot one variable 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

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Procedure:Procedure:๏ 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

๏ 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

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Entering the interpolation formulaEntering the interpolation formula๏ 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:

๏ 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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SOES6047 - Global Climate CyclesCleaning the interpolated

valuesCleaning the interpolated

values๏ For depths where there are not sufficient data around the point 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”)

๏ For depths where there are not sufficient data around the point 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”)

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values๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

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values๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

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Replacing NULL valuesReplacing NULL values๏ We can now simply replace the -9999 values by

replacingthe first one with “=na()”, and filling down across the rest

๏ We can now simply replace the -9999 values by replacingthe first one with “=na()”, and filling down across the rest

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Replacing NULL valuesReplacing NULL values๏ We can now simply replace the -9999 values by

replacingthe first one with “=na()”, and filling down across the rest

๏ after unchecking the “Autofilter” menu, we havenow what we want:for each measured CaCO3value we have exactlyone interpolated GRA value

๏ We can now simply replace the -9999 values by replacingthe first one with “=na()”, and filling down across the rest

๏ after unchecking the “Autofilter” menu, we havenow what we want:for each measured CaCO3value we have exactlyone interpolated GRA value

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Plotting the first resultsPlotting the first results๏ 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 .....

๏ 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 .....

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Simple! linear regressionSimple! linear regression๏ we observe a general positive correlation, which we can

quantify with Excel’s “Fit Trendline” function .....๏ but the fit is relatively poor ....๏ nevertheless, let’s see how well we can calibrate our

proxy...

๏ we observe a general positive correlation, which we can quantify with Excel’s “Fit Trendline” function .....

๏ but the fit is relatively poor ....๏ nevertheless, let’s see how well we can calibrate our

proxy...

This is the formula we can now apply

to all GRA values

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Evaluating the fitEvaluating the fit๏ For every single GRA density value, we can now

calculate the estimated %CaCO3 value in a new column๏ For every single GRA density value, we can now

calculate the estimated %CaCO3 value in a new column

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advanced methods: “Solver”advanced methods: “Solver”๏ Rather than relying on the regression options that Excel

offers 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

๏ Rather than relying on the regression options that Excel offers 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

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SOES6047 - Global Climate Cycles more Solver ...more Solver ...

๏ calculate an arbitrary function from your proxy data, in this case %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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SOES6047 - Global Climate Cycles more Solver ...more Solver ...







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Looking at the code ...Looking at the code ...๏ open “Visual Basic”

Editor to see andmodify methods ...

๏ open “Visual Basic”Editor to see andmodify methods ...

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Key point summaryKey point summary๏ 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 ...

๏ 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 ...

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๏ This resource was created by the University of Southampton and released as an open educational resource through the 'C-change in GEES' project exploring the open licensing of climate change and sustainability resources in the Geography, Earth and Environmental Sciences. The C-change in GEES project was funded by HEFCE as part of the JISC/HE Academy UKOER programme and coordinated by the GEES Subject Centre.

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