1. 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

2. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 2 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, including palaeo-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, including palaeo-salinity proxies

3. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 3 Objectives & learning outcomes ๏ A hands-on approach to calibrating proxy data to a set of “calibration” data

4. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 4 Principles 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 through a 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 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.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

5. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 5 Regression techniques ๏ For some proxies, such as U 37 K 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.

6. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 6 ๏ 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: CaCO 3 calibration ODP Site 1218, Shipboard Sci. Party 2001 From: Lyle, M., Wilson, P.A., Janecek, T.R., et al., 2002. Site 1218. Proceedings of the Ocean Drilling Program, Initial Reports v. 199

7. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 7 Proxy data for %CaCO 3 calculation: ๏ shipboard analysis showed that proxy measurements that co- vary with %CaCO 3 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 %CaCO 3 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

8. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 8 ๏ The GRA bulk density measurements are also calibrated to 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

9. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 9 GRA 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 bright colour reflectance ๏ AIM: do a regression fit with 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 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

10. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 10 Procedure ๏ First step: acquire all of the necessary data: ๏ direct CaCO 3 measurements ๏ GRA bulk density data ๏ First step: acquire all of the necessary data: ๏ direct CaCO 3 measurements ๏ GRA bulk density data

11. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 11 Procedure ๏ First step: acquire all of the necessary data: ๏ direct CaCO 3 measurements ๏ GRA bulk density data ๏ First step: acquire all of the necessary data: ๏ direct CaCO 3 measurements ๏ GRA bulk density data

12. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 12 Interpolating 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 CaCO 3 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 CaCO 3 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

13. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 13 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

14. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 14 Entering 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:

15. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 15 Cleaning 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”)

16. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 16 Cleaning the interpolated values ๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

17. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 17 Cleaning the interpolated values ๏ Need to do this for entire column, can use Excel’s “Autofilter” function:

18. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 18 Replacing NULL values ๏ We can now simply replace the -9999 values by replacing the first one with “=na()”, and filling down across the rest

19. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 19 Replacing NULL values ๏ 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 ๏ 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

20. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 20 Plotting 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.....

21. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 21 Simple! 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

22. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 22 Evaluating the fit ๏ For every single GRA density value, we can now calculate the estimated %CaCO 3 value in a new column

23. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 23 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

24. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 24 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 ๏ 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

25. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 25 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 ๏ 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

26. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 26 Looking at the code... ๏ open “Visual Basic” Editor to see and modify methods...

27. L8 Calibrating proxy data sets SOES6047 - Global Climate Cycles 27 Key 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... http://heiko.paelike.de/SOES6047 ๏ 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... http://heiko.paelike.de/SOES6047

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