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Prepared for SSAC byDorien McGee – University of South Florida

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006.

From Isotopes to Temperature

Working with a Temperature Equation

Supporting Quantitative concepts and skillsNumber sense: RatiosAlgebra: Manipulating an equationData analysis: Correlation and regression Coefficient of determination Correlation coefficientVisualization Line and column graphs XY-scatter plot

Much of our quantitative information about past climates comes from analysis and interpretation of stable isotopes in geologic materials. In this module you will become familiar with the kind of

equation that relates the concentration of oxygen isotopes in a coral to the temperature of

the water in which it lives.

Core Quantitative IssueData analysis

SSAC2006.QE445.DKM1.1

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Slide 3 states the problem.

Slides 4 and 5 introduce the terminology describing oxygen isotope concentrations, and Slides 6 and 7 discuss the behavior of oxygen isotopes that enables determination of past temperatures.

Slides 8 presents the dataset for analysis.

Slides 9 and 10 examine the correlation between temperature and the oxygen isotope concentration in the water.

Slides 11-16 examine how well the oxygen isotopes of corals living in the water can be used to determine the temperature of the water.

Slides 17 and 18 wrap up and provide your end of module assignments.

Overview

Stable isotope ratios in geologic materials have the potential to tell us a lot about how our planet has changed over time. One common use of

stable isotope analyses is to determine past temperature as a function of time and, therefore, a history of climatic change.

This module will introduce the basic concepts of oxygen isotope behavior, how to translate isotope values to temperature values, and

variables that impact temperature reconstruction. The dataset you will be using is similar to an actual dataset currently being utilized by the author

and data in NASA’s Global Seawater Oxygen-18 Database.

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You are an ocean researcher studying global warming. You are interested in seeing whether or not water temperatures on a coral reef in your field

area have changed over the last 200 years. To do this, you must first establish whether or not the isotopic ratios in the coral species in this reef

provide a good record of temperature.

Previous research has established a working equation that can calculate temperatures within 1 °C from isotope ratios for a genus of coral that lives

in your study area. Unfortunately, the equation was derived from a species that is different from the two species of the genus that occur at your reef. We will call them Species A and Species B. Will the equation

work for either of them?

You collect a live specimen of Species A and Species B. You microdrill the aragonite from four years of growth from their annual growth bands

and determine the succession of 18O ratios from the samples using a mass spectrometer. You have records in your marine lab of the water

temperature at a monitoring site at the reef, as well as the isotope ratio of the water there.

Problem

Does the equation provide a means to calculate the water temperature from the 18O ratios in the corals?

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Before we can answer the question, we need to talk a little about oxygen isotopes.

Temperature reconstructions rely on variations in the isotope ratio (R) of 18O to 16O in seawater and the record of those variations in the shells of marine

organisms. The 18O/16O ratio of oxygen atoms among the H2O molecules of seawater is very small: only about 0.2% of the oxygen atoms are 18O; the

remaining 99.8% are 16O. Variations in the 18O/16O ratios, of course, are smaller than the ratios themselves.

Instead of using the small values of R to report the varying 18O concentrations, geochemists use δ18O, a relative difference ratio:

Thus δ18O is the difference of the oxygen-isotope ratios between a sample and standard relative to the ratio in the standard; it is a ratio derived from ratios. The value of δ18O is stated as per mille (‰, parts per thousand in the same way that

% is per cent, for parts per hundred; end note 1). The mass spectrometer, which measures the oxygen-isotope concentration, reports out the per mille δ18O of the

sample.

Quantifying the 18O Concentration

δ18O = 1000tan

tan

dards

dardssample

R

RR

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Understanding δ18O

A common alternative definition of δ18O is

δ18O = 10001tan

dards

sample

R

R

Show that this definition is

equivalent to the definition on the preceding slide

Create a spreadsheet that uses this definition to calculate the 18O/16O ratio in a seawater sample in which δ18O is 1.18 per mille.

Then use the definition on the preceding slide to check your answer (i.e., calculate δ18O from the 18O/16O ratio). Use SMOW (Standard Mean Ocean Water) as the standard. The 18O/16O of

SMOW is 0.0020052.

Notice how small the differences in R are. What is

the difference in R that corresponds to a difference in δ18O values of 1.18 and

1.16 per mille?

B C

2 δ18Ow (per mille) 1.183 Rstandard 0.00200524 Rsample 0.002007656 Rsample-Rstandard 2.366E-067 ΔR/Rstandard 0.001188 ‰ 1.18

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In the tropics where most corals grow, conditions are typically warm and humid. At high temperatures, evaporation occurs at faster rates such that during warm periods the air is

often near saturation with respect to water vapor, causing more frequent precipitation. As a result, when water (containing the 16O) is evaporated from the sea surface, it is not

transported far before it precipitates as rain. Precipitation under these conditions is more local and the loss of 16O in the seawater through evaporation can be roughly equal to the

gain of 16O through precipitation.

Understanding 16O and 18O Behavior

Warmer atmosphere depleted 18O in seawaterCooler atmosphere enriched 18O in seawater

Because an atom of16O has less mass than an atom of 18O, it is preferentially taken up when

seawater evaporates, causing the relative amount of 18O in the sea

water to rise, or become enriched (i.e., the δ18O increases). The 16O in

the evaporated water is then transported through the

atmosphere to where it condenses and falls out as precipitation.

When air temperatures are cooler (such as during cold fronts, seasonal changes, or global cooling), evaporation is slower and it takes longer for the air to reach saturation. Hence, the

water (and contained 16O) evaporating from the sea surface can travel further before saturation is reached and precipitation occurs. Therefore, 16O may not be replaced by local

precipitation, leading to relatively higher concentrations of 18O in the remaining water.

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Providing Records of the Varying δ18O

Some marine organisms precipitate calcium carbonate (CaCO3) from the seawater to make their shells or exoskeletons. Some of these organisms are able to secrete their

hard parts in isotopic equilibrium with the water. Simply stated, the isotopes incorporated into the CaCO3 of the organism are of the same ratio as that in the

seawater. Since δ18O values vary with temperature, we can use these ratios from the CaCO3 of the organisms that are “recording” in equilibrium with the environment to

track temperature trends back over time. Hence, their isotope records are considered to be good proxies for records of past temperatures.

Biological factors relating to photosynthesis and metabolism, and external factors such the chemistry of the water, can also influence the isotope values of carbonate

organisms. As a result, not all species of carbonate organisms provide a faithful record of environmental δ18O.

What are some examples of organisms that precipitate

and secrete CaCO3?

Gastropods

Foraminifera

Bivalvesand corals!

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Looking at a record

Create your own spreadsheet by double-clicking the

spreadsheet to the left, and copy/pasting all the values into

a new Excel file (you need to be in the “Normal view” of

PowerPoint to do this).

IMPORTANT: Only part of the spreadsheet is visible here. Be sure you copy all of the cells.

Below is the simulated dataset that you will be using. It contains:

• Average daily water temps (as recorded approximately every 15 days for four years from the monitoring station at the modern reef)

• The δ18O value of the water at the reef (sampled at the same time the temperature was recorded)

• The δ18O value of the living specimens of Species A and B (microsampled at growth intervals of approximately every 15 days over the last four years)

First we will examine the correspondence of temperature and δ18Ow

B C D E F G

2 Date

Average Daily Temp (°C)

δ18Ow

(SMOW)

Species

A δ18O)c

(SMOW)

Species

B δ18Oc

(SMOW)3 Year 1 1/15 22.86 1.18 1.54 0.994 1/30 22.54 1.21 1.68 1.195 2/15 21.64 1.26 1.82 1.466 2/28 22.95 1.15 1.39 0.497 3/15 23.21 1.14 1.09 0.468 3/30 22.93 1.17 1.13 0.679 4/15 23.51 1.14 0.73 0.4510 4/30 24.64 1.05 0.28 -0.1211 5/15 26.03 0.92 -0.85 -0.3412 5/30 26.51 0.92 -1.11 -0.4913 6/15 27.48 0.84 -1.62 -1.4014 6/30 27.82 0.81 -1.78 -0.9115 7/15 28.59 0.75 -0.99 -1.5116 7/30 29.61 0.65 -2.22 -1.83

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Comparing δ18Ow and water temperature

Create a line graph comparing the recorded water temperatures with the recorded δ18O of the water. You may want to add an axis or adjust the y-axis values, and other graph properties to better see the trends.

For help on how to do this, click here.

What do you notice about the relationship of δ18Ow to the recorded temperature?

Seasonal Reef Water Temperature and Reef Water δ18O Values

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0.500.600.70

0.800.901.001.10

1.201.30

δ1

8O, S

MO

W (‰

)

AverageDaily Temp(°C)

δ18Ow(SMOW)

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Create a scatter plot of δ18Ow vs. temperature. Determine the regression equation and the value of R2. Note the

slope of the regression line – particularly its sign.

It is an inverse correlation

If R2 (the coefficient of determination) is 0.9943, what is R, the correlation coefficient? What sign would be appropriate?

(end note 2)

Note: The R here is not the same R we were using

to discuss 18O concentrations.

Comparing δ18Ow and water temperature, 2

For help with the scatter plot, click here

δ18O of Water versus Average Daily Water Temperature

y = -0.0762x + 2.9156R2 = 0.9943

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

20 22 24 26 28 30 32Temperature (°C)

δ1

8O

, SM

OW

(‰

)

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Returning to the problem

Climatologists have developed equations to calculate past seawater temperatures from δ18O values in corals. The variables in the equations are temperature (dependent variable) and δ18O of both the coral and the water (independent variables; end note 3). The constants in the equations vary

according to the type of coral. No such equation has been established for either Species A or B. However an equation has been established for

another species of the same genus. The equation is reported to produce calculated temperatures to within 1 °C of the measured temperatures. The

equation is:

(like your dataset, this equation is adapted from actual temperature equations used for corals):

0.34

55.7)OδO(δC)T(

w18

c18

Does the equation do as well for Species A and B?

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Add four columns to your spreadsheet. In the first, calculate the temperature from Species A using the temperature equation of

the previous slide. In the second, calculate the difference between the calculated temperature and the measured

temperature. In the third and fourth, do the same for Species B. For convenience, here is the temperature equation again:

Calculating temperatures

0.34

55.7)OδO(δC)T(

w18

c18

Cell with a given value

Cell with a formula

B C D E F G H I J K

2 Date

Average Daily Temp (°C)

δ18Ow

(SMOW)

Species

A δ18O)c

(SMOW)

Species

B δ18Oc

(SMOW)

Species A Calculated

Temp

Average Daily Temp -Calculated Temp (°C), Species A

Species B Calculated

Temp

Average Daily Temp - Calculated Temp (°C), Species B

3 Year 1 1/15 22.86 1.18 1.54 0.99 21.16 1.70 22.76 0.104 1/30 22.54 1.21 1.68 1.19 20.83 1.71 22.27 0.275 2/15 21.64 1.26 1.82 1.46 20.55 1.09 21.61 0.036 2/28 22.95 1.15 1.39 0.49 21.51 1.44 24.15 -1.207 3/15 23.21 1.14 1.09 0.46 22.35 0.86 24.22 -1.018 3/30 22.93 1.17 1.13 0.67 22.31 0.62 23.66 -0.739 4/15 23.51 1.14 0.73 0.45 23.41 0.10 24.25 -0.7410 4/30 24.64 1.05 0.28 -0.12 24.46 0.18 25.64 -1.0011 5/15 26.03 0.92 -0.85 -0.34 27.41 -1.38 25.90 0.1312 5/30 26.51 0.92 -1.11 -0.49 28.17 -1.66 26.36 0.1513 6/15 27.48 0.84 -1.62 -1.40 29.44 -1.96 28.78 -1.30

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Are the calculated temperatures within a degree of the measured temperatures? Illustrate with a bar graph for each species.

Examining the results

Average Daily Temp -Calculated Temp (°C), Species A

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per

atu

re (

°C) Species A seems to miss the

mark. It obviously tends to calculate high.

Species B seems better. How many of the calculated temperatures are within 1o of the target? What is the average difference?

Average Daily Temp -Calculated Temp (°C), Species B

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94 10/30 27.55 0.86 -1.51 -0.92 29.18 -1.63 27.46 0.0995 11/15 26.98 0.85 -1.38 -0.75 28.77 -1.79 26.91 0.0796 11/30 25.86 0.96 -1.05 -0.20 28.11 -2.25 25.60 0.2697 12/15 25.23 0.98 -0.56 -0.03 26.74 -1.51 25.18 0.0598 12/30 24.13 1.07 -0.05 0.35 25.49 -1.36 24.31 -0.1899 Avg 0.97 0.06100 Nbr > 1 61 6101 Nbr < -1 25 5102 Nbr Inside 10 85103 Max 4.79 2.21104 Min -4.04 -1.63105 STDEV 2.05 0.65

Calculate some easy statistics at the bottom of your spreadsheet to represent how closely the corals came to hitting the correct

temperature with the test equation.

Examining the results, 2

B C D E F G H I J K

2 Date

Average Daily Temp (°C)

δ18Ow

(SMOW)

Species

A δ18O)c

(SMOW)

Species

B δ18Oc

(SMOW)

Species A Calculated

Temp

Average Daily Temp -Calculated Temp (°C), Species A

Species B Calculated

Temp

Average Daily Temp -

Calculated Temp (°C), Species B

3 Year 1 1/15 22.86 1.18 1.54 0.99 21.16 1.70 22.76 0.104 1/30 22.54 1.21 1.68 1.19 20.83 1.71 22.27 0.275 2/15 21.64 1.26 1.82 1.46 20.55 1.09 21.61 0.036 2/28 22.95 1.15 1.39 0.49 21.51 1.44 24.15 -1.207 3/15 23.21 1.14 1.09 0.46 22.35 0.86 24.22 -1.018 3/30 22.93 1.17 1.13 0.67 22.31 0.62 23.66 -0.73

Top of spreadsheet

Bottom of spreadsheet

On average, the test equation misses by about a degree with Species A. More than 60 of the 97 values are a degree or more above the actual temperature, and only 10 are within a degree. In contrast, the test equation produces temperatures within a degree for 85 out of the 97 microsamples for Species B.

Excel functions: AVERAGE COUNTIFMAXMINSTDEV

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Examining the results, 3

Make a scatter plot of the calculated vs. the measured temperatures for each species to illustrate how close the individual calculated values come to the

measured ones . Be sure your axes values are the same (since you’re plotting temperature on both).

The scatter of the points around the line of perfect prediction is quantified by the standard deviation of Tcalculated – Tmeasured in the spreadsheet (previous slide).

The dark green line with 45-degree slope

shows where the points would plot if all of the calculated values reproduced the corresponding measured values.

Species A and B Calculated Temperatures versus Average Daily Water Temperatures

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26

28

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20 22 24 26 28 30 32 34

Average Daily Temperature (°C)

Sp

ecie

s A

an

d B

Cal

cula

ted

T

emp

erat

ure

(°C

) Average Daily Temp(°C)

Species ACalculated Temp

Species BCalculated Temp

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By all measures, the equation does not work for Species A. To visualize how well (or poorly) the two species would fare at reproducing the time

series of temperature, create a line graph showing the calculated temperatures for each species together with the measured temperature

over the period of measurement.

Examining the results, 4

Average Daily Temperatures and Species A & B Calculated Reef Water Temperatures

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Date

Te

mp

era

ture

(°C

)

AverageDaily Temp(°C)

Species ACalculatedTempSpecies BCalculatedTemp

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What we have shown, and a final thought

It is possible to calculate a time series of seawater temperature from the 18O/16O ratio in the growth bands of corals. The

calculation uses a simple linear equation of temperature vs. δ18O. Care must be taken, however, when applying such a temperature equation to the δ18O record from corals other than the species for

which it was derived.

The equation clearly does not work for Species A. This result brings up the possibility that a different equation might work for Species A. From

the information in the spreadsheet of Slide 8, you can find the regression line for water temperature vs. the difference between δ18Oc and δ18Ow for

Species A. It is:

R2 = 0.735

In contrast, the regression line for water temperature vs. the difference between δ18Oc and δ18Ow for Species B is

R2 = 0.940

What do these results tell you about the value of Species A for paleotemperature reconstruction?

2.24716.1 1818 wc OOT

5.22735.2 1818 wc OOT

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End of Module Assignments

1. Answer the question on Slide 5 and turn in the spreadsheet that allows you to calculate the answer.

2. Answer the question in the green box of Slide 10.

3. Convert the equation in Slide 11 to the form of the equations in Slide 17. What do you conclude from the comparison of the equations?

4. Answer the question at the end of Slide 17. Test your answer by doing the same kind of analysis for the best-fit equation for Species A (Slide 17) as we did for the equation in Slide 11. Specifically, redo the spreadsheets and graphs in Slides 12-16 using the new equation (replace the columns for Species B with the new values for Species A using the new equation). Turn in:

a. A revised spreadsheet, including the statistics, for Slide 14 using the new equation.

b. A new version of the bar graph in Slide 13 using the new equation.

c. A new version of the scatter plot in Slide 15 using both the old and the new equation for Species A.

d. A new version of the line plot in Slide 16 using both the old and the new equation for Species A, comparing the calculated temperatures to the measured ones.

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End Notes

1. Mille as in millenium (1000 years) and cent as in century (100 years). (Return to Slide 4.)

2. You can select the sign of the square root by remembering that a perfect positive correlation has a correlation coefficient of +1 and a perfect negative correlation has a correlation coefficient of -1. For more see: http://mathbits.com/MathBits/TISection/Statistics2/correlation.htm (Return to Slide 10.)

3. In practice, one does not know δ18Ow when projecting back into the past. In that case, a single likely value is used in the equation, and so the equation becomes a straightforward linear equation of temperature vs. δ18Oc. As written in this box, the equation is a linear equation of temperature vs. the difference between δ18Oc and δ18Ow. (Return to Slide 11)

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References

DataSchmidt, G.A., G. R. Bigg and E. J. Rohling. 1999. "Global Seawater Oxygen-18 Database". http://data.giss.nasa.gov/o18data/

Images:Slide 6

NOAA Ocean Explorerhttp://www.oceanexplorer.noaa.gov/explorations/03mex/background/plan/media/bandedtulipsnail.html

Natural History Museum of Londonhttp://www.nhm.ac.uk/hosted_sites/quekett/Reports/Forams.jpg

Jacksonville Shellshttp://www.jaxshells.org/atlanticb.htm

ABC News Online, Australiahttp://www.abc.net.au/news/newsitems/200511/s1514675.htm

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1. What is δ18O and how is it related to 18O and 16O?

2. Describe the difference between R2 and R?

3. For which correlation of calculated temperature to actual temperature is R2 the largest for the two species in the following figure?

4. You are using the equation below to calculate the temperature based on two variables, a and b, using Excel. The values for a occupy the range A3 to A32, and the values for b occupy the range B3 to B32. Write out the Excel formula for the equation below, as you would enter it into cell C3 (prior to dragging and copying the equation down to C32).

5. You are using two brands of water temperature sensors. The two bar graphs depict the deviation of the two sensors from the actual water temperature. Which sensor is more accurate?

Pre-Post Test

0.34

55.7)-(C)T(

ba

Calculated Species Temperature vs. Actual Water Temperature

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20 25 30 35Actual Water Temperature (°C)

Cal

cula

ted

Sp

ecie

s T

emp

erat

ure

(°C

)

Actual WaterTemp

Species ACalculated Temp

Species BCalculated Temp

Temperature Deviation, Sensor A

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