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Transcript of 1 Prepared for SSAC by Dorien McGee – University of South Florida © The Washington Center for...
1
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
2
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.
3
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?
4
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
5
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
6
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.
7
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!
8
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
9
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
20
22
24
26
28
30
32
1/15
3/30
6/15
8/30
11/1
51/
304/
156/
309/
15
11/3
02/
154/
307/
159/
30
12/1
52/
285/
157/
30
10/1
512
/30
Date
Tem
per
atu
re (
°C)
0.500.600.70
0.800.901.001.10
1.201.30
δ1
8O, S
MO
W (‰
)
AverageDaily Temp(°C)
δ18Ow(SMOW)
10
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
(‰
)
11
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?
12
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
13
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
-5.00
-3.00
-1.00
1.00
3.00
5.00
1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15 1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15
Date
Tem
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
-5.00
-3.00
-1.00
1.00
3.00
5.00
1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15 1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15
Date
Tem
per
atu
re (
°C)
14
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
15
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
20
22
24
26
28
30
32
34
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
16
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
17
19
21
23
25
27
29
31
33
1/15
4/15
7/15
10/1
51/
154/
157/
15
10/1
51/
154/
157/
15
10/1
51/
154/
157/
15
10/1
5
Date
Te
mp
era
ture
(°C
)
AverageDaily Temp(°C)
Species ACalculatedTempSpecies BCalculatedTemp
17
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
18
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.
19
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)
22
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
23
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
20
25
30
35
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
-5.00
-3.00
-1.00
1.00
3.00
5.00
1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15 1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15
DateT
emp
erat
ure
(°C
)
Temperature Deviation, Sensor B
-5.00
-3.00
-1.00
1.00
3.00
5.00
1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15 1/15
3/15
5/15
7/15
9/15
11/15 1/
153/
155/
157/
159/
1511
/15
Date
Tem
per
atu
re (
°C)