Assignment_4_iso_2023_Student (1)
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Arizona State University *
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101
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Date
Dec 6, 2023
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Assignment 4: What was the last ice age like?
Mar 2023
In this assignment, you will use the skills learned in class (Day 12 and 13), and apply
them to investigate the climate of the last ice age. How cold was it? Was the temperature
change the same at the equator and in polar regions?
Learning objectives:
-
Use the Rayleigh distillation model to understand potential biases in temperature
reconstruction from precipitation
d
18
O.
-
Interpret quantitatively ice core
d
18
O over the last glacial cycle.
-
Interpret benthic foraminifera
d
18
O in terms of biological fractionation, sea water
temperature and sea level.
-
Investigate the climate of the last ice age.
Work on the questions here, and then, enter your answers in Gradescope. Note that Part
1 is moved to the end (Part 4) on Gradescope.
https://www.gradescope.ca/courses/9745/assignments/42474
Part 1. Water isotopes in precipitation. (21 points)
In this question, we will use the Rayleigh distillation model to investigate various factors
influencing the
d
18
O composition of precipitation.
The equation for the
saturation vapor pressure
, that determines the fraction of vapor
remaining is:
࠵?
!"#
(࠵?) = 6.1094 exp
/
17.625 ࠵?
243.04 + ࠵?
6
࠵?࠵?࠵?ℎ ࠵? ࠵?࠵? °࠵? ࠵?࠵?࠵? ࠵? ࠵?࠵? ℎ࠵?࠵?
The
Rayleigh distillation
equation is:
࠵? = ࠵?
$
࠵?
(&’()
1.1. Control situation:
Take an initial temperature of 25°C, and an end temperature of -10°C.
a. Calculate the saturation vapor pressure at the starting temperature:
P
0
(25°C) = ___ hPa
b. Calculate the isotopic ratio of the water vapor, at equilibrium with the ocean,
(R
l
= 1) using
a
= 1.0115 (at 25°C)
R
v
(25°C) =
____
c. Calculate
the
saturation
vapor
pressure
at
the
end
temperature:
P
1
(-10°C) =
____
hPa
d. Calculate the fraction of vapor remaining at -10°C: f = ____
If you don’t remember what this means, check the in-class worksheet of Day 12.
e. Calculate the isotopic ratio of the water vapor at -10°C, using the Rayleigh
distillation equation: R
v
= ____
f.
Calculate the isotopic ratio of the precipitation at -10°C, using the fractionation
factor
a
:
R
l
= ____
g. Calculate the isotopic composition of the precipitation
d
18
O
l1
= ____ ‰
1.2. Colder precipitation temperature:
Reproduce the steps above to find the
d
18
O
l
of the precipitation falling at -20°C:
a. P
2
(-20°C) = ____ hPa
b. f = ____
c. R
v
= ____
d. R
p
=____
e.
d
18
O
l2
= ____ ‰
f.
Calculate the difference between this answer and the control:
d
18
O
l
(-20°C)
-
d
18
O
l
(-10°C) = ____ ‰
1.3. Colder source temperature:
Imagine now, that the origin of the vapor in the air has changed, and cooled to
+15°C
.
Using the updated
a
corresponding to this temperature
a
= 1.013
, reproduce the steps
above to find the isotopic composition of the precipitation at -10°C:
a. P
0
(15°C) = ____ hPa
b. R
v
(15°C) = ____
c. f(-10°C) = ____
d. Rl(-10°C) = ____
e.
d
18
O
l
= ____ ‰
f.
Calculate the difference between this result and the first result:
d
18
O
l3
-
d
18
O
l1
= ____ ‰
1.4. Interpret the result:
According to this calculation, which parameter is more important in controlling the
d
18
O of
precipitation:
a) the precipitation temperature
b) the source temperature
1.5. Apply to a real situation:
With global warming, we expect that the sea ice extent around Antarctica will decrease.
As a result, more local vapor, with colder source temperature, will contribute to the
precipitation isotope signal recorded in ice cores.
1.5a. The warmer temperature will:
a) increase the
d
18
O of precipitation
b) decrease the
d
18
O of precipitation
1.5b. Will this signal be:
a) amplified due to the change in source of humidity to a colder source
b) reduced due to the change in source of humidity to a colder source
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Part 2. Temperature of the last glacial maximum in Antarctica. (10 points)
The last glacial maximum was 20,000 years ago. On the graph below, you can find the
d
18
O record measured in an ice core at
WAIS-Divide
in
Antarctica
:
Figure 1: WAIS-Divide isotope record, 100-year averages. Source: Steig et al., Nature,
2016
2a. Identify the
minimum
d
18
O value:
d
18
O = ____
2b. Does this value correspond to:
a) the coldest time
b) the warmest time
2c. Identify the timing of this minimum: t
1
= ____ years
2d. Identify the
maximum
d
18
O value:
d
18
O = ____
2e. Identify the timing of this maximum: t
2
= ____ years
2f. Has the temperature been warming or cooling
over the last 2000 years
at this
location?
a) warming
b) cooling
2g. Calculate the change in d18O between the last glacial maximum and the Holocene:
Dd
18
O
= ____
2h. Independent evidence from borehole temperature indicates that the amplitude of the
deglacial warming was
D
T = 11.3°C.
Using the equation
d
18
O =
g
*T+b, find the calibration parameter
g
=
____
Note that you can write the equation this way:
Dd
18
O =
g
*
D
T.
2i. The classic calibration for water isotopes in Antarctica has been established by looking
spatially at the relationship between
d
18
O and T:
Figure 2: Isotope calibration curve for Antarctica (Masson Delmotte et al., 2008)
Do your results agree with this slope? Keep in mind the uncertainty in both your
calculation and the curve presented here.
a) yes
b) no
Explain:
Part 3. Ocean temperature. (18 points)
The isotopic composition of benthic foraminifera has been measured in many different
ocean sediments around the world. We are going to look at 3 sites at different latitudes in
the Atlantic Ocean:
Species
Core
Latitude
Longitude
Water
depth, m
Ocean
N. pachy s.
BOFS Core 5K
50.69
-21.87
3547 Atlantic
G. bullo
BOFS Core 5K
50.69
-21.87
3547 Atlantic
G. bullo
CH69-K09
(2)
41.76
-47.35
4100 Atlantic
N. pachy s.
CH69-K09
(2)
41.76
-47.35
4100 Atlantic
G. sacc
GeoB1515-1
4.24
-43.67
3125 Atlantic
The first column refers to the species of foraminifera analyzed. Two different species have
been analyzed at the first two sites.
In the same cores, the temperature change between the Holocene and the Last Glacial
Maximum (LGM) has been independently determined using foraminifera species
assemblages.
We will fill out the following table:
Species
Latitude
d
18
O
f
Hol
d
18
O
f
LGM
∆
d
18
O
f
∆
T foram
∆
d
18
O
temp
∆
d
18
O
sea
Difference
between
species
(G. bullo -
N. pachy s.)
N. pachy s.
50.69
1.64
4.16
-11.05
G. bullo
50.69
0.78
2.87
-11.05
G. bullo
41.76
1.18
2.70
-5.64
N. pachy s.
41.76
2.16
3.48
-5.64
G. sacc
4.24
-1.52
0.09
-1.52
Columns 3 and 4 show the measured
d
18
O
f
of the calcite of foraminifera for the Holocene
(recent period, column 3), and the last glacial maximum (LGM, column 4).
3.a. Fill out column 5, calculating the difference of
d
18
O
f
between the LGM and the
Holocene (LGM - Holocene).
The temperature change between the LGM and the Holocene has been calculated
independently by species assemblages, and is shown in column 6. The fractionation
factor depends on the species:
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Species
g
N. pachy s.
-0.26
G. bullo
-0.25
G. sacc
-0.21
3.b. Using the fractionation factors for the appropriate species, calculate for each line the
isotopic fractionation due to the temperature change, and fill out column 7:
∆
d
18
O
temp
=
g
*∆T
3.c. Finally, compute the change in sea water,
∆
d
18
O
sea
, after correction from the
temperature effect, and fill it out in column 8.
3.d. For the two sites having multiple species, compare the results obtained by each
species, by computing the difference in
∆
d
18
O
sea
for the two species (
G. bullo - N. pachy
s.
), and filling it out in column 9.
3.e. Compare your results: Which effect dominates the changes in
d
18
O
f
of foraminifera
between the LGM and today?
a) Temperature effect
b) sea water composition
c) biological effects due to which species is looked at.
Part 4. Global temperature change. (11 points)
The following map shows a model simulation of the LGM-Holocene temperature change:
Figure:
Multi-model
ensemble
mean
surface
temperature
change.
Source:
https://cp.copernicus.org/articles/17/1065/2021/
On this map, North America stands out as a region that has cooled the most, and this is
partly due to the presence of the Laurentide ice sheet, which raised the surface.
4.a. Based on the measured data from
Parts 2 and 3
, do you find a good agreement with
the model results presented here? Fill out the table below:
Core
Latitude
Measured
D
T
PMIP4
D
T
BOFS Core 5K
50.69
CH69-K09
(2)
41.76
GeoB1515-1
4.24
WAIS-Divide
-79
4.b. Based on this map and the table, which region is cooling more?
a) High latitude
b) low latitude
4.c. Which type of surface cooled the most?
a) sea surface
b) land surface
We will see towards the end of the course how the pattern of cooling at the LGM
resembles the pattern of warming in the next century.
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