Exploring the Relationship Between Vertical Mixing,

Overturning Circulation, AABW Volume, and

Ventilation Age During the Last Glacial Maximum

by

Margaret Valerio

A.B. (Geology), Brown University, 2015

Thesis Submitted in Partial Fulfillment of the

Requirements for the Degree of

Master of Science

in the

Department of Geography

Faculty of Environment

© Margaret Valerio 2019

SIMON FRASER UNIVERSITY

Summer 2019

Copyright in this work rests with the author. Please ensure that any reproduction or re-use is done in accordance with the relevant national copyright legislation.

ii

Approval

Name: Margaret Valerio

Degree: Master of Science (Geography)

Title: Exploring the Relationship Between Vertical Mixing, Overturning Circulation, AABW Volume, and Ventilation Age During the Last Glacial Maximum

Examining Committee: Chair: Suzana Dragicevic Professor

Kirsten Zickfeld Senior Supervisor Associate Professor

Karen Kohfeld Supervisor Professor School of Resource & Environmental Management

Roger Francois External Examiner Professor Department of Earth, Ocean and Atmospheric Sciences University of British Columbia

Date Defended/Approved: June 26, 2019

iii

Abstract

One interpretation of Last Glacial Maximum (LGM) paleo-environmental data is the

expansion of poorly ventilated Antarctic Bottom Water (AABW) coinciding with

weakened AABW overturning, which is reflected in few modelling efforts. This research

addresses the relationship between vertical mixing, AABW volume, overturning

circulation, and ventilation age using the UVic Earth System Climate Model with five

vertical mixing parameterizations that differ in the value of diapycnal diffusivity in the

deep ocean. In all simulations AABW volume and overturning strength increases during

the LGM relative to pre-industrial (PI), with small differences between mixing schemes.

All mixing schemes yield older bottom water during the LGM relative to PI, indicating that

a decrease in overturning strength is not required to decrease ventilation age. Our

results offer insights into the relationship between AABW overturning, volume, and

ventilation, with little impact based on mixing scheme.

Keywords: Paleoceanography; Climate Modelling; Mixing Parameterization; LGM;

AABW; Radiocarbon

iv

Dedication

For Mom,

I would not have been able to come this far without you. Thank you for everything that

you have done for me. Love you!

v

Acknowledgements

Thank you to my incredibly supportive and insightful supervisors, Dr. Kirsten

Zickfeld and Dr. Karen Kohfeld. Thank you to our co-author, Dr. Agatha De Boer, whose

input has been vital to the direction of this study. Thank you to Dr. Michael Eby for his

technical support and encouragement during the implementation of our experimental

design. Thank you to Dr. Mea Cook for taking the time to speak with me about

radiocarbon dating in oceanography. Thank you to Dr. Andreas Schmittner and Dr. Juan

Muglia for sharing their code and methods, which were very helpful in working through a

solution to a few research roadblocks. Finally, for personal support, encouragement,

advice, and revision support, thank you to my friends and family.

vi

Table of Contents

Approval ............................................................................................................................ ii

Abstract ............................................................................................................................. iii

Dedication ........................................................................................................................ iv

Acknowledgements ........................................................................................................... v

Table of Contents ............................................................................................................. vi

List of Tables .................................................................................................................... vii

List of Figures.................................................................................................................. viii

Chapter 1. Introduction ................................................................................................ 1

Chapter 2. Methods ...................................................................................................... 4

2.1. Model Description ................................................................................................... 4

2.2. Model Set-up ........................................................................................................... 4

2.3. Experimental Design ............................................................................................... 5

2.4. 14C Radiocarbon Analysis ....................................................................................... 8

Chapter 3. Results ...................................................................................................... 12

3.1. Overturning Streamfunction, Volume, and Residence Time ................................. 12

3.2. 14C Radiocarbon Ages .......................................................................................... 19

Chapter 4. Discussion ............................................................................................... 30

Chapter 5. Conclusions ............................................................................................. 35

References ..................................................................................................................... 37

Appendix A. Supplemental Information ................................................................ 42

A1. Tidal Mixing Parameterization ................................................................................. 42

A2. LGM – PI Differences in Ventilation Age ................................................................. 43

vii

List of Tables

Table 1 Boundary condition parameters that differentiate the PI simulations from the LGM simulations .................................................................................. 5

Table 2 Pre-formed phosphate endmembers for AABW and NADW for each simulation (µmol kg-1). ............................................................................. 10

Table 3 ∆14C endmembers for AABW and NADW for each simulation (‰). ........ 11

Table 4 The maximum (NADW) and minimum (AABW) of the overturning streamfunction in Sv for each simulation calculated from northward meridional velocity over the global ocean. ............................................... 13

Table 5 Depth in meters (measured from the surface) of the boundary between positive overturning (NADW, Pacific Deep Water, Indian Deep Water) and negative overturning (AABW), averaged over 30ºS to 30ºN, for the global ocean. A greater depth from the surface indicates a larger volume of NADW, Pacific Deep Water, or Indian Deep Water and a smaller volume of AABW. ................................................................................................. 14

Table 6 Thickness of AABW in meters, calculated as the average depth of topography below AABW from 30ºS to 30ºN (4389 m) minus the depth of the boundary between positive overturning (NADW, Pacific Deep Water, Indian Deep Water) and negative overturning (AABW), averaged over 30ºS to 30ºN, for the global ocean. ......................................................... 14

Table 7 An approximation of global AABW residence time, expressed in s/m2 and calculated from the thickness of AABW divided by overturning strength. 14

viii

List of Figures

Figure 1 Diapycnal diffusivity (kv) as a function of depth. ........................................ 7

Figure 2 Atlantic Ocean overturning streamfunction in Sv, Pre-Industrial (PI). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure. ............................................................................................. 15

Figure 3 Indo-Pacific Ocean overturning streamfunction in Sv, Pre-Industrial (PI). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure. ............................................................................................. 16

Figure 4 Atlantic Ocean overturning streamfunction in Sv, Last Glacial Maximum (LGM). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure. ............................................................................................. 17

Figure 5 Indo-Pacific Ocean overturnign streamfunction in Sv, Last Glacial Maximum (LGM). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure. ................................................................................ 18

Figure 6 Pre-Industrial (PI) radiocarbon ages for the Atlantic Ocean calculated according to equation 2. .......................................................................... 22

Figure 7 Pre-Industrial (PI) radiocarbon ages for the Indo-Pacific Ocean calculated according to equation 2. .......................................................................... 23

Figure 8 Last Glacial Maximum (LGM) radiocarbon ages for the Atlantic Ocean calculated according to equation 2. Circles are benthic minus atmosphere radiocarbon ages using data from [Skinner et al., 2017]. .... 24

Figure 9 Last Glacial Maximum (LGM) radiocarbon ages for the Indo-Pacific Ocean calculated according to equation 2. Circles are benthic minus atmosphere radiocarbon ages using data from [Skinner et al., 2017]. .... 25

Figure 10 Pre-Industrial (PI) circulation age for the Atlantic Ocean. ........................ 26

Figure 11 Pre-Industrial (PI) circulation age for the Indo-Pacific Ocean. ................. 27

Figure 12 Last Glacial Maximum (LGM) circulation age for the Atlantic Ocean. ..... 28

Figure 13 Last Glacial Maximum (LGM) circulation age for the Indo-Pacific Ocean. ................................................................................................................. 29

Figure 14 The percent change of AABW overturning, thickness, and residence time between the LGM and PI simulations, relative to PI ................................ 34

1

Chapter 1. Introduction

The Last Glacial Maximum (LGM, 18-24,000 years ago) is the most recent glacial

period, characterized by a gradual decrease in global temperature from the end of the

last interglacial period (115,000 years ago) until the LGM, and a sudden increase in

global temperature from the end of the LGM until the beginning of the Holocene (11,000

years ago) [Kohfeld and Chase, 2017]. The initial temperature change is attributed to

lower insolation from a change in orbital forcing amplified by a later decrease in

atmospheric greenhouse gas concentrations [Kohfeld and Chase, 2017; Jouzel et al.,

2007], resulting in the LGM climate being much colder than pre-industrial (PI, 1800), with

atmospheric CO2 concentrations that were 85-90 ppm lower than PI [Siegenthaler et al.,

2005; Monnin et al., 2001]. The carbon was most likely stored in the glacial deep ocean

[Kohfeld and Ridgwell, 2009; Sigman et al., 2010; Lund et al., 2011], as result of

changes in the structure and character of the deep ocean. Multiple sediment proxy

records have been interpreted to suggest that North Atlantic Deep Water (NADW)

shoaled to ~2000 m depth, compared to 4000 m for the modern ocean [Howe et al.,

2016], and that Antarctic Bottom Water (AABW) likely occupied a greater volume of the

ocean [Curry and Oppo, 2005; Howe et al., 2016; Burke and Robinson, 2012; Burke et

al., 2015; Lynch-Stieglitz et al., 2007; Lynch-Stieglitz and Marchitto, 2014]. Furthermore,

the deep ocean is also thought to have been colder, more saline, more stratified [Adkins

et al., 2002], and poorly ventilated relative to today’s ocean. Radiocarbon evidence has

been interpreted to suggest that NADW was relatively young and therefore well-

ventilated (radiocarbon rich) while AABW was relatively old and therefore poorly

ventilated (radiocarbon poor) [Burke and Robinson, 2012; Burke et al., 2015; Lynch-

Stieglitz et al., 2007]. The proxy data for ventilation has been used to make the case for

weak AABW and strong NADW overturning [Burke and Robinson, 2012; Burke et al.,

2015].

Enhanced deep-water stratification during the LGM has been interpreted to

suggest that the degree of mixing between NADW and AABW was reduced relative to

abyssal overturning strength [Lund et al., 2011]. Lund et al. [2011] used δ18O and δ13C

2

of benthic foraminifera to estimate that the ratio of overturning to mixing in the deep

Atlantic Ocean Basin was 2-8 times greater during the LGM when compared with the

modern ocean. They noted that decreased vertical mixing between NADW and AABW

was a more probable response than a 2-8 fold increase in abyssal overturning, in

particular as the boundary between these two water masses shoaled away from the

influence of turbulent mixing associated with interactions with topography at the bottom

of the ocean [Lund et al., 2011]. According to this theory, stratification between the

water masses increases if mixing is reduced, promoting the shoaling of NADW and the

thickening of AABW. A feedback ensues where slight increases in AABW thickness

decrease mixing, which promotes stratification, encouraging further thickening of AABW

until an equilibrium is reached [De Boer and Hogg, 2014].

Simulating the glacial-interglacial changes in deep ocean circulation behavior is

crucial to understanding the role of ocean circulation in modulating atmospheric CO2, but

simulating these changes successfully remains a challenge. Several studies have

highlighted the potential role of vertical mixing in determining the structure and

overturning strength of water masses in models. Simmons et al. [2004] and Jayne

[2009] have both found that the overturning strength and volume of NADW and AABW in

modern ocean simulations depend heavily on the diffusivity profile, which is dependent

on the choice of mixing parametrization. Green [2009] found that NADW overturning

strength increases with stronger diffusivity under both PI and LGM conditions, though

LGM NADW overturning was consistently weaker than PI NADW overturning. By

contrast, Montenegro et al. [2007] did not find a clear relationship between diffusivity and

overturning circulation, though they did find a weak correlation between overturning

strength and the power consumed by vertical mixing. De Boer and Hogg [2014] tested

the sensitivity of overturning rates and deep water volume to changes in vertical mixing

schemes using a simple three-box model. This study showed that only a vertically

variable diffusivity scheme — in which diffusivity in the deep ocean varied as a function

of the area of bottom topography — was able to simulate an increase in AABW

thickness with a concomitant decrease in overturning, consistent with the previously

described interpretation of the paleoenvironmental data. While based on a simplified

modelling scheme, the De Boer and Hogg [2014] study signals the potential importance

of vertical mixing schemes in simulating bottom water volume and overturning rates in

more complex models.

3

In this study, we use the University of Victoria Earth Systems Climate Model

(UVic ESCM) to examine the impact of vertical mixing on AABW and NADW formation

rate and volume. Specifically, we analyze the effects of mixing schemes on the strength

of the overturning streamfunction, the depth of the interface between NADW and AABW,

the ventilation age of AABW, and the relationships between these variables, under both

pre-industrial and LGM conditions.

4

Chapter 2. Methods

2.1. Model Description

LGM and PI simulations were performed using the UVic ESCM, version 2.9 [Eby

et al., 2009]. A coupled 1-layer energy and moisture balance atmosphere and an ocean

general circulation model comprise the UVic ESCM, as well as coupled sea-ice, an

inorganic carbon cycle, a nutrient-phytoplankton-zooplankton-detritus marine ecosystem,

a land-surface exchange scheme, and a dynamic vegetation model [Weaver et al.,

2001]. The ocean component of the model is based on the Geophysical Fluid Dynamic

Laboratory (GFDL) Modular Ocean Model version 2.2 (MOM 2.2) [Pacanowski, 1996],

and has been updated over time. The resolution of the model is 3.75º zonal by 1.8555º

meridional, with 19 layers of depth in the ocean. In the standard version of the model,

diapycnal mixing is simulated with a Bryan and Lewis diffusivity profile [Bryan and Lewis,

1979], which is included in our study along with four other model versions with other

mixing parameterizations as the basis for our testing (see section 2.3). In addition to

vertical mixing, diffusion also occurs along isopycnals [Gent and McWilliams, 1990], and

parameterization of mesoscale eddies is based on Gent et al. [1995].

2.2. Model Set-up

The boundary conditions for pre-industrial simulations with the UVic ESCM are in

accordance with CMIP5 protocol [Zickfeld et al., 2013; Taylor et al., 2012], while LGM

simulations were based on PMIP4 protocol at the time of set-up for the simulations in

July 2016 [Kageyama et al., 2017] (Table 1). At that time, the aerosol forcing protocol

was not yet decided, so our simulations do not use aerosol forcing, and the minimum

requirement for changing topography and coastlines was to convert the Bering Strait, the

Hudson Bay, and the Barents Sea to land. The current PMIP4 protocol provides multiple

dust aerosol forcing data sets to choose from, and the changes to topography and

coastlines are determined from the ICE6G data set [Peltier et al., 2015; Argus et al.,

2014]. The primary difference between the coastlines used in the current PMIP4

protocol and those used in our simulations is that our simulations do not include a land

5

bridge between Australia and Papua New Guinea whereas the ICE6G data set does. A

wind feedback is parameterized in the UVic ESCM whereby the model calculates wind

stress anomalies based on surface air temperature changes, which are added to a

prescribed present-day wind climatology [Weaver et al., 2001]. The Southern

Hemisphere Westerlies in our LGM simulations are weaker in strength relative to the PI

simulations. Paleo-environmental proxies indicate uncertainty regarding the position and

strength of the Southern Westerlies; the theories most consistent with the proxies are a

strengthening, an equatorward shift, or no shift compared to PI [Kohfeld et al., 2013].

Although they are not strongly supported by the available proxies, simulated LGM winds

are not inconsistent with paleodata.

Table 1 Boundary condition parameters that differentiate the PI simulations from the LGM simulations

Boundary Condition PI LGM

Year 1800 -19,000

CO2 283 ppm 190 ppm

Additional Greenhouse Gas Radiative Forcing

0 W m-2 -0.50 W m-2

Land Ice ICE4G ICE6G

Volcanic Forcing 0.143 W m-2 None

Aerosol Radiative Forcing 0 W m-2 0 W m-2

Atmospheric 14C concentration 0‰ 420‰

2.3. Experimental Design

Five different vertical mixing schemes were implemented in the UVic ESCM,

including: (1) a Bryan-Lewis profile for diapycnal diffusivity, (2) a linearized version of the

Bryan-Lewis profile, (3) a Bryan-Lewis profile with enhanced deep mixing, (4) diapycnal

diffusivity calculated from tidal energy dissipation, and (5) constant vertical diffusivity

(Figure 1).

The Bryan-Lewis is a tangent function with an inflection point at 2500 m. Our

simulations use a surface diapycnal diffusivity value of 0.4 cm2/s and a diapycnal

diffusivity value at depth of 1.4 cm2/s.

The linearized version of the Bryan-Lewis profile was designed based on the

principle that the vertical mixing coefficient should increase as the surface area of

6

bottom topography increases with depth, and was implemented by changing the

coefficients of the Bryan and Lewis tangent equation to represent a point-slope line

between the surface and deepest coefficient of the Bryan-Lewis profile (Figure 1). The

surface diapycnal diffusivity of this profile is 0.4 cm2/s and diapycnal diffusivity at depth is

1.3 cm2/s.

The modified version of the Bryan-Lewis profile with enhanced deep mixing was

implemented to test the effects of a stronger mixing at depth on overturning circulation

and volume. This enhanced deep mixing scheme is the most similar in profile to that of

the variable diffusivity scheme from De Boer and Hogg [2014], which is based on the

average surface area of topography at each depth level. The surface diapycnal

diffusivity value remains 0.4 cm2/s, but the inflection point of the tangent equation shifts

down to 3000 m and diapycnal diffusivity at depth is 1.8 cm2/s.

Vertical mixing from tides occurs when surface tides (barotropic) flow against

rough topography and create internal (baroclinic) tides with long wavelengths of about

6000 km. Roughly two thirds of the energy generated from the clashing of barotropic

tides against topography propagates away with the baroclinic tides, while the remaining

one third acts as local turbulence, enhancing vertical mixing in that area. A tidal energy

dissipation map is prescribed in the model, which is then used to calculate vertical

mixing based on such factors as background diffusivity (chosen as 0.3 cm2/s), tidal

dissipation efficiency, buoyancy frequency, and the vertical decay of turbulence. A

detailed description of the tidal mixing parameterization can be found in appendix A1.

The diffusivities used for each of the mixing schemes differ slightly from the

standard values of the UVic ESCM [Eby et al., 2009] because under LGM boundary

conditions, the simulated Atlantic Meridional Overturning Circulation (AMOC) stabilizes

at unrealistically weak overturning rates (1-2 Sv) using the standard diffusivities. As a

result, an increase in diffusivity of the entire vertical mixing profile by 0.1 cm2/s (0.15

cm2/s for the constant vertical mixing scheme) was required to stabilize the AMOC at 12-

15 Sv under LGM conditions (Table 4). The increased diffusivity was applied to both PI

and LGM simulations to facilitate comparison between simulations for the two time

periods.

7

Values of vertical diffusivity in the PI simulations were chosen to produce similar

NADW overturning rates between the mixing schemes (22.7 Sv – 24.3 Sv). The aim of

our study is to determine the impact of the vertical mixing profile on overturning, volume,

and ventilation age during the LGM. In order to ensure that any differences between the

mixing schemes in the LGM simulations are created by how each vertical mixing profile

interacts with the LGM boundary condition forcing, we chose the vertical diffusivities

such that differences in Atlantic overturning are minimal between mixing schemes under

PI conditions.

UVic ESCM spinup simulations were run for PI and LGM boundary conditions

with each mixing scheme. Each simulation was run for 10,000 years, at which time the

rate of change for global average potential temperature and global average salinity was

less than 0.02ºC per thousand years and 0 psu per thousand years respectively for all

simulations.

Figure 1 Diapycnal diffusivity (kv) as a function of depth.

8

2.4. 14C Radiocarbon Analysis

In the broader context of glacial-interglacial studies, ocean ventilation plays an

important role in the sequestration of carbon into the deep ocean during glacial periods;

therefore, we have elected to include simulated ages in this study as another facet of

ocean structure and circulation during the LGM. Ventilation refers to the exchange of

water mass properties between the surface ocean, the mixed layer, and the deep ocean.

If the deep ocean is poorly ventilated, it is capable of storing more carbon, as it can

accumulate carbon from organic matter settling from the surface, which re-mineralizes at

depth, without re-releasing this carbon immediately to the atmosphere. Calculating the

age of a water mass as the time elapsed since a water parcel was last at the surface is a

way of quantifying ventilation. For the purposes of this study, ventilation age refers to

any method of calculating the age of a water parcel. We use three methods of

calculating ventilation age; residence time, radiocarbon age, and circulation age.

Residence time measures the time required to replace all the water in a

reservoir. To do so, the volume of water in the reservoir is divided by the rate at which

water either enters or leaves the reservoir, in this case the overturning strength, to arrive

at the amount of time it would take to flush out or refill that volume at that given rate. We

estimate residence time using the thickness of AABW; because the width of the global

ocean is fixed, the only change in AABW volume between mixing schemes is a result of

a change in the thickness of the water mass, and the estimate is approximately

proportional to residence time calculated from volume. These concepts give us the

equation:

𝑅∗ = 𝑇/Ψ (1)

Where 𝑅∗ is the residence time estimate in s/m2, T is AABW thickness in m, and Ψ is

AABW overturning strength in Sv.

While residence time is a useful estimate of water mass age, calculating the

radiocarbon content of the ocean allows for analysis of the spatial distribution of water

age, which is necessary both for a more accurate understanding of age as it relates to

circulation and as a means of comparing to observational data. 14C is at the core of two

methods to calculate ventilation age: the benthic minus atmosphere method, and the

circulation age method. Radiocarbon dating relies on the known decay rate of 14C into

9

12C to determine at any point in the ocean the time elapsed since that parcel of water

was last at the surface. The benthic minus atmosphere method (“B-Atm” or “radiocarbon

age”) assumes that the ratio of 14C/12C in the surface ocean is set by the ratio in the

atmosphere, and any change from this ratio in the ocean interior results from aging and

decay [Cook and Keigwin, 2015]. The B-Atm method is one of the standard methods of

calculating the age of water masses from sediment, which allows for comparison

between model data and observed data. Another advantage of the B-atm method is that

it facilitates comparison between the LGM and PI results, as this method accounts for

the difference in the atmospheric concentration of 14C between these two time periods

[Cook and Keigwin, 2015]. A second method, calculating the circulation age of the

water, corrects for two processes which could impact the apparent age of the water.

Disequilibrium between the atmosphere and surface water can result in the surface

water not having the same 14C/12C ratio as the atmosphere, and this disequilibrium may

not be uniform between different regions of the surface ocean. Mixing between water

masses with different levels of disequilibrium with the atmosphere can further impact the

apparent age of the water. By calculating the age of water using the ratio of 14C/12C from

surface water, rather than the atmosphere, and accounting for the mixing of water

masses from different source points from the surface, a more accurate age can be

calculated for any point in the ocean and spatial differences in age can be attributed to

circulation rather than different levels of disequilibrium with the atmosphere.

UVic ESCM 2.9 estimates ∆14C, the depletion of 14C in ‰, from the concentration

of atmospheric ∆14C based on the parameterization of Stocker and Wright [1996]. PI

simulations used the default atmospheric 14C concentration of 0 ‰, whereas 420 ‰ was

chosen as the atmospheric 14C concentration during the LGM [Mariotti et al., 2013; Hain

et al., 2014].

To calculate the radiocarbon age t of a water parcel, we use the equation

[Menviel et al., 2016]:

𝑡 = 𝜆−1ln (∆ 𝐶14

𝑎𝑡𝑚+1000

∆ 𝐶14 +1000) (2)

where 𝜆 is a decay constant and ∆14Catm is 0 ‰ for PI and 420 ‰ for the LGM. The

Libby decay constant of 8330-1 yr-1 was chosen for 𝜆 for better comparison with sediment

data from Skinner et al. [2017].

10

We also calculate circulation based radiocarbon ages, which represent the time

since a parcel of water has left the surface, using the method of Matsumoto [2007].

First, model simulated phosphate and oxygen concentrations are used to calculate pre-

formed phosphate (PO4*) at all grid points using the apparent oxygen utilization equation

[Broecker et al., 1985]:

𝑃𝑂4 ∗ = 𝑃𝑂43− +

𝑂2

175− 1.95 𝜇𝑚𝑜𝑙 𝑘𝑔−1 (3)

where PO43- is the concentration of phosphate and O2 is the concentration of oxygen.

Next, the pre-formed phosphate endmembers for NADW and AABW (Table 2) were

used to calculate the fraction of each water mass in the rest of the ocean:

𝑓𝑛 = 𝑃𝑂4∗𝐴𝐴𝐵𝑊−[𝑃𝑂4∗]

𝑃𝑂4∗𝐴𝐴𝐵𝑊− 𝑃𝑂4∗𝑁𝐴𝐷𝑊 (4)

where fn is the fractional component of NADW for a given parcel of water, PO4*AABW is

the pure AABW endmember, PO4*NADW is the NADW endmember, and [PO4*] is the

concentration of pre-formed phosphate for the given parcel of water [Broecker et al.,

1991; Matsumoto, 2007].

The empirical constants for present day PO4*AABW and PO4*NADW are 1.95 µmol

kg-1 and 0.75 µmol kg-1, respectively, as determined in Broecker et al. [1998]. Our

simulation specific endmembers can be found in Table 2, and were chosen as an

average of surface values in the Ross and Weddell Seas for AABW and an average of

all values that are both north of 55°N and deeper than 1500 m within the Atlantic Ocean

for NADW.

Table 2 Pre-formed phosphate endmembers for AABW and NADW for each simulation (µmol kg-1).

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

AABW

PI 1.94 1.93 1.95 1.95 1.94

LGM 1.65 1.63 1.68 1.60 1.67

NADW

PI 1.05 1.06 1.07 0.95 1.04

LGM 0.82 0.86 0.91 0.74 0.82

11

The fraction of NADW in each grid cell (fn) was then used, along with ∆14C

endmembers, to determine the appropriate correction to apply at each point in the ocean

to account for any disequilibrium between the surface ocean and the atmosphere with

respect to 14C. The ∆14C endmembers represent the starting concentration of 14C at the

formation sites of NADW and AABW, and differ from the atmospheric concentration

based on the level of disequilibrium between the atmosphere and the surface ocean at

each of the two sites. The ∆14C endmembers are calculated for each simulation with the

same method used for determining pre-formed phosphate endmembers. The corrected

∆14C values (∆14C*) are calculated as follows [Matsumoto, 2007]:

∆14𝐶∗ = ∆14𝐶 − (∆14𝐶𝑁𝐴𝐷𝑊 × 𝑓𝑛 + ∆14𝐶𝐴𝐴𝐵𝑊 × (1 − 𝑓𝑛)) (5)

Table 3 ∆14C endmembers for AABW and NADW for each simulation (‰).

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

AABW

PI -109 -103 -103 -113 -109

LGM 124 134 141 120 123

NADW

PI -56 -55 -56 -56 -56

LGM 285 285 286 284 284

Finally, the corrected ∆14C values (∆14C*) are used as input for the Stuvier and

Polach [1977] age equation, and the result is the circulation age:

𝑡 = −8033 ln (1 +∆ 𝐶14 ∗

1000) (6)

12

Chapter 3. Results

3.1. Overturning Streamfunction, Volume, and Residence Time

All mixing schemes demonstrated increases in AABW volume and overturning

during the LGM when compared with the PI simulations (Figures 2-5, Tables 4-6).

AABW overturning is 13-21% stronger in the LGM simulations compared to PI,

increasing from a range of 9.7-12.3 Sv in the PI simulations to 11.8-14.3 Sv in the LGM

simulations. The simulations with the constant mixing scheme demonstrated the

greatest percent increase in AABW overturning between PI and LGM, and the

simulations with tidal mixing showed the least change. In the PI simulations, AABW only

spreads as far north as 30N in the Atlantic Ocean, whereas in the LGM simulations

AABW spreads to 60N (Figures 2 and 4). NADW shoals in the LGM simulations

relative to PI, and AABW fills the formerly occupied space. AABW is 34-46% thicker in

the LGM simulations relative to PI, increasing from 1730-1870 m in the PI simulations to

2440-2550 m in the LGM. The greatest percent change in thickness between the LGM

and PI occurs in the simulations with the constant mixing scheme, while the least

percent change occurs in the simulations with the linear mixing scheme. NADW

overturning strength weakens 40-47% from 22.7-24.3 Sv in the PI simulations to 12.6-

14.2 Sv in the LGM, with NADW changing the most in the simulation with tidal mixing

and changing the least in the simulation with linear mixing.

All mixing schemes produce similar overturning rates for NADW under PI

conditions by design (Figure 2, Methods 2.3). For most of the PI simulations, choosing

to make sure the simulations produce similar NADW overturning rates has resulted in

the simulations also displaying similar AABW overturning rates and similar volumes for

each of the water masses. The exception is the simulation with the constant mixing

scheme which exhibits NADW overturning strength under pre-industrial conditions that is

nearly identical to the other mixing schemes (as designed), but pre-industrial AABW

overturning rates that are approximately 20% weaker than the other mixing schemes

(Table 4, Figure 2). Volume is inferred from the depth of the 0 Sv contour boundary

13

between positive (northern sourced) overturning values, and negative overturning values

(southern sourced) (Figure 2). The PI boundary, measured from the surface, ranges

from 2520 m for the simulation with tidal mixing to 2660 m for the simulation with

constant mixing (Table 5). Just as the simulation with the constant mixing scheme is the

most dissimilar from the other PI simulations for AABW overturning, it is also the most

dissimilar from the others regarding water mass volume. Excluding the simulation with

constant mixing, the range between the shallowest and deepest water mass boundaries

for the other simulations is 50 m.

NADW and AABW volume and overturning are also similar between the mixing

schemes for the LGM simulations. As with the PI simulations, there is a 1.6 Sv

difference in NADW overturning strength between the simulations with the strongest

overturning and the weakest overturning (the simulations with constant and enhanced

deep mixing respectively, Table 4, Figure 4). The absolute difference in AABW

overturning between simulations with different mixing schemes is also very similar under

PI and LGM conditions (2.6 Sv for PI, 2.5 Sv for LGM). The difference in the depth of

the NADW-AABW boundary between the LGM simulations is small, apart from the

simulation with linear mixing. Between the other four LGM mixing simulations the

difference in boundary depth is only 20 m, with an average boundary depth of 1850 m.

The LGM simulation with linear mixing has a much deeper boundary at 1950 m.

Table 4 The maximum (NADW) and minimum (AABW) of the overturning streamfunction in Sv for each simulation calculated from northward meridional velocity over the global ocean.

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

AABW

PI 12.3 9.7 12.1 12.1 12.3

LGM 14.3 11.8 13.8 13.7 14.1

NADW

PI 22.8 23.8 23.2 24.3 22.7

LGM 12.9 14.2 13.9 12.9 12.6

14

Table 5 Depth in meters (measured from the surface) of the boundary between positive overturning (NADW, Pacific Deep Water, Indian Deep Water) and negative overturning (AABW), averaged over 30ºS to 30ºN, for the global ocean. A greater depth from the surface indicates a larger volume of NADW, Pacific Deep Water, or Indian Deep Water and a smaller volume of AABW.

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

PI 2570 2660 2564 2522 2560

LGM 1840 1858 1951 1858 1837

Table 6 Thickness of AABW in meters, calculated as the average depth of topography below AABW from 30ºS to 30ºN (4389 m) minus the depth of the boundary between positive overturning (NADW, Pacific Deep Water, Indian Deep Water) and negative overturning (AABW), averaged over 30ºS to 30ºN, for the global ocean.

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

PI 1819 1729 1825 1867 1829

LGM 2549 2531 2438 2531 2552

Table 7 An approximation of global AABW residence time, expressed in s/m2 and calculated from the thickness of AABW divided by overturning strength.

Bryan and Lewis

Constant Linear Tidal Enhanced Deep Mixing

PI 148 178 150 154 149

LGM 178 214 176 185 181

15

Figure 2 Atlantic Ocean overturning streamfunction in Sv, Pre-Industrial (PI). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure.

16

Figure 3 Indo-Pacific Ocean overturning streamfunction in Sv, Pre-Industrial (PI). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure.

17

Figure 4 Atlantic Ocean overturning streamfunction in Sv, Last Glacial Maximum (LGM). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure.

18

Figure 5 Indo-Pacific Ocean overturnign streamfunction in Sv, Last Glacial Maximum (LGM). Positive overturning values represent northern-sourced water flowing clockwise with respect to the figure. Negative overturning values represent southern-sourced water flowing counter-clockwise with respect to the figure.

19

3.2. 14C Radiocarbon Ages

The PI simulations exhibit very little difference in the B-Atm ages between the

mixing schemes, and all share distinct spatial patterns for the Atlantic Ocean and Pacific

Ocean (Figures 6, 7). Surface water ages calculated using the B-Atm method are older

than 0 years because this method does not include a correction for disequilibrium

between the atmosphere and ocean. In the Atlantic Ocean, the youngest water extends

as deep as 500 m in the downwelling zones at 30N and 30S and down to the bottom of

the ocean just below 3500 m in the North Atlantic Ocean where NADW forms. After the

formation of NADW, the water ages moving from the north to 40S between the surface

water and the boundary between NADW and AABW, which in the Atlantic Ocean occurs

at roughly 3300 m depth. At the NADW-AABW boundary a sharp increase in age

occurs. South of 40S, AABW forms in a column from the surface ocean to the bottom

topography. Below 3300 m, AABW ages increase, with the oldest water at the bottom of

the Atlantic Ocean between 15S and 45S, in between the newly formed AABW and the

northern boundary where AABW mixes up into NADW. The Pacific Ocean is

predominately made of AABW, which is evident in the B-Atm ages; the youngest water is

near the location of AABW formation, and age increases from south to north, with the

oldest ages in the North Pacific Ocean between 2000 m and 3000 m. One subtle

difference between simulations with different mixing schemes is that the water in the

simulations with constant and tidal mixing ages more in the oldest parts of the Atlantic

and Pacific Oceans than in the other simulations. The surface ocean exhibits the same

ages and pattern in the Pacific Ocean as in the Atlantic Ocean. Unlike the Atlantic

Ocean, in the Pacific Ocean, the oldest ages are not at the bottom of the ocean, but

rather in a stagnant pocket between 2000 m and 3000 m.

The LGM simulations also demonstrate very little difference in B-Atm ages

between the mixing schemes, with spatial patterns in the Atlantic and Pacific Oceans

that are reminiscent of the PI simulations, yet with key differences (Figures 8, 9). As in

the PI simulations, in the Atlantic Ocean all LGM simulations exhibit a north to south

direction of aging from young to old above the NADW-AABW boundary, and a south to

north age gradient below the boundary. However, as NADW does not penetrate as

deeply in the LGM compared to PI simulations, the NADW-AABW boundary is closer to

2400 m in the LGM Atlantic Ocean. Additionally, the age gradient separating NADW and

20

AABW is much sharper in the LGM compared to PI. In the Pacific Ocean, both the PI

and LGM simulations are dominated by AABW so the spatial patterns in age are nearly

identical between all PI and LGM simulations in the Pacific Ocean. AABW in the North

Pacific Ocean in the simulation with linear mixing does not age as much as in the other

simulations.

The LGM – PI difference for the B-Atm ages indicates that the water masses in

the LGM simulations are older than those of the PI simulations everywhere, but the

aging does not occur uniformly (Appendix A2, Figures A1, A2). In the Atlantic Ocean,

the difference between the LGM and PI simulations is greater for AABW than NADW.

NADW is at least 300 years older in the LGM compared to PI, whereas AABW is at least

900 years older during the LGM compared to PI. For both water masses, in both the

Atlantic and the Pacific, the LGM – PI difference in B-Atm ages is greater where the

oldest water occurs. Additionally, in the Pacific Ocean there is a small region at 50N

and 1000 m depth where LGM ages are younger than PI because the region of young

water extends deeper from the surface.

Simulated changes in radiocarbon ages are in rough agreement with B-Atm ages

estimated using paleodata [Skinner et al., 2017], with exceptions in the Southern and

deep North Atlantic Oceans (Figures 8, 9). Both the sediment data and our model

simulations demonstrate aging from north to south in the upper 2500 m of the Atlantic

Ocean and from south to north below 2500 m, with a sharp increase in age at the

transition between NADW and AABW. The paleodata and the simulated ages also

exhibit aging from south to north for AABW in the Pacific Ocean with the maximum ages

at mid-depth in the North Pacific Ocean. Notable exceptions from these patterns exist in

both ocean basins. In the North Atlantic Ocean, an east-west gradient exists in the

paleodata such that the Eastern Atlantic Ocean paleodata matches our simulated B-Atm

ages, but the paleodata from the Western Atlantic is much younger than the simulated

ages, which show older NADW ages rather than older AABW. In the South Pacific

Ocean, a wide range of ages from the paleodata are clustered together, ranging from

711 years to 4331 years. Some of the observed ages in the South Pacific within the

range are in agreement with our simulated ages, which are roughly 2100-2400 years old

in that region.

21

The circulation ages (Figures 10-13, and Appendix A2, Figures A3, A4) show

similar patterns as the B-Atm ages, with the greatest difference being that the circulation

ages are considerably younger than the B-Atm ages. The PI simulations are 500-800

years younger using the circulation-based method of calculating age compared to the B-

Atm, and the LGM simulations are 700-1700 years younger in circulation age than B-

Atm age. The choice of method for calculating age has a particularly strong impact on

the age of newly formed NADW and AABW. The circulation ages corroborate the age

distribution derived with the B-Atm ages and confirm that LGM AABW was more poorly

ventilated than PI AABW. The circulation ages also indicate that accounting for

disequilibrium between the atmosphere and ocean and mixing between water with two

different surface sources has a particularly strong impact on the LGM simulations.

Applying these corrections, the range of ventilation ages for NADW is 0-300 years under

PI conditions and 0-400 years under LGM conditions. For AABW in the Atlantic, the

range is 300-500 years under PI conditions and 400-1100 years under LGM conditions.

For AABW in the Pacific, the range of ventilation ages is 300-1300 years under PI

conditions and 400-1700 years under LGM conditions.

22

Figure 6 Pre-Industrial (PI) radiocarbon ages for the Atlantic Ocean calculated according to equation 2.

23

Figure 7 Pre-Industrial (PI) radiocarbon ages for the Indo-Pacific Ocean calculated according to equation 2.

24

Figure 8 Last Glacial Maximum (LGM) radiocarbon ages for the Atlantic Ocean calculated according to equation 2. Circles are benthic minus atmosphere radiocarbon ages using data from [Skinner et al., 2017].

25

Figure 9 Last Glacial Maximum (LGM) radiocarbon ages for the Indo-Pacific Ocean calculated according to equation 2. Circles are benthic minus atmosphere radiocarbon ages using data from [Skinner et al., 2017].

26

Figure 10 Pre-Industrial (PI) circulation age for the Atlantic Ocean.

27

Figure 11 Pre-Industrial (PI) circulation age for the Indo-Pacific Ocean.

28

Figure 12 Last Glacial Maximum (LGM) circulation age for the Atlantic Ocean.

29

Figure 13 Last Glacial Maximum (LGM) circulation age for the Indo-Pacific Ocean.

30

Chapter 4. Discussion

The broad agreement between the B-Atm radiocarbon ages and the paleodata

[Skinner et al., 2017] indicates that the LGM circulation produced by the model, with

weaker NADW occupying shallower depths and stronger AABW filling a larger volume, is

a reasonable representation of the real world glacial ocean circulation, with a few

caveats. While our ages do increase in the Southern Ocean during the LGM relative to

PI, the paleodata displays a wide range of ages in the Southern Ocean including ages

older than those of our simulations, and the pattern of the North Atlantic Ocean

paleodata does not match our model; the sediment data implies that NADW should be

deeper in the Northwestern Atlantic Ocean than the model results (Figure 8).

The depth to which NADW ventilates the Atlantic Ocean during the LGM is a

topic of ongoing discussion in the field of paleoceanography. Multiple

paleoceanographic proxies demonstrate distinctly different characteristics between

NADW and AABW, and therefore the ratios between different isotopes or between two

related trace elements have been used to identify where the boundary between NADW

and AABW might have been during the LGM. Many studies of these proxies, in

particular δ13C, Cd/Ca, and εNd, have found evidence of a shoaling of NADW and high

stratification between these water masses [e.g., Curry and Oppo, 2005; Peterson et al.,

2014; Menviel et al., 2016; Howe et al., 2016; Lynch-Stieglitz et al., 2007]. Several

studies of modelled radiocarbon during the LGM, including ours, fit this interpretation

[Menviel et al., 2016; Meissner et al., 2003; Mariotti et al., 2013; Burke et al., 2015;

Muglia et al., 2018]. In particular, Muglia et al. [2018] simulated an LGM ocean with

multiple AMOC states and compared the results to observed radiocarbon, δ13C, and

δ15N. These authors found that simulations with weak and shoaled NADW overturning,

but not completely collapsed, are the best statistical match to these data, in spite of the

mismatch with the younger deep Northwest Atlantic Ocean radiocarbon ages. However,

Gebbie [2014] indicates that while the core mass of NADW likely shoaled and AABW

spread further north, these same proxies do not require the complete absence of NADW

in the deep North Atlantic Ocean, provided that the deeper portion of NADW is more

31

efficient at accumulating nutrients than upper NADW. The radiocarbon data compilation

from Skinner et al. [2017] would fit well with the interpretation from Gebbie [2014].

The large range of ages reconstructed from paleodata collected from adjacent

core sites in the South West Pacific (~1300-4300 years, Figure 9) poses a unique

challenge with regard to determining the degree to which the model accurately simulates

the observed LGM ventilation. Below 2000 m in the West Pacific between 37S and

47S, our simulations do not reproduce the youngest B-Atm ages from the paleodata

(~1300-1500 years) or the oldest B-Atm ages (~3200-4300 years). Instead, our

simulations are consistent with the young B-Atm ages found at shallower depths, around

1000 m depth between 37S and 45S (~ 800-1500 years), and the intermediate ages at

depth, between 2000 m and 4500 m (40-45S, ~ 2300-2700 years). The intermediate

ages below 2000 m are also consistent with the larger pattern in the Pacific basin of

deep water aging from south to north.

Interestingly, Menviel et al. [2016] found that in their simulation with very weak

AABW overturning produced a better match to the measured water mass ages

reconstructed from the radiocarbon paleodata, as well as to δ13C. However, in our LGM

simulations, water mass ages in the Southern Ocean are older than those found in the

PI simulations despite stronger overturning. Furthermore, the simulations with tidal and

enhanced deep mixing are older in the Southern Ocean than the simulations with

constant and linear mixing despite having stronger AABW overturning. Importantly, this

observation indicates that weaker AABW overturning is not a requirement for older

Southern Ocean radiocarbon ages.

Given that none of the mixing schemes exhibits a decrease in AABW overturning

strength during the LGM relative to PI, the hypothesis that topographically based mixing

schemes can simulate decreased AABW overturning during the LGM with increased

AABW volume [De Boer and Hogg; 2014] is not supported by this research. Our study

does not find strong differences between the mixing schemes, and is supported by the

results of other studies. Montenegro et al. [2007] found little difference in overturning

strength (less than 1 Sv) between their simulations with Bryan and Lewis and tidal

mixing schemes. Simmons et al. [2004] found that meridional transport is very similar

between simulations with Bryan and Lewis and tidal mixing, but different for their

simulation with constant mixing.

32

One potential explanation for the similarity between simulations with different

mixing schemes is that the surface diffusivity values of each mixing profile are very

similar. Jayne [2009] found that changing mixing in the upper ocean in the CCSM3

model has a bigger impact on overturning than changing mixing in the abyssal ocean.

Our study uses mixing schemes that all have similar diffusivity of approximately 0.45

cm2/s in the upper ocean because of our decision to choose values that would result in

similar NADW strength in the PI simulations. The Montenegro et al. [2007] and

Simmons et al. [2004] studies both compared mixing schemes with similar diffusivity

values in the upper ocean, except for the constant vertical diffusivity in Simmons et al.

[2004].

When comparing overturning, volume, and radiocarbon for each mixing scheme

across boundary conditions and oceanic basins, minimal differences exist between the

simulations, which may be a result of the experimental design. The diffusivity values for

our simulations were chosen to produce similar NADW overturning for each mixing

scheme under PI conditions; this was done to ensure that any differences between LGM

simulations could be attributed to differences in the diffusivity profile shapes rather than

other variables such as average diffusivity. Although only the PI simulations were

designed to create similar NADW overturning rates, the LGM NADW overturning values

are also very similar across mixing schemes, which possibly indicates that each of the

schemes reacted to the change in boundary conditions similarly (Table 1, Tables 4-7).

Given that overturning strength is one of the factors that determine the volume of a water

mass, it is reasonable that the simulations with different mixing schemes produce similar

volumes of NADW and AABW based on their similar overturning. Additionally,

circulation greatly influences the ventilation of a water mass, and therefore similar

circulation between the mixing simulations would result in similarities in both the

magnitude and spatial distribution of radiocarbon ages, regardless of the method used to

calculate age.

Although our research does not demonstrate a clear impact of the choice of

mixing parameterization on overturning, volume, or ventilation age, our results offer

insights into the larger question of LGM ocean carbon sequestration that ultimately

motivates the study. The question of whether AABW volume could have increased in

the LGM with a simultaneous decrease in overturning is born from three considerations:

(1) uncertainty in the paleo record regarding any direct proxies of AABW overturning

33

strength, (2) abundant evidence that AABW was poorly ventilated in the LGM, and (3)

physical as well as biogeochemical constraints regarding how 85-90 ppm of atmospheric

carbon could have been stored in the deep ocean during the LGM. Our results indicate

that decreased AABW overturning strength during the LGM is not a prerequisite for a

glacial AABW that is more poorly ventilated than modern AABW, provided that the

volume of glacial AABW grows by a larger factor than overturning strength.

The age of a water mass can affect its ability to store carbon, and estimating

residence time is a simple way to examine the effect volume and overturning strength

have on age. Residence time is the time required for a reservoir of water to replace its

entire volume at a given rate (overturning). An increase in the volume of AABW would

act to increase the residence time and age of AABW, whereas an increase in AABW

overturning strength would act to decrease residence time and age. All of our LGM

simulations increased in both AABW volume and AABW overturning strength relative to

PI. However, the ratio of volume to overturning is higher for the LGM simulations than

for the PI simulations (Figure 14), particularly for the simulations with the constant mixing

scheme. Therefore, more time is required to fill the volume of glacial AABW at the

glacial AABW overturning rate, and glacial AABW has a longer residence time than PI

AABW, implying an older water mass and increased capacity to store carbon.

Residence time increases by about 20% for our LGM simulations compared to our PI

simulations (Figure 14). Circulation ages for AABW in the LGM simulations increase by

30-120% in the Atlantic relative to the PI simulations, and increase by just over 30% in

the Pacific.

34

Figure 14 The percent change of AABW overturning, thickness, and residence time between the LGM and PI simulations, relative to PI

35

Chapter 5. Conclusions

The aim of our study was to understand the impact the choice of vertical mixing

parameterization has on AABW overturning, volume, and ventilation during the LGM. In

particular, one of the motivations of our study was the interpretation of

paleoenvironmental data that AABW volume may have grown while AABW overturning

weakened to decrease ventilation [Curry and Oppo, 2005; Howe et al., 2016; Burke and

Robinson, 2012; Burke et al., 2015; Lynch-Stieglitz et al., 2007]. We chose to examine

the effect of vertical mixing on these three components of ocean structure and dynamics

because decreased vertical mixing is theorized to be at least partially responsible for the

increased AABW volume, increased stratification, and decreased ventilation found in

reconstructions of the LGM ocean relative to today’s ocean [De Boer and Hogg, 2014;

Lund et al., 2011; Ferrari et al., 2014]. The five mixing schemes chosen for our

simulations were: (1) a Bryan-Lewis profile for diapycnal diffusivity, (2) a linearized

version of the Bryan-Lewis profile, (3) a Bryan-Lewis profile with enhanced deep mixing,

(4) diapycnal diffusivity calculated from tidal energy dissipation, and (5) constant vertical

diffusivity (Figure 1). AABW overturning was stronger in all LGM simulations relative to

the PI simulations, and AABW volume was larger for all LGM simulations compared to

the PI simulations as well. AABW was more poorly ventilated in all LGM simulations

than in the PI simulations, as indicated by simulated radiocarbon and circulation ages.

Residence time (the ratio between AABW volume and overturning) increased in all LGM

simulations relative to the PI simulations, indicating that AABW can become more poorly

ventilated alongside an increase in overturning strength, provided that the growth in

AABW volume is greater than the increase in AABW overturning strength. No strong

differences were present between simulations with different vertical mixing, likely

because we used similar diapycnal diffusivity values in the upper ocean for all schemes.

Our results highlight two further lines of inquiry. The first addresses the

difference between our results and those by De Boer and Hogg [2014], which motivated

our study. Their study found strong differences in simulated LGM AABW volume,

overturning, and residence time depending on the choice of mixing scheme, in contrast

to our study, which did not find substantial differences between simulations with different

36

mixing schemes. We did not find that topographically based mixing made a difference in

the relationship between volume and overturning, and all schemes produced increases

in residence time. The question of why our results differ from those of De Boer and

Hogg has not been addressed. Answering this question may provide further insight into

the relationship between mixing, overturning, and volume. The second line of inquiry

regards the mechanism responsible for a portion of the growth in AABW volume during

the LGM. Our simulations suggest that AABW can become more poorly ventilated if

volume increases more than the expected increase from stronger overturning; however,

in such a case the remaining increase in volume that is not explained by overturning

must be explained by another mechanism. What this mechanism could be is unknown.

While our research does not find a significant difference between the results of

simulations with different choices of mixing parameterization, our finding that AABW can

become more poorly ventilated under LGM conditions with increased volume and

overturning is worth consideration in the larger context of paleoceanography.

37

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Appendix A. Supplemental Information

A1. Tidal Mixing Parameterization

The tidal energy dissipation map is generated from the Simmons et al. [2004]

equation:

𝐸(𝑥, 𝑦) = 1

2𝜌𝑁𝜅ℎ2𝑢2 (1)

where 𝜌 is a reference seawater density, N is buoyancy frequency at the bottom of the

ocean, 𝜅 and h are the topographic wavenumber and amplitude for the generation of

baroclinic tides respectively, and u is barotropic tidal velocity [Simmons et al., 2004].

The tidal energy dissipation map is converted into vertical mixing, kv, according to

equation 2:

𝑘𝑣 = 𝑘0 + 𝑞Γ𝐸(𝑥,𝑦)𝐹(𝑧)

𝜌𝑁2 (2)

where k0 is background diffusivity (some of which is from energy brought by baroclinic

tides from other parts of the ocean), q is the tidal dissipation efficiency of 1

3, Γ is a mixing

efficiency of 0.2, and F is the vertical structure function:

𝐹(𝑧) = 𝑒−(𝐻+𝑧)/𝜍

𝜍(1−𝑒−𝐻/𝜍) (3)

where H is total depth and 𝜍 is vertical decay of turbulence [Simmons et al., 2004].

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A2. LGM – PI Differences in Ventilation Age

Figure A1 The difference between Last Glacial Maximum (LGM) and Pre-Industrial (PI) zonal mean radiocarbon ages in the Atlantic Ocean.

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Figure A2 The difference between Last Glacial Maximum (LGM) and Pre-Industrial (PI) zonal mean radiocarbon ages in the Indo-Pacific Ocean.

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Figure A3 The difference between Last Glacial Maximum (LGM) and Pre-Industrial (PI) zonal mean circulation ages in the Atlantic Ocean.

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Figure A4 The difference between Last Glacial Maximum (LGM) and Pre-Industrial (PI) zonal mean circulation ages in the Indo-Pacific Ocean.