Editorial Type:
Article
Article Type:
Research Article

Surface-to-Interior Transport Timescales and Ventilation Patterns in a Time-Dependent Circulation Driven by Sustained Climate Warming

Y. Liu aDepartment of Earth System Science, University of California Irvine, Irvine, California

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https://orcid.org/0000-0003-4901-561X
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F. Primeau aDepartment of Earth System Science, University of California Irvine, Irvine, California

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Online Publication:
29 Dec 2023
Print Publication:
01 Jan 2024
DOI:
https://doi.org/10.1175/JPO-D-23-0113.1
Page(s):
173–186
Free access

Abstract

The effect of climate warming in response to rising atmospheric CO2 on the ventilation of the ocean remains uncertain. Here we make theoretical advances in elucidating the relationship between ideal age and transit time distribution (TTD) in a time-dependent flow. Subsequently, we develop an offline tracer-transport model to characterize the ventilation patterns and time scales in the time-evolving circulation for the 1850–2300 period as simulated with the Community Earth System Model version 1 (CESMv1) under a business-as-usual warming scenario. We found that by 2300 2.1% less water originates from the high-latitude deep water formation regions (both hemispheres) compared to 1850. In compensation, there is an increase in the water originating from the subantarctic. We also found that slowing meridional overturning circulation causes a gradual increase in mean age during the 1850–2300 period, with a globally averaged mean-age increase of ∼110 years in 2300. Where and when the water will be re-exposed to the atmosphere depends on the post-2300 circulation. For example, if we assume that the circulation persists in its year-2300 state (scenario 1), the mean interior-to-surface transit time in year 1850 is ∼1140 years. In contrast, if we assume that the circulation abruptly recovers to its year-1850 state (scenario 2), the mean interior-to-surface transit time in 1850 is only ∼740 years. By 2300, these differences become even larger; in scenario 1, the mean interior-to-surface transit time increases by ∼200 years, whereas scenario 2 decreases by ∼80 years. The dependence of interior-to-surface transit time on the future ocean circulation produces an additional unavoidable uncertainty in the long-term durability of marine carbon dioxide removal strategies.

Significance Statement

The ocean’s circulation, when altered by climate warming, can affect its capacity to absorb heat and CO2, which are crucial for the global climate. In our study, we investigated how global warming, caused by rising CO2 levels, might impact the ocean circulation—the way water moves from deep ocean to the surface and vice versa. We discovered that by 2300, if we continue on our current warming trajectory, the origins of water within the ocean will shift, with less coming from deep, cold zones near the poles and more from subantarctic regions. As a result, deep water will take longer time before it resurfaces than shallow water. How quickly this water travels from deep regions to the surface could change, depending on the state of future ocean circulation. If the circulation remains as predicted in 2300, this journey will take longer. Conversely, if it reverts to the pattern in 1850, the process will be quicker. This variability introduces added uncertainty to strategies aimed at mitigating climate change by storing CO2 in the ocean. Our work highlights the intricate ways in which climate change can influence our oceans, potentially affecting our plans to mitigate global warming.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yi Liu, yil45@uci.edu

Abstract

The effect of climate warming in response to rising atmospheric CO2 on the ventilation of the ocean remains uncertain. Here we make theoretical advances in elucidating the relationship between ideal age and transit time distribution (TTD) in a time-dependent flow. Subsequently, we develop an offline tracer-transport model to characterize the ventilation patterns and time scales in the time-evolving circulation for the 1850–2300 period as simulated with the Community Earth System Model version 1 (CESMv1) under a business-as-usual warming scenario. We found that by 2300 2.1% less water originates from the high-latitude deep water formation regions (both hemispheres) compared to 1850. In compensation, there is an increase in the water originating from the subantarctic. We also found that slowing meridional overturning circulation causes a gradual increase in mean age during the 1850–2300 period, with a globally averaged mean-age increase of ∼110 years in 2300. Where and when the water will be re-exposed to the atmosphere depends on the post-2300 circulation. For example, if we assume that the circulation persists in its year-2300 state (scenario 1), the mean interior-to-surface transit time in year 1850 is ∼1140 years. In contrast, if we assume that the circulation abruptly recovers to its year-1850 state (scenario 2), the mean interior-to-surface transit time in 1850 is only ∼740 years. By 2300, these differences become even larger; in scenario 1, the mean interior-to-surface transit time increases by ∼200 years, whereas scenario 2 decreases by ∼80 years. The dependence of interior-to-surface transit time on the future ocean circulation produces an additional unavoidable uncertainty in the long-term durability of marine carbon dioxide removal strategies.

Significance Statement

The ocean’s circulation, when altered by climate warming, can affect its capacity to absorb heat and CO2, which are crucial for the global climate. In our study, we investigated how global warming, caused by rising CO2 levels, might impact the ocean circulation—the way water moves from deep ocean to the surface and vice versa. We discovered that by 2300, if we continue on our current warming trajectory, the origins of water within the ocean will shift, with less coming from deep, cold zones near the poles and more from subantarctic regions. As a result, deep water will take longer time before it resurfaces than shallow water. How quickly this water travels from deep regions to the surface could change, depending on the state of future ocean circulation. If the circulation remains as predicted in 2300, this journey will take longer. Conversely, if it reverts to the pattern in 1850, the process will be quicker. This variability introduces added uncertainty to strategies aimed at mitigating climate change by storing CO2 in the ocean. Our work highlights the intricate ways in which climate change can influence our oceans, potentially affecting our plans to mitigate global warming.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yi Liu, yil45@uci.edu
Keywords: Abyssal circulation; Meridional overturning circulation; Ocean circulation; Climate change

1. Introduction

The surface patterns and time scales with which the interior ocean is in contact with the atmosphere (hereafter ventilated) determine the ocean’s ability to modulate Earth’s climate by taking up and redistributing heat and carbon (Katavouta et al. 2019). Here we focus on key time scales: the mean age (i.e., the mean transit time for water to be transported from the sea surface into the interior) and the mean first-passage time (i.e., the mean transit time for water to be transported from the ocean interior back to the surface). The theory describing transit-time distributions (TTDs) for stationary flows and its connection to the ideal-age tracer that is included in many Earth system models (e.g., Moore et al. 2018) is well developed (Delhez et al. 1999; Holzer and Hall 2000; Khatiwala et al. 2001; Deleersnijder et al. 2001; Primeau 2005). At steady state in a time-invariant flow, the ideal age is equal to the mean of the last-passage time (i.e., the surface-to-interior transit time) distribution, that is, to the mean age (Primeau 2005). The mean of the first-passage time distribution has received less attention, but it is particularly useful for quantifying carbon sequestration (DeVries et al. 2012; Siegel et al. 2021). For time-dependent situations, TTDs describing both last-passage (i.e., backward TTD) and first-passage times (i.e., forward TTD) have been analyzed in catchment hydrological research (e.g., Benettin et al. 2022). However, in situations where the ocean circulation is evolving in time due to global warming, neither the mean age nor the mean first-passage time has received much attention.

Indeed, most previous studies have focused on the present-day circulation, treating it as stationary with no secular trends in the overturning circulation (e.g., Primeau 2005; DeVries and Primeau 2011; Shah et al. 2017; Rousselet et al. 2021). Recently, Chamberlain et al. (2019) and Holzer et al. (2020) examined mean transit times in ocean circulation states diagnosed from a transient climate change simulation. However, they treated the decadal-mean snapshots captured during a transient climate warming simulation as if they could be applied indefinitely into the past and future without considering the fact that the snapshots were part of a climate state that was evolving on longer time scales. Many Earth system models include an ideal age tracer that evolves according to the changing ocean circulation. However, because these ideal age tracers are typically initialized with an age of zero, their time evolution reflects the effects of the ongoing spinup in addition to those of the changing ocean circulation. As a result, their instantaneous values are not equal to the time-evolving mean of the underlying TTDs, making it difficult to determine how the ideal age tracers are related to the ventilation time scales.

Here we aim to answer three questions: 1) What is the connection between the mean of the time-dependent TTD and ideal age in a time-dependent flow? 2) What are the ocean ventilation time scales in a situation where the circulation is evolving in time due to climate warming? 3) What are the regional variations in the fraction of the interior ocean volume ventilated from different regions of the surface ocean, and how are these regional fractions changing with time? To answer these questions, we apply transit-time diagnostics to a time-evolving flow without making any stationarity assumption. Moreover, we do this in the context of a transient climate change simulation for the 1850–2300 period in a business-as-usual warming scenario in which the global overturning circulation eventually collapses (Moore et al. 2018).

In the methods section (section 2), we describe the development of an offline model for a CESM CMIP5 simulation. We also provide a detailed mathematical strategy based on the theory of Green’s functions to address our questions in a computationally efficient way. The results section (section 3) describes the time-evolving circulation and ocean stratification before presenting our ventilation diagnostics. These include two-dimensional maps showing the fraction of the interior ocean volume ventilated from different surface regions and zonally averaged depth–latitude plots of the mean age averaged over decades separated by 100 years. We also show a time series of the globally averaged mean age and mean first-passage time from 1850 to 2300. The discussion and summary section (section 4) summarizes the paper’s key findings and lists some limitations of the study and prospects for future work.

2. Methods

a. Development of the offline tracer transport model

To investigate ocean ventilation patterns and time scales, we developed an offline tracer transport model using outputs from the Community Earth System Model CESM1.0 POP2. We applied it to a simulation under a high-end warming scenario RCP8.5-ECP8.5 for the period from the year 1850 to 2300 [see Moore et al. (2018) for more details about this particular simulation]. The simulation is part of phase 5 of the Coupled Model Intercomparison Project (CMIP5).

Our offline model is implemented as a series of annual transport operators written in the form of sparse matrices. Previous studies have validated that the transport matrix method (TMM) faithfully represented most aspects of the parent online model (Bardin et al. 2016; Kvale et al. 2017). The action of the transport operator T(t) on a tracer field yields the advective-diffusive flux divergence of the tracer. The transport operator T(t) comprises three physical processes, advection, horizontal diffusion, and vertical diffusion: T(t) ≡ A(t) + D(t) + H(t), where A includes both the explicit advection and the bolus advection driven by the GM eddy parameterization. The Redi diffusive flux divergence associated with the GM scheme is incorporated in the H and D diffusion operators. The vertical diffusion associated with the KPP mixing scheme is also folded into D. We separate the transport operator into these three parts, so that we can use different time-stepping schemes (see below) for the different processes.

To reconstruct the Redi diffusivity tensor, we computed the isopycnal slope from the saved annual-averaged density fields. We also used the saved annual-averaged isopycnal, horizontal, and vertical diffusivity fields. To reconstruct the advection operator, we combined the saved annual-averaged explicit velocity with the GM bolus velocity fields. This approach is similar to the one used in Primeau (2005) and Chamberlain et al. (2019) but different than the method used in Kvale et al. (2017) and Bardin et al. (2014), which used the impulse response functions to construct the advection and diffusion operators (Khatiwala et al. 2005). In terms of the spatial discretization, we followed the scheme described in the POP manual (Smith et al. 2010). However, we neglected the variable thickness of the top layer of the model. We therefore corrected the annual-averaged velocity field to ensure that its three-dimensional divergence vanishes. The correction was applied to the horizontal velocity in the top model layer following the method described in Bardin et al. (2014). No-flux conditions are built into the operator at all the solid basin boundaries and the sea surface.

The offline model’s resolution is the original CESMv1 resolution. In total, there are n = 4 241 988 wet grids in the model, of which ns = 85 813 are in the surface layer. Thus, T(t) consists of 451 n × n sparse matrices for the period from the year 1850 to 2300. The term c represents a tracer concentration field, which can be represented as a n × 1 column vector. The time tendency of the tracer c is governed by the following system of ordinary differential equations:
dcdt+T(t)c=s(t), 
where s(t) is a discretized source and sink function expressed as a column vector. Because we do not know what the circulation will be beyond the year 2300 in our analysis we assume that the circulation is constant after year 2300. We consider two scenarios. In one we simply assume that the year-2300 circulation persists without changing for t > 2300. In the second one, we assume that the circulation abruptly returns to its 1850 state and stays permanently in the 1850 state for t > 2300.

Following previous studies (Li and Primeau 2008; Bardin et al. 2014), this offline model can be stepped forward and backward in time by employing an implicit first-order Euler-backward scheme for vertical diffusion, an explicit (third-order Adam–Bashforth) scheme for advection, and the Euler-forward scheme for horizontal diffusion and source and sink terms. The choice of the Euler-forward method for the horizontal diffusion and the Euler-backward method for the vertical diffusion is consistent with the parent CESMv1, from which we extract the transport operators, and is chosen to ensure numerical stability. The time step is set to one hour.

b. Surface-to-interior ventilation patterns and timescales in a time-dependent flow

If we consider a fluid particle in the ocean interior at time t, its residence time, defined as the time between successive surface contacts, can be decomposed into two parts:
 τ(t)= τ↓(t)+ τ↑(t), 
where τ↓ is the surface-to-interior transit time, also known as the age or last-passage time, and τ↑ is the interior-to-surface transit time, also known as the first-passage time (Primeau 2005; Primeau and Holzer 2006). In an advective-diffusive flow, water parcels have a distribution of transit times. Our focus is on the properties of these time-dependent distributions rather than on the transit times of individual Lagrangian particles.
For our discretized ocean circulation model, each grid box can be characterized by a pair of transit time distributions, which can be organized as g↓(τ↓; t) and g↑(τ↑; t). Note that for a water parcel in the ocean interior at time t, the interior-to-surface transit-time distribution depends on the circulation at times greater than t, while the surface-to-interior transit time distribution depends on the circulation at times less than t. These distributions can be expressed in terms of the Green’s functions for the forward and time-reversed adjoint transport equations subject to a rapid loss term in the top model layer. Specifically, the interior-to-surface transit time distribution is given by
g↑(τ↑;t)=RsVG↑(t+τ↑;t), 
where G↑ is a space-discretized version of the Green’s function for the transport equation
∂∂t G↑(t;t′)+[T(t)+R]G↑(t;t′)=0, 
G↑(t′;t′)= V−1,
in which T(t) is the discretized advective-diffusive tracer flux divergence operator written in matrix form; R is the loss frequency expressed as a diagonal matrix whose only nonzero elements are in the columns (and rows) corresponding to the surface grid boxes. The elements of R are given by Rii = (1 h)−1 if i corresponds to a grid box in the top layer of the model and zero otherwise. In Eq. (2), V is a diagonal matrix whose nonzero elements are the volumes of the model grid boxes. The matrix Rs is an ns × n matrix formed from the ns rows of R corresponding to the model’s grid boxes in direct contact with the atmosphere. Thus g↑(τ↑; t)dτ↑ is an ns × n matrix whose ijth element gives the fraction of the water volume in the jth grid box at time t that will first come in contact with the atmosphere in the ith surface grid box and whose interior-to-surface transit times will be between τ↑ and τ↑ + dτ↑.
Similarly, the surface-to-interior transit time distribution is given by
g↓(τ↓;t)=RsVG↓(t+τ↓;t),
where G↓ is the Green’s function for the time-reversed adjoint equation:
∂∂t G↓(t′−t;t′)+[T†(t′−t)+R]G↓(t′−t;t′)=0,
G↓(t′;t′)= V−1, 
where T†(t′−t)=V−1TT(t′−t)V is the adjoint tracer transport matrix. The ijth element of g↓(τ↓; t) is the fraction of the water volume in the jth grid box at time t that was last in contact with the atmosphere in the ith surface grid box and whose surface-to-interior transit times are between τ↓ and τ↓ + dτ↓. Note that g↓(τ↓; t) is a discretized version of the continuous boundary propagator defined in Holzer and Hall (2000).
The forward and adjoint Green’s functions, G↑ and G↓ can be related to each other. Using the semigroup property (e.g., Padulo and Arbib 1974) of the Green’s function, known as the Chapman–Kolmogorov relation (e.g., Pavliotis 2016), we have
G↑(t1;t0)=G↑(t1;t)VG↑(t;t0). 
Equation (7) simply states that propagating an initial condition from t0 to t1 is equivalent to propagating the solution from t0 to some intermediate time, t, and then from t to t1. Differentiating Eq. (7) with respect to t gives
0=∂G↑(t1;t)∂tVG↑(t;t0)+G↑(t1;t)V∂G↑(t;t0)∂t, 
and then using Eq. (4) to eliminate the time derivative in the second term on the right yields
0=∂G↑(t1;t)∂tVG↑(t;t0)−G↑(t1;t)V[T(t)+R]G↑(t;t0).
Post-multiplying Eq. (9) by [VG↑(t; t0)]−1 yields
∂G↑(t1;t)∂t−G↑(t1;t)V[T(t)+R]V−1=0,
then taking the transpose yields
∂[G↑(t1;t)]T∂t−[T†(t)+R][G↑(t1;t)]T=0.
We now do a change of variables from t=t′−t*  to get
−∂[G↑(t1;t′−t*)]T∂t*−[T†(t′−t*)+R][G↑(t1;t′−t*)]T=0.
Comparing Eq. (11) and to Eq. (6) reveals the relationship between G↑ (t; t′) and G↓ (t; t′):
G↓(t′−t;t′)=[G↑(t′;t′−t)]T.
Equation (12) is known as the reciprocity property of the Green’s function (e.g., Morse and Feshbach 1954).

1) Surface-to-interior ventilation patterns

Computing the full G↑ and G↓ is computationally too expensive because each column requires the simulation of an independent tracer. However, not all the information that could be extracted from the Green’s function is needed for our diagnostics. We are interested in the volume of the ocean re-exposed to the atmosphere through each surface pixel averaged over all possible transit times, that is,
⟨hs↑⟩(t′)=∫0∞As−1g↑(τ↑;t′)V1dτ↑,
where these volumes have been scaled by the area of the surface pixels to get equivalent thicknesses. In the above expressions, As is an ns × ns diagonal matrix formed from the horizontal areas of the model’s grid boxes; 1 is an n × 1 vector of ones so that the factor of V1 to the right of g↑ acts to initialize the tracer concentration to unity everywhere inside the ocean. The fact that g↑V1 is an n × 1 column vector implies that the ⟨hs↑⟩ diagnostic can be computed from a single tracer. Thus we introduce the following tracer equation:
∂∂τ↑ c(τ↑;t′)+[T(t′+τ↑)+R]c(τ↑;t′)=0, 
c(0;t′)= 1,
where c is the tracer concentration so that Eq. (13) can be rewritten as
⟨hs↑⟩(t′)=∫0∞RsVc(τ↑;t′)dτ↑, 
where we used Eq. (3) and the fact that c can be expressed in terms of the Green’s function, c(τ↑; t′) = G↑(t′ + τ↑; t′)V1.
To further limit the needed computation, we evaluate the integral in Eq. (13) for three separate values of t′. Thus, we start three tracer simulations using Eq. (14) starting from t′ = 1850, t′ = 2090, and t′ = 2290 and time-step forward from τ↑ = 0 to τ↑ = 2300 − t′ (i.e., for 450, 240, and 10 years respectively). Those years are chosen to illustrate the growing impacts of climate change. The resulting tracer fields provide the integrand for the τ↑ = 0 to τ↑ = 2300 − t′ part of the integral in Eq. (15). The remaining part of the integral represents the forward integration from the year 2300 and can be obtained by direct matrix inversion because we assume that T is constant after year 2300. To see how, integrate Eq. (4) to get
∫2300−t′∞G↑(τ↑;t′)V1dτ↑=[T++R]−1G↑(2300−t′;t′)V1, 
then again using the fact that c(τ↑; t′) = G↑(t′ + τ↑; t′)V1, we obtain
c∞(t′)≡∫2300−t∞c(τ↑;t′)dτ↑=[T++R]−1c(2300−t′;t′)
where T+ is the time-invariant transport operator assumed to apply for the period after year 2300. We consider two scenarios for T+ after year 2300. In scenario 1 the circulation is assumed to persist in its year-2300 state indefinitely with T+ = T(2300) while in scenario 2 the circulation is assumed to abruptly return to its year-1850 state after 2300 with T+ = T(1850). Putting all this together we have
⟨hs↑⟩(t′)=∫02300−t′As−1RsVc(τ↑,t′)dτ↑+ As−1RsVc∞(t′) .
Finally, using ⟨hs↑⟩, the water volume fractions in 1850, 2090, and 2290 that will be first re-exposed to the atmosphere at each sea surface pixel can be written as
⟨fs↑⟩(t′)=As⟨hs↑⟩(t′)1TV1.
Similarly, to compute the equivalent thickness for the flux of water that enters the ocean through each surface pixel we need to evaluate
⟨hs↓⟩(t′)=∫0∞As−1g↓(τ↓;t′)V1dτ↓.
We thus introduce the following adjoint tracer transport equation,
∂∂τ↓ c(τ↓;t′)+[T†(t′−τ↓)+R]c(τ↓;t′)=0, 
c(0;t′)= 1
so that Eq. (20) can be rewritten as
⟨hs↓⟩(t′)=∫0∞RsVc(τ↓;t′)dτ↓. 
Again, we further reduce the computational costs by focusing on three times t′ = 1850, t′ = 2090, and t′ = 2290. Thus, we start three tracer simulations using Eq. (21) starting from t′ = 2290, t′ = 2090, and t′ = 1850 and time-step backward in time from τ↓ = 0 to τ↓ = t′ − 1850 (i.e., for 440 years, 240 years, and 0 years respectively). The resulting tracer fields provide the integrand for the τ↓ = 0 to τ↓ = t′ − 1850 part of the integral in Eq. (22). The remaining part of the integral represents the backward integration from the year 1850 and can be obtained by direct matrix inversion because we assume that T is constant before 1850:
c−∞(t′)≡∫t′−1850∞c(τ↓;t′)dτ↓=[T†(1850)+R]−1c(t′−1850;t′). 
Thus
⟨hs↓⟩(t′)=As−1RsVc−∞(t′)+∫0t′−1850As−1RsVc(τ↓,t′)dτ↓. 
As before, the volume fractions of water in 1850, 2090, and 2290 that were last ventilated to the atmosphere at each surface pixel can be written as
⟨fs↓⟩(t′)=Ashs↓(t′)1TV1.

2) Surface-to-interior and interior-to-surface timescales

In addition to the volume fractions, we also present mean interior-to-surface transit times (i.e., mean first-passage time) from each interior ocean pixel to anywhere at the surface. Specifically,
⟨τ↑⟩T(t′)=∫t′∞τ↑1sTg↑(τ↑;t′)dτ↑,
where 〈τ↑〉 is a row matrix of size of 1 × n whose components are the mean first-passage times from each of the n model grid boxes. From Eq. (3) and the fact that 1TR=1sTRs, we rewrite Eq. (26) as
⟨τ↑⟩T(t′)=∫t′∞τ↑1TRVG↑(t′+τ↑;t′)dτ↑,
Note that applying the operator 1TV to a tracer field corresponds to the integral over the volume of the ocean. Thus 1TVTf ≡ 0 for any f because the transport operator, written in flux-divergence form, conserves tracer mass. Equation (27) can thus be written as
⟨τ↑⟩T(t′)=∫t′∞τ↑[1TVRG↑(t′+τ↑;t′)+1TVT(t′)G↑(t′+τ↑;t′)]dτ↑, =∫t′∞τ↑1TV[R+T(t′)]G↑(t′+τ↑;t′)dτ↑, 
in which we added a term equal to zero. Doing so allows us to use Eq. (4) to rewrite Eq. (28) as follows:
⟨τ↑⟩T(t′)=−∫t′∞1TV[τ↑∂G↑(t′+τ↑;t′)∂τ↑]dτ↑, =∫t′∞1TVG↑(t′+τ↑;t′)dτ↑,  
where we used integration by parts to go from the first to second line. If we now take the transpose of Eq. (29) and use the reciprocity of the Green’s function in Eq. (12) we get
⟨τ↑⟩T(t′)=−∫t′∞1TV[τ↑∂G↑(t′+τ↑;t′)∂τ↑]dτ↑,=∫t′∞1TVG↑(t′+τ↑;t′)dτ↑,=∫2300∞G↓(t′;t′+τ↑)V1dτ↑+∫t′2300G↓(t′;t′+τ↑)V1dτ↑, 
which is the solution of the following equation:
∂⟨τ↑⟩∂t+[T†(t)+R]τ↑=1,
subject to either of the following initial conditions:
τ↑(2300)=[T†(2300)+R]−11 or
⟨τ↑⟩(2300)=[T†(1850)+R]−11.
The first initial condition corresponds to the scenario in which the circulation is assumed to persist in the year 2300 state (scenario 1). The second initial condition corresponds to the assumption that the circulation abruptly recovers to its year 1850 state (scenario 2).
Similarly, the mean surface-to-interior transit times (i.e., mean last-passage time or mean age) at each pixel can be directly solved from the following equation,
∂⟨τ↓⟩∂t+[T(t)]⟨τ↓⟩=R⟨τ↓⟩+1, 
subject to the following initial condition:
⟨τ↓⟩(1850)=[T(1850)+R]−11.
Equation (32) takes the form of the ideal age equation that is implemented in many ocean general circulation models (e.g., England 1995). It is important to note, however, that Eq. (32) only yields the time-evolving mean of the TTD when it is initialized using the fully spun-up boundary condition given in Eq. (33).

3. Results

a. Global overturning circulation and buoyancy frequency

The global overturning circulation contains the upper cell and abyssal cell (Fig. 1). In our model, the preindustrial circulation is characterized by upwelling in the Antarctic Divergence (14.0 Sv; 1 Sv ≡ 106 m3 s−1) and equatorial upwelling zones (57.6 Sv). This upwelling is balanced by the downwelling that is driven by the convergence of surface wind-driven currents in the subtropical regions. A part of the water that is upwelled in the Antarctic [Circumpolar Deep Water (CDW)] is transported southward as it loses buoyancy. This water forms Antarctic Bottom Water (AABW) and drives the abyssal cell of the Southern Hemisphere meridional overturning circulation (SMOC; 9.0 Sv). In the Northern Hemisphere, the formation of North Atlantic Deep Water (NADW) drives the upper cell of the Atlantic meridional overturning circulation (AMOC) (21.7 Sv). The strength of AMOC and SMOC in our model compares well with the CMIP6 model mean strength of overturning circulation, even though the strength of SMOC is grossly underestimated compared with observational estimates (Liu et al. 2023).

Fig. 1.
Fig. 1.

Ocean circulation and buoyancy frequency. CESMv1 global meridional overturning streamfunctions in the (a) preindustrial era (1850–59), (b) 2090s, and (c) 2290s. CESMv1 zonal mean buoyancy frequency in (d) the preindustrial era (1850–59), (e) the differences between 1850s and 2090s, and (f) the differences between 1850s and 2290s. (g) Key aspects of global ocean circulation: vertical transport at 100 m of the Antarctic Divergence upwelling (SO; south of 60°S), equatorial upwelling (Eq upw; 18°S–18°N), subantarctic downwelling (AAIW dnw; i.e., AAIW/SAMW formation, 60°–35°S), Southern Hemisphere subtropical downwelling (subS; 35°–18°S) and Northern Hemisphere subtropical downwelling (subN; 18°–35°N), and the strength of SMOC and AMOC (Sv).

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

In a warming climate, the formation of AABW and NADW weakens due to the stronger stratification driven by the gain of buoyancy, which leads to a slowdown of the global overturning circulation (Weijer et al. 2020; Heuzé 2021; Liu et al. 2023). Furthermore, stronger westerlies drive stronger upwelling in the Antarctic Divergence zone, which is balanced by stronger downwelling in the subtropical gyres (Fig. 1g). This behavior is consistent with other estimates (Bracegirdle et al. 2013; Waugh 2014; Waugh et al. 2013), even though the magnitude of these changes can vary across different estimates. Also by the end of the twenty-first century, the equatorial upwelling is 6.7 Sv weaker due to weaker equatorial easterlies compared to its preindustrial level in our model. Again, this behavior is generally consistent with other ESMs (Terada et al. 2020). Finally, the weaker equatorial easterlies also lead to a 3.0–6.8-Sv decrease of the wind-driven subtropical downwelling in both hemispheres (Fig. 1g). In the North Atlantic, the formation of NADW weakens by more than 50% by the end of the twenty-first century under the business-as-usual warming scenario, which is consistent with CMIP model studies and accordingly drives the weakening overturning circulation (Liu et al. 2019; Weijer et al. 2020).

Overall, the changes of overturning circulation will affect the ventilation of the ocean, but it is difficult to assess this effect directly. Moreover, most streamlines do not cross the surface mixed layer, making it difficult to relate changes in the overturning circulation with changes in ventilation. The complex relationship between the changing circulation and ventilation in a warming climate motivates us to develop a mathematical method to clearly quantify the transport time scales and ventilation patterns in a time-evolving ocean circulation.

b. Ventilation volumes

The fraction of the ocean ventilated from each surface location provides a useful summary of the ocean’s transport pathways. To summarize the results, we followed DeVries and Primeau (2011) and divided the surface into seven broad zonal bands, which we further divided into separate basins, resulting in 17 patches that cover the whole ocean (Fig. 2). Figure 3 shows a color map of these fractions per unit area for the year 1850 along with the change from 1850 to 2100 and from 1850 to 2300. Under the assumption that the ocean was in steady state up to the year 1850, our calculation shows that disproportionately more water was ventilated from high latitudes. We find that 27.2% and 37.2% of the total ocean volume were last ventilated from the North Atlantic and the Southern Ocean (i.e., Antarctic + Subantarctic), respectively (Fig. 3).

Fig. 2.
Fig. 2.

The separation of 17 surface patches. “Ant”, “Suba”, “Subt”, “Equ”, and “Subp” are short for Antarctic, Subantarctic, Subtropical, Equatorial, and Subpolar, respectively.

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

Fig. 3.
Fig. 3.

The surface sources of global ocean waters. (left) The equivalent thickness from the oceanic volume that originated in each surface pixel, scaled by the surface area of each pixel (a) in the year 1850, (c) the difference between 2090 and 1850, and (e) the difference between 2290 and 1850 (km). The color scale follows a base-10 logarithm of the field in (a). The black number indicates the fraction (in percent) of the whole water column that made last contact with the surface ocean in each region defined by the solid lines. (right) The zonal integration of the fraction along with each latitude bin (1°) (b) in the year 1850, (d) the difference between 2090 and 1850, and (f) the difference between 2290 and 1850 (permille per degree).

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

Generally, our results show similar surface ventilation patterns as those obtained from data-constrained models (Gebbie and Huybers 2010; DeVries and Primeau 2011). One conspicuous exception is in the Southern Ocean. We estimated the fraction ventilated from the Antarctic region to be only 14.4% (Fig. 3), whereas DeVries and Primeau (2011) estimated 36%. This underestimation is possibly due to the inadequate representation of AABW formation in CESMv1. In the model, AABW formation occurs through open-ocean convection instead of sinking along the Antarctic continental slope as is the case in the real world. This is a problem found in many Earth system models (Heuzé 2021).

Our model shows how the simulated global water-mass ventilation changes as the climate warms. Consistent with the MOC weakening in a warming climate, we see the largest ventilation decreases in the North Atlantic and Weddell Sea. Of the total ocean volume, 1.9% less originates from the North Atlantic in 2290 compared to 1850. In the Weddell Sea, the decline is more gradual with 0.9% and 0.7% decreases in the 1850–2090 and 2090–2290 periods. To compensate for the ventilation decreases in the North Atlantic and Weddell Sea, there are significant ventilation increases in the subantarctic region. These increases indicate stronger AAIW and SAMW formation rates (Fig. 1g), which are driven by stronger westerlies as a result of climate warming (Russell et al. 2006; Bracegirdle et al. 2013).

Besides these basin-scale ventilation changes, there are also sub-basin-scale ventilation-pattern shifts in response to climate warming. For example, the NADW formation regions shift, leading to less water originating from the Labrador Seas particularly in the decade of 2290 and more from the Irminger Seas, as well as more regional changes within the Norwegian–Greenland Seas (Fig. 3). This could be due to a weaker NAO in a warming climate, as similar shifts on decadal time scales have been observed in decades with a weak NAO: The NADW originating from the Labrador Sea is weaker compared with the decades with a strong NAO, resulting in a weaker AMOC (Yeager and Danabasoglu 2014). It is important to note that different models show varying subbasin-scale ventilation pattern changes. For example, Lique and Thomas (2018) argue that the shift in NADW formation appears to be more pronounced toward the Irminger Sea and Labrador Sea.

The surface patterns showing where the interior ocean volume will eventually be re-exposed to the atmosphere depend both on the circulation change from the year 1850 to 2300 and after the year 2300. As discussed in section 2, we consider two scenarios that have the same time-dependent circulation up to the year 2300, but that differ afterward. In scenario 1 the circulation is assumed to persist in its year-2300 state indefinitely while in scenario 2 the circulation is assumed to abruptly return to its year-1850 state after 2300. These two scenarios provide crude bounds on what could happen after atmospheric CO2 stabilizes.

In general, most of the total water volume will ventilate the surface in the upwelling zones, regardless of the future circulation scenarios. The Southern Ocean (Antarctic + Subantarctic) is the largest region to ventilate the ocean water in the future, which will re-expose more than 45% of the total volume of the year-1850 ocean water to the atmosphere depending on the circulation scenarios. It is followed by regions with equatorial upwelling and intensified western boundary currents, such as the Kuroshio Extension and Gulf Stream (Fig. 4).

Fig. 4.
Fig. 4.

The fraction of whole water column where it made its next contact with the surface at each ocean grid in the experiment of (a)–(f) scenario 1 and (g)–(l) scenario 2. The fraction of the water column ventilating in each region in (top) the year 1850, (middle) year 2090–year 1850, and (bottom) year 2290–year 1850. The regions are defined by the solid black lines.

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

In scenario 1, most of the ventilation changes occur between years 1850 and 2090 (Fig. 4). Of the total ocean volume in 1850, 62.7% will eventually ventilate to the surface in the Southern Ocean. In 2090, 1.7% more will ventilate in the Southern Ocean compared with the year 1850, whereas the fraction of the total ocean volume ventilating in the Southern Ocean will not change from the year 2090 to the year 2290. This increase is due to stronger Southern Ocean upwelling driven by stronger westerlies as a result of climate warming (Russell et al. 2006). To compensate for the ventilation increase, there is less water ventilation occurring in the Kuroshio Extension and Gulf Stream. In scenario 2, as the Southern Ocean will experience weaker upwelling after the year 2300, only 46.5% of the total ocean volume in 1850 will eventually be exposed to the atmosphere in the Southern Ocean. This number is about 16.2% less than it is in scenario 1. Over time, most of the ventilation changes occur between years 2090 and 2290 in scenario 2. Spatially, the ventilation changes showed contrary patterns with the changes in scenario 1.

c. The mean age

As discussed in the introduction, the mean age is a useful diagnostic to characterize the time scales of ocean ventilation. It represents the elapsed time since a water parcel in the ocean interior made its last contact with the ocean surface. Figure 5 shows zonally averaged latitude–depth sections and a time series of the global mean age from year 1850, along with the difference in the mean ages at year 2090 minus year 1850 and year 2290 minus year 1850. Globally, the deep ocean has the oldest mean age of more than 1600 years for year 1850. The mean ages in the deep water formation regions (high latitudes) are much younger than the low latitudes. The upper ocean becomes slightly younger in the equatorial and subtropics, possibly due to the weakening downwelling despite the ocean becoming more stratified. With climate warming, the upper ocean becomes more stratified (Capotondi et al. 2012; Li et al. 2020), which correlates with the decreasing age in the upper ocean decoupling with the deep water. As the global overturning circulation continues to slow down out to the year 2300, the mean age continues to increase, especially in the deepwater formation regions. It is worth noting that most of the changes in mean ages occur after year 2090 as most MOC slowdown and stratification increase occur after year 2090, supporting the conclusion in Moore et al. (2018) that it is important to extend the climate simulations beyond the twenty-first century.

Fig. 5.
Fig. 5.

The global mean age. The top row shows zonally averaged contour plots of the mean age in (a) year 1850, (b) the differences between the years 2090 and 1850, and (c) the differences between the year 2290 and 1850. (d) The time series of ideal age from the preindustrial era to year 2300 (yr).

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

To summarize, Fig. 5d shows the mean age for the whole ocean as a function of time. As climate warms, the global-averaged mean age increases from ∼670 years in 1850 to ∼780 years in 2300. The upward trend in the mean age is still strong in year 2300 (Fig. 5d).

d. The mean first-passage time

The mean first-passage time is a diagnostic of the time needed for a water parcel in the ocean interior to be transported back to the surface where it comes in contact with the atmosphere. Naturally, the first passage distribution for some time t′ depends on the behavior of the ocean circulation at times t > t′. In particular it depends on the circulation at times beyond year 2300 when our climate simulation ends. As discussed in section 2, we consider two scenarios that have the same time-dependent circulation up to year 2300, but that differ after year 2300. In scenario 1 the circulation is assumed to persist in its year-2300 state indefinitely while in scenario 2 the circulation is assumed to abruptly return to its year-1850 state after year 2300. While the results are qualitatively similar for the two scenarios, there are significant quantitative differences.

Our calculations show that, as expected, the mean first-passage time is longer in the deep ocean than in the upper ocean regardless of the scenario (Figs. 6a,d). Also, independent of scenario, the mean first-passage time for the deep waters is generally shorter at high latitudes compared to lower latitudes. This behavior is due to deep convection at high latitudes that can ventilate the deep ocean by rapidly mixing deep waters with the surface. However, the different assumptions about what happens after year 2300 have a large impact on the deep ocean’s mean first-passage time. For example, in the Northern Hemisphere, the zonally averaged mean first-passage time in the deep ocean is approximately 800 years longer for scenario 1 compared to scenario 2 (cf. ∼2300 years for scenario 1 versus ∼1500 years for scenario 2; Figs. 6a,d).

Fig. 6.
Fig. 6.

The global mean first passage time for (a)–(c) scenario 1, in which the year-2300 circulation is assumed to persist indefinitely, and (d)–(f) scenario 2, where the circulation is assumed to abruptly return to its 1850 state after year 2300. The zonal average of the first-passage time was averaged for the 1850–59 decade is shown in (a) and (d), the differences between the 2090–99 and 1850–59 decadal averages are shown in (b) and (e), and the differences between the 2290–99 and 1850–59 decadal averages are shown in (c) and (f). (g) The time series of the globally integrated first-passage time for each scenario (yr).

Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-23-0113.1

In scenario 1 the mean first-passage time increases almost everywhere and is particularly pronounced in the location of deep-water formation in the Northern Hemisphere and in regions downstream of the North Atlantic deep convection site (Figs. 6b,c). The change shown in Fig. 6b demonstrates the influence of the decline of the maximum AMOC strength from 20 to 12 Sv between 1850 and 2090 (see Fig. 1g). The further decline in the strength of AMOC from 12 to 7 Sv between years 2090 and 2290 has a relatively smaller impact on the mean first-passage time (cf. Fig. 6c vs Fig. 6b). This behavior shows the importance of eddy-diffusive transport, which prevents the first-passage time from increasing to infinity as the overturning circulation collapses. The importance of diffusive transport has also been highlighted by Holzer et al. (2021).

In scenario 2 if we compare the change in the mean first-passage time for year 1850 to that of year 2090, we see an increase in the upper ocean and a decrease in deeper waters (Fig. 6e). This pattern of change can be understood in terms of the mean first-passage time itself. Where the mean first-passage time is on the order of 200 years or less, the weaker ventilation associated with the slowdown in the circulation for the 2090–2290 period will have a relatively large impact. In contrast, where the mean first passage time is much greater than 200 years, the post-2300 circulation dominates. Because in scenario 2 this circulation is a return to the vigorous 1850 circulation, we see a decrease in the year-2090 mean first-passage time over most of the deep ocean. On the other hand, if we compare the mean first-passage time for the year 1850 to that of the year 2290, we see a decrease almost everywhere (Fig. 6f). In this case, the whole ocean experiences the more vigorous 1850 circulation. The AMOC slowdown that occurred during the 1850–2300 period does not affect the year-2300 first passage-time distribution.

To summarize, Fig. 6g shows the mean first-passage time for the whole ocean. What we assume for the circulation after year 2300, when our simulation ends, has a significant impact. Assuming that the year-2300 circulation persists indefinitely, the whole-ocean mean first-passage time is about ∼1140 years in 1850. As climate warms, the global-averaged mean first-passage time increases to ∼1340 years in 2300. If, instead, we assume that in the year 2300 the circulation abruptly returns to its 1850 state, the mean first-passage time is only ∼740 years in 1850 and then decreases back to ∼650 years.

4. Summary and discussion

We applied the theory of transit time distributions (TTD) to a transient circulation obtained from a realistic climate simulation in CESMv1 run from the year 1850 to the year 2300 under the RCP8.5-ECP8.5 climate scenario. We computed how the global ventilation patterns evolve in a transient circulation using the forward and adjoint transport operators derived from the CESMv1 simulation. In addition, we showed that the ideal age equation applied to a transient flow yields the time-evolving mean age provided that the ideal age is initialized with the mean of the TTD at the beginning of the simulation. Similarly, we showed that the mean first-passage time satisfies an equation similar to the ideal age equation except that it uses the time-reversed adjoint transport operator. We used these equations to compute the time-evolving mean age and mean first-passage time.

Ours is the first calculation that provides a proper treatment of the time-evolving ventilation patterns and time scales in a global circulation model subject to climate change. Previous calculations, such as those of DeVries and Primeau (2011) and Gebbie and Huybers (2010), assumed the circulation to be in a steady state. Holzer et al. (2020) considered a time-evolving circulation, but they treated a sequence of decadal averaged transport operators as if they were steady-state circulations frozen in time and computed the ventilation patterns for each decade.

Under ongoing climate warming, of the total ocean volume, 2.1% less originates from the high latitudes (AABW and NADW formation regions) due to the slowdown of the global overturning circulation. In compensation, 2.2% more water originates from subantarctic regions. This indicates that the stronger upwelling in the Antarctic Divergence zone is balanced by stronger downwelling in the subtropical gyres (Fig. 1d). The fractions of the ocean ventilated in the future depend on the post-2300 circulation. The most conspicuous signal of the changes in future ventilation patterns is in the Southern Ocean, where the strongest upwelling zone is located. In the scenario that the circulation persists forever after the year 2300 (scenario 1) of the total ocean volume, 16.2% more of the year-1850 water will eventually ventilate in the Southern Ocean than the scenario with post-2300 circulation abruptly returning to its 1850 state (scenario 2). Of the total ocean volume of the year-2290 water, 15.1% more will eventually ventilate in the Southern Ocean in scenario 1 compared to scenario 2.

The ventilation time scales are also subject to climate change. We found that the slowing of overturning circulation leads to an increase of the global-averaged mean age by 17.2% (110 years) from 1850 to 2300. In contrast, using Holzer et al.’s (2020) approximation, which treated a sequence of decadal averaged transport operators as if they were steady-state circulations frozen in time, we find that the global-averaged mean age increases from ∼670 to 1172 years. This indicates that the Holzer et al. (2020) approximation greatly overestimated the impacts of slowing overturning circulation on the mean age. The time-evolving circulation, along with the future circulation recovery trajectories, has large impacts on the global-averaged mean first-passage time. The Holzer et al. (2020) approximation did not consider the multiple potential circulation recovery trajectories after year 2300. In our study, we considered two circulation recovery scenarios after year 2300. In scenario 1 in which the circulation at year 2300 persists infinitely, the global-averaged mean first-passage time increases from ∼1140 to ∼1340 years from 1850 to 2300. In scenario 2 in which the circulation at year 2300 abruptly recovers to its year-1850 state, the global-averaged mean first-passage time decreases from ∼740 to ∼650 years. Therefore, to better estimate the mean first-passage time, we need to extend the model runs further into the far future (Frölicher et al. 2020; Schmittner et al. 2008). Without extending the simulation into the far future, we can only discuss the short time part of the first-passage time distribution because the mean of the whole distribution would not be available.

The changes in ventilation time scales that we have documented in this warming climate simulation have implications for ocean carbon cycle and biogeochemistry. The increase in water mean age allows more nutrients to accumulate in the deep ocean before it returns back to the surface, leading to a decline of export productivity (Moore et al. 2018). Additionally, the mean age increase allows more time for exported biogenic carbon to accumulate at depth, sequestering more carbon in the deep ocean by the biological pump (Liu et al. 2023) and potentially causing deoxygenation (Gnanadesikan et al. 2007). However, the mean first-passage time (Primeau 2005) has received much less attention, but it is an equally important characteristic of ocean ventilation. The changes in the mean first-passage time will affect the ocean carbon sink by modulating both natural carbon cycling and anthropogenic carbon uptake. The slowing overturning circulation will enhance natural carbon sequestration (e.g., DeVries et al. 2012; Bernardello et al. 2014), whereas it will also decrease anthropogenic carbon uptake by impeding the transport from the surface to the interior (e.g., Moore et al. 2018). Furthermore, the changes in mean first-passage time will affect the long-term durability of certain marine carbon dioxide removal (CDR) strategies by modifying the natural carbon cycle. The mean first-passage time also provides a useful diagnostic for the long-term durability of carbon dioxide removal (CDR) strategies that aim to sequester carbon into the deep ocean (Siegel et al. 2021).

Several caveats apply to our study. First, our offline model is developed from the CESMv1 circulation, which underestimates the strength of the SMOC (Liu et al. 2023). In the offline model, we neglect the seasonal variabilities of the circulation, which could affect the mean age and mean first-passage time. Second, the circulation recovery trajectories after 2300 are highly uncertain, and we considered only two extreme scenarios. This limited exploration of possible future scenarios adds additional uncertainty to our mean first-passage time and ventilation patterns diagnostics. Finally, our study focused on one specific high-end climate scenario; other scenarios should be considered in future work.

Acknowledgments.

Y. L. received support from the Reducing Uncertainties in Biogeochemical Interactions through Synthesis and Computation Scientific Focus Area (RUBISCO SFA) under the Regional and Global Climate Modeling Program and the Earth System Modeling Program in the Climate and Environmental Sciences Division of the Biological and Environmental Research Division of the U.S. Department of Energy Office of Science. F.W.P received support from the U.S. Department of Energy DOE-BER ESMD grants DE-SC0021267 and DE-SC0022177.

Data availability statement.

The CESMv1 model outputs are available through the Earth System Grid Federation (ESGF) data delivery system at https://www.earthsystemgrid.org/dataset/ucar.cgd.ccsm4.randerson2015.html. The offline model code and outputs are available upon request.

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  • Liu, Y., J. K. Moore, F. Primeau, and W. L. Wang, 2023: Reduced CO2 uptake and growing nutrient sequestration from slowing overturning circulation. Nat. Climate Change, 13, 83–90, https://doi.org/10.1038/s41558-022-01555-7.

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  • Moore, J. K., and Coauthors, 2018: Sustained climate warming drives declining marine biological productivity. Science, 359, 1139–1143, https://doi.org/10.1126/science.aao6379.

    • Search Google Scholar
    • Export Citation

  • Morse, P. M., and H. Feshbach, 1954: Methods of theoretical physics. Amer. J. Phys., 22, 410–413.

  • Padulo, L., and M. A. Arbib, 1974: System theory: A unified state-space approach to continuous and discrete systems. Ocean Modell., 23, 13–20, https://doi.org/10.1016/j.ocemod.2008.03.001.

    • Search Google Scholar
    • Export Citation

  • Pavliotis, G. A., 2016: Stochastic Processes and Applications. Springer-Verlag, 339 pp.

  • Primeau, F., 2005: Characterizing transport between the surface mixed layer and the ocean interior with a forward and adjoint global ocean transport model. J. Phys. Oceanogr., 35, 545–564, https://doi.org/10.1175/JPO2699.1.

    • Search Google Scholar
    • Export Citation

  • Primeau, F., and M. Holzer, 2006: The ocean’s memory of the atmosphere: Residence-time and ventilation-rate distributions of water masses. J. Phys. Oceanogr., 36, 1439–1456, https://doi.org/10.1175/JPO2919.1.

    • Search Google Scholar
    • Export Citation

  • Rousselet, L., P. Cessi, and G. Forget, 2021: Coupling of the mid-depth and abyssal components of the global overturning circulation according to a state estimate. Sci. Adv., 7, eabf5478, https://doi.org/10.1126/sciadv.abf5478.

    • Search Google Scholar
    • Export Citation

  • Russell, J. L., K. W. Dixon, A. Gnanadesikan, R. J. Stouffer, and J. R. Toggweiler, 2006: The Southern Hemisphere westerlies in a warming world: Propping open the door to the deep ocean. J. Climate, 19, 6382–6390, https://doi.org/10.1175/JCLI3984.1.

    • Search Google Scholar
    • Export Citation

  • Schmittner, A., A. Oschlies, H. D. Matthews, and E. D. Galbraith, 2008: Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business‐as‐usual CO2 emission scenario until year 4000 AD. Global Biogeochem. Cycles, 22, GB1013, https://doi.org/10.1029/2007GB002953.

    • Search Google Scholar
    • Export Citation

  • Shah, S. H. A. M., F. W. Primeau, E. Deleersnijder, and A. W. Heemink, 2017: Tracing the ventilation pathways of the deep North Pacific Ocean using Lagrangian particles and Eulerian tracers. J. Phys. Oceanogr., 47, 1261–1280, https://doi.org/10.1175/JPO-D-16-0098.1.

    • Search Google Scholar
    • Export Citation

  • Siegel, D. A., T. DeVries, S. C. Doney, and T. Bell, 2021: Assessing the sequestration time scales of some ocean-based carbon dioxide reduction strategies. Environ. Res. Lett., 16, 104003, https://doi.org/10.1088/1748-9326/ac0be0.

    • Search Google Scholar
    • Export Citation

  • Smith, R., and Coauthors, 2010: The Parallel Ocean Program (POP) reference manual: Ocean component of the Community Climate System Model (CCSM) and Community Earth System Model (CESM). LAUR-10-01853, 141 pp., https://www2.cesm.ucar.edu/models/cesm1.0/pop2/doc/sci/POPRefManual.pdf.

  • Terada, M., S. Minobe, and C. Deutsch, 2020: Mechanisms of future changes in equatorial upwelling: CMIP5 intermodel analysis. J. Climate, 33, 497–510, https://doi.org/10.1175/JCLI-D-19-0128.1.

    • Search Google Scholar
    • Export Citation

  • Waugh, D. W., 2014: Changes in the ventilation of the southern oceans. Philos. Trans. Roy. Soc., A372, 20130269, https://doi.org/10.1098/rsta.2013.0269.

    • Search Google Scholar
    • Export Citation

  • Waugh, D. W., F. Primeau, T. Devries, and M. Holzer, 2013: Recent changes in the ventilation of the southern oceans. Science, 339, 568–570, https://soi.org/10.1126/science.1225411.

    • Search Google Scholar
    • Export Citation

  • Weijer, W., W. Cheng, O. A. Garuba, A. Hu, and B. T. Nadiga, 2020: CMIP6 models predict significant 21st century decline of the Atlantic meridional overturning circulation. Geophys. Res. Lett., 47, e2019GL086075, https://doi.org/10.1029/2019GL086075.

    • Search Google Scholar
    • Export Citation

  • Yeager, S., and G. Danabasoglu, 2014: The origins of late-twentieth-century variations in the large-scale North Atlantic circulation. J. Climate, 27, 3222–3247, https://doi.org/10.1175/JCLI-D-13-00125.1.

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    • Export Citation
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  • Liu, Y., J. K. Moore, F. Primeau, and W. L. Wang, 2023: Reduced CO2 uptake and growing nutrient sequestration from slowing overturning circulation. Nat. Climate Change, 13, 83–90, https://doi.org/10.1038/s41558-022-01555-7.

    • Search Google Scholar
    • Export Citation

  • Moore, J. K., and Coauthors, 2018: Sustained climate warming drives declining marine biological productivity. Science, 359, 1139–1143, https://doi.org/10.1126/science.aao6379.

    • Search Google Scholar
    • Export Citation

  • Morse, P. M., and H. Feshbach, 1954: Methods of theoretical physics. Amer. J. Phys., 22, 410–413.

  • Padulo, L., and M. A. Arbib, 1974: System theory: A unified state-space approach to continuous and discrete systems. Ocean Modell., 23, 13–20, https://doi.org/10.1016/j.ocemod.2008.03.001.

    • Search Google Scholar
    • Export Citation

  • Pavliotis, G. A., 2016: Stochastic Processes and Applications. Springer-Verlag, 339 pp.

  • Primeau, F., 2005: Characterizing transport between the surface mixed layer and the ocean interior with a forward and adjoint global ocean transport model. J. Phys. Oceanogr., 35, 545–564, https://doi.org/10.1175/JPO2699.1.

    • Search Google Scholar
    • Export Citation

  • Primeau, F., and M. Holzer, 2006: The ocean’s memory of the atmosphere: Residence-time and ventilation-rate distributions of water masses. J. Phys. Oceanogr., 36, 1439–1456, https://doi.org/10.1175/JPO2919.1.

    • Search Google Scholar
    • Export Citation

  • Rousselet, L., P. Cessi, and G. Forget, 2021: Coupling of the mid-depth and abyssal components of the global overturning circulation according to a state estimate. Sci. Adv., 7, eabf5478, https://doi.org/10.1126/sciadv.abf5478.

    • Search Google Scholar
    • Export Citation

  • Russell, J. L., K. W. Dixon, A. Gnanadesikan, R. J. Stouffer, and J. R. Toggweiler, 2006: The Southern Hemisphere westerlies in a warming world: Propping open the door to the deep ocean. J. Climate, 19, 6382–6390, https://doi.org/10.1175/JCLI3984.1.

    • Search Google Scholar
    • Export Citation

  • Schmittner, A., A. Oschlies, H. D. Matthews, and E. D. Galbraith, 2008: Future changes in climate, ocean circulation, ecosystems, and biogeochemical cycling simulated for a business‐as‐usual CO2 emission scenario until year 4000 AD. Global Biogeochem. Cycles, 22, GB1013, https://doi.org/10.1029/2007GB002953.

    • Search Google Scholar
    • Export Citation

  • Shah, S. H. A. M., F. W. Primeau, E. Deleersnijder, and A. W. Heemink, 2017: Tracing the ventilation pathways of the deep North Pacific Ocean using Lagrangian particles and Eulerian tracers. J. Phys. Oceanogr., 47, 1261–1280, https://doi.org/10.1175/JPO-D-16-0098.1.

    • Search Google Scholar
    • Export Citation

  • Siegel, D. A., T. DeVries, S. C. Doney, and T. Bell, 2021: Assessing the sequestration time scales of some ocean-based carbon dioxide reduction strategies. Environ. Res. Lett., 16, 104003, https://doi.org/10.1088/1748-9326/ac0be0.

    • Search Google Scholar
    • Export Citation

  • Smith, R., and Coauthors, 2010: The Parallel Ocean Program (POP) reference manual: Ocean component of the Community Climate System Model (CCSM) and Community Earth System Model (CESM). LAUR-10-01853, 141 pp., https://www2.cesm.ucar.edu/models/cesm1.0/pop2/doc/sci/POPRefManual.pdf.

  • Terada, M., S. Minobe, and C. Deutsch, 2020: Mechanisms of future changes in equatorial upwelling: CMIP5 intermodel analysis. J. Climate, 33, 497–510, https://doi.org/10.1175/JCLI-D-19-0128.1.

    • Search Google Scholar
    • Export Citation

  • Waugh, D. W., 2014: Changes in the ventilation of the southern oceans. Philos. Trans. Roy. Soc., A372, 20130269, https://doi.org/10.1098/rsta.2013.0269.

    • Search Google Scholar
    • Export Citation

  • Waugh, D. W., F. Primeau, T. Devries, and M. Holzer, 2013: Recent changes in the ventilation of the southern oceans. Science, 339, 568–570, https://soi.org/10.1126/science.1225411.

    • Search Google Scholar
    • Export Citation

  • Weijer, W., W. Cheng, O. A. Garuba, A. Hu, and B. T. Nadiga, 2020: CMIP6 models predict significant 21st century decline of the Atlantic meridional overturning circulation. Geophys. Res. Lett., 47, e2019GL086075, https://doi.org/10.1029/2019GL086075.

    • Search Google Scholar
    • Export Citation

  • Yeager, S., and G. Danabasoglu, 2014: The origins of late-twentieth-century variations in the large-scale North Atlantic circulation. J. Climate, 27, 3222–3247, https://doi.org/10.1175/JCLI-D-13-00125.1.

    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Ocean circulation and buoyancy frequency. CESMv1 global meridional overturning streamfunctions in the (a) preindustrial era (1850–59), (b) 2090s, and (c) 2290s. CESMv1 zonal mean buoyancy frequency in (d) the preindustrial era (1850–59), (e) the differences between 1850s and 2090s, and (f) the differences between 1850s and 2290s. (g) Key aspects of global ocean circulation: vertical transport at 100 m of the Antarctic Divergence upwelling (SO; south of 60°S), equatorial upwelling (Eq upw; 18°S–18°N), subantarctic downwelling (AAIW dnw; i.e., AAIW/SAMW formation, 60°–35°S), Southern Hemisphere subtropical downwelling (subS; 35°–18°S) and Northern Hemisphere subtropical downwelling (subN; 18°–35°N), and the strength of SMOC and AMOC (Sv).

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    The separation of 17 surface patches. “Ant”, “Suba”, “Subt”, “Equ”, and “Subp” are short for Antarctic, Subantarctic, Subtropical, Equatorial, and Subpolar, respectively.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    The surface sources of global ocean waters. (left) The equivalent thickness from the oceanic volume that originated in each surface pixel, scaled by the surface area of each pixel (a) in the year 1850, (c) the difference between 2090 and 1850, and (e) the difference between 2290 and 1850 (km). The color scale follows a base-10 logarithm of the field in (a). The black number indicates the fraction (in percent) of the whole water column that made last contact with the surface ocean in each region defined by the solid lines. (right) The zonal integration of the fraction along with each latitude bin (1°) (b) in the year 1850, (d) the difference between 2090 and 1850, and (f) the difference between 2290 and 1850 (permille per degree).

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    The fraction of whole water column where it made its next contact with the surface at each ocean grid in the experiment of (a)–(f) scenario 1 and (g)–(l) scenario 2. The fraction of the water column ventilating in each region in (top) the year 1850, (middle) year 2090–year 1850, and (bottom) year 2290–year 1850. The regions are defined by the solid black lines.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    The global mean age. The top row shows zonally averaged contour plots of the mean age in (a) year 1850, (b) the differences between the years 2090 and 1850, and (c) the differences between the year 2290 and 1850. (d) The time series of ideal age from the preindustrial era to year 2300 (yr).

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    The global mean first passage time for (a)–(c) scenario 1, in which the year-2300 circulation is assumed to persist indefinitely, and (d)–(f) scenario 2, where the circulation is assumed to abruptly return to its 1850 state after year 2300. The zonal average of the first-passage time was averaged for the 1850–59 decade is shown in (a) and (d), the differences between the 2090–99 and 1850–59 decadal averages are shown in (b) and (e), and the differences between the 2290–99 and 1850–59 decadal averages are shown in (c) and (f). (g) The time series of the globally integrated first-passage time for each scenario (yr).

Fig. 1.

Ocean circulation and buoyancy frequency. CESMv1 global meridional overturning streamfunctions in the (a) preindustrial era (1850–59), (b) 2090s, and (c) 2290s. CESMv1 zonal mean buoyancy frequency in (d) the preindustrial era (1850–59), (e) the differences between 1850s and 2090s, and (f) the differences between 1850s and 2290s. (g) Key aspects of global ocean circulation: vertical transport at 100 m of the Antarctic Divergence upwelling (SO; south of 60°S), equatorial upwelling (Eq upw; 18°S–18°N), subantarctic downwelling (AAIW dnw; i.e., AAIW/SAMW formation, 60°–35°S), Southern Hemisphere subtropical downwelling (subS; 35°–18°S) and Northern Hemisphere subtropical downwelling (subN; 18°–35°N), and the strength of SMOC and AMOC (Sv).
Fig. 2.

The separation of 17 surface patches. “Ant”, “Suba”, “Subt”, “Equ”, and “Subp” are short for Antarctic, Subantarctic, Subtropical, Equatorial, and Subpolar, respectively.
Fig. 3.

The surface sources of global ocean waters. (left) The equivalent thickness from the oceanic volume that originated in each surface pixel, scaled by the surface area of each pixel (a) in the year 1850, (c) the difference between 2090 and 1850, and (e) the difference between 2290 and 1850 (km). The color scale follows a base-10 logarithm of the field in (a). The black number indicates the fraction (in percent) of the whole water column that made last contact with the surface ocean in each region defined by the solid lines. (right) The zonal integration of the fraction along with each latitude bin (1°) (b) in the year 1850, (d) the difference between 2090 and 1850, and (f) the difference between 2290 and 1850 (permille per degree).
Fig. 4.

The fraction of whole water column where it made its next contact with the surface at each ocean grid in the experiment of (a)–(f) scenario 1 and (g)–(l) scenario 2. The fraction of the water column ventilating in each region in (top) the year 1850, (middle) year 2090–year 1850, and (bottom) year 2290–year 1850. The regions are defined by the solid black lines.
Fig. 5.

The global mean age. The top row shows zonally averaged contour plots of the mean age in (a) year 1850, (b) the differences between the years 2090 and 1850, and (c) the differences between the year 2290 and 1850. (d) The time series of ideal age from the preindustrial era to year 2300 (yr).
Fig. 6.

The global mean first passage time for (a)–(c) scenario 1, in which the year-2300 circulation is assumed to persist indefinitely, and (d)–(f) scenario 2, where the circulation is assumed to abruptly return to its 1850 state after year 2300. The zonal average of the first-passage time was averaged for the 1850–59 decade is shown in (a) and (d), the differences between the 2090–99 and 1850–59 decadal averages are shown in (b) and (e), and the differences between the 2290–99 and 1850–59 decadal averages are shown in (c) and (f). (g) The time series of the globally integrated first-passage time for each scenario (yr).
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