Exploring the Possibility of Altered Ocean Circulation Patterns Using the Second Law of Thermodynamics

Home , Cold blob, The Day After Tomorrow

Adrienne Propp ES 112 Semester Project 9 May 2016

The Day After Tomorrow: Exploring the Possibility of Altered Ocean Circulation Patterns Using the Second Law of Thermodynamics

Climate change, one of the most urgent and universal issues of our time, involves a complicated web of interrelated processes, many of which are quite complicated, themselves. As a result, although there is general consensus that climate change is occurring, it is difficult to determine what its effects will ultimately be or when they will be realized. As this has potentially critical consequences for society, a deeper understanding of how human actions affect the climate system must be pursued. Ocean circulation, one of the major processes affecting the climate system, is believed by some to be undergoing a fundamental change. Specifically, warmer temperatures and higher levels of atmospheric CO2 are believed to be contributing to the weakening of what is colloquially called the “great ocean conveyor belt,” or Earth’s network of ocean currents (Marshall, 2012; Weijer, Maltrud, Hecht, Dijkstra, & Kliphuis, 2012). If true, this could be indicative of the level of severity of anthropogenic climate change, and have potentially disastrous consequences. In this paper I will first provide a brief overview of ocean circulation’s role in the global climate system. I will then discuss the nature of the reports being made. Finally, I will present ocean circulation in the context of the Second Law of Thermodynamics, and discuss an investigation of the validity of these claims using this thermodynamic perspective. This approach is valuable because “the sequence of all natural processes is determined by the principle of entropy increase” (Fenn, 1982, p. 242) – in other words, the Second Law of Thermodynamics determines the course that a system will actually follow when multiple courses satisfy the First Law of Thermodynamics, or conservation of energy.

Ocean Circulation and the Global Climate System Earth’s climate is influenced by many factors, including solar radiation, wind, ocean currents, and the interactions between them. As the oceans cover about 71% of the Earth, they are unsurprisingly a major component of the global climate system. Indeed, the oceans are both responsible for and responsive to many changes in environmental conditions. (Pidwirny, 2007) 2

More than their sheer size and volume, the influence exerted by oceans comes largely from their circulation patterns. Ocean currents transport enormous amounts of heat around the world and absorb gases in the atmosphere. In fact, oceans are estimated to transport a maximum of heat just under 3 petawatts, and to have absorbed up to half of all of the CO2 produced by the burning of fossil fuels since the beginning of the industrial revolution (Bollmann et al., 2010). Therefore, whether the climate will change in the future, and by how much, is strongly linked to ocean circulation. Ocean circulation is both mechanically and thermally driven. It is mechanically affected by wind stresses, waves, and the like. Thermally, ocean circulation is affected by the sun, via radiative heating, and the core of the Earth, via geothermal heating. (Bollmann et al., 2010) (Rahmstorf S. , Thermohaline Ocean Circulation , 2006) Overall, most of the large-scale circulation is driven by density, which depends on salinity and temperature. Thus, this characterization of ocean circulation is often called thermohaline circulation. Figure (1) gives a broad overview of what is colloquially called the “great ocean conveyor belt”, or the manifestation of this thermohaline circulation. Density, a measure of how tightly packed together molecules are, governs the direction, location, and depth of currents (Ocean and

Figure 1: The "Great Ocean Conveyor Belt" Climate - The Odd Couple). Warm water and fresh water rise due to low density, while cold water and salty water sink due to high density. Furthermore, water in regions with high concentrations of heat and salt diffuses into regions with low concentrations, dissipating the unequal distributions of heat and salinity, and thus diminishing the density gradients. These unequal distributions of heat and salinity are caused by precipitation and evaporation, as well as differential heating between the polar and equatorial regions. Overall, there are net gains of heat and salt in the equatorial regions, and net losses of heat and salt in the polar regions (Shimokawa & Ozawa, 2002). This flux imbalance results in the inhomogeneous distribution of temperature and salinity at the ocean surface that is often considered to be the driving force behind global-scale thermohaline circulation. One manifestation of this is the water mass produced by these convective processes in the Arctic, termed the North Atlantic Deep Water (NADW). Warm, salty surface water spreads from the tropics into the North Atlantic. In the Labrador and Greenland seas, the cold 3 temperature and formation of ice increases the region’s water density, pulling it down to rest on a layer of even denser, deeper water produced by convection in the Antarctic, the Antarctic Bottom Water (AABW), that extends up the entire length of the Atlantic Ocean. (Bollmann et al., 2010) (Gordon, 2004) Approximately one third of the world’s ocean water is involved in thermohaline circulation, or about 400,000 cubic kilometers of water (Bollmann et al., 2010). Although it transports about 20 million cubic meters of water per second, there may be hundreds of years between sinking and returning to the surface (Conkling, Alley, Broecker, & Denton, 2011). Indeed, oceans react very gradually to change. As a result, though ocean circulation exerts a huge influence on, and is a powerful indicator of, the state of the global climate, the impacts of climate change evident in the oceans today do not yet reflect the total extent of climate change already caused by human activity (Bollmann et al., 2010). Thus, the decisions made today may have consequences that extend far into the future.

Are Humans Altering the Course of Ocean Circulation? In Florida and much of the southeastern United States, citizens anxiously await predictions of the severity of the approaching hurricane season each spring. This year, there is growing concern that the presence of a “cold blob,” or a region of unusually cool water, in the North Atlantic will affect Atlantic Ocean currents. This could potentially initiate a transition from El Niño to El Niña and increase the likelihood of a severe hurricane season (MacMath, 2016). Scientists’ concern reaches even farther – some climate models have predicted that the Atlantic turnover process will weaken by about 25% by the end of this century (Bollmann et al., 2010). The 2004 film, The Day After Tomorrow, may have been inspired by, and probably aggravated, public concern over the issue. Indeed, there is evidence that ice sheets in the North Atlantic are melting at an increasing rate, discharging large amounts of cold fresh water into the ocean (e.g. Frauenfeld, Knappenberger, & Michaels, 2011; Marshall, 2012). Furthermore, rising Arctic temperatures inhibit the formation of sea ice, diminishing the level by which salinity is increased in this region. As a result, the increase in water density that usually occurs in this region is diminished, weakening the convective forces that pull the water down, driving circulation. As a result, many believe the Atlantic Meridonal Overturning Circulation (AMOC) will be weakened, affecting global climate patterns as well as the ocean’s uptake of CO2, likely contributing to a positive feedback cycle. (Bollmann et al., 2010) These changes are significantly tied to human activity, such as the burning of fossil fuels. However, information about past environmental conditions, drawn from ocean floor sediment and paleo-data, indicates that shifts in oceanic circulation patterns have occurred in the past, and corresponded to shifts in overall climatic conditions. Scientists believe that certain cold climate episodes, occurring over a few decades or even less, were caused by abrupt disturbances in the ocean currents of the North Atlantic. (Bond et al., 1993 as cited in Rahmstorf, 1997) The 4 significance of this is multifaceted. On one hand, it is concerning that a major shift in ocean circulation patterns is indeed a possible scenario. On the other hand, changes in ocean circulation are a naturally occurring phenomenon that may be out of our control. That said, there is evidence that this naturally occurring phenomenon is encouraged by the very changes we are exerting on our environment today. For this reason, a holistic and thorough investigation of the likelihood of this occurring is critical to ensuring that we are prepared for the potentially inevitable consequences of our actions.

One Method of Investigation: The Second Law of Thermodynamics Ocean Circulation in the Context of the Second Law As it turns out, thermohaline circulation is a fantastic example of the second law of thermodynamics, manifested in the dissipation of heat and salt gradients. In this context, the second law of thermodynamics will be considered with the ocean as an open dissipative system – it is open because the system exchanges heat and salt with the surroundings, and dissipative because the system is not at equilibrium. Fluxes of heat and salt between the ocean and its surroundings (most notably the atmosphere) produce gradients of temperature and salt concentration, which processes like thermohaline circulation act to diminish. In effect, these processes occur in an attempt to bring the system closer to equilibrium, towards a state of higher entropy. The rate at which the ocean system approaches equilibrium is described as the rate of entropy production. (Ozawa & Shimokawa, 2000) From the Second Law of Thermodynamics, we know that the overall entropy of the universe must increase.

1 ��!"# ≡ ��!"## + ��!"! ≧ 0 , where �� + �� − � �� = !"# = ! ! ! � � Therefore, for any spontaneous process to occur, it must result in an overall increase of entropy. We also know that any spontaneous process in any isolated system always results in an increase in the entropy of that system (Fenn, 1982).

1 ��!"#$%&'( ≧ 0 Furthermore, entropy is additive, and the total change in entropy of a system must be the sum of internal changes (i) and exchanges (e) with the surroundings.

1 ��!"! = �!� + �!� Internal entropy changes are the result of irreversible processes, and entropy exchanges are the result of heat exchanges in a closed system, or heat and matter exchanges in an open system.

1 Obtained from lecture notes and a compilation of articles, books & online sources 5

Thus, for an open system,

�� = !!!"## + !" �� + �� ≥ 0 1 !"# ! ! !! !,!"## !"! !"## !!"## or,

!! �� = − !"! − !" �� + �� ≥ 0 1 !"# ! ! !! ! !"! !"## !!"## since the fluxes from the perspective of the system and the perspective of the surroundings are equal and opposite (��!"## = −��!"! and ��! = ��!,!"! = −��!,!"##). Combining the above expressions,

��!"# = ��!"## + �!�!"! + �!�!"! ≥ 0

!! �� = − !"! − !" �� + � � + � � ≥ 0 !"# ! ! !! ! ! ! !"## !!"##

!! !! �� = − !"! − !" �� + !"! + !" �� + � � ≥ 0 !"# ! ! !! ! ! ! !! ! ! !"## !!"## !"! !!"! Here, the entropy change in the surroundings is a result of the interaction with the system. This is a very simplified case with many assumptions, such as reversible heat transfer, but the main idea is that there are separate components of entropy that contribute to ensuring that the overall entropy is nonnegative. Shimokawa and Ozawa (2000) formulated expressions of entropy specifically relating to ocean circulation. In their expressions, they describe the rate of entropy increase of the system – the ocean, in this case – as depending on heat and salt transports. They do not separate dSsys into deS and diS. However, they do express dSnet as the sum of dSsys and dSsurr. According to them, where, �!"# = �!"!,

� = ! ! !"# + div �� + � div � �� − �� !" + div �� ln � �� 2 !"# ! !" !" In the above expression, the first integral term represents the entropy increase rate due to heat transport, and the second integral term represents the entropy increase rate due to salt transport. They integrate over volume to account for the transport throughout the entire ocean. They also describe the rate of entropy change of the surroundings.

� = !! �� − �� ln � �� 2 !"## ! ! In the above expression, the first integral term represents the entropy increase rate due to heat flux through the boundary surface, and the second integral term represents the entropy increase rate due to salt flux through the boundary surface. They use a surface integral because the

2 Obtained from Shimokawa and Ozawa, 2000 6 entropy increase of the surroundings is due to the interaction between the ocean and surroundings across the boundary of the ocean surface. Together, the rate of entropy increase of the ocean and the rate of entropy increase of the surroundings comprise the overall rate of entropy increase due to ocean circulation.

2 �!!!"# = �!"# + �!"## However, before combining the expressions, we can simplify them by making a few assumptions. When we assume that seawater is incompressible, div v = 0. When we assume that volumetric heat capacity is constant, �� = constant. This removes the divergence terms from the equation for �!"#.

� = !" !" �� + !! �� − �� !" ln � �� − �� ln � �� 2 !!!"# ! !" ! !" ! Through mathematical manipulation, this expression can be rewritten as the following:

� = � ∙ grad ! �� + ! �� − �� !!∙ !"#$ ! �� 2 !!!"# ! ! ! ! The first term on the right side of the equation represents the rate of entropy increase due to thermal dissipation, the second represents the rate of entropy increase due to viscous dissipation (or the dissipation of kinetic energy as heat), and the third represents the rate of entropy increase due to the diffusion of salt ions. The gradient function gives directional information about the gradients of temperature and salinity. Heat flows from hot to cold, the dissipation function is always nonnegative, and molecular diffusion takes place from high to low concentration – therefore, this sum should always be positive, resulting in a positive rate of change of entropy, consistent with the Second Law. (Ozawa & Shimokawa, 2000) Before continuing with this model, it is important to confirm that these are reasonable expressions for the rate of entropy increase due to thermohaline circulation. The separation into surface and volume integrals, as well as the elements of temperature and concentration, indicate that it likely is reasonable. Indeed, another group, Yan et al. (2004), independently arrived at a rather similar expression for the rate of entropy increase due to the boundary interactions.

!!! = − ! ! ∙ !!" + !!" + !!! + !!! �Σ 3 !" ! ! ! ! !!"# !!!" !!!" !!!" !!! = ! !! �Σ 3 !" ! ! ! ! where !!! is the rate of entropy exchange across the boundary of the ocean system, h refers to !" heat, m refers to mass, Σ represents the area of the global sea surface, dΣ represents the area of each cell, Tsun represents the temperature of the sun, Tsst represents the temperature of the sea surface, �!" and �!" are the shortwave and longwave radiant energy fluxes, respectively, �!! and �!! are the latent heat flux and sensible heat flux, respectively, I0 is freshwater flux, and S is

3 Obtained from Yan et al. (2004) 7 salinity. This version exhibits similarities to and differences from the expressions proposed by Shimokawa and Ozawa (2000). We still integrate over the surface to describe interactions across the boundary. The heat transfer expression still exhibits flux divided by temperature, while the salt transfer expression still exhibits division by salt concentration. This indicates that Shimokawa and Ozawa’s (2000) thermodynamic approach to analyzing shifts in ocean circulation is likely based on sound reasoning. Shimokawa and Ozawa (2000) found that the entropy increase rate in the steady state is zero for the ocean system, but positive for the surroundings in both heat and salt transport. If the entropy change for the system is zero,

�!"#,!"#$%"&' = −�!"#,!"#!!"#$% Because the entropy change of a system is the sum of its entropy production and the entropy flux, and we know that the ocean produces entropy through the dissipation of temperature and salt gradients, there must be entropy lost to the surroundings through boundary fluxes of heat and salt. In other words, the entropy exchange is negative from the perspective of the ocean system. This may be partly due to the fact that the gradients are constantly replenished by precipitation, evaporation, glacial melting, and differential heating of the globe – in effect, the ocean’s interaction with its surroundings is actually the cause of the gradients that keep the system away from equilibrium. Overall entropy does increase, however, which makes sense because there are irreversible dissipative processes taking place, though the system itself stays in a state of constant entropy.

Using the Second Law to Predict the Feasibility of Various Scenarios Several methods have been investigated in the attempt to determine whether or not a significant change in ocean circulation is imminent. Shimokawa and Ozawa (2002) explore the issue as an initial-value-boundary-condition-type problem, investigating irreversible transition to a state with a higher rate of entropy production. In this type of analysis, the initial values and boundary conditions determine the outcome that is specific to the situation in question. In the case of ocean circulation, these initial values and boundary conditions would describe properties such as air temperature, water temperature, salinity, wind strength, etc. Under a chosen set of initial values and boundary conditions, one can then examine the resulting steady states and their responses to perturbation. For their investigation, Shimokawa and Ozawa (2002) chose restoring boundary conditions that were symmetric about the equator, with the initial temperature distribution as a function of depth and latitude, initial salinity assumed to be constant at 34.9%, and initial velocity field set to zero. After the system reaches a steady state with northern sinking (approximately 4000 years), they switch to mixed boundary conditions (restoring condition for temperature and a fixed flux condition for salinity), perturb it with a salinity flux in high latitude, and integrate the model described in Shimokawa and Ozawa (2000) for 500 years so that the 8 system moves to a state regulated by the perturbation. They then remove the perturbation and integrate for another 1000 years. If the system finds a new steady state, they repeat this procedure with the same perturbation, using the new state as the initial state. If it returns to the original steady state, they repeat this procedure with a new perturbation. They end up finding a series of steady states of thermohaline circulation that all satisfy the same set of wind forcing and mixed boundary conditions, as well as the rate of entropy increase for each. The results of their study are shown in Figure (2) in the Appendix. In general, a positive salinity perturbation added to a high-latitude region in the northern hemisphere intensifies northern sinking and weakens southern sinking, while a negative salinity perturbation weakens northern sinking and intensifies southern sinking. When transitions to new states occurred, the rate of entropy production was always higher in the final state than in the initial state. Transitions in the opposite direction did not occur, indicating that these were irreversible transitions. For these reasons, it appears that a thermodynamic approach to the issue of changing ocean circulation is extremely useful, as the rate of entropy production seems to govern the behavior of the circulation patterns. One concerning result is that, starting from the initial steady state after spin up with no perturbation, the system transitioned to S1, a southern sinking state. This situation, called the “halocline catastrophe,” or the collapse of the NADW, has been observed in previous models (e.g. McPhaden et al., 1992) and is appropriately named due to its potentially disastrous consequences. Furthermore, in the cases where the initial state was northern sinking, and the perturbation was a decrease in salinity (paralleling what is actually occurring in the North Atlantic, with the influx of fresh water), the system always transitioned to southern sinking. These results are extremely concerning in their implications that the increased melting of polar ice sheets, such as the Greenland ice sheet, may have extremely drastic effects on global ocean circulation. If the ocean were to transition to a state of southern sinking, the entire pattern of global climates to which we have become accustomed would shift – for example, as Western Europe’s current climate is quite temperate due to the Gulf Stream, this region might become more like Canada with the onset of these shifts. Even if the current pattern of thermohaline circulation were to remain intact, but merely weaken, landmasses would likely experience increased temperatures due to the diminished transport of heat around the globe (Bollmann et al., 2010). In other words, these results are not to be taken likely. This approach has limitations, however, as the boundary and initial conditions are very simplified, and in reality, the perturbation would be fresh water flux rather than salinity flux. The equation for calculating the rate of entropy production also involves assumptions about incompressibility and constant volumetric heat capacity, as mentioned earlier. In addition, their model assumes the entropy increase rate due to wind and tidal dissipation to be negligible. They are indeed small – about two orders of magnitude smaller than the total rate – but not zero. Despite these limitations, their approach gives a reasonable indication of how a similar situation might play out, and supports the hypothesis made by Shimokawa and Ozawa (2002), as well as 9

Sawada (1981) and others, that a nonlinear system is likely to move to a state with maximum entropy production by perturbation.

Conclusion In analyzing the dependence of ocean circulation on the Second Law of Thermodynamics, it is clear that significant and prolonged changes in a property affecting temperature or salinity gradients can cause extreme changes in ocean circulation. Given the evidence that the North Atlantic is becoming cooler and fresher due to increased melting of glaciers, the results of Shimokawa and Ozawa’s (2002) experiment are extremely foreboding. Decreasing the salinity of the North Atlantic seawater directly affects its ability to sink and drive circulation in that region. Furthermore, the layout of salinity and temperature gradients will be significantly altered, and thus the most entropically favorable course of ocean circulation may change, as well. Based on past evidence that such transitions are indeed possible, and Shimokawa and Ozawa’s (2002) evidence that in many realistic circumstances, they are indeed favorable, I am unfortunately convinced that these transitions may be in our future. Thankfully, the time scale over which this will occur is likely many generations, if not lifetimes. However, this is not a reason to delay action – as discussed earlier, the actions of today will impact ocean circulation many years from now due to its gradual nature. Furthermore, it is possible that immediate action to stop anthropogenic climate change could prevent the perturbation we have caused from becoming large enough or prolonged enough to cause a complete transition. Conversely, if the North Atlantic ice sheets continue to melt at this rate, we may reach a critical threshold beyond which a transition is unavoidable (Bollmann et al., 2010). Unfortunately, the exact location of this threshold is unclear. Either way, it is likely that the “cold blob” in the North Atlantic will affect weather patterns in the coming years to some extent, such as the severity of next year’s hurricane season. The Second Law of Thermodynamics has provided a valuable and nuanced perspective on this topic. Deeper understanding must obtained yet, however, as it remains unknown where the current state of the climate system stands in relation to these models. Confirmation of Shimokawa and Ozawa’s (2002) results by a separate group, as well as an extension of their method to more initial values and boundary conditions, could provide even more insight into how imminent the threat of altered ocean circulation patterns really is. Hopefully, with a combination of robust scientific evidence and effective policy measures, we will be able to ensure that future generations do not have to cope with the consequences of our era’s actions.

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Appendix

Figure 2: Results of Shimokawa and Ozawa's 2002 experiment

Figure 3: Visualization of the results from Shimokawa and Ozawa's 2002 experiment