sea ice begins to form. By year 160 (Fig. 1c) the depth of the Arctic Ocean approaches the freezing point. The Arctic appears cut off from the circulation taking place in other oceans, which are becoming stratified with warm water pooling at the surface. Fig. 1d is the difference between the model at the end of the simulation and modern-day ocean temperatures. The Arctic Ocean is close to modern day values with the deeper waters being slightly warmer. However, in the tropics and midlatitudes the surface waters are significantly cooler. This is due to the thick layer of stratospheric aerosols defined at the beginning of the simulation. Initially they help limit the amount of excess heating in the tropics. However, once the ocean cools it drives the earth system to a temperature that is cooler than current day values. It is anticipated that an extended run will eventually freeze the ocean surface at the equator leading to what is often called snowball earth. Although the earth system is driven to colder values, a four hundred year simulation is not sufficient to cool the deep oceans to current day values. Sequestration of water in the form of ice sheets lowers sea level, but only several meters below current day values. If our scenario is to match conditions during the last ice age maximum, sea levels need to be 130 meters lower than they are today. Some of that comes from further cooling of the deep ocean. However, most is due to sequestration of water on the continents in the form of ice sheets. This hints at one deficiency of the model, which we will address later when we discuss the buildup of land ice. Regarding ocean cooling, Marshall and Plumb (2008) indicate that a fully mixed ocean has a thermal adjustment time constant of 40 years. Beginning with 24 °C oceans, five time constants, or 200 years, should be sufficient to bring the oceans to a temperature within one percent of modern day values. As illustrated in Fig. 2, the average ocean temperatures cool exponentially. However, the time constant is 238 years. In addition, it is clear from Fig. 2 that the exponential model underestimates cooling during the later 150 years of the simulation. This is due to the thick layer of stratospheric aerosols overcooling the earth system. The buildup of land and sea ice in the higher latitudes also changes the earth’s albedo, thus reducing the equilibrium temperature of earth. B. Ocean mixed layer depth Under modern day conditions, the ocean surface is decoupled from the depths. Heating by the sun and atmosphere forms a stable layer of water near the ocean surface. Vertical circulation is restricted to the mixed layer. As seen in Fig. 3a, the mixed layer of the reference model is mostly restricted to the top fifty meters of the ocean. Deeper ocean mixing occurs between Greenland and England and off the coast of Antarctica. This is where cold surface waters sink to the ocean bottom and become part of the thermohaline circulation. Ten years into the simulation (Fig. 3b) most of the ocean is experiencing circulation with cooler surface water driven to the bottom of the ocean. The only place where the mixed layer is shallow is near the equator where warm surface water forms a stable layer. By year Figure 2. Average ocean temperature by year of simulation. The ocean cools exponentially towards an equilibrium temperature of 4.76. The actual temperature diverges towards the end of the simulation due to over cooling from stratospheric aerosols and buildup of ice sheets. Figure 3. Ocean mixed layer depth. The reference model (a) indicates that most of the ocean has a mixed layer restricted to the surface. In the warm ocean model, b) deep convection occurs over most of the ocean in the first ten years of the simulation. c) By year forty convection in the Arctic is cut off and for the remainder of the simulation d) deep convection is restricted to the boundaries of open sea next to sea ice. a) b) c) d) GOLLMER Rapid ice age 2023 ICC 270
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