ENVIRONMENT AND ENERGY

The regular rise and fall of ocean waters, known as tides, is a phenomenon obvious to any observer of the sea. In fact, the timing of high and low tides plays a crucial role for harbor operations, nautical safety, and predictions of the severity of coastal flood events. Moreover, tidal currents are a source for renewable energy and support coastal mudflats, a transition zone between land and ocean of rich biological activity. The motion of the tides on Earth are generated by Sun and Moon. As such, they should be predictable and periodic, with unchanged amplitude (that is, size) and phase (that is, timing) year in, year out. However, researchers have long noted that ocean tides undergo small and unexpected changes, typically a few millimeters (mm) per decade in amplitude as seen by coastal tide gauge measurements. The reasons for these changes are not yet understood, but in very shallow regions, such as bights and river mouths, it is clear that tidal amplitudes may increase or decrease as a consequence of sea level rise. Another factor, which has been much discussed but never been examined with rigor, is ocean warming – or more precisely, the influence of ocean warming on the three-dimensional distribution of seawater density.

The importance of the ocean’s density distribution for the twice-daily tide (called M₂) is illustrated in Animation 1 for a 4000-km wide box in the Indian Ocean. Initially, the Moon’s gravitational forces move water broadly from one position to another, such that the tide circles around Madagascar and the sea surface swings from –1 m to +1 m over a full M₂ period (12 hours and 25 minutes). If one looked at the currents going along with this broad motion at a specific point, one would see that the currents are the same for all water depths—a phenomenon also known as the “barotropic tide”. However, once these barotropic currents meet steep underwater topography (for example, the Mascarene Ridge east of Madagascar), a new type of tidal flow arises—the three-dimensional “baroclinic tide”. Topography aside, the baroclinic tide needs distinct density surfaces to form, see the lower panel in Animation 1. Water particles are deflected upward near the ridge, but as soon as these moving particles become much heavier than the surrounding ocean water, they drop back to greater depths, before upward motion starts again. The result are wave-like oscillations in the ocean’s interior. These baroclinic waves slowly travel away from the ridge, decay, break, or join with similar waves generated elsewhere. Although their amplitude at the sea surface is fairly small (max. ~6 cm), the waves carry a substantial amount of energy that has been extracted from the barotropic M₂ component. A longstanding idea is that changes in the barotropic tide, which is the signal most directly observed by tide gauges or satellites, can be ascribed to changes in the baroclinic tide and thus the ocean’s density distribution.

The goal of the project was exactly to examine this type of question, not in a specific region but for the global ocean. Focus was on the M₂ tide and the period from 1993 to 2020, a time span with both suitable satellite altimetry observations and a strong upper ocean warming signal. Computations consisted of one big numerical simulation for each of the 28 years, using a three-dimensional computer model to solve the ocean’s flow equations in different density fields. Because each simulation had to resolve both large-scale and small-scale processes at once, especially baroclinic wave generation (see Animation 1), a relatively fine horizontal grid spacing of 9 km was chosen. This in turn called for the use of a supercomputer, the JUWELS Cluster Module CPU of JSC in our case. Every simulation was distributed to 2880 processing units and took about 13 hours to run, producing 6 terabyte of three-dimensional model output. With these means, it was possible to calculate linear changes—in other words “trends”—of the barotropic and baroclinic M₂ tide since 1993, see Figure 1. The message from the plots is very clear: Recent warming in the upper ocean has increased density differences between shallow and deep ocean layers, thus providing more favorable conditions for the generation of baroclinic waves. Trends in the baroclinic M₂ amplitude (Figure 1a) have a positive sign nearly everywhere and reach values of 0.3 mm yr^-1 in the Indian Ocean, the western Pacific, or North of Brazil. Strengthening of baroclinic tides implies that they carry more energy, that is, energy being pulled out from the barotropic tide. By this logic, one expects the barotropic tide in the global ocean to decrease, and that is exactly what we see in Figure 1b. In fact, many of the modeled trends in Figure 1b, e.g., those in the Indian Ocean, the Gulf of Alaska, near Northwest Australia, or in the North Atlantic, are also evident in 28 years of satellite and tide gauge observations.