Tides - A Visual Exploration

As someone who has studied marine science, I have worked with a lot of ocean data. Of all the variables that impact the coastal ocean, I find the tides most interesting because it involves both earth and space science. I created some visualizations (using Python & After Effects) to explore some of the basics behind tidal forcing.

Starting with a broad scope, tidal cycles vary by time and space. Depending on the location, the tidal cycle can be diurnal, semidiurnal, or mixed semidiurnal. This is because the ocean size, bathymetry, and currents all have an impact. Here in California, we experience mixed semidiurnal tides, which means that there are two high tides (called HHW & HLW) and two low tides (LLW & LHW) with different sizes per day (see Fig. 1 below). While, the tides are influenced by many factors, these visuals will mainly focus on the basic forces from the moon and the sun.

Before going further, press play (or move the slider) on the animation below! I downloaded some tidal data to visualize the daily tides in California. I imported the data into python and used plot.ly to create an animated graph.

In the animation above, each frame displays the tidal variations within each day, but the tides also display patterns on longer timescales. Below, the monthly and seasonal scales will be explored. 

Monthly Scale

If we are observing tidal variations within a single month, we will notice the Spring vs Neap cycles, which involve the influence of both the moon and the sun. To understand these cycles, let's start with the gravitational pull from the moon and the sun, which causes the earth to bulge in line with the celestial object. In the very simplistic animation below, the effects from the sun and the moon are separated to illustrate the gravitational pull on Earth from each object. As the moon orbits, the Earth is pulled in its direction, changing its shape. On the right, the Earth orbits around the sun while rotating around its own axis. It’s worth noting that the moon has a greater gravitational force on the Earth relative to the sun (due to proximity) and thus has a bigger impact on the tides.

*Note that nothing is to scale (spatially & temporally). The purpose of the animation is to visualize the major impact of the sun and the moon’s gravitational forces on the Earth. 

During every full or new moon, the gravitational pull from the moon and the sun converge, causing higher high tides and lower low tides. We call this general period of alignment the Spring tides. On the other hand, when the moon, the sun, and the earth form a right angle (during the 1st & 3rd quarter phases of the moon) the bulges diverge and we experience neap tides. We can see this dynamic in the animation below! 

*Note: These are simplified versions of very complicated dynamics. For a realistic temporal scale, the moon’s orbit is about 27 days, and the Earth rotates around its axis every 24 hours. Each tidal cycle is 24 hours and 50 minutes because as the Earth spins around its axis, the moon also orbits the Earth, so a point on the Earth aligns with the moon slightly longer than an Earth day. The tides switch from spring to neap about every 7 days, meaning the converging gravitational bulge occurs about every 14 days. 

In the figure above, I took the same tide data as Figure 1 but added a subplot that includes the moon phases during the same year. You can see the full moon (full bar) and new moon (no bar) create a larger amplitude in the tides - the Spring Tides! 

Yearly Scale

In CA’s mixed semidiurnal tide regime, the highest high tides (HHW) occur in the morning  during the winter and in the evening during the summer (see the figure below). This seasonal difference is due to the declination of the sun and the moon over the year. The declination is the angle of an object from the Earth’s Equator. The sun’s declination is the greatest during the NH’s winter and the summer: 23.5° S & 23.5° N, respectively. The declination cycle of the moon occurs every 27.2 days and moves between 18.5° N to 28.5° N in the northern hemisphere (this also means that the tidal bulge tilts up and down within the month, relative to the equator). The moon and sun’s declination converges more often in the morning during wintertime and in the evening in summertime.

The figure below is an average of each hour of the day for the winter and summer months from 2015-2020 in La Jolla, CA. The differences in seasons are almost perfectly mismatched, where the high tides are predominately in the morning during the winter and during the evening in the summer.

Another thing worth pointing out is that 3 to 4 times a year, during spring or fall, ‘King Tides’ occur where the tidal height amplitude is at its maximum. This happens when Spring tides coincide with the portion of the moon’s orbit that is nearest to Earth.

Other Interesting Things

You may wonder, why are there bulges on BOTH sides of the Earth from the moon/sun? Wouldn’t the gravitational pull only bulge one side of the Earth closer to the moon/sun? To understand why we see bulges on both sides, we must think about the ocean and the Earth’s dry mass as separate entities. The moon pulls the ocean towards it (think about a single bulge here), but also pulls the Earth’s dry mass closer within the ocean. So we have apparent bulges on both sides. And yes, the moon bulges too. BUT the moon’s bulge does not move relative to itself because the moon’s rotation around the Earth is in sync with its rotation around its axis. This is also why we always see the same side of the moon from Earth.

The tide is technically a wave. A long-period internal wave, to be exact. And while it may seem like the tide moves back and forth across an ocean, it rotates. This is why the tides in San Diego and San Francisco are about 1 hour apart. The tide moves counterclockwise in the northern hemisphere and clockwise in the southern hemisphere.

Thank you for reading and looking at the visuals :)

References:

The astronomical origin of tides

Tides and Water Levels

Background on Tides

California tides, sea level, and waves — Winter 2015-2016

Is it just a coincidence that the moon's period of rotation and revolution are identical…?

Time-of-Day of Peak Tides in a Mixed-Tide Regime

MOON TEACHINGS FOR THE MASSES AT THE UMASS SUNWHEEL & AROUND THE WORLD

TIDES