Sea-Level Variability: Redux with a King Tide

Sea-Level Variability: Redux with a King Tide

It's a little too busy for me right now, so I am going to repeat my sea-level rise primer. I had a few scientist colleagues tell me it was a good one, and I am inclined to believe them. It comes with a King Tide, which must have something to do with that fall eclipse thing. This story from NPR tells me that the number of flooding tides in Annapolis has gone from 4 to 40 per year since the 1950s. The increasing flooding that is creeping up along the coast might be a little like slowly turning up the temperature on the pot full of Chesapeake crabs. The Union of Concerned Scientists has a nice new report entitled Encroaching Tides which summarizes things along the U.S. coasts.

Going to try a little experiment here for those of you you who remember my MOOC question. One thing that has been keeping me too busy is my new teaching demands, and I have been trying to record some pedagogical lectures. Here is a link to an annotated MP4 that is an introduction to classification of uncertainty. It's about 28 minutes long. About 190 MB. I am, as stated in Nate Silver's book, a soft-spoken North Carolinian, so I expect soporific as a possible comment. Beyond soporific, I would be interested in your reviews of such lectures. My vision is to provide background pedagogical material in recorded lectures, so that I can use class time for discussion and rumination. Only a couple of you would have to download it to exceed the number of students who have actually downloaded it!

For the blog below. Been involved in a few discussions about the "role of Gulf Stream" in the current King Tide. Anybody with insights into the specific state of ocean dynamics (item 5) right now, have at it in the comments.


Sea-Level Variability: A Primer

The comments in the last blog helped me realize the complexities of sea-level rise. In this entry I am going to explore sea-level rise more rigorously. I will continue using the East Coast of the U.S. as a case study.

One of the most certain consequences of the warming planet is that sea level will rise and land will be flooded. My mantra is that the temperature of Earth’s surface will rise, ice will melt, sea level will rise and the weather will change. It is easy to think of the ocean as a big cup and we are adding more water, from the melting ice, and, therefore, the seas will rise relative to the land. When we look at an individual place, like Norfolk, Virginia in the previous blog, the evaluation of sea level rise takes on many local details. In fact, it is much like talking about a single weather event in the context of a changing climate.

I’ll start with thinking about the factors that contribute to changes in sea level. I will refer to the ideas in the tutorials on modeling that I wrote in 2012, and specifically the entry, Balancing the Budget. In words there is an equation, which is

sea level tomorrow = sea level today + sea level gained – sea level lost

What contributes to sea level gains and loses? For those who want to know more, here is a link to an article by John Church and co-authors, Understanding and Projecting Sea Level Change. The article on sea level in Wikipedia is pretty good as well.

1. Sea level changes due to changing the density of water. This can come from either temperature changes or changes in the amount of salt in the water. These changes are known as “steric.”

2. Sea level changes due to adding water to the sea. Water is added when glaciers and ice sheets (e.g. Greenland and Antarctica) melt. Water is added by river runoff.

3. Sea level changes due to diverting water from the sea. For example, there are estimates that the building of dams offset about 30 millimeters of sea level rise in the last half of the twentieth century (Chao et al., Science, 2008).

4. Sea level changes because the land rises and falls. This could be due to plate tectonics, the large-scale motion of the surface of the Earth. There might also be sinking of the land when ground water is pumped out. And to make it more complicated, when the ice sheets melt, mass is removed from the crust of the Earth, and the land can rise or fall as it adjusts. These changes are often measured by mapping the Earth’s gravitational field; the gravitational force is not constant.

5. Sea level changes because of ocean dynamics. This will be the focus of this blog.

6. Sea level changes because of changes in the atmosphere. Atmospheric pressure and storm surges cause variability in sea level. The stress of wind on the ocean surface causes water to pile up in certain regions.

7. Sea level changes due to tidal forces.


Now I introduce a set of figures that focus on the East Coast of North America and the western Atlantic. These figures are from the nice collection at the web site Ocean Surface Currents hosted at the Rosenstiel School at the University of Miami.

Figure 1 shows the average position of the Gulf Stream, which is colored white in the figure. The colors in the ocean represent temperature, with yellows being warmer than greens that are warmer than blues. The Gulf Stream carries warm water northward, just off of the coast of the U.S. The Gulf Stream starts to leave the coast at North Carolina, more or less at Cape Hatteras. From here, the Gulf Stream flows eastward and then splits into several currents in the North Atlantic.



Figure 1: The Gulf Stream as represented by the Mariano Global Surface Velocity Analysis (MGSVA). The Gulf Stream is the western boundary current in the North Atlantic. The Gulf Stream transports warm water (heat) northwards. The averaging of velocity data from a meandering current produces a wide mean picture of the flow. The core of the Gulf Stream current is about 90 kilometers wide and has peak velocities of greater than 2 meters per second (5 knots). From Ocean Surface Currents hosted at the Rosenstiel School at the University of Miami.

What causes the Gulf Stream? The Gulf Stream is a surface current in the ocean, and it is largely caused by the stress of wind on the ocean surface. The trade winds flow from east to west across the Atlantic in the subtropics and tropics. In this figure, the trade winds are between 20 and 30 degrees north. Up at 40 degrees north, the average wind is from west to east. The wind, therefore, blows water towards North America in the southern part of the figure. Water is blown away from North America in the middle and northern part of the figure. The water being blown towards the coast in the south has to go somewhere. The Earth’s rotation and the presence of continent turn the water northward and it is guided along the coast.

This blog is about sea level. The winds from east to west in the subtropics are persistent and pile up water. This increases sea level. Since pressure in the ocean is related to amount of water above a point in the ocean, as the wind moves water around at the surface the pressure in the ocean changes. These changes in pressure cause the motion that becomes the Gulf Stream. The pressure in the ocean is directly related to sea level, the amount of water above a particular point.

Geography is important to climate. In Figure 2 the blue colors in the ocean are the depth of the ocean. The light blue near the edge of the continent is shallower than the deep blue. The light blue is the continental shelf, and the edge of the shelf is steep. Comparing Figure 2 to Figure 1, the Gulf Stream follows the shelf. This reveals the importance of the oceanic edge of the continent in shaping the Gulf Stream. I have marked the Grand Banks in the northern part of the figure. The Grand Banks guide the Gulf Stream, and as the stream of water moves beyond the Grand Banks, the Gulf Stream splits into several splinters. Important to sea level, there is bulge in the water off of the East Coast of North America caused by the wind stress and the continental shelf. The bulge of water associated with the Gulf Stream is about a meter in height. One meter is about the amount of rise in sea level expected from warming and ice melting in the next 100 years.



Figure 2: Topography/bathymetry of eastern North American and the western Atlantic. Topography is the height of the features on land. Bathymetry is the depth of the ocean. The units are not provided on the original web site, but are consistent with feet. From Ocean Surface Currents hosted at the Rosenstiel School at the University of Miami.

Let’s start to bring this information together to explore sea level rise and variability on the East Coast. Globally, the sea-level rise observed in the previous century is attributed to change in temperature (steric, Item 1 in the list above) and to adding water from melting glaciers and ice sheets (Item 2).

In the last blog and more completely in the comments, it was pointed out that Norfolk experiences subsidence, that is, the elevation of the land is declining. Up to half of the change in sea level at Norfolk is attributed to subsidence (Item 4). The U.S. Atlantic Coast, including Norfolk, has often been called a “hot spot” in sea level rise (also, press release from U.S. Geological Survey). It is easy to look at the subsidence of the land and attribute this hot spot to subsidence – not climate change. However, examination of the rate of sea-level rise reveals that the rate and changes of the rate of increase are faster than associated subsidence. What is the explanation of this regional change?

The most likely explanation lies in ocean dynamics. These changes can be viewed as centered on the Gulf Stream, and more broadly, the role of the Gulf Stream in the global circulation. Above, I wrote about how the wind stress and the continental boundary pile up water in the western Atlantic. The bulge of water is not at the coast, but off the coast a bit. This bulge is nearer the coast in the Southeast of the U.S. It is straightforward to hypothesize that changes in the Gulf Stream might have significant effects on the U.S. Coast. This is the subject of Oceanic control of sea level rise patterns along the East Coast of the United States by Jianjun Yin and Paul B. Goddard. Yin and Goddard make a convincing argument that “In response to the 21st century climatic forcing, the rise (fall) of the dynamic sea level north (south) of Cape Hatteras is mainly induced by the significant decline of ocean density contrast across the Gulf Stream.” The density change is largely related to the temperature, hence, a regional impact of the steric effect. Interestingly, there is also a potential impact from the fresh water inflow from the melting ice sheets in Greenland. Fresh water is lower density than salt water.

Figure 3 helps to place this Gulf Stream effect into a more regional and global context. This figure shows the Labrador Current, which is a cold-water current from the north that strongly influences the sea surface temperature of the U.S. North East and the Canadian Maritime Provinces. I have also placed arrows on Figure 2 showing the positions of the Gulf Stream and the Labrador Current. The Labrador Current directly receives the fresh water from the melting ice. Hence, as the Gulf Stream and Labrador Currents (cool and warm water, fresh and salt water) interact, there are many mechanisms that define the regional behavior of sea level. In the near term, decades, these regional factors can dominate the global rise, due to adding more water to the ocean. They can also act on faster times than are typical of the land rising and falling.

Final question: How does climate change affect sea level? The usual suspects are listed as changing the temperature of the ocean and adding water to the oceans from melting ice. These are important and act globally. Climate change and climate variability are also realized in changes to ocean currents. Since these currents are often close to the coasts, there are potential large, rapid and localized changes to sea level. The changes in surface currents in the ocean are related to changes in the stress of winds on the surfaces; hence, there are changes related to atmosphere pressure patterns. There is local variability due to storms and storm surges. And as the ice melts, the land might rise, might fall, also an effect due to climate change. These sources of variability will be important to planning in the next decades, but on the time of a century or longer, adding water to the ocean from melting ice will dominate; there’s really nothing working against it.



Figure 3: Labrador current as represented by the Mariano Global Surface Velocity Analysis (MGSVA). The Labrador Current is southward flowing and transports cold waters (blue) into the warmer Gulf Stream region (green). From Ocean Surface Currents hosted at the Rosenstiel School at the University of Miami.