A quick look at the Eastern Mediterranean Sea

First a large view of the bathymetry covering (almost) the entire Mediterranean Sea. The deeper parts are found around (18E, 36N) with a large area deeper than 4000 m.


A zoom on the Eastern-most part of the basin where flight MS804 might have crashed. The search area (as of now, May 20th) is around (29E, 34N). This part of the basin is “swallower” than the basin just to the West. Still, the sea floor is around 3000 m deep. Note a very deep trough near (29E, 36N) that extends below 4000 m. The search area seems to be further south, on the Southern flank of the ridge.



These two plots show profiles of the bathymetry (from Egypt/left to Turkey/right) along 28E and 29E, cutting through the search area around 34N.



A snapshot of the surface currents on April 18th, 2016. More precisely, this shows the magnitude of the absolute zonal (East-West direction) geostrophic flow. These currents are obtained from satellite measurements (measurement of the “bumps” in the sea surface, the bumps are just of a few inches high, from AVISO). The se currents do not include the wind-driven currents (Ekman flow).

In the Eastern Mediterranean, currents reach ~10-20 cm/s (half or a quarter of a mile per hour). The currents looks very messy, they change direction every 100 km or so. This reflects mesoscale eddies and fronts (the oceanic turbulence that is big enough to be influenced by Earth rotation). These eddies, or vortices, are almost circular, 50 to 150 km wide.




Melting of floating ice and sea level

By Remi Tailleux

Sea level rise due to global warming is an important societal issue. This motivated me a few years ago to make it part of my “Introduction to Oceanography’’ module. The main effects are easy to understand. Global sea level mostly changes as the result of adding mass to it, due to melting of land ice sheets, or as the result of expansion caused by warming. One “known fact” that I had been teaching, and thought to understand well, is that sea level does not increase when floating ice melts. Sea level rise only occurs when land ice sheet falls into the ocean, not when it subsequently melts. I was shocked, therefore, to learn at a recent conference on satellite altimetry that I was wrong. One of the talks pointed out a paper by Noerdlinger and Brower (2007), arguing that contrary to popular belief, the melting of floating ice actually increases sea level! The effect had apparently been  completely missed by the experts who wrote the sea level chapter in the 4th IPCC assessment report, and only recently included in the 5th IPCC assessment report.

This was quite vexing. Surely, sea level physics is not particle physics, how could have experts been ignorant of basic physics for so long?




As it turns out, the effect had been missed because of a misapplication of Archimedes principle. Archimedes is the famous Greek scientist who is mostly remembered for coming out of his bath shouting ‘Eureka’ (“I discovered it”) upon discovering the principle that bears his name. This principle states that if a body is plunged into a liquid or gas, it will feel a force that is equal to the weight of the fluid displaced.


Schematics of an ice sheet initially on land ending up in the ocean as an iceberg or ‘floating ice’. Because ice is much less dense than seawater, part of it remains out of the water, and only the submerged part contributes to increasing sea level. All the volume of the iceberg contributes to sea level, however, once melted, explaining why the melting of floating ice can further contribute to increasing sea level.

This principle is quite powerful, and allows one to easily predict the emerged fraction of an iceberg (the tip of the iceberg). In order for the iceberg to stay in place (to be in equilibrium), its weight must be opposed by the Archimedes force (Figure 1). If Vice, ρice, and mice=Vice ρice denote the volume, density and mass of the iceberg, its weight is  miceg, where g is the acceleration of gravity. The Archimedes force, on the other hand, is equal to the weight of the seawater displaced, that is Vice-submerged ρseawater g, where ρseawater is the density of seawater, and Vice-submerged is the submerged volume of the iceberg. This implies that

Vice-submerged = (ρice /ρseawater)Vice

This formula explains that the tip of an iceberg owes its existence to ice having a much lower density than seawater. As to the sea level increase Δhice due to dumping the iceberg into the sea, it is due to the volume displaced Vice-submerged, not the total volume Vice. This volume is equal to Δhice times the total area of the ocean Aocean, leading to

Δhice= Vice-submerged / Aocean = (ρiceseawater)Vice/Aocean

In contrast, the sea level increase Δhmelt due to the melted iceberg will be due to the total mass of the iceberg. If ρfreshwater denotes the density of freshwater, one will have the equalities mice=Vice ρice =Vfresh ρfreshwater =ρfreshwater Δhmelt Aocean, which yields the result


which is different from Δhice. One verifies that the difference is given by

Δhmelt – Δhice = (ρseawaterfreshwater)Δhicefreshwater

This formula shows that the difference arises because the density of freshwater is lower than that of salty seawater.

How big is the effect? Typical representative values for the densities of ice, freshwater and seawater are  ρice=917 kg/m3, ρfreshwater=1000 kg/m3 and ρseawater=1026 kg/m3, which yields  (ρseawater – ρfreshwater)/ρfreshwater=0.026. It means that if an ice sheet dumped into the ocean increases the sea level by 1 metre, its subsequent melting will further increase it by 2.6 centimetres. This is a small effect, but one that needs to be included in discussions of error bars.

In reality, the effect might be somewhat more complex. Indeed, Jenkins and Holland (2007) argue that melting floating ice requires energy, which must come primarily from the ocean. In the same way that warming causes sea level rise due to expansion, cooling will cause a sea level decrease due to contraction, which may largely negate the effect of melting. Modelling this effect is significantly more complex, however, and beyond the scope of this blog.

Whoever said that the physics of sea level change was simple?


Jenkins A. and D. Holland, 2007. Melting of floating ice and sea level rise. Geophys. Res. Lett34, L16609, doi:10.1029/2007GL030784
Noerdlinger, P. D. and K. R. Brower, 2007. The melting of floating ice raises the ocean level. Geophys. J. Int.170, 145-150.

West Antarctic Ice sheet: a collapse underway ?

From meteorological considerations, one would expect that, in a global warming world, the Antarctic Ice Sheet would grow. With higher temperatures, air parcels can hold more water. This effect would increase the amount of moisture delivered to Antarctica where it would precipitate as snow (even in a warmer world, air temperatures would remain feel below freezing).

But another side of the story is that the Antarctic ice sheet also loses mass through iceberg discharge at the continental margin, the calving process.

Grab_from NASA_image

B51 just after its birth on November 13rd, 2013. Credit to the Earth Observatory (NASA) website (http://earthobservatory.nasa.gov/NaturalHazards/view.php?id=82388) where more pictures can be found. B51 recently (April 2014) left the Amundsen bay to enter the open ocean.

One such calving event was well observed (from space) in November 2013 when iceberg B51 (a 20×30 km wide and a few hundreds of meter thick piece of ice, Figure 1) broke off from Pine Island Glacier (West Antarctica). In this case, a transverse crack in the fast ice stream was detected as early as October 2011 and the massive discharge was expected. A similar event also occurred in 2001.

It is difficult to estimate decadal changes in the ice sheet mass balance from such sporadic events. However, monitoring of the ice sheet from space now makes clear that numerous glaciers and ice streams around Antarctica have speeded up and thinned over the last decade.  Overall, the West Antarctic Ice sheet is losing mass, contrarily to the meteorological expectation.

Two papers, released simultaneously on 12 May 2014, further suggest that the West Antarctic Ice Sheet may have entered a state of irreversible collapse: ice loss leads to more ice loss (Rignot et al. 2014Jouhin et al. 2014). This instability is caused by the fact that the ice discharge of an ice stream scales with the ice thickness at the grounding line. The grounding line is that location where the ice stream is lifted off the ground and becomes afloat. Where the ground is tilted downward toward the interior of land, an instability can occur: as the grounding line moves inland, it sits under a thicker layer of ice which results in a stronger ice flow (Figure 2).


Schematic of the ice sheet/ice shelf in a configuration favourable to unstable behavior. As shown by the dashed vertical lines, if the grounding line were to retreat inland, the thickness at that location would increase.

From satellite measurements (and some assumptions), Rignot et al. 2014 estimated the displacement of the grounding line of four glaciers in the  Amundsen sector between 1992 and 2011. All four showed a retreat, typically a few tens of km, on depressed ground, suggesting that they had passed a threshold and their discharge would keep accelerating. Using a modeling approach, Jouhin et al. 2014 computed the future evolution of the Thwaites Glacier (one of the four above). After tuning their model so that it is consistent with observed melt rates, they found that this glacier was in fact on an unstable trajectory in most cases considered (a range of parameter sensitivity tests). In the most extreme case, the full collapse would only occur at the end of the 21st century, but large ice discharge (and associated sea level rise) would build up well before this.

So, what triggered this irreversible trend ? A change in the properties of the sea water bathing the base of the ice sheets is the most probable culprit. Although very sparse, observations of the temperature and salinity of the water masses in the Amundsen Sea are available during summertime in 1994, 2000, 2007, 2009, 2010, and 2012. The waters which move along the continental shelf are called the Circumpolar Deep water (CDW) and originate from mid-depth in the Antarctic Circumpolar Current. They are relatively warm (a couple of degrees above the freezing point). The CDW, intruding into the shelf cavity, melts the ice shelf from below, influencing its thickness and the location of the grounding line. This ultimately drives the speed of the grounded ice stream inland. Despite a large variability, it appears that the CDW on the Amundsen shelf has warmed by a few tenths of a degree since the 1990s (Jacobs et al. 2012). A small change, but enough to increase the basal melting of the ice shelf by as much as 50%, and the accelerated thinning of the Pine Island Glacier.

The reasons why the temperature (and amount) of the CDW on the shelf has increased over the last decade are unclear. Changes in the Southern Hemisphere atmospheric circulation (and in particular a positive trend of the Southern Annular mode) appear the most likely cause. These changes have been largely attributed to the Ozone Hole. It is interesting to think about possible future evolutions as the Ozone Hole recovers, the associated atmospheric changes vanish and the CDW properties are restored to their 1990s values. Could this be enough to slow down or stop the ice sheet retreat? The above studies suggest it is too late.

Simulating the trajectories of surface debris in the Southern Indian Ocean

Here, I discuss the possible fate of the debris of flight MH370 if indeed it crashed in the Southern Indian Ocean, West of Perth.

To do this, I use a numerical model (MITgcm) to advect particles using observed currents of past years (these currents are estimated from satelite altimetry, AVISO dataset). Satellite altimetry measures the (small) variations of the sea surface height over 10s of kilometers, from which we can compute the surface geostrophic currents.

To simulate the behavior of the debris, I assume that initially (at the time of the crash) the debris are spread over a very small area (500 m wide). These small clusters will be released in two places, to the North (30S) and to the South (32S) of the search area (where the plane is though to have crashed, see big red dots in first figure below). Finally, to test the sensitivity of the results to the state of the ocean, I use currents from March 1992, March 1993,…, and March 2007.

The figures below shows the computed trajectories. Each spaghetti is a cluster of 5 particles (you can’t distinguish the particles on this scale) over a 30-day period. The thick dashed black box represents approximately the search area. To give a sense of the scale, the squares (light dashed lines) in the close up view are about 100×100 km. A video of these float trajectories is available here: http://youtu.be/hInOLnwAbRc

 Float_25days_LargeAreab Float_25days_Zoomb


It is clear that the debris could travel in any direction. They could follow a nearly straight line or go around in circles. In some cases, the debris move very slowly, covering as little as a few 10s of km in 30 days. In other cases, they move by as much as 400 km. These trajectories are the results of mesoscales eddies. These eddies are quasi-circular currents with a diameter of about 50 km. They are the equivalent of cyclones and anti-cyclones in the atmosphere. Particles at the center of an eddy might not move at all. Those at the rim of an eddie could travel relatively fast (0.5 m/s). Particles outside an eddy could move slowly (if far from eddies) or very fast (if caught in between two counter-rotating eddies).

Note that, even though the clusters are released in the middle of the search area, some are able to leave the  search area within 30 days.



If we zoom on a cluster, we can see how the particles within a cluster are pulled apart. In the particular example on the right, the debris are initially well ordered in a 500 m wide square (bottom right insert). By day 30, the debris have been stretched 3 km apart (top left).



There are a few take-home messages:

  • two things happen in these simualtions: 1) the small clusters of particles widen with time and 2) the small clusters travel very long distance,
  • assuming the initial cluster of debris was 500 m wide, it could have grown to 1 to 3  kilometers by now (30 days),
  • the small clusters could travel 100s of kilometer within 25 days, in ANY directions (although it could have travelled as little as of few 10s of km from its initial position),
  • the small cluster could be OUTSIDE of the search area (if indeed the plane had crashed within the search area),
  • each March current gives a different outcome,
  • if a cluster of debris is found, it could have been anywhere in 300 km radius 30 days ago.


This figure shows the averaged size of the clusters and how it evolves with time. The result from the numerical simulation is shown in blue. The clusters are initialized with a size of about 400 m. By now (30 days), the patch of debris may be about 1.5 km wide. The red curve is an exponential with an e-folding timescale of 20 days.




A few caveats are worth mentioning. Here the direct influence of the surface winds on the particles is neglected.  One can imagine that light debris (e.g. a cushion) would be pushed around more efficiently by the winds than by the currents. Wind-driven Ekman current are also neglected. Finally, the satellite altimetry from which the currents are estimated does not capture the smallest scales. Because of the spacing between the satellite tracks, some details (the submesoscale currents) are missing. If anything the above calculations give a lower bound on dispersal  of the debris.