*In ERA5

Written ~2019. Published 01/27/23

Growing up near the coast in South-West England I developed a keen interest in the Ocean.  I have been lucky enough to pursue this passion through academic endeavors. When I was younger I enjoyed surfing, kayaking and sailing with the Sea Scouts. I took a specific interest in Ocean waves due their beauty and complexity. Extreme waves - also know as freak waves or rouge waves - are a subset of Ocean waves where folk lore meets complex, nonlinear physics. The earliest record of extreme waves comes from the attempted invasion of Japan  by Kublai Khan in the 13th century (image below). The term divine wind comes from two typhoons faced by the Mongol fleet. Extreme waves also got attention recently with the sinking of the SS El Faro (Fedele et al, 2017).

The math and physics behind extreme waves is fascinating and many scholars devote their life to understanding it. Here's a paper by Peter Jansen who discusses the nonlinear Schrödinger equation and nonlinear four-wave interactions to explain extreme waves... It's fair to say it's not for the faint hearted. It reminds me of a quote by Richard Feynman "I think I can safely say that nobody understands quantum mechanics".

Recently ECMWF (European Center of Medium-range Weather Forecasting) released their fifth generation re-analysis: ERA5. A re-analysis is a tool to provide the best estimate of past weather. It uses a modern weather forecasting model and constrains it with past weather observations. The full documentation can be found here but it's fairly technical so I point the reader to a summary page.

The data can be freely obtained here. The website is useful for finding the variables you are interested in. Once you know which variables you want, download them using the Climate Data Store API developed by ECMWF. This can easily be used with python and there are instructions on how to setup it up here.

ERA5 will eventually provide atmospheric and ocean wave variables at hourly frequency with high spatial resolution going back to 1950. It is estimated the dataset will be 9 Petabytes! Now that is BIG data.

A new variable provided with ERA5 - which was not provided by its predecessor, ERA-Interim - is the Maximum individual wave height (Hmax). ERA5 uses a phase-averaging wave model: the Wave Assimilation Model. Phase-averaging wave models cannot estimate the height of individual waves but instead provide statistics of the sea-state. The maximum individual wave height is deduced by investigating the nonlinearity of surface elevation statistics as well narrow banding of wave energy in frequency and direction. The parameter is derived fully in Bidlot et al (2016) (equation 42) and a snapshot shown below:

Finding the biggest wave in ERA5

To do this I undertook the following steps:

• I downloaded Hmax data as yearly files to an external hard drive. Each file is ~5 Gigabytes and there are 40 years (1979-2018), meaning the entire Hmax dataset is 0.2 Terabytes. I download three files at a time and each one took a couple of hours.

• I sequentially read in the files using Xarray with the Cfgrib engine and found the maximum Hmax for each year.

• Lastly, I found the maximum Hmax out of all the years:

The largest wave in the ERA5 dataset is: 38.3 m and occurred at 47.5 N, 40.7 W on January 4th 2014 at 10 pm UTC.

38.3m! That is the size of a 12 story building! If you have ever stood on the edge of a 10 m diving platform imagine multiplying that by four!

The location is 500 nm to the east of the Island of Newfound.

My first question following this is: is this spurious?

Note: Hmax is a relatively 'new' parameter and is difficult to validate. However we can take a look at some past observed  extreme waves:

• A British oceanographic research vessel near Rockall, west of Scotland experienced waves of 29 m on February 8th 2000. Holiday et al (2006)

• The Draupner wave was ~26 m striking the Draupner offshore oil and gas platform in the North Sea on January 1st 1995. Cavelari et al (2016)

• Satellite Altimeters - which measure the shape of the ocean's surface from space - measured average wave heights (Hs) of 18 m associated with a storm in the North Atlantic on February 14th 2011 (Hanafin et al, 2012) Rouge waves are usually characterized as twice the height of the average wave height so rouge waves (if occurring) would be ~36 m here.

• The Andrea wave was ~15 m which occurred in the North Sea on November 9th 2007 and was noted for how large it was compared to the surrounding waves. Donelan and Magnusson (2017)

It is hard to say if the event is spurious from these examples. I'm sure there is a paper waiting for someone to answer this question fully by doing a complete assessment of ERA5 waves compared to observations to see if the model has any biases.

However, my second question can help answer my first:

What caused this big wave?

Waves are caused by the wind. To understand the waves one has to first understand the wind.

My go to place for a quick look at what the wind conditions were like are the synoptic weather charts produced by the UK Met Office and archived here.

The extreme wave event occurred in the bent-back front of an extratropical cyclone with a mean sea level pressure (mslp) of 934 hPa. I have previously shown that this type of meteorological setup gives rise to extreme waves in the North Atlantic (Bell et al, 2017). This is storm Christina (see image below) named by the The Free University of Berlin*. The UK Met Office didn't start naming extratropical cyclones until 2015.

ERA5 has the mslp of this storm at 936 hPa. Not bad!

To investigate this event further let's look at a time series of the extreme wave event:

The sea state grew quickly going from 10 m Hmax at 9 am to 39 m at 10 pm. That is 2.6 m every hour! I'd be interested to find other events which grew at this rate but that's for another rainy day.

Let's also take a look at time series of the mslp and 10 m wind speed at the same location:

The maximum wave height occurred at the same time as the lowest mslp. The 10 m wind speed also stayed at 30 m / s for a few hours.

Let's zoom out and take a broader look at the evolution of the event:

You can see the event ramps up quickly (around 6 pm) and the event occurs to the south of the low pressure system.

It will be beneficial to also take a look at what the spatial pattern of the wind was like:

You can see there is a large wind field with very strong winds. This type of situation is conducive for extreme waves given the strength of the wind and the fetch (the distance it blows over).

Conclusion

The extreme wave event is feasible given the synoptic situation. I leave it to the academics to give me more insight on this event.

Things I learn in this blog:

• Querying ECMWF data

• Geoviews

• Demonstrating my (small PR) in xvelocity developed by Ben Bovy which got added to ipyleaflet as a velocity layer by David Brochard (https://github.com/jupyter-widgets/ipyleaflet/pull/178)