How High was the Tsunami?

One of the most important questions for looking back onto the Fukushima Daiichi disaster is how high the tsunami was, and how far that is from what was taken into account when designing the plant (the design basis). Unfortunately, the answers do not come very easy, I will try to address the physical attributes of these plants here. The design basis is...

Firstly, many have said that the Fukushima Daiichi tsunami design basis was 5.7 m (height of the sea wall actually), I believe this is wrong to say, although not necessarily wrong. I wish I still had this pdf, but either NEI or ANS specifically said at the end of one of the fact sheets or Q&A papers that they didn't have information specifically giving the design basis tsunami. Had they not heard the 5.7 m number? Hardly. They were well aware of the number, but there was not a solid source for it. You can notice, searching around for design basis numbers for the Fukushima plant, that the earthquake values are given often and clearly. Not so for the tsunami. While I expect the translations have been contorted and pass on like a game of telephone, Tepco themselves use words that indicate 5.7 m as being roughly the "previously considered height for a tsunami", but I do not believe, or at least can not say for sure, this translates into a design basis. As you will see, however, the act of measuring a tsunami itself is not all that clear-cut of a process, and for the technical rigor of licensing of a plant, I would expect a long answer to this question, and not a short one.

The Japanese National Geophysical Data Center reported measurements for the Tsunami heights measured at locations all along the coast. Different values will be reported by different measuring methods. Sometimes the "run-up" height is reported and other times just a height is measured before the run-up, the inundation height. A slightly objective value can be taken from sea-based measurement mooring platforms which, to the extent of my understanding, experience the tsunami height without the momentum converted into height. And example of this is the observation station used on the Wikipedia page for the disaster. I reproduce this here, and add in the heights as would be reported by the nuclear plants in terms of run-up height.

Tsunami Heights and Where I Think the Nuclear Plants Fit In

There is a lot to be said from this. The epicenter is marked on the graph, and predictably, the highest waves were seen around that latitude. I made a gray box to indicate the latitudes that no data was available for due to the evacuation order made regarding Fukushima Daiichi. This makes things a little bit harder because we categorically seem to not have diverse measurements for the wave height in that area. There could be some geometry factors that made it higher there, and it's difficult to tell. Either way, the run-up height looks strangely high compared to the neighbors for the Fukushima plants. The wave height, which has another basis for measurement (more later), seems to be in line with the region's other measurements. The Onagawa plant, however, was right in the hardest-hit regions but suffered a wave no higher than the other plants, which I find to be the most interesting data to come from this. Of course, the height of the plants themselves are now the determining factor, which is history.

Exactly what happened at the site needs to be covered. Let's start with this fact, when the quake occurred, Japan sunk up to a meter (this isn't surprising when you consider it moved around 2 meters horizontally and accelerated at up to 2 g). I was happy to stumble upon a specific topographic map of this. Here are my interpreted values and the image.

Onagawa NPP, by way of Ishimaki: 84 cm
Fukushima NPPs, by way of Minamisoma: 29 cm

Color Map of Elevation Drop of Japan

Early reports (including Tohoku Power), it would appear just estimated a drop of 1 m, but this was only for the most extreme case, and my concern about extrapolating this number to places like Fukushima turned out to be founded. Now, in order to understand what on earth a measurement means, you need to understand what the measurement was taken from, and all measurements are, indeed, relative. Most measurements of "run-up" are from the observed height on the building that the water reached. If you know what elevation grade is for the building, then you know the elevation the wave reached. It appears to be the case that this is where all the run-up measurements come from and is how the height is usually reported for the nuclear plants.

So, how much of the plant sites were flooded? Daiichi had the entire block of reactors 1-4 flooded to a maximum of 4 to 5 meters, Daini had the reactor area partially flooded less than 1 m and Onagawa didn't have the water reach the reactor grounds.

In order, Fukushima Daiichi 4-5 m flooding, Fukushima Daini 0-1 m, and Onagawa 0 m

Sources for this and most other information:

• Fukushima Daiichi - Tepco
• Fukushima Daini - Tepco
• Onagawa NPP - Tohoku Power
  

I want to add that the units 5 and 6 of the Fukushima Daiichi site should probably look more like the Fukushima Daini plant. It seems that they were similarly flooded up to 1 meter. The diagram makes a distinction between water that just ran over the area (for Daini) and water that flooded the area. I understand for some areas why, and doubt the utility of it for other areas.

As for some other values, I'll offer this table here. I wanted to make an infographic for it, but I'll just not.

Tsunami and Related Values for the Nuclear Plants (all meters)

Values:

• Sea wall - Height of barrier in front of the intake structures and in the water. This is often given as the design basis. I do not know why I can't find the number reported for the Onagwa NPP, but I tried.
  
• Wave height - Height of wave defined by total elevation reached in the intake area before the main slope at the Daini plant. As best I can tell, this would be the "inundation" height, although I have significant uncertainty about that. There is no value for Daiichi because there were no structures standing in this area to deduce the height from.
• Grade - Elevation of ground as it meets the intake structures. This is the elevation that many buildings and intake pumps are built on, but lies below the main slope up to the reactors themselves
• Wave run-up - Maximum elevation that the flooding reached on the plant site, this is after the ground level is added to the height read on the side of the buildings. Note this didn't occur at the reactor building at Daini.
  
• RB grade - Grade around the reactor buildings. This is the most key variable in looking at why one plant was flooded and another was not.
• Shift - All of these numbers are "pre-quake" numbers. Since Japan itself sunk down by these values, all the previous values should uniformly have this number subtracted from them.
  

It's actually amazing just how close the height of the tsunami was at each of these 3 afflicted plants. However, the maximum elevation that the tsunami reached was significantly different from what flooded the plant at Daini, which is not true for Daiichi. Looking at the maximum elevation reached at each site:

Daiichi: 15 - 10 = 5 meters
Daini: 12.4 - 12 = 0.4 meters

The difference between these two subtractions is the difference between surviving this disaster with some damage and a INES 7 scale historic nuclear disaster. Amazingly, this can't even be told by just understanding the heights of the waves. It can't be explained by the difference in the elevations in the plants. It certainly can't be explained by the difference in the seawall height (favored Daiichi). It can't be explained by proximity to the epicenter.

So how did Daiichi find itself under 5 m of water while the others didn't? The best attempt at explanation I can manage is that the site layout left more flow paths open to the reactor building area at Daiichi. Or maybe it just came in with more force, after all, the intake are structures did suffer much greater damage than Daini.

It seems we are left with more questions than what we started with, and this is just the first-cause discussion. It is probably the case the the story of this accident is far from settled.