Near the center of Jutland, Denmark, lies a city called Herning. One of the main attractions is the Elia sculpture, by Ingvar Cronhammar. According to its wikipedia:
"It is a large, spherical dome with four columns reaching 32 meters (105 ft). The dome, itself, has a diameter of 60 meters (200 ft). A large tube located in the center of the sculpture randomly blasts flames 8 meters (26 ft) into the air for about 25 seconds. These random bursts can occur anytime in periods of about two months and will not occur if it is too windy or if people are too close. The work was inaugurated in September 2001 and cost 23 million Danish krone."
Above, I marked the interesting bits. Random, but then, not quite. Or is it?
Luckily the date and time of all 357 (at the time of writing this, 25-08-2020) eruptions are freely available. I find it interesting to note that the first recorded eruptions are from 2005, even though the sculpture was inaugurated in 2001. Someone might have forgotten to fill the gastanks? Who knows.
Overview of the data
The 357 times fire was released can be seen in the above plot. What is immediately obvious is that it looks rather linear in time and not at all random, as was suggested. We can also note that there are flat areas, perhaps during times of maintenance?
In the following, we will try looking at some histograms of the data. Of immediate interest could be
- Time of day
- Day of week
- Month of year
Time of day
It seems to be that the hours around 10 to 15 has the overall lowest probability of an eruption occuring. This could be explained by this part from the wiki page
"Flames..will not occur if people are too close"
These hours could be the period where the sculpture is most heavily visited and thus no eruption.
Day of week
Looking at the above plot, we can see that the lowest overall probability is in the weekend, Saturday and Sunday. This perhaps reaffirms the thought, the these are the days with most visitors, and thus, fewer eruptions.
What is more interesting is the fact that Friday seems to be significantly more likely than any other day.
I do not really have a good explanation for this but perhaps the data size is too small to draw direct conclusions.
Month of year
Looking at this it seems as if all months are just as likely. If the dataset had been larger, it is possible that a correlation in the average wind speed per month would reflect more eruptions in low wind speed months.
Time since last eruption
The wiki article mentions
"These random bursts can occur anytime in periods of about two months"
We can check this claim by plotting the time difference between eruptions.
As can be seen, the distribution maximum lies around 10 days with maximum values of about 60 days (the few values seen around 120 days are considered to be outliers, possibly stemming from maintenance as mentioned earlier). So it seems like the wiki article holds true.
If we take the cumulative sum of the above, we get the aggregated probability of seeing an eruption as a function of days since last eruption.
Thus, to get a 75% probability of an eruption, it is advised to wait ~17 days since last eruption.
Maximum wind speed
The second part of the wiki states
"..bursts will not occur if it is too windy"
To investigate that I used the coordinates of the sculpture and got historical wind speed data for the eruptions for which it was available. The closest weather station is about 20 km from the sculpture, in a town called Isenvad, but these data will have to do.
Of the 357 eruptions, valid wind speed data was available for 285 (~80%). Binning these valid datapoints we see a clear pattern.
Seems like the max allowed wind speed is around 8 m/s.
Elia is a fire spewing sculpture that has had 357 eruptions since its inauguration (at the time of writing this, 25-08-2020). Each eruption takes ~25 seconds, according to the wiki page. The sculpture has eruption data for 15 years. The cost of the sculpture is 23 m dkk (~3.1 m euro).
That means that each eruption is "worth" ~64'000 dkk (~8700 euro).
So bear that in mind when you camp near (but not too near!) the sculpture approx. 10 days from the last eruption, with wind speeds lower than approx. 8 m/s and preferably on a Friday.