Sunspotting
For thousands of years humans have had at least some significant portion of our collective attention pointed towards the large, bright, and very hot disk that would traverse the sky from one side to the other. Indeed, many religions, both old and modern, hold the Sun as an object of worship. The first recorded observations of the sun date back to China, circa 2300 BC. These were mostly just observations for tracking seasons, until about a thousand years later when the Egyptians invented the Sun Dial, allowing us to utilize the sun for keeping track of time in a more precise manner throughout each day. For millennia after this, not much changed. Records were kept of its movement through the sky, its eclipses and other phenomena as our limited ability to observe allowed, but it was not until 1610 when, using a telescope, the first detailed observations of sunspots were recorded by Galileo.
It was centuries later, around the middle of the 19th century, that scientists began to recognize patterns in how the number of sunspots changed on the sun, and only in the last 100 years or so that we’ve really started to observe exactly how changes in the solar weather can have environmental effects here on Earth.
Today, most people are aware that what happens on the sun has an effect to at least some degree on what happens here on Earth. It’s fairly well known that Aurora Borealis, the Northern Lights, are the result of solar winds passing over our Magnetic Field. Movies and other stories in popular culture have often referenced the potential dangers of solar flares, and more recently, you may have even seen articles recently discussing about how our Sun is entering into a “Solar Minimum”, a period in the 11 year solar cycle where solar activity is at its lowest, and there are few if any sun spots on the Sun. We can actually see this in our data:
The relationship between sunspot activity in particular and electromagnetic interference here on earth is a well established and documented phenomena, if not as well known publicly. If you’ve ever had days where wireless communications may not have worked as well, cellular calls dropped more often, etc; this may have been due to a day where solar activity was high, and conditions allowed for increased interference. We will be looking at whether or not we can predict the number of sunspots on the sun at any given time, based on fluctuations in the electromagnetic spectrum here on Earth.
To accomplish this, I needed to join two different datasets; One containing daily sun spot totals, and one containing radio fluctuations in the relevant frequencies. I was able to find datasets for both of these on Kaggle, and links to the sets are provided below. After cleaning the datasets and normalizing dates to join them on, to ensure that we maintain the correct radio telescope readings with the correct number of sunspots, we are left with the following dataset containing both:
A first glance at this data set might be confusing with so many columns with names that might not make any sense to someone not trained in Radio Frequency Theory. That’s OK, all we really need to take away from this is that these different features represent different RF frequencies, and that we will be comparing power fluctuations at these frequencies to the number of sunspots, to see if we can determine the number of sunspots currently active by monitoring these frequencies.
In order to validate and test our data, we split the data into Training, Validation, and Testing sets.
Every good prediction requires a good model, and so to make sure that we are using a model that will best predict our sunspots based on these fluctuations, I tried two different models: Linear Regression, and Random Forests. Of course, to make sure that our model is actually predicting well, we need to establish a good baseline. Since this is a regression problem, all of our data is numeric in nature, we will look at Mean Absolute Error. For our baseline prediction, we calculated MAE, assuming we predicted the average number of sunspots for each prediction. This gives us an MAE of 67.69.
So with our baseline in hand, let’s start looking at models!
Linear Regression
Being a regression problem, linear regression is definitely our first go to. After fitting our data we ran our test metrics and got the following results:
- Training Accuracy: 0.9276294474130982
- Validation Accuracy: 0.9350867465372686
So for a first run, and no hyper-parameter tuning, these are not bad results. Our validation accuracy is actually slightly higher than our Training accuracy, so it doesn’t appear we have any issues with over-fitting. But what does this number mean exactly? When we test with a linear regression model, the scoring metric we get is our coefficient of determination, or our R² score. In other words, this is telling us how well our model replicates our observations that we put into it. But our baseline was Mean Absolute Error. When we calculate our MAE for our trained model, we get 15.78. That’s not bad, considering a baseline of almost 70.
Random Forests
However, in data science, “not bad” usually isn’t good enough, so I also fitted a Random Forest Regressor model to our data and got the following scoring metrics:
- Training Accuracy: 0.9954101921440627
- Validation Accuracy: 0.9707435623549717
Now these are some nice numbers! It looks like there might be a tad amount of over-fitting with our training accuracy being so close to 1, however with a validation accuracy (R² score) of .97, any over-fitting is minimal. Let’s look at our scores from our testing dataset and our MAE:
- Testing Accuracy: 0.9710094368330254
- Mean Absolute Error: 7.61
So this looks pretty good. We get an R² score just above 0.97 and our MAE is quite low, even compared to our initial Linear Regression model. Now that we’ve got a model with our testing metrics looking pretty good, let’s drive into the model and look at which features are giving us such good results:
Unexpectedly, it looks as if the vast majority of our importance is distributed across a few features, with the remaining small amount of importance distributed across all the other features. So what are these features?
The top two features are ‘f10.7’ and ‘f10.7_c’. Yea don’t worry, I have 2 decades of experience in wireless technology and even I was not familiar with these terms at first. f10.7 is the frequency name, specifically, the frequency where the wavelength is 10.7 centimeters in length. So what f10.7 and f10.7_c are is the power measurements at 2800 MHZ across two different phases, or axis.
The plot above gives us the number of sunspots over a 70 year period and is colored by the amount of flux read at the f10.7 frequency. We can see that as the number of sunspots rise, so does the reading on that particular frequency. As previously stated, there is a well known and documented relationship between this frequency and solar activity. f10.7 is actually a commonly used index for monitoring solar activity, and after this exploration into predicting sun spots, I think it’s quite evident why! We can see similar relationships with solar activity and other bands, but the fluctuations are not as large as they are at the f10.70 band, and this is probably why we don’t see those features having as high an importance in our analysis.
In the graph above we see that readings in the f15 band go up to around 300, and up to around 200 for the f30 band.
Electromagnetic fluctuations within our own atmosphere can be highly dependent on how active the sun is, though this dependence varies across different frequencies. The relationship between fluctuations within the electromagnetic spectrum and the number of active sunspots is quite clear from the above visualizations. Being able to predict solar activity via radio wave can be highly advantageous for the future design of long term spacecraft as they can, with a high degree of accuracy, determine the number of active sunspots on the sun without using visual detection technology. This allows simple RF based sensors to be utilized for determining current activity levels, assuming such readings would be useful, without needing additional expensive, and likely heavy technology on the vehicle.
How useful this information might be is something that might be up for debate, as the data shows, the activity may fluctuate from day to day to some degree, but largely follows a much larger and longer pattern. An 11 year cycle actually, so we should not expect massive changes in sunspot activity from one day to the next. But if there were to be massive changes on a day to day basis for whatever reason, we would be able to detect them through reading fluctuations in the electromagnetic spectrum here on earth without ever turning an eye to the sun.
Data Sources:
Sunspots: Kaggle Sunspots
Radio Flux: Kaggle Radio Flux
Project Repo: GitHub
Originally published at https://jeremyspradlin.github.io.
