Gain a Visual For Climate Issues-An Article from Kraket
If you are a data scientist who is looking to contribute to climate issues, this piece is for you. The most valuable asset a data scientist can bring to the table is interactive visualization. You cannot fight what you cannot see so naturally to see the relationship between CO_2 and temperature is the 1st step in dealing with climate issues. And “interactive” is not just a cool adjective, it’s basically predictive analysis via model (unless you live under a rock, it’s really trendy to fit a model with computer). So what kind of visual can we gain? Let’s look at what Prof. Hande Karabiyik has to say in an article published with Kraket, a study association for Econometrics and Operational Research at the VU, on February 17th 2020.
ECS
In vacuum, earth will be 1c warmer if CO_2 doubles. Ok, useless-talk, we all know most things don’t operate in vacuum, what’s throwing in the wrench? It’s Climate feedbacks such as water vapour, cloud covers, ice and snow cover which changes the surface radiation that can either amplify or decrease the CO_2 effects causing a variation in temperature between 1.5c-4.5c. For example, a reduce in temperature due to radiation is call “aerosol cooling’’. But don’t worry, the author got a model for us already that deals with this issue. This model can accurately estimates the amount of increase in the global temperatures when CO_2 concentration doubles without the interference from climate feedbacks. This measurement is also known as earth’s climate sensitivity (ECS). Let’s look at how this ECS is estimated.
So what is γ3, β1 and γ1 and where are they even from? They are coefficients from other functions. Let’s look at the function that yields γ1 and γ3 first.
Ok, we know what the natural log of CO_2 concentration at times t means, but what is T_bar, R_bar, subscript “t”, and λt? Let’s look at T_bar and R_bar.
T_bar and R_bar is the average global temperature and radiation (effects of climate feedbacks) respectively. If I use the word global, does that mean we also have local temperature and radiation? Yes, and the answer to that will also answer 2 more question: what is λ, and how we come up with β1.
λ is the time specific effects, such as 5am will be cooler than 12pm. φ is just a coefficient like β and it’s different at each i. This is also the function where we got β1. But 1 answer always leads to many more questions: what is subscript “i”/”t”, α, and u.
Since most of the climate variables are observed and recorded in different locations/stations, subscript “i” and “t” for both T and R represents location and time respectively. α represents location specific effects, such as humidity, wind, and temperature. u is an error term. In case you forgot what an error term is, it’s the difference between population regression line and sample regression line for reasons that’s unknown to us. This error term has left many rooms to tweak to improve the accuracy of the model. Does this entail our regression line is bad? Not necessary because the error term, in this context, is considering factors that are highly volatile and random like neighboring cities temperature and movement of gas particles, which is very chaotic. Let’s put everything together.
The flow is this: with the averages of global temperature and radiation you replace the λ variable with the λ function. Since temperature, radiation, and CO_2 data are recorded, we can easily train this model to fit β1, γ1, and γ3 that we will need to calculate ECS.
Congratulation, you just learned how to find ECS with zero understanding of how that works. Before we conclude, let’s look at 2 things: “t+1” and the ECS function.
Since the ECS is a models for time series data, the error term has to be 1 period ahead, because we have to measure the difference between the predicted and the actual (1 period ahead) data.
So intuitively what exactly is happening here? The following will be my own logical conclusion and research, so take it with a grain of salt.
ECS utilizes fraction, and the whole point of a fraction is to see that there is x amount of numerator in y mount of denominator. It’s also important to remember that we are not using the data on CO_2 density or temperatures directly. We are using the coefficients of those data, in other words we are using the sensitivity of those data. For example, a very small γ3 will mean we can tolerate a lot of CO_2, and a large amount of γ3 entails a tiny changes of CO_2 will cause huge increase in the function, and the same goes with temperature. What does it mean when we throw them in side fraction? Let’s go through a few scenarios.
When γ3 is bigger than the denominator, ECS will increase, that means CO_2 is more sensitive than temp (β1&γ1). As β1 and γ1 decrease, ECS will converge to CO_2 sensitivity, since the denominator is 1-β1-γ1. But as β1 and γ1 increase there are 2 possibilities: If the increase does not exceed 1, then ECS will get larger, otherwise, ECS will turn negative. Since I never dealt with climate data, I cannot rule out the possibility of β1 or γ1 not exceeding 1.
Conclusion
After reading all this you might be scratching your head thinking what’s the point of all this? I hope you will leave with 3 things. 1, besides just getting fitted, coefficients have other utilities. 2, this utility is as useful and important as making predictions. 3, the result of taking full advantage of coefficients lets us to extract more information out of the existing data.
Now that you gain some familiarity with climate related model building logic, hopefully similar model building literature wouldn’t be so off putting. And maybe one day we can start building better models and extract more useful information to help with climate issues.
https://kraket.genkgoweb.com/en/sector/article/2020-02-17-econometrics-of-climate-change
