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It turns out that this is a really good reference for our work on the final project.
G. Kukla, T. Karl, M. Riches
D. E. Parker
D. R. Easterling, T.C. Peterson
DJ. Smith
K. McGuffie, A. Henderson-Sellers
E. Kaas, P. Frich
Patrick J. Michaels, Paul C. Knappenberger and David A. Gay
For me, it's just puzzles, and a chance to play with mathematical weapons.
We'll base those simulations on what the climate has looked like in Wood County in the past. So there are two data sets, and two graphics which I would like you to reproduce based on those data sets. These will help us to create a weather simulator which will resemble the weather of Wood County.
I'm going to make it a little easier on you than I made it on me: I had to digitize some of the data. But I'll just give it to you!
We might hope that this would give us a good approximation to the mean across the span of a year.
You might get something like this:
Here's all the data: use regression -- linear or non-linear -- to find that function. Either will work!
This is kind of an odd regression problem, because, as you can see, we don't do a very good job of fitting the data! But we're trying to construct an average of all of this data -- not fit any particular data point.
We can fit pretty nice sine functions to those three data sets too, and here they are:
Here's all the data: use regression to find those three function.
The mean curves are the blue in the middle. The exceptional thing is that the two mean curves (in blue, one solid, one dashed) are almost exactly on top of each other -- but one was created using 1464=4*366 data points (all of Fletcher's extreme temperature from his tables), whereas the other was created from 12 pieces of data (the climate averages). The two red curves are the fits to the Mean(Max) and the Mean(Min) climate variables (again, 12 pieces of data each).
In my mind I imagine the trajectory of weather getting off "the climate track" (which is represented by the blue -- mean -- and red -- max and min -- curves). Imagine a normal distribution of potential temperatures, whose mean is supposed to be along the blue track, but it wanders; and, as it does, its maximum may go way up there (as will its maxmin); or it could wander low, and its minimum will go way down there (as will its minmax).
That's the story, featured in version 1.0, of our paper.
So the next question is this: how is the weather wandering?
We have the rest of the semester to figure that out....
Feel free to Zoom with questions, or email them. Some of you are doing this already; others don't seem to feel the need; some of you need to ask more questions! Please do.
Some good links that I might recommend (a few of which we'll focus on):
In particular, we will implement The SIR Model for Spread of Disease - The Differential Equation Model in InsightMaker.
(An excellent introduction to SIR models, from both the infectious disease and mathematical sides)
Questions:
This on-line estimator (i.e., a model!) allows one to estimate deaths, as well as death by age-category.