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Jesterface23

CME Math

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Here is the math I have on CME arrival times. The one thing that all of the full halo CMEs have in common is this, 'y=(1/(40x+28500))(x+1765)^2-100' (or at least really really close). First, you need to get three times, 1st the time when the CME exits the sun in a SDO AIA 131 image, 2nd is the time of when the CME edge first hits the outer circle in the LASCO C3 image, and the 3rd from that point where the CME first hit the outer edge of the circle in the C3 image, go around the outer circle 180 degrees and get the time of when the CME hits that point. Then the math, get the difference of time #2 and #3 and write that down as time #4, get the time that is between time #2 and #3 and write that down as time #5, then get the difference of time #1 and time #5 and turn that into all minutes and write it down as number #6. Next, turn time #4 into minutes and put that number as x into the equation y=(1/(40x+28500))(x+1765)^2-100 and you now have #7. Now multiply #7 by #6 and you have the estimated travel time in minutes, just change that to days hours and minutes and add it to time #1. 

The issues are mainly if the image isn't clear like CME #1 a week ago, or there is a big chunk or missing images, then you are left to guessing the time of when it gets to the edge of the C3 circle edge and the time will likely be way off. Currently what I have is for CMEs where you need to guess one of either time #2 or #3 is likely +-3 hours off the arrival time and perfectly clear CMEs are at +-1.5 hours off the arrival time.

For the equation, there is a lack of data before x=80 and after x=580, so I just went with the pattern and guessed and will need to modify the equation once there are some clear events to get that data from. The next thing I want to work on is get the arrival time from inside of the C3 image circle and not need to get times #2 and #3 from faint CMEs all the way at the edge of the C3 circle.

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I assume your math if flawless and invite you to predict the next CME impact. :)

The problem is however, between the outer edge of LASCO C3 and ACE at L1... how much will the CME slow down? Still a lot of variables we can't know. It's not easy. :)

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Well, currently the equation was made off of the average of 18 data points, so it should be fairly close like with the arrival time like with CME #2 a week ago at 1 hour and 20 minutes off.

You did give me an idea though, I need to go back and through those CMEs again and write down any other possible info around the event then see if there are any other patterns with it. 

Edit: Started work on version 3. One thing I completely forgot about in making this version and the first is that the earth is a moving target, then I'll need to see if there is a pattern in the density once I get all of the data.

Edited by Jesterface23

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Looks like a quick one, it looks fairly close to the last CMEs direction, so I'm not making any estimated changes. Arrival time looks like somewhere around December 30th at 3:36z and it looks like the possible error time is just over +-3 hours.

Then an update on version 3, I believe I have the math done to get the CME direction, now I just need to figure out how to make a chart off of that to get the CME speed, then make another chart for impact times at the earths orbit.

Edited by Jesterface23

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It would be GMT or UTC+-00:00. And one of the points I am going off of is in the area of the very faint halo in C3 near the top side to the left side, if that actually does count as a halo.

 

Edit: I am going to check back through the C3 images and see if there were any big changes recently.

Another Edit: Well, either it is fast or I am looking at something that looks like the halo but isn't the halo. Guess time will tell lol.

Edited by Jesterface23

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Jesterface23 might be onto something. NOAA goes for 11:00 UTC tomorrow on their ENLIL model. Will be interesting to see who will be closest with their predictions.

Stephane: that model shows the polarity of the IMF. That has nothing to do with the Bz.

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Welp, there goes my time. But now going off of NOAA's ENLIL model, if it did add around 5 hours from the CME plowing through the denser plasma, it would be closer to their time at around 8:36z +-3 hours.

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I just wonder what kind of speed you used for your calculations. It seems NOAA used a similar speed as you did as your and NOAA's arrival time were pretty similar. I am curious to what speed you got with your methods.

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What I was going off of is one point hits the edge of the image at around 16:30, then a very faint halo hits the other end at around 18:06. Now looking back the real 2nd point may have been somewhere around 3:42 when the halo was more clear instead of 18:06. So off of that it might be a far side hit instead of a near direct hit. A new arrival time could be somewhere around the 31st mid day UTC but is very unclear from lack of data.

Edited by Jesterface23

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Just out of interest Jesterface have you considered that the CHS from CH707 is it may be pushing the CME along in your speed calculations? I saw no one had mentioned to I thought i'd ask. 

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I think I found one of the big issues. There are no big changes to the C3 camera, there is just the change to keep the field of view 32 solar radii, so that is ruled out for there being a big difference between one line of data points over a second line of data points. What looks to be the thing that is making the big difference is the top line of data points are a direct hit of a CME and the line below is a side hit. 
So I guess now I need to go back, get more data, and find out more about the lines in the CME lol

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First real test run of the new second equation. The second point in C3 seems to fall somewhere near the data gap, but I'm going with an Earth arrival time at around 9:30UTC on the 15th. Not sure of the +/- on it, I just want to see how far off it ends up.

Edited by Jesterface23
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It should be pretty obvious when the CME arrives. The EPAM protons should spike and you will likely see a distinct increase in the solar wind speed and the IMF Bt.

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That latest crazy sunspot region pushed me back into space weather a bit more. I ended up redoing the formula below to try and make it work at any angle or distance (not perfect yet) and I am hoping someone might be able to answer a question. In the formula, x is difference in hours from when the CME first hits the 30 solar radii edge of the C3 imagery and the second point when the back of the CME hits the edge. The m is the multiplier and this is where things get tricky. A multiplier 1 is most common before the first trough in the formula and 0 is most common after the first trough. But that CME on the 10th made it into a rare category with a multiplier of 2. I haven't had much time to do more research, but I've only had 3 other data points in that multiplier. This is where I would have my question, would anyone possibly know what might be the cause of those multiplier and how to spot it? I thought it might have been a direct hit vs side hit, but going back though some CMEs I don't think that adds up. Thanks

y = cos(120x/213) - (((120x/213)/4.9358)^(pi/2)) + (((sqrt(pi/2)^m)*0.68*213)/30) + (pi/2)

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I have around 100 useable CMEs with clear enough C2 and C3 imagery archived now, so hopefully that will be enough to finish up this project haha. I have another guess on that might be causing those 3 different multipliers, and there might actually be a 4th lower multiplier. Guess I'll find out once I get the time to go through everything.

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