Calculating When Highstorms Occur

[+hwiles]

Warning!  Meaningless Math Jargon Follows.  Request:  I earned a math-minor but it's been a while since I stepped foot in a math class; if something looks screwy in my logic or word choices, do speak up.

 

So, disclaimer: I'm assuming stormwardens estimate when highstorms will occur by running a summation on a set of linearly independent wave functions, using the day of the year, or possibly the hour of the year, as the common independent variable.  We know from numerous in-book references that the highstorms are almost, but not quite, mathematically predictable; ie: stormwardens' estimates are usually pretty good, but are sometimes off by, IIRC, as much as half a day (10 hrs).  We also know that the weeping, as well as the highstorm that occurs in the middle of every other weeping, are particularly regular in their occurrence (though I don't recall anyone ever saying they occurred at exactly the same time for each two year cycle, meaning the length of each year could vary a little.)

It sounds to me like the stormwardens (or really...Sanderson) literally fit a combination of sine-waves together to mark the days when highstorms start at the Origin, then use the average speed a storm travels across the continent to predict when the storm will hit their location (my guess would be 10 different waves, though that's purely speculation).  This would be complicated and mathematically intense for the stormwardens to accomplish, but totally feasible with enough data and free-time.  The caveat of course would be that they may need an infinite number of data points (and time) to perfectly reconstruct the wave function that describes the cycle of highstorms; however, they could probably fit the data fairly well with just a handful of functions.

Kaladin's father makes a hobby of predicting highstorms and is able to guess the right day ~80% of the time.  This tells us that solving for when a highstorm will occur is probably not trivially easy to do by hand, otherwise it'd be weird that he, a reasonably well-educated man, did it recreationally and that people were paid to do it.  I'm guessing then that they either use a Taylor Expansion, or large sine-table (which would be easier), to approximate values for sine, then use multiplication and addition to solve the equation, followed by mapping the solutions onto the Rosharan calendar; a little tedious in my opinion, but I'm also a resident of the age of computers.  Those who are really dedicated would also probably spend time trying to identify combinations of wave functions to better fit their real-life observed data, as well as correction coefficients for each function.  Ultimately, I think the equation they would start off with would look something like this:

0 = A*sin(a*x + B) + C*sin(c*x + D) + E*sin(e*x + F) + ... + N*sin(n*x + M) + K ; I'd start off by guessing K = 0 for simplicity.

where x is a day, or possibly hour, when a highstorm will pass through (or be created at) the Origin.  Interestingly, though not coincidentally, if plotted out, this function would probably look fairly similar to words written in the Alethi script.

So my question to the community is this:  Has anyone ever gone through TWoK and WoR and determined the dates when highstorms reached specific locations, and does anyone know how fast a highstorm travels across the continent?  If so, can you point me to where to find this information so I don't waste a whole bunch of time trying to recreate it? 

 

Any thoughts, opinions, or additions?

[The One Who Connects]

 

Quote

 

North Wall Coda

Windowsill region

“   1173090605 1173090801 1173090901 1173091001 1173091004
   1173100105 1173100205 1173100401 1173100603 1173100804”

—Paragraph 2^[14]

This is a sequence of dates corresponding to the last ten highstorms leading up to the arrival of the everstorm.

 

From the Diagram. Granted, I don't know if these dates are for when they hit Kharbranth or somewhere else, but it's a start.

Edited August 21, 2016 by The One Who Connects

[Oversleep]

I recall someone making a detailed, day by day timeline for WoR with highstorms marked. I can't remember who it was, though... perhaps @WeiryWriter?

[+hwiles]

1 minute ago, The One Who Connects said:

 

From the Diagram. Granted, I don't know if these dates are for when they hit Kharbranth or somewhere else, but it's a start.

Thanks!  It's been a while since I looked at those numbers; I was originally trying to use them to determine if Taravangian was able to predict that the Stormfather would send the last storm in WoR early, but I think I ultimately concluded that we needed one or two more dates to be able to tell...go figure...still, a great start!

[WeiryWriter]

2 minutes ago, Oversleep said:

I recall someone making a detailed, day by day timeline for WoR with highstorms marked. I can't remember who it was, though... perhaps @WeiryWriter?

I didn't do the bulk of the work building the timeline but I did fill in some gaps, but I did cite it and format it nicely for the Coppermind.

[+hwiles]

@WeiryWriter , @Oversleep

You people are Gods.  I think I'm gonna settle in, enjoy a drink, and brush up on my Fourier Synthesis.

EDIT:

@Cheese Ninja is also deserving of praise.

Edited August 21, 2016 by hwiles

[Oversleep]

8 minutes ago, hwiles said:

@WeiryWriter , @Oversleep

You people are Gods.  I think I'm gonna settle in, enjoy a drink, and brush up on my Fourier Synthesis.

I just remembered correct person  All hail and glory should go to @Cheese Ninja and @WeiryWriter.

Also, I'll be followint that thread since the highstorm pattern interested me for a long, long time. I just don't have the necessary math knowledge to work it out, although I think (I hope :P) I'll be able to follow your thoughts, @hwiles.

Edited August 21, 2016 by Oversleep

[galendo]

I don't know that the Roshar peoples are that mathematically advanced.  Taylor expansions are fairly complex mathematical ideas that have calculus as a prerequisite; trigonometry is somewhat simpler, but we've seen no particular evidence of either so far.  The closest we come is the resonant frequencies that build the sand models of the major cities, but even that has much more the feel of trial and error than mathematical derivation.  Even the "engineering" that Navani and company do seems rather more trial and error than not.

When Jasnah is interviewing Shallan, for instance, neither woman ever mentions trigonometry, nor anything close to it.  Shallan mentions herself "accomplished in basic mathematics...and I often helped with minor accounts for my father."  This sounds a far cry from trigonometry to me, and given the importance of predicting highstorms and the general critiquing of Shallan's skills by Jasnah in general during that scene, if Roshar had any higher mathematics, it should certainly have been mentioned.

I rather suspect that predicting highstorms is less rigorous than otherwise.  Probably more a matter of "Well, highstorms occur every __ days on average, and the last one was pretty strong, and the moons are in the following locations, and...."  A bit more mysticism than science.  After all, if highstorms were terribly easy to predict in advance, Tavargian wouldn't have bothered writing down the dates of the ten storms prior to the Everstorm, nor would his followers have had difficulty identifying those dates as days that highstorms would occur.

[Oversleep]

@galendo, the fact that Rosharans may not have required tools to make precise calculations do not mean that they are not needed. BTW, we don't even know how far science has advanced on Roshar because of all that Investiture flying around and magitech. And spren. So we don't get to see clever engineering or anything because "SOULCASTERS!" and stuff.

If we go by Earth analogue... and assuming wikipedia to be right on History of Mathematics... I think Rosharans may be quite advanced. Trigonometry was known in some regions well before Christ and some touched upon calculus.

I think I want more ardentia Interludes. Just for math.

Edited August 22, 2016 by Oversleep

[Argent]

I'll say, while I don't have any kind of degree in math, I understand a lot of it pretty easily, and your original write-up is... confusing. I think it would be more interesting to more people if you explained your theory (and I'll be honest, I am most interested in why you chose the functions you chose) in a way that does not require a degree. Unless you are looking only for feedback that has nothing to do with the math; then it's your show.

[+hwiles]

1 hour ago, Argent said:

I'll say, while I don't have any kind of degree in math, I understand a lot of it pretty easily, and your original write-up is... confusing. I think it would be more interesting to more people if you explained your theory (and I'll be honest, I am most interested in why you chose the functions you chose) in a way that does not require a degree. Unless you are looking only for feedback that has nothing to do with the math; then it's your show.

Thanks for the feedback, looking back on it, I think it's fair to say I made a few too many logical leaps without justification.

Let's start at the beginning:  Some of the weather events on Roshar appear to occur more-or-less at the exact same time each year.  This implies that, to a good approximation, their occurrence can be described using a wave function.  For example, the first day of each Weeping follows the function:

y = sin(pi*x/500 - 10) , where each root (place where y = 0) represents the initiation of another Weeping.  (Note: there are many other valid ways to describe this phenomenon)  This equation has a 1000 day period, with a root occurring every 500 days.

It's a little old-fashioned, but the value of Sine for a given input can be measured by hand by carefully drawing right-triangles with a ruler and protractor and then using long division to take the ratio of the length of each side.  Back before computers, people used massive tables of Sine values that had been found experimentally.  Rosharans seem to have some basic concepts for finance, debt, credit, and economic theory judging from passing comments made in-book, so I would posit that they definitely have at least basic trigonometry nailed down, as trigonometry predates these concepts in real-life by a significant amount of time and is extremely vital in map-making.

The way ancient mathematicians tracked natural phenomenon (IE: the movement of stars and planets past a point in the sky) in real life was to simply write down the date/time it occurred.  After they had, over several decades, accumulated enough data points they could plot them out and try to fit a function to them.  For more complicated and, for lack of a better term, "wavy" wave functions (see attached) with unevenly spaced roots, determining the underlying function described by your data points analytically can be difficult or impossible without a computer.  However, if you know enough of the past roots (IE: the days when highstorms occurred) and you don't care about the wave's behavior between the roots, you can construct an approximation of the wave by adding several simple wave functions together.  This process still isn't trivially easy, but is doable using only trial and error in the event that Rosharans haven't discovered calculus and more complicated mathematical concepts, which I admit is entirely possible.

I picked the method of combining Sine waves because I suspect it would be the easiest method to accomplish Stormwardens' basic task of approximating when highstorms will occur without having to rely on computers or advanced techniques.

My ultimate goal here is to compile a list of in-book references that show when highstorms occur at specific places on Roshar.  From this we might be able to derive, 1) how fast storms move across the continent, and 2) a function whose roots describe approximately when highstorms will occur.

It should be noted that it's entirely possible that specific data points may have been deliberately omitted to prevent this kind of back calculation from being readily performed, however, we won't know until we try. 

TLDR;

I speculate that Sanderson, in his development for the time-line of events in the Stormlight Archive identified key points when he wanted highstorms to occur.  His track record for internal consistency in his novels leads me to suspect that he may have had a real and decipherable pattern (mathematical function) generated to describe when highstorms occur for his own use during writing (with the caveat that it doesn't need to be spot on because weather is complicated and subject to fluctuation) so he can quickly and easily tell if he's in the right continuity-ballpark when adding new events or shuffling things around (so he doesn't inadvertently create a series of scenes no highstorms for 20 days outside the weeping).  This isn't as crazy as it might sound, there are plenty of mathematicians in the world that could readily knock out such a task.

wavy-wave.bmp

Edited August 22, 2016 by hwiles

[Argent]

Ah, see, this is better. I like

I think it's a sensible theory. My only objection to it, as I understand it, as that the highstorms would hit at exactly the same dates each two-year cycle because it's just the same function repeating over and over. How would you introduce variations while keeping the Weepings fixed?

[+hwiles]

26 minutes ago, Argent said:

Ah, see, this is better. I like

I think it's a sensible theory. My only objection to it, as I understand it, as that the highstorms would hit at exactly the same dates each two-year cycle because it's just the same function repeating over and over. How would you introduce variations while keeping the Weepings fixed?

You see deeply indeed!  The function would represent only an approximate general solution for any given year.  In truth, I'm skeptical that the Weeping actually does occur exactly every 500 days, in my opinion, it would be far more likely that it would shift at least a little, say, half a day to maybe as much as several days.  It's important to remember that predicting weather is so hard because so many things affect it; even though Roshar's weather appears to be relatively well controlled by an external force, that force should not be expected to be omnipotent, in other words, it should have some limit on what it can do, which would necessarily introduce some measure of variance in all meteorological phenomena (though how much, only Sanderson can truly say). (IE: it probably can't control the trajectory of every single molecule in the atmosphere, but even if it can, it probably can't control their speed simultaneously, and even if it can, it probably can't control that speed to an infinite number of decimal places, ect. Hence - year-to-year variance; maybe a little, maybe at lot, but always at least some.)

What all this means for those still reading is that, in practice, a more iterative approach would need to be used to predict highstorms.  Every year a small correction factor would need to be added to account for any change in the length of the year, and coefficients adjusted as predicted highstorms are observed to occur at different times than expected.  For example, if you tell your High Prince that a storm won't hit for 12 hours, and it arrives after only 2, you better believe you'll be riding out that storm by adjusting the coefficients of your chosen wave function to agree with the newly observed data and refining your estimates for the arrival of the next few storms.  (that is, if you don't want to spend the next storm lashed to a post outside...)  

I'm not trying to develop weather radar for Roshar, far from it, nor am I trying to troll the series and scour its pages for inconsistencies (not that anyone has suggested as much, but it's always in the back of my mind when I post about continuity).  But I think it would be interesting and possibly useful for the community to develop a method of more clearly identifying when a scene takes place in reference to the last storm that passed and the next one to arrive.  Granted, a good rule of thumb seems to be about 3-5 days between storms, but I believe there are in-book references suggesting there are occasionally back-to-back days with storms, or stretches almost as long as the weeping without any.  We may even be able to figure out the maximum number of highstorms that can occur in a single month.

[The One Who Connects]

I almost noticed a pattern with these numbers, but since they approach the Weeping, how useful this is for the rest of the year is uncertain.

Quote

North Wall Coda

Windowsill region

“   1173090605 +6 1173090801 +5 1173090901 +5   1173091001 +3   1173091004 +6
   1173100105 +5 1173100205 +6 1173100401 +12 1173100603 +11 1173100804”

—Paragraph 2^[14]

This is a sequence of dates corresponding to the last ten highstorms leading up to the arrival of the everstorm.
Ok it isn't as useful as I'd hoped it would be, but any result is a result.

One quick snippet to ease confusion for those unfamiliar with the Rosharan Calendar:
5 Day Week, 10 Week Month, 10 Month Year
1173090605 = Year 1173, Month 9, Week 6, Day 5

[+hwiles]

35 minutes ago, The One Who Connects said:

I almost noticed a pattern with these numbers, but since they approach the Weeping, how useful this is for the rest of the year is uncertain.

One quick snippet to ease confusion for those unfamiliar with the Rosharan Calendar:
5 Day Week, 10 Week Month, 10 Month Year
1173090605 = Year 1173, Month 9, Week 6, Day 5

Here's a graphical representation of this data for reference.  Each point is a day, each point on the x-axis is a day with a highstorm.  The height of peaks difficult to describe without getting all calculusy.  Suffice it to say that it has to do with whether the frequency of storms is increasing or decreasing, which is why leading up to the Weeping the peaks are so large (big slow down in storm frequency compared to previous weeks).

 

EDIT: This is only one of the simplest first order solutions.  IE: I have artificially introduced the criteria that none of the peaks occur precisely on the X-Axis.  A real general solution to highstorm prediction would need to consider this possibility.

Edited August 22, 2016 by hwiles

[The One Who Connects]

I posted 11 minutes ago. Upvote for the chart and for just how fast you did that.

Also, I see what you're getting at now. Maybe I am a visual learner..
One other thing to note, is that Everstorm Day was set for a Weeping with no Highstorm

[+hwiles]

1 minute ago, The One Who Connects said:

I posted 11 minutes ago. Upvote for the chart and for just how fast you did that.

Also, I see what you're getting at now. Maybe I am a visual learner..
One other thing to note, is that Everstorm Day was set for a Weeping with no Highstorm

Haha, truth be told, I made most of it last night, I pretty much just added some quick formatting and refined a few of the calculations.  Afraid I'm not quite that magnificent (but I am close)

[Argent]

One thing I feel we should address when considering all this is that we (or at least I) don't know whether the highstorms orbit the planet, or get launched from the Origin every so often. Furthermore, in the former case we don't know whether the strength of a highstorm is directly proportional to its (surface?) distance from the Origin, or inversely proportional to the amount of time it has been "alive." In other words, I see three - well, four - scenarios:

1. Highstorms are generated at the Origin periodically, and then launched leeward, towards the supercontinent Roshar. They lose strength the farther away from the Origin they are, ultimately dying off sometime after they pass Shinnovar.
2. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it goes around the entire circumference of the planet. In this scenario, the highstorm continues losing strength until it returns to the Origin, at which point it recharges. This means the highstorm is weakest just as it is about to reenter the Origin.
3. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it gets to the other side of the planet. In this scenario, the highstorm continues losing strength until it becomes diametrically opposite of the Origin, at which point it starts gathering strength again. In other words, this means the strength of the highstorm depends entirely on how far away it is from the Origin - which would suggest it is continuously (and remotely) recharged from it. 
4. I don't remember what this scenario was, but it was a minor deviation of the ones above. Not important.

Then again, maybe it doesn't matter what the nature of the highstorms is, since we are trying to predict them based on past data points, not based on understanding the laws the govern them...

[+hwiles]

11 minutes ago, Argent said:

One thing I feel we should address when considering all this is that we (or at least I) don't know whether the highstorms orbit the planet, or get launched from the Origin every so often. Furthermore, in the former case we don't know whether the strength of a highstorm is directly proportional to its (surface?) distance from the Origin, or inversely proportional to the amount of time it has been "alive." In other words, I see three - well, four - scenarios:

1. Highstorms are generated at the Origin periodically, and then launched leeward, towards the supercontinent Roshar. They lose strength the farther away from the Origin they are, ultimately dying off sometime after they pass Shinnovar.
2. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it goes around the entire circumference of the planet. In this scenario, the highstorm continues losing strength until it returns to the Origin, at which point it recharges. This means the highstorm is weakest just as it is about to reenter the Origin.
3. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it gets to the other side of the planet. In this scenario, the highstorm continues losing strength until it becomes diametrically opposite of the Origin, at which point it starts gathering strength again. In other words, this means the strength of the highstorm depends entirely on how far away it is from the Origin - which would suggest it is continuously (and remotely) recharged from it. 
4. I don't remember what this scenario was, but it was a minor deviation of the ones above. Not important.

Then again, maybe it doesn't matter what the nature of the highstorms is, since we are trying to predict them based on past data points, not based on understanding the laws the govern them...

You bring up excellent points/questions that ultimately this endeavor should help to answer.  If the speed at which highstorms travel across Roshar ends up being shown to be more-or-less constant, or shown to obey one of several discrete values, or shown to change unpredictably, then we should be able to more-or-less establish if there is one continuous storm, several continuously circulating storms, or if storms are created and then dissipate at some point.

As a general point, I believe storms tend to get more aggressive as they travel over water, so recharging after passing Shinnovar is a serious possibility in my mind.  But like we always say, weather is super complicated.

[WeiryWriter]

2 hours ago, Argent said:

One thing I feel we should address when considering all this is that we (or at least I) don't know whether the highstorms orbit the planet, or get launched from the Origin every so often. Furthermore, in the former case we don't know whether the strength of a highstorm is directly proportional to its (surface?) distance from the Origin, or inversely proportional to the amount of time it has been "alive." In other words, I see three - well, four - scenarios:

1. Highstorms are generated at the Origin periodically, and then launched leeward, towards the supercontinent Roshar. They lose strength the farther away from the Origin they are, ultimately dying off sometime after they pass Shinnovar.
2. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it goes around the entire circumference of the planet. In this scenario, the highstorm continues losing strength until it returns to the Origin, at which point it recharges. This means the highstorm is weakest just as it is about to reenter the Origin.
3. There is only one highstorm, and it orbits the planet Roshar. It is strongest at the Origin, and strong enough to not dissipate completely by the time it gets to the other side of the planet. In this scenario, the highstorm continues losing strength until it becomes diametrically opposite of the Origin, at which point it starts gathering strength again. In other words, this means the strength of the highstorm depends entirely on how far away it is from the Origin - which would suggest it is continuously (and remotely) recharged from it. 
4. I don't remember what this scenario was, but it was a minor deviation of the ones above. Not important.

Then again, maybe it doesn't matter what the nature of the highstorms is, since we are trying to predict them based on past data points, not based on understanding the laws the govern them...

I know when Brandon was asked about this he said that the traditional (i.e. mythological) thought is that a new highstorm is generated each time at the Origin but that the current prevailing model among modern scientists and thinkers is that there is a single storm that rounds the world.

A possibility for scenario four is the simple: highstorms lose strength while over land and gain strength while over water (which is how hurricanes and tropical storms work, I think).

[Argent]

15 hours ago, WeiryWriter said:

A possibility for scenario four is the simple: highstorms lose strength while over land and gain strength while over water (which is how hurricanes and tropical storms work, I think).

But that's boring...

[+hwiles]

19 hours ago, WeiryWriter said:

I know when Brandon was asked about this he said that the traditional (i.e. mythological) thought is that a new highstorm is generated each time at the Origin but that the current prevailing model among modern scientists and thinkers is that there is a single storm that rounds the world.

A possibility for scenario four is the simple: highstorms lose strength while over land and gain strength while over water (which is how hurricanes and tropical storms work, I think).

I hear the theory of one continuous storm often, and I think that it's even supported as a theory by characters in the books, however, I've never seen anyone post anything to back it up as a truly legitimate possibility, so I feel like it often gets unfairly discounted.  So, without further ado, I ran some estimates for the circumference of Roshar from the in-book maps with latitudes marked by cross-referencing them with maps of Alethkar that show distance scales and came up with a minimum of 11,000 miles (really small for a planet...) I believe Isaac Stuart, who drew the maps and next to Sanderson would probably know best, has previously suggested the real figure is closer to around 15,000-18,000 miles (Earth's is about 25,000 miles for reference).  The two closest highstorms I've identified in book occur about 60 hours away from each other at the same location (shattered plains).  This means that in order to circle the globe the storm would only have to be traveling about 250 to 300 miles per hour (slightly higher than the most violent gust of wind ever observed on Earth).  These would be devastatingly fast wind speeds, capable of collapsing buildings and, with the associated changes in pressure, probably create the necessary lift to launch boulders, particularly those that are long and flat, high into the air.

Basically, the math is all there for one storm, which is periodically speeding up and slowing down, to be circling Roshar.  The best way to prove that there is more than one highstorm present on Roshar at a given time would be to identify an instance of 2 highstorms hitting the same location within about 30 ish hours of each other.  I think there are in-book references suggesting things like this might occur occasionally (still looking to make sure) but to my knowledge it's never happened on screen.  The wind speed required for the storm to circle the globe in that amount of time would be virtually impossible.  They would super heat the planet's surface simply by the friction of their passing (also suck buildings off the ground, regardless of any tilt in their walls), creating a chain reaction of steam blasts (resulting in earthquakes) that further fueled the storm.  Sea creatures would be boiled alive, land creatures would be buried alive and swallowed by the planet's crust before being drowned, mountains would crumble, and the final result would be a hot liquid-gas interface of an atmosphere where, due to the ferocious thermodynamics of the situation it would be entirely unclear where the boiling sea ends and the burning air begins.  Basically, it would be Damnation. 

TLDR;

Wind speed is a delicate thing.  When you're talking about super-storms, a simple factor of two can take a planet from "devastatingly inhospitable" to "completely uninhabitable."

[galendo]

9 hours ago, hwiles said:

Wind speed is a delicate thing.  When you're talking about super-storms, a simple factor of two can take a planet from "devastatingly inhospitable" to "completely uninhabitable."

Wow, really?  Can you please elaborate further?  My rudimentary physics suggests that a storm moving twice as fast would have four times the energy, which wouldn't be nearly as impressive as what you describe, I wouldn't think.  I'm probably missing something obvious, but whatever it is isn't coming to mind.

[+hwiles]

9 hours ago, galendo said:

Wow, really?  Can you please elaborate further?  My rudimentary physics suggests that a storm moving twice as fast would have four times the energy, which wouldn't be nearly as impressive as what you describe, I wouldn't think.  I'm probably missing something obvious, but whatever it is isn't coming to mind.

It's a lot more complicated than a simple square law; you're dealing with a planetary storm that already stresses life and habitability tremendously.  Once the speed is high enough the water cycle would break down, ie: no more evaporation, condensation, and precipitation, but a turbulent mix of liquid-gas.  Erosion and destruction of buildings don't operate on a square law; 100 mph gusts of wind can be tolerable, but 200 mph gusts of wind can knock a building over.  When a building collapses into another building, you can create a chain reaction where, sure, only one building was weak enough to be destroyed by the initial blast, but everything still falls over anyway.  Also, 600ish mph would just be the average speed of the storm normal to the planet's rotational axis.  There would almost certainly be cross-winds and gusts that exceeded supersonic speeds.

When it comes to a planet being habitable, there isn't as much wiggle-room as with most aspects of physics and engineering.  Surface temperature, double it and everything dies.  Distance from the sun, double it and everything dies.  Gravity, double it and...well okay, things die off slowly, but huge swaths of the biosphere would probably be replaced by new species in a, relatively speaking, short period of time.  I appreciate and respect the skepticism, so thank you.  The point I'm hoping I'm getting across is that, once a storm reaches a certain level of violence, it doesn't dissipate or move on like a "normal" storm, the turbulence and chaotic conditions it causes actually begin to fuel its continuation and make it get even worse (Just ask Jupiter).

Edit: Typo

Edited August 24, 2016 by hwiles

[+hwiles]

First attempt at fitting a real curve to days with highstorms, using 4 functions and the days with highstorms identified by the Diagram.  Starting to look decent, but further refining will just have to wait until we have more data, because it turns out this is kind of boring to do.  I'll try to keep some notes on my next read through in a month or two, but I suspect I won't be making much more progress until book 3 is out.

For those interested, the equation I came up with is: f(x) = sum[ A_n *sin( pi*[x/B_n + C_n])]  for n=0 to n=3

A = {2 , 1.2 , 1, 1.1} ; B = {5 , 7 , 9 , 33} ; C = {2 , 1.75 , 0.75 , 0.5}

Very obviously not perfect, but, despite the relative lack of data, I hope it at least serves as a proof of concept that my original idea could work. (potentially)

For any who didn't read everything above, points on the X-axis are days with highstorms, the red line is a fitted curve, the blue line is numerical data taken from in-book.  Ultimately, the only thing that matters is where the lines cross the X-axis, the peak behavior is largely meaningless. (but just showing dots on a line isn't very flashy...)

#RespectForStormwardens