Regarding the hexadecimal RGB color representations: Having already gotten the conversion working you probably already got all this, but in case it helps, the typical hexadecimal representation for colors (at least when using RGB which is commonplace) is really closely related to the delimited R,G,B - as you said, the hex number is split into three parts for the red green and blue, each two digits in base-16 meaning each part is 0-255 like often seen in common delimited/separated R,G,B representations.
So for example, that very reddish magenta shade in the corner of your table above (#FA0046) is Red FA, Green 00, Blue 46 which written in base-10 is Red 250, Green 0, Blue 70.
So the hex representations in general are just #RRGGBB, where the R's are digits of the red value (FA in the above example), G's digits of the green (00 in the above example), B's the blue (46 in the above example). Updating or changing one of red, green, or blue for a given color just means changing the value in the two digits that represent that one of red, green or blue.
Sorry if you're already familiar with all of that and I'm being terribly presumptuous - but I'm used enough to the representation of RGB in hex that I don't usually think of it offhand as a separate representation, so thought I'd offer an explanation of my own on the off chance it can help your understanding. I guess what I'm getting at is it hopefully shouldn't be too much more complicated to use than separated RGB, because the conversion itself is pretty much a direct mapping - the only parts that get more complicated are trying to operate on the values, in which case you just need to make sure to treat the separate parts of the whole hexadecimal value appropriately as separate sections for red, green and blue.
Prior to doing this, I never actually noticed that hexadecimal colours are exactly as you described.
I was thinking that different colours had totally different code but it is actually pretty simple.
Addition is easy since I'm using blue and red for winter and summer temperature respectively.
Green is for precipitation and I can manage to have only 1 variable by grouping them. Instead of having 1 for each season.
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Very nice work! I should note that personally I used slightly different averages:Originally Posted by Azelor
I made most of the averages to have linear 6 °C intervals since that doesn't change them too much from the actual values, and simplifies the calculations because you can merge a lot of the categories. For example, S. Hot (38 avg) + Warm (20 avg) would have a mean annual temperature of 29 °C (taking the average between the two months). But V. Hot (32) + Hot (26) would also have the same annual mean (29 °C) if the jumps between the categories are linear, so you can merge these combinations (since they have the same climate class (A) and the same mean annual temperature, and therefore the same aridity threshold).
Btw, how are you planning to differentiate between which threshold to use (S, W, F)? I used the 2/3 scheme so almost everything is considered either S or W for the purposes of determining the aridity, and only the prec combos along the central diagonal (for the most part) use F.
However, this can result in some weird jumps around the equator potentially, when the threshold suddenly drops/rises a lot as you cross the equator because the difference between S and W thresholds is pretty huge. Especially apparent if the ITCZ has a strong bias towards either hemisphere (like on Earth, so you see some As turning up in Colombia and the Kongo basin).
Edit:
I guess I should also add that in the scripted version for GIMP I merged the temperature categories even further for the purposes of determining the aridity. I used the following overall scheme (Tann=annual mean temp):
Hot temp combos (hotter A climates): Tann 38-29
- I used Tan 33 as an average for this group (so thresholds F: 800, W: 940, S: 660)
Warm temp combos (milder A climates and most Ca): Tann 28-19
- Tann 23 for this group (thresholds F: 600, W: 740, S: 460)
Temperate temp combos (cool Ca, Cb, warm Da): Tann 18-11
- Tann 13 (thresholds F: 400, W: 540, S: 260)
Cold temp combos (Cc, Db, cooler Da): Tann 10-0
- Tann 5 (thresholds F: 240, W: 380, S: 100)
Very Cold temp combos (Dc, Dd, very cold Da): Tann 0 to -15 (coldest non-E temp combo)
- Tann -6 (thresholds F: 20, W: 160, S: -)
It's a simplification, but since the precipitation categories are so broad, I don't think you lose much overall by doing this.
To give an example, a change of 1 °C in mean annual temperature equals a 20 mm difference in precipitation threshold. As you probably noted, the avg. Tann values I used are roughly 10 °C apart (=200 mm). Let's say we have 70-140 mm in winter and 20-40 mm in summer. Using the min. and max. precipitations from that combination, the annual precipitation (Pann) would be 540-1080 mm. The next combo in that column (40-70 mm in winter, 20-40 mm summer) would have Pann 360-660 mm. For the purposes of determining the aridity we'd use the averages of course (810 mm and 510 mm), but you can see why I don't think it's necessary to use a separate aridity threshold for every temperature combination: the precipitation varies so much within a single prec combo that it doesn't result in increased accuracy. And also the gaps in avg. precipitation between the prec classes are so broad as well, that only differences on the scale of ~200 mm in the aridity threshold can actually be represented in any case.
Last edited by Charerg; 01-29-2018 at 08:50 AM.
I made most of the averages to have linear 6 °C intervals since that doesn't change them too much from the actual values, and simplifies the calculations because you can merge a lot of the categories. For example, S. Hot (38 avg) + Warm (20 avg) would have a mean annual temperature of 29 °C (taking the average between the two months). But V. Hot (32) + Hot (26) would also have the same annual mean (29 °C) if the jumps between the categories are linear, so you can merge these combinations (since they have the same climate class (A) and the same mean annual temperature, and therefore the same aridity threshold).
That is not something I have considered before. I did a quick test and since everything is linked, it's updated automatically.
There are 40 combinations instead of 55? If I counted correctly.
Coming soon.Btw, how are you planning to differentiate between which threshold to use (S, W, F)? I used the 2/3 scheme so almost everything is considered either S or W for the purposes of determining the aridity, and only the prec combos along the central diagonal (for the most part) use F.
Edit:
I use different and less categories but I believe the way we estimate yearly precipitations is the same. So I get the value for each combination.
I gave them some names but they are not necessarily representative.
6*(Summer precipitation + winter precipitations)
To determine if S, F or W
The parameter are different with C/D versus A
C/D : a certain % of the yearly precipitations has to fall during the dry season, I used the value of summer everywhere to make things less confusing.
Also, a certain quantity of precipitation in millimetres has to fall during summer.
The result I get is slightly different than the previous one, or is it?
I tweaked the previous model to make it fit with reality. Since my numbers are supposed to be identical, I will probably come to the same conclusion again. The values are usually pretty close anyway.
Because we are using categories, the maximum and minimum of each is overlapping the others. Having more precipitations categories doesn't solve this problem but it makes it less bad.
But before I start using more categories for precipitation, we need a better method for placing them on the map.
sheet3.png
A climates are different. this is where I might have made a big mistake in the older version apparently.
According to the spreadsheet:
Af is easy, must be above 60 all the time.
As and Aw need a very dry season, less than 4% of precipitations falling during the driest month and no more than 60 ml.
In theory Am includes everything left. It has a dry season but it is not very strong. it has 7 combo but 3 of them are on the central axis which should not even have a dry season in theory but are too dry to be Af.
Well they are often too dry to be Am anyway and fall into the steppes or deserts climates.
Again there is a comparison on the left between the old and new model.
It's very different but take in consideration that the old model made no effort to differentiate As from Aw.
As is very rare and the difference between the two is marginal.
sheet4.png
Edit 2:
On the temperature sheet I added a table to indicate if an arid climate is hot or cold. The yearly average temperature must be above 18 in order to be hot.
I used a condition to do it.
sheet 5.png
and here is the modified version of the temperatures using your averages.
Same combinations share a colour, those that are unique don't have one. I added them manually.
i see little reason no to use your numbers since it make the thing easier and it doesn't seems to have a negative impact of the precision of the simulation. Anyway, the differences would be marginal I suppose.
sheet2b.png
Lastly, I haven't set any maximum/minimum temperatures for the extremes. I thin it's 43 and -68.
Last edited by Azélor; 01-27-2018 at 01:16 PM.
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Next will be creating the master table for the aridity index (and maybe other things will be included in the table as well)
the idea is to have a table that will automatically tells us if a climate is humid, a steppe or a desert.
But will also tell us if it is S, F or W according to the position in the table.
Basically, it's a huge table containing 36 aridity index tables (6x6). one for each of the rain combinations.
I will use different aridity tables depending if the rain combo is S,F or W. So the numbers won't be identical, there will be 3 different sets.
Then I compare the aridity threshold with the actual precipitations. for example, it mean the threshold first block in the top left (the wettest) will be compared to the precipitation of that block (2400).
If precipitations are higher than the threshold, it will return a certain output, not sure what yet. Another output if it is less than the threshold but more than threshold/2. And a last output if it's something else.
Maybe it will be on different table or just in one. I think it could work all in one but requires more planning maybe.
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I think you already know this, but just to make sure, be careful not to confuse the f, w and s climate categories with the precipitation thresholds. For the climate categories, the definition would be as follows:
C/D climates:
- At least 3/4 precipitation occurs in winter-> s (dry summer)
- At least 10/11 precipitation occurs in summer-> w (dry winter)
- Otherwise f (no dry season)
Of course, those aren't the official definitions, but they apply in our case since we only use data from two months. They come from the requirements that the rainiest winter month must have at least 3x the precipitation as the driest summer month for an s climate, and for w climates you need 10x the rain in the rainiest summer month than the driest winter month.
Whereas to determine which threshold to use for the aridity calculations (I'll use capital letters F, W and S to refer to the aridity categories to avoid confusion), the following seems to be the usual formula (though I understand some authors have used a different one):
- At least 2/3 precipitation occurs in winter -> S (use summer dry threshold)
- At leat 2/3 precipitation occurs in summer-> W (use winter dry threshold)
- Otherwise use F (evenly spread precipitation threshold)
Btw, you definitely have the Am categories a bit off. It's a transitional category between Af and the more dry climates, and ideally Am should surround Af . But even Am requires a lot of rainfall. As a reminder, the formula for Am is as follows:
Pann= mean annual precipitation
Pmin= precipitation of the driest month
Pann >= 25 (100-Pmin)
Meaning that if Pmin (precipitation of driest month) is 0 mm, you need at least 2500 mm annual prec for a climate to qualify as Am. And if Pmin is 60 mm (which is the maximum, since Am needs to have at least one month with less than 60 mm), then only 1000 mm would be required. Which means that the absolute minimum annual precipitation for an Am climate is 1000 mm.
The Bh/Bk boundary in your table is the exact one I used in the GIMP script as well. Although originally I classified anything with a Cool (0-10 °C) season or colder as Bk, I switched to the mean temperature-based classification in the scripted version.
As a sidenote, here are the equivalent tables I've used in the most recent version of the GIMP script:
A precipitation class table:
APrecClasses.png
C/D precipitation class table:
CDPrecClasses.png
Anything coloured in white is always considered arid (either BS or BW).
Last edited by Charerg; 01-29-2018 at 08:52 AM.
Ok, I think we are talking about the same thing but I tend to use minus and capital letters interchangeably. I don't find it confusing.
I know Am is a transition. but
The blue in the graphic are excluded because the driest months are over 60ml.
The orange and purple are too dry compared to the rest of the year. under 60ml.
Only the area in the middle remains.
Also, as I said in the previous message, some of these combination are considered A... but are actually too dry and fall into B climates.
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Yes, probably all categories marked as Am in the new table would be considered arid. Btw, I forgot to mention that you need to be a bit careful when merging temperature combos with the same mean annual temp, because you can't merge them in cases when they occur in two different climate categories. As an example, Hot+Hot has the same average (26 °C) as S. Hot+Mild, but the former would be classified as A and the latter as Ca, because the temperature falls below 18 °C. So they would have to be still coloured separately.
Although in the scripted version I merged many of the categories with a similar Tann value (not just those that have the same exact value) so I ended up with ~15 temp combos in total. Like I mentioned, I don't think it had a huge effect on the accuracy of the overall results because the precipitation categories are too broad for minor differences in annual mean temperatures to have a meaningful effect.
Last edited by Charerg; 01-27-2018 at 05:19 PM.
Just as I thought.
sheet6.png
So there are 7 combinations in the top left blue area.
Do you know many functions in Excel?
I had a crazy idea.
I think it would be possible to enter certain parameters for the corresponding climates and Excel would tell you what climate it is.
Not only that, but he would also return an hexadecimal code to create a color key.
But there could be more. Imagine if we could export a map to Excel in a spreadsheet.
Everything would be done by Excel and there would be no need for scripts that are complicated to make and hard to monitor if there are errors in it.
Last edited by Azélor; 01-27-2018 at 05:24 PM.
My Deviantart: https://vincent--l.deviantart.com/
That definitely sounds like an idea worth exploring. Unfortunately I can't claim to be much of an Excel guru, but at least I own the program and have used it to some extent (that's something, right). And it never hurts to learn some new stuff like scripting in GIMP and what-not. Anyway, here's the spreadsheet about which temperature combos I merged in the GIMP script. Apparently I narrowed them down to 14 overall (though many of these like Da (Very Cold), Dc, Dd, ET and EF were already merged in the original).
TempSheet.png
But yeah, you're right that there definitely should be some method to generate the climates other than scripting a long series of colour-picking and replacing operations. I mean, the professionals who create Köppen maps of Earth definitely don't use that method (well, actually they use GQIS for the most part, I believe).
Edit:
Btw, I think you're using a too low average value for the highest precipitation category (200 mm+). Because you use only 200 mm as the average, all Am climates are eliminated. And the precipitation in the highest category could definitely go much higher than 200 mm.
If we consider the precipitation of the driest month in a precipitation combo bordering Af to be 25 mm, then the "Am threshold" would be 1875 mm. So, you'd need to use at least 285 mm as the average ((285+25)*6=1860 mm for the annual precipitation), in order for Am climates to appear.
Last edited by Charerg; 01-27-2018 at 09:31 PM.
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