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The climate must be somewhat realistic (it's okay if there isn't a real-world approximate, but it shouldn't be ridiculous, like e.g. a wintery month out of place in what would otherwise be summer). Feel free to reference a very similar real-world climate if it exists, though.
A month's average temperature should be the mean of its average high and average low.
Bonus questions: What changes if the mean temperature were 0C? 20C? Or rainfall of 500mm? 2000mm? You don't have to spell out the whole new climate, but I'm curious to see the general pattern of where you would "distribute" extra temperature or precipitation (as it'll quite possibly not be uniform).
I'd go for something akin to Lake Tahoe. The mean temperature is a few degrees too low, I'd distribute it to warmer summer lows and winter highs, and uniformly increase the precipitation. Warm (but rarely hot) summers where fruits and vegetables can be grown, and snowy winters with cool days.
If the annual mean had to be only 10C, I'd take a climate like Denver with real summer warmth, days above 80F, and thunderstorms and mostly sunny, dry feeling winter days that are above freezing during the afternoon most of the time with the occasional snowstorm/cold spell. My fictional climate gets a lot more precipitation then the real Denver but not at the expense of sunshine since the rain comes in harder and faster downpours.
Invercargill is a real world example... if I had to make up a fictional one...
It would average a high of 15C and a low of 5C every month of the year. Record high of 24C and a record low of -3C. Sunshine about 2200 hours a year. Rainfall about 1200mm spread evenly. About 100 rain days a year. So basically it would be a subtropical highland climate.
If the annual mean had to be only 10C, I'd take a climate like Denver with real summer warmth, days above 80F, and thunderstorms and mostly sunny, dry feeling winter days that are above freezing during the afternoon most of the time with the occasional snowstorm/cold spell. My fictional climate gets a lot more precipitation then the real Denver but not at the expense of sunshine since the rain comes in harder and faster downpours.
Not completely sure what OP meant with "somewhat realistic", but I don't know of a climate that gets 1000 mm and more than 3000 hours of sunshine.
Also, December is colder than January.
And from March to June it goes: 4 → 8 → 9 → 18. That makes little sense. This is how it looks if you graph it:
10C is higher than I'd like. But Erie looks better than what I was thinking of. Snowy winters, but warm enough that summer doesn't have to be very hot to average 10C.
https://en.wikipedia.org/wiki/Almaty
Has better winters but summer's getting too warm. If summer was that warm I would make the summer dry (maybe 50mm) so it's not as humid in the hot days. And have the extra precipitation the other months.
For something averaging 20C year-round, I'd pick a climate that was roughly 25/15C year-round. 29/17 in summer and 21/13 in winter would be nice. Maybe a wet and dry season for variety. Anything with cold winters would have to be way too hot in summer.
For 0C year-round...Something like Novosibirsk (Dfb), but 1C cooler in summer and 2C cooler in winter. Double the precipitation for the 1000mm. https://en.wikipedia.org/wiki/Novosibirsk
Chibougamau (Dfc) is 0C average and 1000mm. But summer is getting too short, I would make summer a bit warmer and winter a bit colder. https://en.wikipedia.org/wiki/Chibougamau
500mm rainfall, not much change. Just make it even year-round or a slight summer peak to keep it greener then. 2000mm rainfall, have a few months be very wet. 167mm a month for 12 months would be too wet. 110 for 9 months and 330 for the other three is much better. Probably have fall be wet, spring "dry", so then winter starts off snowy.
Not completely sure what OP meant with "somewhat realistic", but I don't know of a climate that gets 1000 mm and more than 3000 hours of sunshine.
There might be a few in California where topography increases rainfall without reducing sunshine much. Somewhere near Redding? But anyplace with that combination has long, dry summers (when days are longest) and most of the rain in the winter; which maximizes sunshine hours. ABrandNewWorld's example doesn't.
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