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I can only compare it to a game like Stellaris.
In Stellaris, you have a visible monthly income of all your various resources that appear at the top of the screen, like Energy Credits, Food, Minerals, etc... And next to your 'Income' amount, there's your stored total.
In Three Kingdoms, gold (money) seems to function exactly the same way. All your incomes and expenses are calculated out and you can plainly see how much money you currently have right next to how much money you can expect to gain (or lose) next turn.
But the Food category seems a bit simplified. All you can see is your Surplus (or Deficit). There is apparently no stored food, like there is with gold.
Well, there is -- And food stores (or Reserves) are managed by each of your Cities/Commanderies individually.
The size of each city's Reserves capacity depends on the level of the city and can be further increased by certain buildings such as the Grain Storage. This represents the amount of emergency food that the city has stored away in the event of a faction-wide food deficit or siege.
The rate at which the reserves decrease each turn appears to be directly tied to your city's food distribution rate (which is based on its Settlement Administration level). I'm not 100% sure, but this value might be offset by that city's own capacity to generate food.
Each turn your empire has a faction-wide food deficit (or a city is under siege), the Reserves are subtracted by their Food Distribution amount. The amount of turns this can happen while your Reserves are above 0 represents how long the city can hold out under siege with the supplies it has, or how long your cities will last before Public Order becomes an issue.
The rate at which your Reserves build up is definitely slower than the rate at which they can deplete -- It may be tied (at some ratio that I don't know off the top of my head) to your total food surplus.
This is likely why even though you're able JUST get your food into a small surplus after a long drought that your cities still suffer from Public Order problems for a few turns after you've sorted out the food crisis.
There may be other people who understand the numbers behind it better... This is just what I've come to understand -- My own observations. I could be completely wrong... Dunno!
Things you could do to sort out your food problems:
Have a look at all of your cities -- See which ones can be downgraded without losing building slots. If none of 'em can be, see which ones have unnecessary buildings that you can do without. Favor cities that are farther from your front lines for downgrading.
-126 Distribution is pretty intense though. You're gonna have to downgrade a ton of cities to sort that out.
Upgrading cities recklessly is always gonna get you into trouble. It's tempting to go around upgrading everything you have when you've got the money coming in... But you always need to consider your food infrastructure before you do so.
And not just how your food is looking right then and there -- How's your food gonna look when winter comes? Can you stand to lose a rice paddy or two during the next war?
Edit:
After messing around in my current game (drastically raising and lowering taxes, tax-exempting my major food-generating commanderies) it seems that the amount of food that's subtracted from your cities' reserves is also partly dependent on your empire's overall food deficit.
Having a minor food deficit like -2 does not incur as much of a hit to a city's reserves as a deficit of -50, for example. And that makes sense as your displayed food surplus (or deficit) that is displayed in the top left corner of the screen represents your faction's net profit or loss in food (all of your food generation is added up and all of your food distribution subtracted from it).
Ya, that Reserves explanation sounds about right. Did a little googling and makes a lot more sense now.
I also noticed that in a lot of my contested provinces, my vassals owned the "rice paddy" or "livestock farm", which probably explains why the city centres could never produce enough food to sustain itself.
This campaign might be a right-off at this point. But I got offered to be a vassal, something I've never accepted before in any TW game, so I said yes assuming I'd be trashing this campaign anyway. Now my income per turn is over 13k... with that kind of cash, and having lost all my vassals, I can probably scoop up enough farm land and re-jig my towns!
Province produces X amount of food. City Centre/buildings deplete Y amount of "distribution."
X-Y= amount put into Reserve.
When winter comes:
Reserves-Y
I assume fishing continues in the winter?
Your real food generation comes from stacking bonuses from techs, other buildings, and characters. Build the building that gives a % bonus to food production in your main food producing commandries. Start researching the green techs that give you better farms and % bonuses of their own.
Raising taxes also boosts food generation.
The AIs are bad at feeding themselves. If the player gets food production in order early and keeps it that way throughout the campaign the AI will pay thousands for the player's extra food. Food is also a good stat pad for bartering deals when the player does not want to give up gold or items.
Apparently not taxing in this game is the same as farmers taking a year off? It's a very silly catch-22. Not taxing is obviously not the same as not working...