How dark would the sky have to be to stunt crops?

Question

So basically in my world solar geoengineering has gotten to the point that (with added smog) it's basically impossible to grow crops like wheat or barley without artificial light. My question is: How dark would the sky have to be to stunt plants like wheat or barley? Would it basically be like a regular overcast day, or would it be like a thunderstorm with no rain?

Answer 1

A "regular overcast day" (all the sky covered with clouds, cannot guess the position of the sun) is about 10 to 15 times dimmer (about 3 to 4 f-steps, for photographers) than the light available on a sunny day from the blue sky alone, for example in the shadow of a parasol.

Outdoors with overcast but not heavy overcast or rainy sky the illuminance (summer, midday) is about 1500 lux; in summer at midday in the shade (light only from the blue sky) is about 20,000 lux; in summer in direct sunlight at midday is about 50,000 to 100,000 lux. (At reasonable latitudes, of course; the illuminance is obviously lower at high latitudes.)

^{For comparison, artifical lighting indoors provides some 300 to 600 lux, depending on how bright one wants their rooms to be. Brightly lit work areas may reach 750 lux, about half the illuminance of an overcast day.}

^{For those readers who prefer ye olde traditionall Englysshe units, 1 foot-candle is about 11 lux. 1,500 lux is about 140 foot-candles, 20,000 lux is about 1,800 foot-candles.}

Most crops are grasses. Grasses are adapted to life in, well, grasslands, in direct sunlight. Common crops need 15,000 to 20,000 lux for optimal growth. Below 10,000 lux growth slows significantly, and below 5,000 lux you cannot grow most common cereals.

Answer 2

About as bright on Jupiter: 20-60 watts/m²

Sorry for the astronomy reference, I just thought it would be cool to add something like a planet to the answer

On Jupiter, a typical sunny day is about as bright as 50 watts/m², about as dark as a dimly-lit room, if I remember correctly.

Similarly, since your geoengineering projects have bungled up so far, you have likely ejected a ton of aerosols into the atmosphere, the result, you have a dimly-lit planet, with a brightness of a really dimly-lit room.

If my sources are correct, you need atleast 20-60 watts/m² of natural light (solar irradiance) before your plants either die, or are severely stunted, due to lack of light for photosynthesis. Basically, far from a overcast sky, you need an extremely dark sky, before your crops are actually severely affected

If you want low-yielding crops and other mundane stuff, fine, just an cloudy sky is fine.

However, if your situation demands such that any plants grown in the open are severely stunted or die quickly, you need an extremely dark sky. The closest thing would either be a really dimly-lit room or a thunderstorm on steroids.

Note that this is not the only factor that decides plant growth. As @JBH mentioned in the comments, you need also heat and length of day-time. This is just one factor. I'll leave the rest to you as homework, but a small hint: it would be very cold and dark, with short day-time hours.