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Providing there are low wind conditions and a clear sky, will the 1 km x 1 km black surface create an upward convention?
Let’s say I were to do this at 60$^\circ$ N longitude in march month, the elevation of the site to be at 2000 feet, by just building a surface of 1 km x 1 km and painted in black, how high would the convection go? What other side effects will it cause? My goes to have air going up to 7000 feet constantly.
In principle: yes. But i won't give exact numbers for a mere km², though i'd expect a skilled paraglider under optimal atmopsheric conditions to be able to make some use of it ;-)
Actually, gliders use industrialized areas exactly because of this, a low albedo created by asphalt, concrete, dense construction/building.
How high and strong the resulting thermal convection will be depends on the weather, atmospheric layering, solar irradiation, wind, cloud cover, temperature and moisture. The ability of the ground to store heat (e.g. street canyons, or heat strored in the air of a high grown cornfield) also influences the triggering of convection. In some cases a rising thermal is visualized by a dust devil.
Thermal convection can be calculated/estimated and predicted from atmospheric soundings, instrumented weather balloons to measure the state of the atmopshere from ground to tropopause. The results are visualized in Skew-T or Stüve diagrams.
Reading and interpreting them is an art. But they can tell when the trigger temperature for thermals will be reached, how high they go, if there will be clouds and at which level their base is, etc.
Side effects of this are called urban heat islands or generally heat islands due to low albedo ground. They can cause local low pressure due to the rising air over the hotter ground, which can result in showers or even thunderstorms in the evening/afternoon.
Quite obviously, these effects can also be triggered by naturally occurring differences in ground albedo and plant cover. They are a driving force for local weather phenomena.
Yes. You don't even need concrete or black paint, just a plowed field will do, or grass vs forest, a south facing slope... (Ask anyone who's done much sailplane flying.)
How high the convection will reach depends on a lot of factors. Hereabouts (east side of the Sierra Nevada) you can easily thermal to 14,000 ft (~4500 m) or more. (Going higher requires you to use supplemental oxygen.) If there is the proper amount of moisture in the air, it will reach a height at which the moisture starts to condense and form clouds. These can be simple cumulus clouds https://en.wikipedia.org/wiki/Cumulus_cloud or they can develop into cumulonimbus, which can reach heights of 69K ft/21K m) or more.
