How the super-chimney will produce water
Efficiency of the super-chimney will greatly depend on the climate at its location. Ideal locations for super chimneys would be tropical deserts, because they are warm all year. Another good reason for choosing a desert as a location is the inherent ability of the super-chimney to induce water precipitation in the surrounding atmosphere.
When warm air is expelled from the super-chimney, it is cooled down by mixing with the surrounding air. Once cooled, the air becomes oversaturated with water vapors, so water naturally precipitates, causing precipitation (clouds and rain) in the surrounding area. High winds at high altitude will carry the newly formed clouds to long distances before pouring out as rain. This will allow covering large areas with additional rain, which otherwise these areas will not receive.
Given this fact, if we wish to use the super-chimney to maximize the production of water for agriculture, we would seek to not only to use the existing landscape, but also to amplify it with artificial features such as terraces and dikes. Given the average wind speed and directions, we can estimate the area that will receive the precipitation during the year as well as amount of that precipitation depending on the season.
Depending on particular local conditions, we can vary the super-chimney's height to receive optimal water distribution. In addition, if there is an array of super-chimneys, we can vary the amount of precipitation by turning different super-chimneys of different height on and off, as necessary. The resulting system will provide controlled and sustainable water source in a desert.
Depending on the local conditions, the rain will cover a radius of at least 16 kilometers, but probably a whole lot more. Rain droplets come down at approximate speed of 18 km/h. Thus, each droplet will travel at least 15 minutes from the super-chimney exit to the ground. Given that wind speed at and altitude of 5000 m is roughly 85 km/h, we will come up with 16 kilometers radius.
However, in reality it will take some time to condense water particles on the super-chimney exit to the size of a drop. Therefore, the clouds of those particles will be carried away and dispersed on much greater distances. An array of super-chimneys will obviously produce much greater amounts of rain sufficient to water greater desert areas.