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Rooftop wind turbines seem great in principle, but in practice, especially in urban areas their usefulness and efficiency is debated, such as in this article.
The most general consensus seems to be that in urban areas where there are too many tall buildings around, there may be too much blocking the wind to make a decent amount of energy. However, this is all very vague. Is there a more scientific measure I can use to determine whether this method of collecting energy would be profitable?
There is an empirical measure. Install a small weather station device and record the wind conditions. Then you can compare your charts to what turbine vendors promise and see how much of the time you have enough wind for the turbine to be useful.
One approach is to look for studies in this area and decide whether the idea is even plausible. Is it "a bit more expensive but I like the technology" or is it "much more expensive and doesn't work very well"? If it's the former you can start looking at your exact site, if the latter... do you have a lot of money to spend on something that just looks green? The latter reason is why small turbines on roofs are popular with corporations trying to greenwash.
The Australian "Alternative Technology Association" has done a study on whether small turbines can be viable.
The short summary is that small turbines need consistent strong winds, and because the wind is significantly disturbed by the house, it helps a lot of the wind is almost always from the same direction so you can mount the turbine on the upwind side of the house. The exception would be if you're in a site with exceptionally steady, strong wind, and you need to go off-grid/can't get a grid connection.
I wrote this on another forum in response to the same question:
I have a friend with an offgrid property in the Otways on the south coast in Victoria. It's windy pretty much year round. But even there the two 200W turbines have to be ~8m up on a grassy hilltop to get clear of ground noise and over a year they run about 60% of capacity. Sure, that's better than PV (~15%-25%) but they're noisy, the installation was difficult and they have to be taken down and serviced every year. Of the parts of the system (wind, pv, battery, inverter, genset), the wind takes more maintenance than the rest of the setup combined and only the generator comes close. 400W of wind also cost as much as the 3kW PV system, but the PV gives more power, more reliably.
Note that is is on a 10Ha+ block where no-one cares about what it looks like, how much noise it makes, or how much space you need to drop the tower and service the turbine. In the city you're likely to have 8m roof heights (or you will have in a couple of years when the neighbours rebuild), so you need an 18m tower. Then you need to be 3.5m from the boundary, and need ~20m to drop the tower. So you need 23 metres of clear space in your backyard - assuming you have an unguyed tower. Tower costs get scary. A standard lattice-and-guy tower 18m tall is $5k-$10k just for hardware, but if you want self-supporting it gets pricey fast (Randwick Council in Sydney paid ~$45k for 2.4kW up a 13.5m freestanding tower - pdf, case study page 51).
It's obviously silly to spend $10k on a tower then put a little 200W or even 2kW turbine on top of it, so finding information about those systems is basically impossible. In the pdf above case study 5 says an 18m mast with a 6kW turbine cost $50k, so doubling the turbine size added 10% to the system cost compared to Randwick (roughly speaking, not all things are equal between the two).
But then if you look for $50k solar RAPS systems (because for that money why not go off grid) I picked a random one out of a search engine you get 15kW of PV, 80kWh of battery and 30kWh of consumption a day (base cost $37k, I just assumed that the extra $13k would take you to the top end of their quoted range).
jkj's suggestion of measuring the profile at wind height is sound (and necessary!) but it won't tell you whether the turbine you choose will be an efficient solution.
The article you linked to is correct that the wind speeds in urban environments are likely to be very low.
Another factor why they are unlikely to become popular is that roof-top turbines are usually quite small. That means that they are likely to be very inefficient relative to large turbines. Without going into the fluid dynamics in too much detail, it is simply because the Reynolds numbers are too low which means that the lift generated by the blades is very small.
Of course, you could opt for "drag" type turbines (e.g Savonius rotors), but they are very inefficient, often very heavy, and they require very strong support structures.
