Ozone or 03 is good if it is in the stratosphere. There it helps to absorb the ultraviolet rays from the sun and the cosmic radiation. It is bad if it is near the ground. The total proportion of O3 in the troposphere is about 0.01 ppm, yet it is a substantial greenhouse gas because it forms by uv radiation in the stratosphere and mesosphere, and thus protecting us from uv damage. See figure:
The O3 in the troposphere on the other hand is bad. It is normally around 0.01 ppm, but is considered damaging if people are exposed to more than 0.08 ppm in an 8 hour period. This can happen in urban environments in warm and steady weather, typically through car traffic. It is a great greenhouse gas because its main absorption band is at 9.5 micron, right in the atmospheric window where the outgoing black body radiation is the greatest. See fig:
The dotted blue line at 9.5 microns represents the tropospheric absorption, the total absorption is between the brown and the solid blue line. The total greenhouse effect from O3 is 0.88C, but the stratosphere does not interact very much with the troposphere, so the stratospheric O3 does not count as a greenhouse gas, only tropospheric O3. The total contribution to the greenhouse effect from tropospheric O3 is about 1/6 of the total, or 0.15C. When the earth’s temperature rises by 1.5C, from pre-industrial times to 2050, the amount of tropospheric O3 probably rises by 3% (I am guessing wildly here, in urban areas it may be much more, but this is global average). This comes to 0.005C temperature increase from O3, from pre-industrial times until 2050.
Len Bilén's blog, a blog about faith, politics and the environment. 