A simple parameterization for the height of maximum ozone heating rate

It is well-known that the height of the maximum ozone heating rate is much higher than the height of the maximum ozone concentration in the stratosphere. However, it lacks an analytical expression to explain it. A simple theoretical model has been proposed to calculate the height of maximum ozone heating rate and further understand this phenomenon. Strong absorption of ozone causes the incoming solar flux to be largely attenuated before reaching the location of the maximum ozone concentration. By comparing with the exact radiative transfer calculations, the heights of the maximum ozone heating rate produced by the theoretical model are generally very close to the true values. When the cosine of solar zenith angle μ0=1.0, in US Standard atmosphere, the heights of the maximum ozone heating rate by the theoretical model are 41.4 km in the band 0.204-0.233 μm, 47.9 km in the band 0.233-0.270 μm, 44.5 km in the band 0.270-0.286 μm, 37.1 km in the band 0.286-0.303 μm, and 30.2 km in the band 0.303-0.323 μm, respectively. The location of the maximum ozone heating rate is sensitive to the solar spectral range. In band 1, the heights of the maximum ozone heating rate by the theoretical model are 52.3 km for μ0=0.1, 47.1 km for μ0=0.3, 44.6 km for μ0=0.5, 43.1 km for μ0=0.7, 41.9 km for μ0=0.9, 41.4 km for μ0=1.0 in US Standard atmosphere, respectively. This model also illustrates that the location of the maximum ozone heating rate is sensitive to the solar zenith angle.