Effect of solar zenith angle specification in models on mean shortwave fluxes and stratospheric temperatures

Abstract

Many weather and climate models call their radiation schemes only every 3 h, which we show can lead to a stratospheric temperature overestimate of 3–5 K and wavenumber 8 fluctuations in top‐of‐atmosphere (TOA) net shortwave flux around the tropics of amplitude 1.6 W m−2. Solving this problem while retaining a 3h radiation time step requires careful treatment of the cosine of the solar zenith angle, μ0, which appears twice in the calculation of shortwave fluxes, scaling the following: (1) TOA incident flux and (2) the path length of the direct solar beam through the atmosphere. If μ0 is calculated as the average over the radiation time step, rather than at the central time, then the fluctuations are removed, but the stratosphere is still too warm by 2–3 K. It is only if the second μ0 is averaged only over the sunlit part of the radiation time step that the temperature bias is removed.

SEAS5: the new ECMWF seasonal forecast system

“…For computational efficiency, the radiation calculations are only called every 3 h, which gives a poor representation of the diurnal cycle. In cy- cle 43r1, this is mitigated by approximate updating at higher time frequency, reducing biases in stratospheric temperature and errors in the diurnal cycle of near-surface temperature (Hogan and Bozzo, 2015;Hogan and Hirahara, 2016). The parameterisation of convection is based on the massflux approach (Tiedtke, 1989;Bechtold et al, 2008).…”

A Flexible and Efficient Radiation Scheme for the ECMWF Model

“…The magenta line in Figure b shows that the upgrade to the CAMS ozone climatology reduced the bias by up to 3 K in the upper stratosphere but increased it in the lower mesosphere. The dark blue line shows the additional effect of introducing the Hogan and Hirahara () method in which the solar zenith angle seen by the radiation scheme is the average over the sunlit part of the 3‐hr radiation time step, rather than the instantaneous value for the time corresponding to the middle of the radiation time step. This leads to a further 1–4 K cooling between the midstratosphere and the top of the model, bringing it much closer to the temperature of the model when the radiation scheme is called every model time step.…”

“…Otherwise, these mixing ratios are computed from a climatology on the radiation grid. The cosine of the solar zenith angle is also passed to the radiation scheme, having been computed as the average value over the sunlit part of the radiation time step as described by Hogan and Hirahara (). The top‐of‐atmosphere solar irradiance provided to the radiation scheme accounts for the seasonal variation in Sun‐Earth distance, the equation of time and an approximate representation of the solar cycle.…”

“…The Hogan and Bozzo () scheme performs approximate updates to the irradiances at every time step and model grid point to correct for errors due to sharp temperature and albedo transitions at coastlines. The improved treatment of solar zenith angle described by Hogan and Hirahara () addressed problems in IFS configurations that call the radiation scheme only every 3 hr, reducing the associated stratospheric warm bias, and largely eliminating spurious longitudinal variations in tropical solar irradiances and heating rates.…”

A round Earth for climate models

“…Several climate models use a curvature correction to SZA that limits the air mass factor (1/cos(SZA) in a flat atmosphere) approaching sunset but still treat the atmosphere as flat (Fig. 1 B ) and shut off the sun for SZA ≥ 90° (5–7). The light paths in a spherical atmosphere can be simplified as straight lines (3) or can bend to include refraction (8, 9) ( Methods ).…”