# Large-Scale Modeling of Absorbing Aerosols and Their Semi-Direct Effects
## 3 Results
### Radiative Effects
#### 3.2.2 Top of Atmosphere Radiative Effects  
The aerosol radiative effect is computed as the difference of net of incoming and outgoing radiative fluxes (shortwave and longwave) at the top of the atmosphere. The forcing due to a specific aerosol type was computed as the difference between radiation fluxes of the simulation containing all aerosol and the simulation excluding the specific aerosol type. Figure 4 and Table 2 summarize the eight-year annual average differences for the direct radiative effect (DRE), instantaneous direct radiative effect (IDR) and the residual semi-direct effect (SDE) for the differences between the experiments BASE and noBC to evaluate the effect of BC absorption on the radiation budget. Only grid cells where Student's \(t\) statistics indicate a confidence level above 95% are shown for DRE and SDE. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Simulation** & **DRE** & **IDR** & **SDE (Net)** & **SDE (SW)** & **SDE (LW)** & **Cloud Cover** \\ \hline  & \(\mathbf{Wm^{-2}}\) & \(\mathbf{Wm^{-2}}\) & \(\mathbf{Wm^{-2}}\) & \(\mathbf{Wm^{-2}}\) & \(\mathbf{Wm^{-2}}\) & \% \\ \hline BASE\(-\)noAER & \(-1.13\) (0.45) & \(-1.22\) (0.05) & \(0.08\) (0.45) & \(0.08\) (0.57) & \(0.01\) (0.47) & \(-0.01\) (0.40) \\ BASE\(-\)noBC & \(0.51\) (0.47) & \(0.42\) (0.06) & \(0.09\) (0.47) & \(0.19\) (0.58) & \(-0.10\) (0.49) & \(-0.25\) (0.41) \\ GFAS\(-\)noBC & \(0.62\) (0.46) & \(0.36\) (0.04) & \(0.26\) (0.47) & \(0.43\) (0.58) & \(-0.16\) (0.50) & \(-0.27\) (0.10) \\ noDUST\(-\)noABS & \(0.24\) (0.46) & \(0.27\) (0.01) & \(-0.03\) (0.46) & \(-0.03\) (0.57) & \(0.00\) (0.50) & \(-0.08\) (0.41) \\ BASEind\(-\)noBChid & \(0.46\) (0.47) & \(0.41\) (0.04) & \(-0.05\) (0.47) & \(-0.16\) (0.58) & \(-0.12\) (0.49) & \(-0.12\) (0.32) \\ \hline \hline \end{tabular} Numbers in brackets are standard deviations based on results for individual model years.  
\end{table} 
Table 2: Results of the global annual average top-of-atmosphere direct radiative effect (DRE), instantaneous direct radiative effect (IDR) and semi-direct radiative effect (SDE) computed from pairs of model simulations (see Table 1). Additionally, results for solar (SW) and thermal (LW) parts of the spectrum are provided, as well as total cloud cover changes. All model grid cells are considered for the averages. Figure 4: **(a)** Direct radiative effect (DRE) of BC aerosol calculated from TOA radiative fluxes as difference of experiments BASE-noBC; **(b)** instantaneous radiative effect (IDR) calculated as **(a)** but excluding changes in cloud cover by BC forcing via double call to the radiation scheme in the model, and **(c)** semi-direct effect (SDE) at the top of atmosphere in \(\mathbf{Wm^{-2}}\) calculated as DRE-IDR. **(d)**: as **(c)**, for the GFAS simulation. Grey areas indicate regions where the results are not statistically significant at 95% level. The direct forcing by BC aerosol is positive overall, which is due to the aerosol absorption in the solar spectrum. In the global annual mean the DRE is +0.51 Wm\({}^{-2}\) and the IDR is +0.42 Wm\({}^{-2}\), which is close to the value in IPCC [2] for BC direct radiative forcing for BC from fossil fuel and biofuel burning, which is 0.40 Wm\({}^{-2}\) with minimum and maximum estimates ranging from 0.05 Wm\({}^{-2}\) to 0.80 Wm\({}^{-2}\). Since on one hand here we consider all BC sources including non-anthropogenic wildfires, but on the other hand the AAOD from the model may be underestimated as indicated by the comparisons with the OMI AAODs, this estimate appears to be at least within the range of uncertainties from earlier studies. The semi-direct effect computed as residual between the DRE and the IDR shown in Figure 4c has overall positive values. In the global average, the SDE forcing is +0.09 Wm\({}^{-2}\), with a standard deviation of 0.47 Wm\({}^{-2}\) computed as standard deviation from the annual averages of the individual model years (Table 2).