## 2 Data and Methods
### Methodology
#### 2.2.2 A System for Radiative Transfer Calculations--SBDART-NO\({}_{2}\)  
A system that implements radiative transfer calculations at any spatial and temporal resolution using gridded atmospheric properties data was developed (see Figure 1). It comprises an interactive data language (IDL) interface and an updated version of the well-established Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) model [79]. The interface gathers all the information from the gridded data and builds all the necessary input parameters for the radiative transfer model. Then, it executes SBDART for the following three sky conditions: clear, liquid and ice cloud-covered skies. The system uses AOD\({}_{550}\) from MODIS/Aqua and climatological MACv2 AOD values at 8 different wavelengths (Section 2.1.2) to account for the spectral dependence of AOD. SSA and ASY come from MACv2. The MACv2 parameters characterize the aerosol mixture over each location. Climatological CALIOP/CALIPSO aerosol extinction profiles account for the shape of the vertical profile of aerosols. The CALIOP/CALIPSO profile is scaled accordingly in every simulation to make sure that the total AOD is equal to that of MODIS/Aqua. For clouds, MODIS/Aqua CF, COT, CER and CTP data for liquid and ice clouds separately are used. Cloud bottom pressure (CBP) is calculated from CTP for low (CTP > 680 mbar), medium (440 mbar < CTP < 680 mbar), and high clouds (CTP < 440 mbar) using the corresponding cloud depth (CD) values (100, 50 and 50 mbar) from [PERSON] and [PERSON] [80] (CBP = CTP + CD). CTP and CBP are converted to cloud top and bottom height and temperature using the [PERSON] et al. [81] standard atmospheres. From the cloud top and bottom temperatures the mean temperature at the cloud layer (T\({}_{\rm c}\)) is derived. The relative humidity at the cloud layer, which is used by SBDART to define the water vapor profile, is calculated from T\({}_{\rm c}\) following [PERSON] and [PERSON] [82]. MODIS/Aqua PW is used for water vapor column while broadband surface albedo is from CM SAF CLARA-A2.1. SBDART is mostly oriented on aerosol- and cloud-related studies and the spectral absorption of NO\({}_{2}\) in the UV/Vis is missing from the original version. To account for the radiative effect of NO\({}_{2}\), we updated SBDART by incorporating into the model the NO\({}_{2}\) cross sections from [PERSON] et al. [83] in the spectral range from 231 to 794 nm with a spectral resolution of 20 cm\({}^{-1}\). On top of that, the updated version of SBDART (hereafter also denoted as SBDART-NO\({}_{2}\)) was further modified so as to account for tropospheric and stratospheric NO\({}_{2}\), separately. The predefined SBDART tropospheric and stratospheric profiles are shifted accordingly (multiplied by a factor) so that the tropospheric and stratospheric NO\({}_{2}\) columns are equal to the satellite-based ones from OMI/Aura. The ability of SBDART-NO\({}_{2}\) to determine the radiative heating produced by NO\({}_{2}\) within the atmosphere has been validated. More specifically, the calculated radiative heating values produced by 0.5 DU of NO\({}_{2}\) distributed within the first 1 km of the atmosphere under different solar zenith angle and surface albedo scenarios were identical to the ones appearing in [PERSON] et al. [30] for the same specifications. Figure 1: Flowchart with the datasets, the methodology and the radiative transfer system used in this work. Dark grey is used for the core and light grey for the ancillary data. The radiative transfer calculations are implemented with SBDART-NO\({}_{2}\) for 185 wavelengths in the range from 250 to 4000 nm with a decreasing resolution of 4-10 nm in the UV/Vis and 10-60 nm thereafter. The daily average solar zenith angle (SZA\({}_{d}\)) is derived following [PERSON] and Koutoulaki [84]. As the radiative transfer calculations here are implemented on a monthly basis, the monthly mean SZA\({}_{d}\) is used as input by SBDART.