# The DLR FireBIRD Small Satellite Mission: Evaluation of Infrared Data for Wildfire Assessment
## 2 Materials and Methods
### Atmospheric Correction of FireBIRD Infrared Band Information  
To obtain results of optimal quality, the top-of-atmosphere (TOA) HSRS radiance data has to be calibrated regarding radiometric parameters. As a first step, all nadir looking channels (MWIR, LWIR, and the red channel in case of daytime acquisitions) are co-registered using the MWIR band as reference image. Consecutively, the stacked images are geo-coded manually to obtain an accurate positioning on the Earth's surface, using auxiliary data such as administrative boundaries, roads, and rivers. Several further external data sources are required in order to perform the atmospheric correction [14]:  
* The emissivity of the surface is derived from the ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) GED (Global Emissivity Database [22]). Unfortunately, the ASTER sensor does not feature a MWIR band. Therefore, the emissivity can only be derived using the LWIR information. The emissivity of the combined ASTER bands at 8.6 um and 9.1 um is used as these bands are similar to the LWIR band of HSRS. A high spatial resolution global MWIR emissivity database is not available. Therefore, following [PERSON] and D'Aria [23] and [PERSON] et al. [24], the approximation \(\epsilon(MWIR)=\epsilon(LWIR)\) was chosen for the processing since it was found to be more valid than the regularly used assumption of \(\epsilon(MWIR)=1\).
* Since atmospheric water vapor, which strongly influences the radiation, cannot be derived from the available HSRS bands, the dataset of the MODIS MOD05 water vapor product [25] featuring the shortest temporal distance to the FireBIRD acquisition is used as an external source.
* As the water vapor also depends on the topographical elevation of the ground, the ASTER GDEM (Global Digital Elevation Model [26]) is used as an auxiliary dataset during the atmospheric correction. This correction is based on look-up tables derived from the MODTRAN-5 radiative transfer code [27]. Finally, the resulting MWIR and LWIR surface radiances are converted to surface temperatures according to [PERSON]'s equation.  
Figure 1: Schematic representation of the processing workflow.  
The processing steps of the atmospheric correction are described consecutively. An exhaustive description is provided by [PERSON] et al. [6]. The following equations are taken from this source without alteration. The surface radiance is calculated using the following formula:  
\[L_{k}^{s}(T)=\frac{1}{\epsilon_{k}}\{\frac{L_{k}^{TOA}-L_{p,k}}{\tau_{k}}-(1- \epsilon_{k})\frac{F_{k}}{\pi}\} \tag{1}\]  
\(k\) refers to the channel index (1 for MWIR, 2 for LWIR), \(L_{p,k}\) is the thermal path radiance, \(\tau_{k}\) is the atmospheric ground-to-sensor transmittance, \(\epsilon_{k}\) is the emissivity, \(L_{k}^{s}\) is the surface radiance, \(T\) is the surface temperature, and \(F_{k}\) is the downwelling thermal flux on the surface. The MWIR signal is slightly influenced by the solar irradiation (\(L_{solar}\)). Therefore, during daytime, Equations (2) and (3) have to be used for the MWIR channel to calculate \(L_{s}\).  
\[L_{1}^{s}(T)=\frac{1}{\epsilon_{1}}\{\frac{L_{1}^{TOA}-L_{p,1}}{\tau_{1}}-(1- \epsilon_{1})\frac{F_{1}}{\pi}-L_{solar,1}\} \tag{2}\]  
\[L_{solar,1}=\rho_{1}exp(\ln(\tau_{1})/\cos\theta_{s})E_{0}\cos\theta_{s}/\pi \tag{3}\]  
\(\rho_{1}\) is the MWIR surface reflectance, \(\theta_{s}\) is the solar zenith angle, \(E_{0}\) is the MWIR extraterrestrial solar irradiance, \(\tau_{1}\) is the atmospheric nadir transmittance. The exponent represents the transmittance of the slant path corresponding to \(\theta_{s}\).