## 3 HJ-1B images simulation
### Simulation of HJ-1B images  
The RED and NIR channel of HJ-1B sensor were denoted as channels 1 and 2, which correspond to the B3 and B4 bands of the CCD Camera, respectively. The MIR and TIR channel were denoted as channels 3 and 4, which correspond to the B3 and B4 bands of the Infrared Scanner, respectively. The VNIR, MIR and TIR channel of HJ-1B sensor have 30 m, 150 m and 300 m resolution, respectively, and the VNIR and MIR channel data should be aggregated to the TIR channel's resolution. Because only the daytime AHS data was available, both the simulation and fire detection algorithm were focused on the daytime situation.  
First, the real-time atmospheric profile was used to correct the atmospheric effect of AHS data based on MODTRAN 4 [34]. The surface temperature and emissivity of an AHS pixel were obtained by the TES algorithm [35]. Secondly, the surface temperature and emissivity at the scale of a HJ-1B pixel were got by spectrum transform [36] and spatial aggregation at a 300 m scale, which is the resolution of HJ-1B's thermal channel [37]. The results are shown in Figure 1.  
Thirdly, fires with varied temperature and area were added randomly into the HJ-1B pixels. In order to enable the fire simulation to be much more rational, the fire was added only to the vegetation covered pixels. Thus, fire was not simulated for bare soil, water surfaces and clouds. Two hundred fire pixels were generated by the following steps:  
(1) The pixels were selected randomly in the image to add simulated fire.  
(2) Cloud pixels were removed by the limitation of \(T_{4}>265\) K.  
(3) Vegetation covered pixels were selected by the condition of \(\mathrm{NDV}\geq 0.3\).  
(4) Fire temperatures were assumed to be from 600 K to 1,200 K.  
(5) Fire fractions were assumed to be from 0.0001 to 0.1.  
Finally, the apparent radiances of the MIR and TIR data of HJ-1B were generated by equations (1) and (2). MODTRAN 4 was used to obtain the atmospheric parameters in these two equations under various solar and atmospheric conditions which may provide a statistical evaluation of fire detection algorithm proposed in the next section. Standard atmospheric conditions which include Tropical, Mid-Latitude Summer, Mid-Latitude Winter and US Standard Atmosphere were adopted in the simulation.  
\[L(T_{3})=\tau_{3}\times\varepsilon_{3}\times p\times B(T_{\gamma},\lambda_{3}) +(1-p)\times L(T_{3_{b}})+p\times Latm,3 \tag{1}\]  
Figure 1: Retrieval of land surface emissivity and temperature (K) of HJ-1B from simulated AHS data, (a) land surface emissivity, (b) land surface temperature.  
\[L(T_{4})=\tau_{4}\times\varepsilon_{4}\times p\times B(T_{f},\lambda_{4})+(1-p) \times L(T_{4b})+p\times Latm,4 \tag{2}\]  
where, \(L(T_{3})\) and \(L(T_{4})\) are the TOA radiances of HJ-1B MIR and TIR channels respectively; \(\tau_{3}\) and \(\tau_{4}\) are the atmospheric transmittances calculated by MODTRAN \(4;\varepsilon_{3}\) and \(\varepsilon_{4}\) are channel emissivities of fire; \(p\) is the fraction of fire area; \(T_{f}\) is fire temperature simulated; \(\lambda\) is the center wavelength of each channel; \(B(T,\lambda)\) is the Planck function; \(L(T_{3b})\) and \(L(T_{4b})\) are background radiance; \(Latm,3\) and \(Latm,4\) are the upwelling atmospheric radiance obtained from MODTRAN 4. Because \(p\) and \(Latm,i\) (\(i\)=3, 4) are both small, the quantities of \(p\times Latm,3\) and \(p\times Latm,4\) are usually omitted [11]. The sensitivity analysis of each parameter can be found in literature [38].