## 5 Results and analysis  
The performance of the fire detection algorithm can be evaluated using of the probabilities of successful detection and the probabilities of false alarms (i.e. commission error). It is evident that the higher probability of fire detection and the lower probability of false alarms, the better performance of the algorithm. Here the probability of fire detection is defined as the ratio between the true fire pixels which can be detected by the algorithm and the total number of fire pixels simulated. Four different solar zenith angles, 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\) and 60\({}^{\circ}\) were considered under US Standard Atmospheric conditions in the simulation (Figure 5). It can be found that the probability of fire detection will be greatly affected by fire temperature and fire area. Solar zenith angle can also slightly affect the performance of algorithm  
Figure 4: The flow chart of fire detection. if the background temperature had not changed. In fact, if we consider the diurnal variation of temperature, a fire may be easier to be detected in nighttime or when the solar elevation is low. This is because the temperature difference between a fire pixel and its neighborhood in MIR channel is relative large. It is clear from the simulation results that the contextual algorithm exhibits a good performance for the larger/hotter fires detection under standard atmospheric conditions. It also can be seen from Figure 5 that when the simulated fire area is larger than 45 m\({}^{2}\) and the simulated fire temperature is larger than 800 K, the algorithm has a higher probability of detection. But if the fire area is smaller than 10 m\({}^{2}\), only when the fire temperature is larger than 900 K may the fire be detected. Figure 5: Probabilities of fire detection in nadir view for different fire area (m\({}^{2}\)) and temperature (K) under US standard atmospheric conditions with a visibility of 23 km. The solar zenith angles are 0, 30, 45 and 60 degree for (a), (b), (c) and (d), respectively. The probabilities of fire detection in nadir view for different fire areas and temperatures under three standard atmospheric conditions are shown in Figure 6. It can be found that different atmospheric conditions can also slightly affect the results of fire detection only when the fire temperature and fire area are small. As in Figure 5, from Figure 6 it is also evident that with the increase of the fire area and fire temperature, the probability of fire detection increases quickly. When a fire area is smaller than 9 m\({}^{2}\) and fire temperature is less than 800 K, the probability of detection is zero, i.e. fires cannot be detected under these conditions. But with an increasing in fire area, such as a 45 m\({}^{2}\) fire area and about 800 K temperature, the probability of fire detection is about 95%. The omission pixels are defined as the pixels including fire, but which cannot be detected using the algorithm. The omission error is equal to the difference between one hundred percent and probability of fire detection [28]. The results of omission errors shown in Figure 7 are the difference  
Figure 6: Probabilities of fire detection in nadir view for different fire areas (m\({}^{2}\)) and temperatures (K) under standard atmospheric conditions with a visibility of 23 km; (a) tropical; (b) midwenter; (c) midsummer. between 100 percent and the detection probability shown in Figure 5. Omission errors will occur when the fire area and fire temperature are small. This may also happen when many fire pixels assemble and form a \"cluster\". Because the temperatures of all neighboring pixels are high and homogeneous in this \"cluster\", a pixel with a lower temperature can be misidentified as a non-fire pixel. Another reason is the high thresholds. Higher thresholds can lead the higher omission errors, while lower thresholds can cause the higher commission errors.