# Potential of a SAR Small-Satellite Constellation for Rapid Monitoring of Flood Extent
## 3 Results
### Evaluation of Observation Performance  
Specific observation behavior offered by each constellation was already shown in Figures 4 and 5, but it is still difficult to judge whether each observation performance is sufficient or not in the context of flood disaster management. In order to evaluate this observation performance quantitatively in terms of the damage assessment in flood disasters, an original performance index was devised in this paper. This performance index was defined as the ratio of observed damage extent to damage extent in the final phase, and it was named the 'capture ratio.' The capture ratio describes how much area of damaged extent was acquired as a result of time series observation excluding overlapped information. The main reason why we defined this value as the performance index is that the capture ratio has its highest limit, which is 1 (= 100%). This limitation is crucial from the perspective of cost estimation in the practical implementation of SAR small-satellite constellation. The observation performance is generally improved as the number of satellites increases, but the larger number of satellites requires a more expensive cost. Therefore, it is difficult to determine the optimal condition of the constellation if the performance index is getting higher infinitely. For example, the total area of observed flood extent has no limitation, so it is not an appropriate indicator for the performance evaluation. On the other hand, the capture ratio (= observed damage extent/damage extent) must eventually reach its highest value. This is because observed damage extent consists of only the 1 st area, and the accumulation of the 2 nd > 6 th areas does not contribute to this flood damage assessment anymore. In short, the capture ratio is a performance index that simultaneously expresses the sufficiency and efficiency of observation and it provides the comprehensive result of flood damage assessment on a spatiotemporal scale. The calculation result of the capture ratio in case 1 and case 2 is presented in Table 3. Here, the result of one large satellite (\(T\) = 1) is also shown beside that of \(T\) = 8, 12, 20, 24, 28, 40, and 56. As can be seen from this table, the capture ratio usually grew higher as the number of \(T\) increased, but it varied with the number of \(P\) even under the same number of \(T\), and sometimes the smaller number of \(T\) has a better result for the capture ratio. This implies that the number of satellites (= \(T\)) is of course a dominant parameter that determines observation performance, but the configuration of satellite constellation (= \(T/P/F\)) should be also carefully selected. This performance index, the capture ratio, allows us to compare the result of multiple case studies. When we focus on the difference between case 1 and case 2, it can be seen that in case 1 more than 56 satellites are required to achieve 81% acquisition, while even 20 satellites accomplish 87% in case 2. This is considered to be mainly because of the characteristics of each flood event. In case 1, the peak flooding was happening in a short time, which means flood extent was expanding and shrinking quickly. Thus, if the observation timing was missed or the observed area was insufficient in that peak time, data acquisition would be difficult to recover. On the other hand, in case 2, the flood was gradually expanding and shrinking, so it was easier to capture most of the damage extent during that period. This result demonstrated that  
Figure 5: The virtual observation of the simulated flood extent with constellations of (**a**) \(T\) = 8, \(P\) = 4; (**b**) \(T\) = 8, \(P\) = 2; (**c**) \(T\) = 12, \(P\) = 6; (**d**) \(T\) = 12, \(P\) = 1; (**e**) \(T\) = 20, \(P\) = 10; (**f**) \(T\) = 20, \(P\) = 5; (**g**) \(T\) = 24, \(P\) = 12; (**h**) \(T\) = 24, \(P\) = 8; (**i**) \(T\) = 28, \(P\) = 4; (**j**) \(T\) = 28, \(P\) = 7; (**k**) \(T\) = 40, \(P\) = 20; (**l**) \(T\) = 40, \(P\) = 10; (**m**) \(T\) = 56, \(P\) = 8; (**n**) \(T\) = 56, \(P\) = 28 in case 2 (Typhoon No.