**5. Discussion**

Regarding the limitations of traditional urban flood analysis, lacking high-resolution rainfall records should be one of the primary issues [61]. Although many models and frameworks were proposed to solve this issue, many inherent limitations still exist [16,62]. Therefore, a modeling framework for urban flood analysis is introduced based on shortrecord rainfall from remote sensing, RainyDay, and urban hydrological model, which effectively overcomes the high-temporal-resolution and long-term rainfall requirements for urban flood analysis. It should be emphasized that this work does not seek to show the proposed framework better than the traditional methods, but rather to provide an alternative framework for urban flood analysis based on short-term remote sensing rainfall records, and discuss its feasibility and rationality.

The results of this study for design rainfall estimates are very similar to Wright et al. [27] , though simulated at a much smaller scale (0.155 km<sup>2</sup> vs. 4000 km2) based on a different time-space resolution (hourly vs. hourly, and 3 h; 0.1◦ grid vs. 4-km, and 0.25◦ grid) and length of rainfall records (nine-year vs. 13-year, and 17-year). These two studies show that the design rainfall is generally underestimated with remote sensing data at low return periods or short durations. The underestimation could be explained by the length of rainfall records and spatial resolution (nine-year and 0.1◦ grid for the remote sensing rainfall record vs. more than 20 years and approximately 0.1 m<sup>2</sup> for the rain gages) in this study. For short duration rainfall, temporal resampling using RainyDay is significantly affected by rainfall detection errors on bias correction and conditional biases [63–66]. Also, this can be attributed to the fundamental structure of RainyDay, i.e., the Poisson distribution is utilized in this study (see Kim and Onof [67] for discussion). Conversely, the slight overestimation of RainyDay-based estimates are showed at high return periods and long durations, but the overestimation is not as severely as the underestimation. This might potentially be attributed to conditional bias for rain rate [68] and the domain area including coastal areas where the typhoon landed. Some existed studies show that the accuracy of the estimates may be improved by higher temporal-spatial resolution remote sensing data, which can better address and understand some rainfall biases [27,69].

The main parts of this study include estimating design rainfall based on nine-year remote sensing rainfall and RainyDay, and revealing the relationship between design rainfall and runoff through hydrological model. Previous studies showed that the design rainfall can be well estimated by RainyDay at different scales (e.g., 14.3 km<sup>2</sup> in Zhou et al. [70], 4400 km<sup>2</sup> in Wright et al. [66]). Though the feasibility is shown varying from small to large scales, the limit on the size of study area can arise since the presence of complex terrain features. The reader is directed to Wright et al. [27] for more discussion. On the other hand, the selected hydrological model (i.e., SWMM) has been widely used for modeling rainfall-driven flood at different scales, especially for urban areas. The proposed modeling framework offers opportunities to analyze urban flooding based on short-record remote sensing rainfall and hydrologic model. However, the size of the case-study area is small, it may cannot represent all the urban flood conditions. We will continue to expand the capabilities of the proposed modeling framework.

Case study shows that the runoff process at the outlet of case-study area and the flood characteristics (i.e., flood time, maximum rate, total inundation volume) of each manhole can be simulated well at relatively high return periods (20-yr or higher) or long durations (6 h or longer) based on the selected rainfall record. But the flood characteristics are more sensitive to the return period and duration of design rainfall than runoff process. The main difference in the rainfall hydrographs between RainyDay-based and IDF formula-based is from the peak rainfall, which can significantly impact the flood characteristics.

Our findings indicate that the rainfall estimates play a key role in flood analysis, similar results are also showed in Peleg et al. [26]. That is, improving the accuracy of the rainfall estimates is the most important in the proposed framework. Lots of studies indicated that rainfall estimates based on historical rainfall records might not be appropriate due to climate change [71]. Doing so would require higher-resolution remote sensing rainfall data and considering climate change [27,70,71]. We are developing frameworks for considering both rainfall space-time structure and climate change based on Regional Climate Model (RCM) simulations for RainyDay-based rainfall estimates.

Despite the proposed framework overcomes some drawbacks (e.g., rainfall records) of traditional approaches for urban flood analysis, there still remain several limitations. (i) Applicability of the proposed framework is insufficient for low return period or short duration rainfall scenarios. The undervaluation of design rainfall and urban flood characteristics are generally showed at these scenarios. The main reason is mentioned above, and the applicability can be improved by utilizing higher resolution and longer rainfall records [70,72]. (ii) The uncertainties from the rainfall data and RainyDay are hard to minimize, which have direct impacts in design rainfall estimates and urban flood analysis. The dominant uncertainty in the input rainfall data comes from the difference between remote sensing rainfall data and ground-based observations [27,73]; and the uncertainty in Rainyday comes from the input requirements (e.g., geographic transposition domain, rainfall record) and its structure [70]. (iii) The proposed framework uses idealized assumption (i.e., Chicago rainfall pattern) to determine the distributions of design rainfall. That is consistent with the guidelines of design rainfall [46]. On the other hand, the rainfall temporal resolution of remote sensing records is general coarser than 30-min. Comparing the relationships between RainyDay-based and IDF formula-based analysis results sugges<sup>t</sup> that the proposed framework is an applicable way for analyzing urban flooding at high return periods (20-yr or higher) or long durations (6 h or longer). Though limitations still remain, we continue to develop its capabilities.
