## 4. Discussion
### Statistical Models  
In recent years, the development of joint probability models among flood-driving factors has progressed rapidly, becoming the main statistical modeling method for compound flood research under climate change. The Copula model, a function that connects multidimensional joint distributions with their marginal distributions, overcomes the limitations of classical multivariate statistical models by allowing independent consideration of the marginal distribution and correlation of random variables. It has become the most widely used model for analyzing compound flood drivers [93]. Table 5 presents recent applications of joint distribution models in compound flood research under climate change over the past five years. From Table 5, it can be observed that current research mainly focuses on the superposition of two compound flood driving factors under climate change, such as sea level rise and extreme river floods, or rainfall and storm surges.  
Due to the challenges in expressing and computing three-dimensional joint probability models, research on the interaction of three or more driving factors remains limited. For example, [PERSON] and [PERSON] (2023) [94] analyzed the dependence structures among three primary flood drivers (precipitation, streamflow, and total water level) across different locations using copula functions. The results indicate that multivariate analysis under climate change can evaluate the flood return period and economic losses more accurately than univariate scenarios. Despite its complexity, analyzing multi-factor compound floods driven by climate change is a promising area for future research.  
The study of statistical models for compound floods primarily relies on the assumption of consistency in flood frequency and intensity distribution between historical and future flood patterns, as well as across different locations. However, global climate change and urbanization have led to more frequent extreme climate events, challenging the feasibility of hydrological risk analysis based on these consistency assumptions for precipitation, runoff, and tide levels [101]. [PERSON] et al. (2020) [102] found that even a slight rise in sea level can significantly impact the frequency of coastal floods. [PERSON] et al. (2021) [96] applied a time-varying copula model and observed a decrease in the AND return period (RP) of sea level and streamflow from 2020 to 2050. The study by [PERSON] and [PERSON] (2023) [94] showed that the return period of compound floods along the Atlantic coast decreased from 50 years in 1960 to 19 years in 2015. In summary, time-varying copula models better capture the dependence structure of flood magnitudes compared to stationary copula models, underscoring the need for non-stationary models in hazard analyses of compound floods under climate change scenarios [103].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Study Area** & **Study Objective** & **Statistical Model** \\ \hline [PERSON] et al. [95] & Northwestern Europe & High coastal water levels and river peaks & Copula \\  & compound flood & & Copula \\ [PERSON] et al. [96] & U.S. Coasts & SLR and changes in extreme river flows & \\  & compound flood & Copula \\ [PERSON] et al. [93] & Haikou, China & Precipitation and storm tides compound flood & Copula \\ [PERSON] et al. [97] & Venice, Italy & Storm surge and SLR compound flood & Copula \\ [PERSON] et al. [98] & New York, US & Precipitation and extreme sea level & Copula \\ [PERSON] and [PERSON] [99] & US coastlines & compound flood & Copula \\ [PERSON] et al. [100] & Haikou, China & Sea level rise (SLR) and future rainfall & \\ [PERSON] and [PERSON] [94] & Canada’s coastal zones & & Changes compound flood of precipitation, streamflow, and total water level & Vine copula \\ \hline \hline \end{tabular}
\end{table}
Table 5: Case studies of compound flood joint distribution model under climate change.