\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,english]{babel}



\usepackage{float}








\begin{document}

\title{Evaluating the effect of building patterns on urban flooding based on a
boosted regression tree: a case study of Beijing, China}



\author[1]{Zhen Li}%
\author[1]{Zhuowei Wang}%
\author[1]{Leixiang Wu}%
\author[1]{Wei Huang}%
\author[1]{Wenqi Peng}%
\affil[1]{China Institute of Water Resources and Hydropower Research}%


\vspace{-1em}



  
  \date{May 18, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Rapid urbanization and global climate change are likely to exacerbate
urban flooding intensity, frequency, and uncertainty. Thus, it is
fundamental and crucial to investigate the dominant influencing factors
for the mitigation of urban flooding. However, the influence of building
patterns on urban flooding remains limited. Taking Beijing, a typical
megacity, as a case study area, we quantified the importance of building
patterns and their interaction effect at the subwatershed scale using
the boosted regression tree (BRT) and geographical detector model
(GeoD). The results indicated that (1) the landscape shape index, slope,
green space ratio and waterbody ratio were the most important
influencing factors determining urban flooding, with a total relative
contribution of 67.23\%, (2) building metrics had a certain impact on
urban flooding, and the sum of the relative contribution can reach
21.03\%, (3) with urban flooding density, the landscape shape index,
slope, and green space ratio exhibited a combination of negative and
positive correlation, and (4) an enhancement effect existed between
building metrics, especially the building congestion degree and building
density. These findings provide quantitative insights that rational
urban morphology planning can improve stormwater management and promote
urban sustainability in megacities.%
\end{abstract}%



\sloppy


\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{1. INTRODUCTION}

Along with rapid urbanization, the proportion of world urban residents
is expected to increase from 56.2\% in 2020 to 67.2\% in 2050 (DESA,
2018). It was estimated that global urban landscape area has increased
by 19.1 million hm\textsuperscript{2} between 1985--2015, and
approximately 70\% of the newly urban landscape witnesses in Asia and
North America (Liu et al., 2020). Unprecedented rate of global
urbanization, whose most significant feature is the natural and semi
natural surface being replaced by the impervious surface, causes a
series of ecological challenges, such as urban flooding, urban heat
islands, air pollution, and loss in natural habitat (Kulmala et al.,
2020; Oke et al., 2017; Grimm et al., 2008; Foley et al., 2005). Urban
flooding, refers to the fact that the heavy rainfalls overwhelm the
capacity of self absorption and drainage pipelines drainage. Urban
flooding causes great economic losses, and even kills the urban dwellers
(Rentschler et al., 2022; Paprotny et al., 2018). It was reported that
more than half of the world's population was affected by flooding from
2010 to 2019. China suffered from the flooding with 400 events
contemporaneous. Meanwhile, global warming is likely to exacerbate urban
flooding risks (Touma et al., 2022; Debele et al., 2019). Thus, how to
reduce urban flood loss is of great significance to urban
sustainability. Fortunately, a series of practices have been conducted,
such as ``best management practices'', ``low impact development'', and
``sponge city construction'' (Davis et al., 2005).

Urban flooding has attracted more and more attention for its frequent
occurrence and severe damage (Kim et al., 2022; Lin et al., 2022; Ma et
al., 2022; Chen et al., 2021; Sun et al., 2021; Yang et al., 2021;
Paprotny et al., 2018). Previous related studies have tended to reveal
urban hydrological mechanism by adopting field investigations,
laboratory modeling and urban hydrological modeling (Ma et al., 2022;
Shrestha et al., 2022; Li et al., 2022; Muthusamy et al., 2021). Among
these, a comprehensive understanding of the spatial--temporal patterns
of urban flooding and its most influencing factors was vital and
fundamental (Steinhausen et al., 2022; Li et al., 2022). Urban flooding
events were significantly clustered and mainly distributed in the
central urban area (Li et al., 2022; Zhang et al., 2020). The
distribution pattern of urban flooding events can be caused by
topographic conditions (i.e., elevation, slope, roughness, and
microtopography), rainfall intensity, land cover composition and
configuration, stormwater storages, and drainage systems (Hettiarachchi
et al., 2022; Li et al., 2022; Wang et al., 2022; Dumedah et al., 2021;
Liang et al., 2021). For example, Tehrany et al. (2019) found that
elevation was significantly impacted urban flooding in small catchments.
When the digital elevation model resolution increased from 50 m to 1 m,
flooding extent and mean flood depth decreased by 30\% and 150\%,
respectively (Muthusamy et al., 2021). However, it is difficult to alter
topographic and heavy rainfall, so more and more researches seek to
mitigate urban flooding through rational urban planning. On the one
hand, an improvement in urban drainage system was beneficial to manage
urban runoff. On the other hand, optimal blue--green--grey spaces were
also important to alter urban hydrological process and reduce flooding
risks.

Numerous studies have shown that land cover and land configuration have
direct effects on urban flooding in the horizontal (Hettiarachchi et
al., 2022; Wang et al., 2022; Li et al., 2020). However, fewer studies
have investigated the impact of buildings on urban flooding in the
vertical dimensions (i.e., building height and its heterogeneity).
Although buildings and roads may have roughly the same permeable
capacity, their roles in regulating urban runoff can vary greatly (Cao
et al., 2021). Specifically, building height and building coverage ratio
alter runoff generation time. Building facades increase the surface
contact with raindrops and thus decrease runoff. In addition, the
interaction effect of building and its surrounding miniature garden has
direct effects on the ground runoff. Furthermore, buildings alter its
surrounding microclimate, which has direct or indirect effect on soil
moisture and evapotranspiration. Thus, three-dimensional building
pattern might change the local hydrological process. Lin et al. (2021)
noted that adding building metrics can better explain the probability of
flooding occurrence in Shenzhen, especially the building coverage ratio.

A large number of three-dimensional building metrics have been developed
to comprehensively characterize building patterns (Kedron et al., 2019;
Liu et al., 2017). A series of studies further explored the relationship
between three-dimensional building pattern and land surface
temperature/air temperature, air pollution. However, the effect of 2D/3D
building patterns on urban flooding remains unclear. We attempt to
address the following two questions: (1) how urban flooding events
affected by 2D/3D building patterns in megacies? And (2) does an
enhancement effect exist between 3D building metrics? Addressing these
questions can promote our further understanding on the role of buildings
in urban flooding. Such understanding can provide insights for urban
flooding mitigation.

\textbf{2. DATA AND METHODS}

\textbf{2.1} \textbf{Study area}

Beijing (115\selectlanguage{ngerman}°25\selectlanguage{english}'-117deg30\selectlanguage{english}' E, 39deg28\selectlanguage{english}'-41deg05\selectlanguage{english}' N), a typical megacity, is
located in northern of North China Plain (Fig.1). It covers an area of
16.4 thousand km\textsuperscript{2}. The climate of Beijing belongs to
temperature continental monsoon climate. The annual precipitation is 600
mm, and 80\% of precipitation is concentrated in summer. The western and
northern of the study area lie on mountains, and the central city lies
largely on flat land. The main rivers are the Yongding River, Chaobai
River, Jvma River, Beiyun River, and Jiyun River. Beijing has witnessed
rapid urban sprawl in the horizontal and vertical dimensions since the
reform and ``opening up'' policy. The urban built-up area increased 3130
km\textsuperscript{2} from 1980 to 2018 (Yin et al., 2021). The oldest
part of the city is mainly composed of ancient buildings with low
building height within the second ring road, such as Sihe yuan. In 2020,
more than 25 buildings were taller than 200 m. Beijing has undergone
serious urban flooding. Although a large-scale drainage system was
constructed, the city still faces the challenge of frequent urban
flooding. For example, 79 people were killed and more than \$1.6 billion
were lost in Beijing on July 21, 2012. With the renewal of drainage
facilities and the development of sponge city construction, a heavy
rainstorm caused 37 road collapses within the whole city on July 16,
2018. Based on previous studies (Liu et al., 2022), highly urbanized
areas are the most vulnerable area to flooding. Therefore, it is still
necessary to mitigation flooding risks through urban planning and
management in highly urbanized areas.

\textbf{2.2} \textbf{Data sources}

A total of 139 flood points from 2011 to 2021 were collected from the
Water Resources Bureau of Beijing (Table 1). However, the available data
only provide the address of the urban flooding events without accurate
coordinates. Thus, we first vectorized these positions according to the
occurrence types. When the urban flooding event occurred on the road, we
determined the geometric center of the road as the position following
the method recommended by Zhang et al. (2018) (Fig.2). Building
footprint and floor number information in 2017 were collected from Baidu
Maps (map.baidu.com) (Table 1). By referring to the Gaofen-1 image
(chromatic sensor with 2 m resolution), the location of the buildings is
highly accurate. The building floor height was set 3 m through the
building design regulations. The overall accuracy of building height was
beyond 85\% according to field surveys, which is satisfying. The digital
elevation model (DEM) with a resolution of 12.5 m was acquired from
https://search.asf.alaska.edu/. The land use data in 2020 with a
resolution of 10 m was produced by European Space Agency (ESA)
(https://viewer.esa-worldcover.org/worldcover) (Fig.2). Then, the land
use types were integrated into four categories: impervious surface,
green space, waterbody, and farmland. The landscape indices were
calculated by Fragstats 4.2 based on the land use data. In addition,
other potential explanatory factors of rainfall and drainage capacities
were utilized as independent variables to explain the urban flooding (Li
et al., 2022). The average rainfall was calculated by the annual
precipitation data obtained from the National Earth System Science Data
Center (http://www.geodata.cn/). Due to lack of drainage system,
distances to river and road density were used to represent urban
drainage capacity (Li et al., 2022). The river data and road data were
acquired from the National Geomatics Center of China (http://www.
ngcc.cn/).

\textbf{2.3} \textbf{Subwatershed unit}

Urban hydrology has complex natural-artificial features. Urban flooding
was closely related to the watershed surface characteristics, such as
topography, land cover and land configuration. Thus, it is suitable to
explore the relationship between urban flooding and explanatory factors
from the perspective of the subwatershed unit in considering urban
hydrological processes. Previous studies have proposed the concept frame
of ``watershed-land'' in the field of urban hydro-ecology, fully
considering the hydrological watershed unit and easy connection with
urban planning (Yu et al., 2018). Following the method recommended by Yu
et al. (2018), the DEM data was utilized to divide the subwatershed
units using the D8 algorithm. Finally, the study area was divided into
130 subwatershed units with an average area of 15.7
km\textsuperscript{2} (Fig.1).

\textbf{2.4} \textbf{Subwatershed unit}

Local Morman's index in ArcGIS 10.3 was used to identify the
distribution patterns of urban flooding points. The cluster types can be
mainly divided into high-high agglomeration, low-low agglomeration,
high-low agglomeration, and low-high agglomeration. The formula is as
follows:

\begin{equation}
I=n\times\frac{(x_{i}-\overset{\overline{}}{x})\times\sum W_{\text{ij}}(x_{i}-\overset{\overline{}}{x})}{\sum{(x_{i}-\overset{\overline{}}{x}\ )}^{2}}\nonumber \\
 \end{equation}

Where, \(I\) is the local Morman's index;
\(x_{i}\) and\(\overset{\overline{}}{x}\) are the observation and the
average of all observations, respectively.

\textbf{2.5} \textbf{Landscape metrics}

Numerous landscape metrics have been developed to measure landscape
composition and configuration. Considering the ecological meaning and
previous researches (Li et al., 2022a; Lin et al., 2021), five landscape
metrics were selected, including: percentage of green space, percentage
of water body, percentage of impervious surfaces, patch density, and
landscape shape index (Table 2). For the three-dimensional building
metrics, we adopted the building coverage ratio (BCR), building density
(BD), building congestion degree (BCD), building height (BH), floor area
ratio (FAR), 3D shape index (3DSI), and 3D fractals (3DF). The BCR, BH,
and FAR were the most commonly adopted indicators in urban planning (Liu
et al., 2021). 3DSI and 3DF were comprehensive indicators, which were
based on the surface area and volume of buildings.

\textbf{2.6} \textbf{The boosted regression tree (BRT) analysis}

The density of flooding hotspots was chosen as the response variable.
First, we conducted Pearson correlation analysis to examine the
relationship between the density of flooding hotspots and the
explanatory factors. Before BRT analysis, Pearson correlation analysis
was conducted between the explanatory factors. Pearson correlation
analysis was effective to exclude multicollinearity between explanatory
factors. Pearson correlation coefficient ranges from -1 to 1, indicating
a positive/negative relationship and the strength.

The BRT has been widely applied in land science and urban heat island
researches in recent years for its superior performance in explaining
the complex relationship between response variable and explanatory
factors (Sun et al., 2020; Elith et al., 2008). A BRT uses recursive
binary splitting to generate a regression tree algorithm and then uses
boosting to obtain the nonlinear relationship between the response and
its predictor variables. When the correlation coefficient between two
explanatory factors was [?]0.7, one of the predictor variable was removed.
Finally, the percentage of impervious surface, population density, and
floor area ratio were removed. Additionally, the BRT model also outputs
partial dependency plots, which can concisely explain the marginal
effects of the explanatory factors. The marginal effects represent the
potential impact of the specific factor with other explanatory factors
holds constant. With the BRTs, the contributions of the selected
indicator were determined by the coefficients. The sum of the relative
contribution was 100\%. Development of the BRT models was based on dismo
package of the R software. The main parameters of the BRT were set to
0.0001 (learning rate), 0.6 (bag fraction), 10 (tree complexity), and
10-fold cross validation.

\textbf{2.7} \textbf{Geographical detector model}

The geographical detector model (GeoD) could identify the interactive
effect between variables, which is a spatial analysis model based on the
theory of spatial heterogeneity (Song et al., 2020). It assesses the
strength of association between two variables by comparing the
association which is definited as ?, which ranging from 0 to 1. A large
value in ?, indicates the explanatory power is stronger. The formula is
as follows:

\begin{equation}
q=1-\frac{1}{N\sigma^{2}}\sum_{h=1}^{L}{N_{h}\sigma_{h}^{2}}\nonumber \\
 \end{equation}

Where, \(\sigma^{2}\ \)is the variance of the response variables; ? is
the number of category of the response variables; 1\ldots{}\ldots{}? is
the study population of the response variables.

The ? (?1\(\cap\)?2), which represents the interaction between
the factors (?1, ?2 \ldots{} ), can be calculated by the interaction
detector. The interaction effect can be divided into 5 categories,
including: independent, nonlinear weaken (NW), nonlinear enhancement
(NE), single-factor nonlinear weaken (SNW), double-factor enhancement
(DE), and independent (I) (Yan et al., 2021). Additionally, the model
requires category variables. Here, K-means method is used to convert the
response and explanatory variables into category variables. Development
of the GeoD models was based on the R-software, ``GD 1.10'' package.

\textbf{3. RESULTS}

\textbf{3.1 Distribution patterns of urban flooding points}

From 2011 to 2021, urban flooding points were mainly of the districts
Haidian and Fengtai (Fig.3). The low-density area of urban flooding
points was mainly distributed in the edge of the study area.
Interestingly, the historic districts of Beijing, such as Dongcheng and
Xicheng districts, had fewer flooding points. Results of Local Morans I
showed that the urban flooding hot spots were obvious (Fig.3). The hot
spots were mainly distributed in Haidian and Fengtai districts, while
cold spots were small and aggregated in northeast of the study area and
dispersed in the southeastern part of the study area.

\textbf{3.2 Relative contributions of driving forces to urban flooding}

Based on the two fitted BRT models (one for considering the driving
forces without buildings, and another for considering all driving
forces), the relative contributions of the explanatory factors to the
urban flooding across the study area are presented in Fig. 4. The
results indicate that landscape shape index, slope, green space ratio,
and waterbody ratio play dominant roles in influencing the density of
flooding hotspots, with total relative contributions reach at 82.36\% in
model without considering the buildings. Specifically, the relative
contributions of landscape shape index, slope, green space ratio, and
waterbody ratio are 38.19\%, 25.5\%, 11.13\%, and 7.54\%, respectively.
The results are robust in model with considering all driving forces.
However, we found that building metrics play a certain role, with total
contributions is 21.03\%. Among these building metrics, the relative
contributions of the building congestion degree, building density, 3D
shape index, and building coverage ratio exceed 3.76\%. For the category
levels, land cover configuration has the largest relative contribution
(33.69\%), whereas the drainage capacity has the least importance
(3.87\%). The importance of the topography, land cover composition, and
3D building morphology are nearly equal.

\textbf{3.3 Relative contributions of driving forces to urban flooding}

The marginal effects of the six most important driving forces are shown
in Fig. 5. With urban flooding density, the landscape shape index is
complex, with a positive correlation ranging from 2.5 to 2.8 and a
negative correlation ranging from 2.8 to 3.1. The slope shows a stepwise
positive correlation with urban flooding density. As the green space
ratio increased from 20\% to 28\%, the urban flooding density decreased
from 0.010 to 0.005. The urban flooding density varies from 0 to 0.005
when the building congestion degree increases from 0.02 to 0.03.
Building density experiences an initial increase and then stabilizes and
finally drops.

\textbf{3.4 Interactive effect between 3D building metrics}

Among the building metrics, the GeoD factor detector demonstrated that
three-dimensional fractal was the most influential factors, followed by
building density (q = 0.186) and building congestion degree (0.176),
then building height (0.153) (Table 3). The results were inconsistent
with BRT analysis results, which also suggested occlusion effects in BRT
model.

The GeoD interaction detector indicated that enhancement effect exist
between building metrics. The interaction effect of building congestion
degree with building density (BCD\(\ \cap\ \)BD) was greater than
that from the two sub-factors individually. Here, `\(\cap\)'
represents interactions. These finding indicated that the occurrence of
urban flooding would be increased when the building congestion degree
included building density. For building coverage ratio and building
height, the interaction effect was double-factor enhancement, which
suggested urban flooding risks would be enhanced when building coverage
ratio included building height. The interaction effect was nonlinear
between building height and three-dimensional fractal. It means that the
explanatory power of the GD model would not increase when adding both
into the model.

\textbf{4. DISCUSSION}

\textbf{4.1 Influencing factors}

Urban hydrological processes have altered with urban development, and
thus distribution pattern of flooding points has changed (Chang et al.,
2021; Zhao et al., 2014). In this study, we integrated a series of
driving factors (i.e., topography, building metrics) and identified the
major driving factors of urban flooding by adopting BRT method. The
reasons for urban flooding are complex, including natural and
anthropogenic factors. Through BRT analysis, land cover configuration
has the greatest impact on flooding. The fragmentation of green spaces
would increase occurrence of urban flooding events on a given land cover
composition (Zhang et al., 2020). Higher fragmentation at landscape
level might lead to serious urban flooding, and its role varied across
different megacities in China (Li et al., 2022). In our study, it
suggests that the optimal landscape shape index was nearly 2.8. The
results were not consistent with previous studies, the difference was
caused by the response variable selected, explanatory factors selected,
analysis units, and analysis methods. Similarly, contribution of patch
density was only 2.54\%, which reflects the patch density was not
important.

Through BRT analysis, land cover composition has important impact on
flooding. Increasing the green space and waterbody could mitigate the
flooding risks. It was also suggested that increase the impervious
surfaces would be inevitably increase urban flooding risks. This is
attributed to large difference between impervious surfaces and
green-blue space (green space and waterbody). Specifically, it is
difficult for waterflow to penetrate into the impervious surfaces.
Additionally, less surface roughness of the impervious surface promotes
rainwater flow and accumulation. On the contrary, urban green space can
reduce runoff and regulate rainwater storage. This finding is consistent
with case study in other cities (Zhang et al., 2020). Zhang et al.
(2020) found that land composition plays a dominant role in determining
urban floods with analysis scale range from 1 km to 5 km in metropolitan
coastal cities of Guangzhou, China (Zhang et al., 2020).

Fewer studies explored the impact of the building metrics on urban
flooding, and the importance of building has not yet been agreed. For
example, Lin et al. (2022) found that 3D building metrics exert the
greatest influence on urban flooding. Li et al. (2022) revealed 3D
building metrics had slight impact on urban flooding. Our results
suggested that 3D building morphology played an important role in urban
flooding, and the contribution of 3D building morphology was equal to
that of land cover composition. In fact, contributions of building
congestion degree and building density reached at 6.35\% and 4.81\%,
respectively. However, the current study also found that the importance
of three-dimensional fractal and building height was relatively low? The
possible reason was that green space is correlated with impervious
surfaces, and impervious surfaces is highly correlated with building
coverage ratio. Meanwhile, buildings with higher three-dimensional
fractal generally occupy larger base area and taller building height.
The green space, building height, and 3D fractal had occlusion effects
on urban flooding and thereby the importance of building coverage ratio
and building height became weaker.

\textbf{4.2 Interaction effect between 3D landscape metrics}

Although numerous studies conduct multivariate analysis in urban
flooding by using traditional statistical methods (i.e., pearson
correlation, logistic regression, partial least squares, structural
equation model) or machine learning method (i.e., random forest), fewer
studies explore the interaction effect among explanatory factors (Ma et
al., 2022). Urban morphology was complex and high heterogeneous,
especially in the vertical direction. Existing 3D landscape metrics was
still insufficient to analysis the urban canopy. Thus, it was necessary
to explore the interaction effect among 3D landscape metrics. For
example, more and aggregation impervious surfaces tend to rise the land
surface temperature in urban heat island field. However, high-rise
building can mitigate heat island effect through improve surface
roughness and cast more shadows (Sun et al., 2020). How to simultaneous
adjust the impervious surfaces and building height became vital to
alleviate heat island. In our study, we revealed that enhancement effect
exist between 3D building metrics. In particularly, when the 3D fractal
as an given value, it is important to reduce 3D shape index to avoid
urban flooding risks.

\textbf{4.3 Urban planning implications}

Our results can provide guidance to optimize urban morphology for urban
flooding risk management. This study emphasize that land cover
configuration was the dominant factor influencing the urban flooding.
Therefore, it is necessary and important to properly allocate urban
components (e.g., impervious surfaces, green space, and waterbody). As
terms of the land use cover, with urban green space decreased and
fragmented, rainwater runoff reduction rate decreased from 23\% to 17\%
during the period 2000 to 2010 in Beijing (Zhang et al., 2015).
Decreasing impervious surfaces and increasing urban green-blue spaces
were beneficial for mitigating the urban flooding risks dramatically.

3D building patterns also have a certain impact on urban flooding. It is
a good choice to control the floor area ratio under given 3D fractal. In
generally, urban planners restrict building height strictly in Beijing.
Buildings induced rainfall redistribution is expected to increase the
peak flow and become more important with the increase of rainfall
intensity (Cao et al., 2021). Thus, slowing down the building coverage
ratio became another choice. In practice, green roofs were beneficial
for urban stormwater regulation, and the runoff mitigation capacity
varied with the spatial variability of green roofs and greening on
effective roof surfaces in small urbanized catchments in Beijing (Yao et
al., 2020). Additionally, 3D building landscape alters microclimate and
changes rainfall pattern.

\textbf{4.4 Limitations and future research}

There are some limitations in this study. When exploring the impact of
urbanization on hydrological process, it is best to conduct research on
the watershed level. This study only involved one single city (the
developed urban areas), it needs to validate the results in other
similar areas. Owing to coarse time resolution of urban flood records
(2011--2021), we cannot accurately assess the relationship between the
position of flooding events and rainfall intensity. Additionally, the
amount and depth of flooding were unavailable, and thus hinder further
comprehensively understanding the relationship between urban flood and
its explanatory factors. Despite these limitations, this study provided
quantitative insight into the nonlinear relationship and magnitude
between the 3D building morphology and urban flooding.

\textbf{5. CONCLUSIONS}

This study identified the dominant influencing factors of urban flooding
by integrating series driving forces (topography, drainage capacity,
land cover composition, landscape configuration, building patterns) by
adopting BRT model. Moreover, we further revealed the interaction
effects among building metrics in Beijing's central area by using GD
method. The urban flooding points present a aggregation pattern, and was
mainly concentrated in Haidian and Fengtai districts. The landscape
shape index, slope, green space ratio, and waterbody ratio were the most
important factors affecting urban flooding, with total relative
contribution of 67.23. Building metrics has a certain impact on urban
flooding, and sum of relative contribution can reach at 21.03\%.
Anymore, enhancement effect exist between building metrics, especially
the building congestion degree and building density. The results also
demonstrated the occlusion effects in BRT model. This study provides
practical suggestions to improve stormwater management via optimizing
urban morphology in 2D and 3D.

\textbf{ACKNOWLEDGEMENTS}

This work was supported by the National Natural Science Foundation of
China (No. 51879279).

\textbf{REFERENCES}

Cao, X., Qi, Y., Ni, G., 2021, Significant Impacts of Rainfall
Redistribution through the Roof of Buildings on Urban
Hydrology,\emph{Journal of Hydrometeorology} \textbf{22} (4)\textbf{:}
1007-1023. https://dx.doi.org/10.1175/jhm-d-20-0220.1

Chang, C., Li, Y., Chen, Y., Huang, J. J., Zhang, Y., 2021, Advanced
statistical analyses of urbanization impacts on heavy rainfall in the
Beijing metropolitan area, \emph{Urban Climate} \textbf{40} .
https://dx.doi.org/10.1016/j.uclim.2021.100987

Chen, X., Zhang, H., Chen, W., Huang, G., 2021, Urbanization and climate
change impacts on future flood risk in the Pearl River Delta under
shared socioeconomic pathways, \emph{Science of the Total
Environment}\textbf{762} .
https://dx.doi.org/10.1016/j.scitotenv.2020.143144

Davis, A. P., 2005, Green engineering principles promote low-impact
development, \emph{Environmental Science \& Technology}\textbf{39}
(16)\textbf{:} 338A-344A. https://dx.doi.org/10.1021/es053327e

Debele, S. E., Kumar, P., Sahani, J., Marti-Cardona, B., Mickovski, S.
B., Leo, L. S., Porcu, F., Bertini, F., Montesi, D., Vojinovic, Z., Di
Sabatino, S., 2019, Nature-based solutions for hydro-meteorological
hazards: Revised concepts, classification schemes and
databases,\emph{Environmental Research} \textbf{179} .
https://dx.doi.org/10.1016/j.envres.2019.108799

DESA, U., 2018, World Urbanisation Prospects, 2018
Revision,\emph{Retrieved from New York} .

Dumedah, G., Andam-Akorful, S. A., Ampofo, S. T., Abugri, I., 2021,
Characterizing urban morphology types for surface runoff estimation in
the Oforikrom Municipality of Ghana, \emph{Journal of Hydrology-Regional
Studies} \textbf{34} . https://dx.doi.org/10.1016/j.ejrh.2021.100796

Elith, J., Leathwick, J. R., Hastie, T., 2008, A working guide to
boosted regression trees, \emph{Journal of Animal Ecology}\textbf{77}
(4)\textbf{:} 802-813.
https://dx.doi.org/10.1111/j.1365-2656.2008.01390.x

Foley, J. A., DeFries, R., Asner, G. P., Barford, C., Bonan, G.,
Carpenter, S. R., Chapin, F. S., Coe, M. T., Daily, G. C., Gibbs, H. K.,
Helkowski, J. H., Holloway, T., Howard, E. A., Kucharik, C. J.,
Monfreda, C., Patz, J. A., Prentice, I. C., Ramankutty, N., Snyder, P.
K., 2005, Global consequences of land use, \emph{Science}\textbf{309}
(5734)\textbf{:} 570-574. https://dx.doi.org/10.1126/science.1111772

Grimm, N. B., Faeth, S. H., Golubiewski, N. E., Redman, C. L., Wu, J.,
Bai, X., Briggs, J. M., 2008, Global change and the ecology of
cities,\emph{Science} \textbf{319} (5864)\textbf{:} 756-760.
https://dx.doi.org/10.1126/science.1150195

Hettiarachchi, S., Wasko, C., Sharma, A., 2022, Rethinking urban storm
water management through resilience - The case for using green
infrastructure in our warming world, \emph{Cities} \textbf{128} .
https://dx.doi.org/10.1016/j.cities.2022.103789

Kedron, P., Zhao, Y., Frazier, A. E., 2019, Three dimensional (3D)
spatial metrics for objects, \emph{Landscape Ecology}\textbf{34}
(9)\textbf{:} 2123-2132. https://dx.doi.org/10.1007/s10980-019-00861-4

Kim, J., Lee, J., Hwang, S., Kang, J., 2022, Urban flood adaptation and
optimization for net-zero: Case study of Dongjak-gu, Seoul,\emph{Journal
of Hydrology-Regional Studies} \textbf{41} .
https://dx.doi.org/10.1016/j.ejrh.2022.101110

Kulmala, M., Kokkonen, T. V., Pekkanen, J., Paatero, S., Petaja, T.,
Kerminen, V.-M., Ding, A., 2021, Opinion: Gigacity - a source of
problems or the new way to sustainable development, \emph{Atmospheric
Chemistry and Physics} \textbf{21} (10)\textbf{:} 8313-8322.
https://dx.doi.org/10.5194/acp-21-8313-2021

Li, C., Liu, M., Hu, Y., Wang, H., Zhou, R., Wu, W., Wang, Y., 2022a,
Spatial distribution patterns and potential exposure risks of urban
floods in Chinese megacities, \emph{Journal of Hydrology} \textbf{610} .
https://dx.doi.org/10.1016/j.jhydrol.2022.127838

Li, L., Uyttenhove, P., Vaneetvelde, V., 2020, Planning green
infrastructure to mitigate urban surface water flooding risk - A
methodology to identify priority areas applied in the city of
Ghent,\emph{Landscape and Urban Planning} \textbf{194} .
https://dx.doi.org/10.1016/j.landurbplan.2019.103703

Li, X., Erpicum, S., Mignot, E., Archambeau, P., Pirotton, M., Dewals,
B., 2022b, Laboratory modelling of urban flooding, \emph{Scientific
Data} \textbf{9} (1). https://dx.doi.org/10.1038/s41597-022-01282-w

Liang, R., Thyer, M. A., Maier, H. R., Dandy, G. C., Di Matteo, M.,
2021, Optimising the design and real-time operation of systems of
distributed stormwater storages to reduce urban flooding at the
catchment scale, \emph{Journal of Hydrology} \textbf{602} .
https://dx.doi.org/10.1016/j.jhydrol.2021.126787

Lin, J., He, P., Yang, L., He, X., Lu, S., Liu, D., 2022, Predicting
future urban waterlogging-prone areas by coupling the maximum entropy
and FLUS model, \emph{Sustainable Cities and Society} \textbf{80} .
https://dx.doi.org/10.1016/j.scs.2022.103812

Lin, J., He, X., Lu, S., Liu, D., He, P., 2021, Investigating the
influence of three-dimensional building configuration on urban pluvial
flooding using random forest algorithm, \emph{Environmental
Research}\textbf{196} . https://dx.doi.org/10.1016/j.envres.2020.110438

Liu, L., Sun, J., Lin, B., 2022, A large-scale waterlogging
investigation in a megacity, \emph{Natural Hazards} .
https://dx.doi.org/10.1007/s11069-022-05435-3

Liu, M., Hu, Y.-M., Li, C.-L., 2017, Landscape metrics for
three-dimensional urban building pattern recognition, \emph{Applied
Geography} \textbf{87:} 66-72.
https://dx.doi.org/10.1016/j.apgeog.2017.07.011

Liu, X., Huang, Y., Xu, X., Li, X., Li, X., Ciais, P., Lin, P., Gong,
K., Ziegler, A. D., Chen, A., Gong, P., Chen, J., Hu, G., Chen, Y.,
Wang, S., Wu, Q., Huang, K., Estes, L., Zeng, Z., 2020,
High-spatiotemporal-resolution mapping of global urban change from 1985
to 2015, \emph{Nature Sustainability} \textbf{3} (7)\textbf{:} 564-+.
https://dx.doi.org/10.1038/s41893-020-0521-x

Ma, C., Qi, W., Xu, H., Zhao, K., 2022, An integrated quantitative
framework to assess the impacts of disaster-inducing factors on causing
urban flood, \emph{Natural Hazards} .
https://dx.doi.org/10.1007/s11069-022-05375-y

Muthusamy, M., Casado, M. R., Butler, D., Leinster, P., 2021,
Understanding the effects of Digital Elevation Model resolution in urban
fluvial flood modelling, \emph{Journal of Hydrology} \textbf{596} .
https://dx.doi.org/10.1016/j.jhydrol.2021.126088

Oke, T. R., Mills, G., Voogt, J., 2017, Urban climates, Cambridge
University Press

Paprotny, D., Sebastian, A., Morales-Napoles, O., Jonkman, S. N., 2018,
Trends in flood losses in Europe over the past 150 years, \emph{Nature
Communications} \textbf{9} .
https://dx.doi.org/10.1038/s41467-018-04253-1

Rentschler, J., Salhab, M., Jafino, B. A., 2022, Flood exposure and
poverty in 188 countries, \emph{Nature Communications} \textbf{13} (1).
https://dx.doi.org/10.1038/s41467-022-30727-4

Shrestha, A., Mascaro, G., Garcia, M., 2022, Effects of stormwater
infrastructure data completeness and model resolution on urban flood
modeling, \emph{Journal of Hydrology} \textbf{607} .
https://dx.doi.org/10.1016/j.jhydrol.2022.127498

Song, Y., Wang, J., Ge, Y., Xu, C., 2020, An optimal parameters-based
geographical detector model enhances geographic characteristics of
explanatory variables for spatial heterogeneity analysis: cases with
different types of spatial data, \emph{Giscience \& Remote
Sensing}\textbf{57} (5)\textbf{:} 593-610.
https://dx.doi.org/10.1080/15481603.2020.1760434

Steinhausen, M., Paprotny, D., Dottori, F., Sairam, N., Mentaschi, L.,
Alfieri, L., Luedtke, S., Kreibich, H., Schroeter, K., 2022, Drivers of
future fluvial flood risk change for residential buildings in
Europe,\emph{Global Environmental Change-Human and Policy
Dimensions}\textbf{76} .
https://dx.doi.org/10.1016/j.gloenvcha.2022.102559

Sun, F., Liu, M., Wang, Y., Wang, H., Che, Y., 2020, The effects of 3D
architectural patterns on the urban surface temperature at a
neighborhood scale: Relative contributions and marginal
effects,\emph{Journal of Cleaner Production} \textbf{258} .
https://dx.doi.org/10.1016/j.jclepro.2020.120706

Sun, X., Li, R., Shan, X., Xu, H., Wang, J., 2021, Assessment of climate
change impacts and urban flood management schemes in central
Shanghai,\emph{International Journal of Disaster Risk Reduction}
\textbf{65} . https://dx.doi.org/10.1016/j.ijdrr.2021.102563

Tehrany, M. S., Jones, S., Shabani, F., 2019, Identifying the essential
flood conditioning factors for flood prone area mapping using machine
learning techniques, \emph{Catena} \textbf{175:} 174-192.
https://dx.doi.org/10.1016/j.catena.2018.12.011

Touma, D., Stevenson, S., Swain, D. L., Singh, D., Kalashnikov, D. A.,
Huang, X., 2022, Climate change increases risk of extreme rainfall
following wildfire in the western United States, \emph{Science
Advances}\textbf{8} (13). https://dx.doi.org/10.1126/sciadv.abm0320

Wang, Y., Zhang, X., Xu, J., Pan, G., Zhao, Y., Liu, Y., Liu, H., Liu,
J., 2022, Accumulated impacts of imperviousness on surface and
subsurface hydrology-continuous modelling at urban street block
scale,\emph{Journal of Hydrology} \textbf{608} .
https://dx.doi.org/10.1016/j.jhydrol.2022.127621

Yan, H., Wang, K., Lin, T., Zhang, G. Q., Sun, C. G., Hu, X. Y., Ye, H.,
2021, The Challenge of the Urban Compact Form: Three-Dimensional Index
Construction and Urban Land Surface Temperature Impacts, \emph{Remote
Sensing} \textbf{13} (6)\textbf{:} 23.
https://dx.doi.org/10.3390/rs13061067

Yang, Q., Zheng, X., Jin, L., Lei, X., Shao, B., Chen, Y., 2021,
Research Progress of Urban Floods under Climate Change and Urbanization:
A Scientometric Analysis, \emph{Buildings} \textbf{11} (12).
https://dx.doi.org/10.3390/buildings11120628

Yin, C. L., Meng, F., Guo, L., Zhang, Y. X., Zhao, Z., Xing, H. Q., Yao,
G. B., 2021, Extraction and Evolution Analysis of Urban Built-Up Areas
in Beijing, 1984-2018, \emph{Applied Spatial Analysis and Policy} .
https://dx.doi.org/10.1007/s12061-021-09374-7

Zhang, B., Xie, G.-d., Li, N., Wang, S., 2015, Effect of urban green
space changes on the role of rainwater runoff reduction in Beijing,
China, \emph{Landscape and Urban Planning} \textbf{140:} 8-16.
https://dx.doi.org/10.1016/j.landurbplan.2015.03.014

Zhang, H., Cheng, J., Wu, Z., Li, C., Qin, J., Liu, T., 2018, Effects of
Impervious Surface on the Spatial Distribution of Urban Waterlogging
Risk Spots at Multiple Scales in Guangzhou, South
China,\emph{Sustainability} \textbf{10} (5).
https://dx.doi.org/10.3390/su10051589

Zhang, Q., Wu, Z., Zhang, H., Dalla Fontana, G., Tarolli, P., 2020,
Identifying dominant factors of waterlogging events in metropolitan
coastal cities: The case study of Guangzhou, China, \emph{Journal of
Environmental Management} \textbf{271} .
https://dx.doi.org/10.1016/j.jenvman.2020.110951

Zhao, J., Yu, K., Li, D., 2014, Spatial characteristics of local floods
in Beijing urban area, \emph{Urban Water Journal}\textbf{11}
(7)\textbf{:} 557-572. https://dx.doi.org/10.1080/1573062x.2013.833636

\textbf{TABLES}

\textbf{Table 1} Details of the main data used in the study.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
Data\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
Description\strut
\end{minipage} & \begin{minipage}[b]{0.30\columnwidth}\raggedright\strut
Source\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Flooding points\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
flooding points from 2011 to 2021\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
the Water Resources Bureau of Beijing\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Building data\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Including building footprints and building height\strut
\end{minipage} & \begin{minipage}[t]{0.30\columnwidth}\raggedright\strut
Baidu Maps (map.baidu.com)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Land use data\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
10 m resolution, classified into 11 classes, such as: trees,
cropland\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
European Space Agency (ESA)
(https://viewer.esaworldcover.org/worldcover)\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2} Summary of 2D/3D landscape metrics considered in this
study.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Categories\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Name\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Description\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
Formulas\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Topography\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Average elevation\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The average elevation in the subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(AE=average(elevation)\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Drainage capacity\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Distance to river\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Average distance from each grid to the river in the subwatershed
area.\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
\[d=\sqrt{\sum_{i=1}^{n}{(x_{i}-y_{i})}^{2}}\]\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Road density\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Ration of road area to the subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(Rd=\frac{A_{\text{roads}}}{\text{Ssite}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Land cover composition\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Green space ratio\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The proportion of green space area to the total subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(GSR=\frac{A_{\text{green\ space}}}{\text{Ssite}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Waterbody ratio\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The proportion of waterbody area to the total subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(WR=\frac{A_{\text{waterbody}}}{\text{Ssite}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Impervious surface ratio\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The proportion of impervious area to the total subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(\text{ISR}=\frac{A_{\text{impervious}\ \text{surfaces}}}{\text{Ssite}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
land cover configuration\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Patch density\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The ratio of the number of patches to the total subwatershed area.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(PN=\frac{n_{i}}{A_{\text{subwatershed}}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Landscape shape index\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The shape index is a measure of the shape complexity.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(LSI=\frac{0.25E}{\sqrt{A_{\text{subwatershed}}}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3D building morphology\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building coverage ratio\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building coverage ratio of the subwatershed.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(BCR=\frac{\sum_{i=1}^{n}\text{BSi}}{\text{Ssite}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building density\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Number of buildings in the subwatershed.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(BD=\frac{N}{A}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building congestion degree\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The density of buildings in 3D space.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(BCD=\frac{\sum_{i=1}^{n}V_{i}}{\max\left(H_{i}\right)*A}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building height\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The area-weighted average building height.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(BH=\frac{\sum_{i=1}^{n}{BSi*BHi}}{\sum_{i=1}^{n}\text{BSi}}\)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Floor area ratio 3D shape index 3D fractal\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Building area unit area of the subwatershed. The degree of shape
complexity. The compactness of the buildings.\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\[FAR=\frac{\sum_{i=1}^{n}{c*F}}{\text{Ssite}}\] \[3DSI=\frac{\sum_{i=1}^{n}{(BSi+Li*BHi)}}{3*v*\sqrt{3v/4\pi}}\] \[\lg{N(r)}=\operatorname{-Dlg}{r+c}\]\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Notes: \(x_{i}\), \(y_{i}\) were coordinate;
\(A_{\text{roads}}\),\(A_{\text{green\ space}}\),\(A_{\text{Impervious\ surfaces}}\),and
\(A_{\text{waterbody}}\) were the area of roads, green space, waterbody, and
impervious surfaces;\(n_{i}\) was the number of patches;
\(E\) was the length of the patches; \(\text{BS}_{i}\):
building projected area; n: the number of buildings; \(S_{\text{site}}\):
area of the subwatershed.BHi: height of
building.\selectlanguage{ngerman} F: floor of building.\(c\):
constant.  Li: perimeter of the buildings.
\(v\): volume of buildings of the subwatershed.
\(N(r)\): number of none-empty boxes; \(r\):
scale; \(D\): 3D fractal dimension.

\textbf{Table 3} Results of Geo-Dector interaction detector.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
& BCR & BH & FAR & 3DSI & 3DF & BD & BCD\tabularnewline
\midrule
\endhead
BCR & 0.082 & & & & & &\tabularnewline
BH & 0.349DE & 0.153 & & & & &\tabularnewline
FAR & 0.197DE & 0.329DE & 0.100 & & & &\tabularnewline
3DSI & 0.221DE & 0.315DE & 0.362DE & 0.074 & & &\tabularnewline
3DF & 0.196NW & 0.249NW & 0.372DE & 0.305NW & 0.208 & &\tabularnewline
BD & 0.328DE & 0.432DE & 0.355DE & 0.412DE & 0.184NW & 0.186
&\tabularnewline
BCD & 0.313DE & 0.309NW & 0.381DE & 0.294DE & 0.121NW & 0.415DE &
0.176\tabularnewline
\bottomrule
\end{longtable}

\textbf{FIGURE LEGENDS}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Fig. 1} Geographic location, elevation, rivers, roads, and
administrative boundaries of the study area.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Fig. 2} Spatial distributions of urban flooding points from 2011
to 2021.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Fig. 3} Spatial distribution of urban flooding density.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\par\null

\textbf{Fig. 4} Relative contributions (\%) of the influencing factors
(without and with considering buildings) on urban flooding in Beijing.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Fig. 5} Marginal effects of the six most important explanatory
variables in model considering all driving forces.

\selectlanguage{english}
\FloatBarrier
\end{document}

