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Urban storm inundation, which frequently has dramatic impacts on city safety and social life, is an emergent and difficult issue. Due to the complexity of urban surfaces and the variety of spatial modeling elements, the lack of detailed hydrological data and accurate urban surface models compromise the study and implementation of urban storm inundation simulations. This paper introduces a Constrained Delaunay Triangular Irregular Network (CDTIN) to model fine urban surfaces (based on detailed ground sampling data) and subsequently employs a depression division method that refers to Fine Constrained Features (FCFs) to construct computational urban water depressions. Stormrunoff yield is placed through mass conservation to calculate the volume of rainfall, runoff and drainage. The water confluences between neighboring depressions are provided when the water level exceeds the outlet of a certain depression. Numerical solutions achieved through a dichotomy are introduced to obtain the water level. Therefore, the continuous inundation process can be divided into different time intervals to obtain a series of inundation scenarios. The main campus of Beijing Normal University (BNU) was used as a case study to simulate the “7.21” storm inundation event to validate the usability and suitability of the proposed methods. In comparing the simulation results with
Urban areas serve as the center of populations, property and resources, and one severe storm flood can result in dramatic property damage and financial losses. In recent years, numerous cities have been inundated by storm floods, which are the major cause of urban flooding. Two thirds of Chinese cities have endured storm inundation, with a portion experiencing more than three storms per year. These severe storms are characterized by maximum water depth greater than 1 meter and inundation durations of longer than 30 min. Urban storm flood inundation has drawn increasing attention in watershed flood research. The proliferation of recent modeling efforts is a direct consequence of significant storm flood events in urban areas and the perceived increased risk from these high rainfall events [
Prevailing researches on urban storm flood inundation employ the concept of dual urban drainage system. The urban storm water system is composed of two parts: a surface system and a subsurface system [
Geographic Information System (GIS) based stormrunoff models that employ a flatwater concept [
As a consequence, this research introduces a new method for urban flood inundation simulation. It employs a CDTIN to represent the fine urban surface, including all types of FCFs (e.g., water drain grates, street curbs, walls, and buildings). As
The flow chart of the proposed method.
The CDTIN is an appropriate method for representing the FCFs on an urban surface in detail. Compared with traditional topography which cannot represent these features accurately, a highresolution DEM acquired from LiDAR data may provide a suitable solution for detailed urban flood modeling [
Therefore, we utilized total station, digital level and terrestrial LiDAR to survey the urban surface in detail, including all types of FCFs. According to the national gradeIV surveying standard, the surveyed results are of cm precision—sufficiently detailed to represent small scale urban features.
Constrained features defined data types and organization.
Constrain Features  Data Type  Data Organization 

Water drain grates, Down comers, Outlet of a region, 
Constrained point  Shapefile PointZM 
Road cambers, Street curbs, Road isolation strip, Walls, 
Constrained polyline  Shapefile PolylineZM 
Buildings (or other manmade structures), Grass lands, Playgrounds, Lakes (or other water bodies), 
Constrained polygon  Shapefile PolygonZM 
A CDTIN representation is introduced to consider the complexity of urban surface and model the detailed FCFs, (illustrated in
Urban surface representation with CDTIN. The blue stars label the water drain grates; the red lines represent the constrained features such as street curbs, walls, grass lands boundaries and buildings; the green lines represent the normal triangle edges; the blue rectangle labels the detailed illustration area.
The illustration of property and topology for CDTIN in terms of point, edge, and triangle.
In the following explanation, several key terminologies related to hydrological analysis are provided as follows: (1)
This paper generates a computational urban water depression, which is the basic computational unit to simulate urban storm flood inundation, by employing the facet to edge flow mode [
Definition of cofluent edges, transfluent edges, and difluent edges. (
Illustration of computational water depression; lines with different colors represent different edge types.
A flatwater concept [
There is an obvious mass balance principle in a certain water depression: the accumulated water
Historic rainfall data is useful data to calculate the accumulative rainfall volume on the condition that all the historic data can be obtained. Otherwise, a design storm can be employed as an option. Based on the relationship of intensitydurationfrequency (IDF), the design storm is defined from a hyetograph to depict the precipitation along the time distribution. In the case study, the IDF equation of a Beijing storm is employed to calculate the rainfall. It is designed by TongJi University through an analytical method [
The mass balance illustration in a certain computational water depression, the red dashed line represents the profile crossing one road.
A complex urban surface has diverse capacities of infiltration. Previous researches has utilized the time condensation method of hydrograph analysis [
The runoff coefficient of different land types.
Land type  Runoff coefficient 




Building surface, concrete, or asphalt pavement road  0.85~0.95 



Large rubble paved road, or gravel road with asphalt surface  0.55~0.65 



Gradation macadam road  0.40~0.50 



Masonry brick or gravel road  0.35~0.40 



Unpaved soil road  0.25~0.35 



Garden or green land  0.10~0.20 



Water area  0 



Because of data complexity and time consuming computation, also not all the data can be immediately obtained after an urban storm event. In particular, underground sewer system can be very difficult to monitor [
As a consequence, Equation (4) can be replaced by Equation (6) to feasibly compute the accumulative excess water volume feasibly. The simulation duration (
We assume the inundation in each depression complies with the flatwater concept, but it is potential for uneven inundated surfaces between adjacent depressions. Therefore, we propose a novel water confluence between depressions. The flowchart of the algorithm is proposed as shown in
When the accumulated water surface in depression A arrives at the outlet point O, the confluence between depression A and B begins. Taken
Judge whether the water level of depression A (
Refer to the conditions of urban surface (land type, slope) and water level; employ empirical Equation (7) [
Search the water depressions that connect with O; Judge Ha>Hb, then the accumulated water in depression A flows to depression B at the volume of
All urban water depressions repeat Steps (1)–(3) to calculate the water confluence which are quantified as the
Calculate the final accumulated water volume in each depression referring to Equation (6).
Algorithm flowchart of confluence between urban water depressions.
Confluence mode between neighbor water depressions, red point labels the pit point of the depression; point O is the outlet point of the depression A and depression C; blue polygon represents the water surface. (
The accumulated excess water volume on the terrain converts to the runoff water volume to inundate urban surface. This is equal to the water volume between water surface and urban surface at a certain time. This can be expressed as Equations (8) and (9).
Referring to Equations (6)–(9), the inundation water level can be expressed associating with rainfall, terrain features and drainage parameters. Analytical solution cannot be evidently obtained to solve the equations due to the complexity of the urban surfaces. Numerical solutions through dichotomy [
Initialize the maximum (H_{1}) and minimum (H_{0}) inundation depth;
Within each basin which consist of triangularprism sets, calculate the water volume Q_{0}, Q_{1} under the inundation depth of H_{0} and H_{1};
If Q_{0} = Q_{r} then H_{r} = H_{0}; else if Q_{1} = Q_{r} then H_{r} = H_{1}; otherwise calculate the water volume Q_{0.5} under the water surface of H_{0.5}, which equals
If Q_{0.5} = Q_{r}, then H_{r} = H_{0.5}; else if Q_{0.5} > Q_{r}, then Q_{1} = Q_{0.5} and H_{1} = H_{0.5}; otherwise if Q_{0.5} < Q_{r}, then Q_{0} = Q_{0.5} and H_{0} = H_{0.5};
Go to Step (2) until obtaining the H_{r}.
Therefore, continuous inundation can be divided into discrete time intervals to simulate inundation scenarios during the storm event. Each scenario can obtain the water surface (including inundation extent and water depth) by employing the above methods.
Triangularprism sets of the depression and three inundation phases of one triangularprism blue represents the accumulated water,
Dichotomy numerical solving iteration method to obtain inundation depth
Located between the second and third rings of municipal Beijing, China, campus of BNU is a typical urban surface. The campus experiences severe inundation storm events on an annual basis, particularly on the FuRen Road in front of the Geography & Remote Sensing Building. The drainage system around FuRen road existing faults have been shown through an investigation with the staff at the logistics management center of BNU.
This urban surface was surveyed by total station, an S3 digital level according to levelIV national surveying standard and the 1:500 national data capturing standard. The total length closing error of traverse surveying result was 0.1528 m. The relative length closing error of traverse is 1/1,7127 less than the surveying standard error (1/10000). The closed error of elevation was 8 mm. These are all within the range of national 1:500 cartography standard. The surveyed data were organized with Shapefile (with elevation z value) format shown as in
Surveyed data of the main campus of BNU with Shapefile organization.
Utilizing the modeling method in
BNU main campus surface representations with CDTIN at different draw modes and views.
BNU main campus CDTIN representations with aerial imagery.
The storm event on 21 July 2011 in Beijing (called the “7.21” storm) was a 61yearfrequency high storm rainfall event, and it has affected approximately 1.9 million people and caused 1.6 billion dollars in economic loss [
To simulate the “7.21” storm, the inundation scenario can be timely acquired by employing the runoff coefficient as #2 (Experiment environment: Intel^{®}Core™2 Duo CPU p8600 @ 2.4GHz, 1.93GB RAM). As shown in
BNU main campus “7.21 storm” inundation scenario and comparison with insitu captured photos. The most severe submerged spots are labelled with A and B on the FuRen Road in front of Geography Building and Kindergarten.
The lack of abundant
Excess runoff volume with different runoff coefficient at rainfall duration of 1 h, 2 h, and 3 h, respectively. (
Inundation water depth and simulation result (Unit: cm).
Used Runoff Coefficient  Record Depth A  Simulation Result  Relative Error  Record Depth B  Simulation Result  Relative Error 

Value #1  42  35  16.7%  36  34  5.6% 
Value #2  42  37  9.6%  36  33  8.3% 
Value #3  42  38  9.5%  36  33  8.3% 
From
For further validation of the simulation result, we compare the result with the inundation risk perception map. As shown in
Inundation risk map from questionnaires for the “7.21” storm event.
Referring to FCFs, we employed the CDTIN to model urban surface in detail. An edge flow mode was utilized to subdivide the potential urban water depressions into computational depression polygons. Stormrunoff yield was evaluated through mass conservation principles to calculate the volume of rainfall, runoff and drainage. Water confluence between neighboring depressions was provided when the water level exceeded the outlets. Numerical solution through a dichotomy was employed to obtain the inundation water levels. During storm events, continuous inundation processes can be divided into different time intervals to obtain the inundation extent and submerged water depth. Simulation experiments of the BNU main campus “7.21” storm event in 2011 were conducted to validate the usability and suitability of the proposed methods. The results show that CDTIN based methods are reasonable, effective, and less timeconsuming, thus providing a practical new method for urban inundation simulation. Hence, the characteristics of the proposed model can be summarized as follows:
The model focuses on the detailed surveyed urban surfaces with fine CDTIN representation instead of raster. It couples the fine constrained urban features, such as street curbs, road cambers, ans water drain grates, which greatly influence urban water flow;
The model can handle the storm flood with a lack of detailed drainage data, especially the discharge of the subsurface drainage system, or urban environments with a builtin sewer system;
The model employs the GISbased dichotomy numerical simulation method, which avoids the timeconsuming problem of 1D or 2D equation numerical calculation. It can provide a practical rapid inundation solution for urban storm flood simulation.
Due to the complexity of urban surface and modeling elements, some simplifications must be noted. This research accepted the flatwater concept which does not consider physical hydrodynamics. Therefore, several assumptions and simplifications must be discussed. (1) Physical factors such as gravity and friction were not considered; mass conservation was applied as the governing equation; (2) Although the historical value of surface friction and runoff were adopted from previous researches, this may have overestimated the total volume of distributed surface runoff and inundation conditions; (3) Any interactions between the surface flow and the underground sewer system were not considered. All conveyance were assumed to be equal to design conveyances (a permanent flow rate), even though they actually vary with time during and after a storm event. The conveyance could be very low at the beginning and gradually reach the full permanent flow. Thus, the assumption of permanent sewer conveyable full flow leads to underestimation of flood water volume, so does inundation depth [
Although this research has a number of assumptions and limitations, it is useful for urban storm inundation risk analysis, urban drainage design and emergency preparation because of its more timely performance, fine representation of urban surface and minimal drainage data requirements during a storm. This method can incorporate real world sewer system situations including the dynamics of drainage systems and the interaction between surface and subsurface, and flow without changing the concept and framework of the proposed methods in our future work.
We would like to acknowledge the financial support from the Beijing Municipal Natural Science Foundation Key Program (No. 8111003), the National Basic Research Program of China (No. 2011CB707102) and the Fundamental Research Funds for Central Universities (No. 105565GK). We would like to acknowledge the BNU logistics division office for the drainage data and inundation photos of the BNU in the “7.21” storm event, and the Disaster Risk Management Center of BNU for their questionnaires and inundation risk map.
Zhifeng Li designed the inundation model and wrote the original manuscript of the paper. Lixin Wu proposed the conceptual framework of the paper and revised the manuscript. Wei Zhu provided the drainage data and conducted the experiment of Beijing Normal University (BNU) “7.21” storm event. Miaole Hou surveyed the detailed urban surface and organized them into database. Yizhou Yang wrote the C++ code for the simulation algorithms. Jianchun Zheng provided the inundation validation analysis for simulation of BNU “7.21” inundation.
The authors declare no conflict of interest.