City flood disaster scenario simulation based on 1D-2D coupled rain-flood model: A case study in Luoyang, China.

In order to realize the reproduction and simulation of urban rainstorm
and waterlogging scenarios with complex underlying surfaces. Based on
the Mike series models, we constructed an urban storm-flood coupling
model considering one-dimensional river channels, two-dimensional ground
and underground pipe networks. Luoyang City was used as a pilot to
realize the construction of a one-dimensional and two-dimensional
coupled urban flood model and flood simulation. where is located in the
western part of Henan Province, China. The coupled model was calibrated
and verified by the submerged water depths of 16 survey points in two
historical storms flood events. The average relative error of the
calibration simulated water depth was 22.65%, and the average absolute
error was 13.93cm; the average relative error of the verified simulated
water depth was 15.27%, The average absolute error is 7.54cm, and the
simulation result is good. Finally, 28 rains with different return
periods and different durations were designed to simulate and analyze
the rainstorm inundation in the downtown area of Luoyang. The result
shows that the R2 of rainfall and urban rainstorm inundation is 0.8776,
and the R2 of rainfall duration and urban rainstorm inundation is
0.8141. Therefore, rainfall is the decisive factor in the formation of
urban waterlogging disasters, which is actually the rainfall duration.
The study results have important practical significance for urban flood
prevention, disaster reduction and traffic emergency management.


33
With the acceleration of urbanization, population density and economic output 34 increase, urban flood disasters have gradually become a research hotspot 1 . As the 35 process of urbanization continues to accelerate, the natural and ecological systems in 36 the main urban area and surrounding areas have changed 2 . The changes in urban 37 hydrological processes have gradually increased the threat of urban rainstorm disasters 3 . 38 As an important method for evaluating and preventing urban rainstorm disasters 4 , 39 numerical models can provide important technical support for flood control and 40 drainage 5 . 41 The city is a region, not a closed watershed 1 . It has both the problem of 42 overflowing rivers and waterlogging caused by heavy rains 6 . The simulation forecast 43 of heavy rain and waterlogging in cities with complex underlying surfaces is much more difficult than that of natural basin flood forecasts 7 . The complexity of the underlying 45 surface of the city is mainly reflected in the hard ground and the underground drainage 46 pipe network, but often only consider the hydrodynamic simulation calculation of the 47 urban pipe network, it is difficult to describe the real urban rainstorm and waterlogging 48 process, which leads to urban rain flood. The simulation forecast accuracy of the model 49 is also difficult to guarantee 8 . 50 Urban storm flood model is essentially a type of hydrological model or 51 hydrodynamic model, and its basic development process is basically the same as that 52 of traditional hydrological or hydrodynamic model 9 . In 1986, the first generation of 53 MIKE model was launched 10 , which integrated many new algorithms and data pre-54 processing and other new technologies in the algorithm innovation stage into the same 55 simulation platform, which promoted the development of urban flood simulation 56 technology and made urban flood modeling more convenient and efficient 11 . In the 57 meantime, many representative urban rain and flood models have also been produced. 58 In 1998, the Wallingford model was improved and introduced the Inforworks CS model     100 We selected Luoyang city center, in the northern Henan Province of China, as our 101 study area (34°29'06″-34°45'47″N, 112°15'44″-112°41'57″ E, at 150 m asl) (Fig. 2).
Luoyang city center, which constitutes the northern part of Luoyang city, is a typical 103 small basin city with an area of 803 km 2 , and is situated within the Yi-Luo River Basin.

104
The two rivers of Yi he and Luo he passed through the downtown area of Luoyang. The annual average temperature and rainfall are 14.6℃ and 600.2 mm. And June 108 to September accounted for 63.3% of the annual precipitation. Study area has a semi-109 arid area with an average water surface evaporation of 1200 mm and an aridity index 110 of 2.0. Luoyang city center is a highly urbanized area, containing numerous businesses, 111 campuses, and residential areas. The coverage of impervious areas reaches 72%.

112
Although Luoyang city center is a newly developed area, its sewer system is 113 insufficient for its current drainage needs. Most of the sewer system is designed for one-114 or two-year return periods. Thus, inundation is a normal occurrence during rainstorms 115 in Luoyang city center. In 2019, a rainstorm hit the entire Luoyang City, causing direct economic losses of $9.693 million. Luoyang City experienced significant damage from 117 that rainstorm and many streets were severely flooded. Therefore, it is a suitable site to 118 study the characteristics of rainfall-induced inundations.    In addition, three patterns of rainstorms, with return periods of 1a, 2a, 5a, 10a, 20a, 151 50a, and 100a ( Fig. 4), were used as model inputs to study the inundation response.

152
According to the Bureau of Municipal and Rural Construction, the rainfall intensity on 153 Luoyang city can be summarized using Eq. (1). The Chicago approach 23 was used to 154 redistribute the rainfall amounts before and after the peaks. The main difference among 155 the four rainstorm patterns is the position of the rainfall duration, the rainfall duration 156 was set to 60min, 120min, 360min, and 720min (Fig.4). We named these four 157 rainstorms (Fig.4)  where q is the rainfall intensity, mm/hr; P is the return period of rainstorms, yr; t is the rainstorm duration, min.   (3)

187
In the formula, q is the side flow, Q is the total flow, s is the distance coordinate, in the x and y directions respectively; n is the roughness; g is the acceleration of gravity;

214
VT is the water flow. Turbulent diffusion coefficient; f0 is the Coriolis force coefficient, The coefficient of determination (R 2 ) is often used to describe the degree of fit 267 between data. When R 2 is closer to 1, it means that the reference value of the related 268 equation is higher; on the contrary, when it is closer to 0, it means that the reference 269 value is lower. It is described as follows: where n is the total number of measured data, Si is the simulated water depth for The mathematical expressions of these metrics can be described as follows:    of 16 survey points in 2 historical storms and flood events (Table.2 and Table.3). The We conducted a data analysis on the simulation results of two flood events (Fig.7).

317
The R² of the simulated and measured water depths of the 16 water accumulation points 318 in the calibration period was 0.7837, and the R² in the verification period was 0.9548.

319
The overall simulation results during the calibration period are all within a reasonable     361 We know that the maximum amount of inundated water is an important indicator 362 to measure urban flood disasters. Generally speaking, the greater the maximum amount 363 of inundated water, the more serious the urban flooding.

Total inundation volumes
364 Table 4 presents the peak inundation volumes in each rainstorm, which ranged  respectively. under the condition that the return period is 1 to 2 years, inundation will 370 also occur, which shows that the urban drainage capacity is insufficient, which is also 371 one of the direct causes of urban waterlogging. (Fig.13) 372

Inundation positions and depths 374
Cities, especially central cities, have concentrated dense buildings and populations.

375
Once urban flooding occurs, it will cause inevitable losses. Therefore, it is particularly 376 important to simulate the spatial distribution of urban inundation scenarios. 377 Fig. 9-12 shows the submerged space distribution under four rain patterns, which 378 highlights the differences in in the degree of inundation, and spatial distribution. Even during the same return period, there were considerable differences in the inundation 380 extent between different rain duration. The overall trend is that as the rainfall duration 381 increases, the submerged water depth and submerged area become larger. The 382 inundation extents of Pattern 2 were close to those of Pattern 3, and Pattern 3 were close 383 to those of Pattern 4. (Fig.13) 384 Table 5 presents the average submerged depth in each rainstorm, which ranged

Inundation area 393
After the occurrence of urban waterlogging, the submerged area is also one of the 394 key indicators to measure its severity. and 4. Considering the spatial distribution ( Fig.9-12), the flooding situation is more serious in densely constructed areas, and the flooding area is relatively large. In this study, a torrential rain and waterlogging simulation calculation was carried 401 out in the downtown area of Luoyang. We selected the submerged water depth, the 402 number of submerged points, the submerged area and the submerged water volume for 403 statistical analysis of the submerged situation (Fig.13). The study found that these four 404 indicators are closely related to the rainfall return period and rainfall duration, and they 405 all show a good linear relationship. The average correlation coefficient with the rainfall 406 return period is 0.8776 (Fig.14), and the average correlation coefficient with the rainfall 407 duration is 0.8131 (Fig.15). Therefore, it is concluded that the decisive factor that 408 determines the severity of urban inundation is rainfall, followed by rainfall duration.

448
In the previous conclusion part, it is concluded that the decisive factor affecting 449 the severity of urban inundation is the amount of rainfall, the second is the rainfall 450 duration. Therefore, we analyze the correlation between the rainfall and the rainfall 451 duration of the 28 design rains, the two main factors affecting inundation and the 452 amount of inundation.

453
As shown in Figure 16, there is no doubt that the greater the rainfall, the greater 454 the amount of flooding. However, Figure 16 also shows a trend that the longer the 455 rainfall duration, the greater the amount of inundation, which is consistent with the 456 analysis in the conclusion part, but it is different from the common-sense conclusion 457 that "short duration and heavy rainfall cause serious urban waterlogging disasters" 32-33 , even in contrast. We also conducted detailed and rigorous discussion and research on 459 this. In the study, we designed 28 rainfall using the Chicago rain pattern and used it as 460 the rainfall input of the coupling model. In order to avoid the complexity of the research 461 results, we uniformly set the rain front coefficient to 0.4. That is to say, the proportion 462 of the rain fronts of 28 rains is the same, which leads to the longer the rain lasts, the 463 more prominent the rain peaks, and the more concentrated most of the rainfall of a rain.

464
This leads to a trend that the longer the rainfall lasts, the greater the amount of flooding.

465
In fact, this is not inconsistent with the common-sense conclusion mentioned earlier, 466 and even indirectly confirms this conclusion.

471
Based on the research results, we have compared and analyzed the correlation 472 between rainfall and inundation (Fig.17) and quantitatively described. Rainfall and 473 inundation show a good secondary correlation, R 2 is 0.8672, which is helpful to the 474 study of the relationship between urban waterlogging and rainfall threshold. Schematic diagram of urban rain ood inundation principle. (Compared with natural watersheds, the underlying surface conditions of cities are more complicated. Urban oods also include three parts: pipe network over ow, river over ow, and surface over ow.) Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 2
Research region and sewer system distribution. We selected Luoyang city center, in the northern Henan Province of China, as our study area (34°29'06″-34°45'47″N, 112°15'44″-112°41'57″ E, at 150 m asl) (Fig.  1). Luoyang city center, which constitutes the northern part of Luoyang city, is a typical small basin city with an area of 803 km2, and is situated within the Yi-Luo River Basin. The two rivers of Yi he and Luo he passed through the downtown area of Luoyang. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Synthetic hyetograph of four rainstorm patterns. The main difference among the four rainstorm patterns is the position of the rainfall duration, the rainfall duration were set to 60min, 120min, 360min, and 720min (Fig.4). We named these four rainstorms (Fig.4) as Pattern 1, Pattern 2, Pattern 3, and Pattern 4. 1D-2D rainfall ood model coupling scheme (The process frame diagram of this study) Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Comparison of simulated water depth and measured water depth of Storm 1 and Storm 2. Spatial distributions of inundation for 60min rainstorm scenarios. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 10
Spatial distributions of inundation for 120min rainstorm scenarios. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 11
Spatial distributions of inundation for 360min rainstorm scenarios. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 12
Spatial distributions of inundation for 720min rainstorm scenarios. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Trend chart of relationship between submerged water depth, submerged grid points, submerged area, submerged water volume and rain duration. (The rain duration and the four submergence indicators are linearly correlated, with an average R2 of 0.8131.)

Figure 16
The relationship between submerged water volume and rainfall duration and rainfall.

Figure 17
The relationship between submerged water volume and rainfall.