Emergency management decision of urban rainstorm and flood disasters based on similar cases analysis

Under the background of global climate change and rapid development of urbanization, urban extreme occurs more frequently. In consideration of the existing problems in the emergency management decision-making of urban rainstorm and flood disasters in China, this study put forward the decision-making method of urban rainstorm and flood disaster emergency management based on similar cases analysis method. Based on the evolution process of urban waterlogging disaster, the problem attribute system of urban rainstorm and flood disasters was established. The case-based reasoning (CBR) method was used to calculate the global similarity to determine the best historical case. The case-based decision theory (CBDT) method was used to calculate the comprehensive utility value of alternative cases to determine the optimal alternative cases. The empirical analysis was took in Xi'an city, one of the national center cities of China. Results show that the CBR method was used to obtain the highest similarity of historical case P3, which is 0.481. The CBDT method was used to calculate the high similarity of historical cases P3 and P4 to form the similar case set, with the similarity of 0.820 and 0.851, respectively. Combined with the event development, the comprehensive utility values were calculated. When the decision-maker pays the same attention to the emergency effect and response cost, the comprehensive utility value of P3 and P4 is 0.922 and 0.900, respectively, and P3 is the best reference scheme. By comparison, the latter is more suitable. The results can provide scientific basis for emergency management of urban rainstorm and flood disasters.


Introduction
In recent years, global warming has affected the local climate characteristics of cities globally, leading to frequent short-term heavy rainfall (Allan and Soden 2008;Yin et al. 2015;Prathipati et al. 2019;Jiang et al. 2019). In flood season on July 16, 2021, continuous heavy rain swept across Europe, causing floods in western Germany, Belgium and the Netherlands. Affected by the monsoon climate, China is one of the countries with serious urban rainstorm and flood disasters ). On July 20, 2021, the cities of Zhengzhou and Xinxiang in Henan Province were hit by extreme rainstorms, causing severe economic losses and casualties. According to the Sixth Assessment Report of IPCC, climate change caused by human activities has affected extreme weather and climate events around the world. In the Americas, Europe and Asia, the extreme precipitation caused by human activities had increased. The rapid development of urbanization has caused a large number of hardened roads to replace the original natural surface that can contain water and prevent the infiltration of heavy rainfall (Sun et al. 2018;Ren et al. 2020;Guo et al. 2022). Urbanization produces a large amount of domestic and industrial heat, which causes the "urban heat island" and "urban rain island" effects. The intensity and frequency of urban local rainfall increase, which increases the risk of urban rainstorm and flood disasters (Su et al. 2018;Zhang et al. 2020;Cheng et al. 2020). According to the United Nations estimate, the urbanization rate of the world's developed countries in 2050 will reach 86.0%, China's urbanization rate in 2050 will reach 71.2%. Urban rainstorm and flood disasters threatened the personal and property safety of urban residents seriously and restricted the sustainable development of cities (Tang et al. 2019). Urban rainstorm and flood events are highly affected by nature and society, which are frequent, sudden and uncertain, and have the characteristics of emergency events. How to make effective emergency decision-making method quickly after the occurrence of an emergency? It is the goal and urgent task that emergency experts and scholars all over the world strive to pursue in the field of emergency decision-making (Jia and Wu 2020). Decision-making errors will not only directly aggravate the consequences of emergencies, but also seriously affect economic development, social stability and ecological health. The emergency management of urban rainstorm and flood disasters has become an important part of urban governance (Nassif 2014;Deng et al. 2020).
In view of the key problems of urban rainstorm and flood disasters, many scholars have carried out relevant studies on sponge city, urban drainage and risk assessment. For example, in the research field of sponge city construction, Xia et al. (2017) investigated the current problems in sponge construction and put forward suggestions for future urban planning and construction. Li et al. (2019) used the storm water management model (SWMM) and the analytical hierarchy process (AHP) method to establish a comprehensive evaluation system for sponge city construction under different combinations. Urban drainage research mainly focuses on model simulation. Sadler et al. (2019), Kourtis et al. (2021) and Kwon et al. (2021) adopted SWMM model to simulate urban drainage system. Zhi et al. (2019) presented a 3D dynamic visualization method of an urban drainage model. The emphasis of risk assessment research is to construct different risk assessment systems. For example Zhang and Chen (2019), combined the AHP and multifactor analysis using GIS and the comprehensive weighted evaluation.
The irreversible damage caused by urban rainstorm and flood disasters highlights the necessity of implementing corresponding measures to alleviate waterlogging disasters and making scientific emergency management decisions (Su et al. 2018). In urban rainstorm and flood disaster emergency management, Wu et al. (2020) constructed the location-routing problem model of urban emergency logistics in the situation of rainstorm and flood disasters and found the dynamic emergency distribution path of Nanjing city in the situation of flood disasters using NSGA-III algorithm. Guo et al. (2020) developed a new economic loss assessment system for urban severe rainfall and flooding disasters based on big data fusion. The research on emergency management decision-making methods of emergencies mainly focuses on the optimization of emergency schemes based on case-based reasoning (Li et al. 2014). For example, Ding et al. (2018) combined dynamic network game technology, Bayesian analysis and multi-attribute utility theory to put forward an emergency decision-making method for urban waterlogging. Wang et al. (2020a, b) constructed an emergency decision-making model for environmental emergencies based on case-based reasoning. Some scholars optimize case-based reasoning by improving the weight method. For example, Yan et al. (2014) proposed an attribute weight optimization method based on membrane computing. Liang et al. (2020) and Leng et al. (2020) used the technique for order preference by similarity to ideal solution to rank the design schemes and determined the optimal scheme for sponge city construction. Chen et al. (2021) deduced the similarity measure between heterogeneous multi-attribute cases through the global indicator and combined with the relative entropy method based on GWO considering the correlation of dual information. At present, the research on urban rainstorm and flood disasters mainly focuses on the characteristics analysis of the flood process, mechanism analysis and simulation. There are relatively little research on emergency management decision-making of urban rainstorm and flood disaster events. When urban rainstorm and flood disaster strikes, it is usually necessary to take effective and feasible emergency plan in as short a time as possible to minimize the loss and ensure the safety of people's life and property. The effect of emergency decision-making has a direct impact on the success or failure of rescue work (Wang et al. 2020a, b;Ding et al. 2021). However, there is lack of scientific and effective decision-making methods in the emergency practice of urban rainstorm and flood disasters.
The purpose of this study is to make full use of the case data accumulated in the emergency management of urban rainstorm and flood disasters to establish the optimization method of urban waterlogging event response plan based on similar case selection, so as to improve the timeliness and scientificity of emergency decision-making. According to the characteristics and evolution process of urban rainstorm and flood disaster events, an attribute system of urban rainstorm and flood disasters was established based on the pressure-state-response (PSR) model, and the weights of problem attributes were calculated by entropy weight method. The case-based reasoning (CBR) and case-based decision theory (CBDT) were used to select similar cases as reference cases for emergency decisionmaking. Taking Xi'an, an important central city in western China, as the research area, the proposed method was applied to verify the feasibility of the method. Data and methodology are described in Sect. 2, followed by results in Sect. 3. Discussion and conclusions are presented in Sect. 4.

Data sources
Under the pressure of short-term heavy rainfall, urban rainstorm and flood disaster occurs, and people's subjective role will put forward emergency response measures to prevent its 1 3 further deterioration. The model of "pressure", "state" and "response" was used to construct the problem attributes of urban rainstorm and flood disaster events. Pressure properties refer to the negative influence factors of natural environment pressure caused by sudden short-term heavy rainfall on the original balance system. State properties refer to the result of urban rainstorm and flood disasters under the influence of environmental pressure and represent the current status of the system. Response properties refer to emergency measures to reduce the loss caused by urban rainstorm and flood disaster.
In conclusion, the scope of urban rainstorm and flood disaster events and the difficulty of data acquisition were taken as the basis for case selection, and the problem attribute system of urban rainstorm and flood disaster events was established, as shown in Table 1.
This study took Xi'an city, the central city in northwest China and one of the national central city of China, as an example to verify the method. Xi'an city (107.4°-109.49°E, 33.4-34.5°N) is the political, economic and cultural center of Shaanxi Province. It is located in the middle of Shaanxi Province, south of the Weihe River and north of the Qinling Mountains. It is about 204 km long from east to west and 116 km wide from north to south. The total area of the city is 9983km 2 , among which the urban area is 1066 km 2 . The Xi'an city is a continental monsoon climate, and summer is rainy. In recent years, the urbanization construction of Xi'an city has developed rapidly, rising from 37% in 1990 to 79.49% in 2021. Urban rainstorm and flood events occurred frequently in Xi'an city, and the urban rainstorm and flood disaster were further aggravated. Five urban rainstorm and flood events in Xi'an city were selected as sample data, which were the urban rainstorm and flood events in Xi'an city on July 24, 2016, August 22, 2018, July 10, 2020, July 30, 2020, and August 7, 2020. Data are obtained from the Statistical Bulletin of Xi'an Bureau of Statistics (available at http:// tjj. xa. gov. cn/ tjsj/ tjgb/1. html), Xi'an Meteorological WeChat Official Account founded by Xi'an Meteorological Bureau and news and information from various web pages. P 0 is the target case and {P 1 , P 2 , P 3 , P 4 } is the historical case set. The attribute system of urban rainstorm and flood disaster events is expressed as X = {X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 , X 9 }. The attribute value information of each attribute is given in Table 2.

Research methodology
The selection of emergency plans based on similar cases analysis method is a new perspective for the optimization of emergency decision plans of urban rainstorm and flood disaster events. New ideas and new methods can be obtained from historical experience to effectively solve the problem that knowledge expression is difficult or even impossible to express (Liu et al. 2008). Thinking patterns are similar to the process of human reasoning and judgment. The decision-making problem of selecting similar emergency cases based on historical cases can not only improve the efficiency of emergency response, but also better cope with the situation lacking effective response plan. In this paper, the CBR and CBDT in similar cases analysis method were used for practical application of emergency management decision of urban rainstorm and flood disaster events. Figure 1 shows the flowchart of the similar cases analysis method.

Entropy weight method
The entropy weight method is used to calculate the weight of all kinds of problem attributes. The information entropy e j of the j evaluation index can be determined by Eq. (1): ln m , m is the number of evaluation objects and n is the number of evaluation attributes of evaluation objects. If f ik = 0, define f ij lnf ij = 0.

Case-based reasoning
Case-based reasoning originated from the dynamic memory theory proposed by Roger Schank of Yale University in 1982. In 1994, Aamodt and Plaza (1994) conducted further research on the CBR theory and obtained the 4R model of case reasoning, which consists of four cyclic stages: retrieve, reuse, revise and retain. The thinking process of CBR is similar to the process of human reasoning and judgment . By learning from the experience of historical events, new ideas and methods can be obtained to effectively solve the problems that are difficult or even impossible to express knowledge (Liu et al. 2008;Khan et al. 2019).
(i) The missing attribute values of the target case The attribute values of the urban rainstorm and flood disaster events in these case are all of numerical type (R type). Let Ĥ ′ K represent the missing attribute value of the attribute number k of the current target case event P 0 . The calculation formula is determined by Eq. (3): where T' k is the character information of the question number k in the historical case P i , j = {1, 1, 2, …, m}, T = {T 1 , T 2 , T 3 , …, T j , …, T m }.
(ii) Numerical attribute similarities In this case, the attribute values are all numerical type (R type), and the similarity calculation of numerical type attribute value can be expressed as Eq. (4): where P 0 represents the target case, P i represents the ith historical case in the historical case set P, H' k represents the character information of the kth attribute of the target case P 0 and T' k represents the character information of the kth attribute of the historical case P i .
(iii) Global similarities between target case P 0 and history case P For the ongoing target case P 0 , there may be missing problem attribute values, given = { k | k = 1, 2, 3, ... , m } , and the global similarity between target case P 0 and historical case P is given as Eq. (5): and F represents the proportion of the current target case in the total attributes, F = ∑ k∈ 2 w k . Finally, according to the global similarity between the target case P 0 and the historical case P, the historical case with the greatest similarity P* is selected as the reference scheme of the emergency response plan of the current target case. The global similarity can be expressed as Eq. (6):

Case-based decision theory
In 1995, Gilboa & Schmeidler (1995) put forward the case-based decision theory for the first time for the decision problem of uncertain events. The theory regards each choice scenario as a case, including three elements: problem, action and result (Krause 2009). The case-based decision theory method is to calculate the similarity between the current target case and the historical case, extract the set of similar cases and select the optimal scheme for the current target case by evaluating the utility value of the implementation result.

(i) Similarities of problem attributes
Based on the k-nearest neighbor (KNN) algorithm, it is often used for case similarity comparison (Guo et al. 2019). The k-nearest neighbor algorithm calculates the similarity between the target case and historical case based on the attribute weight and attribute value of the target case, and selects the most similar case according to the similarity degree as the basis of case reuse.
According to the actual situation of emergency response, attribute values are usually divided into symbolic and numerical types. The calculation of similarity of symbolic attribute values can be expressed as Eq. (7): where P i represents the ith historical case in the historical case set P, H' k is the character information of the kth attribute of the target case P 0 and T' k is the character information of the kth attribute of the historical case P i .
The calculation of similarity of numerical attribute values can be expressed as Eq. (8): where the maximum and minimum values of the target case attributes are expressed as Eq.
(9) and Eq. (10): (ii) Similarities between target case P 0 and history case P (6) Sim P 0 , P * = max Sim i P 0 , P | i = 1, 2, 3 , ... , n The case similarities are calculated by multiplying the attribute values of each problem of target case P 0 and historical case P with the attribute weight w k , as follows Eq. (11): where Sim i P 0 , P ∈ [0 , 1] . Sim i P 0 , P is larger, indicating that the problem attributes involved in the current target case P 0 are more similar to the problem attributes involved in the historical case. That is, the higher the similarity between the current target case P 0 and the historical case is, the more applicable the emergency decisions made in this case are to the target case.
(iii) The effectiveness of emergency response and response costs in similar cases Firstly, the similarity case set is extracted by setting the similarity threshold, and the similarity threshold between the historical case and the current target case is represented by ε. When Sim i P 0 , P ≥ is satisfied, the historical case P i will be extracted to form the similarity cases set P Sim , that is, Secondly, in order to eliminate the influence of different dimensions on calculation, the emergency response effect and coping cost of urban rainstorm and flood disasters are standardized. Let E e i and C c i represent emergency response effect and response cost, respectively. Generally, emergency response effects and response costs are divided into numerical and linguistic types. Among them, f(·) and g(·) represent the integration of emergency response effect and cost utility value of urban rainstorm and flood disaster events.
(iv) Identification of the similar case Comprehensive utility values A i of similar cases can be expressed as Eq. (18): where α and β represent the attention degree of decision-makers to the emergency response effect and response cost of urban rainstorm and flood disasters.
By calculating the comprehensive utility value of similar cases, the similar response plan P * of the target case is determined.

Calculation of problem attribute weights
The positive attribute refers to the problem attribute that the higher the attribute value is, the greater the risk is, including maximum precipitation intensity, single precipitation  period, average precipitation, maximum water depth, broken road, damage area and rescue response time. The negative attribute refers to the problem attribute that the higher the attribute value is, the lower the risk is, including the number of rescue worker and emergency plan grade. The results of attribute value standardization are shown in Fig. 2. The entropy weight method was adopted to calculate the weight, as shown in Table 3. The weight of damage area and maximum water depth are relatively large, with the weight of 0.115 and 0.102, respectively. They are direct embodiment of the severity of urban rainstorm and flood disasters. The second are rescue workers and rescue response time, with weights of 0.094 and 0.093, respectively. They are direct yardstick by which emergency response operations are judged. Finally, the average precipitation, maximum precipitation intensity and other attributes are natural factors, which are difficult to control. The importance of selecting similar cases lies in the severity of the disaster, followed by the emergency action plan. The purpose of taking emergency measures for urban rainstorm and flood disasters is to reduce the loss caused by the disaster.

Emergency plan selection based on the CBR method
The CBR method was used to select emergency plan of urban rainstorm and flood disasters. Urban rainstorm and flood disaster historical case collection is represented as P = {P 1 , P 2 , …, P 4 }. Based on the problem attribute information values of case data, the eigenvalue similarity of problem attribute Sim k (P 0 , P 1 ), Sim k (P 0 , P 2 ), Sim k (P 0 , P 3 ) and Sim k (P 0 , P 4 ) were calculated, where k ∈ {1, 2, …,9}, as shown in Fig. 3.
According to the problem attribute weights and their similarities, the global similarities between the target case P 0 and the historical case P i were calculated, as shown in Table 4.
The global similarities were calculated. The result is Sim 3 (P 0 , P) > Sim 4 (P 0 , P) > Sim 2 (P 0 , P) > Sim 1 (P 0 , P). Historical urban rainstorm and flood disaster event P 3 has the highest similarity. Therefore, for this urban rainstorm and flood disaster event, the emergency  response plan of historical case P 3 has greater reference value, and case P 3 is selected as the emergency response reference plan of the current target case. Based on the actual situation of the event, modify the similar case, and use the modified plan as the emergency response plan.

Emergency plan selection based on the CBDT method
The k-nearest neighbor method was used to calculate the similarity between the attribute characteristics of target case P 0 and historical case P, Sim k (P 0 , P 1 ), Sim k (P 0 , P 2 ), Sim k (P 0 , P 3 ) and Sim k (P 0 , P 4 ), where k ∈ {1, 2, …,9}. The calculation results of problem attribute similarity are shown in Fig. 4. The case similarity was calculated by multiplying the problem attribute values of target case P 0 and historical case P by the problem attribute weight w k , as shown in Table 5.
The attributes of emergency response effect of historical case include the effect of casualty control E 1 i and the effect of economic loss control E 2 i , while the attribute of coping cost includes the direct economic loss C 1 i . The description of emergency response effect adopts phrase evaluation information set {poor, good and excellent}. The attributes of emergency effect of the historical case P 3 and the historical case P 4 in similar case sets are E 1 = {excellent, good} and E 2 = {good, excellent}, and the attribute values of response cost are C 1 3 = 20.46 (million yuan) and C 1 4 = 2 (billion yuan). In combination with decision-makers' risk attitude, the functions of emergency response effect and response cost can be expressed as Eq. (19) and (20):  According to the emergency response of urban rainstorm and flood disasters, the comprehensive utility values of similar cases {P 3 , P 4 } are calculated, respectively. ① When α = β = 0.5, it indicates that decision-makers are equally concerned about the emergency response effect and cost of urban rainstorm and flood disasters. In this case, A 3 = 0.922, A 4 = 0.900, and similar case P 3 is the best emergency plan. ② When α > 0.5 and β < 0.5, it indicates that decisionmakers attach more importance to the emergency response effect of urban rainstorm and flood disasters. For example, α = 0.8 and β = 0.2, A 3 = 0.889 and A 4 = 0.840 were obtained, and similar case P 3 is the best emergency response plan. ③ When α < 0.5, β > 0.5, it indicates that decision-makers attach more importance to the coping cost of urban rainstorm and flood disasters. For example, if α = 0.2, β = 0.8, A 3 = 0.955 and A 4 = 0.960, and similar case A 4 is the best emergency plan.
Comparing the two methods, it can be found that the differences between the CBR method and the CBDT method mainly include two points.
Firstly, the calculation process of the CBR method and CBDT method is different. The CBR method calculates the similarity between the historical case and the target case and selects the case P 3 with the largest similarity as the reference scheme for emergency response, with a similarity of 0.481. The CBDT method determines the threshold of 0.8 in advance and screens out the cases with large similarities to form the similar case set {P 3 , P 4 }. The comprehensive utility value is calculated, and the case with the largest comprehensive utility value is taken as the reference case of the target case. The latter considers the effect and cost of the contingency plan.
Secondly, the CBR method and CBDT method calculate the similarity differently. The CBDT method is more accurate than the CBR method to calculate the similarity. In the CBR method, the similarities of problem attributes are roughly calculated by fast classification, and the final similarity is obtained by weight. The latter calculates the exact similarity of each problem attribute to obtain the final similarity. It can be seen from the calculation results that the similarity of problem attributes obtained by the CBR method is quite different, and there are many cases where the similarity is 0 or 1. The similarity of problem attributes obtained by the CBDT method is more accurate.
Decision-makers need to combine the emergency response plan with the actual situation of the event development. The CBDT method makes up for the problem that the casebased reasoning method cannot fully extract similar cases. The occurrence of urban rainstorm and flood disasters has the characteristics of uncertainty, complexity and stages. The CBDT method is more open to decision-making and is more suitable for urban rainstorm and flood disaster emergency decision-making.

Conclusions
1. Based on the characteristics of urban rainstorm and flood disaster events, this paper proposed the optimization method of urban rainstorm and flood disaster response plan based on similar cases analysis. Taking Xi'an city as an example, the CBR and CBDT methods were used for comparison. Using the CBR method, the similarity of historical case P 3 was the highest, which was 0.481. Therefore, the case P 3 is selected as the refer-ence scheme for emergency response of the current urban rainstorm and flood disasters. The CBDT method was used to calculate the similar cases P 3 and P 4 with high similarity constitute the similar case set. The similarity of P 3 and P 4 was 0.82 and 0.851. The comprehensive utility values of similar case set {P 3 , P 4 } were calculated, and different emergency plans were selected considering the emergency effect and response cost. 2. By comparing the two methods, it can be found that the CBDT method is not limited to the similar cases with the highest similarity, but sets the historical cases with high similarity to form a similar case set, which makes up for the insufficient extraction of similar cases by the CBR method. In addition, it takes into account the impact of the final implementation effect of the historical emergency plan and the response cost on the emergency decision and makes full use of the historical case data. Because of the uncertainty and stage characteristics of urban rainstorm and flood disaster events, the decision openness of the CBDT method is more suitable for urban rainstorm and flood disaster emergency decision problems, and this method can update the emergency decision scheme according to the actual situation of urban rainstorm and flood disaster events. It provides a new decision-making technique or a new way to solve the problem of generating emergency plans for urban rainstorm and flood disasters, which has maneuverability and practical value.