Method for site selection of relief supply warehouses in earthquakes with Ms ≥ 7—a case study of western Yunnan, China

Relief supply warehouses are material warehouses built to cope with natural disasters and guarantee the supply of life necessities. Great earthquakes (with Ms ≥ 7) are overwhelming natural disasters beyond human control. The efficiency in rescuing earthquake victims depends on if the construction preparations of large relief supply warehouses have fully assessed the influence weights of the factors of large earthquake disasters. We innovatively proposes a method for selecting ideal site of relief supply warehouses in terms of seismic evaluation and the quantification of site selection criteria. We assess disaster-affected areas and screen the transport mode of relief supplies based on seismic prediction and remote sensing recognition, quantify and classify the site selection criteria of relief supply warehouses in China, and finally determine the ideal site. Taking a seismically-active region as a study case, we identify seven major disaster-affected areas, estimate the largest safe flight range (255 km) of a helicopter in post-earthquake transport of relief supplies, and pre-selecte 37 candidate sites. We suggest that the spatial distances between candidate sites and essential transport hubs (such as airports, railway stations, and highway entrances/exits) and the construction planning of the city are crucial indicators for the ideal site selection.


Introduction
In terms of the experience from disaster relief of the 1998 Zhangbei Ms 6.2 earthquake, the Chinese government issued the Notice of the Ministry of Civil Affairs and the Ministry of Finance on Establishing a Central-level Reserve System for Relief Supplies in July 1998 to effectively deal with the livelihood issues brought by earthquake-derived natural disasters. It started the Chinese government's construction of the relief supply warehouse system (Li et al. 2019). The Construction Standards of Relief Supply Warehouses (Jian Biao 121-2009) (Ministry of Civil Affairs 2009), issued in January 2009, stipulates the conditions for the site selection, construction, approval, and acceptance of relief supply warehouses, and followingly has served as a reference frame for the site selection of relief supply warehouses in China. Up to now, the Chinese government is constantly advancing the construction of relief supply warehouses at all levels. Thanks to the advancements of meteorological, geological, and other multi-disciplinary observation technologies, natural disasters have gradually became predictable and preventable, making it possible to take a series of preventive measures in advance, such as guarding against disaster risks, evacuating disaster victims, dispatching relief supplies, etc.
Earthquakes are natural disasters characterized by low occurrence frequency, strong destructive power, and poor predictability. With the seismic capacity of buildings being continuously improved, the damages caused by small earthquakes are limited in most cases. Furthermore, their aftershocks often have a low magnitude (Tian et al. 2014), so concentrated earthquake avoidance is unnecessary in small earthquakes. However, great earthquakes with Ms ≥ 7 can cause the emergence of a large number of victims and the shortage of relief supplies within a short period of time (Benini et al. 2009;Baghaian et al. 2022), as well as complex situations such as continuous strong aftershocks (Tian et al. 2014), damaged transport arteries, and failure of relief supply warehouses in disasteraffected areas. In this context, the key to the effective rescue of earthquake victims within a short period of time lies in the site selection of large relief supply warehouses based on the risk evaluation of great earthquakes.
In the past two decades, western China mainland has been stricken by several earthquakes with Ms ≥ 7, where there was a lack of amount and timely arrival of adequate relief supplies (Ge et al. 2010). Therefore, conducting a scientific site selection for large relief supply warehouses and providing adequate support to post-earthquake disaster relief in super-strong earthquakes have emerged as a key research direction in the field of emergency relief in China.
In existing studies on the site selection of relief supply warehouses in China, site selection methods have been developed to concern single dominant factors such as earthquake disasters (Geng et al. 2021;Guan et al. 2020;Jana et al. 2021;Lu and Xu 2014), typhoon disasters (Cong and Yu 2020), warehouse capacity constraints (Balcik and Beamon 2008;He et al. 2017;Yan et al. 2021), road damages (Han et al. 2011;Zhang et al. 2019;Sun et al. 2019), and victims' pain perception (Geng et al. 2021). However, these studies mostly resorted to subjective assumptions in solving these problems and have not yet conducted refined research based on the research achievements in related disaster fields. Since now, no study have been carried out on site selection following the Construction Standards of Relief Supply Warehouses (Jian Biao 121-2009) (Ministry of Civil Affairs 2009). If a model is built only for a particular focus area using hypothetical information without adopting the standard requirements as basic site selection conditions, the site selection approach designed would have obvious defects. Therefore, by taking into account the occurrence of earthquakes with Ms ≥ 7 in the study area as a factor, we adopted the site selection requirements specified in the Construction Standards of Relief Supply Warehouses (Jian Biao 121-2009) (Ministry of Civil Affairs 2009) as the basic site selection conditions, and innovatively quantified and classified these conditions to identify the final ideal site. Compared with widely-accepted methods of site selection, the method we proposed here fully involves research results of seismology, remote sensing, geology, and other disciplinary fields. The optimal site would not only satisfactorily avoid of earthquakes with Ms ≥ 7 in the study area but also conform to the site selection criteria, finally making the site selection process of relief supply warehouses more feasible and practical.
In recent decades, a series of strong earthquakes, including the 1941 Gengma Ms 7.0 earthquake, the 1976 Ms 7.3/7.4 Mangshi-Longling double earthquakes, and the 2011 Ms 7.2 Mong Hpayak earthquake in Burma, have occurred successively in the southeastern margin of the Qinghai-Tibet Plateau. This suggests that the proper conditions for the occurrence of earthquakes with Ms ≥ 7 exist in the southeastern margin of the Qinghai-Tibet Plateau, and this is a potential risk area for earthquakes with Ms ≥ 7 in the future (Wang and Huang 2020;Zhao et al. 2022). Because of this, this study selected an area in western Yunnan Province, located in the Yunnan-Burma active block of the southeastern margin of the Qinghai-Tibet Plateau, as the study area for investigating the site selection of relief supply warehouses. Based on super-strong earthquake evaluation and the Construction Standards of Relief Supply Warehouses (Jian Biao 121-2009) (Ministry of Civil Affairs 2009), it fully utilized research results in seismology, remote sensing, geology, and other disciplinary fields to quantify and classify site selection conditions, thereby identifying the ideal site.
First, a literature review was conducted to analyze earthquake-prone areas and the highest seismic magnitude in western Yunnan Province, and the seismic intensity attenuation model and the satellite remote sensing recognition technology were adopted to determine earthquake-affected areas. Second, the mode of post-earthquake transport of relief supplies was predicted based on historical earthquake types, aftershocks, and other seismic information of western Yunnan Province. The longest safe transport distance was calculated after selecting facilities and evaluating post-earthquake transport environments. Third, the declaration and acceptance standards of relief supply warehouses, i.e., the Construction Standards of Relief Supply Warehouses (Ministry of Civil Affairs 2009), were sorted and perfected to quantify and classify site selection conditions. Fourth, earthquake-prone areas and the most extensive safe flight range were considered necessary condition constraint factors. Candidate sites meeting necessary conditions were ranked based on optimization conditions, and referential sites were selected from top candidate sites according to reference conditions. Finally, earthquakeprone areas and the largest safe flight range were considered as constraints. Candidate sites were ranked based on optimization conditions, and referential sites were screened from top candidate sites according to reference conditions to identify the ideal site. The detailed process flow is shown in Fig. 1. Taking western Yunnan Province for a case study, this study used the proposed method to investigate the site selection of relief supply warehouses in earthquakes with Ms ≥ 7.
1 3 2 Analysis of disaster-affected areas and transport facilities of relief supplies 2.1 Analysis of seismic sites Min (1989) divided seven major seismic belts in Yunnan Province based on historical strong earthquakes and modern moderate-strong earthquakes distribution. By summarizing the laws of historical earthquakes occurring in various active tectonic belts, it was found that each active tectonic belt has a recurrence interval of about 50-70 years. Based on predicting the recurrence intervals of earthquakes and analyzing the energy release and tectonic stress fields formed by moderate-strong earthquakes in strikeslip fault belts, Liu et al. (2015) predicted that major earthquakes with Ms ≥ 7 would occur along the three fault belts of the Dayingjiang River, the Wanding River, and the Nantinghe River (Fig. 2) and their adjacent areas in the future. Three predicted areas fell within the scope of the study area and were taken as the primary research objects of this study to investigate earthquakes with Ms ≥ 7. The site selection of relief supply warehouses in the study area was examined.

Analysis of seismic intensity zones
Currently, China's seismic intensity scales follow The Chinese Seismic Intensity Scale (State Administration of market supervision and State Standardization Administration, 2020) issued by the State Administration for Market Supervision and the Standardization Administration of China. Since the beginning of the twentieth century, the earthquake with the highest seismic magnitude in China was the 1970 January 5 Ms 7.7 Tonghai earthquake in the Yunnan Province, with a seismic intensity in the meizoseismal region of X (Li et al. 2010). The earthquake with the second highest seismic magnitude in the study area was the 1988 Ms 7.2 Lancang/Gengma double shock earthquake, with a seismic intensity of X in the meizoseismal region (Wang et al. 1991 casualties. Therefore, it was predicted in this study that the study area has a seismic intensity in meizoseismal region of X in earthquakes with Ms ≥ 7, and the highest seismic magnitude of Ms 8. According to the house damage caused by earthquakes of different intensities from The Scale (State Administration of market supervision and State Standardization Administration, 2020) and the historical records of the 1970 Ms 7.7 Tonghai earthquake (Li et al. 2010) and the 1988 Ms 7.2 Lancang/Gengma double shock earthquake (Wang et al. 1991), areas with a seismic intensity of ≥ IX are hard-hit areas. Therefore, it was predicted in this study that areas with a seismic intensity of ≥ IX are the hard-hit areas of earthquakes with Ms ≥ 7. Zhang et al. (2016) divided Yunnan Province into three grade-I zones (i.e., the western Yunnan zone, the Sichuan-Yunnan zone, and the eastern Sichuan-Yunnan zone) (Zhou et al. 2011) and statistically analyzed the seismic intensity of 146 earthquakes with Ms ≥ 5.0 occurring in Yunnan Province in 1900-2014. Li et al. (2003) and Ren et al.
(2020) deduced a seismic intensity attenuation model for these three zones based on the "oval-shaped" isoseismal pattern in Yunnan Province. The equations for western Yunnan Province are: where I denotes seismic intensity; a and b denote major axis and minor axis, respectively; Ms denotes seismic magnitude; R a and R b denote the lengths of the semi-major axis and semi-minor axis of the oval-shaped isoseismal pattern with a seismic intensity of I, respectively.
Substituting Ms = 8 into the equation, the result is obtained as shown in Table 1. Based on the calculation results of the seismic intensity attenuation model for the western Yunnan zone based on earthquakes with Ms 8 (Table 1) and the areas prone to major earthquakes with Ms ≥ 7 in the northern part of the Yunnan-Burma active block, the areas prone to earthquakes with Ms ≥ 7 and with a seismic intensity of ≥ IX in the study area can be predicted as follows (Fig. 3) (Liu et al. 2015).

Identification of disaster-affected areas
According to the historical statistics of earthquakes with Ms ≥ 7, the hard-hit areas with massive casualties vary with the occurrence time of earthquakes. For instance, when an earthquake strikes an anthropic zone on a working day, workplaces, factories, and schools are likely to become hard-hit areas with massive casualties. By contrast, when an earthquake occurs during non-working hours or a vacation, residential buildings, dormitories, (1) I a = 6.8053 + 1.2972Ms − 4.7603 log R a + 22 (2) I b = 5.3315 + 1.2013Ms − 4.1917 log R b + 10 and hotels often become hard-hit areas. To analyze the hard-hit areas caused by earthquake disasters, this study extracted buildings, delineated a seismic intensity zone with a predicted seismic intensity of ≥ IX, and took buildings in these seismic intensity zones as disaster-affected bodies.
The building area in this study was extracted using MODIS three-layer land cover data product MCD12Q1. The data product was developed by supervising and classifying the data observed by satellites Terra and Aqua worldwide throughout the year. MCD12Q1 has a spatial resolution of 500 m, contains 17 major land cover types, and uses five different land cover classification systems (Friedl et al. 2002;Shi et al. 2000), as detailed below: (1) Land cover classification system 1: IGBP global vegetation classification system.
Based on the characteristics of disaster-affected bodies in the study area, this study selected the IGBP global vegetation classification system and took cities and buildings (classification code: 13) as the main targets of building area extraction. A buffer zone was designed around this area through pixel filling, and isolated pixels around cities were judged using visual interpretation. Ground object types such as villages and factories were included within the scope of disaster-affected bodies to ultimately generate the building distribution map of this study. Corrosion expansion operations were performed for building distribution data to eliminate the effect of isolated buildings. Seven disaster-affected body zones ( Fig. 4) were identified in the delineated ≥ IX seismic intensity zone by adopting the 8-adjacent connection method as the judgment basis and taking connected areas as disaster-affected bodies (Fisher et al. 2005;Sonka et al. 1999). Disaster-affected areas were predicted using this method in this study.

Earthquake types and aftershocks
According to the statistics of moderate-strong earthquakes in strike-slip fault belts, the three earthquakes in the Nujiang Fault were all swarm earthquakes. The earthquakes in the Lancangjiang Fault in 1988 and the Wanding Fault in 1976 were double earthquakes. The earthquakes along the Nantinghe Fault in 2015 and between the Chafang Fault and the Puwen Fault in 2014 were major earthquakes/aftershocks. The type of earthquake occurring along the Nantinghe Fault in 1941 could not be ascertained, mainly due to the limitation of historical data. In combination with the statistics of earthquakes and the zoning of earthquake sequences with Ms ≥ 5 occurring in Yunnan Province from 1965-2005 (Huangpu et al. 2007), it was predicted that the types of earthquakes with Ms ≥ 7, which may occur in the study area in the future, would include swarm earthquakes, double earthquakes, and major earthquakes/aftershocks, all of which are very destructive. The possibility of isolated earthquakes with weak destructive power is low.
According to the statistics of 181 earthquake sequences in Yunnan Province from 1965-2012, 60% of the largest aftershocks occurred in the first three days after the major earthquake. When the seismic magnitude of the major earthquake estimated by the magnitude difference method was 7.0-7.9, the seismic magnitude of the largest aftershock would be Ms max = Ms − 0.8 ( Ms = seismic magnitude ). Among the 181 earthquake sequences, nine earthquakes were Ms ≥ 7. The dominant time of occurrence of the largest aftershocks was uniformly 20 d after the major earthquake (Tian et al. 2014), except the Ms 6.0 largest aftershock occurring within 20 d after the 1996 Ms 7.0 Lijiang earthquake. Taking a Ms 7.8 earthquake occurring in Yunnan Province as an example, the seismic magnitude of the largest aftershock is predicted to be 7.0 by the corresponding equation. For the same 1 3 earthquake with Ms ≥ 7, the strong aftershock occurring based on the major earthquake will have extraordinary destructive power.
For earthquakes with Ms ≥ 7, the strongest aftershocks occurred within 20 d after the major earthquake eight out of nine times, but the sample size was small. In addition, the overall sample statistics of the 181 earthquake sequences in Yunnan Province from 1965-2012 indicate that 60% of the largest aftershocks occurred in the first three days after the major earthquake. Therefore, this study assumed that aftershocks of high seismic magnitudes occur in the first three days after an earthquake with Ms ≥ 7 in the study area and that the largest aftershocks may also occur in this period.

Analysis of road damages
Road damage is widespread during earthquakes (Zhou et al. 2022;Li et al. 2016), especially with Ms ≥ 7. Earthquakes with Ms ≥ 7 cause damage to bridges, tunnels, roads, and railways to varying degrees in ≥ VII seismic intensity zones (State Administration of market supervision and State Standardization Administration, 2020). Subsequent aftershocks and secondary geological disasters also cause severe damage to roads (Li and Huang 2013).
By investigating the earthquake types and aftershocks in the study area, it can be concluded that, after the occurrence of an earthquake with Ms ≥ 7 in the study area, the roads to disaster-affected areas will be inevitably damaged, and aftershocks (even the largest aftershock) and secondary disasters will follow within three days. In that case, any blind emergency road repair will likely cause more casualties. Therefore, once an earthquake with Ms ≥ 7 occurs in the study area, it is challenging to transport relief supplies by road to disaster-affected areas within a short period.

Analysis of helicopter transport of relief supplies
In cases where road transport cannot guarantee the distribution of relief supplies, helicopter transport offers an effective way for post-earthquake transport. This study examined the practice of the Southern Theater Command and Yunnan Military Region of the Chinese People's Liberation Army and the fire and public security departments of Yunnan Province and reviewed the news coverage of earthquake emergency relief in China in recent years. Overall, the helicopters available for the emergency transport of bulk relief supplies in the next five to ten years consist primarily of 13 t-level Mi-171 helicopters.
Standard Mi-171 helicopters have a range of 490 km under maximum take-off weight (maximum standard fuel, without remaining oil) and a maximum cruising speed of 240 km/h. According to the fuel limit specified in the General Flight Rules for Mi-171 Helicopters (PLA Air Force 1992) formulated by the Chinese Air Force, a helicopter must land when the fuel content reaches 10%. Helicopters have a higher human error probability in search and rescue missions than in other circumstances (Kim and Myung 2018). After an earthquake, helicopters are also extensively used to transport rescuers and wounded persons in disaster-affected areas (Xue et al. 2018). In this sense, reducing the take-off and landing of helicopters in the rescue process, especially in disaster-affected areas, effectively lowers the human error probability of helicopters (Kim and Myung 2017). Therefore, the safest way for helicopters to transport relief supplies is to take off and land only for unloading in the rescue process and then directly return to the loading area of relief supply warehouses. For a standard Mi-171 helicopter filled with fuel upon take-off for working under this mode, the flight limit according to the general flight rules is the greatest safe flight range and the shortest transport time obtained in this study. The calculation equations are: where D max denotes the greatest safe flight range; TSR denotes the total standard range; FLR denotes the fuel limit range; STS denotes the standard test speed; MP denotes the maximum payload; T min denotes the shortest transport time.
According to the calculation results of this study, standard Mi-171 helicopters in the transport of relief supplies have the most extended safe flight range of 225 km and the shortest transport time of 0.94 h. After being loaded, the first batch of relief supplies can arrive at a disaster-affected area within 1 h at the soonest.

Requirements for site selection of relief supply warehouses
Currently, the approval and construction of relief supply warehouses in China implement the Construction Standards of Relief Supply Warehouses (Ministry of Civil Affairs 2009). This document divides the construction of relief supply warehouses in China into four levels (Table. 2). This standard requires that site selection complies with local urban planning, following the principles of safe storage and convenient transport, and meets the following requirements: ① High terrain, with favorable engineering and hydrogeological conditions; ② favorable municipal conditions; ③ kept away from fire sources and flammable or explosive factories and warehouses; ④ convenient traffic and transport conditions, adjacency to a railway freight station or highway entrance in the case of municipal or higher-level relief supply warehouses; ⑤ flat terrain, broad vision, convenient for the emergency take-off and landing of helicopters in the case of municipal or higher-level relief supply warehouses.
Relief supply warehouses are constructed mainly to guarantee the adequate supply of necessities for life to victims before and after a disaster. After earthquakes with Ms ≥ 7, relief supply warehouses are mainly used to timely and effectively supply sufficient necessities of life to disaster-affected areas. After comprehensively considering factors such as construction standards, population size, and city scale, it can be judged that if an earthquake with Ms ≥ 7 strikes the study area, the municipal and county-level relief supply warehouses nearby may fail or become inadequate. Thus, a safe provincial-level relief supply warehouse with proper site selection and rapid post-earthquake transport capacity should be built near disaster-affected areas.

Quantification and classification of site selection criteria
By detailing and decomposing the 1 premise and 5 requirements proposed in the construction standards, we obtained four categories and 10 elements: planning (in line with urban planning, far from fire sources), transportation (convenient transportation, close to railway freight stations or highway entrances), municipal facilities (favorable municipal conditions), and geological conditions and natural disasters (high terrain, favorable engineering geological conditions, low relief, convenience for helicopter take-off and landing). Among these ten elements, planning and transportation elements are known conditions. Based on three of those conditions (geological conditions, natural disasters, and the site selection of relief supply warehouses in practice), the "high terrain" element was proposed to avoid flooding. "Favorable engineering geological conditions" and "favorable hydrogeological conditions" were put forward to protect the site from earthquakes and other geological disasters. In combination with municipal facilities and the site selection of relief supply warehouses in practice, "favorable municipal conditions" was introduced to ensure that the site was located in a region with favorable urban infrastructure and economic conditions. This study holds that most elements can be quantified according to the characteristics of different categories, but there is still the problem of mutual constraints between individual elements or the difficulty in quantifying the expressions of certain elements. For instance, it is difficult to satisfy the site selection requirements of "adjacency to a highway entrance" and "kept far away from fire sources" in practice, as a gas station is built near almost every highway entrance. The requirement of "favorable municipal conditions" is also difficult to quantify, as municipal conditions involve many aspects of urban construction. Because of the above situation, this study took the construction of large-scale (provincial-level) relief supply warehouses as the objective, decomposed site selection conditions, and defined the basis of quantification (Table 3).

Quantification and classification of perfected construction standards
Based on the decomposition of the above premise and five requirements in the construction standards, this study reorganized seven perfected construction standards in combination with the disaster-affected areas of earthquakes with Ms ≥ 7 and the largest safe flight range above for the study area. To avoid the mutual constraints between site selection conditions and the impossibility of site selection in extreme circumstances, this study classified these seven standards into necessary conditions, optimization conditions, and reference conditions, imposed quantitative constraints on necessary conditions, and defined the ranking indices of optimization conditions. To be specific, necessary conditions are the conditions that must be met by site selection. After site selection results were obtained through China's national standard query, literature research, and expert interview of necessary conditions, they were further ranked based on optimization conditions to ultimately meet reference conditions to the largest extent (Table 4).

Selection of candidate sites within the safe flight range of helicopters
Based on necessary condition 3 in Table 4, the 5 km ranges around various highway entrances and railway freight stations were taken as candidate sites. Using the data on highway entrances in Yunnan Province (Yunnan Provincial Highway Bureau 2022), this study made statistics of the geographical information of the highway entrances in the study area and surrounding areas that had been put into use before March 2022. This study calculated statistics on the geographical information of the railway freight stations in the study area and surrounding areas that had been put into use before March 2022 using the data on railway freight stations from Yunnan Railway Group Co., Ltd. (2022). Based on the necessary condition 4 in Table 4, the crow-fly distances from highway entrances and railway freight stations to the farthest points of disaster-affected areas were calculated by importing geographical information and setting the constraint value. The constraint value was set as 225 km, the safe flight range of helicopters. Then the areas with a predicted seismic intensity of ≥ IX in Fig. 4 were excluded. In the end, the coordinates of 72 candidate sites were obtained (No. 1-No. 72, Fig. 5).
The equations are as follows (Frederick 1990; UTM 2018): (5) a = 6378137 m where L denotes longitude; B denotes latitude; L 0 denotes the standard longitude (selfdefined); B 0 denotes the standard latitude (self-defined); (x, y) denotes the converted coordinates; a denotes the semi-major axis of the ellipsoid; b denotes the semi-minor axis of the ellipsoid; e denotes the first eccentricity; e′ denotes the second eccentricity; N B 0 denotes the radius of curvature in prime vertical; K denotes the radius of the parallel circle at the longitude and latitude positions (L 0, B 0 ). Objective function is defined as: where ( x i , y i ) denotes the coordinates of a disaster-affected area; ( x j , y j ) denotes the coordinates of a candidate site.

Exclusion of candidate sites threatened by floods
Based on necessary condition 1 in Table 4, the occurrence laws of historical floods in the study area were summarized to avoid flood-prone areas in site selection. According to the statistics on the average occurrence frequency of floods in Yunnan Province from 1961-2010, the high-value areas were mainly concentrated in southwestern and southeastern Yunnan Province, with an average occurrence frequency above 0.4 time/a (Fig. 6) (Wu et al. 2015). This result is consistent with the distribution of the high-value areas of the average occurrence frequency of rainstorms in Yunnan Province in the Collection of Meteorological Disasters in China-Yunnan Province (Editorial Committee of China Meteorological Disaster code 2006). According to the observations of flood disasters in southwest China (Feng and Luo 1995), the study area is mainly within a region with moderate flood disasters, in which the areas with a below-average flood frequency are considered areas not prone to flood disasters (Wu et al. 2015;Wang et al. 2017). Therefore, taking the average flood frequency of western Yunnan Province (0.4 time/a) as the criterion, this study excluded 20 candidate sites with a flood frequency of above 0.4 time/a and ultimately had a total of 52 remaining candidate sites (Fig. 6).

Exclusion of candidate sites ranked at the bottom in terms of per capita GDP
To some extent, per capita GDP reflects a region's affluence and living standards to a certain extent. Therefore, necessary condition 2 was set as "the county (city) where the candidate site is located not to be ranked last in the city in terms of per capita GDP" so that it could be quantified. After completion of necessary conditions 1, 3, and 4, four candidate sites were left in the cities of Dehong, Baoshan, Lincang, and Yunlong and the Yongping Counties of Dali Prefecture. According to the per capita GDP statistics of various counties (cities) in Yunnan Province in 2021 and 2022 compiled by the Yunnan Provincial Bureau of Statistics (2022a, b), the counties (cities) with the lowest per capita GDP in the five regions were Lianghe County, Shidian County, Yongde County, Midu County, and Fugong County. Three candidate sites were excluded on this basis, and 49 candidate sites were left (Fig. 7).

Exclusion of candidate sites with unqualified terrain indices
The terrain is a vital reference frame for the site selection of relief supply warehouses. In this study, the terrain indices calculated by the digital elevation model (DEM) were adopted as a quantitative reference for site selection. The DEM data used in this study, with a spatial resolution of 30 m, denoted the elevations within 30 m × 30 m scopes. The terrain indices adopted in this study included regional slope, average regional elevation, and the standard deviation of regional elevation. The equations for terrain indices are as follows: The equation for average elevation is (Ministry of Housing and Urban-Rural Construction of the People's Republic of China 1999): Fig. 6 Distribution of candidate sites after excluding earthquake-prone areas and flood-prone areas (Wu et al. 2015) 1 3 The equation for the variance of elevation is: The equation for the standard deviation of elevation is: where Xi denotes the elevation of each pixel; N denotes the number of pixels in a region.
Based on necessary condition 5 in Table 4, 5 × 5 windows were taken as units in this study to satisfy the construction scale of provincial-level relief supply warehouses and the convenient take-off and landing of helicopters. The units involved in candidate sites must have less than 25% slope (Ministry of Housing and Urban-Rural Construction of the People's Republic of China 1999). The units must also be ranked among the top 50% of all candidates in the study area for average elevation and the bottom 15% standard deviation of elevation. Twelve candidate sites were excluded based on this necessary condition, and 38 candidate sites were left (Fig. 8).

Optimization conditions
Based on optimization condition 1 in Table 4, three objective points were calculated in this study: the road traffic hub closest to the road network of the candidate site, the railway Distribution of candidate areas after excluding the last area of GDP freight station (highway entrance), and the airport. The areas prone to natural disasters described above were excluded from the selection of objective points. A traffic hub must be an intersection of two highways, with at least two directions judged to be free of earthquake risks. The road traffic distances from thirty-seven candidate sites to these three objective points were calculated and then ranked by the p-median method. The top ten obtained are shown in Table 5. The equations are the same as Eq. (5)-(11) in 6.1.1, and also include the following: Decision-making variable: Constraint conditions: 1 Transportation hub f provision of services to candidate area j 0 Transportation hub f not provision of services to candidate area j (19) h j,g = 1 Airport g provision of services to candidate area j 0 Airport gnot provision of services to candidate area j h j,p = 1 Station (Expressway exit)p provision of services to candidate area j 0 Station (Expressway exit)pnot provision of services to candidate area j  k: traffic hub, airport, or railway freight station (highway entrance), k ∈ K. K: set of traffic hubs, airports, and railway freight stations (highway entrances), k ∈ K.

Reference conditions
The top ten candidate sites were obtained by excluding candidate sites based on five necessary conditions and ranking them according to one optimization condition. According to reference condition 1 in Table 4, only candidate sites meeting comprehensive urban planning could serve as referential sites for relief supply warehouses. By combining the DEM slope data of Baoshan with the requirements of the Code for Vertical Planning on Urban Field (Ministry of Housing and Urban-Rural Construction of the People's Republic of China 1999), this study determined the use status of regional construction land by considering a series of factors constraining the construction of relief supply warehouses, including airport clearance limitation, hydrological conditions, mineral resources distribution, and helicopter take-off and landing. The referential sites for relief supply warehouses were obtained in combination with the locations of the top ten candidate sites (Fig. 9). This study concluded that the ideal site selection scheme is to select a referential site that can ∑ p∈P h j,p = 1, j ∈ J keep the relief supply warehouse away from fire and flammable or explosive factories and warehouses.

Status of large relief supply warehouses in the study area
In reality, a relief supply warehouse has been built on the south side of Haitang Road in Longyang District, Baoshan. The road traffic and straight-line distance between the warehouse and the center of candidate site #6 are about 4.5 km and 3 km, respectively. Candidate site #6 was ranked second based on optimization conditions. The relief supply warehouse has a total building area of 20,000 m 2 and a warehouse area of 4,900 m 2 . According to Table 2, the warehouse is a provincial-level warehouse in terms of area and a small national-level warehouse in terms of total building area, so it meets the requirement of building a provincial-level warehouse raised in this study. According to the overall objectives stipulated in the Comprehensive Plan of Yunnan Province for Disaster Prevention, Mitigation, andRelief in the "14th Five-year Plan" Period (2021-2025) (General Office of Yunnan Provincial People's Government 2022), the arrival time of relief supplies in natural disasters needs to meet the following requirement: The necessities of life of victims need to be effectively guaranteed within 10 h after the occurrence of a natural disaster. According to the primary earthquake prevention and disaster reduction indices stipulated in the Plan of Yunnan Province for Protecting against and Mitigating Earthquake Disasters in the "14th Five-year Plan" Period (2021-2025 (General Office of Yunnan Provincial People's Government 2021), the guaranteed level of earthquake emergency response should meet the following requirement: A rapid assessment should be conducted and completed within 20 min after an earthquake, and the trend of the earthquake should be predicted within 30 min.
By analyzing the scheme for the post-earthquake helicopter transport of relief supplies proposed in this study, it can be concluded that, after being loaded with relief supplies, the helicopter can arrive at a disaster-affected area within 1 h at the soonest. By controlling the efficiency of helicopter dispatching and relief supply loading at a certain level, the objective of offering effective relief to victims in an earthquake with Ms ≥ 7 within 10 h can be achieved in the study area in the "14th Five-year Plan" period. Since the completion of the provincial-level relief supply warehouse, no earthquake with Ms ≥ 7 has occurred in the study area, so if the warehouse can effectively deal with earthquakes with Ms ≥ 7 has yet to be confirmed. However, in the future, the local government can take the disasteraffected areas identified in this study as potential disaster-affected areas and organize emergency drills for earthquake relief with Ms ≥ 7 based on joint military presence. In this way, they can estimate the time taken for relief supplies to arrive in these disaster-affected areas. Beyond continuously improving the emergency response plan, efforts should also be made to increase the efficiency of emergency response preparations, thus ensuring the timely arrival of relief supplies in disaster-affected areas.

Uncertainty factors and quantitative accuracy of indicators
Relevant theoretical and empirical methods developed for western Yunnan Province, such as the division scheme of areas prone to earthquakes with M ≥ 7 (Liu et al. 2015), the seismic intensity attenuation model (Li et al. 2003;Ren et al. 2020), and the evaluation of the highest seismic magnitude (Li et al. 2010;Wang et al. 1991), are difficult to be used for accurate prevention of earthquake disasters. Although the current research results of seismological science pose uncertainties to predictive research, they can still be fully utilized as an important way to effectively assess earthquake disasters and emergency rescue.
Following the Construction Standards of Relief Supply Warehouses (Jian Biao 121-2009) (Ministry of Civil Affairs 2009), this study systematically sorted and quantified several evaluation indicators, such as "within the 5 km radius range of a highway entrance," "flood frequency > 0.4 time/a," "county-level area whose GDP is not the lowest," "among the top 50% of all the units in the study area in terms of average unit elevation," and "among the bottom 15% of all the units in the study area in terms of the SD of unit elevation." So far, no Chinese or international standard is available for reference for the above indicators. This study, utilizing a literature review and expert interviews, restored an actual situation of post-earthquake disaster relief in western Yunnan Province to the greatest extent. Therefore, the selection of these indicators is reasonable and feasible. It is indicated that scholars in the future can effectively evaluate the site selection of relief supply warehouses by referring to existing indicators when sorting out and editing historical information.

Contribution and innovation
This study proposed a method of site selection for relief supply warehouses based on the prediction of earthquake disasters and the quantification of site selection criteria and finally obtained an ideal site. Compared to studies on site selection methods that focused on a single factor, such as the transport roads of relief supplies (Zhang et al. 2019), victims' pain perception (Geng et al. 2021), rescue satisfaction, and minimization of warehouse number (Yan et al. 2021), this study comprehensively considered the conditions required for the site selection of relief supply warehouses. It fully utilized the site selection of the current research results of seismology and adopted the disaster-affected areas formed by earthquakes with Ms ≥ 7 and the constraint factors of disaster relief as constraint conditions for site selection. Therefore, it is both practical and innovative. First, when identifying disaster-affected areas, this study took the results of scientific research on the prediction of disaster-affected areas as its basis instead of making blind assumptions. It successfully identified disaster-affected areas by delineating seismic intensity zones according to the regional seismic intensity attenuation model and recognizing buildings in the region using remote sensing recognition technology. Second, by comprehensively analyzing the occurrence laws of earthquake disasters in the study area and fully utilizing the research findings on earthquakes, this study predicted the mode and facilities for the transport of relief supplies within a short time. It obtained the maximum range of transport of relief supplies, offering a scientific calculation basis for the maximal covering location method.
Third, it sorted out the site selection conditions described in the Construction Standards of Relief Supply Warehouses (Ministry of Civil Affairs 2009) and quantified the requirements of various conditions based on the actual needs of the study area and the maximum range of transport of relief supplies. Next, it set the necessary conditions, optimization conditions, and reference conditions based on the logical relationships of these conditions. Finally, it obtained an ideal site that could meet construction, declaration, acceptance criteria, and practical demands. In summary, this study differed most prominently from existing studies in following the principle of "people-oriented, cost-ignoring" disaster relief in China. It avoided introducing assumed conditions in prediction and adopted quantitative conditions closely related to declaration and acceptance as constraints over subjective methods in weight assignment, thus bringing research results closer to reality.

Conclusions
In dealing with earthquakes with Ms ≥ 7 occurring in anthropic zones, the Chinese government upholds the principle of "people-oriented, cost-ignoring" disaster relief to provide adequate relief to victims at the earliest time possible. The timely arrival of relief supplies at disaster-affected areas depends on whether the site selection of the closest large relief supply warehouse is scientific. This study has elaborated on how to predict the disasteraffected areas of earthquakes with Ms ≥ 7, the mode of post-earthquake transport of relief supplies, and the safe transport distances of different modes of transport. It has ultimately obtained an ideal site by quantifying and classifying the site selection criteria of relief supply warehouses in China. This method comprehensively considers the destructive power of disasters, the constraints of the mode of transport, and the construction standards of relief supply warehouses. It can be used for site selection of large relief supply warehouses in dealing with disasters with poor predictability and significant relief demand according to the realities of different regions.
This study examined the site selection of relief supply warehouses in detail, but some practical problems are still worth further exploration. First, it predicted disaster-affected areas based on judgments about seismic intensity zone and building distribution. The method for recognizing the seismic grades of buildings can be introduced into subsequent research to more accurately identify disaster-affected areas (Renkli and Duran 2015). Next, municipal conditions were quantified in this study based on regional per capita GDP data in site selection criteria. In future research, in-depth discussion can be provided to better quantify municipal conditions. Future research can be combined with studies in the field of safe production to give further thought to the requirement of "kept away from fire sources and flammable or explosive factories and warehouses" to avoid the contradiction between site selection conditions and turn it into a necessary condition for site selection after the quantification. Moreover, with the increase in the number of military and civilian emergency drills, relatively accurate evaluation criteria can be established on related issues, such as the number of helicopters to be used for transporting relief supplies and the time taken to load and unload relief supplies. We can more precisely predict the demands for relief supplies and the timeliness of their arrival and conduct more in-depth research on the psychological states of victims (Benini et al. 2009).