Data envelopment analysis of flood retention area management for a large-scaled catchment: a case study of Huai River basin, China

ABSTRACT According to China’s national standard, the design of flood retention areas should cover four hydrological situations associated with 10–100-year return period events, and their capacities should be kept operational for at least 30 years after completion. The Huai River basin is one of the large river basins in China, with an area of 270,000 km2 and 31 flood retention areas. To achieve integrated flood management by combining various uses in the flood retention areas, three scenarios were developed for three reference retention areas. The relative efficiency of each flood retention area is assessed using a data envelopment analysis model according to various standards over a period of 35 years after completion. The results show that by considering 10 indexes that refer to flood control capacity and social and economic influences, the partial wetland restoration solution would be the optimal flood management option for the Huai River basin, with highest efficiency. Moreover, by considering the 50-year return period flood standard as the threshold value, maintaining the status quo would be the more efficient approach. This strategy for the sustainable management of flood retention areas in the Huai River basin is promising and can be generalised for other large catchments in China.


KEYWORDS
Integrated flood management; flood retention areas; data envelopment analysis; Huai River basin

Introduction
Large hydrological catchments play an important role in economic development and the social structure in large countries such as China, India, Brazil, Russia, etc. The frequent occurrence of storms and floods associated with inundations has become a major bottleneck that restricts the sustainable development of societies and the associated economy, and floods also impact the ecology of rivers. For millennia, the Chinese people have faced numerous challenges related to flood management at the catchment scale. During the last few decades, to reduce the consequences of flooding, China has implemented a series of large-scale water conservancy and flood control projects to develop an innovative and original flood control approach based on structural and nonstructural systems. These have significantly improved the flood control standards for large catchments within the country (Liu, 2003). The massive development of flood retention areas, also known as flood plains or flood expansion areas, are a key component of the approach and play an important role in peak and flood reduction. These elements have become a key component of the Chinese flood defence system (Y. Wang & Xiang, 2013). Flood diversion and retention areas have significantly improved flood control benefits at the overall catchment scale. However, the implementation of these retention areas has generated additional losses that need to be compensated for or mitigated to ensure economic and social sustainability. This current complex situation demonstrates that the single-target flood control concept cannot serve as an operational approach that answers all of the needs that are appearing with the creation of retention areas. To answer the current challenges, an inclusive approach is needed to reconcile flood control with social and economic development. It is apparent, therefore, that flood management at the catchment scale has to enter a new period based on a holistic approach oriented towards the implementation of "integrated flood management" (Charnay, 2011;Dawson et al., 2011;De Warchien et al., 2011;Mingxuan et al., 2018;Thieken et al., 2007;Tunstall et al., 2004).
A sustainable development approach for a flood retention area can include three types of strategies: • The first solution is based on a multi-objective flood storage area approach. It considers economic benefits, the water supply and leisure functions (Scholz, 2007). This approach first divides the flood retention area into different categories: hydraulic flood storage areas (flood storage reservoirs that target hydropower, the water supply and flood control), traditional flood storage areas (common flood control and water supply reservoirs), sustainable flood storage wetlands (large areas of wetlands and storage ponds), aesthetic flood control wetlands (constructed wetlands for water quality improvement), comprehensive flood storage wetlands (small watershed wetlands with high landscape value, mostly in parks) and natural flood storage wetlands (typical natural water bodies, such as lakes; Yang et al., 2012). In addition, it implements a specific management strategy according to land use, ecological protection and water conservancy projects. • The second approach is based on the development of a flood storage reservoir. According to this concept, the stored water within the reservoir can be reused for various purposes after the flooding period. Using this classical approach, a dam can be constructed to initiate the storage area and used for hydropower generation by taking advantage of the characteristics of large upstream flows and the potential head loss offered by the topographic characteristics of the valley (Danso-Amoako et al., 2012). This approach has been implemented in Switzerland in the Wallis Canton and Oberhasli power stations (Schaefli et al., 2005). • The third approach is the transformation of a flood plain using multiple-target development for flood control, ecological protection and water resource preservation purposes. This concept was used for the "Plan Stork" project established by the Netherlands in the 1980s (Fliervoet et al., 2013). In this approach, nature-based restoration concepts are combined with flood defence measures. Intensive agricultural farming activities in the flood plains are strongly decreased or banned to reduce soil erosion and sedimentation processes. Agricultural practices are also revised using extensive farming with large herbivores to help restore the biodiversity of the flood plain and to improve the environmental quality.
In China, until now, flood retention areas have primarily been designed with the single purpose of storing flood waters to reduce the occurrence of peak flows. The retention areas have been located in the most sensitive places and have been created using various technical solutions such as reservoir water storage (Liu et al., 2004), rubber dam water storage (Luo et al., 2004), plain depression water storage (Ding et al., 1984) and pond water storage (Mao et al., 2003). All of these solutions are part of the national flood control approach. The diversity of situations requires the definition of a global strategy that can be deployed at the country scale. To elaborate on this new approach, an in-depth analysis was conducted on the Hai River catchment (318 200 km 2 ), where various retention areas, such as the Dahuangpuwa flood storage area (C. Li & Wang, 2006;Peng et al., 2005;Y. Wang et al., 2009), have been built and managed for several decades. The analysis concluded that the development of a large-scale flood storage reservoir is one of the most suitable approaches to manage floods in the Hai River basin. Although the most relevant approach for the Hai River basin could be formulated easily, this is not always the case in all catchments due to the complexity of the initial conditions and the multiplicity of the objectives to be achieved. In such a situation, various options should be formulated and analysed before making decisions. In this paper, using a new methodology, three scenarios for the future development of flood retention areas are explored for the Huai River basin (270 000 km 2 ) -(1) maintaining the status quo; (2) partial farmland wetland restoration; and (3) partial farmland reservoir utilisationand an indicator system that integrates the aspects of flood control and socio-economic and ecological development is established. These scenarios are applied to evaluate the relative efficiency of the different design options. This analysis is constructed based on an assumption that all of the retention areas will continuously operate over the entire evaluation period. The primary goal of the study is to provide a scientific basis for the sustainable management of floods in retention areas within large catchments (greater than 100 000 km 2 ) and to improve the management of those areas.

Methodological framework
Based on the analysis of the flood control functions, the need to coordinate social and economic development, and the flood storage operation in the retention areas of the Huai River basin, this approach considers and evaluates three potential development plans based on the following scenarios: (1) maintaining the status quo; (2) introducing a partial wetland restoration; and (3) introducing a partial permanent reservoir. For each scenario, the population, agricultural losses and economic benefits are considered and analysed. An indicator system was then further established and a data envelopment analysis (DEA) model was applied to evaluate the benefit of each flood control approach in terms of the social, economic and ecological dimensions. Based on the evaluation results, a sustainable development approach for flood retention areas under different activation frequencies was explored. The technical framework is summarised in Figure 1.

DEA model
The DEA model is a non-parametric mathematical model used to evaluate the relative effectiveness of multi-input and -output decision-making units (DMUs). As its input and output objects are clear, the lack of consistency and subjectivity of the judgement matrix in the analytic hierarchy process can be fabricated (Zeng et al., 2000). The C2r (Charnes, Cooper and Rhodes) mode is one of the classical DEA calculation methods that has advantages for evaluating both the scale and the technical effectiveness at the same time. In addition, it is widely used in evaluation research in the field of sustainable development (Zhang, 2007).
In the chosen approach, the challenge of retention area management is defined as a typical decisionmaking assessment that requires comprehensive consideration of multiple objects, including the social, economic and ecological dimensions, in addition to flood control operations. As the core work focuses on the assessment of input and output efficiencies of the different scenarios, the C2R model was applied to quantitatively evaluate the relative efficiency under different development approach scenarios in flood retention areas. The three scenarios corresponded to three DMUs. Each DMU j (j = 1, 2, 3) has m types of inputs and s types of outputs. x ij is the input of the j th DMU to the i th input, x ij >0; y rj is the output of the j th DMU to the r th output, y rj >0; v i is a measure for the i th input; u r is a measure of the r th output, i = 1, 2, 3, . . ., m; r = 1, 2, 3, . . ., s; and j = 1, 2, 3. The equation is as follows: For the coefficients v and u, the efficiency evaluation index of the decision-making unit DMU j is: According to the indicator system constructed in this paper (Table 1), the input and output items in the C2R model can be clarified. Input indicators include: the water storage risk (C2), the area affected by inundation (C3), the population affected by inundation (C4), inundation loss (C5), construction cost (C6) and the water pollution load purification benefit (C9). The output indicators include: the flood water storage benefit (C1), the total net economic benefit (C7), the clean water supply benefit (C8), and climate and other ecological benefits (C10). By constructing an input-output matrix for the flood retention areas, the relative efficiency of the different development approaches, h j , can be evaluated objectively. Represents the water storage capacity under different development approaches in flood retention areas. Water storage risk (C2) Represents the negative benefits brought by flood control benefits expressed by the submerged water depth (B. Li et al., 2013). See Equation (3) for the calculation method of reservoir water depth, and see Equation (4) for the wetland water storage depth (B. Li et al., 2013;Wu & Zhu, 1995;Xie, 2006 Represents the amount of clean water that the flood retention area provided in short-term water storage, construction of the water storage facilities, and wetland storage under the current situation. Water pollution load purification benefit (C9) Represents the increase in the water pollution load when the three scenarios reach the maximum carrying capacity of aquaculture.
Climate regulation and other ecological benefits (C10) Represents the benefits of climate and humidity regulation, air purification benefits, aesthetic benefits, carbon fixation, and oxygen release benefits quantified according to the water surface area (Han et al., 2008;H. Wang, 2007;Z. Wang, 1998) after water storage in the flood retention area.
For the main index they are flood water storage benefit (C1), water storage risk (C2), area affected by inundation (C3), population affected by inundation (C4) and inundation loss (C5); these have a higher sequence. As for construction cost (C6), total net economic benefit (C7), clean water supply benefit (C8), water pollution load purification benefit (C9) and climate regulation and other ecological benefits (C10), they are lower.
Among the numerous variables and tools, Equation (3) is used for the calculation of the reservoir storage. In addition, Equation (4) is used for the wetland water storage volume calculation.
where V is the water storage volume (m 3 ); A is the inundated area (m 2 ); and H is the water storage depth (m).

Selection of the typical flood retention areas
The Huai River basin consists of the Huai River itself and its main tributary, the Yishu River (Figure 2). The basin spans the Henan, Anhui, Shandong and Jiangsu provinces and portions of Hubei province in China. It has an area of approximately 270 000 km 2 and a population of 164 million. The Huai River basin is one of the most flood-prone areas in China. The control of the inundation processes within the catchment is particularly complex and requires constant effort. In the past 500 years, 350 major floods have occurred in the Huai River basin. As of 2006, 27 flood retention areas had been created along the Huai River (Figure 3), with a total area of 3926 km 2 , including 2281 km 2 of cultivated land and a population of 2.85 million inhabitants.
According to the characteristics of the area that must be protected against inundations, China's current national standards for flood retention/protection areas are defined according to four levels associated with the 10-year, 20-year, 50-year, and 100-year return period floods (National Construction and Management Plan for Flood Retention Areas, 2009). The flood retention areas constructed using a 10-year return period flood design were planned to be used merely when the flood level in the primary river channel exceeds the 10-year return period threshold. Therefore, with the design of a longer return period flood, the planned activation frequency of the flood retention area would be relatively reduced. However, the national standards require that the life cycle of the flood retention area should be longer  Control Projects, 1998). Therefore, considering the needs of flood control and socio-economic development in the Huai River basin, three flood retention areas in the basin were selected as the managing objects for the integrated flood management and sustainable development approach for their future development. The initial conditions of the selected flood retention areas are shown in Table 2. The three selected flood retention areas were respectively designed for the 10-, 20-, and 50-year return period floods. However, in reality, they were operated for floods within a lower standard. All three flood retention areas were constructed in the 1950s and frequently used during the period from 1950 to 1990, when the region was relatively undeveloped. Since the 1990s, with an increase in local economic activity, these flood retention areas were operated only during floods that were over their respective design standard. Thus, during the period from 1990 to 2020, only the Mangwa flood retention area, which was designed with a 10-year return period, has been frequently used (approximately once per decade).

Dynamic scenarios for future development
The approach for managing a flood retention area can be classified into two categories: temporary storage and permanent storage. The temporary storage approach is used to store floodwaters during the flood season and to release that amount of water into the main stream after the floods. This procedure is the current flood management approach widely applied in China. The permanent storage approach is considered a type of optimisation strategy for future flood management. It attempts to optimise the land use in flood retention areas for the long-term storage of flood water for detention and continuous uses.
Based on the current management approach and considering the optimal management options for the future, three scenarios for the flood retention areas can be defined: (1) maintaining the status quo; (2) partial wetland restoration; and (3) partial reservoir transformation (Table 3).
The first scenario is an extension of the current conditions. This scenario assumes both the present management strategy and the present operational mode will be maintained during the evaluation period. The flood retention area will only go into operation when the flood is over a standard threshold, and the losses of local residents will be compensated by the government on the basis of "Interim measures for compensation for flood storage and detention areas".
The second scenario is a water resources optimisation scenario that considers flood water a natural resource that requires an integrated management approach. The approach considers the losses and benefits of flood defence facilities, land uses, reservoirs Table 2. Details of the selected flood retention areas in the Huai River basin .

Flood retention area
Designed use Actual use of the retention area Used for flood management Mengwa area 10-year return period 5-year return period 1954,1956,1960,1968,1969,1971,1975,1982,1991,2003,2007, 2020 Chengxi Lake 20-year return period 15-20-year return period 1950,1954,1968,1991 Huangdun Lake 50-year return period 50-year return period 1957 Note. The underlined year is considered the starting year of each typical flood retention area in the scenario analysis. and the migration of local residents. This scenario aims to optimise water resources allocation during the flood season to reduce losses and to realise the integrated utilisation of floodwater resources. The third scenario is a multi-objective utilisation scenario. On the basis of flood water resource optimisation and referencing the strategy of sustainable development, this scenario aims to realise multiple objectives including flood control and management, improvements in social and economic conditions, and the promotion of the local ecological environment.
By defining the flood retention area as a dynamically changing system, many indicators, such as rates of births, deaths and migration; agricultural production; economic losses; and the flooded population, are considered in the analysis model. The corresponding growth and reduction rates are also included.
The basic values of those indicators are defined by references obtained from published documents: • Population: according to the "Work Report of the Anhui Provincial Government, 2007", the annual population growth rate of the Huai River basin in Anhui province is 8.7‰, and the migration rate is 8% every 10 years. • Losses: according to the "Anhui Province County Economic Statistical Yearbook 2007", the gross domestic product (GDP) growth rate of the counties in the flood retention area is 6.95%. Therefore, for the first scenario (S1), the losses will maintain the current situation. For S2, the assumption is that when the flood retention area is used to restore the flood waters, all of the agricultural income from this area would be lost. (The annual growth rate of the agricultural income in the flood retention area is nearly 3.91%.) For S3, the losses caused by the reservoir occupation of farmland were considered to be the same as those in S2. • Benefits: for S1, the economic benefit was calculated by referencing the growth rate of the annual agricultural income (3.91%). For S2, the local economy will be developed, through, for example, the planting of Salix (a common economic crop in the Huai River basin that can be used for making willow handicrafts). The annual economic growth rate was modified to 2.86%; compared to the direct agricultural benefits, this is relatively lower. For S3, the constructed reservoirs could be used for aquaculture. Thus, to quantify its economic benefits, it was assumed that the annual economic growth rates of S2 and S3 were the same (2.86%).

Design of flood retention areas under the different scenarios
In the analysis, the C2R model was run for a period of 35 years with the values presented in Table 3 and with the rules defined for the flood retention areas in the Huai River basin. The evaluation indexes defined in the different scenarios indirectly refer to the flood cycles that occur in the Huai River basin and assume that the activation frequency of the flood retention areas is highly related to the design standard for the different flood return periods.

Design of the 10-year return period flood standard
In the case of a 10-year return period flood retention area in the Huai River basin, and over a period of 35 years, the assumption is that the flood retention area will begin operation after the 10th year, and the use of this retention area will have a high frequency. The flood retention area indexes were then updated according to the influence of the different development scenarios. The storage risk (C2), area affected by inundation (C3) and inundation loss (C5) are the indexes directly related to the area utilisation, and these will obviously increase at the 10th year when the area begins to be used. The construction cost (C6) is a one-off investment that will last for the entire 35year period (following Chinese law). The water pollution load purification benefit (C9) is not used in S1. For S2 and S3, due to the benefit from water resource purification, C9 will increase. By assuming that the use frequency will be the same as its designed standard, the number of flood-affected residents (C4) in S1 will change every 10 years. However, in S2 and S3, this The natural growth rate is 0.87%, and the migration rate is 8% every 10 years.
Calculated based on the 6.95% GDP growth rate in flood retention areas.
The growth rate of agricultural income is 3.91%. Partial wetland restoration (S2) Calculated based on the agricultural losses caused by wetland restoration occupation of farmland, with an annual growth rate of 3.91%.
The wetland economic benefit growth rate is 2.86%. Partial reservoir transformation (S3) Calculated based on the agricultural losses caused by reservoir occupation of farmland, which the same growth as S2 (3.91%).
The growth rate of aquaculture benefit is 2.86%.
Note. GDP: gross domestic product. The setting of indicator values under the different development scenarios is determined according to the multi-year average growth rate or reduction rate of the relevant indicators in flood retention areas.
index will be modified every year as the flood retention area is used more frequently. The total net economic benefits (C7) will be considered in all three scenarios. For S1, this index will be affected by the operation frequency of the flood retention area.

Design of the 20-year return period flood standard
In the case of a 20-year return period flood retention area in the Huai River basin, over a period of 35 years, the use of this retention area would be characterised by lower frequency floods than the 10-year return period retention area mentioned previously. By applying similar flood cycle conditions as in the 10-year period flood case, all of the indexes, except the affected population (C4) and the total net economic benefit (C7), will change with a consistent trend in the three different scenarios, with the highest fluctuations in S1 and lower fluctuations in S2 and S3.

Design of the 50-year return period flood standard
For the retention area designed for the 50-year return period flood in the Huai River basin, its activation frequency will obviously be lower compared to the 10-and 20-year return period flood retention areas. However, as Huangdun Lake (50-year return period design) has been used only once between 1950 and 2020 (in 1957), the analysis integrated the use of the retention area at least once in the future, 35 years after its completion. Therefore, the change trends of each index in S1 will be quite different from those in the other two scenarios. In S1, with the exception of two indexes related to the affected population (C4) and the total net economic benefit (C7), all of the indexes will remain consistent during the entire 35-year period.

Design of the 100-year return period flood standard
In the case of a flood retention area designed for a 100year return period flood, its likelihood of operation is quite low compared to the other areas with lower design standards. For the analysis, no 100-year return period flood was recorded over the reference period of 35 years. Therefore, in the S1 scenario, with the exception of the C4 and C7 indexes, all of the indexes will remain consistent during the evaluation period. However, compared to the case of the 50-year return period flood design, some of the indexes will steadily increase in the S2 and S3 scenarios.

Results and analysis
To identify the optimised development of the flood retention areas in the Huai River basin, the relative efficiencies between the inputs and outcomes of the flood retention areas were calculated using the C2R model within a time interval of 5 years during the 35year period after the completion of the various cases and under the different scenarios. The values calculated from the model corresponded to the relative efficiencies with a higher value, indicating more integrated benefits that could be obtained from the design scenario.
Within the standard of defending against a 10-year return period flood, the designed flood retention areas in the catchment showed the highest relative efficiency in the S2 scenario based on the partial wetland restoration approach. Despite the values showing a decreasing trend during the period from 5 to 10 years after the construction was completed, this approach still showed high levels of self-recovery and self-regulation capabilities and returned to the highest level among the three scenarios ( Figure 4). Therefore, for flood retention areas designed for a 10-year return period flood standard, the partial wetland restoration approach could be considered a long-term and sustainable development strategy for flood management. The solution allows both an efficient flood hazard management strategy and the optimisation of economic, social and ecological development in the catchment.
In the case of the flood retention area designed for the 20-year return period flood standard, the relative efficiency calculated using the three different scenarios showed a consistent trend in the first 15 years after construction completion. However, after 15 years, the relative efficiency calculated for S2 showed a major increase, from 0.488 to 1.505, and then continuously maintained a higher level in the remaining years ( Figure 5). Compared to the case of the 10-year return period flood design, with a lower use frequency, the flood retention area showed fewer benefits for short-term flood management. However, over time, the advantages of applying the partial wetland restoration approach for flood management of the Huai River basin became more obvious than for the other two approaches.
For the case of lower use frequency (the flood retention area designed using a 50-year return period flood), the partial reservoir transformation approach showed obvious advantages in short-term flood management, with high relative efficiency value (8) during the first 10 years after implementation. However, the benefits produced by the partial reservoir transformation approach will rapidly decrease over time with the growth in the maintenance cost of these reservoirs ( Figure 6). According to the model assessment, the approach of maintaining the status quo has been identified as an inefficient solution for the management of flood retention areas in the Huai River basin. The approach of partial wetland restoration was determined to be the most suitable strategy for managing flood retention areas in the basin. This strategy is able to simultaneously provide flood control and socio-economic and ecological benefits. According to the relative efficiency calculated at the end of the assessment period (35 years after the baseline years of three existing flood retention areas in the catchment), the partial wetland restoration approach has been confirmed as the best measure for flood management (Figure 7).
In terms of the three scenarios, if S1 is applied the current conditions will be maintained for the next 35 years, and the local residents will be affected when the flood retention area is used for protecting against floods over a certain threshold value. Thus, the costs of migration, agricultural losses and the non-efficient utilisation of flood water resources will reduce the benefits. However, in both S2 and S3, flood waters would be stored in the retention area for relatively longer terms. Due to the cost of constructing and maintaining the reservoir in the S3 scenario, the S2 scenario, which implements a partial wetland approach, is recommended for frequently used flood retention areas.
According to the records (SL206-98), more than 70% of the flood retention areas in the Huai River basin are designed with a standard lower than the 50-year return period. The affected population of those areas accounts for 61.8% of the total number of residents who live near the flood retention areas. By implementing a wetland restoration strategy in these areas in a coordinated manner, the optimisation of flood control, social and economic benefits, and ecological improvement in these areas will be reached.

Conclusions
The current work focused on the management of flood retention areas in the Huai River basin. The study identified the optimal strategy to foster social and economic development and ecological preservation along with inundation control. Based on three dynamic scenarios, the C2R model was applied to assess the efficiency of these management approaches. The primary conclusions are as follows In cases where different design standards have been used for construction of flood retention areas, the approach of a partial wetland restoration showed the greatest promise from a long-term flood management perspective. This solution is able to balance the losses and benefits in terms of the economic, social and ecological aspects and further enhances the effects of flood retention areas at the catchment scale. Therefore, the implementation of this approach could strongly improve the current flood management capacity in the Huai River basin.   The design standard of the 50-year return period flood was applied as the threshold value for defining the use frequency of the flood retention areas in the different scenarios. For the high-use-frequency measures, the economic, social and ecological development in the flood retention areas would be restricted by the frequent use of flood storage, while a partial wetland restoration could help residents near the flood storage areas to eliminate the large impact on their activities and to obtain additional economic income associated with the improvement in living standards. For the low-use-frequency measures, the economic activities and the ecological environment were found to be less affected by the flood control function. Although the approach of a partial reservoir transformation could bring more benefits in the short term, when additional flood events occurred, its relative efficiency would be significantly reduced over time as the cost of maintenance rose.
The management of flood retention areas is a complex global issue requiring a holistic analysis that integrates various scenarios including flood issues and all their various dimensions related to specific application areas. The results obtained within the Huai River basin support the implementation of the concept of "integrated flood management". The proposed approach has been applied successfully to support the decision-making process within the Huai River basin. Obviously, the approach should be embedded within a global process that integrates the multiple objectives of retention areas. The results of this proposed method can significantly support the decision-making process and may help to develop a hierarchy of priorities for the strategic planning of retention areas at the catchment scale.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
This work was supported by the National Key R&D Program of China [grant number 2019YFC1510603].