1 Introduction

The effective allocation of disaster reduction funds is crucial for governments to strike a balance between investing in disaster risk reduction (DRR) and promoting economic development. However, decision makers may hesitate to invest in DRR if they lack quantitative information on the economic and social benefits of such investments (Miyamoto et al. 2014). Moreover, the fragmentation of disaster reduction tasks across multiple government sectors often leads to competition in the allocation and utilization of DRR funds (OECD 2014). Therefore, it is essential to assess and quantify the effectiveness of DRR projects. Cost-benefit analysis (CBA) is a valuable tool for evaluating the costs and economic benefits of mitigation measures (Botzen et al. 2017), as it facilitates coordination among different policy areas and levels of government.

Flood risk management projects, which typically involve considerable investment in both structural and non-structural measures, often exhibit significant variations in their investment-return ratios (Genovese and Thaler 2020). Furthermore, these measures often require long-term and continuous investment, regardless of whether they involve engineering structures like dams and levees (Boulange et al. 2021) or other green measures (Hartmann and Spit 2016). The costs of flood DRR projects can stem from various sources, such as structure construction, land acquisition, resettlement, environmental management, project design, and supervision. On the other hand, the benefits of flood DRR projects encompass flood risk reduction, resettlement opportunity, water resources provision, hydropower generation, and more. Consequently, a comprehensive and quantitative CBA must be employed to effectively assess these flood DRR projects.

While a variety of previous studies have examined the CBA of flood risk management projects, there are still research challenges and practical gaps that exist in ensuring reliable assessments (Botzen et al. 2017; Casajus Valles et al. 2021). With regards to cost evaluation, existing studies predominantly focus on quantifying one-time upfront costs, such as construction and financing, while giving insufficient consideration to the ongoing costs of operation, maintenance, and management (Roy and Remco 2004). Additionally, dynamic changes in parameters throughout a project’s life cycle, such as fluctuations in interest rates and depreciation rates, are seldom considered when calculating financial and operations and maintenance (O&M) costs, thus compromising the accuracy of cost assessments (Tajziehchi et al. 2022). As for benefit evaluation, the direct economic benefits of flood control projects, such as hydropower generation, water supply, navigation, and irrigation, are relatively straightforward to calculate and evaluate, and thus are more likely to be included (Kotchen et al. 2006; Udayakumara and Gunawardena 2018; Nobi 2022). However, quantifying the direct economic benefits stemming from future disaster loss reduction requires more complex methods, such as probabilistic risk analysis. To generate the annual average loss (AAL), a key indicator representing the effect of disaster loss reduction, a sequence of modeling steps is necessary, including probabilistic flood event analysis, numeric flood inundation simulation (Husnain et al. 2020), vulnerability curve quantification, and loss exceedance probability analysis (Grossi et al. 2005). Due to the considerable input data and modeling efforts required, probabilistic risk analysis has rarely been used in previous CBA of projects. Instead, simplified data or methods have been more commonly employed, such as leveraging the losses from historical flood events (Barredo 2009), or conducting deterministic scenario analysis (Saint et al. 2015). Another significant but often overlooked challenge is the omission of certain costs or benefits during the CBA process. For instance, there are few detailed studies on the cost and benefit of resettling local residents, which may result in an under or overestimation of the returns from DRR projects.

In recent years, flood management measures, such as green infrastructure and low-impact development, have gained popularity (Liu et al. 2016). Flood disasters in small or medium basins still account for a significant portion of human and economic losses in China (Cheng 2019). In response, 172 flood disaster risk management projects for small and medium rivers, with a total budget exceeding RMB 1 trillion yuan, were planned and implemented by 2020 (Wang and Hu 2011). However, due to methodological gaps and data availability issues in CBA, a quantitative and reliable assessment of the effectiveness of these projects has not been fully realized during the planning and post-completion stages.

One of such projects, the Wuxikou Integrated Flood Management Project (WIFMP), was initiated in 2016 and has been in full operation since 2020. Besides receiving substantial investment from the local government, the project also obtained a loan from the World Bank as part of the China Country Partnership Strategy (FY2013-2016), aiming to achieve environmentally-friendly and socially-inclusive disaster mitigation (World Bank 2012). Despite some analyses such as flood hazard assessment (Sun et al. 2017) and flood risk perception (Wang et al. 2018) in the WIFMP region, few studies have quantitatively assessed economic benefits.

In this study, we aimed to demonstrate a refined quantitative cost and benefit analysis using the WIFMP as a case study. We refined the CBA framework by incorporating hydrological analysis, a hydrodynamic model to capture the probability distribution of flood risks, and economic loss models to quantify damages across probability scenarios. By integrating spatial data and numerical models, our cost-benefit analysis can reduce reliance on sparse statistics and better represent flood risks spatially. Additionally, we quantified the social benefits of resettlement based on survey data and analyzed the future average annual flood losses and capital recovery period of the project. This refined CBA approach can help reduce uncertainty in loss assessment, provide detailed economic benefits information for stakeholders, and guide local governments in making more effective disaster mitigation investments.

2 Materials

This section describes the background of the WIFMP, the hydrological characteristics of the study area, and the data used in this study in relation to the costs and benefits of the WIFMP.

2.1 Study Area

The WIFMP, located in the northeast of Jingdezhen City, Jiangxi Province, China, is a large-scale flood control project constructed during 2013–2020 for flood management, water supply, and hydropower generation. The reservoir dam (Fig. 1, red dot), the primary flood management measure, is on the mainstream of the Changjiang River in Fuliang District, about 40 km upstream of Jingdezhen City. The distribution of the river network and hydrological stations in the Changjiang River basin (Fig. 1, the dark blue dashed line indicates the boundary of the river basin) is shown in Fig. 1.

Fig. 1
figure 1

Location of the water system, hydrological stations, and Wuxikou reservoir dam (WXK) in the Changjiang River basin and the districts of Jingdezhen City in the study area. DFK represents Dufengkeng hydrological station, and ZSK represents Zhangshukeng hydrological station

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The convergence of the Changjiang River and several tributaries in the Jingdezhen city center (Fig. 1, the red dashed line indicates the boundary of the Jingdezhen urban area) results in the city’s susceptibility to frequent flooding. Moreover, weak flood prevention infrastructure in Jingdezhen City has resulted in severe economic losses and human casualties, and flood mitigation measures are in urgent need. The flood in 1998 (peak discharge 9100 m3/s) flooded 31.4 km2 of land and affected 354,000 people and 2355 economic entities, causing direct losses of 322.6 million yuan. As part of Jingdezhen City’s flood risk management strategy, the WIFMP is considered the most cost-effective approach to enhancing the city’s flood protection level from a 20-year to a 50-year event. It involves the adoption of priority structural and non-structural measures and contributes towards the establishment of an integrated flood risk management system for the city.

2.2 Data for Cost Calculation

The cost estimates for the WIFMP are derived from project design and economic evaluation reports obtained from the WIFMP Management Office, the World Bank, and third-party independent evaluation agencies (Jiang 2019; JCMG-PMO 2020). The collected reports indicate that the WIFMP’s tangible costs comprise construction (civil works, equipment, transmission, environmental risk mitigation, owner management), bank loan interest, and operation and maintenance expenditures. The report content adheres to national laws and regulations and World Bank policies, and thus has high reliability.

2.3 Data for Benefits Estimation

The hazard and exposure data collected provide the foundation for estimating the flood risk reduction benefits of the project.

2.3.1 Hazard Data

The hydrometeorological data for hydraulic model simulations were collected, processed, and analyzed by the Hydrological Bureau and Meteorological Center of Jingdezhen City. In addition, the social impact assessment report of the project provided information on land acquisition, house demolition, and cash compensation for resettlement. An independent expert team and an experienced design institute offered technical support and guidance on the WIFMP, guaranteeing the reliability of the data.

2.3.2 Exposure Dataset

The flood loss assessment encompasses direct and indirect economic impacts, including losses of agricultural output value, fixed assets and secondary production output, fixed tertiary production assets, and primary industrial enterprise income. To improve assessment accuracy, the economic indicator data at the district level were collected from the local statistical yearbook (JMBS 2015) and comprehensive strength assessment reports, respectively. Furthermore, the socioeconomic data downscaling of statistical units from district to township level (Fig. 2) used the ratio of the two datasets regarding flood losses. The districts with a high social economic development level are mainly located on the downstream section of the WIFMP along the Changjiang River, which is also the area that suffered more severe flood damage in the past. The pie chart shows the share of value of different economic sectors, with industry and services being the main socioeconomic activity types in the city.

Fig. 2
figure 2

Distribution of the primary, secondary, and tertiary industry and total economic values of each district in the study area. The intensity of yellow and red in the figure indicates the size of the economy of the districts (billion yuan). WXK represents Wuxikou dam station, ZSK represents Zhangshukeng hydrological station, and DFK represents Dufengkeng hydrological station

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3 Methods

This section presents the methods for cost estimation and benefit evaluation. Flood protection benefit with AAL as representative indicator is estimated by risk modeling, and resettlement benefit is estimated by considering the income change of immigrants. The cost of the project includes capital investments and O&M expenditures.

3.1 Quantification of Cost and Benefit

The CBA method estimates flood losses by combining hydrology, GIS, and economic modeling. It calculates economic evaluation indices such as the annual average loss (AAL), the net present value (NPV), and the internal rate of return (IRR) to evaluate the economic benefits of disaster reduction projects.

The CBA consists of five steps: (1) statistical analysis of the tangible costs of the project construction; (2) quantification of the mitigation impact of the project construction using a hydraulic model compared to a scenario without the mitigation project; (3) assessment of the mitigation effect of the project through economic quantification, calculation of the flood risk reduction benefits of the project, and other benefits; (4) establishment of a costs and benefits table, and the calculation of comprehensive index values such as NPV and IRR; and (5) sensitivity analysis to measure the impact of different assumptions on the project results. All future benefits and costs, including nonmonetized benefits and costs, are discounted in the calculation, and the benefits and losses in different periods are converted into the same unit of measurement.

The AAL represents the integral overall probabilities of the flood risk density curve, which is used to quantify the flood risk under different conditions by weighting the damage caused by each flood with the likelihood of flood occurrence (Eq. 1). The expected average annual flood loss reduction \(\Delta {\text{AAL}}\) in Eq. (2) is the area enclosed by the two AAL curves before and after the construction of the project, which is the flood risk reduction benefit of the project.

$${\text{AAL}} = \mathop \int \limits_{0}^{\infty } D\left( q \right)p\left( q \right){\text{d}}q$$
(1)
$$\Delta {\text{AAL}} = {\text{AAL}}_{n} - {\text{AAL}}_{w}$$
(2)

where \(D\left( q \right)\) is the expectation of a loss of recurrence period event q; \(p\left( q \right)\) is the probability of recurrence period event q; \({\text{AAL}}_{w}\) is the average annual flood loss after dam completion; and \({\text{AAL}}_{n}\) is the average annual flood loss before dam construction.

The NPV refers to the difference between the present value of the project’s benefits and costs and is often used to assess the economic benefits of a project when performing a CBA. It is expressed by Eqs. (3) and (4).

$${\text{NPV}} = \mathop \sum \limits_{t = 1}^{T} \frac{{\left( {I_{t} - O_{t} } \right)}}{{1 + \tau_{t} }}$$
(3)
$$\left\{ {\begin{array}{l} {I_{t} = I_{p,t} + I_{o,t} + I_{i,t} } \\ {O_{t} = \Delta {\text{AAL}}_{t} + B_{r,t} + B^{\prime}_{t} } \\ \end{array} } \right.$$
(4)

where \(T\) is the project life cycle; \(I_{t}\) is the cost in year \(t\) of \(T\); \(I_{p,t}\), \(I_{o,t}\), and \(I_{i,t}\) are the project construction investment costs, operation and maintenance costs, and loan interest in year \(t\) of \(T\), respectively; \(O_{t}\) is the benefit in year \(t\) of \(T\); \(\Delta {\text{AAL}}_{t}\), \(B_{r,t}\), and \(B^{\prime}_{t}\) are the flood risk reduction benefit, resettlement benefit, and other benefits of the project in year \(t\) of \(T\), respectively; \(\tau_{{\text{t}}}\) is the discount rate in year \(t\) of \(T\), and there are significant differences in public discount rate policies among countries around the world, with the discount rate in developing countries (8–15%) being higher than that in developed countries (3–7%) (Gunatilake 2013).

The IRR refers to the discount rate when the cash outflow and cash inflow generated by investment in the future are equal, that is, the discount rate when NPV is zero. In general, when the IRR is greater than or equal to the benchmark rate of return, it indicates that the project is feasible. According to Eq. (5), the IRR value of the project is calculated when the NPV is zero.

$$\mathop \sum \limits_{t = 1}^{T} \frac{{C_{t} }}{{\left( {1 + {\text{IRR}}} \right)^{t} }} = {\text{NPV}} + C_{0}$$
(5)

where \(C_{t}\) is the net cash inflow in year \(t\) of \(T\), \(C_{t} = I_{t} - O_{t}\). \(C_{0}\) is the total initial investment cost.

3.2 Categorization of Project Costs

Costs \(I\) of the WIFMP is the investment in civil works \(I_{p}\), loan interest \(I_{i}\), and annual operating costs \(I_{o}\) of the project life cycle (Eq. 6). The investment costs includes (1) costs of constructing or improving new or existing flood control work (civil works, equipment, and vehicles); (2) land acquisition and resettlement fees; and (3) other project costs such as surveys, design, supervision, and environmental management. \(I_{i}\) is the interest in production loans, calculated as the interest in long-term loans and current fund loans to be spent in that year. \(I_{o}\) includes staff salaries and benefits, repairs, reservoir maintenance, materials, and environmental protection costs.

$$I = \mathop \sum \limits_{{t_{p} = 1}}^{{T_{p} }} I_{{p,t_{p} }} + \mathop \sum \limits_{{t_{i} = 1}}^{{T_{i} }} I_{{i,t_{i} }} + \mathop \sum \limits_{t = 1}^{T} I_{o,t}$$
(6)

where \(I_{{p,t_{p} }}\) is the project investment in year \(t_{p}\) of project investment cycle \(T_{p}\); \(I_{{i,t_{i} }}\) is the loan interest in year \(t_{i}\) of the interest repayment cycle \(T_{i}\); \(I_{o,t}\) is the annual operating costs in year \(t\) of the project life cycle \(T\).

3.3 Estimation of Flood Risk Reduction Benefit

The flood protection benefit calculations use flood frequency and loss data to estimate the AAL for both no-dam and with-dam scenarios, where the loss difference provides the flood protection economic benefit of reduced flood losses from the project. Flood losses encompass direct economic impacts like property damage as well as indirect effects including casualties, production shutdowns, and lost output.

3.3.1 Development of Flooding Scenarios

As floods are low probability events, estimating AAL requires modeling multiple flood scenarios across a range of intensities to reflect the inherent randomness of these disasters. First, a series of potential flood events with different return periods was selected to reflect the uncertainty in the probability distribution of the risk. Second, the hydrological-hydraulic model was used to calculate flood impacts, and the economic model then quantifies the economic losses. The flood protection capacity of the river embankment in the downstream urban section is 20 year, and the protection standard of the reservoir dam is 100 year. Therefore, five return period flood scenarios—20 year, 30 year, 50 year, 75 year, and 100 year—and an actual flood event in 2020 were selected based on the peak flood discharge.

The design flood process line of the return period flood scenario was derived by the same-ratio amplification method based on the 1998 flood process line. The design flood data (P-III, Cv = 0.56) and peak discharge (Jiangxi Provincial Storm Flood Projection Manual) of typical frequency floods (1%, 1.33%, 2%, 3.33%, 5%) of the Dufengkeng hydrological station (DFK) in the mainstream of the Changjiang River were obtained from the WIFMP Management Office. Meanwhile, the peak discharge and flood process at the boundary sections of the DFK, Wuxikou dam station (WXK), Zhangshukeng hydrological station (ZSK), Xi River (XH), Dong River (DH), and Nan River (NH) during the 1998 flood were known. Finally, the ratio of flood peak discharge under the above five frequencies to 1998 flood peak discharge at DFK was calculated, and the peak discharge value of other river sections was calculated (Table 1). The 2020 flood process lines were obtained from the actual measurement data at the hydrological stations.

Table 1 Flood peak discharge under no-dam (Si) and with-dam (Si′) scenarios at the boundary cross-sections for Wuxikou dam station (WXK), Zhangshukeng hydrological station (ZSK), Dong River (DH), Xi River (XH), Nan River (NH), and Dufengkeng hydrological station (DFK) of five recurrence periods and the 2020 flood
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The WIFMP combines engineering and non-engineering measures to achieve flood control and disaster reduction. Modeling of the non-engineering measures includes a hydrodynamic model built with MIKE 21 for flood forecasting, warning, emergency preparedness and response, and optimal flood scheduling. The model boundary conditions consist of time series of discharge or water level processes at WXK, ZSK, DH, XH, NH, and DFK. Based on the peak discharge at different frequencies in Table 1 and the cross-section discharge process during the 1998 flood at the five boundaries, the discharge processes for various frequencies were scaled using the same amplification ratio (see Fig. 3). Measured discharge processes during the 2020 flood were also incorporated as hydrological inputs for the model simulations.

Fig. 3
figure 3

Boundary conditions for the five return period flood scenarios and the 2020 flood under no-dam and with-dam conditions. RP represents return period, WXK represents Wuxikou dam site, ZSK represents Zhangshukeng hydrological station, DH represents Dong River, XH represents Xi River, NH represents Nan River, and DFK represents Dufengkeng hydrological station

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3.3.2 Estimation of Reduced Annual Average Loss (AAL)

The AAL assessment requires calculation of losses for different probability flood events. Given scarce historical data and similar regional vulnerability, flood loss rates were estimated using inundation depth as a proxy for the study area in Jingdezhen City. The correspondence between the inundation depth and the flood loss rate of each type of property (Table 2) was obtained from the project assessment report. The flood loss rate of Jingdezhen City is estimated by referencing existing technical specification (FEMA 2022), flood loss assessment methods (Eqs. 7 and 8), and historical flooding statistics of the city.

Table 2 Flood loss rates of different sectors in Jingdezhen City
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The direct economic and shutdown losses for the primary, secondary, and tertiary industries were estimated at the district units by using factors including inundation depth and duration. The losses of agricultural, secondary industry fixed assets, and tertiary industry fixed assets in the inundation area were calculated by Eq. (7). The losses of secondary industry output value and tertiary industry main income were estimated based on shutdown during, determined by inundation calendar time per Eq. (8).

$$D_{1} = \mathop \sum \limits_{i} \mathop \sum \limits_{j} W_{i,j} \eta \left( {i,j} \right)$$
(7)
$$D_{2} = \mathop \sum \limits_{i} \mathop \sum \limits_{j} Y_{i,j} \cdot \frac{{t\left( {i,j} \right)}}{{T_{D} }}$$
(8)

where \(W_{i,j}\) is the property value of class i at inundation depth j for the assessment unit. \(\eta \left( {i,j} \right)\) is the property loss rate of class i at inundation depth j for the assessment unit. \(Y_{i,j}\) is the annual operating income of class i at inundation depth j for the assessment unit. \(t\left( {i,j} \right)\) is the shutdown time of class i at inundation depth j. \(T_{D}\) is the total time, taken as 1 year.

3.4 Assessment of the Resettlement Benefit

A major challenge for social impact assessment is to quantify the economic value of relocation (World Commission on Dams 2001; Downing et al. 2021). Migration has a positive effect on maintaining and increasing income levels in migrant communities (Mcdonald et al. 2008), including higher income levels in resettlement communities (Galipeau et al. 2013) and promoting rural cooperative health insurance (Wang et al. 2013; Huang et al. 2018). Other benefits include improving transportation and housing conditions (Tullos et al. 2009). Huang et al.(2018) investigated the social impacts of dam relocation in China, using questionnaire surveys, archival documents, and interviews to comparing near-resettlement and far-resettlement approaches regarding housing, cash income, and land replacement. Xia et al. analyzed stakeholder interests in the Xiluodu project in China, finding a 7.79% IRR for reservoir resettlement among core stakeholders.

Based on the above research, this study made a CBA of the resettlement project: (1) The annual resettlement investment during the project construction period is calculated based on the proportion of total resettlement investment to overall project investment; (2) The difference in residents’ income before and after resettlement is treated as resettlement benefit, and its value in the first year after project completion is estimated by Eq. (10); (3) Given assumed annual resident income growth and population decline rates, annual resettlement benefits are calculated using Eq. (9) over the project life cycle; and (4) the NPV and IRR of the resettlement project are calculated using the cost-benefit table and the social discount rate.

$$B_{r,t} = B_{r,t - 1} \left( {1 + \alpha_{t - 1} } \right)\left( {1 - \beta_{t - 1} } \right)$$
(9)
$$B_{r,1} = N \times I$$
(10)

where \(B_{r,t}\) and \(B_{r,t - 1}\) are the resettlement benefit in year t and year t–1, respectively; \(\alpha_{t - 1}\) is the annual average resident income growth rate in year t–1; \(\beta_{t - 1}\) is the yearly average population reduction rate in year t–1; \(B_{r,1}\) is the resettlement benefit in the first year (\(t = 1\)) after project completion; \(N\) is the working population resettled by the resettlement program in the first year (\(t = 1\)); \(I\) is the per capita income growth value of the working population resettled in the first year (\(t = 1\)).

3.5 Other Project Benefits

Project benefits include water and electricity provision benefits in addition to flood risk reduction and resettlement benefits, see Eq. (11). The power generation benefits of the hydropower project are determined by the annual power supply volume and the power supply price in Eq. (12). China’s hydropower on-grid price depends on the operating period, benchmark, and the average market price. The transregional and trans-provincial transaction prices are set through the negotiation between the suppliers and consumers. Most provinces use a standard pricing system, while some employ time-of-use or tiered pricing for certain plants based on their role in the grid (NDRC 2014).

The water supply benefits of water conservancy projects are calculated as the product of the water supply price and quantity, see Eq. (13). Water price follows government guidance according to engineering conditions, geographical environments, and water resource conditions. Projects with similar attributes are approved within a region at comparable supply price. For new water conservancy projects, the water supply volume is estimated from multi-year averages at metering points, accounting for the designed annual supply and expected actual supply over 3–5 years (NDRC and MWR 2003).

$$B^{\prime} = \mathop \sum \limits_{t = 1}^{T} B^{\prime}_{e,t} + \mathop \sum \limits_{t = 1}^{T} B^{\prime}_{w,t}$$
(11)
$$B^{\prime}_{e,t} = P_{e,t} \times V_{e,t}$$
(12)
$$B^{\prime}_{w,t} = P_{w,t} \times V_{w,t}$$
(13)

where \(B^{\prime}_{e,t}\) is the power generation benefits in year t of T; \(B^{\prime}_{w,t}\) is the water supply benefits in year t of T; \(P_{e,t}\) and \(P_{w,t}\) are the electricity supply price and water supply price in year t of T, respectively; and \(V_{e,t}\) and \(V_{w,t}\) are the electricity supply volume and water supply volume in year t of T, respectively.

4 Results and Analysis

The results of this study encompass project cost summaries, pre- and post-construction flood risk alterations, total project benefit calculations (flood control, migration, and auxiliary benefits), and economic evaluations with sensitivity analysis.

4.1 Project Costs

The costs of the WIFMP includes construction costs, bank loan interest, and operation costs. The construction period of the WIFMP is 8 years, and the total static investment at the 2020 price level is 3684.7 million yuan. The investment completion of each part is shown in Table 3, and the completion of the acquisition in each year is shown in Table 4. The project investment plan includes a 20-year bank loan of 959.1 million yuan, comprising 26.03% of the total investment, and the interest to be repaid after year 2020 is shown in Table 5. The loan interest is estimated based on the annual principal repayment over 18 years (2020–2037) and the World Bank’s 2.8% interest rate. The WIFMP’s annual operating costs include maintenance and repair costs, employee wages and benefits, material costs, and other costs. Based on local price levels, the project’s average annual operating cost is estimated at 12.1 million yuan.

Table 3 Summary of project costs/financing plan by component (RMB 100 million yuan)
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Table 4 Annual investment schedule of the Wuxikou Integrated Flood Management Project (WIFMP) converted to 2020 price (RMB 100 million yuan)
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Table 5 Annual interest payments on bank loans for the Wuxikou Integrated Flood Management Project (WIFMP) (RMB 100 million yuan)
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4.2 Flood Risk Reduction Benefit

First, flood inundation depth and duration were analyzed under six scenarios to identify potential flood hazards. Based on the hazard results, flood damage to affected assets was then simulated under six scenarios to estimate the flood losses. Finally, comparisons between with-dam and no-dam scenarios were conducted to quantify the reduction of AAL attributable to the WIFMP.

4.2.1 Flood Inundation Scenarios

The maximum inundation depth and inundation duration results of the flood simulation for the S1–S6 (no-dam) and \(S_{1}^{\prime }\)–\(S_{6}^{\prime }\) (with-dam) scenarios are shown in Figs. 4 and 5. As shown in Fig. 4a and g, the city benefited from the construction of the urban flood control embankment system, with fewer inundation areas occurring during the 20-year flood. The construction of the WIFMP also significantly reduces inundation from flood events exceeding the 50-year event (see Fig. 4c–e, i–k). The same trend is shown in the inundation duration in Fig. 5.

Fig. 4
figure 4

Maps of flood inundation depth for the five return period flood scenarios and the 2020 flood under no-dam and with-dam scenarios. RP represents return period, and WXK represents Wuxikou dam station

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Fig. 5
figure 5

Map of inundation duration for the five return period flood scenarios and the 2020 flood under no-dam and with-dam scenarios. RP represents return period, and WXK represents Wuxikou dam station

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In this study, the extent of water bodies from 2 to 15 July 2020 was extracted from Landsat and Sentinel-2 imagery based on the NDWI (normalized difference water index) with threshold values derived by the Otsu method, which determines optimal thresholds by maximizing inter-class variance (Dash and Sar 2020). The extracted results are compared with the inundation extent in the 2020 flood under the with-dam scenario (Fig. 6), and the distribution range of flooding is roughly the same between the two models, indicating that the simulation results are reliable.

Fig. 6
figure 6

Flooding areas extracted from satellite imagery (Sentinel-2 and Landsat). WXK represents Wuxikou dam station, ZSK represents Zhangshukeng hydrological station, and DFK represents Dufengkeng hydrological station

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4.2.2 Flood Loss Scenarios

The areas of different inundation depths and inundation duration levels in each district were counted. The flood losses for agriculture, secondary industry fixed assets, tertiary industry fixed assets, secondary industry output value, and tertiary industry main revenue were calculated using loss rates from Table 2 and Eqs. (1) and (3) under scenarios S1–S6 and \(S_{1}^{\prime }\)–\(S_{6}^{\prime }\). The results are shown in Fig. 7. A comparison of the no-dam and with-dam scenarios shows that the construction of the WIFMP significantly reduced the districts’ flood losses, especially for extreme floods beyond the design standards (30-year, 50-year, 75-year, and 100-year floods). Flood loss reduction for the 20-year flood is less significant due to the existing Changjiang River embankments.

Fig. 7
figure 7

Asset and revenue losses corresponding to the five return period flood scenarios and the 2020 flood under no-dam (right bar) and with-dam (left bar) scenarios. RP represents return period

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4.2.3 Reduced Annual Average Loss (AAL)

Based on the simulation results of the flooding loss under the no-dam and with-dam scenarios (Fig. 7), the scatter plot of flood disaster loss and its exceeding probability are plotted (Fig. 8). To evaluate the flood risk reduction benefits of the project, the flood loss results of the S1-S5 (no-dam) and S'1-S'5 (with-dam) scenarios are used to calculate the AAL of the no-dam and with-dam scenarios, and the difference between the two curves indicates that there are flood risk reduction benefits by implementing the project (Fig. 8). According to Eq. (1), the losses under 20-year to 100-year floods of different exceedance probabilities were used to calculate the AAL for the with-dam and no-dam scenarios (Table 6), and the difference (\(\Delta {\text{AAL}}\) = 117.1 million yuan) between the two AALs is the value of the direct flood risk reduction benefit of the WIFMP. It can be seen that for more than 20-year return period flood events, the flooding loss is significantly reduced by constructing the WIFMP.

Fig. 8
figure 8

Annual average loss (AAL) curve and ΔAAL area under the no-dam and with-dam scenarios

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Table 6 Average annual flood loss and flood risk reduction benefit of the Wuxikou Integrated Flood Management Project (WIFMP)
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Flood loss calculations based on the inundation depth-loss rate curve only consider the direct economic losses of assets within the submerged range above the ground. However, indirect flood losses tend to have more significant and prolonged impact, as they can include high-value asset types, urban underground spaces, and infrastructure failures in transport and power supply that may not be accounted for. In this study, the indirect economic loss coefficient (indirect losses/direct losses) was used to simply estimate the indirect losses from flooding. According to the internal data of the WIFMP Management Office, the indirect losses of the historical flood disasters in the study area are about two times of the direct losses, which is similar to the results of Liu et al. (2022) (indirect economic loss coefficient = 1.8). Taking an indirect economic loss coefficient of 2, the reduction in indirect losses on completion of the WIFMP is estimated at 234.2 billion yuan (117.1 multiplied by 2), and the expected total flood risk reduction in 2020 after project completion is 351.3 million yuan (117.1 + 234.2).

4.3 Resettlement Benefit

The resettlement plan includes three types of investment: resettlement \(B_{r1}\), special infrastructure \(B_{r2}\), and railway restoration and reconstruction \(B_{r3}\) (Table 3). The long term benefits of resettlement mainly stem from productive investments in \(B_{r1}\) (rural immigrant resettlement and relocation fees, compensation for relocation, and construction of new settlements) (Huang et al. 2018). Thus, the resettlement plan costs exclude expenses from \(B_{r2}\) (compensation for restoration and reconstruction of special infrastructure, protection engineering, reservoir bottom cleaning, basic reserve fees, relevant taxes, and other fees) and \(B_{r3}\) when calculating cost-benefit ratios. According to the completion statistics, \(\sum B_{r,t}\) is 1,905.3 million yuan, accounting for 51.71% of the total investment (Table 3). Annual resettlement investment was calculated proportionally from the total annual investment in Table 4, assuming a constant ratio of interannual resettlement investment to total interannual investment.

Quantifying improvements in the living environment is challenging. Thus, to assess the economic benefits of resettlement projects, only the increase in immigrant income was used. Since \(B_{r,t}\) only considers the value-added income of the resettlement project, the economic assessment conducted represents the most conservative estimate of the resettlement project. Resettlement benefits in the first year after project completion were calculated from the difference in resident income before and after resettlement. The mean change in residents’ income before and after resettlement was calculated from Huang et al’s (2018) questionnaire survey on the social impact of water conservancy project-related resettlements in China. The average annual income growth was 2.66 × 10−2 million yuan for near-resettlement migrants (\(I_{n}\)) and 3.28 × 10−2 million yuan for far-resettlement migrants (\(I_{f}\)). The WIFMP flooded 20 villages, affecting 2926 households, with a total migrant population of 10,864 (Jiang 2019). Assuming two working persons per household, 5852 (N = 2926 × 2) people would experience increased income after resettlement.

The growth rate of residents’ income in the life of the water conservancy project was determined to calculate the future resettlement benefits. According to China’s 14th 5-Year Plan and the long-term goal of 2035, the expected growth rate (\(\alpha\) in Eq. 9) of the average resident income from 2021 to 2035 is 5%. This study also considers the flow of population in the resettlement area. A 2% annual reduction rate (\(\beta\) in Eq. 9) of China’s rural population was assumed until 2035 according to the relevant literature and China’s national conditions, with stabilization of total rural population in 2035 (Wang et al. 2020). According to these assumptions and Eq. (9), the resettlement benefits at the 2020 price are calculated to be 155.7 (near-resettlement) to 191.9 (far-resettlement) million yuan, and the IRR for the project life cycle is expected to reach 8.6% (near-resettlement) and 10.0% (far-resettlement), see Fig. 9.

Fig. 9
figure 9

Long-term cost-benefit cash flow of the Wuxikou Integrated Flood Management Project (WIFMP) resettlement. IRR is the internal rate of return

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4.4 Other Benefits

The WIFMP supplies electricity to Jingdezhen City, which is also the main area of water consumption. The current on-grid price for new power stations in Jiangxi Province is 0.33 yuan/kWh without value-added tax (VAT) and 0.34 yuan/kWh with VAT at 6%. The final on-grid price for the WIFMP is 0.40 yuan/kWh. The WIFMP has an installed capacity of 32 MW and a multiyear average power output of 8,152 × 104 kWh. With the hydropower station’s 1% auxiliary power rate, the adequate power supply is 8,070 × 104 kWh. According to Eq. (11), the multiyear average power supply benefit \(B^{\prime}_{e,t}\) of this project is 32.3 million yuan.

The WIFMP regulates runoff from the Changjiang River in dry years and dry seasons and provides raw water for the Jingdezhen Water Supply Plant. In 2020, Jingdezhen’s urban resident water price was 1.48 yuan/t, while nonresidential and special industrial prices were 2.22 yuan/t and 7.00 yuan/t, and with an overall average water price of approximately 2.07 yuan/t. With the city’s 2020 water demand at 2.03 × 108 t, increasing by 0.26 × 108 t annually until 2040, the annual water supply benefit \(B^{\prime}_{w,t}\) can be calculated using Eq. (12) based on the projected additional water supply each year.

4.5 Cost-Benefit Ratio

The economic efficiency of the WIFMP was assessed by comparing costs to expected benefits, using an 8% social discount rate (\(\tau_{t}\)) per the national specification (Gunatilake 2013). The unit value of flood losses was increased annually by 3% (\(AAL_{t} = AAL_{t - 1}\) × (1 + 0.03)) to reflect the expected development of the study area. With an 8-year construction period and 50-year operation, the WIFMP’s life cycle T is 58 years.

The costs of the WIFMP at the 2020 price include total investment (\(\sum I_{p,t}\) = 3,684.7 million yuan), average operating costs (\(I_{o,t}\) = 12.11 million yuan/year), and financial costs, including bank loan interest \(I_{i,t}\), see Table 5. The main benefit of the WIFMP is the reduced losses of flood disasters. The flood risk reduction benefit is 351.3 million yuan in 2020 after the completion of the project, and the cash income after project completion is mainly composed of the water and power supply charges (\(B^{\prime}\) = 32.3 +\(B^{\prime}_{w,t}\)). In addition, the resettlement of migrants is expected to increase the growth of residents’ annual per capita income. The benefit of near-resettlement (\(B_{rn,1}\)) and far-resettlement (\(B_{rf,1}\)) in 2020 after project completion are 155.7 and 191.9 million yuan, respectively. Figure 10 summarizes the long-term cost and benefit projections of the project. Based on the various types of costs and benefits of project completion (year 2020) quantified above, the project surplus under the near-resettlement scenario of the WIFMP in 2026 would be 663.2 million yuan (which starts to be greater than zero), indicating that the payback period of the project will be about 6 years.

Fig. 10
figure 10

Long-term cost-benefit cash flow of the Wuxikou Integrated Flood Management Project (WIFMP). IRR is the internal rate of return, O&M means operations and maintenance

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To analyze the influence of the measurement error of investment and benefits on the economic evaluation results, the impact on the evaluation indicators when the investment and benefit factors become negative was considered. The economic evaluation index value of the project is calculated based on the calculated costs and benefits results, and the sensitivity analysis uses six scenarios to test the robustness of the economic benefits evaluation of the project: (1) Basic scheme; (2) O&M costs increase by 10%; (3) Other benefits decrease by 10%; (4) O&M costs increase by 5%, while other benefits decrease by 5%; (5) Indirect economic loss coefficient = 1; and (6) Other benefits decrease by 5%, while indirect economic loss coefficient = 1. The results of the sensitivity analysis are shown in Table 7. The CBA results for the project are essentially unchanged when the O&M costs increase by 10% because O&M is less than 3% of the total cost. When indirect flood loss is equal to direct flood loss, the IRR and NPV of the project show significant changes, and the benefits of the project mainly come from reducing the losses caused by flooding.

Table 7 Cost-benefit analysis (CBA) evaluation and six-scenario sensitivity analysis of the Wuxikou Integrated Flood Management Project (WIFMP)
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5 Discussion

This study demonstrates the value of a comprehensive CBA framework in assessing the economic efficiency of flood disaster risk reduction projects. By considering a wide range of costs and benefits and utilizing various techniques, this holistic approach to CBA provides a more reasonable evaluation of project effectiveness.

A significant improvement in this study is the inclusion of a quantitative estimation of annual average loss (AAL), a crucial indicator for assessing the impact of flood control projects. The AAL for the flood control project assessed in this study was estimated through probabilistic risk analysis, which involved hydrological frequency statistics, and numerical flood propagation and inundation simulation using hydrodynamic models under different probabilistic conditions. The validity of the hydrodynamic model was confirmed by comparing its results with ground-observed and satellite-derived flood inundation data from historical events. By combining spatial exposure data with quantitative vulnerability analysis, the probability of potential damage and loss could be estimated, thus allowing for the calculation of the project’s AAL.

One critical aspect that should not be overlooked in the assessment of project benefits is the quantification of resettlement benefits. Resettlement costs often make up a significant portion of the total project costs, and ignoring the associated benefits can lead to a severe underestimation of overall project benefits and potentially result in incorrect policy conclusions. This study estimated that neglecting the resettlement benefits of the flood control project would lead to an underestimation of total benefits by more than 30%. Even though the assessment of resettlement impacts in this study was preliminary and quantitative in nature, it still significantly improved the accuracy of the CBA compared to completely omitting these impacts. While the precision of the estimates is limited, they highlight the importance of considering resettlement effects and provide valuable information for decision making.

It is important to note that this study does not address the optimization of non-engineering measures such as pre-disaster prevention, disaster resilience, and post-disaster relief. These measures can also effectively reduce future flood risks and enhance the economic sustainability of the project through appropriate operational strategies and flood forecasting. While further refinements are necessary, the research framework developed in this study can be extended to other regions facing similar probabilistic flood risks and resettlement needs. The integration of hydrological model and flood inundation model to estimate flood losses, along with the adoption of an income comparison approach to quantify intangible resettlement benefits, represents valuable contributions. Although the methodologies for valuing resettlement impacts are still in their early stages, quantitative resettlement studies can stimulate theoretical innovation and enrich the overall methodology.

6 Conclusion

The application of the refined CBA framework to the WIFMP case illuminates the value of flood DRR interventions in flood-prone areas, furnishing local governments with essential insights to inform resource allocation for disaster mitigation. The main conclusions are:

The CBA results indicate that the WIFMP should have been the top priority measure for constructing Jingdezhen City’s flood control system. Quantitative analysis demonstrates that the WIFMP provides substantial flood mitigation benefits. Hydrological simulations reveal a minimum 60% reduction in inundation under flood events exceeding the 30-year return period with the WIFMP implemented. Damage model further quantifies approximately one-third lower direct losses across the districts/counties under the WIFMP. For economically prosperous regions like Zhushan District, flood losses are markedly reduced under extreme events above the 30-year threshold. Additionally, the WIFMP yields a positive cash flow and achieves project cost recovery within 6 years according to the CBA. The results of six sensitivity scenarios show that the project is economically feasible under all scenarios, with the IRR remaining above the 8% social discount rate, and the NPV of the economy being positive.

Resettlement costs exceed half of the total investment for the WIFMP, substantially improving immigrant living standards, enhancing resident income, and yielding excellent public welfare benefits. Resettlement evaluation shows IRR of 8.9% and 10.2% for near- and far-resettlements respectively, above the 8% social discount rate. However, this migrant income growth-based analysis provides a conservative estimate, potentially underestimating resettlement viability by excluding numerous indirect and unquantified benefits such as upgraded housing, one-time compensation, and poverty alleviation. Considering the socially beneficial nature and unquantified gains, the resettlement investment demonstrates robust economic feasibility.

The research results provide a quantitative monetary detail of the economic, social, and public welfare values of the WIFMP. The CBA assessment is based on more complete and reliable cost and benefit values rather than values from simple historical or scenario analysis, and considers the uncertainty of the disaster probability, which is crucial for sustainable development and the promotion of the disaster reduction project investment.