The Huai River basin is located between 30°55′N–38°20′ 30 ∘ 5 5 ′ 38 ∘ 2 0 ′ N and 111°55′E–120°45′E 111 ∘ 5 5 ′ 120 ∘ 4 5 ′ , between the Yellow River and the Yangtze River (Figure 1). It originates in Tongbai Mountain of Henan Province and flows into the Yangtze River, flowing through four provinces (i.e., Henan, Anhui, Shandong, and Jiangsu provinces). The total area of the Huai River basin is 191,200 km², and the length of the main channel is 1,000 km. The Xixian basin is located in the upper reaches of the Huai River, with a catchment area of 10,191 km², which is chosen for study in this study. The Xixian basin is located in the transition zone of warm temperature region and northern subtropical zone. The main crops are rice and wheat in this area. The multi-year average air temperature is 15.4°C. The long-term average annual rainfall is 1,028 mm (calculated by the data from 1980 to 2014). Rainfall for the flood season (from June to September) is mainly affected by monsoon, and more than half of the precipitation (∼60%) falls in the flood season. Owing to the monsoon and windward mountain terrain conditions, flood has become the most serious natural hazard in the Huai River basin.

In this study, the 1980–2014 daily precipitation and temperature data are obtained from observational gridded datasets, with a 0.25° horizontal resolution, which can be downloaded from the website of the National Meteorological Information Center of the China Meteorological Administration (http://cdc.cma.gov.cn/). These observational gridded datasets are interpolated from observations of nearly 2,400 quality-proven stations all over China (Xu et al., 2009). Moreover, the Thiessen polygon method is used to calculate the basin-averaged daily precipitation and temperature data by the gridded datasets for the study basin. The 1980–2014 daily runoff data of Xixian station are obtained from the Hydrology Bureau of the Huai River basin.

To analyze the future climatic scenarios, four GCM outputs (BCC-CSM2-MR, CanESM5, CESM2, and MRI-ESM2-0) from the latest CMIP6 are chosen under two SSP-RCP scenarios (i.e., SSP245 and SSP585). Meanwhile, we downloaded the essential model outputs (daily precipitation and daily temperature) for both the historical period (1980–2014) and future period (2015–2100). The detailed information of the chosen models is listed in Table 1. According to the latest studies (O’Neill et al., 2013; Simpkins, 2017; Su, et al., 2021), the state-of-the-art scenarios become more plausible as the shared socioeconomic pathways (SSPs) work in harmony with RCPs by shared policy assumptions. There are five SSP scenarios that represent the possible future socioeconomic conditions and describe various combinations of mitigation and adaptation challenges, including SSP1: sustainability; SSP2: middle of the road; SSP3: regional rivalry; SSP4: inequality; and SSP5: fossil fuel development (Huang et al., 2019; Su et al., 2021). Among these scenarios, SSP245 and SSP585 are selected for this study as the updated versions of the RCP 4.5 and RCP8.5 scenarios from CMIP5.

Figure 2 displays the methodology framework of this study, including three major modules of climate scenario projection, hydrological model, and impact assessment. The module of scenario projection produces climatic scenarios during historical and future periods. The hydrological model module involves the calibration and validation of the XAJ model and calculation of daily runoff simulation under historical and future climatic scenarios. The impact assessments module is applied to investigate the runoff seasonality variations and to quantify the potential impacts of climate change on future design flood.

The XAJ model, a conceptual hydrological model, is developed by Zhao (1992). The physical basis of this model is the theory that runoff generation occurs until the saturated condition of soil water is reached. The XAJ model involves 16 free parameters (see Table 2) and has been extensively and successfully applied in runoff simulation and flood forecasting for the humid and semi-humid zones over China. The detail of the XAJ model can be found in Zhang et al. (2012). The basin-average daily precipitation and daily potential evapotranspiration (PET) data are calculated as the inputs of this model, and then the discharge at the basin outlet is the final output. The PET is calculated by the Oudin temperature–based method (Oudin et al., 2005) in this study. Although this method requires only average daily temperature data as input, it has been proved to be an alternative to other complex methods, such as the Penman method, for the hydrological simulations (Oudin et al., 2005). Specifically, the formulas for potential evapotranspiration are presented as follows: P E T = R e λ ρ T a + 5 100   i f   T a + 5 > 0 P E T = 0   i f   T a + 5 ≤ 0 , (1) where PET refers to the potential evapotranspiration (mm day⁻¹), R _e refers to extraterrestrial radiation (MJ m⁻² day⁻¹), depending only on latitude and Julian day, λ refers to the latent hear flux (MJ kg⁻¹), ρ refers to the density of water (kg m⁻³), and Ta is mean daily air temperature (°C).

Furthermore, we select the shuffled complex evolution optimization algorithm (SCE-UA, Duan et al., 1992) to calibrate the XAJ hydrological model. The Kling–Gupta efficiency (KGE) is selected as the evaluation index in this study, and the objective function is to maximize the KGE value during calibration. The KGE value could be calculated as follows (Gupta et al., 2009): K G E = 1 − ( r − 1 ) 2 + ( α − 1 ) 2 + ( β − 1 ) 2 , (2) where r indicates Pearson’s linear correlation coefficient between the observed and simulated streamflow, α is the ratio of standard deviations of observed and simulated streamflow, and β is the ratio of the mean value of observation and simulations. The value of KGE ranges from −∞ to 1, with KGE = 1 indicating a perfect fit between the observed and simulated series.

The DBC approach is an empirical statistical downscaling approach and has recently been used to correct the systematical errors of raw GCM scenarios (Chen et al., 2013b). The procedures of these methods are calculated as follows: First, the precipitation occurrence of each GCM output is revised by a determined threshold defined month by month from the historical period, which can ensure that the corrected historical precipitation has the same frequency as observations. Then those thresholds are employed to correct the frequency of rainy days for the future period. Furthermore, the daily precipitation distribution of each month is revised by multiplying (or adding) the quantile ratios (or differences) between the observations and GCM simulations during the historical period. Finally, those quantile ratios (or differences) are applied to correct distribution of daily precipitation during the future period. Definitely, these procedures can also be used for temperature correction. The formulas can be expressed as follows: P a d j , d = P G C M , d × ( P o b s , Q / P G C M , r e f , Q ) T a d j , d = T G C M , d × ( T o b s , Q / T G C M , r e f , Q ) , (3) where the subscript Q is a quantile for a month, the subscript d is a specific day in the historical or future period, and the subscript adj is the corrected variables.

In this study, the POT approach is employed to extract a number of flood samples each year that are required to exceed the threshold S determined by certain criteria. Compared to annual maximum series method (AMS), this method has the core advantage, allowing more reasonable events to be identified as “floods” for extreme value analysis. Thus, the POT method can not only overcome the shortcoming of short historical data but also provide a more comprehensive description of the “flood” process (Lang et al., 1999). Accordingly, this method has been commonly employed in the estimation of extreme precipitation and temperature and the frequency analysis of flood runoff, and so on (Solari et al., 2017; Lee et al., 2019; Bian et al., 2020; Yang et al., 2020). In this study, the POT method is conducted for flood frequency analysis. The first key step is to ensure that the sampled flood events satisfy the independence condition. Here, the criteria evaluated by Silva et al. (2012) are employed, which indicates that the successive two flood peaks can be accepted when they meet the following formula: D < 5   d a y s + log ( A ) Q min < 3 4 min ( Q 1 , Q 2 ) , (4) where D refers to the interval time between two flood peaks in days, A denotes the basin area in km², and Q ₁ and Q ₂ are the magnitudes of two flood peaks in m³/s, respectively.

In addition, an appropriate threshold is required to determine to guarantee that the frequency distribution of floods meets a Poisson function, which is another key point here. The mean number of over-threshold events per year μ should be more than two times per year as recommended by Mediero et al. (2014). Therefore, the mean annual number of flood events is set as μ = 3 under the independence assumption in this study. Last, the extracted series of flood peaks are fitted with a generalized Pareto (GP) distribution.

The performances of GCMs are discrepant for different climate variables among various climate regions; thus, there is no common conclusion on how to select suitable GCMs in a particular basin. Therefore, it is necessary to assess the performances of the chosen models (i.e., BCC, CanESM, CESM, and MRI models) in order to investigate the influences of climate change on seasonal runoffs and floods in the Xixian basin. The systematical errors of raw GCM outputs are tackled by the DBC method. Afterward, 23 metrics (Table 3) are selected to describe mean and extreme values of precipitation and temperature series under climate change. The raw GCM simulations have the same historical period 1980–2014 with the observed data.

Figure 3 is a color-coded “portrait diagram” showing the deviations of precipitation and temperature before and after DBC method during the historical period. It is can be seen that raw outputs of precipitation and temperature from four GCMs exhibit obvious deviations. The raw precipitations of GCMs deviate from observed precipitations by more than ±50% for most metrics, whereas the deviations of temperature are generally above ±2°C. However, the systematic biases of GCMs are significantly reduced after the DBC. The biases of precipitation effectively reduce to below 5% in most cases for the selected GCMs, and as for temperature, the biases reduce to lower than 0.1°C. Overall, the performances of bias correction for both precipitation and temperature simulation of GCMs are satisfied for the research requirement. Those results indicate that the DBC method is reliable for reproducing future climate variables in the study basin.

The long-term changes of annual mean precipitation and temperature over the upper Huai River basin are detected during the period of 1980–2100 for each GCM under two different SSP–RCP scenarios (SSP245 and SSP585). Relative to the change of precipitation over the baseline period, there is a general rising trend during the future period, although the rising rate varies with different GCM and SSP scenarios (Figure 4). More specifically, BCC model projects the highest increasing rate of annual mean precipitation with a rising rate up to 28 mm per decade under SSP585 scenarios, while the minimum rising rate of annual mean precipitation with 10.3 mm per decade is projected by the MRI model. For SSP245 scenario, the increasing tendency of precipitation is more insignificant than that under SSP585 scenario.

In the field of the long-term tendency of annual mean temperature, Figure 5 shows that a significant increasing trend in temperature is observed during the period 1980–2100, and more significant increasing changing of temperature is observed under SSP585 scenario compared to the SSP245. In detail, the CanESM model releases the most pronounced warming signal, which projects that the annual average temperature has a significant rising rate of 0.37°C and 0.57°C per decade under SSP245 and SSP585 scenarios, respectively. The MRI model exhibits the most optimistic warming condition with an increase of 0.23°C and 0.33°C per decade under the two scenarios, respectively. The BCC and CESM models project that annual average temperature has a significant increase with a rate of 0.28 and 0.23°C per decade under SSP245, respectively, and with a maximum rate of 0.37°C per decade under SSP585 scenarios.

In this study, XAJ model is adopted to simulate hydrological processes in the Xixian basin. Initially, we used the basin-averaged precipitation and temperature data during 1980–1999 to carry out the calibration of the XAJ model, and then the optimum model parameters are obtained with the largest KGE value. The 15-year period during 2000–2014 are used for model validation. To further investigate the performance of the XAJ model, the Nash–Sutcliffe efficiency coefficient (NSE) and relative bias (PBIAS) criteria are also employed.

Table 4 presents the results of calibration and validation periods for the Xixian basin. Furthermore, the comparisons between observed and simulated runoffs in two periods at the daily and monthly scale are presented in Figure 6, which suggest that the XAJ model performs well in the study basin though with overestimates or underestimates in the flood peaks in some cases. From Table 4, it can be seen that the KGE values are 0.86 and 0.91, respectively, at the monthly scale, and 0.79 and 0.82 at the daily scale for calibration and validation periods. In addition, the NSEs are 0.88 and 0.86, respectively, at the monthly scale, and 0.74 and 0.71 at the daily scale, and the PBIAS of the calibration and validation are both lower than 10%. These results indicate that the XAJ model can perform satisfactorily so that it can be used to project hydrological scenarios in subsequent research.

To investigate the influence of climate change on monthly runoff over the Xixian basin, the XAJ model is used to simulate runoffs during the historical period (1980–2014) and two future periods: 2050s (2031–2060) and 2080s (2071–2100). Figure 7 demonstrates the monthly average runoff during the two future periods for each GCM under SSP245 and SSP585 scenarios. Broadly speaking, the selected GCMs perform similarly for change of monthly runoff under two scenarios, but there still exist some differences. Under SSP245 scenario, all GCMs project that runoffs of most months are generally smaller than those in the baseline period over the 2050s, while runoffs of high-flow season over the 2080s are larger than those in the baseline period, reflected in May to September. Moreover, the change patterns of seasonal runoffs under SSP585 scenario are similar to those under SSP245 scenario during the two future periods. These can be explained by the fact that precipitation simulations in the 2050s are equal to or less than those in the baseline period under SSP245 and SSP585 scenarios, while the higher temperature is projected. Thus, the projected monthly runoffs are smaller in the 2050s than those in the baseline period. In contrast, the precipitation simulations in the 2080s are obviously larger than those in the baseline period, which results in higher monthly runoffs. In addition, compared with SSP245, the monthly runoffs under SSP585 scenario are obviously higher, especially for high-flow months.

Then, we further analyzed the variations of monthly runoff between the baseline and the two future periods under SSP245 and SSP585 scenarios, as shown in Figure 8. There is a large discrepancy between the changing trends of average monthly runoffs in the two future periods. During the 2050s, the monthly average runoffs in most months have seen decreasing trends for each GCM under SSP245 and SSP585 scenarios, generally occurring in the low-flow season such as January to April and September to December. It can be seen that the monthly average runoffs are lower than that in baseline period and have decreased by about 10 and 8% under SSP245 and SSP585 scenario, respectively. These indicate that there will be more serious water shortage and higher risk of drought during the 2050s in the upper Huai river basin. In addition, Figure 8 shows that there has been an obvious increasing trend of monthly average runoff in the high-flow season during the 2080s. In detail, compared to the baseline period, the GCMs project that the monthly runoffs have generally increased by about 29% from May to September under the SSP245 scenario. Under the SSP585 scenario, the monthly runoffs are projected to increase by approximately 39% from May to September. These may be caused by increasing seasonal precipitation in high-flow season under two future scenarios. Thus, there will be higher flood risk in high-flow season during the 2080s in the upper Huai river basin, especially under the SSP585 scenario, which also are proved in subsequent analyses of impacts of climate change on design floods.

In order to analyze the changes of flood frequency, the flood peaks are extracted by the POT method in this study, which has been certified to be more reasonable than the annual maximum sampling approach (Mediero et al., 2014; Bian et al., 2020). Moreover, the L-Moment approach (Hosking and Wallis, 1997) is used to estimate the parameters of GP distribution. The design floods under SSP245 and SSP585 scenarios for each GCM during the two future periods are demonstrated in Figure 9. It can be seen that the change patterns of design floods are quite different between the 2050s and 2080s for each GCM under SSP245 and SSP585 scenarios. In detail, during the 2031–2060, the design floods are generally lower than those in baseline period for small return period under the two scenarios for each GCM. However, BCC and CanESM models project that the design flood with a 100-year return period is obviously bigger than that in baseline period under SSP585 scenario. As for the 2080s, there have been the obviously larger design floods for all GCMs under SSP245 scenarios comparing to the near future period. When the return period exceeds 20 years, the design floods of 2080s are larger than those of baseline period. Moreover, the design flood runoffs are projected to increase more significantly when the return periods increase. Under SSP585 scenarios, the design floods of 2080s are larger than those of baseline period when the return period exceeds 10 years. In addition, the flood magnitude with the same return period is greater than that under SSP245 scenario. These indicate that flood extremes are projected to increase during the future periods in the upper Huai River basin, especially under SSP585 scenario.

To further investigate the results as mentioned above, the changes of future floods are calculated for the 10, 20, 50, and 100-year return period, shown in Figure 10. It can be observed that the design floods of the 100-year return period are increasing for all GCMs under the SSP245 and SSP585 scenarios during the 2050s, especially the CanESM model, which exhibits the largest increasing rate with the 17.9 and 38.4% under SSP245 and SSP585 scenarios, respectively. However, there has been a general decreasing tendency of the design floods with 50, 20 and 10-year return periods during the 2050s under SSP245 scenario. As the return period decreases, the reducing range of design flood runoffs is exacerbated. In addition, Figure 10 demonstrates that the change patterns of design floods for 2080s show great differences from those in 2050s. All GCMs project obvious increasing trends of the design floods for all return periods under the two scenarios, except the design floods with a 10-year return period of CESM and MRI. In detail, CanESM projects that under SSP585 scenario, the rising rate of design floods for the 100-year and 50-year return periods in the 2080s can go up to 106 and 72%, respectively. For the BCC model, the design floods for 100-year and 50-year return periods increase by 60.6 and 48.7%, respectively, under SSP585 scenario. CESM model projects that the increasing rates of design floods for these two return periods are 45.4 and 36.4%, respectively, under SSP585 scenario, and those of MRI model increase by 42.8 and 26.5%, respectively. However, under SSP245 scenario, the increases of design floods with 100-year and 50-year return periods are far below that under the SSP585 scenario. These could be explained by the fact that the heavier emission of gas such as SSP585 scenario causes the larger extreme precipitation. These results indicate that the flood events are likely to occur more frequently during the far future period in the Xixian basin.