According to the sixth Assessment Report, global surface temperature from 2011 to 2020 was 0.95–1.20°C higher than that from 1850 to 1900 (Lee et al., 2021). Human activities and greenhouse gas emissions have accelerated global warming, leading to significant changes in the hydrological cycle. These changes have direct impact on human life, property, food security, and water resources, which are essential for sustainable socio-economic development (Hu et al., 2018; Q. Zhang et al., 2013). Global Disaster Data Platform reports that the global flooding frequency from 2001 to 2020 increased by 119% compared to 1981 to 2000, surpassing other natural disasters (
Accurate climate change estimation is essential for assessing streamflow and flooding magnitude. The CMIP6 represents an updated version of previous CMIPs (Eyring et al., 2016). Compared to CMIP5, CMIP6 offers insights into past, present, and future climate changes resulting from both natural and unforced variations (Z. C. Ma et al., 2022). CMIP6 provides a fundamental basis for related hydrological research, and combining these prediction scenarios with hydrological models aids in better understand the impact of global warming and socio-economic factors on the physical processes of hydrological systems (C. Chen et al., 2022). Previous research has confirmed that the multi-model ensemble (MME) can improve climate projection performance over China (Xu & Xu, 2012), and that the use of downscaling methods can further reduce errors (A. Chen et al., 2021). This work couples MME and downscaling methods to further improve accuracy in climate and hydrological simulations.
The physical mechanisms, algorithms, spatial-temporal scales employed in hydrological models significantly influence the flooding magnitude, introducing additional uncertainties (You et al., 2021). Furthermore, the nonlinearity of hydrological processes, coupled with human activities such as water consumption, irrigation, reservoir management, and deforestation, complicates the translation of precipitation changes into streamflow alterations. Translating precipitation variations into changes in streamflow, remains a challenge, making it impossible to fully link hydrological cycle to climate signals. To gain a better understanding of regional hydrological process, it is inadequate to analyze the observed precipitation and streamflow solely through statistical methods; a novel method or tool is essential. The Variable Infiltration Capacity (VIC) model, developed by X. Liang et al. (1994) and grounded in physical principles, provides a solution. This model can independently calculate streamflow at any raster within a basin and has been extensively applied worldwide, including in the United States (Hidalgo et al., 2013), China (Q. Zhang et al., 2014; X. J. Zhang et al., 2014), and the Pacific Northwest (Najafi & Moradkhani, 2015), India (Hengade & Eldho, 2016) and Canada (Islam et al., 2019). However, research combining CMIP6 GCMs with VIC models to estimate hydrological processes remains limited.
In recent years, extensive research has utilized GCMs to assess the impact of climate change on flooding magnitude, primarily focusing on univariate frequency analysis (Anjum et al., 2019; Das et al., 2011; Gädeke et al., 2022). However, flooding magnitude is determined by multiple factors such as peak (Q) and volume (W), and univariate analysis provides limited insights into these characteristics. Copula theory emerges as a suitable approach for examining bivariate flooding characteristics (Jeong et al., 2014; Yin, Guo, He, et al., 2018; Yin et al., 2020). Consequently, it is essential to incorporate bivariate flooding characteristics when assessing the influence of climate change on flooding magnitude, particularly when employing Copula theory.
The Yellow River basin (YRB) is one of the most susceptible watershed systems to climate change (Lin et al., 2019). Over the past 2,500 years, the downstream of the Yellow River have experienced severe flooding, resulting in over 1,500 dike breaches and 26 diversions, causing devastating impacts on the communities living along the riverbanks (Tian et al., 2016). Despite numerous studies conducted on the YRB, most of them have focused on the spatiotemporal pattern of extreme precipitation (K. Liang et al., 2015; Tao & Wang, 2017; Y. Zhang et al., 2019). It is anticipated that the frequency of short-term continuous rainstorms over the YRB will increase, potentially elevating the downstream flooding risk (Q. Zhang et al., 2014; X. J. Zhang et al., 2014). Additionally, the duration of rainstorms appears to have shortened, and the intensity of rainstorms may have been enhanced across the YRB (Y. Zhang et al., 2019). While considerable efforts have been made to investigate the potential risks that extreme precipitation could pose to the YRB, there has been relatively little focus on examining flooding risks within the basin.
In our research, the copula functions are employed to structure the bivariate flooding risk under climate change to compensate for the limitations of univariate flooding risk assessments. The future bivariate flooding risk at three stations from the source region to the downstream region of the YRB were selected for the assessment. The specific objectives are: (a) estimating the alterations in precipitation and temperature under three shared socio-economic pathways (SSPs), (b) disclosing the potential effects of climate change on streamflow under three SSPs, (c) examining the univariate/bivariate flooding risks under three SSPs. This study aims to provide a scientific foundation for the development of mitigation and adaptation strategies to address future flooding risks across the YRB.
Study Area and Materials Study AreaAs shown in Figure 1, the study area is the Yellow River basin (YRB) over China. The YRB, being the second largest basin over China, is widely regarded as the “Mother River of China” (Gao & Wang, 2017). The total length of the Yellow River is approximately 5,464 km, with a drainage area of approximately 75.24 × 104 km2. The basin is home to approximately 107 million people, which accounts for 8.6% of the Chinese people (X. Wang et al., 2021). However, approximately 60%–80% of the annual precipitation falls as rainstorms, causing frequent flooding across the YRB. This study divides the YRB into four sub-regions based on the characteristics of the watershed system (Figure 1b).
Enlarge this image.Figure 1. Location, topography and hydrometeorological stations across the YRB. The sub-region I represents the source region (SRYR), II denotes the upstream (UYRB), III refers the midstream (MYRB), IV represents the downstream (DYRB). TNH, TDG, and HYK denotes the Tangnaihai, Toudaoguai and Huayuankou Hydrological Stations, respectively.
The daily precipitation (P), maximum temperature (Tmax) and minimum temperature (Tmin) data from 1961 to 2019, encompassing 493 quality-controlled meteorological stations (Figure 1b), were provided by the National Meteorological Centre (
Given the consistency of CMIP6 GCMs in climate change estimation, the research selected the historical period and three SSPs (SSP126, SSP245, and SSP585) among nine GCMs, including the first member (r1i1p1f1). Each GCM encompassed daily P, Tmax, and Tmin data (Eyring et al., 2016). The detailed information was provided by
Table 1 Basic Information of CMIP6 Models
| No | Model | Institution | Country | Resolution |
| 1 | ACCESS-CM2 | CSIRO-BOM | Australia | 1.25° × 1.875° |
| 2 | BCC-CSM2-MR | BBC | China | 1.125° × 1.125° |
| 3 | CanESM5 | CCCma | Canada | 2.81° × 2.81° |
| 4 | CMCC-ESM2 | CMCC | Italian | 1.25° × 0.94° |
| 5 | GFDL-ESM4 | NOAA- GFDL | USA | 1.25° × 1.00° |
| 6 | IPSL-CM6A-LR | IPSL | France | 2.50° × 1.26° |
| 7 | MIROC6 | JAMSTEC | Japan | 1.40° × 1.40° |
| 8 | NorESM2-LM | NCC | Norway | 2.50° × 1.895° |
| 9 | NESM3 | NUIST | China | 1.25° × 1.875° |
The VIC hydrologic model necessitates the terrain, soil properties, and vegetation characteristics. A digital elevation model (DEM) with a spatial resolution of 90 m was obtained from Geospatial Data Cloud (
Enlarge this image.Figure 2. Spatial distribution of projected changes in LUCC across the YRB under the (a) reference period, (b) SSP126, (c) SSP245, and (d) SSP585.
Figure 3 presents the flowcharts of future projections regarding streamflow and flooding risk over the YRB under climate change, consisting of three parts. The probable climate changes give rise to three SSPs through nine CMIP6 GCMs, and the daily P, Tmax, and Tmin series are statistically bias-corrected using the MME and Delta methods. The projected streamflow impacted by climate change is driven by the corrected future climate scenarios utilizing the VIC model. The flooding risk estimation module is employed to deduce the univariate flooding risk through the optimal marginal distribution function, and it is further combined with the optimal copula function to derive flooding risk for three SSPs under different joint return periods and co-occurrence return periods.
Enlarge this image.Figure 3. Flowcharts of future projections of streamflow and flooding risk over the YRB under climate change.
The MME has been widely employed in predicted climate change due to its ability to compensate for discrepancies among GCMs (Han et al., 2021; Y. Li et al., 2020). Given the low resolution of GCMs, it becomes challenging to accurately depict regional climate change. Previous study has demonstrated the exceptional performance of Delta downscaling in investigating precipitation and temperature across the loess plateau (Peng et al., 2017). Therefore, this study employs Delta downscaling to enhance the accuracy of climate predictions generated by GCMs. The advantage of this method lies in its ability to simultaneously calibrate multiple meteorological stations, featuring simplicity, efficiency, and broad application (J. Chen et al., 2013; Prudhomme et al., 2002; Yin et al., 2020). It is worth noting that data set from 1961 to 1994 was utilized to calculate the deviation correction coefficient for Delta downscaling, while the data set from 1995 to 2014 was defined as the benchmark for assessing the accuracy of Delta downscaling. The fundamental equation of Delta downscaling is as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where Phigh and Thigh are the daily P and temperature (including Tmax and Tmin) after downscaling; Pobs and Tobs are the multi-year daily mean P and T during the calibration period; (Plow-fut)day and (Tlow-fut)day are the simulation of the GCMs under the validation periods and three SSP scenarios; (Plow-his)day and (Tlow-his)day are the simulation of the GCMs during the calibration period.
VIC Hydrological ModelThe VIC hydrological model, a physically based macro-scale model, was employed to predict streamflow under three SSPs. This model divides the basin into sub-grids, which are connected to the mainstream. These sub-grids, referred to as Hydrological Response Units, are a comprehensive combination of climate, soil, terrain, and LUCC. Moreover, a semi-distributed conceptual rainfall-runoff model (ARNO) is utilized to describe the base flow in the VIC. The vertical water transfer process between soil layers is represented by the one-dimensional Richard equation (Todini, 1996). The fluxes estimated by the VIC model at the sub-grids include surface streamflow, evapotranspiration, and base flow. These are transferred to the land surface hydrological model (Lohmann et al., 1996, 1998) and utilized to direct surface streamflow and base flow to the outlet of the corresponding catchments.
Model Calibration and VerificationThe performance of the VIC model was assessed by utilizing Nash-Sutcliffe efficiency (NSE), correlation coefficient (R), and bias evaluation indices. As per He et al. (2015) and Y. Chen et al. (2018), seven sensitive parameters listed in Table 2 were selected for calibration, which have a significant impact on hydrological processes. Given the availability of the 1966–1985 data set and the minimal human intervention during that time horizon, this study opted to utilize natural streamflow from 1966 to 1975 for the calibration of seven sensitive parameters. Furthermore, the validation of seven sensitive parameters was authenticated using natural streamflow from 1976 to 1985. The adjustments to seven sensitive parameters are as follows:
Table 2 Seven Parameters Generally Calibrated for the VIC Hydrologic Model, Their Meaning of Physics, and Confirming Parameter Values
| Parameters | Meaning of physics | Unit | Numeric range | Confirming parameter values | ||
| TNH | TDG | HYK | ||||
| B | Infiltration curve parameter | N/A | 0–0.9 | 0.68 | 0.3 | 0.38 |
| Dsmax | Maximum velocity of the baseflow | mm/day | 0–1 | 0.32 | 0.2 | 0.14 |
| Ds | Fraction of Dsmax where the non-linear baseflow begins | Fraction | 0–30 | 4.1 | 15 | 30 |
| Ws | Fraction of the maximum soil moisture where non-linear baseflow occurs | Fraction | 0–1 | 0.24 | 0.98 | 0.98 |
| d1 | Thickness of the top thin soil moisture layer (SML) | m | 0.01–0.1 | 0.07 | 0.04 | 0.01 |
| d2 | Thickness of the middle SML | m | 0.1–2 | 0.1 | 0.1 | 0.45 |
| d3 | Thickness of the lower SML | m | 0.5–4 | 1.9 | 2.1 | 2.3 |
Compare the observations and simulations of winter streamflow during the calibration period, then adjust Ds, Dsmax, and d3 to ensure that the multi-year average winter streamflow closely aligns with the simulations.
Analyze the change process of streamflow approaching the base flow, then adjust the Ws accordingly.
Modify d1 and d2 to make the multi-year average simulations align with the observations.
Adjust the b parameter to bring the observations closer to the simulations during the flood season.
Employ the SCE-UA optimization algorithm to fine-tune the seven parameters to achieve the optimal NSE value during the calibration period.
Evaluate the simulations using NSE, R, and BIAS during the validation period.
According to the simulated daily streamflow data set from the MME-Delta, we calculated the Q (annual maximum streamflow) and W (annual maximum 7-day W) values. The W is widely regarded as a primary indicator of flooding (Yin, Guo, He, et al., 2018; Yin, Guo, Liu, et al., 2018), and it has been extensively employed in the risk assessment of natural disasters across China (T. Li et al., 2016; Liu et al., 2018; Yin et al., 2020). Consequently, this study focused solely on the W influenced by climate change to space saving.
The research investigated the Q and W to uncover the marginal probability of flooding occurrences under three SSPs via the marginal distribution function (MDF), as well as the joint probability (JP) and co-occurrence probability (CP) under three SSPs using the Copula function (CF). The CF is a versatile statistical method utilized to characterize interconnected hydrological variables. To ensure a better fit of Q and W time series to the observations, six MDFs (including Gamma, Weibull, Log-normal, Generalized Extreme Value, Exponential, and P-III) were selected to fit the Q and W time series of the reference period separately. The maximum likelihood method (MLM) was employed to evaluate MDF parameters and the K-S test was used to verify the fitting accuracy.
Furthermore, this study constructed the two-dimensional JP of Q and W during the reference period using two Elliptic CFs (T and Gaussian) and three Symmetric Archimedean CFs (Frank, Clayton, Gumbel). The MLM was utilized to estimate the CF parameters, with the root mean square error (RMSE) and Akaike Information Criterion (AIC) employed to assess the goodness of fit. A lower RMSE and AIC values signified a better fit.
Among these, the joint return period (To) and co-occurrence return period (Ta) are usually employed in flooding risk assessment: [Image Omitted. See PDF] [Image Omitted. See PDF]where To(x, y) is the To of Q and W; Ta(x, y) is the Ta of Q and W; u is the MDF of Q; v is the MDF of W; C(u, v) is the JP of Q and W.
Results Probable Climate Change Bias Correction Performance VerificationThe performance of all GCMs is assessed using the Taylor diagram (Figure 4) method (Taylor, 2001). This method evaluates the discrepancies between simulations and observations in terms of R, RMSE, and Standard Deviation (SD). Among the four sub-regions studied, the daily P simulations performed best in Region I, while the daily Tmax and Tmin simulations demonstrated their best performance in Region IV. We observed that the daily P, Tmax, and Tmin simulations were most satisfactory after the coupling of the MME and Delta downscaling (Delta-MME). In comparison to other GCMs, the daily Delta-MME simulations showed excellent consistency with daily observations, achieving the highest R and lowest RMSE.
Enlarge this image.Figure 4. Applicability of CMIP6 GCMs compared to daily observations across the YRB during reference period (1995–2014).
Furthermore, Figure 5 compares the multi-year monthly average simulations and observations of CMIP6 GCMs during the reference period. It is evident that the monthly precipitation simulated by the majority of CMIP6 GCMs is significantly overestimated, while the monthly maximum and minimum temperatures are severely underestimated. In comparison to other CMIP6 GCMs, the Delta-MME has notably enhanced its capability to replicate monthly precipitation and temperature, with the simulated and observed annual variation curves being virtually identical. These findings corroborate that the Delta-MME demonstrates strong applicability in simulating climate change over the YRB during the reference period.
Enlarge this image.Figure 5. Comparison of multi-year monthly average values between the CMIP6 GCMs and observations across the YRB during reference period.
Figure 6 discloses the climate variables of the Delta-MME, showcasing the climatic transformations across the YRB under three SSPs. As shown in Figure 6a, the P across the YRB from 2015 to 2099 exhibits a fluctuating upward trend under three SSPs. Under SSP585, the annual P variation across the YRB registers the largest increase (14.71 mm/10a). Compared to the reference period (Figure 6b), the amplitude of the average annual P change across the YRB from 2015 to 2099 ranges from 1.27% to 24.85% (SSP126), −3.52% to 23.09% (SSP245), and −5.07% to 34.86% (SSP585), respectively. In the far-future, the average annual P is projected to escalate by 12.71% (SSP126), 15.47% (SSP245), and 25.01% (SSP585).
As shown in Figures 6c and 6e, the trends of Tmax and Tmin across the YRB from 2015 to 2099 under three SSPs demonstrate a continuous upward movement. Under SSP585, the annual Tmax and Tmin exhibit the highest rising rates (0.7°C/10a and 0.8°C/10a), respectively. Compared to the reference period (Figures 6d and 6f), the amplitude of change in the average annual Tmax across the YRB ranges from 0.5 to 2.3°C (SSP126), 0.5 to 3.5°C (SSP245), and 0.4 to 6.9°C (SSP585) from 2015 to 2099, respectively. Similarly, the amplitude of change in the average annual Tmin across the YRB varies from 0.2 to 2.1°C (SSP126), 0.4 to 3.4°C (SSP245), and 0.5 to 7.0°C (SSP585) from 2015 to 2099, respectively. In the far-future, it is anticipated that the average annual temperature will rise by 1.7°C (SSP126), 3.0°C (SSP245), and 5.7°C (SSP585).
Hydrological Simulations Under Climate Change Calibration and ValidationConsidering the available data sets, the VIC hydrological model simulation was executed from 1966 to 1985. The time series from 1966 to 1975 were selected as the calibration periods, while the time series from 1976 to 1985 were utilized for the validation periods. Moreover, the time series from 1960 to 1964 were designated as the warm-up periods. The VIC hydrological model was calibrated for daily and monthly streamflow, and seven calibration parameters in Table 2 were determined thought the validation periods. Comparisons between simulations and observations at the outlet of TNH, TDG, and HYK (Figure 7) demonstrated that the VIC hydrological model was effectively calibrated and could successfully simulate daily and monthly streamflow under climate change. It is worth noting that, except for TNH, the simulations at the other two hydrological stations exceeded the observations. The VIC hydrological model is preferred as it emulates natural streamflow, thereby minimizing the influence of reservoirs, dams, irrigation, and providing a more accurate depiction of the evolution of water resources and flooding across the YRB.
Enlarge this image.Figure 7. Observed and simulated streamflow of (a), (b) TNH, (c), (d) TDG, (e), (f) HYK across the YRB, (a, c, e) monthly streamflow; (b, d, f) scatter density plot of Daily streamflow.
The inter-annual variability and relative changes in annual streamflow under three SSPs relative to the reference period are presented in Figure 8. The average streamflow recorded across the YRB during the reference period (1995–2014) was 210 × 108 m3 in TNH, 361 × 108 m3 in TDG, and 603 × 108 m3 in HYK, respectively. Simulation analysis revealed that annual streamflow is expected to increase under three SSPs. The change rates of annual streamflow for each of the three hydrologic stations are projected to reach their maximum under SSP585, among 4.39 × 108 m3/10a in TNH, 8.76 × 108 m3/10a in TDG, and 28.07 × 108 m3/10a in HYK, respectively (Figures 8a, 8c, and 8e). Throughout projection period (2015–2099), streamflow in TNH is anticipated to increase by −10.2%–21.0% under SSP126, by −9.9%–25.9% under SSP245, and by −9.5%–28.0% under SSP585. Streamflow in TDG is projected to increase by 2.4%–39.1% under SSP126, by −3.9%–32.0% under SSP245, and by −2.8%–45.1% under SSP585. Streamflow in HYK is expected to increase by 0%–36.9% under SSP126, by −7.7%–36.7% under SSP245, and by −6.7%–59.6% under SSP585 (Figures 8b, 8d, and 8f). In the far-future, three SSPs exhibit a significantly increasing behavior in annual streamflow compared to the near-future and mid-future. Under SSP585, the average annual streamflow in HYK is anticipated to increase by over 35%. This suggests that amid global warming,the increase in streamflow across the downstream of the YRB is substantial, and the flooding risk in the downstream region of YRB may escalate significantly in the far-future.
Enlarge this image.Figure 8. Projected changes in the annual streamflow of TNH (a–b), TDG (c–d), HYK (e–f) hydrological stations under SSP126, SSP245, and SSP585 scenarios.
Table 3 presents the changes in the Q and W in future time horizons compared to the reference period under three SSPs. The findings indicate that both Q and W are likely to escalate in the three future time horizons. Under SSP126, the Q at HYK may experience the most substantial (30.4%) in the near-future, while the W at TDG could witness the largest rise (29.0%) in the mid-future. For SSP245 and SSP585, the Q and W at HYK may register the highest increments in the far-future, with Q increases of 26.69% and 52.73%, and W increases of 23.75% and 44.75%, respectively. This analysis suggests that the flooding risk across the downstream of YRB could be comparatively higher than the upstream and midstream regions under climate change.
Table 3 Relative Changes (Compared to the Reference Period (1995–2014) in Q and W Under Three SSPs Across the YRB (Unit: %))
| Sub-regions | Scenario | Change in Q | Change in W | ||||
| Near-future | Mid-future | Far-future | Near-future | Mid-future | Far-future | ||
| TNH | SSP126 | 3.29 | 9.45 | 12.67 | 5.03 | 9.87 | 14.15 |
| SSP245 | 3.45 | 10.89 | 20.71 | 4.40 | 11.58 | 20.90 | |
| SSP585 | 5.09 | 20.08 | 25.55 | 6.61 | 20.46 | 27.77 | |
| TDG | SSP126 | 22.72 | 30.10 | 21.31 | 23.71 | 28.99 | 22.12 |
| SSP245 | 15.11 | 20.33 | 21.47 | 16.3 | 22.02 | 21.47 | |
| SSP585 | 22.30 | 21.64 | 44.69 | 22.38 | 22.66 | 41.66 | |
| HYK | SSP126 | 30.39 | 24.27 | 13.38 | 25.52 | 25.39 | 12.03 |
| SSP245 | 15.92 | 25.00 | 26.69 | 14.95 | 22.47 | 23.75 | |
| SSP585 | 9.81 | 24.45 | 52.73 | 9.45 | 22.96 | 44.75 | |
To further explore the flooding risk across the YRB, we employed MDF to uncover the univariate flooding risk influenced by climate change. The fitting test and correlation coefficient of the six MDFs are presented in Table 4. As shown in Table 4, the correlation between Q and W across the YRB is impressive. The strongest correlation between Q and W is observed at HYK (0.9816), followed by TDG (0.9678), and the weakest correlation is found at TNH (0.9508). At a confidence level α = 0.05, all statistical values k are less than the critical value (0.3443), satisfying the K-S test. Hence, the MDF with a higher p-value and lower statistical value k is considered as the optimal fitting function for Q or W.
Table 4 Fit Test Statistics and Correlation Coefficient for Marginal Distribution Function
It's worth noting that there are discrepancies in the optimal fitting functions of Q or W for different hydrological stations, and possibly some variations in the optimal fitting functions of Q or W at the same station. Specifically, the Q and W of the TNH follow the P III distribution. The Q of TDG follows the Gamma distribution, while the W follows the GEV distribution. The Q and W of HYK are consistent with Exponential distribution. Therefore, we select the optimal MDF to fit the Q and W of three hydrological stations, enabling us to derive the theoretical values of Q and W under varying probability conditions.
The Q and W under the reference period and three SSPs were predicted by constructing marginal probability curves (Figure 9). Compared to the reference period, the Q and W of the same probability could increase significantly, and they gradually rise as the marginal probability decreases, especially at the HYK. A once-in-a-century Q at HYK may escalate by 40.4% under SSP126, 32.9% under SSP245, and 61.3% under SSP585 relative to the reference period. A once-in-a-century W at HYK may increase by 43.9% under SSP126, 43.3% under SSP245, and 64.1% under SSP585 relative to the reference period. It's evident that with global warming, the univariate flooding risk across the YRB demonstrates a pattern of “increase-decrease-increase.”
Enlarge this image.Figure 9. MDF of flooding characteristics in the TNH (a–b), TDG (c–d), and HYK (e–f) of the YRB under three scenarios.
We constructed the JP of Q and W using the CFs and applied the AIC and RMSE to select the optimal CF. Table 5 displays the goodness of fit of the chosen CF for TNH, TDG, and HYK hydrological stations. Notably, the optimal CF differ for each hydrological station. The Clayton Copula, Frank Copula, and Gumbel Copula demonstrated superior performance compared to other CFs for TNH, TDG, and HYK hydrological stations, respectively. Consequently, we selected the optimal CF fitted for each hydrological stations to construct the JP of Q and W.
Table 5 Variable Parameter Values and Goodness of Fit Evaluation
| Sub-regions | Copula function | Q-W | ||
| Parameter | RMSE | AIC | ||
| TNH | Gumbel | 4.90 | 0.0161 | −161.2 |
| Clayton | 7.90 | 0.0154 | −163.0 | |
| Frank | 17.33 | 0.0167 | −159.6 | |
| Gaussian | 7.00 | 0.5617 | −19.1 | |
| t | 9.30 | 0.3371 | −39.5 | |
| TDG | Gumbel | 6.52 | 0.0176 | −157.7 |
| Clayton | 10.00 | 0.0187 | −155.1 | |
| Frank | 25.77 | 0.0152 | −163.4 | |
| Gaussian | 7.00 | 0.5782 | −17.9 | |
| t | 9.20 | 0.3387 | −39.3 | |
| HYK | Gumbel | 7.66 | 0.0130 | −169.9 |
| Clayton | 7.93 | 0.0231 | −146.8 | |
| Frank | 27.34 | 0.0120 | −173.0 | |
| Gaussian | 7.00 | 0.5815 | −17.7 | |
| t | 9.40 | 0.3477 | −38.3 | |
The To of the three hydrologic stations across the YRB is explicitly depicted by the isopleth in Figure 10, wherein different marking symbols represent distinct scenarios. It is observed that the To of Q and W is susceptible to climate change. The To of Q and W with identical magnitude across the YRB is notably reduced under SSP585, and the joint risk of flooding at HYK is higher than that of both TDG and TNH. Compared to the reference period, a To of 20-year Q and W (Q = 11,914.3 m3/s, W = 53.7 × 108 m3) at HYK may advance by 3.9 times under SSP126, 4.6 times under SSP245, and 7.0 times under SSP585. A To of 50-year Q and W (Q = 14,131.9 m3/s, W = 63.1 × 108 m3) at HYK may advance by 3.8 times under SSP126, 4.5 times under SSP245, and 6.6 times under SSP585. A To of 100-year Q and W (Q = 15,809.40 m3/s, W = 70.15 × 108 m3) at HYK may advance by 3.3 times under SSP126, 3.9 times under SSP245, and 6.3 times under SSP585. Overall, the bivariate joint risk of flooding across the YRB will significantly advance under three SSPs. With global climate warming and reduced return periods, the increase in the JP of Q and W will become more pronounced, indicating that the impact of global warming on the bivariate joint risk of small and medium flooding is greater than that of catastrophic flooding.
Enlarge this image.Figure 10. Bivariate joint return isolines for historical and future periods under three SSPs.
The Ta of the three hydrologic stations across the YRB is explicitly depicted by the isopleth in Figure 11, wherein distinct marking symbols represent various scenarios. We observe that the Ta of Q and W is likewise susceptible to climate change. The Ta of Q and W along the YRB exhibits a significantly reduced magnitude under SSP585, and the co-occurrence risk for flooding at HYK is higher than that of both TDG and TNH. Compared to the reference period, a Ta of 20-year Q and W at HYK may advance by 12.5 times under SSP126, 14.6 times under SSP245, and 27.1 times under SSP585. A Ta of 50-year Q and W at HYK may advance by 10.1 times under SSP126, 11.0 times under SSP245, and 40.0 times under SSP585. A Ta of 100-year Q and W at HYK may advance by 6.6 times under SSP126, 7.0 times under SSP245, and 51.3 times under SSP585. Overall, the bivariate co-occurrence risk of flooding across the YRB will significantly advance under three SSPs. Under both SSP126 and SSP245, as the Ta increases, the co-occurrence probability of flooding gradually decreases. Under SSP585, as the Ta increases, the co-occurrence probability of flooding increases more prominent, indicating that the medium and low carbon emissions have a greater impact on the co-occurrence risk of small and medium flooding than catastrophic flooding, while the high carbon emissions have a greater impact on the co-occurrence risk of catastrophic flooding than small and medium flooding.
Enlarge this image.Figure 11. Bivariate co-recurrence return isolines for historical and future periods under SSPs.
The YRB, a representative basin in China, lies in a semi-arid and semi-humid zone, making it particularly sensitive to hydro-climatic changes (Omer et al., 2020; Ren et al., 2022). This study aims to investigate the impacts of future climate change on the streamflow and flooding risk of the YRB. The performance of Delta-MME and nine GCMs during the reference period (1995–2014) was assessed using the Taylor diagram, indicating the best consistency between Delta-MME simulations and observations. Climate change was projected under the reference period and three SSPs to calibrate and validate the VIC model through measured streamflow. Delta-MME estimates demonstrated a strong agreement with the observations during the reference period (1995–2014). This could be attributed to the relatively higher performance of Delta-MME in reproducing climate change over the YRB (Jian et al., 2023; P. Ji et al., 2023). Analysis of Delta-MME outputs revealed a continuous warming and increased humidity across the YRB throughout the 21st century. This is consistent with the findings in the North China Plain (Bai et al., 2020), Northwest China (Yang et al., 2022), and Qinghai Lake Basin (Luo et al., 2023). A significant factor behind these changes could be the reinforcement of westerly and East Asian monsoon circulation, which transport more water vapor from the Atlantic and Pacific oceans, providing sufficient water vapor across the YRB (Q. Zhang et al., 2022).
The analysis of VIC model simulations revealed an upward trend in streamflow for all future time horizons estimated by Delta-MME under the three SSPs, primarily driven by increased precipitation. Research conducted by Lan et al. (2010) highlighted the sensitivity of streamflow to changes in precipitation, and G. Ji et al. (2021) noted a general rise in streamflow across the YRB. Our study goes beyond this by predicting that the increase in Q and W across the YRB under the three SSPs will surpass the growth in average streamflow. Furthermore, we also expose the intensification of bivariate flooding risks across the YRB, with the co-occurrence risk of catastrophic flooding under high emission pathways projected to increase by over 50 times. In essence, global warming will result in an elevated flooding risk across the YRB. Although this study provides a comprehensive examination of streamflow and flooding risk under climate change across the YRB, the underlying physical mechanisms remain uncertain. Unlike precipitation, which is primarily influenced by water vapor, streamflow and flooding risk are also significantly affected by changes in surface conditions such as irrigation, deforestation, grazing, desertification, and urban expansion. Variations in soil properties, from loose to dense, can either increase or decrease streamflow (Bronstert et al., 2007). Numerous studies have demonstrated that increased forest cover can reduce streamflow, while deforestation has the opposite effect (Bronstet et al., 2002; Eckhardt et al., 2003; Stednick, 1996). Urbanization introduces modifications in urban climate, land use, and land cover, leading to increased Q and decreased lag time (Kang et al., 1998). This research quantitatively evaluated the changes in streamflow and flooding risk, but it fails to investigate or attribute these variations to human-induced global warming. Future research should delve into the impact of human-induced global warming on flooding risk across the YRB.
The issue of uncertainty is of increasing concern, particularly in hydrological simulations, as climate change assessments that ignore uncertainties may lead to biased conclusions. Uncertainty in streamflow and flooding estimates under climate change is generally attributed to LUCC, GCMs, and hydrological models. First, LUCC has a significant influence on streamflow and flooding predictions. Ding et al. (2023) compared six LUCC products and confirmed that the LUCC provided by the RESDC has the highest accuracy over the Loess Plateau, reaching an accuracy of 91.7%. Using the LUCC products of the RESDC, we applied the FLUS model to predict LUCC under three SSPs. Compared to the LUCC products of the RESDC from 2020, the overall accuracy reached 0.888, and the Kappa coefficient was 0.836, indicating that the simulation results were more consistent with the actual situation. However, it is crucial to consider LUCC uncertainties and their impact on streamflow and flooding risk, particularly in the context of YRB land use plans. Second, GCMs possess a certain influence on streamflow and flooding predictions. Addressing this concern, we have employed observations to statistically downscale GCMs derived from the MME, thereby reducing the uncertainty in simulations. Nonetheless, precipitation across the YRB exhibits significant spatiotemporal variability and uneven spatial distribution (W. Wang et al., 2020).The precision of spatially explicit precipitation greatly influences the accuracy of hydrological prediction. In future study, greater emphasis should be placed on exploring various statistical downscaling techniques to mitigate the uncertainty inherent in climate simulations. For instance, ESD and SDSM methods should be considered (Olmo & Bettolli, 2022; Singh et al., 2015). Ultimately, hydrological model estimations also bear a considerable degree of uncertainty. The VIC model, for instance, fails to take into account the effects of domestic water consumption, irrigation, and reservoir regulation on streamflow and flooding risk. Consequently, employing a single hydrological model may lead to inaccuracies in assessing streamflow and flooding risk across the YRB. In the future, the impacts of domestic water consumption, irrigation, and reservoir regulation on streamflow and flooding changes should be taken into account, and a diverse array of hydrological models should be employed to minimize errors caused by relying on a single model. Despite the substantial uncertainty derived from multiple sources, our main conclusion remains unchanged: global warming will likely result in an increased flooding risks across the YRB. Addressing and systematically dividing the different uncertainty components pose a challenge, and future efforts may focus on investigating the comprehensive uncertainty associated with assessing streamflow and flooding risk influenced by climate change.
ConclusionsThe research investigated the impacts of potential climate change on Yellow River streamflow and flooding risk by employing the VIC hydrologic model under three SSPs (126, 245, and 585). Nine GCMs outputs were downscaled and consolidated across the YRB for the projected climate change. The VIC hydrologic model was calibrated and validated for the periods from 1966 to 1975 and 1976 to 1985, respectively. Evaluation indices (NSE, R, and BIAS) for both calibration and validation periods demonstrated the excellent performance and reliability of the VIC model in estimating the potential effects of climate change on Yellow River streamflow and flooding risk. The primary findings of this study are as follows:
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P and T demonstrated an increasing trend, accompanied by notable spatial heterogeneity under three SSPs. In the far-future, it is projected that average annual P will increase by 12.71% (SSP126), 15.47% (SSP245), and 25.01% (SSP585), while average annual T is anticipated to rise by 1.7°C (SSP126), 3.0°C (SSP245), and 5.7°C (SSP585).
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The simulation results for the three SSPs demonstrated a consistent upward trend in terms of streamflow, Q, and W in the far-future. Under the SSP585, the largest increase in Q was observed. When comparing these findings to the reference period (1995–2014), the projected once-in-a-century Q was expected to rise by 40.4% (SSP126), 32.9% (SSP245), and 61.3% (SSP585), respectively. Similarly, the projected once-in-a-century W was expected to rise by 43.9% (SSP126), 43.3% (SSP245), and 64.1% (SSP585) at the total water outlet (HYK). It is evident that as global warming intensifies, the univariate flooding risk across the YRB exhibits a pattern of “increase-decrease-increase.”
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The CF predicted a consistent upward trend in bivariate flooding risk across various return periods. With global climate warming and reduced return periods, the increments in JP of Q and W will become more pronounced. Compared to the reference period (1995–2014), the JP of Q and W for 20-year and 100-year return periods increased by 3.3–7.0 times. The Ta of Q and W across the YRB with the same magnitude was significantly reduced, particularly for catastrophic flooding, which are 6.6 times under SSP126, 7.0 times under SSP245, and 51.3 times under SSP585 earlier than the reference period, respectively. These findings underscore the urgent need to enhance social resilience to climate change across the YRB.
This research has been supported by the National Natural Science Foundation of China Major Projects (Grant 42041006); the National Natural Science Foundation of China (Grant 42271037); the Science Foundation for Excellent Young Scholars of Anhui, China (Grant 2108085Y13); the Major Science and Technology Project of High-Resolution Earth Observation System (Grant 76-Y50G14-0038-22/23); the Key Research and Development Program Project of Anhui Province, China (Grant 2022m07020011); the Science Foundation for Distinguished Young Scholars of Anhui Universities, China (Grant 2022AH020069); Collaborative Innovation Project of Universities in Anhui Province, China (Grant GXXT-2021-048); Special Support Plan for Anhui Province, China (Grant 2019); Science Research Key Project of Anhui Educational Committee (Grant 2023AH051603). The author also thanks the China Meteorological Administration and the Yellow River Water Conservancy Commission for providing meteorological and streamflow data for this study.
Data Availability StatementMoreover, the CMIP6 GCMs were obtained from online (
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; Sun, Peng 2
; Hu, Li 2 ; Chen, Donghua 1 ; Liu, Yufeng 1 ; Zou, Yifan 3 ; Kang, Jiang 4 1 School of Computer and Information Engineering, Chuzhou University, Chuzhou, China
2 School of Geography and Tourism, Anhui Normal University, Wuhu, China
3 School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, China
4 College of Resources and Environmental Sciences, China Agricultural University, Beijing, China