Assessment of Future Climate Change in the Huaihe River Basin Using Bias-Corrected CMIP5 GCMs with Consideration of Climate Non-Stationarity

Abstract

The Huaihe River Basin is particularly vulnerable to climate change. This paper first evaluated interpolation methods for different meteorological elements, followed by an assessment of the simulation performance of various Coupled Model Intercomparison Project 5 (CMIP5) Global Climate Models (GCMs) for these elements. We then applied the Improved Quantile Mapping (IQM) method for bias correction of the GCMs. Finally, we analyzed the characteristics of future climate change in the Huaihe River Basin. The results show the following: (1) The radial basis function interpolation method is the most effective for rainfall, while Kriging performs best for air temperature. (2) The HadGEM2-AO model provides the most accurate rainfall simulations, MIROC-ESM best simulates maximum air temperature, and HadGEM2-ES is most effective for minimum air temperature. (3) The IQM method outperforms other approaches for bias correction of climate variables in the basin. (4) Future projections show an increase in both rainfall and air temperature, with more pronounced rises under the RCP8.5 scenario. Additionally, rainfall and maximum air temperature show considerable spatial variation across emission scenarios, while minimum air temperature consistently exhibits an upward trend.

1. Introduction

Climate change has led to a range of impacts, including global warming and a higher frequency of extreme weather events, which pose new challenges for regional meteorological and hydrological management [1,2,3,4]. In the Huaihe River Basin, global climate change has altered the spatial and temporal dynamics of the hydrological cycle, significantly increasing the risks of both floods and droughts [5]. Accurately predicting future climate change in the Huaihe River Basin is essential to understanding these impacts and developing effective adaptation and mitigation strategies.

Since the 1970s, numerous studies have focused on the impacts of climate change [6,7]. Global Climate Models (GCMs) [8] are widely used tools for predicting climate change, as they mathematically represent the interactions and feedback processes between the different layers of the Earth’s climate system. Many assessments of climate change have relied heavily on GCM simulations of future conditions [9,10,11]. In 1995, the World Climate Research Programme (WCRP) proposed the Coupled Model Intercomparison Project (CMIP) [12], which greatly enhances comparison and collaboration among GCMs. By 2008, more than forty GCMs from twenty research groups had participated in the CMIP5, which is capable of simulating historical climate and projecting future climate change based on the RCP2.6, RCP4.5, RCP6.0, and RCP8.5 scenarios. Notably, CMIP5 features a more robust parametric design and higher resolution than the previous CMIP1~CMIP3 [13]. The IPCC Fifth Assessment Report (AR5) highlighted that the distribution of global temperature and rainfall simulated by the CMIP5 GCMs closely aligns with observed data [14].

Numerous studies have evaluated the performance of CMIP5 GCMs. For instance, Xu [15] analyzed CMIP5 rainfall using ten climate indices. Taylor diagrams are frequently employed to assess CMIP5 GCMs [16,17]. Dong [18] utilized Taylor diagrams to evaluate 22 CMIP5 GCMs, revealing that MPI-ESM-Lr and CanESM2 performed better in simulating air temperature in the study area. Taylor diagrams display the correlation coefficient (R), root mean square error (RMSE), and standard deviation (SD) for multiple GCMs. However, Taylor diagrams cannot directly present the model’s mean bias, potentially obscuring issues related to the model’s performance in terms of mean values. Furthermore, it is challenging to ensure that each metric achieves its optimal value within a particular GCM.

Due to the varying spatial resolutions of GCM simulation results, spatial interpolation is necessary before evaluating GCM performance. For example, Mirza [19] employed a spatial interpolation method to convert coarse-grid raw GCM data into station-scale data. Various spatial interpolation methods can be applied to GCM results, such as the inverse distance weight method [20], the Kriging method [21], and the radial basis function [22]. However, not all spatial interpolation methods are suitable for processing GCM simulation results.

The CMIP5 GCMs offer higher horizontal and vertical resolutions compared to previous CMIP GCMs [12]. However, their outputs remain relatively coarse in terms of their spatial resolutions (>100 km²), which is inadequate for accurately representing hydrologic processes [23]. Consequently, downscaling and bias correction of long-term GCM simulations are essential [24,25,26]. Common bias correction methods include the Delta method [27] and Quantile Mapping (QM) method [28], among others. The Delta method is a mean-based bias correction approach widely used for generating future climate change scenarios. Mperlasoka [29] utilized the Delta method to develop future climate series. Chen [30] highlighted its significance in delineating uncertainty when assessing climate change impacts on hydrology. The QM method is a bias correction method based on probability distribution. Themeßl et al. [31] pointed out that the QM method significantly reduced the bias of temperature, rainfall, and extreme indices. Ngai et al. [32] further demonstrated that the QM method effectively corrects biases in temperature and rainfall. Although the Delta method is simple and feasible, it only addresses variability in the mean value and neglects changes in the standard deviation and the skewness coefficient. While the QM method addresses some limitations of the Delta method, its fundamental assumption of stable statistical relationships may overlook distribution changes, potentially leading to underestimation of future extreme climate events [33].

To more accurately assess future climate change in the Huaihe River Basin, this study utilized twelve CMIP5 GCMs, incorporating bias correction methods that account for climate non-stationarity to simulate rainfall (Pr), maximum air temperature (T_max), and minimum air temperature (T_min). We first evaluated five spatial interpolation methods and then applied the optimal methods to the simulation results from twelve GCMs, selecting the best-preforming GCMs for Pr, T_max, and T_min. Next, we applied three bias correction methods to the CMIP5 GCMs. Finally, we analyzed the temporal and spatial characteristics of future climate elements. The key innovations of this study include the following: (1) We propose a Comprehensive Index of Spatial Interpolation (CISI) that integrates multiple evaluation metrics (MAE, MRE, and RMSE) to assess the performance of different spatial interpolation methods. (2) In evaluating GCM performance, we introduce a Comprehensive Index of Evaluating model Skill (CIES) to address two challenges: the difficulty of ensuring that R, SD, and RMSE achieve optimal values for a given GCM, and the inability to distinguish between errors arising from bias between variables and differences in their means. (3) Recognizing the non-stationarity of frequency distribution of climate elements in historical and future periods, we propose an Improved Quantile Mapping (IQM) method to overcome the limitations of the Delta and QM methods.

2. Study Area and Data

2.1. Study Area

The Huaihe River Basin (30°55′~36°36′ N, 111°55′~121°25′ E) lies between the Yangtze River Basin and the Yellow River Basin, covering an area of approximately 270,000 km². While the western, southern, and northeastern regions of the basin are characterized by hilly terrain, the rest consists primarily of plains. The Huaihe River Basin transitions from a subtropical climate in the south to a warm temperate climate in the north. The average annual air temperature of the basin is 14.6 °C. The T_min gradually decreases from south to north. Due to the influence of the ocean, the T_max decreases from the southwest to the northeast of the basin. The relative humidity ranges from 66% to 81%. The basin receives an average annual rainfall of 868 mm. Over 60% of the rainfall in the basin occurs from June to September, leading to frequent flooding during this period. The spatial distribution of rainfall is uneven, with annual rainfall generally decreasing from south to north across the basin. The distribution of rivers and stations in the Huaihe River Basin is shown in Figure 1.

2.2. Observed Data

The observed data include daily rainfall and daily maximum/minimum air temperature in the Huaihe River Basin from 1961 to 2020. These data were collected from 61 meteorological stations located around the Huaihe River Basin (Figure 1).

Table A1. The coordinates of the study stations in the Huaihe River Basin.

No.	Name	Longitude	Latitude	No.	Name	Longitude	Latitude
1	Yiyuan	118°05′ E	36°06′ N	32	Shouxian	116°28′ E	32°19′ N
2	Dingtao	115°19′ E	35°03′ N	33	Bengbu	117°13′ E	32°34′ N
3	Yanzhou	116°30′ E	35°20′ N	34	Dingyuan	117°24′ E	32°19′ N
4	Feixian	117°34′ E	35°09′ N	35	Gaoyou	119°16′ E	32°28′ N
5	Juxian	118°30′ E	35°21′ N	36	Dongtai	120°11′ E	32°31′ N
6	Zhengzhou	113°23′ E	34°25′ N	37	Liuan	116°18′ E	31°27′ N
7	Xuchang	113°31′ E	34°01′ N	38	Huoshan	116°11′ E	31°14′ N
8	Kaifeng	114°10′ E	34°28′ N	39	Anyang	114°14′ E	36°01′ N
9	Baofeng	113°01′ E	33°31′ N	40	Xinxiang	113°31′ E	35°11′ N
10	Xihua	114°18′ E	33°28′ N	41	Shenxian	115°24′ E	36°08′ N
11	Zhuma	114°00′ E	33°00′ N	42	Jinan	117°01′ E	36°21′ N
12	Xinyang	114°01′ E	32°04′ N	43	Pingdu	119°33′ E	36°27′ N
13	Shangqiu	115°24′ E	34°16′ N	44	Weifang	119°06′ E	36°27′ N
14	Tangshan	116°12′ E	34°15′ N	45	Rizhao	119°19′ E	35°15′ N
15	Pizhou	117°34′ E	34°10′ N	46	Mengjin	112°15′ E	34°29′ N
16	Xuzhou	117°05′ E	34°10′ N	47	Xixia	111°18′ E	33°10′ N
17	Tancheng	118°11′ E	34°21′ N	48	Nanyang	112°21′ E	33°01′ N
18	Shuyang	118°27′ E	34°03′ N	49	Zaoyang	112°27′ E	32°05′ N
19	Ganyu	119°04′ E	34°30′ N	50	Tongbai	113°15′ E	32°13′ N
20	Guanyun	119°08′ E	34°10′ N	51	Suizhou	113°13′ E	31°25′ N
21	Bozhou	115°27′ E	33°31′ N	52	Dawu	114°04′ E	31°20′ N
22	Yongcheng	116°16′ E	33°34′ N	53	Macheng	115°00′ E	31°06′ N
23	Mengcheng	116°19′ E	33°10′ N	54	Xuyi	118°18′ E	32°35′ N
24	Xiuzhou	116°35′ E	33°22′ N	55	Chuzhou	118°10′ E	32°10′ N
25	Suining	117°33′ E	33°31′ N	56	Nanjing	118°28′ E	32°00′ N
26	Sihong	118°07′ E	33°16′ N	57	Rugao	120°20′ E	32°13′ N
27	Funing	119°30′ E	33°28′ N	58	Lvsi	121°21′ E	32°02′ N
28	Sheyang	120°09′ E	33°27′ N	59	Tongcheng	116°34′ E	31°02′ N
29	Dafeng	120°17′ E	33°07′ N	60	Hefei	117°10′ E	31°28′ N
30	Fuyang	115°26′ E	32°31′ N	61	Yingshan	115°24′ E	30°26′ N
31	Gushi	115°22′ E	32°06′ N

shows the coordinates of the study stations.

From 1961 to 2020, the T_max in the Huaihe River Basin ranged from 31.0 °C to 43.7 °C, with the extreme T_max of 43.70 °C recorded at the Mengjin station in 1966. The annual T_min ranged from −23.4 °C to −2.9 °C, with the extreme T_min of −23.40 °C observed at the Tancheng and Yongcheng stations in 1969. Extreme high air temperatures (>20 °C) and extreme low air temperatures (<−15 °C) predominantly occurred between 1962 and 1972. The annual rainfall in the basin ranged from 595.3 mm to 1246.6 mm, with extreme rainfall events mainly recorded at specific stations, such as the Huoshan and Yingshan stations. Inter-annual variations in annual Pr and T_max in the basin were relatively moderate, whereas T_min fluctuations were more pronounced, showing a slight warming trend over the study period.

3. Methodology

3.1. Coupled Model Intercomparison Project 5

In this paper, twelve CMIP5 GCMs (

Table 1. Basic information of 12 CMIP5 GCMs.

No.	GCMs	Institution (Country)	Resolution (°)
1	CSIRO-Mk3.6.0	CSIRO-QCCCE (Australian)	1.88 × 1.87
2	GFDL-CM3	NOAA-GFDL (USA)	2.50 × 2.00
3	GFDL-ESM2G	NOAA-GFDL (USA)	2.50 × 2.02
4	GFDL-ESM2M	NOAA-GFDL (USA)	2.50 × 2.02
5	HadGEM2-AO	NIMR/KMA (Korea)	1.88 × 1.25
6	HadGEM2-ES	MOHC (UK)	1.88 × 1.25
7	IPSL-CM5A-LR	IPSL (France)	3.75 × 1.89
8	IPSL-CM5A-MR	IPSL (France)	2.50 × 1.27
9	MIROC5	JAMSTEC/AORI (UTokyo) (Japan)	1.41 × 1.40
10	MIROC-ESM	JAMSTEC/AORI (UTokyo) (Japan)	2.81 × 2.79
11	MIROC-ESM-CHEM	JAMSTEC/AORI (UTokyo) (Japan)	2.81 × 2.79
12	MRI-CGCM3	MRI (Japan)	1.13 × 1.12

) were selected to assess future climate change in the Huaihe River Basin. All twelve GCMs have completed projection experiments under four forcing scenarios: RCP2.6, RCP4.5, RCP6.0, and RCP8.5, with the simulation period extending beyond 2095. The projection results from twelve GCMs are available at https://aims2.llnl.gov/search/ (accessed on 4 January 2025). The historical period was defined as 1961–2005 (Period I), while two future periods were designated as 2006~2050 (Period II) and 2051–2095 (Period III).

3.2. Spatial Interpolation Methods

Based on the observed data, five spatial interpolation methods were used to analyze the spatial distribution of rainfall and air temperature in the Huaihe River Basin. These interpolation methods were implemented using ArcGIS 10.8 software.

3.2.1. Inverse Distance Weighting

Inverse distance weighting (IDW) is classified as a deterministic method. It assumes that everything is related to everything else, but near things are more related than distant things [34]. The formula is given as Equation (1):

$$Z\left(x_0\right)=\sum _{i=0}^n{\lambda }_{i}Z(x_i)$$

(1)

where Z(x₀) is the estimated value at the interpolation point x₀; n is the number of observation points; Z(x_i) is the gauged value at the observation point x_i; and λ_i is the weight coefficient. As the distance between the observation point and the interpolation point increases, the value of λ decreases:

$${\lambda }_i=d_{i0}^{-p}/\sum _{i=0}^n{d}_{i0}^{-p}$$

(2)

where p is the power parameter, p = 2; d_i0 is the distance between the interpolation point x₀ and the observation point x_i.

3.2.2. Ordinary Kriging

Ordinary Kriging (OK) [35] is one of the best linear unbiased estimation methods for estimating a specific mean trend value and is also one of the most widely used interpolation methods. Compared to simple and universal ones, Ordinary Kriging does not require the assumption of a known or constant mean, which makes it more flexible. It is a multi-stage method that involves exploratory statistical analysis of the data, variogram modeling, and the construction of response surfaces. The formula for the OK method has the same form as Equation (1), but the weights are determined by a semivariance function:

$$r\left(d\right)={\displaystyle \frac{1}{2N\left(d\right)}}\sum _{i=1}^{N\left(d\right)}{[Z\left(x_i\right)-Z(x_i+d\left)\right]}^2$$

(3)

where r(d) is the semivariance value at the distance interval d; N(d) is the number of sample pairs within the distance interval d; and Z(x_i + d) and Z(x_i) are values at two locations at a distance d.

Semivariogram parameters are necessary for spatial prediction. The values of these parameters can be estimated by using variogram models (i.e., Gaussian, Spherical, and Exponential). In this study, we selected the commonly used Spherical model:

$$r\left(d\right)=\left\{\begin{array}{c} 0, d=0 \\ C_0+C_1\left[\left(3d/2a\right)-\left(d^3/2a^3\right)\right], 0<d\le a\\ C_0+C_1, d>a\end{array}\right.$$

(4)

where C₀ is the nugget effect, C₁ is the structured variance, C₀ + C₁ is the sill, and a is the variogram range (C₀ ≥ 0, C₁ ≥ 0, and a ≥ 0).

3.2.3. Global Polynomial Interpolation

Global polynomial interpolation [36] (GPI) is a fast global interpolator. It fits a smooth surface defined by a mathematical function to the input sample points. The GPI surface changes gradually and captures coarse-scale patterns in the data. GPI estimates the value Z at any location based on the (X_i, Y_i) coordinates of that location:

$$Z=f\left(x_i, y_i\right)$$

(5)

A second-order trend surface was used in this study:

$$f\left(x,y\right)=a_0+a_{1}x+a_{2}y+a_3{x}^2+a_4{y}^2+a_5\mathit{xy}+\epsilon$$

(6)

where a₁~a₅ are the parameters, which are obtained using a regression technique utilizing all of the measured points.

3.2.4. Local Polynomial Interpolation

Local polynomial interpolation [37] (LPI) is a smooth, medium-speed interpolator. This method uses different polynomials according to specified overlapping neighbors and only utilizes the surrounding data points. LPI has the same mathematical representation and fitting procedure as GPI, except LPI fits a local formula by utilizing measured points within a specified area. The curve surface it produces is more dependent on local variation in the data. The polynomial order can be specified (zero, first, second, or other) based on the defined neighbors. LPI is more flexible than GPI and involves more parameters to be set up.

For this study, a polynomial of the second degree was used. LPI fits local polynomials through the weighted least squares method. The local least squares parameters are computed by minimizing the weighted sum of the squared residuals.

3.2.5. Radial Basis Function

The radial basis function [38] (RBF) is a method to construct high-order accurate interpolants in a high-dimensional space and to achieve a global interpolation of response points for discrete data points. In this study, we tested five different basis functions: thin-plate spline, spline with tension, completely regularized spline, the multiquadric function, and the inverse multiquadric function. The spatial distribution of the results from these five basis functions showed minimal differences, with the completely regularized spline yielding the smallest error. Therefore, the completely regularized spline function was utilized to investigate the spatial interpolation accuracy of various meteorological elements across different time scales in the Huaihe River Basin. The formula is as follows:

$$Z\left(x,y\right)={\displaystyle \frac{1}{2\pi }}\left({\displaystyle \frac{d_i^2}{4}}\left(\ln \left({\displaystyle \frac{d_i}{2\tau }}\right)+c-1\right)+{\tau }^2\left(K_0\left({\displaystyle \frac{d_i}{\tau }}\right)+c+\ln \left({\displaystyle \frac{d_i}{2\pi }}\right)\right)\right)+a+\mathit{bx}+\mathit{cy}$$

(7)

where Z(x, y) is the estimated value at the interpolation point (x, y); n is the number of observation points; d_i is the distance between interpolation point (x, y) and observation point (xi, yi); τ is the weight; c = 0.577215; $K_0\left({\displaystyle \frac{d_i}{\tau }}\right)$ is the modified zero-degree Bessel function; ${\displaystyle \frac{1}{2\pi }}\left({\displaystyle \frac{d_i^2}{4}}\left(\ln \left({\displaystyle \frac{d_i}{2\tau }}\right)+c-1\right)+{\tau }^2\left(K_0\left({\displaystyle \frac{d_i}{\tau }}\right)+c+\ln \left({\displaystyle \frac{d_i}{2\pi }}\right)\right)\right)$ is the primary function; a + bx + cy is the local trend function; and a, b, and c are coefficients obtained by solving linear system of equations.

3.2.6. Comprehensive Index of Spatial Interpolation

The mean absolute error (MAE), mean relative error (MRE), and root mean squared error (RMSE) are used to evaluate the accuracy of five interpolation methods. The smaller the values of the three evaluation metrics, the higher the precision of the model simulation.

It is challenging to ensure that the evaluation metrics of spatial interpolation methods consistently achieve minimum values across different periods for any given method. For example, in 2003, the MAE for the OK method of Pr was the lowest, yet both the MRE and RMSE were higher compared to the LPI method. This discrepancy makes it challenging to determine the most accurate interpolation method based on these three metrics alone. Thus, this paper takes all three metrics into account and proposes the Comprehensive Index of Spatial Interpolation (CISI) to assess the accuracy of various spatial interpolation methods. The CISI is calculated as follows:

$${ \mathit{CISI}}_j=\sqrt{{({\mathit{NMAE}}_j-{\mathit{NMAE}}_0)}^2+{({\mathit{MRE}}_i-{\mathit{MRE}}_0)}^2+{({\mathit{NRMSE}}_j-{\mathit{NRMSE}}_0)}^2}(j=1,\dots ,m)$$

(8)

where m is the number of interpolation methods; NMAE_j, MRE_j, and NRMSE_j are the normalized MAE, MRE, and RMSE of the jth spatial interpolation method, respectively. NMAE₀ = 0, MRE₀ = 0, and NRMSE₀ = 0. Thus,

$${\mathit{CISI}}_j=\sqrt{{{\mathit{NMAE}}_j}^2+{{\mathit{MRE}}_j}^2+{{\mathit{NRMSE}}_j}^2}$$

(9)

The geometric meaning of the CISI is the distance from the point (NMAE_j, MRE_j, and NRMSE_j) to the origin (NMAE₀, MRE₀, and NRMSE₀). From a spatial perspective, the interpolation method corresponding to a point closer to the origin is considered the most optimal. Thus, a smaller CISI value indicates higher accuracy for the spatial interpolation method.

3.3. GCMs Performance Evaluation Methods

The optimal interpolation methods were used to interpolate the simulated annual Pr, T_max, and T_min of different GCMs in the Huaihe River Basin from 1961 to 2005 onto gauged grids. The interpolated results were then compared with the observed data.

3.3.1. Taylor Diagram

A Taylor diagram [39] displays the correlation coefficient (R), standard deviations (SD), and centered-pattern root-mean-square difference (RMSD) between observed and simulated values on the same polar graph to directly reflect the advantages and disadvantages of the simulation results for each GCM. The R, SD of observations (SD_obs), SD of simulations (SD_sim), and RMSD follow the cosine theorem:

$${ \mathit{RMSD}}^2={{\mathit{SD}}_{\mathit{obs}}}^2+{{\mathit{SD}}_{\mathit{sim}}}^2-2{\mathit{SD}}_{\mathit{obs}}{\mathit{SD}}_{\mathit{sim}}\mathit{R}$$

(10)

$$\mathit{R}={\displaystyle \frac{1}{n}}\sum _{i=0}^n({\mathit{Obs}}_i-\overline{\mathit{Obs}}\left)\right({\mathit{Sim}}_i-\overline{\mathit{Sim}})/{\mathit{SD}}_{\mathit{obs}}{\mathit{SD}}_{\mathit{sim}}$$

(11)

$${\mathit{SD}}_{\mathit{obs}}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=0}^n{({\mathit{Obs}}_i-\overline{\mathit{Obs}})}^2}$$

(12)

$${\mathit{SD}}_{\mathit{sim}}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=0}^n{({\mathit{Sim}}_i-\overline{\mathit{Sim}})}^2}$$

(13)

$$\mathit{RMSD}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=0}^n{[\left({\mathit{Obs}}_i-\overline{\mathit{Obs}}\right)-\left({\mathit{Sim}}_i-\overline{\mathit{Sim}}\right)]}^2}$$

(14)

where n is the length of the study series; Obs_i and Sim_i are the observed and simulated values in year i, respectively; and $\overline{\mathit{Obs}}$ and $\overline{\mathit{Sim}}$ are the mean observed and simulated values, respectively.

3.3.2. Comprehensive Index of Evaluating Model Skill

Based on the RMSD alone, it is challenging to ascertain the extent to which the error arises from bias between variables versus differences in their means. Additionally, ensuring that the R, SD, and RMSE achieve optimal values for a given GCM is difficult. To address this, we propose a Comprehensive Index of Evaluating model Skill (CIES) to assess the performance of different GCMs in simulating the climate of the Huaihe River Basin. The CIES is calculated as follows:

$$\mathit{CIES}=\sqrt{{(R_{\mathit{sim}}-R_{\mathit{obs}})}^2+{({\mathit{NSD}}_{\mathit{sim}}-{\mathit{NSD}}_{\mathit{obs}})}^2+{({\mathit{NRMSE}}_{\mathit{sim}}-{\mathit{NRMSE}}_{\mathit{obs}})}^2}$$

(15)

where R_sim, NSD_sim, and NRMSE_sim represent the R, normalized SD, and normalized RMSE for the GCM simulated values and observed values, respectively; R_obs, NSD_obs, and NRMSE_obs are the three evaluation metrics of observation to observation, respectively, all of which are constant.

The geometric meaning of the CIES is the distance of a point (R_sim, NSD_sim, and NRMSE_sim) to the point OBS (NMAE_obs, MRE_obs, and NRMSE_obs). Spatially, the point closest to OBS indicates the best GCM simulation results. The larger the R, the smaller the |NSD_sim-NSD_obs| and NRMSE, and the higher the precision of the GCM simulation. Consequently, the GCM with the minimum CIES value is regarded as having the best simulation accuracy.

3.4. Bias Correction Methods

3.4.1. Delta Method

Based on the climate elements simulated by GCMs, the Delta method (also called the constant scaling method) [40] calculates the characteristics of future climate change and reconstructs future climate elements by applying these changes to the historical climate series. The calculation formula is as follows:

$$P_{\mathit{Of}}\left(t\right)={\overline{P}}_{\mathit{Oh}}\cdot {\displaystyle \frac{P_{\mathit{Gf}}\left(t\right)}{{\overline{P}}_{\mathit{Gh}}}}$$

(16)

$$T_{\mathit{Of}}\left(t\right)={\overline{T}}_{\mathit{Oh}}+[T_{\mathit{Gf}}\left(t\right)-{\overline{T}}_{\mathit{Gh}}]$$

(17)

where t is time; P_Of and T_Of are the future rainfall/air temperature series in different periods after the bias correction of the Delta change method; ${\overline{P}}_{\mathit{Oh}}$ and ${\overline{T}}_{\mathit{Oh}}$ are the annual mean rainfall/air temperature observed at each station during the historical period; P_Gf and T_Gf are the rainfall/air temperature simulated by GCMs for future periods; and ${\overline{P}}_{\mathit{Gh}}$ and ${\overline{T}}_{\mathit{Gh}}$ are the annual mean rainfall/air temperature simulated by GCMs in the historical period.

3.4.2. Quantile Mapping

The Quantile Mapping (QM) method [41] reduces bias between the Cumulative Distribution Functions (CDFs) of GCM simulations and observed data by establishing a transfer function. This method ensures that the frequency distributions of observed and simulated climate element values are aligned, maintaining consistency in the frequency distribution of both historical and future climate data.

In the historical period:

$$y_{\mathit{Oh}}=F_{\mathit{Oh}}^{-1}\left[F_{\mathit{Gh}}\left(y_{\mathit{Gh}}\right)\right]$$

(18)

The transfer function can be applied to the future period:

$$y_{\mathit{Of}}=F_{\mathit{Oh}}^{-1}\left[F_{\mathit{Gh}}\left(y_{\mathit{Gf}}\right)\right]$$

(19)

where $y_{\mathit{Oh}}$ and $y_{\mathit{Of}}$ are the climate elements after the bias correction in the historical and future periods; $y_{\mathit{Gh}}$ and $y_{\mathit{Gf}}$ are the climate elements simulated by GCMs in the historical and future periods; $F_{\mathit{Gh}}$ is the CDF of climate elements simulated by GCMs in the historical period; and $F_{\mathit{Oh}}^{-1}$ is the inverse function of the CDF of observed climate elements in the historical period.

3.4.3. Improved Quantile Mapping

As mentioned before, the frequency distribution of climate elements in the historical and future periods may not be consistent; therefore, we propose an Improved Quantile Mapping (IQM) method.

As shown in Figure 2, the values of climate elements simulated by GCMs in the future period ($y_{\mathit{Gf}}$) provide the frequency distribution from the CDF of these elements. Then, we obtain the values of climate elements simulated by GCMs in the historical period ($y_{\mathit{Gh}}$) from the CDF of climate elements simulated by GCMs in the historical period, and the values of observed climate data ($y_{\mathit{Oh}}$) from the CDF of observed data. Subsequently, we calculate the climate change characteristics based on the simulated and observed values from the historical period. Finally, the future scenarios for the climate elements are reconstructed by overlaying these change characteristics onto the future simulated values.

The calculation formula is as follows:

$${ P}_{\mathit{Of}}=P_{\mathit{Gf} }\cdot {\displaystyle \frac{F_{\mathit{Oh}}^{-1}\left[F_{\mathit{Gf} }\left(P_{\mathit{Gf}}\right)\right]}{F_{\mathit{Oh}}^{-1}\left[F_{\mathit{Gf} }\left(P_{\mathit{Gf}}\right)\right]}}$$

(20)

$$T_{\mathit{Of}}=T_{\mathit{Gf}}+F_{\mathit{Oh}}^{-1}\left[F_{\mathit{Gf}}\left(P_{\mathit{Gf}}\right)\right]-F_{\mathit{Gh}}^{-1}\left[F_{\mathit{Gf}}\left(P_{\mathit{Gf}}\right)\right]$$

(21)

where $P_{\mathit{Of}}$ and $T_{\mathit{Of}}$ are the rainfall and temperature after bias correction in the future period; $P_{\mathit{Gf}}$ and $T_{\mathit{Gf}}$ are the climate elements simulated by GCMs in the future period; F_Gh and F_Gf are the CDFs of climate elements simulated by GCMs in the historical and future periods; $F_{\mathit{Oh}}$ is the CDF of observed climate elements in the historical period; and $F_{\mathit{Oh}}^{-1}$ and $F_{\mathit{Gh}}^{-1}$ are inverse functions of the CDFs of observed climate elements and climate elements simulated by GCMs in the historical period.

4. Results and Discussion

4.1. Optimal Spatial Interpolation Method

4.1.1. Rainfall

Table 2. The CISI values of 5 interpolation methods for annual/monthly Pr.

Year	IDW	OK	GPI	LPI	RBF	Month	IDW	OK	GPI	LPI	RBF
2003	0.1937	0.1797	0.1768	0.1759	0.1825	1	0.2962	0.2159	0.2153	0.2291	0.2434
2004	0.2786	0.2676	0.2726	0.2648	0.2536	2	0.2303	0.1722	0.1755	0.1680	0.1728
2005	0.2826	0.2636	0.2816	0.2431	0.2621	3	0.2171	0.1428	0.1496	0.1320	0.1216
2006	0.2806	0.2878	0.2708	0.2731	0.269	4	0.1969	0.1298	0.1364	0.1274	0.1156
2007	0.242	0.2123	0.2366	0.2203	0.1804	5	0.1856	0.1236	0.1878	0.1540	0.1179
2008	0.2283	0.2318	0.2433	0.2111	0.2109	6	0.2126	0.1773	0.1860	0.1612	0.1824
2009	0.2335	0.2253	0.2231	0.2211	0.2306	7	0.1314	0.1329	0.1482	0.1331	0.1227
2010	0.2537	0.2552	0.2842	0.2174	0.2227	8	0.1830	0.1768	0.2010	0.1847	0.1744
2011	0.2318	0.2656	0.2588	0.2411	0.2239	9	0.1835	0.1678	0.1660	0.1568	0.1684
2012	0.2589	0.245	0.2538	0.2227	0.2357	10	0.1532	0.1458	0.1479	0.1483	0.1399
2013	0.2266	0.2217	0.2595	0.2207	0.214	11	0.1976	0.1806	0.1855	0.1637	0.1469
2014	0.3181	0.3166	0.2833	0.2924	0.2986	12	0.2360	0.1856	0.1940	0.1892	0.2049

Note: The bolded values represent the optimal CISI values.

presents the CISI values for five interpolation methods applied to annual (e.g., 2003~2014) and monthly rainfall data. As shown in the table, the RBF method demonstrates the highest overall accuracy for both annual and monthly rainfall interpolation, followed by the LPI method. In contrast, the IDW method exhibits the lowest accuracy.

Taking the 2007 rainfall data as an example, Figure 3 presents the results of the five interpolation methods. The IDW method is notably affected by extreme observed values. The GPI and LPI methods produce relatively smooth results, but their results show obvious homogenization. The interpolation results of the OK and RBF methods not only exhibit a smooth overall trend but also achieve higher interpolation accuracy. Compared to the OK method, the RBF method can predict values greater than the maximum observed value and less than the minimum observed value.

To further evaluate the performance of the RBF method, we compared its interpolation results for 2007 with the observed values (Figure 4). From Figure 4, the RBF method demonstrates high interpolation accuracy, with the results for all stations closely matching the observed rainfall values. Only seven stations exhibited interpolation errors exceeding 20%. Additionally, the RBF method showed the lowest values for all evaluation metrics (MAE = 95.64, MRE = 0.10, and RMSE = 119.70) compared to the other four methods. Therefore, this study employs the RBF method for the spatial interpolation of rainfall in the Huaihe River Basin.

4.1.2. Air Temperature

Table 3. The CISI values of five interpolation methods for annual/monthly T_max.

Year	IDW	OK	GPI	LPI	RBF	Month	IDW	OK	GPI	LPI	RBF
2003	0.0416	0.0389	0.0415	0.0387	0.0400	1	0.0879	0.0840	0.0878	0.0844	0.0810
2004	0.0347	0.0366	0.0395	0.0378	0.0347	2	0.0640	0.0645	0.0639	0.0637	0.0635
2005	0.0345	0.0332	0.0417	0.0340	0.0336	3	0.0493	0.0519	0.0518	0.0504	0.0489
2006	0.0345	0.0321	0.0371	0.0336	0.0331	4	0.0519	0.0484	0.0503	0.0487	0.0503
2007	0.0328	0.0335	0.0357	0.0342	0.0315	5	0.0351	0.0308	0.0316	0.0314	0.0335
2008	0.0341	0.0309	0.0357	0.0339	0.0304	6	0.0330	0.0290	0.0338	0.0310	0.0310
2009	0.0446	0.0393	0.0398	0.0392	0.0425	7	0.0344	0.0370	0.0384	0.0378	0.0342
2010	0.0295	0.0278	0.0275	0.0274	0.0288	8	0.0332	0.0308	0.0306	0.0314	0.0325
2011	0.0387	0.0374	0.0437	0.0370	0.0355	9	0.0364	0.0359	0.0421	0.0382	0.0359
2012	0.0296	0.0292	0.0350	0.0307	0.0295	10	0.0397	0.0429	0.0408	0.0396	0.0375
2013	0.0262	0.0271	0.0285	0.0277	0.0258	11	0.0389	0.0422	0.0438	0.0391	0.0372
2014	0.0338	0.0314	0.0301	0.0305	0.0328	12	0.0751	0.0731	0.0827	0.0773	0.0698

Note: The bolded values represent the optimal CISI values.

and

Table 4. The CISI values of five interpolation methods for annual/monthly T_min.

Year	IDW	OK	GPI	LPI	RBF	Month	IDW	OK	GPI	LPI	RBF
2003	0.2424	0.2137	0.2155	0.2106	0.2206	1	0.1879	0.1781	0.1876	0.1806	0.1808
2004	0.2184	0.2245	0.2161	0.1981	0.2136	2	0.2072	0.1683	0.1976	0.1743	0.1779
2005	0.2406	0.2404	0.2409	0.2439	0.2398	3	0.3114	0.2827	0.2949	0.2729	0.2744
2006	0.252	0.2484	0.2587	0.2469	0.2438	4	0.7912	0.7428	0.7926	0.7695	0.7568
2007	0.3544	0.3513	0.3426	0.345	0.3532	5	0.4590	0.5004	0.4924	0.4706	0.4609
2008	0.1847	0.1754	0.1820	0.1794	0.1876	6	0.1485	0.1521	0.1447	0.1484	0.1492
2009	0.2443	0.242	0.2248	0.2307	0.2401	7	0.0715	0.0716	0.0781	0.0764	0.0693
2010	0.2608	0.2428	0.2456	0.2469	0.2531	8	0.0786	0.0785	0.0823	0.0766	0.0738
2011	0.2804	0.2517	0.2592	0.2524	0.2719	9	0.2985	0.2877	0.2922	0.2859	0.2960
2012	0.2309	0.2169	0.2062	0.2135	0.2268	10	1.4720	1.4480	1.3640	1.3870	1.4570
2013	0.2431	0.2119	0.2085	0.2062	0.2304	11	0.2345	0.2397	0.2458	0.2460	0.2354
2014	0.2502	0.2178	0.2149	0.2183	0.2404	12	0.2359	0.2265	0.2183	0.2248	0.2336

Note: The bolded values represent the optimal CISI values.

present the CISI values for the five interpolation methods applied to annual (e.g., 2003~2014) and monthly maximum/minimum air temperature (T_max and T_min) data.

As shown in Table 3, the RBF method demonstrates the highest overall accuracy for both annual and monthly T_max interpolation, followed by the OK method, while the IDW method shows the lowest accuracy. From Table 4, the CISI values for the five interpolation methods are relatively similar, with no single method emerging as the absolute best for spatial interpolation.

Using the 2007 T_max (Figure 5) and T_min (Figure 6) as examples, it is evident that both the IDW and RBF methods are influenced by extreme observed values. The GPI and LPI methods produce smooth and similar results, but their maximum values are lower and minimum values are higher compared to other methods. The OK method maintains a generally smooth overall trend while achieving higher interpolation accuracy.

Figure 7 presents the interpolation results for T_max and T_min at 61 stations in 2007 using the OK method. As shown in the figure, the OK method demonstrates high interpolation accuracy for T_max, with 80.3% of stations showing errors within 1 °C, and only two stations exhibiting errors greater than 2 °C. The accuracy of T_min interpolation is slightly lower than that for T_max. However, 41 stations still show errors within 2 °C. Therefore, the OK method is selected for the spatial interpolation of air temperature in the Huaihe River Basin.

4.2. GCM Performance Evaluation

The RBF and OK methods were employed to interpolate the GCM simulation results from 1961 to 2005. Figure 8 illustrates the Taylor diagrams for annual Pr, T_max, and T_min.

Table 5. The evaluation metrics for Pr, T_max, and T_min simulated by 12 GCMs.

GCMs	Pr				Tmax				Tmin
	R	SD	RMSE	CIES	R	SD	RMSE	CIES	R	SD	RMSE	CIES
OBS	1	154.6	0	0	1	1.2	0	0	1	2.93	0	0
CSIRO-Mk3-6-0	0.41	155.9	235.2	0.65	0.46	2.61	2.92	0.55	0.42	2.01	3.58	0.64
GFDL-CM3	0.35	162.3	255.8	0.71	0.39	2.32	4.51	0.62	0.17	2.26	4.34	0.89
GFDL-ESM2G	0.28	159.5	236.1	0.77	0.43	2.47	4.91	0.59	0.59	2.29	4.38	0.53
GFDL-ESM2M	−0.04	188.8	331.1	1.11	0.38	1.46	4.99	0.63	0.45	1.94	4.25	0.64
HadGEM2-AO	0.61	149.6	194.5	0.45	0.66	2.26	4.09	0.36	0.40	2.63	5.11	0.72
HadGEM2-ES	0.17	145.1	250.7	0.88	0.52	2.37	2.65	0.49	0.90	3.04	4.34	0.34
IPSL-CM5A-LR	0.20	144	218.3	0.84	0.50	1.07	3.38	0.51	0.26	1.87	3.66	0.80
IPSL-CM5A-MR	0.03	144.8	236.2	1.01	0.44	1.35	1.82	0.56	0.21	1.86	4.1	0.85
MIROC5	0.19	150.7	357.6	0.91	0.17	1.16	3.63	0.84	0.60	2.18	5.93	0.60
MIROC-ESM	0.19	147.9	260	0.86	0.86	1.29	3.16	0.17	0.40	2.14	8.14	0.86
MIROC-ESM-CHEM	0.44	173.2	251.8	0.63	0.51	1.41	3.56	0.50	0.14	2.21	7.90	1.05
MRI-CGCM3	0.13	95.9	376.5	0.97	0.24	1.49	2.17	0.76	0.55	2.87	4.16	0.55

presents the evaluation metrics of the GCM simulation results.

As shown in Figure 8a and Table 5, for the twelve GCMs, the R of Pr ranges from −0.04 to 0.61, with the HadGEM2-AO model achieving the highest R value. The MRI-CGCM3 model has the smallest SD (95.9). The HadGEM2-AO model exhibits the smallest RMSE (194.5). Moreover, HadGEM2-AO also has the lowest CIES (0.45). Thus, the HadGEM2-AO model performs best in simulating Pr for the Huaihe River Basin.

As shown in Figure 8b and Table 5, the MIROC-ESM model achieves the highest R (0.86), while the IPSL-CM5A-LR model exhibits the smallest SD (1.07), and the IPSL-CM5A-MR model shows the lowest RMSE (1.82). Furthermore, the MIROC-ESM model has the lowest CIES (0.17), with its SD closely aligning with the observed values. Therefore, the MIROC-ESM model offers the most accurate simulation of T_max in the Huaihe River Basin.

According to Figure 8c and Table 5, the HadGEM2-ES model exhibits the highest R (0.90), while the MRI-CGCM3 model shows an SD that closely aligns with observed values. The CSIRO-Mk3-6-0 model records the lowest RMSE (3.58). The HadGEM2-ES model has the lowest CIES (0.34), so it is selected for simulating the T_min in the Huaihe River Basin.

4.3. Evaluation of GCM Bias Correction Methods

The GCM simulation results for Period I were sorted in descending order, with the lowest 30 years selected to represent the historical period and the highest 30 years selected to represent the future period. The Delta, QM, and IQM methods were used for bias correction of Pr, T_max, and T_min for January and July in the future period (Figure 9). The performance of the three methods was evaluated against the observed data corresponding to the future period.

As shown in Figure 9, all three bias correction methods successfully adjusted the GCM simulation results. The evaluation metrics and CIES for the Delta, QM, and IQM methods are presented in

Table 6. Evaluation of bias correction performance of Delta, QM, and IQM methods.

Climate Elements	Method	January				July
		R	SD	RMSE	CIES	R	SD	RMSE	CIES
Pr	OBS	1.00	14.69	0.00	0.00	1.00	55.39	0.00	0.00
	GCM	0.51	12.77	17.29	0.87	0.45	68.30	101.42	0.73
	Delta	0.51	17.46	20.52	0.98	0.47	77.19	106.99	0.73
	QM	0.58	19.32	22.99	1.05	0.62	67.32	99.72	0.60
	IQM	0.63	15.61	18.20	0.84	0.67	54.93	96.45	0.55
Tmax	OBS	1.00	2.67	0.00	0.00	1.00	1.25	0.00	0.00
	GCM	0.35	1.06	3.27	0.70	0.63	1.46	1.99	0.37
	Delta	0.35	1.06	3.33	0.70	0.63	1.46	1.82	0.37
	QM	0.15	2.81	4.81	0.91	0.52	1.86	2.22	0.48
	IQM	0.78	1.70	3.02	0.31	0.76	1.20	1.61	0.25
Tmin	OBS	1.00	2.23	0.00	0.00	1.00	1.32	0.00	0.00
	GCM	0.52	1.83	5.08	0.66	0.44	1.35	1.95	0.57
	Delta	0.52	1.83	5.21	0.67	0.44	1.35	2.11	0.57
	QM	0.54	1.38	5.09	0.65	0.47	0.99	2.00	0.54
	IQM	0.63	1.52	4.89	0.58	0.75	0.98	1.85	0.27

. The IQM method achieved the highest R, the lowest RMSE, and the smallest CIES, indicating its superior bias correction performance for the simulated climate variables in the Huaihe River Basin.

Figure 10 shows the spatial distribution of bias between the simulated and observed values for July Pr, T_max, and T_min in the future period. The GCM simulations display considerable spatial bias when compared to the observed values. The bias correction performance of the three methods for July Pr is similar. However, the IQM method shows smaller bias for July T_max compared to the other two methods, while the Delta method exhibits a larger bias for July T_min.

Figure 11 shows the CDFs for observed (Period I) and GCM-simulated (Period I and Period II) Pr, T_max, and T_min in January and July. The CDFs of the observed values differ greatly from those of the GCM-simulated values in the historical period, highlighting the inadequacy of relying solely on mean value variability. Furthermore, the CDFs of the GCM simulations for the historical and future periods exhibit notable differences, particularly in terms of mean value variation. Consequently, the IQM method is applied to correct the bias in the GCM simulation results for the future periods.

4.4. Future Climate Projections

The projected Pr, T_max, and T_min for Period II and Period III are compared with those of Period I. Subsequently, the future climate characteristics of the Huaihe River Basin are analyzed in terms of inter-annual variation, intra-year variation, and spatial distribution.

4.4.1. Inter-Annual Variation

Table 7. The future annual-scale changes in Pr, T_max, and T_min in the Huaihe River Basin.

Climate Elements	Period II				Period III
	RCP2.6	RCP4.5	RCP6.0	RCP8.5	RCP2.6	RCP4.5	RCP6.0	RCP8.5
Pr/%	7.81	17.16	6.47	11.93	13.70	28.36	6.87	21.83
Tmax/°C	1.24	1.52	1.44	1.78	3.52	4.67	4.01	6.67
Tmin/°C	1.96	1.11	1.17	1.06	1.19	2.37	2.66	3.88

presents the projected changes in annual Pr, T_max, and T_min for the Huaihe River Basin in future periods. Both Period II and Period III show an increasing trend in annual Pr (Period II: 6.47–17.16%, Period III: 6.87–28.36%). Similarly, T_max and T_min are expected to rise, with T_max showing a more pronounced increase than T_min. The upward trends in both rainfall and air temperature are more significant in Period III compared to Period II.

Under the four emission scenarios, Pr, T_max, and T_min all exhibit inter-annual variability (Figure 12). The order of increasing trends in Pr, from largest to smallest, is RCP4.5, RCP8.5, RCP2.6, and RCP6.0. For T_max, the increase follows the order of RCP8.5, RCP4.5, RCP6.0, and RCP2.6, while the T_min increases rank as RCP8.5, RCP6.0, RCP4.5, and RCP2.6. Observations from 2006 to 2020 indicate that current emissions align most closely with the RCP8.5 scenario.

4.4.2. Intra-Year Variation

Figure 13 illustrates the monthly variations in Pr, T_max, and T_min in the Huaihe River Basin for the two future periods. In Period II, Pr shows a slight decreasing trend in May, July, and from September to December under certain emission scenarios, while January, March, April, June, and August show a clear increasing trend. In Period III, Pr in July (RCP2.6 and RCP6.0) and September (RCP6.0) shows a slight decrease, while the other months display an increasing trend, with changes being more significant compared to Period II.

In the two future periods, T_max in the Huaihe River Basin shows a consistent warming trend across all months (Figure 13). In Period II, T_max increases by 0.37 °C to 2.98 °C, with more pronounced warming observed in February and October compared to the other months. In Period III, changes are even more significant, with an increase ranging from 1.30 °C to 8.47 °C, and the most notable warming occurs in October. Additionally, T_max shows a greater increase across all months under the RCP8.5 emission scenario compared to other emission scenarios.

From Figure 13, T_min also shows a consistent warming trend across all months in the future. In Period II, the change ranges from −0.08 °C to 3.00 °C, while in Period III, it ranges from 0.77 °C to 6.20 °C. For both Period II and Period III, the changes in T_min for March and November are minimal. Additionally, under the RCP8.5 emission scenario, T_min shows a more pronounced increase across all months compared to other scenarios.

4.4.3. Spatial Distribution Variation

Figure 14 and Figure 15 illustrate the spatial variation patterns of climate elements relative to the historical period under four emission scenarios across two future periods. The results indicate that changes under the RCP8.5 scenario are more significant compared to other scenarios. Furthermore, variations in Period III are more significant than those in Period II, with average increases of approximately 10% for Pr, 2 °C for T_max, and 1 °C for T_min in Period III compared to Period II.

For Pr, under the RCP2.6 and RCP4.5 scenarios, the northern part of the Huaihe River Basin experiences a more significant increase compared to the southern part. The RCP6.0 scenario shows varying spatial patterns in the two future periods, with a larger increase in Pr observed in the northeast during Period II and in the northwest during Period III. Under the RCP8.5 scenario, rainfall increases are more significant in the northwest. For T_max, the RCP2.6 scenario shows a more pronounced increase in the central basin, while RCP4.5 and RCP6.0 exhibit smaller increases in the northeast. In contrast, the RCP8.5 scenario reveals more substantial warming in the northwest and southeast regions. In Period III, the RCP2.6, RCP4.5, and RCP6.0 scenarios indicate more significant temperature increases in the northeast, while RCP8.5 shows notable warming in the southern region. For T_min, the spatial patterns of temperature changes are relatively consistent across all emission scenarios in the two future periods, with nearly the entire basin showing an increasing trend. Only the southeastern and southwestern regions exhibit less significant increases in T_min.

4.5. Discussion

Although the CMIP is currently in its sixth phase, CMIP5 remains highly precise and continues to be widely utilized in climate forecasting [42]. Different from other research [43], we proposed the CIES to assess CMIP5 GCMs. According to the results (Table 5), the HadGEM2-AO model provides the best simulation for rainfall. Previous studies have also found that the HadGEM2-AO model performs well in simulating rainfall [44]. The optimal GCMs for T_max and T_min in Huaihe River Basin are the MIROC-ESM and HadGEM2-ES models, which differs from some other studies [45]. The possible reason for this discrepancy is that the climate and hydrological characteristics of different study areas are inconsistent.

Accurate rainfall and temperature data are of prime importance for meteorological and hydrological applications [46]. Compared to other studies [47,48], we employed multiple evaluation metrics for a comprehensive assessment and proposed the CISI to evaluate the accuracy of different spatial interpolation methods. In addition, appropriate bias correction for different GCMs is essential in climate change research. Unlike previous bias correction approaches [49,50], we introduced an IQM method that addresses the inconsistencies between historical and future climate data. The IQM method significantly reduces the bias in climate variables simulated by GCMs (Table 6, Figure 11). The IQM method may also be applicable to other GCMs (i.e., CMIP6 GCMs).

Numerous studies indicate that Pr, T_max, and T_min in the Huaihe River Basin are expected to increase in the future [51,52], which aligns with our research findings. These changes may lead to more extreme flood events in the basin, particularly in the southern region (Figure 14 and Figure 15). Therefore, it is crucial to enhance the capacity for rainfall and flood forecasting and to implement strategies for mitigating greenhouse gas emissions in the basin moving forward.

5. Conclusions

This paper mainly assessed future climate change in the Huaihe River Basin. First, we proposed the CISI to identify the optimal spatial interpolation methods for climate variables. Next, we utilized Taylor diagrams and the CIES to assess the simulation performance of different GCMs. We then introduced an IQM method to correct the bias in the GCM simulation results. Finally, we analyzed future climate change in the basin. The aim of this research is to enhance the prediction of future climate change in the Huaihe River Basin.

Among the five spatial interpolation methods, the RBF demonstrates the highest effectiveness for rainfall interpolation, while OK excels in air temperature interpolation. Both interpolation methods yield high accuracy and smooth results. The results obtained using the RBF and OK methods showed that the HadGEM2-AO model provides the best simulation of Pr, the MIROC-ESM model is most effective for simulating T_max, and the HadGEM2-ES model is optimal for T_min.

The IQM method, which addresses inconsistencies between historical and future climate distributions, demonstrates superior bias correction performance compared to both the Delta and QM methods. Its evaluation metrics (R, RMSE, and CIES) significantly outperform those of the Delta and QM methods.

In the future, the Huaihe River Basin is projected to experience an increasing trend in Pr, T_max, and T_min. Notably, the upward trend in Period III is more pronounced than in Period II, with T_max showing a more significant increase than T_min. Furthermore, the rise under the RCP8.5 scenario is more substantial compared to other emission scenarios. There are significant spatial variations in Pr and T_max across different emission scenarios. In contrast, the spatial pattern of T_min changes remains relatively consistent.

6. Study Limitations and Prospects

While this paper evaluates future climate change in the Huaihe River Basin, it does not extend to assessing the impacts of climate change on hydrological processes, particularly extreme flood events. Future research will integrate GCMs with hydrological models (i.e., the SWAT model) to develop more effective flood prevention and disaster mitigation strategies for the Huaihe River Basin.