Projecting Daily Maximum Temperature Using an Enhanced Hybrid Downscaling Approach in Fujian Province, China

Abstract

The rise in global temperatures and increased extreme weather events, such as heatwaves, underscore the need for accurate regional projections of daily maximum temperature (T_max) to inform effective adaptation strategies. This study develops the CNN-BMA-QDM model, which integrates convolutional neural networks (CNNs), Bayesian model averaging (BMA), and quantile delta mapping (QDM) to downscale and project T_max under future climate scenarios. The CNN-BMA-QDM model stands out for its ability to capture nonlinear relationships between T_max and atmospheric circulation factors, reduce model uncertainty, and correct bias, thus improving simulation accuracy. The CNN-BMA-QDM model is applied to Fujian Province, China, using three CMIP6 GCMs and four shared socioeconomic pathways (SSPs) to project T_max from 2015 to 2100. The results show that CNN-BMA-QDM outperforms CNN-BMA, CNNs, and other downscaling methods (e.g., RF, BPNN, SVM, LS-SVM, and SDSM), particularly in simulating extreme value at the 99% and 95% percentiles. Projections of T_max indicate consistent warming trends across all SSP scenarios, with spatially averaged warming rates of 0.0077 °C/year for SSP126, 0.0269 °C/year for SSP245, 0.0412 °C/year for SSP370, and 0.0526 °C/year for SSP585. Coastal areas experience the most significant warming, with an increase of 4.62–5.73 °C under SSP585 by 2071–2100, while inland regions show a smaller rise of 3.64–3.67 °C. Monthly projections indicate that December sees the largest increase (5.30 °C under SSP585 by 2071–2100), while July experiences the smallest (2.40 °C). On a seasonal scale, winter experiences the highest warming, reaching 4.88 °C under SSP585, whereas summer shows a more modest rise of 3.10 °C. Notably, the greatest discrepancy in T_max rise between the south and north occurs during the summer. These findings emphasize the importance of developing tailored adaptation strategies based on spatial and seasonal variations. The results provide valuable insights for policymakers and contribute to the advancement of regional climate projection research.

1. Introduction

One prominent feature of climate change is the continuous rise in global temperatures [1]. The increase in temperature has led to longer duration, greater intensity, higher frequency, and broader coverage of extreme weather events, including heatwaves [2,3]. Such changes have profound implications for various socioeconomic and ecological sectors, particularly affecting public health [4], agricultural productivity [5], water resources [6], and energy production [7]. The Sixth Assessment Report (AR6) of the Intergovernmental Panel on Climate Change (IPCC) projects that extreme events will become increasingly frequent and severe under future climate scenarios [1]. To develop effective climate adaptation strategies and mitigate the cascading impacts of extreme heat events on society, the economy, and the ecological environment, there exists an imperative requirement for robust projections of future daily maximum temperatures (T_max).

Global climate models (GCMs) are foundational for climate change research, providing essential projections at the global scale. The latest Coupled Model Intercomparison Project Phase 6 (CMIP6) is more complex and accurate than its predecessor CMIP5, particularly through its combinations of shared socioeconomic pathways (SSPs) with representative concentration pathways (RCPs) [8,9]. Nevertheless, GCMs still face inherent limitations when applied at the local scale due to their coarse spatial resolution [10]. To bridge this scale mismatch, downscaling techniques that employ low-resolution GCM output data for high-resolution climate predictions have emerged as indispensable tools. Current downscaling techniques can generally be bifurcated into dynamical downscaling (DD) and statistical downscaling (SD). DD leverages regional climate or numerical weather prediction systems to simulate physical processes within coupled land, atmosphere, and ocean systems to provide high-resolution climate factors [11,12]. While physically consistent, DD demands intensive computational resources, limiting its application to only a few GCMs [13,14]. SD establishes statistical relationships between large-scale predictors and local-scale predictands and applies these relationships to future data to obtain local variables [15]. Owing to computational tractability, operational accessibility, and non-inferior performance, SD has gained broader implementation across diverse regions [16,17,18].

Over the past few decades, SD techniques have seen significant advancements, evolving from stochastic weather generators [19], simple weather-type methods [20], multivariate linear regression (MLR) [21], and statistical downscaling models (SDSMs) [22] to advanced machine learning techniques encompassing artificial neural networks (ANNs) [23], support vector machines (SVMs) [24], and random forests (RFs) [25]. These techniques have demonstrated proficiency in downscaling average temperature and general precipitation. However, persistent challenges remain in capturing fine-scale spatiotemporal variability of localized climate signals, especially in robustly representing extreme events like extreme heat and heavy precipitation [26,27]. In recent years, with the improvement of computational power and the development of big data technologies, deep learning, as a significant branch of machine learning, has emerged as a transformative tool for climate downscaling [28,29]. In particular, convolutional neural networks (CNNs) rely on their multi-layered structure and automatic feature extraction capabilities, enabling them to process and analyze high-dimensional spatial climate data. For instance, Rampal et al. [30] demonstrated that CNNs exhibited superior performance over an MLR model in extreme precipitation characterization, demonstrating a 25% reduction in 90th percentile rainfall biases. Sun et al. [31] assessed the performance of CNNs for downscaling CMIP6 monthly precipitation over China, concluding that CNNs significantly outperformed MLR and RFs with the highest of comprehensive rating metric 0.96. Asfaw and Luo [32] employed a CNN-based downscaling framework for East Africa’s seasonal precipitation forecasts, showing a 42% reduction in extreme index biases. Overall, CNNs demonstrate good generalization ability, enabling them to better capture nonlinear relationships and dynamic changes in the climate system under different climate conditions. This is particularly important for addressing the non-stationarity and extreme events brought about by climate change.

Although downscaling techniques improve simulation fidelity, overreliance on individual GCM outputs introduces significant uncertainty due to structural disparities among GCMs in their physical processes, model structures, and initial conditions [33,34]. Multi-model ensemble (MME) is an effective technique to mitigate these uncertainties through the integration of multi-source model information. Contemporary MME approaches include simple model averaging (SMA) and Bayesian model averaging (BMA) [35,36]. SMA typically combines multi-model data by calculating arithmetic means, which neglects inter-model skill heterogeneity and amplifies the risk of extreme value biases [37]. In contrast, BMA is derived as a convex combination of individual model probability density functions (PDFs) weighted by their posterior probabilities [38]. These weights are determined through Bayesian evidence approximation, reflecting each model’s relative contribution in replicating historical observations. Empirical analyses show that BMA is more effective at simulating extreme values because it preserves the tail behavior of each individual model, while SMA tends to diminish these extreme signals [39,40,41]. Building on these findings, a CNN-BMA hybrid framework represents a novel attempt to further enhance the performance of multi-GCM ensemble downscaling.

In fact, extreme value simulation remains a significant challenge for downscaling techniques, particularly for T_max and precipitation extremes [42,43]. Effective postprocessing is crucial to align simulated extremes with observed climate conditions. For instance, Fulton et al. [44] combined unsupervised image-to-image translation (UNIT) neural network architecture with QM for multivariate bias correction, showing that the UNIT-QM model outperformed either approach alone in reproducing extreme values. Li et al. [45] integrated SDSMs with BMA, followed by quantile mapping (QM) bias correction, enhancing the accuracy of GCM outputs for both precipitation and temperature. Taie Semiromi and Koch [46] integrated discrete wavelet transform (DWT), ANNs, and QM for downscaling daily precipitation, which demonstrated the DWT-ANN-QM approach performed better with higher extreme precipitation skill scores. In general, QM effectively corrects distributional moments (mean and variance) and extremal quantiles by aligning historical model–observation statistical relationships. However, its assumption of stationarity poses a risk of artificially dampening climate change signals under non-stationary warming trends [47,48]. Quantile delta mapping (QDM), an advancement upon QM, can account for changes in the cumulative distribution functions (CDFs) over different time periods, thereby more effectively mitigating extreme bias in climate model outputs [49,50]. Although QDM shows advantages in extreme value correction, to the best of our knowledge, no existing study has yet coupled QDM with CNN-BMA for T_max downscaling.

Therefore, the innovation of this study lies in the development of an integrated CNN-BMA-QDM model for downscaling T_max. The CNN-BMA-QDM model can address challenges associated with coarse resolution, uncertainty, and non-stationary extremal bias in GCM outputs. For the first time, CNN-BMA-QDM will be applied in Fujian Province, China, to assess its capability in downscaling T_max. Additionally, future changes in T_max will be projected using multiple CMIP6 GCMs (e.g., CanESM5, MPI-ESM1-2-HR, and NorESM2-MM) and four representative concentration pathways (SSP126, SSP245, SSP370, and SSP585). The results will not only enhance the downscaling accuracy of GCM outputs but also provide a reliable technical tool for future climate predictions and regional studies on the impacts of extreme climate events.

2. Methods

As shown in Figure 1, this study presents the CNN-BMA-QDM model, which integrates convolutional neural networks (CNNs), Bayesian model averaging (BMA), and quantile delta mapping (QDM). The model consists of three main steps: (i) data collection and factor selection, (ii) construction of the CNN-BMA-QDM model, and (iii) future T_max projection. In the first step, five atmospheric circulation factors are selected based on the Pearson correlation coefficient, using observed data from 18 meteorological stations and outputs from three GCMs. A CNN is then applied to model the relationship between the selected atmospheric circulation factors and the observed T_max. To evaluate the performance of the CNN model, five additional SDs are applied for comparison, including SDSM, RF, SVM, least squares support vector machine (LS-SVM), and backpropagation neural networks (BPNNs). For model integration, the BMA method is employed, followed by bias correction using the QDM method. Finally, atmospheric circulation factors from the three GCMs under four SSPs for the period 2015–2100 are used to project future T_max in Fujian Province.

2.1. Statistical Downscaling Model

2.1.1. CNN

Convolutional neural networks (CNNs) are a deep-learning model widely used in time series prediction and data pattern recognition. They comprise convolutional layers, pooling layers, flatten layers, fully connected layers, and dropout layers. By stacking multiple convolutional and pooling layers, CNNs can automatically extract local features from input data and learn complex nonlinear relationships, enabling them to establish a relationship between T_max and atmospheric circulation factors [51]. Furthermore, CNNs’ end-to-end learning capability ensures a seamless connection from data input to prediction output, eliminating the need for manual feature engineering typically required in traditional methods [52].

In this study, a CNN is developed in R using the Keras framework to establish nonlinear relationships between synoptic-scale atmospheric circulation patterns and localized T_max. The architecture comprises three sequential convolutional layers with 512 filters per layer, utilizing kernel sizes of 3 × 3, 2 × 2, and 1 × 1 to progressively extract spatial features across varying scales. A max pooling layer with a 2 × 2 window follows the first convolutional layer. After the convolutional and pooling layers, the data are reshaped by a flattening layer for the fully connected layers. The network has two fully connected layers with 1024 and 512 neurons, respectively. Dropout layers, with a rate of 20%, are added after each fully connected layer to reduce overfitting. The final output layer uses a single linear neuron to generate temperature predictions. The CNN is compiled using the mean squared error loss function, and the Adam optimizer is used with an initial learning rate of 0.0001. The network is trained for 2500 epochs with a batch size of 512.

2.1.2. SDSM

SDSMs are a widely used decision support tool in climate research for converting large-scale climate model outputs into specific regional climate projections. The core of an SDSM involves establishing statistical relationships between large-scale predictive factors and small-scale climate variables using multiple linear regression analysis [53]. The main SDSM equation is shown in Equation (1):

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\dots +{\beta }_n{X}_n+\epsilon$$

(1)

where Y represents the meteorological variables observed at stations, {X₁, X₂, …, X_n} represents atmospheric circulation factors, {β₁, β₂, …, β_n} is the regression coefficients, and ε is the error term. This study employs SDSM Version 4.2 to conduct climate scenario projection [54].

2.1.3. RF

RF is a powerful ensemble learning algorithm primarily used for classification and regression tasks. It excels in climate change prediction due to its ability to handle high-dimensional data and complex nonlinear relationships [55]. The structural framework of an RF comprises multiple decision trees (DTs) operating in parallel. In regression applications, each DT generates predictive values by analyzing feature subspaces. The final output is obtained by aggregating the predictions of all trees using an arithmetic mean ensemble strategy and expressed as [56]:

$$\overline{y}(x)={\displaystyle \frac{1}{T}}{\displaystyle {\sum }_{t=1}^T\frac{1}{\left|S_t(x)\right|}}{\displaystyle {\sum }_{i\in S_t(x)}{y}_i}$$

(2)

where T denotes the total number of decision trees in the forest, y_i is the true target value of the training sample, S_t(x) represents the set of training sample associated with the leaf node where instance x resides in the t-th decision tree, and $\left|S_t(x)\right|$ indicates the cardinality of the leaf node’s training sample subset. In this study, RF is implemented through the scikit-learn machine learning framework in Python 3.12.0. Critical hyperparameters employ an ensemble of 200 constituent decision trees, with architectural constraints including a maximum tree depth of 10 layers. Regularization thresholds are configured with minimum requirements of 10 samples for node splitting and 1 sample per leaf node to ensure model generalizability while preserving structural flexibility.

2.1.4. SVM

SVMs are a supervised learning model based on structural risk minimization [57]. By employing kernel functions to implicitly map low-dimensional input data into higher-dimensional Hilbert spaces, SVMs achieve linear separability of intrinsically nonlinear relationships. During the regression process, the objective function incorporates an ε-insensitive loss to maintain a critical balance between model simplicity and empirical risk minimization [58]. The mathematical formulation is given by:

$$\begin{array}{l}\hspace{0.33em}\underset{\omega ,b,\xi ,{\xi }^{\ast }}{\min }\hspace{0.33em}{\displaystyle \frac{1}{2}}{‖\omega ‖}^2+C{\displaystyle \sum _{i=1}^n\left({\xi }_i+{\xi }_i^{\ast }\right)}\\ s.t.\hspace{1em}{y}_i-〈\omega ,\varnothing (x_i)〉-b\le \epsilon +{\xi }_i;\hspace{0.33em}〈\omega ,\varnothing (x_i)〉+b-y_i\le \epsilon +{\xi }_i^{*};\hspace{0.33em}{\xi }_i,{\xi }_i^{*}\ge 0\end{array}$$

(3)

where $\varnothing (x)$ denotes the kernel-induced feature mapping, $\epsilon$ defines the insensitivity zone, and C regulates the trade-off between model complexity and training errors quantified by slack variables ${\xi }_i$ and ${\xi }_i^{*}$. In this study, an SVM model with the Radial Basis Function kernel is selected to capture nonlinear relationships between predictors and the T_max. Through a grid search combined with 5-fold cross-validation on the training dataset, the final hyperparameter C is set to 1.0.

2.1.5. LS-SVM

LS-SVM is an improved version of the SVM that solves regression problems by reformulating quadratic programming into a system of linear equations. In LS-SVM, the optimization problem is rewritten as Equation (4) [59]:

$$\begin{array}{l}\hspace{0.33em}\underset{\omega ,b,e}{\min }\hspace{0.33em}{\displaystyle \frac{1}{2}}{‖\omega ‖}^2+{\displaystyle \frac{C}{2}}{\displaystyle \sum _{i=1}^n{e}_i^2}\\ s.t.\hspace{1em}{y}_i=〈\omega ,\varnothing (x_i)〉+b+e_i\hspace{1em}\forall i\end{array}$$

(4)

where e is the prediction error of the i-th sample. Compared to an SVM, LS-SVM demonstrates fundamental improvements in reducing computational complexity through linear system reformation, enhancing numerical stability via elimination of inequality constraints, and simplifying hyperparameter tuning with the removal of ε-sensitive loss parameterization.

2.1.6. BPNN

BPNNs are multi-layer feedforward neural networks that adjust weights through an error backpropagation algorithm to solve regression problems [60]. BPNNs model nonlinear relationships between inputs and outputs by minimizing the error between predicted and observed values using training data. The core of BPNNs lies in the iterative process of forward propagation to compute predictions and backpropagation to update weights. For regression tasks, the output layer typically uses a linear activation function to output the weighted sum, and the formula for predicted value is as follows [61]:

$$\overline{y}=f^{\left[L\right]}\left({\omega }^{\left[L\right]}\times f^{\left[L-1\right]}\times \left(\dots f^{\left[1\right]}\left({\omega }^{\left[1\right]}X+b^{\left[1\right]}\right)\dots \right)+b^{\left[L\right]}\right)$$

(5)

where f^[L] is the activation function for the L-th layer, and ${\omega }^{\left[L\right]}$ and b^[L] are the weight matrix and bias vector, respectively. Based on the hidden layer activation functions, BPNNs can effectively capture the complex nonlinear interactions that may exist among variables in climate data.

2.2. BMA

BMA is a multi-model ensemble method that reduces uncertainty and improves prediction accuracy by weighting the predictions of multiple models. The core concept of BMA is to compute the posterior probability of each model using Bayesian inference and use these probabilities as weights to generate the ensembled prediction [62]. For a set of competing models {M₁, M₂, …, M_K}, BMA considers the posterior probability P(M_k|D) of each model. This probability is determined by the model’s prior probability P(M_k) and the marginal likelihood of the data given the model P(D|M_k). It is as shown in Equation (6) [63]:

$$P(\left.M_k\right|D)={\displaystyle \frac{P(\left.D\right|M_k)P(M_k)}{P(D)}}$$

(6)

where P(D) is the normalization constant, ensuring that the sum of the posterior probabilities of all models equals 1. The calculation formula for P(D) is as shown in Equation (7):

$$P(D)={\displaystyle \sum _{k=1}^{K}P(\left.D\right|M_k)P(M_k)}$$

(7)

Marginal likelihood can be computed by integrating the likelihood of the model parameters with the prior distribution of the parameters, which is shown in Equation (8):

$$P(\left.D\right|M_k)={\displaystyle \int P(\left.D\right|{\theta }_k,M_k)}P(\left.{\theta }_k\right|M_k)d{\theta }_k$$

(8)

where θ_k refers to the parameters of model M_k, which control the behavior and structure of the model; $P\left(D\left|{\theta }_k,M_k\right.\right)$ is the likelihood function, which measures how well the model with parameters θ_k fits the observed data D, reflecting the probability of observing D given θ_k and M_k; and $P\left({\theta }_k\left|M_k\right.\right)$ is the prior distribution of the parameters θ_k representing our prior knowledge or assumptions about the parameters before observing the data.

Assuming that the predictions of the models {M₁, M₂, …, M_K} are {y₁, y₂, …, y_K}, the output ensembled prediction Y from the BMA method can be expressed as:

$$Y={\displaystyle \sum _{k=1}^{K}P\left(\left.M_k\right|D\right)}{y}_k$$

(9)

In this study, a BMA framework based on the expectation–maximization (EM) algorithm is designed and implemented in Python for parameter optimization. During model initialization, all sub-models are assigned equal weights, while the global standard deviation is derived from observational data. The iterative optimization process maximizes the log-likelihood function, updating both component weights and sub-model-specific standard deviations [64]. Parameter estimation is performed using the minimize function from the Scipy library, which enforces parameter constraints via the L-BFGS-B algorithm [65]. The final optimized weights quantify the relative explanatory contributions of individual sub-models to the observational data, with standard deviations characterizing their associated uncertainties. The final weights assigned to the three GCM models (CanESM5, MPI-ESM1-2-HR, and NorESM2-MM) for each meteorological station in the study area were calculated based on historical observations. These weights were estimated using the maximum likelihood approach described above and reflect the relative performance of each GCM in reproducing observed daily maximum temperatures. Detailed values of the BMA weights are provided in Table S1 of the Supporting Materials.

2.3. QDM

QDM is a widely applied non-parametric bias correction technique for climate model outputs. The method first quantifies the differences between model simulations and observations at matching quantiles during a historical period, then adjusts future projections by mapping their quantiles to the observed distribution while preserving the model’s simulated climate change signal [66]. QDM can address key limitations of conventional quantile mapping by not only retaining the relative climate change trends projected in future scenarios but also improving the calibration of extreme values in upper quantiles [67]. In this study, QDM is employed to reduce systematic distributional biases in the T_max outputs generated by CNN-BMA. Importantly, this approach ensures that the absolute climate change signals from GCM projections remain intact throughout the bias correction process. The primary step in the bias correction process is to determine the delta of projection relative to historical simulation at the same quantile, written as [68]:

$$\Delta T(t)=T_{m,p}(t)-F_{m,h}^{-1}\left[F_{m,p}^{(t)}\left(T_{m,p}(t)\right)\right]$$

(10)

where T_m,p(t) is the projected maximum temperature series at time point t, $F_{m,p}^{(t)}$ is the cumulative distribution function (CDF) for the T_m,p(t), and $F_{m,h}^{-1}$ refers to the inverse CDF of the simulated historical data. The final corrected data for projected T_max will be calculated as:

$$T_{m,p}^c(t)=\Delta T(t)+F_{m,o}^{-1}\left[F_{m,p}^{(t)}\left(T_{m,p}(t)\right)\right]$$

(11)

where $F_{m,o}^{-1}$ is the inverse CDF of the historical observation data, and $T_{m,p}^c(t)$ is the projected corrected value. To minimize the additional error inherent in parametric CDF fitting, the empirical CDF is adopted for QDM, thereby avoiding assumptions associated with theoretical distributions.

2.4. Performance Evaluation Metrics

To comprehensively assess the performances of the CNN-BMA-QDM and other comparative models, several statistical metrics are selected, including correlation coefficient (CC), root mean square error (RMSE), standard deviation (STD), and quantile difference (QD), which are defined as follows [69,70]:

$$CC={\displaystyle \frac{{\displaystyle \sum _{i=1}^N(T_{sim,i}-\overline{T_{sim}})(T_{ob,i}-\overline{T_{ob}})}}{\sqrt{{\displaystyle \sum _{i=1}^N{(T_{sim,i}-\overline{T_{sim}})}^2\times {\displaystyle \sum _{i=1}^N{(T_{ob,i}-\overline{T_{ob}})}^2}}}}}$$

(12)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{\left(T_{sim,i}-T_{ob,i}\right)}^2}}$$

(13)

$$STD=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\left(T_i-\left(\frac{1}{N}{\displaystyle \sum _{i=1}^N{T}_i}\right)\right)}}$$

(14)

$$Q{D}_{99\%\hspace{0.33em}or\hspace{0.33em}95\%}=T_{sim}^{99\%\hspace{0.33em}or\hspace{0.33em}95\%}-T_{obs}^{99\%\hspace{0.33em}or\hspace{0.33em}95\%}$$

(15)

where T_i represents the ith observed or simulated value, T_sim,i and T_ob,i are the ith simulated and observed values, $\overline{T_{ob}}$ and $\overline{T_{sim}}$ indicate the average of all observed and simulated values, $Q{D}_{99\%\hspace{0.33em}or\hspace{0.33em}95\%}$ is the 99% or 95% quantile difference between the simulated and observed values, $T_{sim}^{99\%\hspace{0.33em}or\hspace{0.33em}95\%}$ is the simulated value in the 99% or 95% quantile, $T_{obs}^{99\%\hspace{0.33em}or\hspace{0.33em}95\%}$ is the observed value in the 99% or 95% quantile, and N is the total number of data points.

3. Study Area and Data

3.1. Study Area

As shown in Figure 2, Fujian Province, located along the southeast coast of China (from 115°50′ E to 120°43′ E and 23°31′ N to 28°18′ N), is an important economic and cultural center. According to the Statistical Communiqué of Fujian Province on National Economic and Social Development in 2024, Fujian Province covered an area of approximately 124,000 square kilometers and had a resident population of 41.93 million by the end of 2024. In 2024, the gross domestic product (GDP) reached CNY 5776.10 billion, representing a year-on-year growth of 5.5% [71]. The landscape is predominantly mountainous, with the northwest region being higher in elevation and the southeast being lower. Roughly 90% of the province consists of mountains and hills. The province has a subtropical monsoon climate, with significant regional variations. Average annual temperatures range from 17 °C to 22 °C, with warmer winters and hot summers. Annual precipitation varies from 1400 to 2000 mm, decreasing from the southeast to the northwest. Fujian’s forest coverage rate stands at 65.12%, maintaining the highest level in the country for 45 consecutive years. As the first national ecological civilization pilot zone in China, the province has prioritized green development and serves as a model for ecological sustainability.

From 1961 to 2024, Fujian has experienced significant shifts in climate, largely due to global warming. Since 2000, the frequency of high-temperature days has increased, with notable rises in extreme maximum temperatures. Records of high-temperature events are frequently broken, highlighting the growing intensity of these events [72,73]. Economic and population growth have been concentrated in the central and southern coastal regions of Fujian, which are particularly vulnerable to the impacts of climate change. These urban areas have seen rapid development, leading to an intensification of the urban heat island effect and a rise in discomfort for residents. Rising temperatures could also worsen socioeconomic challenges, particularly in agriculture, water resources, and energy demand. Additionally, the region faces risks from high-temperature disasters, which could have detrimental effects on biodiversity and forestry. Given these climate trends and the region’s vulnerabilities, projecting T_max in Fujian is crucial for developing early warning systems, improving disaster preparedness, and formulating effective adaptation strategies.

3.2. Data Sources and Preprocessing

To establish a statistical downscaling model, both predictors (atmospheric circulation factors from GCM dataset) and the predictand (T_max) are desired. T_max data from 18 meteorological stations from 1982 to 2014 are collected from the National Meteorological Information Center (NMIC, http://data.cma.cn, accessed on 5 November 2022). The details of the stations are listed in

Table 1. The details of 18 selected stations.

Station	Longitude (°E)	Latitude (°N)	Altitude (0.1 m)
S1	117.28	27.20	1915
S2	118.02	27.46	2206
S3	118.32	27.55	2769
S4	118.07	27.20	1811
S5	118.19	27.03	1549
S6	119.25	27.32	8294
S7	120.12	27.20	362
S8	116.38	26.14	3589
S9	117.10	26.54	3429
S10	118.10	26.39	1256
S11	120.00	26.53	122
S12	119.17	26.05	838
S13	116.22	25.51	3100
S14	117.01	25.06	3423
S15	118.59	26.55	8695
S16	118.42	25.22	777
S17	119.47	25.31	324
S18	117.30	23.47	533

. A total of 26 atmospheric circulation factors are selected from three CMIP6 GCMs, including CanESM5, MPI-ESM1-2-HR, and NorESM2-MM, from the Canadian Climate Data and Scenarios (CCDS) platform (https://climate-scenarios.canada.ca/, accessed on 5 November 2022) over the period 1982–2100. The selection of these three GCMs is guided by the characteristics of the CCDS dataset, which provides high-quality, bias-corrected, and spatially interpolated outputs with consistent grid systems. Moreover, the dataset offers a comprehensive set of atmospheric predictor variables across multiple pressure levels at daily temporal resolution, facilitating the construction of statistically robust downscaling models. These advantages ensure the reliability, consistency, and accessibility of the data. The information on GCMs is shown in

Table 2. Information on the three GCMs.

No.	GCMs	Resolution	Institutions
1	CanESM5	2.767 3° × 2.812 5°	Canadian Centre for Climate Modelling and Analysis (Canada)
2	MPI-ESM1.2-HR	1.865° × 1.875°	Max Planck Institutefor Meteorology (Germany)
3	NorESM2-MM	0.942° × 1.25°	Norwegian Climate Centre (Norway)

, and the predictors are shown in

Table 3. Candidate 26 atmospheric circulation factors.

No.	Variable ID	Predictor Variable
1	mslp	Mean sea level pressure
2	p1_f	1000 hPa wind speed
3	p1_u	1000 hPa Zonal wind component
4	p1_v	1000 hPa meridional wind component
5	p1_z	1000 hPa relative vorticity of true wind
6	p1th	1000 hPa wind direction
7	p1zh	1000 hPa divergence of true wind
8	p5_f	500 hPa wind speed
9	p5_u	500 hPa zonal wind component
10	p5_v	500 hPa meridional wind component
11	p5_z	500 hPa relative vorticity of true wind
12	p5th	500 hPa wind direction
13	p5zh	500 hPa divergence of true wind
14	p8_f	850 hPa wind speed
15	p8_u	850 hPa zonal wind component
16	p8_v	850 hPa meridional wind component
17	p8_z	850 hPa relative vorticity of true wind
18	p8th	850 hPa wind direction
19	p8zh	850 hPa divergence of true wind
20	p500	500 hPa geopotential
21	p850	850 hPa geopotential
22	prcp	Total precipitation
23	s500	500 hPa specific humidity
24	s850	850 hPa specific humidity
25	shum	1000 hPa specific humidity
26	temp	Air temperature at 2 m

. To standardize the GCM outputs, a bilinear interpolation scheme is applied to remap all GCM outputs onto a uniform 2.8125° × 2.8125° latitude–longitude grid system.

To capture localized circulation influences on station-scale T_max, a nine-grid neighborhood (3 × 3 grid cells) centered on each station is defined for capturing localized circulation influences on station-scale T_max. For each station–GCM combination, the predictor pool comprised 234 candidate variables (26 variables × 9 grids). For each station–GCM pair, predictors are ranked by their coefficient of determination (R²) against T_max over 1982–2014, which is visualized in Figure 3 through heatmaps. The top five predictors from each GCM are retained, provided they exhibited consistent physical linkages to T_max.

After selecting the predictors for each station–GCM pair, the statistical downscaling model underwent a structured training process. To ensure reliability, the observational and GCM datasets for 1982–2014 were randomly divided into two subsets: a calibration subset (70% of the data) and a validation subset (30% of the data). This randomized partitioning helps mitigate temporal bias and tests the model’s generalizability under stochastic sampling conditions. Future T_max projections are generated using the three selected GCMs under four SSPs. The projection period spans from 2015 to 2100, with input data derived from GCM-projected atmospheric circulation variables corresponding to each SSP scenario.

4. Results

4.1. The Performance of CNN-BMA-QDM

The Taylor diagram assesses model performance based on CC, STD, and RMSE. The closer a model’s point is to the T_max-obs point, the better its performance. As shown in Figure 4, models driven by identical GCM outputs in specific station display a consistent performance ranking: CNN-BMA-QDM > CNN-BMA > CNN > RF > BPNN > SVM > LS-SVM > SDSM. For example, at station S4, CNN-BMA-QDM achieves a CC of 0.96 and an RMSE of 2.44, outperforming CNN-BMA (CC of 0.96, RMSE of 2.46), CNN (CC of 0.94, RMSE of 2.95), RF (CC of 0.82, RMSE of 9.75), and other individual machine learning models under CanESM5 forcing. This hierarchy highlights the improvements from the baseline CNN model, enhanced by BMA and QDM.

Despite the overall strong performance, the CNN-BMA-QDM framework exhibits some spatial variation in predictive accuracy across the 18 stations. At station S7, it achieves optimal performance with a CC of 0.96 and an RMSE of 2.34, while station S16 shows the least effective performance with a CC of 0.90 and an RMSE of 3.07. In general, models for stations at lower elevations (DEM < 300 m) tend to have better simulation accuracy than those at higher altitudes. The spatial variation in performance may stem from the complex topography of high-altitude stations, which large-scale circulation factors in GCMs fail to represent effectively. The numerical values of all performance evaluation metrics have been organized into tables for each station and are provided in the Supporting Materials (Tables S2–S19).

To systematically evaluate the ability of models to simulate extreme values, the quantile difference (QD) between the simulated and observed T_max in 99% and 95% percentiles are quantified across 18 meteorological stations. As shown in Figure 5, CNN-CanESM5 displays significant systematic biases in extreme values, with the mean absolute QD reaching 2.03 °C at the 99% percentile and 1.90 °C at the 95% percentile. In comparison, CNN-BMA shows notable improvements, reducing the mean absolute QD to 1.61 °C at the 99% percentile and 1.36 °C at the 95% percentile. These improvements are due to the optimal weighting of ensemble members by BMA. Further enhancement occurs with the integration of QDM into CNN-BMA. The CNN-BMA-QDM framework achieves unprecedented accuracy, with the mean absolute QD dropping to nearly 0.001 °C at both the 99% and 95% percentiles. Spatially, CNN-BMA-QDM performs exceptionally well in areas with significant climate variability, especially at high-elevation stations where conventional models exhibit consistent biases. For example, at station S16, the mean absolute QD decreases from 4.93 °C (CNN-CanESM5) and 4.25 °C (CNN-BMA) to nearly 0.001 °C (CNN-BMA-QDM) at the 99% percentile. Overall, the CNN-BMA-QDM framework demonstrates clear superiority in simulating extreme values at both the 99% and 95% percentiles, consistently showing lower QD compared to both CNN-GCM and CNN-BMA. This improved performance underscores its exceptional capability in predicting extreme events.

After evaluating the ability of CNN-BMA-QDM to simulate T_max extremes, its performance in capturing the overall temperature distribution is further examined. Figure 6 presents the boxplots of simulated monthly T_max for 18 stations, comparing observed values with those from CNN-BMA and CNN-BMA-QDM. These boxplots clearly illustrate the temporal distribution characteristics, showing how well the models capture the overall temperature distribution (mean, median, interquartile range (IQR), and outlier distribution) and T_max fluctuations. The results reveal that CNN-BMA exhibits significant discrepancies, with overestimations in December, January, and February, and underestimations in June, July, and August. These biases highlight systematic errors in the CNN-BMA model, especially during periods of extreme temperature variation. Additionally, CNN-BMA tends to underestimate temperature variability, as evidenced by its narrower IQR and fewer outliers. This indicates that CNN-BMA is less sensitive to temperature fluctuations and struggles to capture the natural variability of temperature. In contrast, CNN-BMA-QDM shows substantial improvements. For instance, in peak months like July and January, QDM reduces CNN-BMA’s median bias from 1.63 °C and 1.31 °C to 0.01 °C and 0.17 °C, respectively. The alignment of the IQR with observed values improves by 99.67%, particularly in summer months, where accurate modeling of temperature fluctuations is crucial for heatwave predictions. Additionally, the distribution of outliers significantly decreases after QDM calibration, demonstrating that QDM reduces deviations of extreme values, resulting in a more stable model for simulating extreme temperature events. These improvements collectively indicate that QDM significantly enhances the model’s accuracy in capturing extreme temperature events and seasonal variations, reducing biases and increasing sensitivity to temperature fluctuations. This makes the model a reliable reference for future climate change simulations and early warning systems for extreme weather events, showing considerable potential for practical applications in climate modeling and extreme weather projections.

4.2. Spatiotemporal Evolution of Projected T_max

Building upon the calibrated CNN-BMA-QDM model, T_max for 18 stations from 2015 to 2100 is projected under different SSPs. Figure 7 illustrates the annual T_max change trends, with Sen’s slope and the Mann–Kendall (M-K) trend test used to quantify and assess the significance of these changes. The Sen’s slope indicates a consistent warming trend in T_max across 18 stations, with spatially averaged rates of 0.0077 °C/year (SSP126), 0.0269 °C/year (SSP245), 0.0412 °C/year (SSP370), and 0.0526 °C/year (SSP585). The M-K test confirms statistically significant trends (p < 0.05) in all simulations across every SSP, underscoring that the warming observed is robust and not due to random variability. The warming rates vary significantly across the different SSP scenarios, with SSP585 showing the sharpest increase in T_max, while SSP126 reflects a more moderate trend. This disparity highlights the crucial role that emission policies play in influencing future extreme temperature outcomes. In addition, spatial heterogeneity in warming trends is evident across the 18 stations. For instance, under SSP585, station S11 experiences a faster warming rate (0.0751 °C/year) compared to S12 (0.0419 °C/year). These spatial differences likely result from a combination of factors such as elevation gradients, urban heat island effects, and oceanic influences. The findings suggest that regional climate adaptation strategies should consider local geographical and socio-economic factors, as these can significantly influence climate vulnerability and response to future warming.

Figure 8 presents a comprehensive comparison of projected monthly and seasonal T_max changes relative to the observational baseline (1980–2014) across four SSP scenarios, spanning three time periods: 2015–2040 (near term), 2041–2070 (mid-term), and 2071–2100 (long term). All months and seasons show a consistent warming signal across all SSP scenarios and future timeframes. The magnitude of this warming increases with greater radiative forcing (SSP126 < SSP245 < SSP370 < SSP585) and becomes more pronounced over longer periods. For instance, under SSP585 in the near term, the median monthly T_max change is 1.04 °C, which is greater than the value of 0.99 °C under SSP126 for the same period. This warming trend becomes more pronounced in the mid- and long term, with T_max increases rising from 2.42 °C in the mid-term to 4.06 °C in the long term. This trend highlights the cumulative effect of greenhouse gas accumulation over time.

The analysis also reveals significant variation in T_max changes across months and seasons. December experiences the largest temperature change, with SSP585 predicting an average rise of 5.30 °C in the long term, while July shows the smallest increase at 2.40 °C. Seasonally, winter (December–January–February, abbreviated DJF) exhibits the greatest warming, with a rise of 4.88 °C under SSP585 in the long term, while summer (June–July–August, abbreviated JJA) shows a smaller increase of 3.10 °C. This pattern may be explained by the lower initial temperatures in winter, where the same greenhouse effect leads to a larger absolute warming.

Figure 9 provides a systematic evaluation of the spatial distribution of interannual Tmax variation relative to the baseline period. The results reveal a clear east–west and south–north gradient in projected warming. Coastal regions experience the highest warming, ranging from 4.62 °C to 5.73 °C under SSP585 in the long term, while inland areas show more modest increases of 3.64 °C to 3.67 °C, resulting in a regional temperature difference of 0.95 °C to 2.19 °C. Spatial heterogeneity in warming intensifies with both the severity of emissions and the time horizon. Under SSP585, the coastal–inland temperature difference grows from 0.59 °C in the near term to 2.19 °C in the long term, while SSP126 shows a more stable difference of 0.30 °C to 0.35 °C. Over time, warming disparities between regions increase progressively. For instance, under SSP370, coastal warming rises from 1.17 °C in the near term to 3.34 °C in the long term, while inland warming increases from 0.58 °C to 2.13 °C, expanding the spatial difference from 0.59 °C to 1.21 °C. This trend reflects the cumulative impact of greenhouse gas emissions, which leads to growing temperature disparities between regions as time progresses. These findings offer valuable guidance for climate resilience planning. Policymakers should focus on urban heat mitigation strategies (e.g., green infrastructure and reflective surfaces) in high-emission coastal cities, while inland regions should prioritize strengthening ecological conservation to preserve the cooling capacity of forests.

Figure 10 illustrates the spatiotemporal evolution of seasonal T_max anomalies relative to the 1980–2014 baseline across Fujian Province under four SSP scenarios and three time periods. The results show that T_max anomalies in spring (March–April–May, abbreviated as MAM), autumn (September–October–November, abbreviated as SON), and winter (DJF) are relatively uniform across the province. In contrast, summer (June–July–August, abbreviated as JJA) exhibits the most significant south–north temperature disparity, especially under high-emission scenarios such as SSP585. For instance, under the SSP126 scenario in the long-term period, the T_max anomaly differences between the southern and northern regions in spring, autumn, and winter are 0.27 °C, 0.13 °C, and −0.37 °C, respectively, while in summer, the difference is 1.19 °C. Under the SSP585 scenario, these values increase to 0.75 °C, 0.49 °C, and −0.29 °C in spring, autumn, and winter, respectively, with the summer difference rising to 1.43 °C. This variation can be attributed to several factors, including the intensification of the urban heat island effect in densely populated southern cities, reduced oceanic thermal buffering under high emissions, and the persistent cooling effect of forest cover in the northern regions. These findings underscore the critical importance of emission mitigation strategies, particularly for southern and coastal regions where warming is most pronounced, and highlight the necessity of urgent action to reduce emissions to avert severe climate impacts in the coming decades.

5. Discussion

This study presents the development and application of an innovative climate downscaling framework, CNN-BMA-QDM, for downscaling and projecting T_max from three GCMs across 18 meteorological stations in Fujian Province, China. The evaluation of simulation performance reveals that CNN-BMA-QDM outperforms traditional methods, including CNNs, CNN-BMA, and other downscaling techniques such as ANNs, SDSMs, SVMs, LSSVM, and RF (Figure 4). Notably, it excels in representing extreme values (99% and 95% percentiles) and capturing seasonal trends, as demonstrated by various statistical metrics (Figure 5 and Figure 6).

The enhanced performance of CNN-BMA-QDM is primarily attributed to its multi-layer architecture. Unlike traditional methods that require manual feature selection and often struggle with complex patterns, CNNs automatically extract features at multiple levels, effectively capturing intricate spatial–temporal relationships while managing high-dimensional, nonlinear data. By combining multiple GCM models, BMA reduces the bias of individual models through weighted averaging, which strengthens overall prediction robustness, particularly in diverse climate scenarios. In extreme value predictions, BMA addresses model discrepancies, leading to more accurate simulations of extreme temperature events. As a postprocessing tool, QDM preserves the climate change signals derived from the GCMs while adjusting the distribution tails, ensuring both bias correction in extreme temperature regimes and trend fidelity maintenance.

Despite these improvements, the performance of CNN-BMA-QDM varies spatially. Coastal stations show a 25% improvement in prediction accuracy due to better simulations of sea–land wind interactions, while high-altitude regions exhibit a 15% higher error in extreme temperature predictions. This variation highlights the limitations of data-driven approaches. Future improvements could include incorporating physical loss functions to ensure better physical consistency, manage non-stationarity in climate systems, and enhance the accuracy of extreme event predictions, particularly in complex terrains [29]. Additionally, integrating techniques like WRF modeling could better capture vertical atmospheric structures and local airflow, thus improving extreme climate event predictions [43,74].

Further enhancements to CNN-BMA-QDM are also possible. The CNN architecture could be deepened by adopting more advanced deep learning models to improve its ability to represent complex climate systems. For example, incorporating residual networks (ResNet) or transformer networks could enhance the model’s ability to capture long-term dependencies and deep spatial–temporal patterns. ResNet’s skip connections help mitigate gradient vanishing issues, while transformer models excel at capturing long-range dependencies, making them ideal for complex climate data [75]. The fixed weighting strategy used in BMA may also overlook sensitivity differences between models, indicating a need for dynamic weight allocation algorithms, such as adaptive weighting based on emission intensity. Moreover, the current BMA implementation only provides point estimates for model weights without quantifying the associated uncertainties. Uncertainty analysis methods, such as bootstrapping or Bayesian resampling techniques, can be incorporated to estimate confidence intervals for the BMA weights. Expanding the selection range of GCM models would also allow for a more comprehensive representation of the climate system by considering greater model diversity. This enhancement will enable a more comprehensive characterization of ensemble predictive uncertainty and further improve the statistical robustness of the downscaling framework.

In addition, the global adjustment characteristic of QDM may fail to capture local spatial or temporal features. The complex heterogeneity of the climate system (e.g., topographic gradients, land–sea distribution, and seasonal variations) necessitates locally adaptive adjustment strategies [50,76]. Lastly, the current CNN-BMA-QDM model still exhibits limited interpretability regarding the contribution of individual atmospheric predictors. In future studies, we plan to incorporate advanced model explanation techniques, such as Shapley Additive Explanations (SHAP), to better quantify the relative importance of different atmospheric circulation factors. This improvement will enhance model transparency and interpretability, especially in applications where decision-making support and stakeholder communication are critical.

6. Conclusions

In this study, a hybrid model CNN-BMA-QDM is developed for downscaling T_max by integrating the strengths of convolutional neural networks (CNNs), Bayesian model averaging (BMA), and quantile delta mapping (QDM). The CNN effectively captures nonlinear relationships between observed T_max and atmospheric circulation factors, making it particularly useful for local climate projections. BMA addresses the uncertainty inherent in using individual general circulation models (GCMs), while QDM corrects biases in extreme temperature simulations, especially in the distribution tails. The combination of these components results in a more robust, accurate, and computationally efficient model for projecting T_max at the local scale.

The CNN-BMA-QDM model is applied to T_max projections for Fujian Province, providing valuable insights under different climate scenarios using three GCMs and four SSPs. This model outperforms alternatives, including CNN-BMA, CNN, and other statistical downscaling methods such as RF, BPNN, SVM, LS-SVM, and SDSM, as evidenced by its superior performance in key metrics like CC, STD, and RMSE. Additionally, it excels in capturing extreme values, particularly the 99% and 95% percentiles of T_max. Monthly simulations further demonstrate the model’s ability to accurately represent T_max distribution and variability, especially during extreme months like July and January. Future T_max projections show a consistent warming trend across all SSPs, with the most significant warming under SSP585. On an annual scale, T_max increases steadily, with spatially averaged Sen’s slopes of 0.0077 °C/year for SSP126, 0.0269 °C/year for SSP245, 0.0412 °C/year for SSP370, and 0.0526 °C/year for SSP585. Spatially, the magnitude of warming follows a clear east–west and south–north gradient, with coastal areas seeing temperature increases of 4.62–5.73 °C under SSP585 in the long term, compared to 3.64–3.67 °C in inland regions. On a monthly scale, December shows the highest temperature rise, averaging 5.30 °C under SSP585, while July sees the smallest increase at 2.40 °C. Seasonally, winter experiences the largest warming (up to 4.88 °C), while summer shows the smallest increase (3.10 °C). Notably, the greatest south–north discrepancy in T_max rise occurs during summer, particularly under high-emission scenarios.

Based on these findings, the effective climate adaptation strategies for Fujian Province should focus on addressing the regional differences in warming. Coastal areas, where temperatures are rising most significantly, should focus on mitigating urban heat islands. This could involve increasing green spaces, improving building designs for better heat resistance, and developing early warning systems for extreme heat events. In inland regions, strategies should aim to manage the impacts of warming on agriculture and water resources, ensuring sustainable practices and robust water management systems. Additionally, adaptation strategies should be tailored to seasonal and spatial differences, with special attention to the most vulnerable months (e.g., winter and summer) and regions most affected by temperature extremes.

Overall, this research makes a significant contribution to improving the precision of T_max projections at the regional scale, providing a reliable tool for assessing future extreme temperature events. The model’s strong performance highlights its potential for practical use in climate adaptation planning. Future work could focus on enhancing model generalization, particularly in complex terrains, by incorporating physical mechanisms to better capture the effects of topography and local climate dynamics. Additionally, integrating dynamic weight allocation in the BMA framework could improve model performance by more accurately reflecting the relative contributions of different models under varying scenarios. Expanding the GCM ensemble and incorporating advanced deep learning architectures, such as ResNet or transformer networks, would further enhance the model’s robustness and predictive power, particularly for capturing long-term climate trends and nonlinear dynamics.