Stepwise Downscaling of ERA5-Land Reanalysis Air Temperature: A Case Study in Nanjing, China

Abstract

Reanalysis air temperature data, characterized by temporal continuity but limited spatial resolution, are commonly downscaled to achieve higher spatial resolution to meet the demands of regional climatological studies and related research fields. However, when large spatial scale differences are involved, the adaptability of statistical downscaling models across different scales warrants further investigation. In this study, a stepwise downscaling method is proposed, employing multiple linear regression (MLR), Cubist regression tree, random forest (RF), and extreme gradient boosting (XGBoost) models to downscale the 3-hourly ERA5-Land reanalysis air temperature data at the resolution of 0.1° to that of 30 m. A comparative analysis was performed to evaluate the accuracy of downscaled ERA5-Land air temperature results obtained from the stepwise and the direct downscaling methods, based on observed air temperatures at meteorological stations and the spatial distribution of air temperature estimated by a remote sensing method. In addition, variations in the importance of driving factors across different spatial scales were examined. The results indicate that the stepwise downscaling method exhibits higher accuracy than the direct downscaling method, with a more pronounced performance improvement in winter. Compared with the direct downscaling method, the RMSE value of the MLR, Cubist, RF, and XGBoost models under the stepwise downscaling method were reduced by 0.48 K, 0.38 K, 0.48 K, and 0.50 K, respectively, at meteorological station locations. In terms of spatial distribution, the stepwise downscaling results demonstrate greater consistency with the estimated spatial distribution of air temperature, and it can capture air temperature variations across different land surface types more accurately. Furthermore, the stepwise downscaling method is capable of effectively capturing changes in the importance of driving factors across different spatial scales. These results generally suggest that the stepwise downscaling method can significantly improve the accuracy of air temperature downscaled from reanalysis data by adopting multiple resolutions as the intermediate downscaling process.

1. Introduction

Near-surface air temperature plays a crucial role in land surface processes [1]. The acquisition of air temperature data with high temporal and spatial resolution is of significant importance for meeting the needs of climatological research, such as discussing the temporal and spatial variations in the regional thermal environment [2,3,4]. Currently, commonly used remote sensing imagery and land-use data with high spatial resolutions typically have resolutions of 30 m (e.g., Landsat imagery, DEM data). Therefore, acquiring matched air temperature data facilitates the synergistic analysis of multi-source datasets. Moreover, air temperature data at a 30 m resolution can reveal fine-scale spatial variations that are often obscured in low-resolution datasets.

There are three primary methods to obtain near-surface air temperature data, including meteorological station observations, remote sensing monitoring, and model simulations. Meteorological station observations offer air temperature with high precision and temporal resolution. However, the sparse distribution of stations leads to spatial discontinuity, and the data collected at each station represent only regional air temperature conditions [5]. Remote sensing monitoring technology estimates near-surface air temperature through atmospheric profile extrapolation [6], the temperature–vegetation index method [7], statistical models [8], and surface energy balance approaches [9]. Each of these methods possesses distinct advantages and limitations. The atmospheric profile extrapolation approach is simple to implement, but it becomes ineffective under cloudy conditions. The temperature–vegetation index method establishes a relationship between land-surface temperature and vegetation index to estimate air temperature. However, it is unsuitable for areas with sparse vegetation or bare soil. Statistical models, though conceptually straightforward, rely heavily on extensive meteorological station observations and corresponding remote sensing data. The surface energy balance approach is based on well-established physical principles, yet its methodology and implementation are relatively complex. While these methods enable large-scale air temperature estimation, they face challenges in achieving continuous spatial and temporal coverage. The accuracy of remote sensing estimation algorithms varies with the input data and the characteristics of the study area. Model simulations, which employ global or regional climate models to estimate air temperatures, often suffer from significant errors and low spatial resolution, thereby limiting their applicability at the regional scale [10].

To obtain air temperature data with high spatial resolution, two widely used approaches are station-based spatial interpolation and downscaling of low-resolution temperature data. Inverse distance weighting and kriging interpolation are used to estimate the spatial distribution of air temperature based on station observations [11,12,13]. However, the accuracy of temperature interpolation decreases when meteorological stations are unevenly distributed, station density is low, and land-surface types and topography vary significantly [14]. Downscaling methods for low-resolution air temperature are primarily classified into dynamical and statistical downscaling. Dynamical downscaling generates high-resolution regional climate data by embedding a regional climate model within a global model [15,16,17]. Although based on well-established physical and mathematical principles, this approach is computationally demanding. The statistical downscaling method assumes that the statistical relationship between low-resolution air temperature and its driving factors remains invariant across scales [18,19].

The statistical downscaling method is widely used in the downscaling of meteorological variables, including air temperature [20,21]. For instance, Zhang et al. [22] downscaled ERA5-Land air temperature data from 0.1° to 1 km resolution over the Yellow River Basin using a stacking ensemble model that integrates ET, XGBoost, and LightGBM. The results indicated that the ensemble model outperformed the individual models, yielding high-resolution outputs with improved spatial detail and accuracy. At present, air temperature downscaling studies typically directly downscale the original resolution to a higher one. However, when the disparity in spatial resolution becomes significant, the assumption of scale invariance in the downscaling model no longer holds [23], leading to a decline in downscaling accuracy as the scale span increases [24].

Based on the above analysis, further research is necessary to evaluate whether a stepwise downscaling method with multi-resolution transitions can improve the accuracy of downscaling results across a wide range of spatial scales. In this study, a stepwise downscaling method is proposed to downscale 3-hourly ERA5-Land reanalysis air temperature data from the resolution of 0.1° to 30 m, in which MLR, Cubist, RF, and XGBoost models were adopted to perform stepwise downscaling. Furthermore, to verify the effectiveness of the stepwise downscaling method, its performance is compared with the direct downscaling method, and the importance of each driving factor at different scales is analyzed through the selection of the optimal downscaling model.

2. Materials and Methods

2.1. Study Area

Nanjing, located in Jiangsu Province, China, was selected as the study area. Nanjing is located in Southwestern Jiangsu Province and the lower reaches of the Yangtze River, which stretches for approximately 150 km from 31°14′N to 32°37′N, as well as for approximately 70 km from 118°22′E to 119°14′E. The city has a subtropical monsoon climate and is one of the regions frequently affected by climate disasters [25]. As a central city in the Yangtze River Delta (YRD) urban agglomeration, Nanjing has been advancing a rapid urbanization process, leading to large changes in the underlying land surface, which in turn has a non-negligible effect on the regional climate [26]. Figure 1 presents a 10 m resolution land-cover map of the research area and its location within the Yangtze River Delta region, with the locations of meteorological stations also indicated.

2.2. Data

2.2.1. ERA5-Land Air Temperature Product

ERA5-Land data, a land reanalysis dataset produced by the European Centre for Medium-Range Weather Forecasts, are the fifth-generation reanalysis product, generated based on the Modified Land Surface Hydrological Model [27]. The dataset has been available since 1950, providing atmospheric reanalysis data at a spatial resolution of 0.1°, and it is accessible through the Copernicus Climate Data Store (https://cds.climate.copernicus.eu, accessed on 17 October 2024). To evaluate the performance of the stepwise downscaling method, the air temperature data with the height of 2 m at eight 3-hourly intervals (02:00, 05:00, 08:00, 11:00, 14:00, 17:00, 20:00, and 23:00 Beijing Time) during four representative months (February, April, August, and October) in 2020 were used. The data were projected using the Albers Equal Area projection and resampled to a spatial resolution of 10,500 m.

2.2.2. Station-Observed Air Temperatures

Hourly air temperature data from 118 automatic weather stations in Nanjing for the year 2020 were selected. These data were provided by the Jiangsu Meteorological Bureau, China. The locations of the stations are shown in Figure 1. The station-observed air temperature data are temporally consistent with the ERA5-Land data. These observations were used both to construct the optimal model for estimating air temperature distribution and to serve as a reference for assessing the accuracy of the downscaling results.

2.2.3. Satellite Imagery Data

Sentinel-2 imagery of the Nanjing area for 1 February, 26 April, 19 August, and 23 October 2020, was downloaded from the European Space Agency’s website (https://dataspace.copernicus.eu, accessed on 17 October 2024). After preprocessing the acquired Sentinel-2 data, the Normalized Difference Vegetation Index (NDVI) and the Modified Normalized Difference Water Index (MNDWI) were calculated from multispectral bands with spatial resolutions of 10 m and 20 m, respectively. These two indices were subsequently employed as driving factors in the construction of the downscaling model. Depending on the resolution required for the downscaling process, the two indices were resampled to the resolution of 30 m, 150 m, 300 m, and 1050 m.

In the Yangtze River Delta region, MOD09GA data for the months of February, April, August, and October 2020 were obtained from the official EARTHDATA website (https://ladsweb.modaps.eosdis.nasa.gov, accessed on 17 October 2024). MOD09GA provides daily land surface reflectance in MODIS bands 1–7 with a spatial resolution of 500 m and allows the calculation of the monthly average NDVI and MNDWI data. The monthly average NDVI and MNDWI data were then resampled to 1050 m, 4200 m, 8400 m, and 10,500 m, respectively, according to the needs of the downscaling model construction.

2.2.4. Digital Elevation Model Data

The digital topographic elevation data were obtained from the Shuttle Radar Topography Mission Digital Elevation Model, which was jointly surveyed and produced by the National Aeronautics and Space Administration and the National Imagery and Mapping Agency of the U.S. Department of Defense, with a spatial resolution of 30 m. These data are available through the U.S. Geological Survey (https://lpdaac.usgs.gov, accessed on 17 October 2024). As a driving factor for constructing the downscaling model, the DEM data were resampled to 1050 m, 4200 m, 8400 m, and 10,500 m for the Yangtze River Delta region, and to 30 m, 150 m, 300 m, and 1050 m for the Nanjing region.

2.2.5. Land-Cover Product

World Cover 2020 is a land-cover dataset produced by the European Space Agency based on Sentinel-1 and Sentinel-2 data, with a spatial resolution of 10 m. It includes 11 categories, such as forested land, cropland, and urban areas [28]. This dataset was used to calculate Impervious Surface Coverage (ISC) as a driving factor in the downscaling model, and ISC data were resampled to the resolutions required for different regions during the downscaling process.

The input variables used for training the downscaling model were selected based on their relevance to air temperature spatial distribution, which is influenced by geographical conditions and surface characteristics [29,30]. Specifically, NDVI, MNDWI, DEM, and ISC were chosen as driving factors. Before model training, all input datasets underwent quality control to ensure data reliability. Outliers were removed, and the spatial resolution and coordinate systems of all datasets were standardized to maintain consistency among variables. Additionally, data from meteorological stations that have missing values were not included in the model training.

2.3. Methodology

2.3.1. Stepwise Downscaling Method

The basic principle of traditional statistical downscaling is based on the assumption that the relationship model between near-surface air temperature and driving factors remains constant across different spatial scales. The model is constructed using near-surface air temperature at low spatial resolution along with driving factors, and high-resolution driving factors are then input to generate air temperature data with high resolution. The main equations for statistical downscaling are as follows [31]:

$$T_c^{\prime }=f\left({var}_c\right)$$

(1)

$$∆=T_c-T_c^{\prime }$$

(2)

$$T_f^{\prime }=f\left({var}_f\right)+∆$$

(3)

where $T_c$ represents the air temperature at low spatial resolution; $T_c^{\prime }$ represents the predicted air temperature at low spatial resolution; $T_f^{\prime }$ represents the predicted air temperature at high spatial resolution; ${var}_c$ denotes the low spatial resolution driving factors; ${var}_f$ denotes the high spatial resolution driving factors; and $∆$ refers to the simulation residual. The driving factors used in the downscaling processes at different resolutions include NDVI, MNDWI, DEM, and ISC.

Due to the low spatial resolution of ERA5-Land data, the number of air temperature grids in the Nanjing region is insufficient to meet the requirements for constructing the downscaling model. Therefore, the stepwise downscaling process is divided into two stages. In the first stage, the ERA5-Land air temperature is downscaled from the resolution of 10,500 m to 1050 m across the Yangtze River Delta region. In the second stage, the air temperature is further downscaled from 1050 m to 30 m within the Nanjing region.

The stepwise downscaling method involves selecting multiple intermediate spatial resolutions between the original and target resolutions during the downscaling process, in which land-surface information is incorporated at intermediate resolutions to minimize the discrepancy between the initial and target resolutions, thereby preventing the statistical relationships from becoming inapplicable due to the large resolution range in the downscaling process. To ensure spatial consistency before and after downscaling, the statistical downscaling method requires an effective multiplier relationship between the resolutions during the simulation of residuals. In the stepwise downscaling process, the multipliers between neighboring resolutions are set to 1.25, 2, 2, 2, 2, 3.5, 2, and 5, respectively. For the specific implementation, downscaling is performed sequentially in the order of 10,500 m, 8400 m, 4200 m, 2100 m, and 1050 m in the Yangtze River Delta region, and sequentially in the order of 1050 m, 300 m, 150 m, and 30 m in the Nanjing region.

Simultaneously, the results of direct downscaling from 10,500 m to 30 m resolution were used as a control group for comparison with stepwise downscaling. Specifically, the direct downscaling method trains the model based on the ERA5-Land reanalysis data with driving factors at 10,500 m resolution in the Yangtze River Delta region. The trained model is subsequently applied to the Nanjing region following Equations (1)–(3) to produce the final 30 m resolution direct downscaling results.

Individual downscaling models may exhibit inherent limitations stemming from their unique characteristics and underlying assumptions. To comprehensively evaluate the effectiveness of the stepwise downscaling method, four models based on different principles were selected for comparative analysis. These models represent a diverse set of algorithm types, learning mechanisms, and levels of complexity, ranging from traditional statistical methods to advanced ensemble learning algorithms. For each hour of the study periods, multiple linear regression, Cubist regression tree, random forest, and extreme gradient boosting were employed to construct the downscaling models. The air temperature data from station measurement and their spatial distribution estimated from the model between field-measurement temperature and corresponding influencing factors were both used as references, allowing the validity of the stepwise downscaling method to be evaluated by comparison with direct downscaling. Figure 2 illustrates the technical route of the stepwise downscaling method.

2.3.2. Statistical Downscaling Model

(1)

Multiple Linear Regression Model (MLR)

Multiple linear regression analyzes the linear relationship between multiple predictor variables and the dependent variable [32]. Let y represent the dependent variable, which is influenced by the predictors $x_1$, $x_2$, …, $x_n$, along with the random error term $\epsilon$. The multiple linear regression model assumes the following linear relationship:

$$y={\theta }_0+{\theta }_1{x}_1+{\theta }_2{x}_2+\cdots +{\theta }_n{x}_n+\epsilon$$

(4)

where ${\theta }_0$, ${\theta }_1$, …, ${\theta }_n$ are the n + 1 unknown regression parameters, and $\epsilon$ represents the unobservable random error.

(2)

Cubist Regression Tree Model (Cubist)

The Cubist regression tree is an enhanced model derived from the M5 model tree, which was proposed by Quinlan in 1992 to address the issue of bias in predictions made by the CART regression tree [33,34]. The Cubist regression tree consists of a series of combined segmented linear models. It is characterized by using a linear prediction model at the leaf nodes, rather than assigning a specific value. The model is weighted and balanced by multiple linear models to improve prediction accuracy, effectively combining the strengths of regression trees and multiple linear regression methods. When constructing the Cubist downscaling model, the number of regression trees and the number of nearest neighbors influence the model’s stability, prediction accuracy, and whether the results need to be adjusted by combining the values of the nearest-neighbor samples. These two optimal parameters can be determined by randomly searching and five-fold cross-validation method.

(3)

Random Forest Model (RF)

Random forest is an ensemble learning model based on the decision tree algorithm proposed by Breiman et al. [35] in 2001. Its main advantage lies in high prediction accuracy and resistance to overfitting. Random forest utilizes random sampling to train decision trees, with node splitting based on a randomly selected subset of features, thereby increasing randomness. The final regression model is determined by averaging the prediction results of all decision trees. In the construction of the random forest downscaling model, the number of decision trees influences both the stability of the model and its computational complexity. The maximum number of features determines the number of features used by each decision tree when splitting a node, affecting both the variability of individual decision trees and the model’s generalization ability. These parameters can be randomly searched and determined by using five-fold cross-validation method.

(4)

Extreme Gradient Boosting Model (XGBoost)

The Extreme Gradient Boosting model, proposed by Chen et al. in 2016, introduces an objective function that incorporates regularization and a weighted least-squares term to penalize model complexity and quantify the error between predicted and actual values [36]. The model is designed to rank all dataset features based on their importance, determine optimal segmentation thresholds for each feature type, and recursively partition the data into left and right subtrees. This is achieved through successive tree construction, in which each new tree corrects the residual errors of the previous one. In constructing the downscaling model using XGBoost, the number of decision trees, maximum depth, and learning rate, respectively, control the number of iterations, model complexity, and prediction accuracy. The optimal parameter set is identified through random search combined with five-fold cross-validation.

2.3.3. Remote Sensing Estimation of Air Temperature Spatial Distribution

Using the geographic coordinates of meteorological stations in the Nanjing region, corresponding NDVI, MNDWI, ISC, and DEM values of each station at the resolution of 30 m were extracted as driving factors. For each time point, all four models were trained using the measured air temperature from all available meteorological stations at that time, along with the driving factors extracted at each station. Their accuracy was evaluated using five-fold cross-validation. Subsequently, air temperature distribution at a spatial resolution of 30 m was estimated across the Nanjing region using the trained model, which was used to evaluate the spatial accuracy of the downscaling results.

2.3.4. Accuracy Evaluation Methods for Downscaled Air Temperature

Meteorological stations measured air temperature and the estimated air temperature distribution as the reference, Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Deviation Bias (Bias), the coefficient of determination (R2) and the Percent Bias (PBIAS) were employed to evaluate the accuracy of the downscaled ERA5-Land air temperature. Lower RMSE and MAE values, Bias and PBIAS values closer to zero, and an R2 approaching one indicate higher estimation accuracy.

3. Results

3.1. Evaluation of Stepwise Downscaling Results Based on Station-Observed Air Temperatures

3.1.1. Analysis of Stepwise Downscaling Results Across Different Seasons

The accuracy of the stepwise downscaling and the direct downscaling results of ERA5-Land air temperature every 3 h for the representative months of the four seasons was evaluated based on the observed air temperature data from Nanjing regional meteorological stations, as presented in

Table 1. Accuracy comparison of stepwise and direct downscaling results across different seasons.

Month	Model	Stepwise Downscaling				Direct Downscaling
		RMSE (K)	MAE (K)	Bias (K)	R2	RMSE (K)	MAE (K)	Bias (K)	R2
February	MLR	2.24	1.69	−0.61	0.82	2.72	1.99	−0.83	0.75
	Cubist	2.11	1.63	−0.33	0.81	2.49	1.92	−0.04	0.75
	RF	1.85	1.44	−0.03	0.84	2.33	1.8	0.00	0.77
	XGBoost	2.02	1.56	−0.24	0.82	2.52	1.95	−0.42	0.74
April	MLR	2.38	1.84	−1.24	0.86	2.63	1.98	−1.24	0.82
	Cubist	2.29	1.81	−0.98	0.85	2.7	2.1	−0.88	0.79
	RF	2.01	1.58	−0.59	0.87	2.37	1.87	−0.77	0.83
	XGBoost	2.25	1.75	−0.77	0.84	2.7	2.11	−0.91	0.79
August	MLR	2.43	1.95	−1.49	0.67	2.65	2.06	−1.45	0.59
	Cubist	2.34	1.88	−1.41	0.68	2.59	2.09	−1.53	0.62
	RF	2.03	1.66	−1.18	0.75	2.21	1.79	−1.26	0.7
	XGBoost	2.2	1.79	−1.31	0.71	2.44	1.97	−1.32	0.63
October	MLR	1.76	1.38	−0.70	0.83	1.91	1.48	−0.71	0.81
	Cubist	1.77	1.39	−0.39	0.80	2.00	1.56	−0.28	0.75
	RF	1.67	1.32	−0.22	0.81	1.89	1.48	−0.33	0.77
	XGBoost	1.75	1.38	−0.31	0.80	2.10	1.65	−0.52	0.74

. According to Table 1, compared to the direct downscaling method, the accuracies for the four models improve after adopting the stepwise downscaling method. Notably, the accuracy improvement of the Cubist model is particularly pronounced in April, with its RMSE and MAE decreasing by 0.41 K and 0.29 K, respectively. Additionally, the MLR, RF, and XGBoost models exhibited the most significant accuracy improvements in February, with the RMSE reduced by 0.48 K, 0.48 K, and 0.50 K, and the MAE reduced by 0.30 K, 0.36 K, and 0.39 K, respectively. These results indicate that the stepwise downscaling method provides a significant advantage in obtaining downscaled reanalysis air temperature data at 30 m resolution with higher accuracy.

A comparative analysis of the performance of four downscaling models reveals clear seasonal and methodological differences in their accuracy rankings. In direct downscaling methods, the accuracy ranking is RF > MLR > Cubist > XGBoost in both spring and fall, RF > XGBoost > Cubist > MLR in summer, and RF > Cubist > XGBoost > MLR in winter. However, under the stepwise downscaling method, the accuracy ranking for all four seasons is RF > XGBoost > Cubist > MLR. These findings suggest that the downscaling performance of the MLR, Cubist, and XGBoost models varies across seasons and methods. In contrast, the RF model demonstrates significant stability across both seasons and methods, achieving higher accuracy than the other models in all seasons. Moreover, the RF model accuracy is further improved under the stepwise downscaling method. These results highlight the strong adaptability and robustness of the RF model, enabling it to effectively account for the influence of seasonal changes.

Based on the downscaling accuracies of the four models under various methods and seasons, the RF stepwise downscaling model was selected as the optimal model. Further analysis of the results from this optimal model reveals that its accuracy is higher in autumn and winter, but slightly lower in spring and summer.

3.1.2. Analysis of Stepwise Downscaling Results at Different Times

Based on air temperature data measured at meteorological stations in Nanjing, the accuracy of direct and stepwise downscaling results at different times was evaluated. Figure 3 illustrates the error changes across four models at eight times under both downscaling methods. As shown in Figure 3, the stepwise downscaling method yielded higher accuracy than the direct downscaling method across different times. Specifically, the MLR model at 08:00, and the Cubist, RF, and XGBoost models at 05:00, exhibited the most significant improvements in accuracy. In these cases, RMSE decreased by 0.35 K, 0.49 K, 0.50 K, and 0.57 K, respectively.

Comparing the accuracies of the four downscaling models at different times, as shown in Figure 3, it was found that the rankings of the four models were consistent under the two downscaling methods. Specifically, the RF model demonstrated the highest performance, followed by the Cubist model with the second-highest performance, the XGBoost model with moderate performance, and the MLR model with the lowest performance. In comparison with the MLR, Cubist, and XGBoost models, the RF model reduced the RMSE by 0.60 K, 0.33 K, and 0.20 K under the stepwise downscaling method, respectively. Under the direct downscaling method, the RMSE was reduced by 0.39 K, 0.31 K, and 0.29 K, respectively.

As shown in Figure 4, the PBIAS variations of the four downscaling models across eight time points were illustrated. The results indicate that all models exhibited negative PBIAS values under both downscaling approaches, suggesting that the estimated temperatures were generally lower than the observed values. The stepwise downscaling method consistently produced lower PBIAS values than the direct method for the MLR, RF, and XGBoost models at all time points. Although the Cubist model tended to slightly underestimate temperatures under the stepwise approach, it achieved lower RMSE values, further demonstrating the advantage of the stepwise method in reducing overall errors. Moreover, a comparison of PBIAS rankings among the four models at different times revealed a different performance order from that of RMSE. The best performance was observed in the RF model, followed by XGBoost. The Cubist model yielded intermediate results, whereas the MLR model exhibited the lowest accuracy across all time periods.

According to the downscaling accuracies of the four models at different times across various downscaling methods (Figure 3 and Figure 4), the RF stepwise downscaling model was identified as the optimal downscaling model. Based on Figure 3, the RF stepwise downscaling model achieves the highest accuracy during the early morning and morning hours (02:00–08:00), while relatively larger errors occur during midday and afternoon (11:00–17:00), peaking at 14:00. Additionally, RMSE errors were higher during the nighttime hours (20:00–23:00) but generally lower than those during midday and afternoon hours.

Based on the above analysis, the accuracy of the stepwise downscaling method is significantly better than that of the direct downscaling method, with the RF model being the most effective among the four models. Therefore, the results of the RF model were selected to analyze the spatial distribution difference between the direct and the stepwise downscaled ERA5-Land air temperature and to further discuss the significant differences of influencing factors at various scales.

3.2. Evaluation of Stepwise Downscaling Results Based on the Estimated Air Temperature Distribution

3.2.1. Accuracy of the Estimated Spatial Distribution of Air Temperature

The spatial distribution of air temperature in the Nanjing region was estimated at a spatial resolution of 30 m using four models: MLR, Cubist, RF, and XGBoost. The estimates were evaluated against observations from automatic weather stations, and the bias values for each model remained below 0.01 K across all months. As shown in

Table 2. Errors of remote sensing-estimated air temperature spatial distribution.

Month	Model	Errors
		RMSE (K)	MAE (K)	R2
February	MLR	1.05	0.73	0.95
	Cubist	0.92	0.64	0.96
	RF	0.46	0.29	0.99
	XGBoost	0.63	0.39	0.98
April	MLR	1.12	0.82	0.96
	Cubist	0.99	0.71	0.97
	RF	0.44	0.31	0.99
	XGBoost	0.71	0.44	0.98
August	MLR	1.32	0.83	0.85
	Cubist	1.14	0.73	0.89
	RF	0.51	0.32	0.98
	XGBoost	0.76	0.45	0.95
October	MLR	0.98	0.72	0.93
	Cubist	0.87	0.64	0.95
	RF	0.39	0.28	0.99
	XGBoost	0.63	0.42	0.98

, the RF model consistently achieved the highest accuracy. Compared to MLR, Cubist, and XGBoost, the RMSE of the RF model was reduced by 0.59 K, 0.46 K, and 0.17 K in February; by 0.68 K, 0.55 K, and 0.27 K in April; by 0.81 K, 0.63 K, and 0.25 K in August; and by 0.59 K, 0.48 K, and 0.24 K in October, respectively. These results indicate that the spatial distribution of air temperature estimated by the RF model has high accuracy and can serve as the reference data for evaluating the accuracy of downscaled ERA5-Land reanalysis air temperature.

3.2.2. Analysis of Stepwise Downscaling Results in Typical Regions

Figure 5 takes the results from multiple dates (i.e., 17 February, 12 April, 11 August, and 8 October 2020) as examples. In the figure, remote sensing-estimated Ta, stepwise-downscaled Ta, and directly downscaled Ta represent the spatial distribution of air temperature at 30 m resolution estimated by remote sensing, and the stepwise and direct downscaling results generated by the RF model, respectively. Notably, the February results were affected by cloud cover, resulting in missing values in certain areas. As shown in Figure 5, compared to the stepwise downscaling distribution, the spatial distribution of air temperature in direct downscaling appears fragmented, air temperature distribution differences across various land surfaces are fuzzier, and texture details are significantly degraded.

The spatial distributions of air temperature estimated by the relationship model between station measurements and influencing factors were used as the reference. The further comparison between the direct and stepwise downscaling methods was conducted by selecting representative areas, including water bodies, urban areas, and cropland. Figure 6 illustrates the estimated spatial distributions of air temperature, as well as the direct and stepwise downscaling results at 30 m resolution during the daytime period. Specifically, Subfigures (a)–(c), (d)–(f), and (g)–(i) depict the spatial distributions of air temperature measured at 11:00 on April 26 in the Jinniushan Reservoir, 14:00 on 7 August in the Jiangning District and the Qinhuai River, and 11:00 on 26 April in Changjiang Village and Jiazhuang, respectively. The estimated spatial distribution of air temperatures indicates that, during the daytime, air temperatures in water bodies are generally lower than in urban areas and cropland regions. It can be seen from Figure 6, the results of the stepwise downscaling were significantly more consistent with the estimated air temperature spatial distribution and can accurately reflect the temperature characteristics difference of various land surfaces. However, a clear temperature bias is observed in the direct downscaling results; the water bodies are incorrectly estimated as an abnormally high temperature region, the air temperature in the urban area is wrongly presented as low temperature, and the air temperature in the cropland is significantly underestimated.

The accuracy of two downscaling methods was quantitatively evaluated by comparing the estimated spatial distribution of air temperature for the region shown in Figure 6. The results show that during the daytime, for the water bodies, urban, and cropland areas, the RMSE for the direct downscaling method is 1.89 K, 2.17 K, and 4.37 K, with corresponding MAE values of 1.65 K, 1.99 K, and 4.24 K, respectively. In contrast, the RMSE for the stepwise downscaling method is 1.06 K, 1.33 K, and 2.33 K, with MAE values of 0.91 K, 1.13 K, and 2.20 K. Comparing the two downscaling methods, the RMSE of the stepwise downscaling method during the daytime for water bodies, urban, and cropland regions are reduced by 0.83 K, 0.84 K, and 2.04 K, respectively, and the MAE is decreased by 0.74 K, 0.86 K, and 2.04 K. These results indicate that the stepwise downscaling method improves accuracy more significantly in these regions.

Figure 7 illustrates the estimated spatial distribution of air temperature at a 30 m resolution during nighttime, along with the results of direct and stepwise downscaling. The regions selected for water bodies, urban areas, and cropland in Subfigures (a)–(c), (d)–(f), and (g)–(i) are consistent with those in Figure 6, respectively, showing the spatial distributions of air temperature at 2:00 and 5:00 on 7 August and at 5:00 on 26 April. The nighttime air temperature estimates indicate that water bodies generally exhibit higher temperatures compared to adjacent cropland and forested areas. Urban areas display lower temperatures than water bodies but higher temperatures than bare soil and forested land. Air temperatures in cropland are typically lower than those in water bodies, while river canals and residential settlements located among cropland areas exhibit relatively higher temperatures. The results of the stepwise downscaling exhibited substantially better agreement with the estimated spatial distribution of air temperatures, enabling a more accurate representation of the thermal characteristics across different regions.

The accuracy of the two downscaling methods was evaluated using the estimated air temperature spatial distribution in the region shown in Figure 7 as the reference. At night, the RMSE of the direct downscaling method for water bodies, urban areas, and cropland are 1.43 K, 2.21 K, and 2.07 K, respectively, while the corresponding MAE are 1.31 K, 2.13 K, and 1.91 K. In contrast, the RMSE of the stepwise downscaling method is 0.89 K, 1.49 K, and 1.30 K, and the MAE is 0.77 K, 1.42 K, and 1.34 K, respectively. Further comparison revealed that the stepwise downscaling method reduced RMSE by 0.54 K, 0.72 K, and 0.77 K, and MAE by 0.54 K, 0.71 K, and 0.57 K in the water bodies, urban, and cropland regions, respectively, compared to the direct downscaling method at nighttime.

These daytime and nighttime results demonstrate that the stepwise downscaling method yields more accurate spatial distributions of air temperature at a 30 m resolution.

3.3. Analysis of the Importance of Driving Factors at Multiple Spatial Scales

Figure 8 illustrates the relative importance of driving factors in the RF model across multiple spatial scales in the Yangtze River Delta region (10,500 m, 8400 m, 4200 m, and 2100 m) and the Nanjing region (1050 m, 300 m, and 150 m). At the 10,500 m spatial resolution, DEM emerged as the most influential factor, followed by NDVI, ISC, and MNDWI. During the stepwise downscaling from 10,500 m to 1050 m, the importance of NDVI and MNDWI showed a decreasing trend, decreasing from 21.78% and 19.37% to 19.37% and 15.03%, respectively. The importance of ISC remained relatively stable, ranging from 20.52% to 21.18%, indicating that the impact of impervious surface coverage on urban air temperatures in the Yangtze River Delta region remains consistent throughout the stepwise downscaling process. In contrast, the importance of DEM increased significantly from 36.67% to 45.19%, suggesting that, as the resolution improves, the contribution of topographic factors to air temperature grows progressively.

In the Nanjing region, DEM exhibits the highest importance at 1050 m resolution, followed by NDVI, MNDWI, and ISC. During the stepwise downscaling to 30 m, the importance of NDVI increases from 22.63% to 23.13%, while that of MNDWI and ISC decreases from 19.11% and 18.48% to 17.69% and 16.00%, respectively. The importance of DEM increases from 39.78% to 43.19%, further confirming the growing contribution of topographic factors in the stepwise temperature downscaling process.

As shown in Figure 8, the importance of the driving factors exhibits less variation between adjacent spatial resolutions, suggesting that the stepwise downscaling model demonstrates greater stability. Meanwhile, the stepwise downscaling method effectively extracts information from DEM and other driving factors at each intermediate scale, thereby capturing changes in these factors more accurately, significantly improving the accuracy and stability of the downscaling results. Therefore, the stepwise downscaling method offers clear advantages in obtaining high-precision temperature data.

4. Discussions

The downscaling accuracy was relatively higher in fall and winter, whereas it was slightly lower in spring and summer. This may be attributed to more stable temperature changes in fall and winter, which allow the downscaling model to capture air temperature variations more accurately. Additionally, land-surface cover types, such as vegetation and water bodies, remain relatively stable in fall and winter, thereby reducing the complexity of model fitting. During the spring and summer months, air temperature variations are influenced by a combination of climatic factors, including convective activities and precipitation events. Furthermore, the dynamic changes in land-surface cover types contribute to the relatively low accuracy of the downscaling results.

The temporal differences in downscaling accuracy may be attributed to the variation in dominant factors affecting air temperature at different times of the day. During the early morning and morning hours, air temperature changes are relatively smooth [37,38] and are mainly influenced by topographic and subsurface factors, which are represented by driving factors such as DEM and various types of remote sensing indices in the downscaling model. In contrast, during the midday and afternoon hours, air temperature is influenced by solar radiation, wind speed, and topographic shadows [39], resulting in a more complex air temperature spatial distribution. This makes it challenging for the downscaled model to accurately capture these processes, leading to a decrease in model accuracy. Compared to midday and afternoon periods, nighttime atmospheric processes are less complex, with air temperature mainly influenced by surface radiative cooling and temperature inversion [40]. These factors are not fully accounted for in the downscaling model, leading to higher RMSE error.

Compared to direct downscaling, the stepwise downscaling approach demonstrates improvements in both accuracy and the spatial representation of air temperature. The reasons for this are as follows. Direct downscaling results, which rely on a single downscaling process, are primarily limited by the quality of the spatial distribution of the ERA5-Land air temperature data. When directly downscaled from a resolution of 10,500 m to 30 m, the spatial resolution increases by a factor of 350. With such a large span, the relationship between the near-surface air temperature and the driving factors obtained at a low resolution of 10,500 m is not suitable for the resolution of 30 m. In comparison, the stepwise downscaling method is more advantageous. It effectively reduces the influence of the scale variance on the downscaling results by incorporating seven intermediate downscaling steps, gradually introducing the effects of driving factors at various scales. Meanwhile, the stepwise downscaling method has a smaller span between adjacent spatial resolutions in the intermediate process, making the downscaling statistical model relatively more stable and changes small with the scale.

5. Conclusions

A stepwise downscaling method is proposed in this study, utilizing ERA5-Land reanalysis air temperature data every 3 h for February, April, August, and October 2020. The method is implemented using four models, including multiple linear regression, Cubist regression tree, random forest, and extreme gradient boosting. A comparative study is also conducted with the direct downscaling method, resulting in a 350-fold increase in resolution from the original 10,500 m to the target 30 m resolution. The following conclusions are drawn:

(1) The accuracy of the stepwise downscaling method is higher than that of the direct downscaling method across different seasons, with the most significant improvement observed in winter. In this season, the RMSE of the MLR, Cubist, RF, and XGBoost models decreases by 0.48 K, 0.38 K, 0.48 K, and 0.50 K, respectively, while the MAE decreases by 0.30 K, 0.29 K, 0.36 K, and 0.39 K. A performance comparison of the four downscaling models across different seasons reveals that the RF model exhibits the highest accuracy under the stepwise downscaling method. Seasonal differences are observed in the downscaling results, with higher accuracy in fall and winter and lower accuracy in spring and summer.

(2) The accuracy of the downscaling results for the four models at different times demonstrates that stepwise downscaling outperforms direct downscaling. The downscaling results exhibit some differences at different times, with the highest accuracy observed in the early morning and morning hours, lower accuracy during the night, and the lowest accuracy in the afternoon and noon hours.

(3) In terms of spatial distribution characteristics, the direct downscaling results exhibit patchy, fuzzy patterns and lack spatial details. In contrast, the stepwise downscaling results exhibit greater consistency with the estimated spatial distribution of air temperature, with richer textural details that more accurately reflect air temperature differences across different land surfaces. Using the spatial distribution of air temperature estimated by remote sensing as a reference, the RMSE of the stepwise downscaling method was reduced compared to the direct downscaling method. Specifically, reductions of 0.83 K, 0.84 K, and 2.04 K were observed during the daytime in typical water bodies, urban areas, and cropland, respectively, while reductions of 0.54 K, 0.72 K, and 0.77 K were observed at nighttime in the same areas.

(4) As the resolution improves, the relative importance of driving factors changes across spatial scales. In comparison to the direct downscaling method, the stepwise downscaling method can more effectively capture the changing characteristics of driving factors across different spatial scales through the multilevel downscaling process, thereby improving the accuracy and reliability of the downscaling results.

In this study, the use of intermediate resolution is innovatively proposed to supplement the effect of auxiliary information on air temperature in the downscaling process. High-precision air temperature downscaling at large spatial resolution spans is realized by constructing a stepwise downscaling model to guarantee that the statistical relationship between air temperature and auxiliary information varies less with scale. This approach serves as an important reference for producing air temperature data with high spatial–temporal resolution by utilizing reanalysis data with long time series and high temporal resolution. Further research is needed to explore the incorporation of time-specific driving factors, such as the solar angle, into the downscaling model. Additionally, optimal scale multipliers should be investigated to improve the accuracy and adaptability of the stepwise downscaling approach.