The reanalysis dataset contains drivers of surface elements in a large area, which can provide highly complementary information and avoid data gaps and low-quality pixels caused by abnormal weather conditions. This study primarily used the CMFD and ERA5 data as reanalysis data sources.

The CMFD is a set of meteorological forcing datasets developed by the Institute of Tibetan Plateau Research, Chinese Academy of Sciences (He et al., 2020; Yang et al., 2010; Yang and He, 2019). It is mainly based on the Global Land Data Assimilation System (GLDAS) as a background dataset, using empirical knowledge algorithms and combining GLDAS with measured data to obtain temperature data with a spatial resolution of 0.1∘. The CMFD contains seven variables: 2 m air temperature, surface pressure, specific humidity, 10 m wind speed, downward shortwave radiation, downward longwave radiation, and precipitation rate. The CMFD covers January 1979 to December 2018 and provides four types of temporal resolution (3 h, daily, monthly, and yearly). The CMFD is comprehensive and has the longest time series and the highest spatial resolution in China. Studies have used the temperature data as input parameters to construct a surface air temperature model, which shows that the correlation coefficient between the CMFD temperature and the measured data is greater than 0.99 and has high consistency, and that grid data can reflect the temporal and spatial changes in regional air temperature (Zhang et al., 2019; Wang et al., 2017). The CMFD as an input element to build a surface temperature model can also significantly reduce model deviation and improve model accuracy (Chen et al., 2011). Therefore, we used the 3 h temperature of the CMFD to build the Ta Model and verified the new product with the daily temperature from the CMFD. The CMFD is available from the China National Qinghai–Tibet Plateau Science Data Center (http://data.tpdc.ac.cn/zh-hans/data/8028b944-daaa-4511-8769-965612652c49/, last access: 1 November 2020).

ERA5 is the fifth-generation product of the atmospheric reanalysis global climate data launched by the ECMWF, replacing the ERA-Interim reanalysis data which were discontinued on 31 August 2019. ERA5 data are generated based on the Cy41r2 model of the integrated forecasting system, which has benefited from the development of data assimilation, model simulation, and model physics, and is generated by assimilating many ground-monitoring, aircraft weather observation, and radio-detection data. ERA5 data are significantly better than ERA-Interim data; for example, the former has a higher spatio-temporal resolution, more vertical mode levels, and more parameter products than the latter. ERA5 provides timely, updated quality checks on the data, which is convenient for providing stable, real-time, and long-term climate information. ERA5 provides many meteorological elements, including 2 m air temperature, 2 m relative humidity, sea level pressure, sea surface temperature, and precipitation. Since the release of the ERA5 reanalysis data, many researchers have tested their applicability and accuracy. The results show that the accuracy of the ERA5 is better than that of the ERA-Interim data, and the higher spatio-temporal resolutions are conducive to the precise description of regional atmospheres. The details of these improvements are convenient for studying changes in small-scale atmospheric environments (Meng et al., 2018; Mo et al., 2021; Hillebrand et al., 2021). These data can be obtained from https://cds.climate.copernicus.eu/cdsapp#!/search?type=dataset&text=ERA5 (last access: 1 December 2020).

The in situ data from 1979 to 2018 used in this study were employed to build a Ta model and evaluate existing datasets and new products. The measured data of meteorological stations were from the China National Meteorological Information Center (http://www.nmic.cn/site/index.html, last access: 1 November 2020), including hourly air temperature, hourly land surface temperature, maximum daily temperature (Tmax⁡), minimum daily temperature (Tmin⁡), daily average temperature (Tavg), and weather condition records. Due to the inconsistency of recorded data of meteorological conditions at many stations, some data are missing. Furthermore, there are no meteorological stations in most areas; thus, the data are used as auxiliary data.

The ground observations obtained from the China Meteorological Administration underwent uniform data processing and homogeneity testing. To further ensure the quality of the data, we checked the in situ data. First, we set a fixed threshold to eliminate the overflow value. Second, we tested the time series of station data and eliminated abnormal and missing data due to instrument damage or bad weather (Zhao et al., 2020). Finally, we checked the spatio-temporal consistency of the in situ data, deleted the meteorological stations with location migration during the study period, and maintained the temperature data of meteorological stations with a long monitoring time and stable temperature values.

China's daily near-surface temperature grid dataset was released by the CMA with a spatial resolution of 0.5∘. This grid dataset contains the daily maximum, minimum, and average temperatures in China (http://www.nmic.cn/site/index.html, last access: 11 April 2021). The CMA dataset was obtained by combining the daily temperature data monitored by meteorological stations and the digital elevation model (DEM) data generated by resampling with three-dimensional geospatial information via a thin-plate spline interpolation algorithm. The spatial resolution of the CMA data is 0.5∘, and we used these data for cross-validation. The Moderate Resolution Imaging Spectroradiometer (MODIS) is an important sensor in the Earth Observation System program and is mounted on the Terra and Aqua satellites. Terra is a morning-orbiting satellite that passes through the Equator at approximately 10:30 local time from north to south. Aqua is an afternoon-orbiting satellite that passes through the Equator at approximately 01:30 local time from south to north. The Terra satellite has been in service since 1999, the Aqua satellite since 2002. Since 2002, surface temperature data can be obtained four times per day from MODIS data through inversion calculation. In this study, we used the MOD11A1 and MYD11A1 products, which provide daily surface temperature data on a global scale with a spatial resolution of 1 km. MODIS LST (land surface temperature) has a quality control (QC) field that indicates data quality and is encoded in binary form. MODIS data can be downloaded from the LAADS DAAC (Level-1 and Atmosphere Archive & Distribution System Distributed Active Archive Center) website (https://ladsweb.modaps.eosdis.nasa.gov/search/order, last access: 1 December 2020).

In addition to the aforementioned data, DEM data were used. The Shuttle Radar Topography Mission (SRTM) DEM used in this study was a radar topographic mapping project jointly implemented by NASA and the National Imagery and Mapping Agency, which was implemented by the Space Shuttle Endeavour. Temperature data were regulated via the topographical correction of the SRTM DEM, with 90 m resolution to eliminate the influence of topographical fluctuations on air temperature. SRTM DEM data can be obtained from the Geospatial Data Cloud (http://www.gscloud.cn/search, last access: 10 February 2021).

Surface temperature is sensitive to changes in altitude and easily affected by the surrounding environment. For non-meteorological station pixels, we use interpolation to fill in the pixel values based on the principle of regional consistency. To improve the accuracy of the pixel temperature at non-meteorological stations, we fully considered the influence of altitude on temperature. First, the in situ Ta was unified to sea level according to the vertical rate of temperature drop. Next, the non-station pixels were interpolated according to the station data, and finally, the interpolated pixel values were restored to the corresponding elevation. This method can reduce the influence of altitude on temperature to a certain extent and improve the accuracy of the dataset. In this study, we used a uniform vertical temperature drop rate (γ), i.e., for every 100 m increase in altitude, the atmospheric temperature decreases vertically by 0.65 ∘C, and vice versa. The height correction formula is provided by Eq. (5) (He and Wang, 2020; Schicker et al., 2015; Wang, 2013): 5TSL=Ta-γ⋅HSL-Ha, where TSL is the sea-level temperature, Ta is the temperature of the meteorological station, and HSL is the sea-level height, where the value of γ is approximately 0.0065 ∘C m-1.

We used the jackknife method as follows: 699 in situ stations across China were divided into 140 verification points and 559 calibration points according to the ratio of 20 to 80 to establish a multiple linear regression equation (Benali et al., 2012; Xu et al., 2017). The preliminary accuracy results (Sect. 5.1) show that although the overall accuracy was high, there remains the problem of abnormal temperature values of the model output data caused by the violent fluctuations in daily temperature changes. Further correction is required to reduce the deviation and improve the accuracy of the dataset. The data correction process is illustrated in Fig. 5. For the abnormal temperature value, we replaced the Ta at the pixel location with the observation Ta from the meteorological station and performed the adjacent pixel temperature correction for the pixel without the meteorological station at the pixel location. The multiple linear regression method was used to process the original temperature, and the stepwise regression relationship between the measured value of the station and the fitted value of the corresponding pixel was established. Next, we calculated the predicted value of the regression temperature according to the regression equation and obtained the temperature residual value by calculating the observed value and the predicted value to obtain the final corrected temperature (Cristobal et al., 2006). The modified expression is shown in Eq. (6): 6Vx,y=m^x,y+ε^x,y, where x and y are the numbers of rows and columns of pixels, respectively; Vx,y is the correction value of the regression equation; m^x,y is the regression prediction value of air temperature; and ε^x,y is the residual value.

We mainly selected areas with a single surface type and flat terrain under clear skies as the comparative study area to verify the original dataset and reconstructed dataset. A scatter diagram can represent the overall distribution and aggregation of the data and intuitively convey accurate information from the data; thus, we used a scatter chart to display the accuracy range of this product. In addition, before establishing the model, we retained a part of the reanalyzed data excluded from the calculation and used it for cross-validation. We used three indicators as metrics to measure the accuracy of variables, i.e., R2, MAE, and RMSE.

We compared Tmax⁡ and Tmin⁡ with the ERA5 data and CMA data. Notably, the ERA5 reanalysis dataset is an hourly temperature grid dataset; thus, we obtained the highest and lowest temperature values of ERA5 by constructing a local sine function similar to that in the prior section and further calculated the average daily temperature. The accuracy of Tavg products in this study was verified with the ERA5 data, CMA data, and CMFD daily temperature data. Because the spatial resolution of CMA is 0.5∘, to facilitate comparison, we resampled the spatial resolution of all datasets to 0.5∘.

We not only compared the output Ta data with the in situ data, but also assessed the climate change trends of Tmax⁡, Tmin⁡, and Tavg in various regions of China, and further tested the effectiveness and regional applicability of the dataset through various climate variables. The World Meteorological Organization defined a series of extreme climate indexes, including 27 core indexes. We used four of them (TXx, TNn, TX90p, and TN10p) to analyze the trend of extreme temperature changes in Tmax⁡ and Tmin⁡ (Karl et al., 1999; Peterson et al., 2001). Specifically, the TXx (TNn) anomaly refers to the difference between the sum of monthly Tmax⁡ (Tmin⁡) and the multi-year average of monthly Tmax⁡ (Tmin⁡) in each year. The multi-year period of this study is 40 years. In addition, linear regression was performed on the TXx (TNn) anomaly to analyze the interannual variation trend. The TX90p (TN10p) means that the daily Tmax⁡ (Tmin⁡) of each month during the study period is arranged in ascending order, and the 90 % (10 %) corresponding value in the time series is used as the threshold for judging warm days (cold nights; Zhang et al., 2005).

To study the spatio-temporal variation trend of Tavg, we used linear regression analysis (K), correlation coefficient analysis (R), and the T test (Du et al., 2020; Yan et al., 2020; Cao et al., 2021). The interannual change rate and correlation of Tavg were calculated by K and R, and the formulae are provided by Eqs. (7) and (8), respectively. We performed a two-tailed significance test on the T test to measure the significance of the temperature and time series changes (Eq. 9): 7K=n∑i=1niTi-∑i=1ni∑i=1nTin∑i=1ni2-∑i=1ni2,8R=n∑i=1niTi-∑i=1ni∑i=1nTin∑i=1ni2-∑i=1ni2⋅n∑i=1nTi2-∑i=1nTi2,9T_test(R)=Rn-21-R2, where n represents the total number of years of the time series length, i represents the year, and Ti represents Tavg in the ith year. K>0 indicates that the temperature increases within the time series, and K<0 indicates that the temperature decreases within the time series.

According to the six subregions in Fig. 1, comparative analyses of this product (Tmax⁡, Tmin⁡, and Tavg) based on in situ data were conducted. Figure 6 shows the accuracy scatter plot between the original data of Tmax⁡ and the in situ data. The R2 fluctuated from 0.91 to 0.99, the MAE ranged from 1.69 to 2.71 ∘C, and the RMSE ranged from 2.15 to 3.20 ∘C. Figure 7 shows the accuracy scatter plot of Tmin⁡. The R2 fluctuated from 0.93 to 0.97, the MAE ranged from 1.34 to 2.17 ∘C, and the RMSE fluctuated from 1.68 to 2.79 ∘C. Figure 8 shows the accuracy scatter plot of Tavg. The R2 fluctuated between 0.97 and 0.99, the MAE ranged from 0.58 to 0.96 ∘C, and the RMSE fluctuated from 0.86 to 1.60 ∘C. As shown in Figs. 6, 7, and 8, the R2 of Tmax⁡, Tmin⁡, and Tavg, and the temperature measured at the meteorological station, were all greater than 0.90. In general, our method performed well in estimating the daily temperature values. However, due to the impact of complex changes in weather, the distribution of temperature values on certain days is discrete, especially in study areas V and VI. Further corrections are necessary to reduce errors and improve the accuracy of the dataset.

The temperature was further corrected using the linear correction method. The data verification results of Ta after correction are shown in Figs. 9, 10, and 11. The results show that the corrected data had a higher consistency with the in situ data. The fitted and observed temperatures were linearly distributed and gradually approached the regression line, and the outliers were significantly reduced. Figure 9 shows the corrected scatter plot of Tmax⁡ for each study area. The R2 fluctuated from 0.96 to 0.99, the MAE ranged from 0.63 to 1.40 ∘C, and the RMSE fluctuated from 0.86 to 1.78 ∘C. Figure 10 shows the corrected scatter plot of Tmin⁡ for each study area. The R2 fluctuated between 0.95 and 0.99, the MAE ranged from 0.58 to 1.61 ∘C, and the RMSE fluctuated from 0.78 to 2.09 ∘C. Figure 11 depicts the corrected scatter plot of Tavg in each study area, where R2 fluctuated between 0.99 and 1.00, the MAE ranged from 0.27 to 0.68 ∘C, and the RMSE fluctuated from 0.35 to 1.00 ∘C. The results show that the distribution of numerical points in each area after the correction was denser, mostly concentrated near the 1:1 line, and the degree of clustering with the measured data was higher than before calibration. Our detailed analysis of the daily temperature in the six study areas demonstrated that the accuracy measurement values differed significantly between the east and west. For example, the accuracy error of study area IV is small, and the accuracy error of study areas VI and V is large, which may be affected by the regional topography and the distribution of meteorological stations. Study area IV is in the tropical monsoon climate zone, affected by latitude and topography, and the temperature is relatively high throughout the year. Moreover, the area is in Eastern China and has densely distributed meteorological stations and relatively flat terrain. Linear correction can significantly improve the agreement between the estimated value and the observed value. Study areas VI and V have the highest RMSE. They are in the Qinghai–Tibet Plateau in Southwest China and Xinjiang in the northwest. Such areas have similar characteristics, such as high altitude, large spatial heterogeneity, and few meteorological stations. This result shows that the temperature has strong spatial heterogeneity. In general, the corrected dataset has higher accuracy than the original dataset, satisfies the spatial heterogeneity of different regions, and better estimates the temperature under different weather conditions.

To further verify the robustness and accuracy of this product, Table 1 shows the cross-validation results of this product and other datasets, the mean average precision (MAP) of each region, and that this product has a high regional consistency with other datasets. Study area IV in the tropical monsoon climate zone has the highest accuracy, and study area VI located in the Qinghai–Tibet Plateau region of China has the lowest data accuracy. This result may be because the reanalysis dataset is also affected by the number and distribution of meteorological stations and the spatial heterogeneity. The accuracy and robustness of the product were confirmed from another perspective. The accuracy comparison of each area shows that this product has higher accuracy and spatial representation than other datasets. R2 is closer to 1, and MAE and RMSE remain low. Through the accuracy evaluation and data comparison between this product and the existing dataset, we found that our product has a better temperature estimation of each area, and the overall accuracy and accuracy of the dataset are higher.

We analyzed temperature changes in various regions of China through extreme climate indexes and change trend values to further test the validity and regional applicability of the dataset. As shown in Figs. 12 and 13, the TXx anomalies and TNn anomalies are consistent in the regional change trend. Although the annual anomalies fluctuated during the study period, they gradually changed from negative to positive. This phenomenon confirmed that the temperature fluctuated and increased, and that the Tmax⁡ and Tmin⁡ gradually increased, which is consistent with the global warming trend. The average temperature rise of TXx anomalies in each study area was 0.42 ∘C a-1, and the average temperature rise of TXx anomalies was 0.47 ∘C a-1. The histograms in Figs. 12 and 13 show that the number of warm days and cold nights fluctuates in an increasing and decreasing trend, respectively. In addition, similarities are seen in the change trends between warm days and cold nights. For example, in 1980, under the continual influence of strong cold air in the north, low-temperature weather occurred continuously in most areas of China and many areas experienced low-temperature disasters, which led to a decrease in the number of warm days and an increase in the number of cold nights. In 2015, 2016, and 2017, the temperature continued to rise, with high temperatures that occurred once in decades. This finding is closely related to the severe El Niño events that occurred in 2015 and 2016, the impact of the subtropical high in 2017, and the overall global warming trend. From 1979 to 2018, there has also been an increase in the number of warm days and a decrease in the number of cold nights. Meteorological events can indirectly verify the accuracy of this product, indicating that the corrected data can be used to analyze long-term temporal and spatial changes in temperature.

To further analyze the change rate and regional differences in Tavg during the study period, we analyzed the temperature change rate (K), correlation coefficient (R), and significance test of the correlation coefficient (T test(R)). As shown in Fig. 14a and a.i, the Tavg in most regions of China shows a weak positive warming trend, accounting for 92.13 % of the total, and the average temperature of Tavg in each region increased by 0.03 ∘C yr-1. The analysis of R in Fig. 14b and b.i shows that they show a strong correlation of approximately 48.77 % and a correlation in the region of 84.06 %, which shows that there is a high correlation between temperature changes and time. Figure 14c and c.i show that after performing a significance test on the R between temperature and time, 83.17 % of the area passed the 95 % significance test and 75.23 % of the area passed the 99 % significance test, which shows that the correlation between temperature and time development is significant.