In this study, data from 398 sites across eight observation networks were collected for the period 2000–2019. The spatial distribution of these sites is shown in Fig. 1a. The sites were globally distributed, with elevations ranging from -4 m to 4104 m a.s.l. (above sea level), and were predominantly located in the mid-to-low latitudes of the Northern Hemisphere. These sites represent diverse land cover types and ecosystem conditions within various climatic zones. In this study, the land covers were categorized into ten major classes based on the International Geosphere-Biosphere Programme (IGBP): Barren land with sparse vegetation 〈BSV〉, Cropland 〈CRO〉, Mosaic of crops and natural vegetation 〈CVM〉, Forest 〈FOR〉, Grassland 〈GRA〉, Ice and Snow 〈IAS〉, Savannas 〈SAV〉, Shrubland 〈SHR〉, Tundra 〈TUN〉 and Wetland 〈WET〉. All sites were used for studying the Ts-a, while 140 sites, marked with red triangle symbols in Fig. 1a, were specifically used for estimating H. The proportions of these sites across the ten land cover types and five elevation ranges for both Ts-a and H studies are presented in Fig. 1b and c. Furthermore, investigations by Li et al. (2022a), Jiang et al. (2023), and Yin et al. (2023) indicated that land cover types within a 5 km radius of most sites exhibited a high degree of similarity or equivalence. Consequently, these sites provide strong spatial representativeness and comprehensiveness.

Table 2 provides detailed descriptions of the eight observation networks encompassing the 398 sites, including Atmospheric Radiation Measurement (ARM), AsiaFlux, Baseline Surface Radiation Network (BSRN), the Institute for Marine and Atmospheric Research (IMAU), Lathuile (including FLUXNET and AmeriFlux), PROMICE, SURFRAD and National Tibetan Plateau/Third Pole Environment Data Center (TPDC). Selection of sites was predicated on the availability of specific measurements: those with Ta, downward longwave radiation (DLW), and upward longwave radiation (ULW) were utilized for Ts-a calculation, whereas sites with LE, G, all four radiation components (DLW, ULW, DSR, and upward shortwave radiation 〈USR〉) or Rn were used for H estimation. As indicated in Table 2, measurement data varied in frequency and format across the sites, necessitating the conversion of all quality-controlled measurements to local time. Subsequently, different methodologies were employed to calculate daily Ts-a and H values. Ts-a was determined at an instantaneous scale using Ta, DLW, and ULW measurements according to Eq. (1). For sites recording data less frequently than hourly, Ts-a data were compiled into hourly averages, tolerating a maximum of 10 min of missing data per hour. These hourly values were then aggregated into daily means with no missing data. Conversely, daily H values were computed directly from days with over 75 % of valid observations, and subsequently adjusted for energy imbalance using the method proposed by Twine et al. (2000) (Eq. 2). Rn measurements were acquired directly from the sites or derived by summing the radiative components (Eq. 3). All calculated daily values underwent manual verification to eliminate any implausible figures. The equations below detail the procedures for calculating instantaneous Ts-a and adjusting daily H values: 1Ts-a=ULW-(1-ε)×DLWσ×ε1/4-Ta where ε represent the surface broadband emissivity and σ is the Stefan–Boltzmann constant (5.67×10-8 W m⁻² K⁻⁴). 2Hcor=Rn-GHuncor+LEuncor×Huncor3Rn=DSR-USR+DLW-ULW where Hcor is corrected H; LEuncor and Huncor are uncorrected LE and H, respectively. It should be noted that this correction method relies on assumptions about the distribution of residual energy, which may still have uncertainties into the corrected flux values. These uncertainties and their potential impacts are further discussed in the Discussion section of this paper.

Ultimately, a total of 649 689 daily Ts-a measurements and 216 542 daily H in-situ measurements were collected from 2000 to 2019 to estimate Ts-a and H on a global scale. Due to significant gaps in the daily in-situ measurements of H after stringent quality control, a distinct strategy was implemented to segregate the samples for H and Ts-a. For H, the methodology involved selecting monthly datasets with fewer than 10 % missing values for the training set, while the rest were allocated to an independent validation set for evaluating model performance. Linear interpolation was employed to impute missing values within the training set, ensuring the integrity of the monthly datasets. The final model was trained using 80 % of the months for training and the remaining 20 % for tuning the model parameters. This process yielded a training set encompassing 121 542 daily H samples and an independent validation set containing 97 982 samples. In contrast, the Ts-a analysis designated measurements from 2018 to 2019 as the independent validation set for model evaluation, with data from preceding years allocated to the training set. Specifically, for each site, 70 % of the samples from 2000 to 2017 were randomly selected for training, and the remaining 30 % were used for tuning the model parameters. These two approaches allow the validation set to assess the model's ability to predict “unseen” time periods and generalize to “unseen” sites (n=32 for Ts-a and 17 for H). As a result, the Ts-a training set included 564 918 daily samples, and the independent validation set comprised 84 771 daily Ts-a samples.

In this study, we utilized three reanalysis datasets: ERA5, ERA5-Land, and MERRA2. The ERA5-Land was employed to evaluate the performance of the generated daily Ts-a, while all three reanalysis products were used to assess the accuracy of the generated daily H product. For the period from 2000 to 2020, all product values were initially resampled to a 1 km resolution using the bilinear interpolation method (downward fluxes considered positive). Below are detailed descriptions of these datasets:

Based on the previous studies mentioned in the Introduction section and multiple experiments, the Ts-a was estimated as: 4Ts–a=f(LST,DLW,DSR,NDVI,elevation,slope,aspect,doy) where doy is the day of the year.

Afterwards, the Ts-a estimated model was built by using the RF method (Breiman, 1996). The RF is a widely used non-linear machine learning algorithm that constructs an ensemble of regression or classification trees. It has gained popularity in parameter prediction and estimation due to its high accuracy, ease of implementation, low computational cost, and fast processing speed (Babar et al., 2020; Liang et al., 2023; Li et al., 2022a; Jiang et al., 2023). In this study, RF regression was applied, with the final results determined by averaging the ensemble of regression output (Fig. 4a). To address common machine learning challenges such as under-fitting and over-fitting, several key hyper-parameters were fine-tuned, including the number of trees in the forest 〈n-estimators〉, the maximum depth of each tree 〈max depth〉, minimum number of samples required to split a node 〈min samples split〉, minimum number of samples per leaf 〈min samples leaf〉, and etc. (Babar et al., 2020). After plenty of experiments, we identified four hyper-parameters as critical for estimating Ts-a. To mitigate overfitting, we adopted a circular approach that minimizes the root mean-squared error (RMSE) between the training and parameter tuning in the RF model, in accordance with the methodology proposed by Li et al. (2022a). Consequently, the optimal hyper-parameters for the RF model were ascertained using these two strategies, and the results are presented in Table 4. This model is implemented on Scikit-learn toolbox (Pedregosa et al., 2012) on the Python platform within a Microsoft Windows 10 system with 32 GB of memory.

Three methods were picked for their representativeness to compare with LSTM in estimating daily H, including RF, DBN and Transformer. The introduction to RF is provided in Sect. 3.1 and its optimal hyper-parameters setting is provided in Table 5. The details of the DBN and Transformer methods are described below, with their structures illustrated in Fig. 4c and d.

Three statistical measures were used to represent the validation accuracy: RMSE, Mean Absolute Error (MAE), and the coefficient of determination (R2). 8MAE=∑i=1NYi-XiN9RMSE=1N∑i=1NXi-Yi210R2=1-∑i=1NXi-Yi2∑i=1NXi-X‾2 where Yi and Xi are the estimation and the measurement values of the ith group of samples, and N represents the number of samples.

To further assess model robustness and spatial generalization, a five-fold leave-sites-out cross-validation (5-CV) was conducted for both H and Ts-a. In this procedure, all sites were split into five folds, and in each iteration, four folds were used for training while one fold was used for validation, ensuring that validation sites were excluded from the training set. The CV results complement the overall independent validation and “unseen” site evaluation, providing additional evidence of the model's ability to generalize across locations.

As described in Sect. 2.1, the measurement values from 2000 to 2017 were used for training, while data from the subsequent two years, 2018 and 2019, served as independent validation samples to assess the model's performance. Figure 5 presents the independent validation accuracy of the estimated Ts-a values using the RF model developed in this study, compared with those derived from GLASS and ERA5-Land. All three were evaluated using the same validation samples from 2018–2019 (n=83284). For GLASS and ERA5-Land, the Ts-a values were calculated by subtracting Ta from LST.

As shown in Fig. 5a–c, the RF-estimated Ts-a over the entire validation set achieved an RMSE of 1.46 K, a MAE of 1.073 K, and an R2 of 0.52, significantly outperforming GLASS and ERA5-Land, which yielded RMSEs of 2.238 and 2.037 K, MAEs of 1.667 and 1.394 K, and R2 values of 0.11 and 0.32, respectively. Moreover, the estimated Ts-a values more closely align with the 1:1 line in the scatter plot, whereas GLASS shows a more dispersed distribution and ERA5-Land significantly underestimates values below 0 K. These results demonstrate that our model has strong capability for temporal extrapolation. To further examine spatial generalization, we tested the model on independent samples from “unseen” sites (Fig. 5d–f). A similar pattern is observed, with the RF model again outperforming the other two products, achieving an RMSE of 1.803 K, compared to 1.955 K for ERA5-Land and 2.543 K for GLASS. In addition, to assess model robustness, a 5-CV was conducted using all available samples. The CV results (RMSE = 1.73 K, MAE = 1.86 K, R2=0.30) are consistent with those obtained for the “unseen” sites and the temporal extrapolation tests, further confirming the strong generalization ability of the RF model. These discrepancies are likely attributable to differences in land cover types, further demonstrating the strong generalization capability of the proposed RF model in estimating Ts-a for both “future” time periods and “unseen” locations.

Building on the previously validated robustness and spatial generalization of the model, we further examined how its performance varies under different environmental conditions. Daily-scale validation accuracies of the estimated Ts-a model and two other products were evaluated using the entire independent validation set across five elevation ranges (0–200, 200–500, 500–1000, 1000–1500 and >1500 m), five NDVI ranges (0–0.2, 0.2–0.4, 0.4–0.6, 0.6–0.8 and 0.8–1), six slope ranges (0–2, 2–4, 4–6, 6–8, 8–10 and >10°) and nine land cover types (BSV, CRO, CVM, FOR, GRA, IAS, SAV, SHR and WET). These subgroup analyses focus on performance variability across different environments rather than additional “unseen” sites evaluation, providing insights into the conditions under which the model performs better or worse. The evaluation results are presented in Fig. 6.

Overall, the RF estimated model exhibited superior accuracy in various conditions, followed by ERA5-Land, aligning with findings from Fig. 5. In terms of terrain factors like elevation and slope (Fig. 6a and g), the RF model showed significant improvements, especially within the 500–1000 and >1500 m elevation ranges, and the 2–6 and >8° slope ranges, with RMSE improvements of approximately 1 K for elevation and between 0.7 and 1.4 K for slope. Regarding NDVI (Fig. 6e), a notable improvement was observed in the 0–0.2 range, with an RMSE of ∼1 K. These outcomes suggest that the RF model more accurately reflects Ts-a variations influenced by vegetation and terrain, which are key factors mentioned in the Introduction. Additionally, the performance across different land cover types was evaluated in Fig. 6c. The RF model performed well across all types, except for a site in CVM, which had an RMSE of approximately 2.2 K, an MAE of 1.8 K and R2 of 0.16, slightly higher than GLASS and ERA5-Land by 0.3 and 0.5 K in RMSE, respectively. Among the eight land cover types evaluated, the RF model demonstrated exceptional performance, especially in areas with high albedo (IAS) and those subject to seasonal variations (WET). In these cases, ERA5-Land recorded an RMSE of approximately 3.3 K for IAS, while GLASS reported around 2.9 K, implying the need for caution when applying these products to studies of icy regions. Regarding the BSV, the accuracy of the RF model was on par with ERA5-Land and surpassed that of GLASS, suggesting that the RF model and ERA5-Land effectively incorporate critical information.

In summary, the accuracy of the RF model and the two comparison products varied significantly under different conditions, with the RF model consistently outperforming the others as indicated by the lowest RMSE and MAE in almost all cases. Consequently, the RF model was used to generate daily Ts-a values globally from 2000 to 2020 for the calculation of daily H.

Table 7 presents the training and validation accuracy of estimated daily H from two LSTM models against in-situ measurements using the same samples. The independent validation results of two models were different but acceptable, with RMSEs of 25.533 and 27.051 W m⁻², MAEs of 18.641 and 20.034 W m⁻², and R2 of 0.54 and 0.51. Compared to the training accuracy, the validation results showed a slight increase in RMSE (3.24 and 2.232 W m⁻²) and MAE (2.147 and 1.469 W m⁻²), but these differences were considered acceptable. Additionally, incorporating ABD into the model improved accuracy, reducing RMSE to 1.518 W m⁻² and MAE to 1.393 W m⁻², underscoring the significance of ABD. Overall, all models exhibited satisfactory performance, as evidenced by their comparable training and validation results.

Due to the lack of ABD data during the polar night, two models were developed. In the final validation phase, the polar night results from model 1 were substituted with those from model 2, as depicted in Fig. 7a. The overall validation accuracy was deemed satisfactory, with an RMSE of 25.54 W m⁻², MAE of 18.649 W m⁻² and R2 of 0.54. To evaluate the model's spatial generalization ability, independent validation samples were split into those from training sites and those from “unseen” sites. The corresponding accuracies are presented in Fig. 7b, where the pink scatter points represent samples from sites not included in the training process. The model performed reasonably well on the “unseen” sites, with an RMSE of 27.53 W m⁻², a MAE of 20 W m⁻² and an R2 of 0.43. These results are only slightly lower than those obtained for the sites included in the training set, which yielded an RMSE of 25.16 W m⁻², MAE of 18.43 W m⁻² and R2 of 0.56. In addition, a 5-CV was conducted across all samples to further assess model robustness. The CV results (RMSE = 27.9 W m⁻², MAE = 20.44 W m⁻², R2=0.49) are comparable to those obtained for the “unseen” sites, indicating that the model maintains stable performance across different data subsets. To provide a comprehensive view of site-level performance, the RMSE was calculated for each validation site, including both training sites (at previously “unseen” times) and “unseen” sites. The spatial distribution of these RMSE values is illustrated in Fig. 8. It was observed that the LSTM model exhibited the highest level of robustness on a global scale, with 80 % of the sites (107 sites) reporting an RMSE below 30 W m⁻² (indicated in red and orange in Fig. 8). Nonetheless, some sites (eight sites) displayed suboptimal performance with RMSE values exceeding 40 W m⁻².

Afterwards, three different methods were employed to estimate H for a comparative analysis with the accuracy of the LSTM models. The independent validation results, based on the full set of samples shown in Fig. 7a are presented in Fig. 9. All comparisons were conducted using this full independent validation set to provide a comprehensive evaluation of the LSTM model against other methods, as the robustness and spatial generalization of the model have already been demonstrated in the previous analyses. The three methods produced closely aligned results, with RMSE values ranging from 25.341 to 26.01 W m⁻², MAE values between 18.757 and 19.165 W m⁻², and R2 values from 0.52 to 0.55, compared to the LSTM model's RMSE of 25.54 W m⁻², MAE of 18.649 W m⁻² and R2 of 0.54 (as shown in Fig. 7). However, all models exhibited varying degrees of underestimation for high values and overestimation for low values. While this issue was particularly pronounced in the Transformer and RF methods, the DBN and LSTM models demonstrated relatively better performance, albeit with similar tendencies. Remarkably, the LSTM model surpassed the DBN model, achieving improvements of 0.47 W m⁻² in RMSE and 0.516 W m⁻² in MAE. To further clarify the performance of these models, we examined each site and randomly selected three sites to illustrate the temporal variations in the values of H based on these four methods and in-situ measurements, compared against validation samples. As shown in Fig. 10, the LSTM model effectively captures the temporal variation of H in relation to in-situ measurements, while the other three models exhibit relatively poorer performance on certain days. A notable mismatch is observed in the RF, DBN, and Transformer models around the 268th day of 2012 at Lath_AU-Dry (Fig. 10a), with RF displaying only a single value and the other two methods showing underestimation on those days. Furthermore, RF and DBN exhibit opposing trends comparing to in-situ measurements during the 152nd and 218th days of 2011 at Lath_US-SRC (Fig. 10c). The variations of the four models at Lath_US-Dia (Fig. 10b) generally coincide with in-situ measurements, but RF shows slight overestimation around the 248th day of 2011 and DBN underestimates before the 196th day of 2012. Therefore, the LSTM model demonstrated superior performance, effectively mitigating the challenges of overestimating low values and underestimating high values in this study, likely due to its incorporation of time series information.

In summary, the LSTM models employed for estimating daily H, which integrate the estimated Ts-a and other GLASS products, have shown satisfactory accuracy. Consequently, this method is deemed appropriate for global 1 km resolution mapping of daily H, establishing it as a viable and dependable approach for these applications.

In this study, daily H estimates were generated globally for the period 2000–2020 by integrating two LSTM models. Specifically, mod2 was applied under polar night conditions when ABD data were unavailable. To assess the accuracy of the estimated H, we examined its spatial and temporal variations and compared the daily estimated H values with other existing products, as outlined below.

Existing research indicates that Ts-a is affected by a blend of atmospheric and surface factors (Feng and Zou, 2019). Theoretically, when the spatial resolution of terrain is finer than 5 km, it can modify the distribution of DSR and DLW reaching the land surface (Wang et al., 2004; Liang et al., 2024a), which in turn influences the distribution of LST. Variations in LST, driven by differences in terrain characteristics and land cover types, can warm the atmosphere, altering atmospheric conditions and consequently affecting radiation variation. In this study, we utilized terrain, vegetation, and radiation-related variables to estimate daily Ts-a on a global scale. The relative importance of each variable within the RF model was quantified and ranked, with the findings detailed in Fig. 19. Among the variables analyzed, the NDVI, as a key vegetation parameter, exhibited the highest relative importance score of 25.2 %. This underscores its pivotal role in estimating Ts-a. Subsequent contributors included slope, LST, elevation, and DSR, with respective importance scores of 16.38 %, 15.17 %, 12.96 %, and 11.16 %. These findings suggest that both terrain and radiation-related variables are integral to accurately estimating Ts-a. Notably, slope and elevation were more critical than the other terrain-related variable, aspect, which accounted for 7.37 %. Although flux towers are generally installed on relatively flat terrain to ensure measurement accuracy, the surrounding complex terrain within and beyond the flux footprint can still influence local surface energy and temperature dynamics near the flux towers. Similarly, LST and DSR proved to be more impactful than DLW, which held a contribution of 4.98 %. In addition, the doy ranked as the second least important variable in our analysis. Although it does not represent a direct physical environmental variable, our experiments demonstrated that it serves as a simple yet informative seasonal indicator that helps the RF model capture temporal variations effectively.

Ts-a is pivotal in influencing various land processes, boundary layer dynamics, weather forecasting, climate studies, and atmospheric profile retrievals. Its critical role extends to understanding atmospheric circulation, weather patterns, agricultural productivity, and ecological systems (Ghent et al., 2015; Zhang et al., 2014a). Previous studies have highlighted Ts-a's significant influence on summer precipitation in the middle and lower Yangtze River (Liu et al., 2009; Zhou and Huang, 2006), and its application in assessing soil desertification (Ai and Guo, 2003). Moreover, Ts-a is instrumental in reflecting various crop development stages, such as seed germination, seedling emergence, and photosynthesis, and affects soil microbial activity and the prevalence of crop diseases and pests (Gu et al., 2012). Additionally, it serves as a crucial parameter in process-based Earth system models, indicating the intensity of land–atmosphere interactions, energy fluxes, and driving key ecological and biophysical processes (Lensky et al., 2018; Qiang et al., 2011). The estimation of Ts-a in this study further facilitates the accurate derivation of Ta values. We estimated daily Ta globally by subtracting the estimated Ts-a from the GLASS LST product. For validation, we compared our Ta estimates with those from GLASS Ta using the same set of validation samples (no. of samples = 84 771). As depicted in Fig. 20, the estimation Ta achieved an RMSE of 2.621 K, a MAE of 1.971 K, and an R2 of 0.95, demonstrating competitive accuracy compared to GLASS Ta (RMSE = 2.307 K, MAE = 1.692 K, R2=0.96). These results underscore the critical role of Ts-a in a wide range of environmental and agricultural applications, highlighting its significant potential for global Ta estimation and further validating the accuracy of the Ts-a model.

We investigated whether the estimated daily Ts-a could enhance the accuracy of daily H values obtained from the physical model mentioned in the Introduction, compared to other data sources typically employed in existing research. To evaluate the uncertainty introduced by varying Ts-a data sources, we calculated daily H using the temperature-derived method in Eq. (10): 11H=ρCpT0-Ta/rah12rah=1ku*ln⁡zm-dzom-Ψ(h)+ln⁡zomzoh Where ρ (kg m⁻³) is the air density, Cp (J kg⁻¹ K⁻¹) is the specific heat capacity of air at constant pressure (1013), rah is the aerodynamic resistance to heat transfer, zom (m) is roughness length for momentum transport, k is the von Karman's constant (0.41), u* is friction velocity, d is zero plane displacement height, zm (m) is the reference height, zoh is the roughness length for heat and related to the aerodynamic parameter KB⁻¹ and zom (KB-1=ln⁡(zom/zoh)), Ψ (h) represent the stability correction functions for heat, T0–Ta represents the Ts-a and data were obtained from GLASS with 1 km resolution, estimated 1 km Ts-a using a RF model, and in-situ measurements.

Table 8 presents the results of daily H calculated from physical model by using different data sources. A total of 3391 independent validation samples were acquired. Note that the uncertainty associated with rah and ρCp were not addressed in this study. Overall, using GLASS and estimated Ts-a resulted in uncertainties of 13.5 % and 5.3 %, respectively, with RMSEs of 58.28 and 54.08 W m⁻², compared to Ts-a from in-situ measurements (RMSE = 51.35 W m⁻²). Additionally, the uncertainty varied across different land cover types, as shown in Table 8. Utilizing Ts-a from GLASS and estimated Ts-a, uncertainty ranged from 6.01 % to 23.1 %, with the highest and lowest uncertainties observed in GLASS for FOR and SAV, yielding RMSEs of 65.72 and 59.45 W m⁻², respectively. However, for certain land cover types such as CRO and GRA, lower RMSEs were noted when employing Ts-a from GLASS and estimated Ts-a compared to in-situ measurements, specifically. Specially, the RMSEs were 35.62 and 46.2 W m⁻² for CRO, and 46.14 and 45.76 W m⁻² for GRA. Moreover, across all five land cover types, RMSE values consistently exceeded 35 W m⁻² when utilizing different Ts-a data sources. This could be due to the fact that the uncertainty of parameterized method in getting rah was not accounted for. Therefore, accurately estimating rah is curial in physical model and the machine learning method used in this study effectively mitigates this issue after our experiments.

As the H in-situ measurements used as ground truth values in this study have undergone energy balance closure (EBC) correction, their reliability warrants thorough discussion. In this study, we adopted the widely used method proposed by Twine et al. (2000), which redistributes the residual energy between sensible and latent heat fluxes in proportion to their original magnitudes. Although this approach has been implemented in many large-scale studies and provides a practical solution when additional constraints are lacking, recent research has underscored its limitations. Notably, Mauder et al. (2024) highlighted that EBC remains a persistent issue in FLUXNET data, with a global average energy balance ratio of approximately 0.82, and identified unresolved processes such as mesoscale secondary circulations and unmeasured energy storage terms as major contributors to the energy gap. These uncertainties are particularly relevant for H, and their effects can propagate into downstream analyses and model training. Although the Twine method does not resolve these underlying physical mechanisms, it remains a necessary and pragmatic compromise for enabling the use of flux tower data in surface energy balance studies.