In situ measurements from sparsely distributed networks worldwide are a critical source of reference data for validating or correcting biases in satellite products. However, due to the substantial difference in spatial scales between in situ and satellite measurements, the two cannot be compared except for the fact that the underlying surface of in situ sites is absolutely homogeneous. Instead, the in situ measurements needed to be upscaled to be matched with the satellite pixels. Based on the upscaling model, we also proposed the consideration that in situ observation generally lacks spatial representativeness due to the widely distributed spatial heterogeneity, and we have developed a coarse pixel-scale ground “truth” dataset based on ground measurements of 416 in situ sites from the sparsely distributed observation networks. Furthermore, we thoroughly assessed the effectiveness of the dataset at sites with different degrees of spatial representativeness. The results demonstrate that using this dataset in validation outperforms the direct comparison between satellite and in situ site measurements over heterogeneous surfaces when in situ measurement footprints are less than satellite pixel size. The accuracy of the reference data employed for validation or bias correction can be boosted by 17.09 % over the regions with strong spatial heterogeneity. However, the degree of improvement with this dataset displays a decreasing trend with the reduction in spatial heterogeneity. At a global scale, the pixel-scale ground “truth” dataset enhances the accuracy of pixel-scale reference data in general, with the overall relative root-mean-square error (RRMSE) decreasing by 6.04 % compared to in situ single-site measurements. Our results suggest that in situ single-site measurements are limited in their ability to capture surface spatial variability information at a coarse pixel scale (i.e., the kilometer scale). The dataset we provided, which merges temporal information from ground-based observations and spatial information from high-resolution data, represents a valuable resource for validating and correcting worldwide surface albedo products over heterogeneous surfaces. To the best of our knowledge, this dataset is unique in providing a coarse pixel-scale ground “truth” with the widest spatial distribution and longest time series. The dataset is publicly available through https://doi.org/10.5281/zenodo.8008454 (Pan et al., 2023).

Validation of satellite albedo products relies on reference value on the coarse pixel scale which is acquired by independent means. In previous research, reference value was generally obtained within the nominal spatial extent of the validation pixel from in situ observations or high spatial resolution airborne/spaceborne albedo references. Nevertheless, the signal of the validation pixel may correspond to different areas due to geometric errors. This geolocation mismatch will introduce large uncertainty into validation results, particularly for pixels covering heterogeneous areas. Therefore, this study first proposed a geometric location matching method on the coarse pixel level to establish the actual position of the validation pixel. The results show that geolocation error of the validation pixels of the high-order satellite products occurs widely. And they are not systematically shifted. The errors in reference values resulting from geolocation errors range from −10% to 25%, which are very likely to be greater than the accuracy requirement of satellite albedo products. Such errors caused by geometric shifts of validation pixels significantly amplify the errors in satellite albedo products. With this geometric location matching method, the reported relative root mean square error (RMSE) of MCD43A3 V061 reduced from 9.8% to 3.2%, and the reported correlation coefficient increased from 0.204 to 0.611. This method is very helpful to reduce the uncertainty of validation results and identify the real accuracy of satellite albedo products. Moreover, it has the generalization ability for other numerical variables over other types of land surfaces.

The spatial scale mismatch between satellite and in-situ -based measurements can be reduced by deploying multiple in-situ sites within the coarse pixel. However, upscaling in-situ measurements from the ground-support scale to the coarse pixel scale is still necessary due to their “point” measurement characteristics. The previous upscaling methods were generally developed merely for the in-situ measurements. Nevertheless, the uncertainty of in-situ measurements such as measurement errors and spatial representativeness errors was not dealt with. Consequently, the upscaling results inevitably suffer from errors, which will finally propagate into the pixel scale ground “truth”. For the first time, this study presents an improved upscaling method with the consideration of the uncertainty of in-situ measurements based on the error theory and measurement adjustment theory. The effectiveness of the corrected upscaling coefficients was evaluated by comparing the accuracy of the corrected upscaling results with those based on the upscaling coefficients without considering the uncertainty of in-situ measurements. The results indicate that the accuracy of the upscaling results can be enhanced by 11.06% in the condition in which in-situ measurements suffer from large uncertainty. However, if the uncertainty of in-situ measurements is negligible, the corrected upscaling model is not necessary because it does not bring many benefits. Although the effectiveness of this method was only tested on a limited study area, it makes an important first step toward a higher precision pixel-scale ground “truth”, especially when the uncertainty of in-situ measurements is non-negligible.

Validation merely provides the “impression of accuracy” of satellite products but does not deal with their errors. There have been several error correction/adjustment models. Nevertheless, their performances have not been evaluated and compared. In this study, three typical models, namely random forests (RF), cumulative distribution function (CDF), and Kalman filter (KF) were comprehensively evaluated based on the pixel scale ground “truth” regarding their ability to correct errors of coarse-resolution satellite albedo products. Moderate-resolution imaging spectroradiometer albedo product (i.e., MCD43A3 V006) was utilized as an example due to its widespread use and application. These three models all show significant improvements regarding the accuracy of the corrected MCD43A3. Root-mean-square error (RMSEs) decreased from 0.037–0.020, 0.021, and 0.025 for RF, CDF, and KF, respectively. Biases were reduced from -0.018–0.004, -0.001, and -0.001 for these three models, respectively. And R ² was increased from 0.585–0.849, 0.823, and 0.764 for RF, CDF, and KF, respectively. Generally, RF shows the best overall performance, followed by CDF and KF. These three models are more adept at handling the bias of MCD43A3 than their consistency with respect to the pixel scale ground “truth”, and the improvement is the most significant at the sites with large errors. Nevertheless, the performance of RF shows dependence on both the number and representativeness of training samples. When these conditions were not satisfied, CDF performs best in this situation. Regarding the stability of their performance, RF performs better in reducing RMSE while CDF performs better in reducing Bias and improving consistency.

The optimized sampling is very important for obtaining representative observations over heterogeneous surfaces. However, spatial heterogeneity (SH) is influenced by both randomness and structure factors and varies with scale. A comprehensive understanding of how the contribution of these factors to SH varies with scale is crucial for optimizing sampling. This study quantified the scale dependence of SH caused by structure and randomness factors based on the geostatistical attributes of semivariogram and explored the relationship between the optimal deployment of ground samples and SH dominated by randomness or structure factors. The results showed that as the plot size increased, the proportion of SH caused by spatial structure factors ( ${P} _{\text {SSF}}$ ) increased. When the plot size was larger than 20 m, the ${P} _{\text {SSF}}$ gradually approached 80%–100%. As the plot size increased, the optimal sample plots were distributed on the typical structural features in the area. However, when the plot size was small, the optimal samples were not necessarily located on the predominant surface types. Optimizing sampling can characterize the SH, and the optimal deployment of ground samples should comprehensively consider the plot size and the number of sample plots.