EAA: Eastern Asia; SAA: South Asia; SEA: Southeast Asia; EUR: Europe; ENAM: Eastern North America; WNAM: Western North America; SAM: South America; NAME: North Africa and the Middle East; SAF: South Africa; OCE: Oceania.

Uncertainty analysis

Aerosol retrieval errors can arise from various sources. To assess the uncertainty of AOD retrievals using the ART-GCT-GEE model, we examined the model’s performance with respect to variations in surface reflectance, surface elevation, NDVI, and land-use type (Figure 6). As surface reflectance increases, the model’s performance gradually declines, with a widening range of AOD biases and a decreasing fraction of retrievals falling within the EE envelope (Figure 6a). This is primarily because of the increased complexity of handling relationships caused by the reduced sensitivity of AOD to apparent reflectance. Nevertheless, the median bias remains relatively close to zero, and the\(f_{\text{EE}}\) consistently exceeds approximately 78%. This illustrates the model’s general stability across different surface reflectance conditions, particularly in the case of bright surfaces. Traditional physical methods have historically struggled with such conditions due to the considerable difficulties in accurately estimating surface reflectance, leading to substantial estimation uncertainties. In low-altitude (height ≤ 500 m) areas, the model exhibits stable performance with slight overall underestimations (median bias = -0.002—0.010) and high proportions (80–91%) of retrievals falling within the EE envelope (Figure 6b). In mid- to high-altitude (height > 500 m) areas, the model’s performance gradually improves with increasing surface elevation. This improvement is evident in the reduced variability of estimated biases and the increased fraction of retrievals within the EE threshold. These findings indicate that our model is relatively insensitive to variations in terrain.
When using NDVI as an indicator of surface conditions (Figure 6c), our model demonstrates stability in sparse and low-vegetation areas (NDVI ≤ 0.3), exhibiting median biases slightly below zero and (within) EE fractions consistently above 80%. Moreover, as NDVI values increase, the model’s overall accuracy gradually improves, with median biases approaching zero. There is also a continuous enhancement in (within) EE fractions, reaching approximately 90% in densely vegetated areas (NDVI ≥ 0.6). Our model consistently delivers reliable AOD retrievals across various land-use types (Figure 6d), particularly excelling in grassland (e.g., median bias = -0.08 and \(f_{\text{EE}}\) = 90%) and forest (e.g., median bias = -0.03 and \(f_{\text{EE}}\) = 86%). Importantly, our model also performs effectively in retrieving AOD over bare land (e.g., median bias = -0.008, and \(f_{\text{EE}}\) = 84%) and urban areas (e.g., median bias = -0.005 and \(f_{\text{EE}}\) = 81%), where populations are densely concentrated despite the presence of complex surface structures and challenging climate conditions. Therefore, our model can more effectively mitigate the challenges posed by complex surface conditions, providing robust aerosol retrievals across a wide range of terrestrial surfaces worldwide, a significant ”pathological” issue often encountered with traditional algorithms.