Our approach consists of the following steps (Fig. 1): First, we identified bare soil periods and extracted corresponding bare soil albedo (αbs) values from Sentinel-2 surface albedo products based on thresholds of satellite-derived indices. Second, we trained two random forest (RF) models on Sentinel-2 surface albedo during bare soil periods for the prediction of spatial distribution and temporal anomaly of αbs at the European cropland scale. Third, we compared the predicted αbs to existing αbs datasets at site or European scales.

Five types of αbs datasets were utilized to evaluate the performance of the final spatiotemporal albedo predictions (αbs,RF) at seven ICOS European cropland sites (BE-Lon, FR-Lam, FR-Aur, FR-EM2, DE-RuS, DE-Geb, DE-Kli), one European Fluxes Database Cluster (EFDC) European cropland site (CZ-KrP), and one Swedish cropland site in Uppsala, and the overall European cropland regions during bare soil periods (Fig. 3, Table 3). The bare soil periods at ICOS and EFDC sites were manually identified by checking daily or weekly site photos from 2018 to 2020, selecting periods when the soil within the visual range of the camera was visibly exposed without any covers (Fig. S2). The bare soil periods at Swedish cropland sites were obtained from records directly provided in the literature.

The αbs datasets of all sites, derived either from site eddy covariance measurements or 5 d 0.3 km Sentinel-2 surface albedo observations, are denoted as αbs,site and αbs,S2 to represent the αbs we used for evaluation at site scale in the following text. The αbs,site at the Swedish site, composed of six cropland fields, was extracted from literature directly for comparison (Sieber et al., 2022). The selected eight sites encompass a broad pedoclimatic and management gradient across European croplands (Table S1 in the Supplement). They represent contrasting soil conditions, including Luvisol, Fluvisol, Cambisol, and Chernozem/Phaeozem, with the ranges of silt, clay and sand contents from 26.6 % to 78.1 %, from 14.7 % to 53.0 %, and from 7.2 % to 38.0 %, respectively. These sites also cover diverse climatic conditions in air temperature, incoming shortwave solar radiation, precipitation and cloud cover at annual scale. Seasonal variability in solar radiation and soil moisture (characterized by the seasonal minimum and maximum values in Table S1) captures the range of environmental conditions experienced across seasons. In addition, these sites implement different agricultural management practices, including crop rotations of 2–8 years and bare soil periods occurring mainly in spring, autumn and winter (approximately 30–180 d, Fig. S2).

We aggregated the field data to represent the αbs,site for this site. The comparison at site scale is only implemented if the sample size at each site is more than three.

We additionally examined the relationships between the daily soil sensor SM measurements and different αbs datasets to evaluate their consistency in expressing the dependence of αbs on SM, including αbs,RF, αbs,MODIS, αbs,Gascoin, αbs,S2 and αbs,site (Table 3).

The random forest models successfully reproduced both the spatial patterns and temporal variability of αbs across European croplands (Fig. 2a and c), providing a basis for diagnosing the dominant controls on αbs at different scales. The spatial model achieved an R2 of 0.46, while the temporal anomaly model explained 35 % of the observed variability, with both models yielding RMSEs of 0.02 based on out-of-bag evaluation datasets.

The long-term spatial distribution of αbs (αbs,spatial) is primarily controlled by temporally averaged solar zenith angle (LSZA), mean soil moisture conditions and elevation (Fig. 2b). In contrast, temporal variability during bare soil periods is most strongly influenced by instantaneous solar zenith angle, the underlying spatial albedo pattern, and soil moisture anomalies (Fig. 2d). The importance of these variables on αbs has been widely explored in previous studies (Idso et al., 1975; Post et al., 2000; Yang et al., 2008; Gascoin et al., 2009; Roosjen et al., 2015; Cierniewski and Ceglarek, 2023). The remaining predictors contribute to weaker but non-negligible impacts. It is reasonable that soil properties (e.g., soil organic carbon, pH) control the spatial distribution of αbs by adjusting soil colors via the contents of organic matter and nutrients (Sirisathitkul and Sirisathitkul, 2025) while time records adjust its temporal variation (Yu et al., 2024).

Partial dependence analysis further illustrates the physical consistency of these controls. Both LSZA and SM have negative effects on αbs,spatial and αbs,temporal predictions (Fig. S3a, b, d and f). The elevation increases αbs,spatial by representing specific soil types with elevation (Fig. S3c) (Badía et al., 2016; Praeg, 2020). An impact of αbs,spatial on αbs,temporal is expected as it represents the location-specific climatic and environmental conditions which are otherwise not represented by the selected predictors (Fig. S3e).

The spatiotemporal average of αbs,RF is 0.15±0.01 over European cropland from 2018 to 2020 which is within the range of αbs found in the literature, which spans from 0.15 to 0.22 derived from 7537 European topsoil samples in 2022 (Szabó et al., 2024). Our αbs dataset has a higher spatiotemporal average than earlier products including αbs,Carrer of 0.12±0.03 (2001–2010) and αorc,bgd of 0.13±0.03 (2000–2009), respectively, which have coarser spatial resolutions of 1 km and ∼ 55.5 km (Figs. 4 and S4) (Carrer et al., 2014; He et al., 2019). The distribution of the final predictions αbs,RF was similar to the distribution of the αbs data extracted from Sentinel-2 observations by vegetation indices within European cropland regions from 2018 to 2020 (Fig. S4). This indicates that our predictions cover the spatio-temporal variations in European croplands.

The multi-year spatial pattern exhibits broad west-east and north-south gradients (Fig. 3a) that align with major soil zones, with darker surfaces where organic matter is higher and brighter surfaces where carbonates are more prevalent, a contrast repeatedly reported for European croplands (Carrer et al., 2018; Rizzo et al., 2023). The Iberian Peninsula, southwestern and southern France, and the Mediterranean coastal regions have bright soils with αbs of 0.18–0.20. While the soil in north-central and eastern Europe (e.g., Germany and Poland) is dark with αbs of 0.12–0.15.

Despite general agreement in continental-scale gradients, spatial correlations between our field-scale αbs,RF estimates and existing coarse-resolution products remain low (Pearson r=0.07–0.15; Fig. 4).

During bare soil windows, αbs,RF has an average of 0.15±0.01 across six eddy-covariance cropland sites, with time series showing coherent field-scale dynamics (Figs. 3b and 6). Time series of αbs,RF exhibit site-specific background levels with short-term fluctuations.

The daily αbs,site and αbs,S2 at the sites, for which bare soil albedo estimates were available, were utilized to compare with daily variations in αbs,RF (Figs. 5 and 6). Results show that the time-averaged predicted albedo was close to observation (R2=0.84, RMSE = 0.12 for comparison with αbs,S2), while the agreement with in-site observations is weaker (R2=0.12, RMSE = 0.11 for comparison with αbs,site) (Fig. 3b). αbs,RF is +21.87±27.71 % (mean ± standard deviation) higher than αbs,site (0.14±0.02) for the same periods (Figs. 5 and 6). While the difference between αbs,RF and underlying training data (αbs,S2, 0.12±0.02) across sites is smaller (+7.11±3.55 %). It implies that the difference between αbs,RF and αbs,site is a mix of biases in the RF to capture Sentinel-2 observations and differences between αbs,S2 from αbs,site. We also found that the difference of the model predictions between αbs,RF and αbs,site varies across different soil types. BE-Lon, FR-EM2 and FR-Lam sites, belonging to alfisols (light brown to reddish-brown), have lower bias compared with site measurements (Fig. 3). While DE-Geb and DE-Kli (dark brown to black molisols) and CZ-KrP (brown to yellowish-brown inceptisols) induce higher differences from measurements.

For reference, αbs,Gascoin (0.17±0.01) and αbs,MODIS (0.16±0.02) are higher than αbs,RF and αbs,site at the same sites and times (Fig. 5). Correlation analyses showed that temporal variations in αbs,RF, as prescribed by Eq. (3), tracked soil moisture dynamics (R2=0.51, RMSE = 0.006), which is darkening after wetting and progressive brightening during dry-downs (Fig. 7). This correspondence is stronger than αbs,site (R2=0.30, RMSE = 0.02) and αbs,S2 (R2=0.06, RMSE = 0.01), comparable to αbs,MODIS (R2=0.46, RMSE = 0.007), and weaker than αbs,Gascoin (R2=0.94, RMSE = 0.001). The particularly high correlation for αbs,Gascoin is expected because αbs,Gascoin is directly derived from soil moisture. Compared with αbs,site, αbs,RF is consistently brighter across the soil moisture range (∼ 0.01–0.02 higher in αbs), with the positive bias most pronounced for soil moisture >50 %. αbs,RF also exhibits a smaller amplitude and variance than αbs,site, smoothing the peak darkening seen in the site observations.

The reconstructed αbs is designed to capture the dominant physical controls on bare soil albedo while balancing the trade-offs behind continuity and representativeness based on Sentinel-2 reflectance. It enables the characterization of bare soil albedo variability at spatial and temporal scales relevant for agricultural surface energy exchange across Europe. Compared with earlier continental-scale estimates (αorc,bgd and αbs,Carrer), the reconstructed αbs resolves sub-kilometer heterogeneity that is critical for diagnosing field-scale radiative contrasts in fragmented cropland landscapes (Pinty et al., 2011; Carrer et al., 2014; He et al., 2019).

The differences among estimates could be attributed to differences in the periods covered: 2001–2009 for αorc,bgd, 2001–2010 for αbs,Carrer, and 2018–2020 for αbs,RF. Changes in climate and environmental conditions during these periods, such as the observed decreasing trend of soil moisture on a European scale from 1991 to 2020 compared to 1991, especially in central and eastern Europe (Almendra-Martín et al., 2022), can theoretically result in average higher 2018–2020 αbs compared to the period before 2010.

The estimation of αbs largely reflects the seasonal variability of αbs in European cropland fields (Fig. 6), providing a basis to quantify measures for radiation management in agriculture (Yu et al., 2024). This dataset reduces sampling discontinuities associated with cloud cover, snow, and vegetation masking (Figs. 6, S1 and S2), allowing seasonal envelopes and inter-site contrasts in αbs to be examined more consistently (Wang et al., 2025). The selected features for RF models enable αbs prediction in regions with limited satellite observations due to cloud cover or aerosols, because the necessary predictors of the RF model, including soil properties and solar-surface-satellite geometry, are not affected by atmospheric conditions (Fig. 2b and d).

The decomposition of bare soil albedo into spatial and temporal components provides a framework for interpreting its physical controls. Intrinsic soil properties affect bare soil albedo by establishing the optical characteristics of the soil surface and regulating soil-water interaction, while soil moisture dynamics and radiative geometry control the temporal fluctuations of the observed bare soil albedo.

Our analysis supports this framework by isolating and quantifying the contributions of soils, weather and management on spatio-temporal variations in bare soil albedo. It reveals that the αbs dynamics arise from the interplay of multiple controls rather than any single dominant driver (Yang et al., 2008). Temporal changes (αbs,temporal) are primarily associated with variations in soil moisture and local solar zenith angle, with additional seasonality represented by time-of-day and day-of-year terms (Fig. 3b). This underscores the role of short-term variations in illumination geometry and surface wetness in shaping bare soil albedo dynamics (Yu et al., 2024). Whereas spatial contrasts (αbs,spatial) reflect long-term patterns associated with soil moisture and solar geometry, further modulated by invariant factors such as elevation and soil type (Fig. 3d). This suggests that stable radiative conditions and soil-related properties (e.g., soil organic carbon and pH) exert dominant controls on large-scale albedo variability (Sirisathitkul and Sirisathitkul, 2025). Approaches that rely solely on soil moisture as drivers of αbs (Gascoin et al., 2009) are thus likely to misestimate αbs such as overestimating αbs during dry-down over dark, carbon-rich Mollisols, and underestimating αbs during wet periods under low solar zenith angles, when viewing geometry elevates apparent reflectance.

Soil moisture acts as a short-term control on αbs by changes in soil color and soil roughness through wetting, darkening and dry-down brightening (Rizzo et al., 2023). The magnitude and duration of these responses depend on the soil water retention capacity (Post et al., 2000), resulting in different αbs responses to the same soil moisture change for different soil textures. The impact of local solar zenith angle is expected due to its impact on the relative position between the spaceborne sensor and the observed areas, affecting the amount of reflected solar radiation (Yang et al., 2008): a small zenith angle (e.g., 25°) results in nearly vertical solar radiation reflectance and a high αbs (Fig. S3a). It is treated as a physical control on the measured radiative signal (Liu et al., 2009). Its contribution is separate from soil moisture and soil properties and reflects the presence of sun-surface-satellite geometry rather than a proxy of unavailable factors, meaning that αbs can be understood in light of seasonal changes in observation geometry as well as surface state.

Soil properties explain much of the stable spatial structure onto which moisture and geometry act (Rizzo et al., 2023). For example, soil texture influences αbs through both direct and indirect pathways. Particle size, mineral composition directly influences soil optical properties (e.g., surface color and scattering characteristics), thereby establishing the inherent αbs. In addition, these properties related with texture regulate the soil hydraulic behaviour (Sadeghi et al., 2018). Variables such as elevation or bulk density do not change αbs directly but act as proxies for topographic setting or soil structure where more specific drivers (e.g., aspect or slope at the same scale) are not available in the RF model (Fig. 2b and d). For instance, higher elevations generally have lighter soil colors, which might increase αbs,spatial (Fig. S3c) (Badía et al., 2016; Praeg, 2020). Because of the collinearity of bulk density and clay content (Heuscher et al., 2005), their importance reflects predictive utility rather than causal influence on αbs. They stabilize spatial patterns and improve field coherence, not to assign mechanistic primacy. A day-of-year term is included to capture recurring within-year patterns that arise from sunlight, crop calendars, and hydro-meteorology (Reichstein et al., 2019). Since the same day-of-year repeats across years, this term is not intended to encode year-specific events. It provides a seasonal envelope that supports interpolation and extension. A consequence is that unusual events that deviate strongly from the typical seasonal trajectory can be damped in the reconstructed series, even if they appear clearly in individual clear-sky observations.

Although soil type is related to soil albedo (Post et al., 2000; Rizzo et al., 2023), we excluded it from the RF because of the coarse soil type map (∼ 55.5 km, USDA NRCS, 2023) and due to significant within soil type variation of surface soil color (not shown). Site comparison reveals that the model performs well for soils of intermediate brightness, but its errors increase for very dark or very bright soils (Fig. 3b). This result indicates that the soil type carries information not captured by bulk density, clay, sand, or SOC (e.g., mineral composition and the type of organic matter). It also implies that the importance rankings of predictors influencing αbs may exhibit spatiotemporal heterogeneity.

Overall, these controls are interacting components governing αbs rather than independent drivers. Among the intrinsic soil properties, soil texture plays an important role because it establishes the background optical characteristics of the soil surface and regulates soil-water interactions, while soil moisture and solar geometry determine the short-term variability of the observed αbs.

Despite the process-oriented reconstruction of bare soil albedo across European croplands, several limitations remain, primarily associated with situations in which surface heterogeneity or dynamics operate at spatial or temporal scales finer than those resolved by the available predictors.

First, the mismatched scales between field and satellite observations introduce representativeness errors. αbs,site is representative for 8–1000 m² (Eichler, 2022) and satellite-based αbs,RF is for 90 000 m². Soils might show substantial variation in soil properties such as texture, color, crusting, residue, and moisture at the scales of meters (Garten et al., 2007), and the bare soil fraction within a 0.3 km footprint can shift rapidly during sowing and post-harvest. Thus, the resulting αbs,RF, possibly represents an area-weighted mixture of exposed soil, crop residues, and smooth signals of αbs dynamics (Yue and Tian, 2020; Dai et al., 2022; Yu et al., 2024).

Second, a sampling bias exists in the training data as periods with crop, clouds or snow covers with extreme soil moisture conditions were excluded. Bare soil is often exposed in autumn or winter periods, only about 35 d in each year from Sentinel-2 data averaged at the 8 ICOS sites satisfied our criteria (Figs. S1 and S2). Fixed local overpass time of Sentinel-2 (∼ 10:30) provides sparse directional sampling of αbs at the pixel level. Thus, anisotropy is averaged and variance related to extreme cases in the subfield is reduced, with a tendency to underestimate high-magnitude fluctuations (Figs. 2, 5 and 6), such as few observed αbs,S2 during the periods of 2019 winter at BE-Lon, DE-RuS, and FR-Lam sites (Figs. 6a, b and d) (Sudmanns et al., 2019; Harmel et al., 2018).

Third, base soil masking is not perfect. Crop residue visible or occasional sparse regrowth normally have a higher albedo than the soil (Fig. S5) (Yu et al., 2024), while surface shadows created by terrain or clouds exhibit low reflectance similar to dark soil (Qiu et al., 2019). Using multiple indices in this analysis mitigates but does not eliminate these confusions entirely.

Fourth, the selection of predictors in the RF model might induce uncertainty. The use of coarse resolution (1 km) soil moisture data together with high resolution data could have led to an underestimation of the effect of spatial variation of soil moisture on αbs. A test of adding soil moisture as a predictor for αbs,spatial led to the elimination of it during the feature elimination procedure, which deviated from the earlier findings of a well-known negative correlation of spatial patterns of soil moisture and αbs (Gascoin et al., 2009). Compared with the stable seasonal variation of local solar zenith angle, soil moisture has a higher potential to be disturbed by the environment such as cloud or snow covering periods, which adds noise and reduces the explanatory power. It might explain the higher ranking of local solar zenith angle than soil moisture in predicting αbs,RF (Fig. 2b and d). In theory, the relative contribution of these two predictors depends on specific scenarios. The comparably higher importance of zenith angle in this study should not be taken to mean that soil moisture is intrinsically less influential in controlling αbs (Yang et al., 2008; Roosjen et al., 2015). In addition, very sharp post-event shifts of αbs, especially caused by frequent agricultural activities in sub-regions such as irrigation or tillage, can be muted if the relevant proxy indicators are missing in RF (Mohr et al., 2023; Yu et al., 2024; Goodwell et al., 2025). One important example is varying soil surface roughness which varies according to agriculture practices, rainfall events and crust formation. Its impact on αbs was not explicitly represented as the required spatiotemporal datasets of soil roughness are currently unavailable at the European scale. In addition, assessing the impact of temporal variation of soil roughness on predicted αbs at site scale remains challenging as no soil roughness measurements are available at the evaluation sites. Our RF framework relies on intrinsic soil properties that may partially capture roughness-related variability (Herodowicz-Mleczak et al., 2022; Rizzo et al., 2023) but cannot explicitly resolve the effects of agricultural practices, rainfall-induced smoothing, or soil crust formation. In their absence, the model smooths these rapid dynamics and underestimates the abrupt changes in αbs, yielding a weak response (Fig. 2a and c). Uncertainty of predicted αbs,RF therefore increases when these rapid physical changes occur on the surface.

Collectively, these scale and sampling properties explain why αbs,RF preserves seasonal envelopes and regional patterns yet under-represents rapid, high-magnitude extremes. These limitations also highlight the need for future integration of higher-resolution meteorological and soil moisture products, improved surface characterization, and more continuous albedo observations to better capture short-term variability in agricultural landscapes.