To run an offline LSM, the atmospheric forcing is needed (e.g., wind, temperature, humidity, precipitation, pressure, short- and long-wave radiation; for details, see ). In this study, we use the WFDE5 forcing dataset . It is generated by applying the WATCH Forcing Data methodology to the surface meteorological variables from the ERA5 reanalysis . The temporal resolution is hourly. Even though its spatial resolution (0.5°×0.5°) is coarser than that (approximately 31km×31km) of the ERA5 reanalysis, the WFDE5 shows comparable performance to the latter and better performance in the estimation of precipitation . Because the soil moisture depends strongly on the scale and intensity of precipitation , a better estimation of the soil moisture and other relevant state variables (e.g., soil temperature) may benefit the LST observation operator and thus potentially improve the analysis.

Observations play a crucial role in the assimilation. Their quality, temporal frequency, spatial resolution, and coverage directly influence both the analysis and the forecast. The land surface temperature observed by the MODIS onboard the Terra polar-orbiting satellite is used in this study, hereafter referred to as MODIS-LST. The MODIS-LST offers global coverage observations twice a day, with a fine spatial resolution of 0.01°×0.01° and a temporal period from 2000 to 2018. Detailed information on this observation dataset can be found in its user guide and algorithm document . Validation of MODIS-LST quality against in situ observations demonstrates its robustness during both daytime and nighttime, with biases typically falling within ±2.0 K .

This study adopts a 3 h assimilation frequency (centered at 00:00, 03:00, …, 21:00 UTC) to balance the physical characteristics of LST against model dynamics. Given that LST varies rapidly, a narrow assimilation window is essential to accurately capture its temporal evolution; conversely, the window cannot be excessively short, as the model requires adequate spin-up time to dynamically adjust following each assimilation step.

The size of MODIS-LST pixels is significantly smaller than that of a CoLM grid cell. For better representativeness, the MODIS-LST observations are aggregated into the closest CoLM grid cell as follows: 17LSTaggi=∑jcos(ϕj)LSTrawj∑jcos(ϕj),Erraggi=∑jcos(ϕj)Errrawj∑jcos(ϕj), where LSTaggi and Erraggi are the aggregated LST and observation error of the ith CoLM grid cell, respectively; LSTrawj and Errrawj are the jth raw MODIS-LST and observation error within the ith CoLM grid cell and the time window, respectively; and ϕj is the latitude of the corresponding pixel. The latitude-dependent weighting accounts for the varying physical area of raw MODIS pixels during aggregation. The raw MODIS-LST observations with a quality control flag of 0 (indicating cloud or aerosol contamination) or with a value of -32768 (representing invalid data) do not participate in aggregations. In addition, to ensure sufficient spatial representativeness and statistical confidence, if the total number of raw MODIS-LST observations aggregated into the ith CoLM grid cell is less than 1500, the LSTaggi is discarded. The observation errors are assumed to be independent, so the observation error covariance matrix is diagonal. No separate representativeness-error term is introduced because preliminary tests showed that the standard deviation of the raw 0.01° LST within a 0.5° grid cell is less than 5 % of the aggregated retrieval uncertainty.

The observation operator described in Sect.  is applied to each patch of the ith grid cell, and then the resulting patch-level estimates LSTsimp,i are area-weighted to yield the grid-cell mean simulated LST 18LSTsimp,i=H(Tlsun(p,i),Tlsha(p,i),Tg(p,i)),LSTsimi=∑pwpLSTsimp,i∑pwp where wp is the fractional area of patch p (patches classified as wetlands, lakes, or ocean are discarded). The observation innovation for grid cell i is therefore OMBi=LSTaggi-LSTsimi. The observation is rejected from assimilation whenever the ensemble-mean innovation exceeds 8 K, i.e., |1K∑k=1KOMBi,k|>8. Through sensitivity tests, this threshold was determined to strike a balance between filtering out gross errors and retaining valid observations.

Owing to the scarce in-situ land surface observations and the high uncertainty of land surface reanalysis, three gridded datasets are initially used to robustly evaluate the performance of the land DA in this study.

The first dataset employed is the land component of the fifth generation ECMWF reanalysis (hereafter ERA5-Land; ), which describes the evolution of water and energy processes of the global land surface from 1950 to the present in a consistent manner and is produced by the Carbon Hydrology-Tiled ECMWF Scheme for Surface Exchanges over Land forced with the ERA5 reanalysis. Although the temporal resolution is the same as the ERA5 reanalysis (hourly), it provides a finer horizontal resolution (9 km) to capture a more realistic and spatially detailed land process. Although it is an open-loop product, observations are indirectly assimilated into the land surface through the atmospheric forcing. Validation against independent global models and both in situ and satellite observations has shown the added value of ERA5-Land, especially for the estimation of soil moisture and other related variables .

In addition to ERA5-Land, the Global Land Data Assimilation System (hereafter GLDAS; ; ) is forced with a combination of model and observation data from 2000 to the present. The spatial and temporal resolution of GLDAS-2.1 is 0.25° and 3 h, respectively. It provides a near-global (180° W–180° E, 60° S–90° N) land surface state generated by the Noah LSM . Like ERA5-Land, GLDAS is an open-loop product in which observations are incorporated indirectly through the atmospheric forcing.

Finally, the Modern-Era Retrospective analysis for Research and Applications version 2 (hereafter MERRA2; ) provides global scale land surface diagnostics from 1980 to the present. While precipitation plays the dominant role in the hydrological process of the land, a model-generated precipitation dataset with significant errors in amounts and timing may bias the prediction of an LSM. The MERRA2 is forced with observation-based precipitation that contains smaller errors, yielding a more accurate depiction of the land surface conditions. The spatial resolution is 0.5°×0.625° (lat × lon), and the temporal resolution is 1 h. Furthermore, to provide independent validation beyond the aforementioned gridded products, satellite retrievals and in-situ station data are incorporated. For the evaluation of snow cover, independent satellite observations retrieved from the ATSR-2 , AVHRR , and MODIS are utilized. Additionally, to evaluate the surface turbulent fluxes, this study incorporates sensible and latent heat flux observations from the globally distributed FLUXNET2015 and AmeriFlux networks.

Comparisons between the two experiments on soil temperature in different layers based on GLDAS and MERRA2 datasets are presented in Figs.  and . The yearly BIASOEXP based on GLDAS is illustrated in the first column of Fig. . It can be inferred that the CoLM exhibits a large positive BIAS in depicting soil temperature in several regions, including western North America, western South America, South Africa, the Tibetan Plateau and Northeast Asia. These regions typically are arid zones, plateau areas, or permafrost soils. In contrast, relatively small negative BIAS is observed in Alaska, the southern part of the Middle East, and some areas of Northeast Asia.

The second and third rows in Fig.  mostly demonstrate the considerable improvements of the assimilation over the open loop based on the third-party datasets. In terms of the yearly BIASd based on the GLDAS dataset (Fig. b, e and h), the maximum improvements in BIAS are centered on Northeast Asia (BIAS is reduced by approximately 1.0, 1.5, and 2.0 K for depths 0–10, 40–100, and 100–200 cm, respectively). This pattern of improvement is also distributed across most parts of eastern Asia, Europe, and eastern North America, which are mostly humid areas. Although improvements are evident in the Northern Hemisphere, small degradations emerge in the Southern Hemisphere, with the maximum centered on southern South America, South Africa, and Australia, which are typical arid zones in the LSM. These results suggest that the assimilation scheme effectively updates soil temperature in relatively humid areas and reduces bias appropriately. However, the effect of bias reduction is not pronounced in arid zones. A similar pattern can be seen in Fig. c, f, and i, which are based on the MERRA2 datasets.

Improvements are also evident from Fig. , where the RMSDAEXP is smaller than RMSDOEXP throughout the assimilation period with both GLDAS and MERRA2 benchmark datasets. The reduction of RMSD approximates 0.1 and 0.2 K for depths 0–10 and 100–200 cm, respectively, in particular, on 31 January 2001 with the GLDAS benchmark dataset. It can also be inferred from the temporal variation of RMSD of both experiments that the influence on soil temperature is depth dependent, as can be seen from Fig. , as the depth increases, taking MERRA2 as an example, the minimum RMSD occurs in August, September, October and November, indicating different memory effects in different soil layers.

Apart from both temporal and spatial improvements, the most promising finding is the dependence of improvements on the depth of soil layers. While relatively small improvements are observed in the upper soil layers (Figs. b and c, a), the improvements tend to become more significant in the deeper soil layers (Figs. e, f, h, and i, b–d), which is consistent with the nature of the land process. Although the soil temperature within the upper layers can be easily modulated by changes in the land-atmosphere interaction, energy stored in the deeper soil layers, especially within 100–200 cm, cannot be directly influenced by this interaction. Consequently, the signals modified by assimilating LST into CoLM can be transferred to and persist longer in these deeper soil layers, maintaining their influence within them for a longer time. Furthermore, the modified signals within the deep layers are not directly updated by assimilating MODIS-LST, but through the vertical exchange of water and energy with the upper layers. In other words, although the energy stored in the upper soil layers cannot persist in the upper layers, its influence can be transferred into the deeper layers through vertical diffusion between different soil layers. After MODIS-LST is assimilated into CoLM to update the upper soil temperature and water content, the changed signals within the upper layer are transferred to deeper layers, as the latter can store this signal for a relatively longer time. This result suggests promising potential for the assimilation scheme presented in this study, which utilizes MODIS-LST to jointly update soil temperature and moisture in the upper soil layer, after which the modified signals are transferred into deeper soil layers through the vertical diffusion by CoLM during the forecast phase.

The temperature of snow is vital for estimating both the energy and the water balance of the land surface layer. Figure  reveals the effectiveness of using MODIS-LST to update both snow temperature and water content consistently. It can be observed from Fig. a that CoLM exhibits relatively large RMSD of snow temperature based on ERA5-Land, centered in Northeast Asia and the northern regions of North America. Similar patterns are evident in Fig. d, g, and j for different seasons, with maximum uncertainties centered in the same areas as in Fig. a (results based on MERRA2 datasets are similar and not shown here). The largest RMSD values occur in February, indicating the challenges faced by CoLM in accurately representing snow temperature, particularly during winter for high-latitude regions (December also exhibits large RMSD values, not shown here). While snow temperature strongly depends on the water content, we attribute this unsatisfactory depiction of snow temperature to the deficient snow processes in LSM.

Compared with the open loop, improvements in snow temperature by assimilation are evident in Fig. b and c. Most regions exhibit improvements, with the maximum enhancements centered in Northeast Asia, similar to the patterns observed for soil temperature shown in Fig. b and c. This similarity suggests that snow water content effectively modulates the updated snow temperature, particularly during winter (Fig. e and f), with maximum RMSDd values larger than 4 K in Northeast Asia for both ERA5-Land and MERRA2 datasets. This indicates that when the snow mass largely covers the soil layers, it insulates the soil beneath.

Unlike previous studies that used LST to update either soil temperature or soil water content, the assimilation scheme proposed in this study employs MODIS-LST to jointly update both soil temperature and water content in the upper layers through the framework of EnKF. Under this assimilation scheme, it is theoretically capable of producing consistent energy and water fields. Furthermore, one potential drawback of soil moisture assimilation is that the analysis increments only apply to soil moisture mass but cannot change its phase which depends on temperature. However, the joint update for both temperature and water content enables the water stored in snow or soil to change its phase between liquid and solid, especially in middle to high latitudes where the surface temperature is around the freezing/melting point. By simultaneously adjusting both state variables, this analysis allows water to redistribute between phases, yielding more realistic frozen/soil water partitions during the forecast phase.

The fraction of snow cover is a key parameter for indicating the temporal and spatial variation of snow water content. In high latitudes the fraction of snow cover may remain unchanged throughout the year due to the relatively low temperature below the melting point; the temporal variations of snow cover are considerably large in middle to high latitudes where the surface temperature range easily accommodates the condition for snow freezing or melting. In this study, we compare the snow cover from both experiments based on the ERA5-Land and MERRA2 datasets in terms of two global-scale metrics, and present the results in Fig. .

It can be inferred from Fig. a that the simulation of snow cover in CoLM has relatively large uncertainties in early summer and early winter (RMSD reaches 60 % and 40 % in May, based on ERA5-Land and MERRA2, respectively), revealing a poor simulation of snow melting and freezing. Relatively small uncertainties emerge in winter and summer months when the temporal variations of snow cover are relatively small. In Fig. b, both experiments reach their minimum R in summer when the snow merely remains in high-altitude and high-latitude regions. Comparison between two experiments demonstrates that the most significant enhancement is in spring and autumn regardless of the benchmark datasets (ERA5-Land and MERRA2). This improvement underscores the promising potential of assimilating MODIS-LST to adjust the snow cover in CoLM, particularly during periods of snow melting and freezing.

To further substantiate these findings with independent observations, the horizontal distribution of the yearly snow cover (in %) RMSDd evaluated against three satellite datasets is presented in Fig. . As depicted, the assimilation of LST yields widespread improvements across the Northern Hemisphere, particularly over the mid-to-high latitudes of North America and Eurasia when evaluated against AVHRR (Fig. b) and MODIS (Fig. c), where most of these areas exhibit an RMSD reduction of approximately 10 %. While the evaluation against ATSR-2 (Fig. a) shows some regional degradations, the overall spatial patterns based on these three datasets robustly demonstrate the capability of the joint assimilation scheme to effectively constrain the surface thermal dynamics, thereby yielding a more physically consistent representation of snow accumulation and melting in the mid-to-high latitudes.

While snow cover is a key parameter indicating the fraction of snow within a grid cell, with strong temporal variations in middle-high latitudes and minimal disturbance in high latitudes, snow depth describes the cumulative effect of snow content within a grid cell. Changes in temperature, mass, and phase of water content all directly influence the simulation of snow depth from middle to high latitudes, making it a comprehensive parameter for estimating energy and water budgets related to snow content. Even excluding the permanent snow regions of Greenland and Antarctica, snow depth still exhibits significant spatial variation across different continents. In this study, the spatial BIAS of snow depth based on the three datasets is provided in Fig. .

It can be seen from Fig.  that the BIAS for snow depth reaches a minimum in summer, as snow mass is relatively low when the Northern Hemisphere receives much solar radiation. The BIAS based on GLDAS and MERRA2 is consistent over either the globe (Fig. a) or different continents (Fig. b–d). In contrast, BIAS based on ERA5-Land exhibits a large discrepancy from those based on GLDAS and MERRA2 over the globe (Fig. a) and North America (Fig. b). This indicates that, over North America, the snow depth simulated by the LSM used in the ERA5-Land is vastly different from that by the CoLM and the LSMs used in the GLDAS and MERRA2. Regardless of the benchmark datasets, the large negative BIAS in simulating snow water content by the CoLM occurs in late winter and early spring, and so does the large improvement by assimilation for snow depth.

Taking into account the seasonal variations in snow depth, RMSDd is shown in Fig.  (summer time is not shown here due to the relatively small magnitude). In general, improvements are observed for most regions in the Northern Hemisphere throughout the year and different seasons, with the largest enhancements (up to 150 mm in February) centered in Northwest Asia. Consistent with snow temperature, the assimilation yields the largest RMSD reductions in winter (RMSD based on GLDAS reduces over 100 mm in northwest Asia as shown in Fig. e), with relatively small improvements in other seasons.

After discussing the results of the water content above the soil layers, the remainder of this section focuses on the water content (solid plus liquid phase) within the soil layers, as shown in Figs.  and . It can be observed from Fig. a and c that large uncertainties emerge in the Northeast regions of North America and Northern Eurasia, as most of these regions are considered humid areas with high soil moisture. The minimum uncertainties are observed in Northern Africa, the Middle East, and the Junggar Basin, as most of these regions are regarded as arid areas with low soil moisture. These results show that CoLM has a relatively adequate simulation of soil moisture in regions with low humidity but an insufficient simulation of soil moisture in regions with high humidity.

Improvements in unbiased RMSD occur in regions with relatively large uncertainty in the soil moisture simulation. Three maximum enhancements are observed in North America, Northern Eurasia, and Northeast Asia, as shown in Fig. b and d. The largest improvements, centered on northern Asia based on MERRA2 datasets, reach a 40 % reduction. It is also noteworthy that significant improvements in soil moisture within the upper soil layer emerge in high latitudes in the Northern Hemisphere, suggesting the effectiveness of the assimilation scheme, which jointly updates temperature and water content to obtain more realistic and consistent updated model fields for energy and water content. In other words, while the updated soil water content has a direct influence on the mass of water, the temperature change in the upper soil layers also drives the water content to change its phase. This joint modification of soil moisture is most pronounced at mid- to high latitudes.

A comparison of the two experiments in different soil layers based on the GLDAS datasets is shown in Fig. . As the depth increases, the absolute value of the (unbiased RMSD)d increases and reaches its maximum in the deepest soil layer within 100–200 cm, as shown in Fig. d. The maximum improvements are observed in northern regions of South America, central Africa, southern Asia, and northern Asia, where most regions are humid. Conversely, large degradations can be found in central areas of North America, eastern South America, and northern Australia, where most regions are relatively dry. Furthermore, localized degradations in Fig.  also occur in western North America and parts of northern Asia, where strong nonlinearity during seasonal freeze–thaw transitions makes the exact timing of phase changes difficult to capture. Additionally, performance degradation around open waters, such as the Great Lakes, is likely caused by the artificial alteration of land–lake thermal gradients. Updating only land grids while excluding water bodies disrupts localized secondary circulations, thereby weakening the assimilation benefits in these specific boundary regions.

Increasing improvements are seen as the soil depth increases, which reveals that the soil moisture modified by the assimilation within the upper layers is transferred down to the deep layers through vertical exchange among soil layers (taking the Amazon Rainforest as an example, the largest reduction in unbiased RMSD is about 0.06, 0.12, 0.15, and 6.58 kgm-2 based on GLDAS datasets for soil layers of 0–10, 10–40, 40–100, and 100–200 cm, respectively). This conclusion aligns with those summarized from the soil temperature comparisons shown in Fig. . Unlike the surface layer, which has a strong connection with the above atmospheric conditions, the water stored in the deep layers can be regarded as a contribution from both the internal variation of soil water content within the layer and the accumulative effect of transferred modified signals from upper layers.

Furthermore, we attribute improvements in South America, central Africa, and southern Asia within the deepest soil layer to the high water conductivity in these humid areas, allowing for fast and efficient vertical transfer from the top soil layer to the bottom. In contrast, in central areas of North America, eastern South America, and northern Australia, it is challenging to transfer the modified information within the upper layers to the deep layers through vertical exchange owing to the relatively low water conductivity.

Although evaporation and heat flux do not directly feedback on the prediction of land surface variables in offline LSMs, they provide key insights for studies in coupled models. Comparing these crucial fluxes against established datasets allows us to assess the model's performance and sheds light on the effectiveness of assimilation in improving the representation of land-atmosphere interactions.

Large RMSD values are observed in eastern North America, northern South America, central Africa, and central Asia for all three variables (Fig. ). These regions are known for their high humidity, indicating relatively large uncertainties in the flux simulated by CoLM in humid regions. Conversely, there is relatively high confidence in areas with low humidity, such as northern Africa and the Middle East, as depicted in Fig. a, d, and h.

The Mediterranean region also exhibits a larger RMSD for evaporation from bare soil (Fig. a) compared with latent (Fig. d) and sensible (Fig. h) heat fluxes, which show no similarity of large RMSD. The RMSD in the Amazon Rainforest for evaporation (Fig. a) is not as significant as that for the latent heat flux (Fig. d). This difference between evaporation and latent heat flux can be attributed to the fact that evaporation from bare soil does not include transpiration from vegetation. There is abundant vegetation in the Mediterranean region and the Amazon Rainforest, where abundant vegetation enhances transpiration, thereby increasing latent heat flux while leaving bare-soil evaporation unchanged.

Obvious improvements can be found for the evaporative heat flux over western North America, the Tibetan Plateau, and Northeast Asia, as can be seen in Fig. b and c. The consistent pattern of RMSDd in soil moisture (Fig. b) and in evaporation (Fig. b) based on the ERA5-Land dataset can be attributed to the fact that the changes in soil moisture within the upper soil layers have a direct influence on the amount of evaporation. This consistency is also found in the comparison between Fig. a and Fig. c based on GLDAS datasets.

The large improvements in Fig. b and c for evaporation flux from the bare soil, are also observed over similar regions in Fig. e–g for latent heat flux regardless of the benchmark datasets. Additionally, considerable improvements in the Amazon Rainforest are consistent with the findings aforementioned, and highlight the importance of considering transpiration from vegetation.

Large degradations are observed in Alaska, western regions of North America, the Tibetan Plateau, and Northeast Asia, while considerable improvements are shown in the Amazon Rainforest, central Africa, and eastern Asia for sensible heat flux. The partition of the available energy between latent and sensible heat fluxes depends strongly on the soil moisture. Taking Fig. e and i based on the ERA5-Land dataset as an example, improvements are observed for both fluxes in regions with high humidity, such as the Amazon Rainforest and central Africa. In contrast, opposite patterns are observed in regions with relatively low humidity, such as western North America and Northeast Asia. This highlights that assimilation-induced changes in soil moisture can simultaneously modulate both fluxes, depending on the prevailing surface energy partitioning.

To further validate the assimilation impact on surface energy partitioning against independent ground truth, in-situ observations of sensible and latent heat fluxes from the FLUXNET2015 and AmeriFlux networks are incorporated. The corresponding site-specific evaluation is presented in Fig. . As illustrated in the spatial distribution (Fig. a), the assimilation scheme yields clear improvements at the majority of the evaluated sites globally. Most locations exhibit enhanced performance in both heat fluxes (green circles) or at least one flux variable (orange triangles). Quantitatively, the site-specific RMSDd (Fig. b) reveals consistent and often substantial error reductions for the latent heat flux across most stations. In contrast, the response of the sensible heat flux exhibits greater site-to-site variability, which aligns with the mixed regional patterns observed in the gridded comparisons.