In this study, a coupled terrestrial biosphere model, LPJ-PM, was used to simulate daily GPP and ET by assimilating satellite-derived LAI and SSM. The LPJ-PM is coupled from LPJ-DGVM and PT-JPLSM. The original input data in PT-JPLSM were all inherited from LPJ-DGVM, with the exception of relative humidity (RH) and surface soil moisture (SMOS and SMAP), including the initial LAI calculated by the LPJ-DGVM or assimilated LAI obtained through the LAI assimilation scheme, canopy height, and the fraction of absorbed photosynthetic active radiation (fPAR). The detailed processes of the LPJ-PM have been described in Li et al. (2020), and the flow chart for the coupling is shown in Fig. 1.

To improve the prediction capability of LPJ-PM, we designed three assimilation schemes: assimilating LAI only (LAI-only, output: ETLAI, GPPLAI), assimilating SSM only (SSM-only, output: GPPSM, ETSM), and joint assimilation of LAI and SSM (Joint LAI and SSM assimilation, output: ETjoint, GPPjoint), i.e., LPJ-VSJA framework) to test the assimilation performance for simulating GPP and ET.

The proposed LPJ-VSJA framework consists of four main components: the model operator (the LPJ-PM), the observation operator (to establish the relation between the assimilation variable and the observed variable), the observation series (GLASS LAI and SMOS or SMAP products), and the assimilation algorithm (POD4DVar). With the surface soil moisture constraint in the PT-JPLSM, the LPJ-VSJA corrects the output fluxes (GPP and ET in this study).

The experiment consisted of six steps.

Step 1. Initialize the LPJ-DGVM, and output the reference state variables without assimilation over the experimental period (2010–2018), referred to as the “control run” scenario.

The proper orthogonal decomposition (POD)-based ensemble four-dimensional variational (4DVar) assimilation method (referred to as PODEn4DVar) (Tian and Feng, 2015) has the advantage of avoiding the calculation of adjoint patterns as its incremental analysis field, which can be represented linearly by the POD base (transformed OP, observing perturbation, and MP, model perturbation). Moreover, the PODEn4DVar can simultaneously assimilate multiple-time observation data and provide flow-dependent (the flow-dependent is the ensembles of forecasting statistical characteristics in the t time) error estimates of the background errors. It has shown advantages in terrestrial assimilation, the Tan-Tracker system (a Chinese carbon cycle data-assimilation system; in Chinese, “Tan” means carbon) and radar assimilation (Tian et al., 2010, 2009, 2014; Zhang and Weng, 2015).

By minimizing the following initial incremental format of the cost function in the 4DVar algorithm, an analysis field can be obtained as follows: 9J(x′)=12(x′)B-1(x′)+12y′(x′)-yobs′TR-1y′(x′)-yobs′. Here, the x′=x-xb, y′(x′)=y(x′+xb)-y(xb), yobs′=yobs-y(xb), y=H[Mto→tk(x)]. x′(x1′x2′xN′) is the model perturbation (MP) matrix​​​​​​​, and y′y1′,y2′,…,yN′ is the observation perturbation (OP) matrix with N samples. Following Rüdiger et al. (2010), the LAI perturbation was set to a fraction (0.001) of the LAI itself. The perturbation of ETPM and ETLPJ conforms to a Gaussian distribution with a mean of 0 and a specified covariance (10 % and 5 % of the ETPM and ETLPJ at time t). The subscript b represents the background field, the superscript T represents a transpose, H is the observation operator of the LAI-only assimilation scheme as described in Sect. 2.2.1, and the SSM-only assimilation scheme is the PT-JPLSM (described in Sect. 2.1.2). M is the forecast model (LPJ-PM in this study), B is the background error covariance, R is the observation error covariance, and obs denotes observation.

Assuming the approximately linear relationship between OP(y′) and MP(x′), POD decomposition and transformation were successively conducted for OP and MP. The transformed OP samples (Φy=y1′y2′yn′) are orthogonal and independent, and the transformed MP samples (Φx=x1′x2′xn′) are orthogonal to the corresponding OP samples, where n is the number of POD modes.

The manifestation of the background error covariance is the same as the ensemble Kalman filter (EnKF; Evensen, 2004), and the incremental analysis xa′ was expressed by the Φx,n, and Φ̃yΦ̃y=n-1In×n+Φy,nTR-1Φy,n-1Φy,nTR-1. Finally, the optimal analysis xa is calculated as xa=xb+Φx,nΦ̃yyobs′. The detailed derivation process of the algorithm is described by a previous study (Tian et al., 2011).

In the ensemble-based method (Evensen, 2004), the number of ensemble members is usually fewer than that of the observation data and the degrees of freedom of the model variables, and spurious long-range correlations occur between observation locations and model variables. A practical method, the localization technique, is applied to address this issue (Mitchell et al., 2002). The final incremental analysis is rewritten as 10xa′=Φx,nΦ̃yyobs′C0dhdh,0⋅C0dvdv,0, where dh and dv are the horizontal and vertical distances between the spatial positions of state and observed variables, respectively; and dh,0 and dv,0 are the horizontal and vertical covariance localization Schur radii, respectively. The filtering function C0 is expressed as 11C0(r)=-14r5+12r4+58r3-53r2+1,0≤r≤1,112r5-12r4+58r3+53r2-5r+4-23r-1,1≤r≤2,0,2<r, where r is the radius of the filter.

The assimilation algorithm is mainly divided into two steps: (1) prediction, by running LPJ-PM in the current assimilation window and generating simulation results and background field vectors, and (2) update, the algorithm being used to calculate the optimal assimilation increment xa′ and analysis solution xa. The simulation results and the initial conditions of the model in the current window are updated using the analysis solution. The updated initial conditions were applied for model LPJ-PM prediction, and the above process was repeated.

The R2 (coefficient of determination), BIAS, and ubRMSD (unbiased root mean square deviation) between simulation and tower-based observations were applied for evaluation. In addition, a Taylor chart was also used to demonstrate the performance of two ET estimations with different SSM observations in terms of R, ubRMSD, and normalized standard deviation (NSD) on 2D plots, to display how closely the datasets matched observations in one diagram (Taylor, 2001). In the Taylor diagram, NSD represents the radial distance from the origin point and the correlation with the site observations as an angle in the polar plot. The ubRMSD is the distance between the observation and the model and is represented in the Taylor chart as a green semi-circular arc with point A as the center of the circle. The closer the model point to the reference point (Point A), the better the performance. This diagram is convenient and visual in evaluating multiple aspects of various models.

The error variance of GPP and ET products was estimated using the triple collocation (TC) approach (Stoffelen, 1998) to validate the global simulation in this study. The method has been extensively applied in the study of hydrology and oceanography (Caires and Sterl, 2003; Khan et al., 2018; O'Carroll et al., 2008; Stoffelen, 1998), particularly in SM studies (Chan et al., 2016; Kim et al., 2018). The TC provides a reliable platform for comparison of spatial assimilation results and in situ measurements. In this experiment, no calculation was performed on the non-vegetated areas, where the correlation was lower than 0.2, in order to have independent datasets and avoid correlated errors (crucial assumptions in TC) (Yilmaz and Crow, 2014).

In this study, the five products were divided into three product categories, including satellite products (MODIS and GOSIF GPP), reanalysis products (GLASS and GLDAS), and data-assimilation products (GLEAM ET and LPJ-VSJA) (C. Li et al., 2018). One product in each category was selected to form a group to calculate their error. The LPJ-VSJA product was set as the reference data.

For GPP products, GOSIF, GLASS, and LPJ-VSJA were treated as a group, and MODIS, GLASS and LPJ-VSJA were treated as another group to calculate the errors; the final errors were determined by the average of these two.

Similarly, to calculate the errors for ET, GLEAM, GLASS, and MODIS were chosen as a group; LPJ-VSJA, GLDAS, and MODIS were treated as a group; LPJ-VSJA, GLASS, and MODIS were considered a group. In order to reduce the influence of orthogonality hypothesis of error, the first and third groups are for indirect and effective comparison between LPJ-VSJA product and GLEAM product.

We screened over 300 eddy covariance (EC) flux sites across the globe from the FLUXNET2015 (https://fluxnet.org/data/fluxnet2015 dataset/, last access: 10 ​​​​​​​April 2021), AmeriFlux (https://ameriflux.lbl.gov/data-and-manifest/​​​​​​​, last access: 10 ​​​​​​​April 2021), and the HeiHe River basin (10.11888/Hydro.tpdc.270888, Xie, 2017) for the evaluation of assimilation performance over the period from January 2010 to December 2018. The in situ half-hourly latent heat flux (LE) and GPP data from the sites were aggregated into daily data. The daily gap-filled data were excluded if the percentage of gap-filled half-hourly values was more than 20 %. Then we corrected the data of energy non-closure using the Bowen ratio closure method (Twine et al., 2000) to improve the energy closure rate (Huang et al., 2015; Yang et al., 2020). The data were selected to cover the 2010–2018 period with at least 1 year of reliable data, and the result from the error of assimilation is relative to the LE value and seasonal variation (Purdy et al., 2018; Zou et al., 2017). It is essential to have available data every month during a 1-year period, and only days with less than 25 % missing data were processed per month (Feng et al., 2015). In addition, for flux tower data, the data were also excluded for the analysis if the SMAP/SMOS SSM data were not of good quality.

Finally, we identified a total of 105 sites across the globe encompassing five major biomes: grassland (18 for GPP and 19 for ET), savanna (11), shrubland (4), forest (49 and 53), and cropland (13 and 14). In the comparative analysis of the performance for simulating ET by assimilating SMOS and SMAP SSM data separately, we selected 46 AmeriFlux sites (Fig. S3) with at least 1 year of reliable data from 2015 to 2018 based on the simultaneous availability of SMAP and SMOS data, including grassland (19), savanna (11), shrubland (5), forest (23), and cropland (7). Figures S2 and S3 illustrate the location and distribution of the 105 and 46 EC flux tower sites, respectively. A more detailed description is summarized in Table S1 in the Supplement.

The GLASS LAI product with an 8 d time step (8 d average) and 5 km resolution was derived from MODIS and CYCLOPES surface reflectance and ground observations using general regression neural networks (GRNNs) (Xiao et al., 2013, 2016). The verification of the product using the mean values of high-resolution LAI maps showed that the GLASS LAI values were closer to these high-resolution LAI maps (RMSD = 0.78 and R2 = 0.81) (Xiao et al., 2016; Liang et al., 2013). Therefore, the GLASS LAI product has satisfactory performance and can be assimilated into terrestrial biosphere models.

The SMAP mission (Entekhabi et al., 2010) and SMOS mission (Jacquette et al., 2010), the two dedicated soil moisture satellites currently in orbit equipped with L-band microwave instruments, provide SSM retrievals. We chose the SMOS-L2 product and the SMAP-L3-Enhanced product, which both provide global coverage every 3 d for soil depth of 5 cm. Only good-quality SMAP and SMOS data were used. The grid cells with water areas larger than 10 % and those with less than 50 % good-quality data in 1 year were masked out, which alleviates the undesirable model simulations caused by the decrease in SMAP retrieval accuracy (Chan et al., 2016; O'Neill et al., 2010). We only adopted the data with an uncertainty below 0.1 m3 m-3, in the actual range (0.00–0.6 m3 m-3), and the temperature of the Land Surface Module (LSM) observation layer (the second layer) was higher than 2 ∘C (Blyverket et al., 2019).

The GLASS LAI, SMOS, and SMAP observations were resampled to 9 km for site simulation and 0.25∘ for regional simulation. The 8 d average of GLASS LAI was assimilated for each day, and the SMAP or SMOS SSM was assimilated every 3 d.

In this study, the meteorological, soil property, and CO2 concentration datasets were used to drive the LPJ-PM. The climate-driven datasets used for the initialization of the LPJ-DGVM are the atmospheric CO2 concentrations (1901–2018) of ice-core measurements and atmospheric observations at the Mauna Loa Observatory and CRU TS4.03 version Climate data from 1901 to 1930 provided by the Climatic Research Unit (CRU) of the Climate Laboratory, University of East Anglia, UK, including monthly precipitation, surface temperature, cloud cover and wet day. In the simulation period of 2010–2018, the Modern Era Retrospective-Analysis for Research and Applications Version 2 (MERRA-2) was adopted, and the variables used included precipitation, temperature, cloud cover, and relative humidity. Soil properties (including limited water content of vegetation at wilting points, field capacity, and soil porosity) from the Harmonized World Soil Database (HWSD) V1.2 dataset (Wieder et al., 2014) were selected as inputs to the PT-JPLSM model. Table 2 provides the spatial and temporal characteristics of the model-forcing datasets in the LPJ-PM (submodule: LPJ-DGVM and PT-JPLSM).

The GLASS LAI product, SMOS-L2 product, and the SMAP-L3-Enhanced product were assimilated to simulate GPP and ET. For site simulation, in order to maintain consistency with the SMAP Enhanced 3 Level product (Entekhabi et al., 2010), model-forcing data were resampled to a 9 km spatial resolution based on EASE-2 projection grid. In the global spatial simulation, the model-forcing datasets were resampled to 0.25∘ based on the bilinear method to ensure the consistency of spatial representation.

We used four global ET products and three global GPP products (S. Li et al., 2018; Li and Xiao, 2019; Wang et al., 2017) that was resampled to 0.25∘ to evaluate the performance of the model with the joint assimilation scheme. Table 3 shows the details of these GPP and ET products.

During the period 2010–2014, monthly GPPjoint and ETjoint performed differently in humid and sub-dry humid regions and semi-arid and arid regions (Fig. 8, Tables S2, S3). Overall, the GPP and ET simulations had good consistency with the tower data in the two regions. For GPPjoint, there was no significant difference in the correlation and fitting coefficients between the two regions. As for ETjoint, the fitting results and R2 values in the semi-arid and arid regions performed better than those in the humid and sub-dry humid regions, which also suggested the importance of SSM for ET estimation in water-limited areas.

On the daily scale, the original GPP simulations (GPPLPJ) performed better in the semi-arid and arid regions than in the humid and sub-dry humid regions with higher R2 and lower ubRMSD (Table S2).

The R2 and BIAS implied that the LAI assimilation alone had a better performance than the SSM assimilation alone. However, for sites in arid and semi-arid areas, the ubRMSD showed that the GPPSM improved better than GPPLAI, which both demonstrated SSM data are essential in water-limited regions. For GPPjoint, the shrubland in the semi-arid and arid regions had the lowest R2 values and the second lowest ubRMSD. The forest in the semi-arid and arid regions had the largest improvement after assimilation. In the humid and sub-dry humid regions, the GPPjoint of the savanna and cropland showed the largest improvement (R2 increased by 64.7 % and 71.1 %, respectively; ubRMSD decreased by 47.0 % and 31.8 %, respectively). The grassland in the semi-arid and arid regions had the highest R2, and the savanna by combining all indicators had the best assimilation results compared to other types in both regions.

Similar to ETjoint (Table S3), the ETLPJ in the semi-arid and arid regions was better than that in humid and sub-dry humid regions in terms of four evaluation indicators (ubRMSD decreased by 34.4 % in semi-arid and arid regions and the ubRMSD decreased by 30.9 % in humid and sub-dry humid regions compared with ETLPJ). The R2 and ubRMSD implied that the SSM assimilation alone had a better performance than the LAI assimilation alone, especially for sites in arid areas. and the BIAS showed that the ETLAI improved better than ETSM for sites in humid and sub-dry humid areas. The performance of the original simulation and assimilation of grassland sites in the semi-arid and arid regions was the best among all five PFTs.

To investigate the reasons for better assimilation performance in water-limited regions, we evaluated the GPP and ET simulated by the LPJ-PM according to R2, ubRMSD, and BIAS (Fig. 9). Compared with the semi-arid and arid regions, the humid and sub-dry humid region had smaller R2 mean, larger BIAS, and no significant difference in mean ubRMSD for GPPSM. In general, the evaluation results of joint assimilation for ETPM were generally consistent with those for GPPSM and GPPSM. ETPM showed underestimation, which was consistent with the underestimation in SSM assimilation. These results indicated that both GPP and ET modeled by LPJ-PM with joint assimilation were less stable and had a lower performance in the humid and sub-dry regions than in the semi-arid and arid regions.

The Taylor chart was used to compare the assimilation performance of ETSMAP and ETSMOS at 46 AmeriFlux sites (Fig. 10 left). The results showed that ETSMAP performed better than ETSMOS for most PFTs, except forest. Both ETSMAP and ETSMOS performed well for grassland (closer to point A), and there was little difference between R2 and ubRMSD. The NSD of ETSMAP in grassland was 0.88, which was closer to 1 than that of ETSMOS. The assimilation of ET had a lower R2 and higher ubRMSD (0.7–0.8) in forest than other PFTs, and the NSD of cropland and shrubland was lower than that of other PFTs (0.6–0.8), indicating that the assimilation for cropland and shrubland could not reproduce the variations in ET effectively. However, ETSMAP showed significant improvement in R2 compared with ETSMOS for shrubland and cropland. The assimilation performance of ETSMAP and ETSMOS for savanna showed the greatest difference. In general, the ETSMAP and ETSMOS were slightly different, and the ETSMAP was more improved than ETSMOS.

Figure 10 (right) shows the assimilation accuracy of ETSMOS and ETSMAP in different humid and arid regions. The ETSMAP had significant advantages for the four indicators. The R2 of ETSMAP was higher than that of ETSMOS in all the areas. However, ETSMOS in some evaluation indicators showed a better performance than ETSMAP (BIAS in the humid region; ubRMSD in the sub-dry humid region). This may be due to the overall more humid nature of SMOS SSM than the SMAP SSM. Moreover, the sensitivity of deep soil moisture contributed more to the ET in humid areas than in the water-limited areas.

To assess the spatial scalability of the LPJ-VSJA assimilation scheme, we simulated the global daily GPP and ET for 2010–2018 with a spatial resolution of 0.25∘. The original results simulated by the LPJ-DGVM and LPJ-VSJA were referred to as LPJ-DGVM GPP(ET) and LPJ-VSJA GPP(ET), respectively. We compared the annual spatial GPP and ET values and the error standard deviation of the LPJ-VSJA with several existing flux products.

Figures 11 and 12 depict the spatial distribution of the annual mean and the differences between our simulation results and the global independent satellite-based products. The developed LPJ-VSJA GPP was the closest to GOSIF GPP (Li and Xiao, 2019) in most regions with the lowest spatial mean deviation (LPJ-VSJA-GOSIF) (27.9 g C m-2 yr-1), followed by GLASS GPP (51.2 g C m-2 yr-1) (Yuan et al., 2010), LPJ-DGVM (-73.4 g C m-2 yr-1), and MODIS GPP (93.1 g C m-2 yr-1). LPJ-VSJA had higher GPP values than GOSIF GPP in tropical regions, such as Amazonia, Central Africa, and Southeast Asia. In general, the annual mean and differences between MODIS, GOSIF GPP, LPJ-DGVM, and our LPJ-VSJA were in broad agreement (with higher R2 ranging from 0.74 to 0.95).

LPJ-VSJA ET was the closest to GLEAM ET on the spatial average with the least spatial average deviation (-13.9 mm yr-1) and highest R2 (0.88), followed by GLASS ET (-23.1 mm yr-1 and 0.82), GLDAS ET (-34.7 mm yr-1 and 0.73), LPJ-DGVM (-48.7 and 0.66 mm yr-1), and MODIS ET (-122.1 and 0.54 mm yr-1).

Figure 13a–e represent the spatial error standard deviation (σ) distribution of MODIS, GLASS, GOSIF, and LPJ-VSJA GPP, respectively. The graphs on the right side depict the corresponding histograms. The σ of the MODIS GPP was evenly distributed between 30 and 60 g C m-2 per month, while the average σ of other products was concentrated in 0–20 g C m-2 per month (90 %). The high errors of all products were concentrated in the hot and humid areas of southern North America, eastern South America, humid and dry sub-humid areas of South Asia, and the savannas of Africa and Australia. The error histogram of GOSIF GPP and LPJ-DGVM GPP was in line with the normal distribution, with an average value of 8.3 and 22.4 g C m-2 per month. The GLASS GPP product had the lowest mean value (3.6 g C m-2 per month), followed by LPJ-VSJA (4.7 g C m-2 per month), but the error variance of the LPJ-VSJA product was the lowest, indicating the stability of the regional error (Table S4). Compared to the LPJ-DGVM, the joint assimilation results showed improvement in all regions (the average error reduced by 17.7 g C m-2 per month), especially in the humid regions of South Asia, Australia, and the United States. Our LPJ-VSJA GPP was generally proven to have high accuracy and stability for spatial analysis and could provide a reference for other model products.

Figure 14a–f show the σ of MODIS, GLDAS, GLEAM, GLASS, and LPJ-VSJA ET (the units are millimeters per month), and the right graphs are the corresponding histograms. The σ values of GLDAS and LPJ-VSJA represented a normal distribution trend. Except for MODIS, GLASS, and LPJ-DGVM (0–60 mm per month), the σ of other products was generally between 0–20 mm per month. The simulation error was relatively smaller in the Northern Hemisphere than in the Southern Hemisphere, especially for GLASS ET and GLDAS ET. Significant improvements in joint assimilation were observed in the Northern Hemisphere (especially in the semi-arid areas of the western United States and savanna and cropland areas of central India) and African savanna areas, and the average error was reduced by 15.1 mm per month. In general, the error mean and variance of LPJ-VSJA and GLEAM products were relatively low (Table S4), and there was no apparent extremely high-value region in the error distribution. Among the five products, LPJ-VSJA had the lowest error mean and variance and the highest accuracy.

The benefit of employing multiple data flows in an assimilation system is the complementarity of the data, which enables constraints on different components of the underlying process-based terrestrial biosphere model. Due to the interaction and feedback between the internal components of the model, the assimilation of multiple observations has a synergistic effect, and the integrated constraints are greater than the individual constraint (Kato et al., 2013). The advantage of our joint assimilation is that it can improve the simulation accuracy of both GPP and ET, especially ET, in arid and semi-arid regions.

In the GPP assimilation experiment, the performance of the LAI assimilation was better than that of the SSM assimilation possibly for two reasons: (1) the LPJ-VSJA is more controlled by LAI data because the ratio of assimilated LAI (daily input) to SSM observations (3 d interval input) is approximately 3 : 1, which makes the likelihood function biased to LAI data; and (2) the SM directly influences the simulation of ET, and the corresponding time function (computes the top layer SM – 50 cm) used here by Zhao et al. (2013) will result in the error of the updated top SM and propagating the error to the GPPSM. In addition, the 8 d interval LAI has the capability to capture the temporal variability of phenology.

Current studies on terrestrial water and carbon flux assimilation mostly focus on the assimilation between a single model framework and observation results, lacking the fusion and comparison between multiple models. The processed models used in DA are simplifications and approximations of reality, and different models focus on different ecological processes. In this study, the updated ET module was integrated to compensate for the simplification of soil stratification and the lack of SM information in the hydrological module of the LPJ-DGVM. Therefore, the integration of multiple types of models and multi-source observation data (remotely sensed data, ecological inventory data; National Ecological Observatory Network, NEON; Keller et al., 2008) and other measurements (Desai et al., 2011; Hayes et al., 2012) is expected to more objectively and effectively simulate the real state of ecosystems.

Global GPP and ET for different products were calculated by multiplying the global mean GPP density flux by the global vegetation area (122.4×106 km2) that originated from the MODIS land cover product (Friedl et al., 2010). The mean global GPP of the LPJ-VSJA (130.2 Pg C yr-1) was approximately 12 % lower than that of PML-V2 (145.8 Pg C yr-1) and 18 % higher than that of GLASS and MODIS, respectively (Table S6). The GPP values of LPJ-VSJA and GOSIF were the most similar. The GOSIF GPP was developed from gridded solar-induced chlorophyll fluorescence (SIF) using simple linear relationships between SIF and GPP. Our global LPJ-VSJA GPP estimates were within the currently most plausible 110–150 Pg C yr-1 range.

As for ET, our results were similar to those of GLEAM ET and lower than those of PML-V2, GLDAS-2, and GLASS ET (∼ 72 000 km2 yr-1). Joint assimilation improved the overestimation of LPJ-DGVM ET. At the daily scale, the estimation accuracy of PML-V2 and GLDAS-2 products, calibrated with flux tower data, was better than that of our estimates, which suggests underestimation of LPJ-VSJA ET in wet regions. It is likely because the SSM of SMAP or SMOS was underestimated in the wet region, or the influence of deep SM was underrepresented. According to Seneviratne et al. (2010), satellite-based ET estimation approaches often overestimate ET in areas of arid and semi-arid climatic regimes in the magnitude of 0.50 to 3.00 mm d-1. The poor performance of these models can largely be attributed to the lack of constraints of SSM or RZSM and more accurate vegetation parameters (Gokmen et al., 2012; Pardo et al., 2014). For instance, the monthly estimated ET modeled by the Penman–Monteith–Leuning (PML) model agreed with flux tower data well (R2 = 0.77; BIAS = -9.7 %, approximately 0.2 mm d-1). Our annual ET simulations were lower than other products and slightly underestimated tower ET with a BIAS of 0.19 mm d-1 (ETOBS–ETjoint).

In general, GPP and ET had better assimilation performance in arid and semi-arid regions than in humid and sub-dry humid regions, likely because of the following reasons. First, the incorporation of SSM is more important for vegetation growth in water-limited areas. The module PT-JPLSM has been proven to have better performance in semi-arid and arid regions (Purdy et al., 2018). Our integrated model LPJ-PM also performed better in semi-arid and arid regions by assimilating SMAP soil moisture (Li et al., 2020). Second, the input performance, including SMOS and SMAP SSM products, is better in arid and temperate regions than in cold and humid regions (Zhang et al., 2019). Third, the vegetation types in humid regions are more complex and relatively less accurately simulated by the LPJ-DGVM within a single grid cell. For comparison, Zhang et al. (2020) used a data-driven upscaling approach to estimate GPP and ET in global semi-arid regions. This data-driven approach (R2 = 0.79, RMSD = 1.13 g C m-2 d-1) had slightly higher performance in estimating GPP than our LPJ-VSJA (R2 = 0.73 and RMSD = 1.14 g C m-2 d-1), and the data-driven method (R2 = 0.72 and RMSD = 0.72 mm d-1) had identical performance for estimating ET with our LPJ-VSJA (R2 = 0.73 and RMSD = 0.72 mm d-1).

Our assimilation performance varied with PFT. The GPP and ET assimilation results of savanna sites performed well in both dry and wet regions, and those of shrubland sites showed the most remarkable improvement for simulations of LPJ-DGVM. The original simulation and assimilation performance of grassland sites in the semi-arid and arid regions were the best for all five PFTs. Consistent with our research, previous studies also showed better GPP or ET simulations for grassland, savannas, and shrublands biomes. For instance, Feng et al. (2015) validated five satellite-based ET algorithms for semi-arid ecosystems and concluded that all the models produced acceptable and relatively better results for most grassland, savanna, and shrubland sites. Yang et al. (2017) demonstrated that the GLEAM ET had a superior performance for the grassland sites. The GOSIF GPP demonstrated better simulation for grassland and woody savannas sites at 8 d time steps with higher R2 (0.77 and 0.83, respectively) and lower RMSD (1.48 and 1.1 g C m-2 d-1) (Li and Xiao, 2019). In contrast, our LPJ-VSJA GPP showed an R2 of 0.87 for grassland and 0.75 for savannas and an RMSD of 1.11 and 1.1 g C m-2 d-1, respectively, in semi-arid and arid regions.

Our validation results at both site and regional scales indicated that uncertainty existed in LPJ-VSJA daily GPP and ET estimates. The errors from the tower EC observations, model-driven data, model structure, error of satellite-based observations (e.g., LAI and SSM), and the spatial scale mismatch between the ground observed footprint size and satellite-derived footprint size were the vital factors affecting assimilation performance.

First, recent studies have revealed errors in the GLASS LAI and SMOS or SMAP SSM compared with ground measurements. By computing the RMSD and R2 of each product, the GLASS LAI accuracy was clearly superior to that of MODIS and Four-Scale Geometric Optical Model-based LAI (FSGOM) in forests, and GLASS and FSGOM led to much higher annual GPP and ET estimates compared to MCD15 (Liu et al., 2018). The vegetation type (or land cover) misclassification caused 15 %–50 % differences in LAI retrieval (Fang and Liang, 2005; Gonsamo and Chen, 2011). Yan et al. (2016) calculated a RMSD of 0.18 for the GLASS LAI over a range of HeiHe River basin sites and used the error to improve the simulation of LAI and fluxes by assimilating GLASS LAI data. Previous studies reported an improvement in the performance of the SMOS and SMAP products (Lievens et al., 2015; Miernecki et al., 2014), which both provide an accuracy of 0.04 m3 m-3 (Zhang et al., 2019). However, the actual observation error of these two products typically depends on the spatial location and time of the year (RMSD varying between 0.035 and 0.056 m3 m-3 for several retrieval configurations) (Brocca et al., 2012). According to Purdy et al. (2018), the ET simulated by PT-JPLSM using the 9 km SM_L3_P_E data showed an inferior agreement (R2 = 0.47) but a relatively low RMSD (0.77 mm d-1), due to the SMAP errors in the grid cell with soil heterogeneity and the climatological differences between model SM forecasts and SMAP SSM (Reichle and Koster, 2004). We rescaled the ETPM to the probability distribution of the ETLPJ through a cumulative distribution function (CDF) to correct the potential seasonal biases of ETPM before assimilation.

Second, there is large uncertainty in the influence of RZSM as the source of water available to plants (Albergel et al., 2008; Bonan et al., 2020). Our GPP results of irrigated sites were largely influenced by US-Ne1, an irrigated site. This site maintained high annual GPP in 2012 despite the drought (Fig. S4). However, the SMOS SSM in 2012 had a lower SSM annual mean than the site observations, likely because the detected soil layer (0–50 cm) of the site observation is deeper than that of the satellite retrieval, and the cumulative deep soil moisture due to the regular irrigation was higher than the SSM that could easily be vaporized during the drought period (Fig. S4). Therefore, the influence of deep SM of some cropland sites during the drought years induced large simulation errors and unsatisfactory assimilation performance. Moreover, some deep-rooted forests maintain a high LAI during drought by absorbing deep SM (> 2 m) and groundwater (Zhang et al., 2016). Thus, joint assimilation of the LAI and SSM may eliminate a portion of the underestimation of GPP of such vegetation in drought periods. Therefore, further research is needed on how to optimally utilize satellite SM data for improving GPP and ET simulations.

Third, the problem of mixed pixels and mismatches in the observation footprints may also have an influence on the accuracy of estimated GPP and ET. The 5 km spatial resolution of the GLASS LAI, 9 km of SMAP, and 25 km of SMOS products cannot capture the sub-grid-scale condition, especially in grid cells for complex land surfaces or strong soil heterogeneity. To ensure the consistency of the grid-cell representativeness for the LAI and SSM, the interpolation results in errors that propagate through the modeling and assimilation, causing the accumulation of output errors (Nijssen and Lettenmaier, 2004). Moreover, the shrubland in the LPJ-DGVM was most likely simulated as C4 grassland in the hydrothermal condition of semi-arid and arid regions. In contrast, the shrubland tended to be hybrid vegetation types (grassland mixed with other types of forest vegetation) in the hydrothermal condition of humid and sub-dry humid regions, and the simulated canopy height is closer to the real condition of shrubland. This might also be the reason for the superior performance of ETLPJ and assimilation results of shrubland sites in humid and sub-dry humid regions.

When assimilating multiple data streams, all data streams could be in the same optimization (simultaneous assimilation) or use a sequential (step-by-step) approach. Mathematically, simultaneous optimization is optimal because strong parametric connections are maintained between different processes. However, complications may arise due to computational constraints related to the inversion of large matrices or the requirement of numerous simulations, particularly for global datasets (e.g., Peylin et al., 2016), and due to the “weight” of different data streams in the optimization (e.g., Wutzler and Carvalhais, 2014). This is particularly true when considering a regional- to global-scale, multiple-site optimization of a complex model that contains many parameters and which typically takes on the order of minutes to an hour to run a 1-year simulation. In practice, it is very difficult to define a probability distribution that properly characterizes the model structural uncertainty and observation errors, accounting for biases and non-Gaussian distributions. Nevertheless, a step-wise assimilation may be useful in dealing with possible inconsistencies on a temporary basis, since the parameter error covariance matrix must be propagated at each step. It is worth noting that the deviation between the model and observational data should be solved in the process of step-wise assimilation; for example, the joint assimilation in this study, the satellite observations, and model simulation were integrated using the CDF method so that the first step of the assimilation will strongly constrain the uncertainty of parameters related to phenology and carbon flux and propagate to the second step. Alternative solutions were found for water-related parameters through soil moisture, providing a better fit for all data streams. The sequence of assimilation is essential in the step-wise assimilation, and if the first observation contains a strong BIAS, then the associated error correlation will also propagate through the first assimilation. If the autocorrelation in the observation error, or the correlation between the data stream errors is not considered, it is likely that the posterior simulation has been overturned. That is, we overestimate the reduction in parametric uncertainty. If two observational data are less uncertain (i.e., high precision of observation data), the model of deviation is smaller (depending on the spatial scale and inversion method). Moreover, the correlation of these observations is stronger, and they contain enough spatiotemporal information to limit all the parameters' optimization accurately, and the step-wise assimilation performance is basically the same as that of simultaneous assimilation.