The ISBA LSM aims to simulate the evolution of LSVs such as soil moisture, soil heat or biomass . In this paper we use the ISBA multilayer diffusion scheme which solves the mixed form of the Richards equation for water and the one-dimensional Fourier law for heat . The soil is discretized in 14 layers over a depth of 12 m. The lower boundary of each layer is 0.01, 0.04, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, 2.0, 3.0, 5.0, 8.0 and 12 m depth see Fig. 1. of. The chosen discretization minimizes the errors from the numerical approximation of the diffusion equations.

Regarding vegetation dynamics and interactions between the water and carbon cycles, we use the ISBA-A-gs configuration . This CO2-responsive version represents the relationship between the leaf-level net photosynthesis rate (A) and stomatal aperture (gs). Dynamics of vegetation variables such as LAI or biomass are induced by photosynthesis in response to atmospheric variations. The LAI growing phase from a prescribed threshold (1.0 m2 m-2 for coniferous trees, 0.3 m2 m-2 for every other type of vegetation) results from an enhanced photosynthesis and CO2 uptake. On the contrary, a deficit of photosynthesis leads to higher mortality rates and a decreased LAI. Leaf biomass is determined from LAI (and vice versa) through dividing LAI by the specific leaf area (one of the ISBA parameters depending on the vegetation type). For arctic regions, hydraulic and thermal soil properties are modified in order to include a dependency on soil organic carbon content .

From a practical point of view, ISBA is run in this paper at a regular 0.25∘ spatial resolution. Each ISBA grid cell is divided into 12 generic patches: nine representing different types of vegetation (deciduous forests, coniferous forests, evergreen forests, C3 crops, C4 crops, C4 irrigated crops, grasslands, tropical herbaceous and wetlands) and three others depicting bare soils, bare rocks and permanent snow or ice surfaces. Each patch covers a varying percentage of grid cells. Denoted α[p] for patch p of a given grid cell, this percentage is also known as the patch fraction. Vegetation and soil parameters for each ISBA patch and grid cell are derived from the ECOCLIMAP II land cover database , which is fully integrated in SURFEX.

The ISBA LSM is coupled with CTRIP to simulate hydrological variables at a continental scale. Based originally on the work of , CTRIP aims to convert simulated runoff into simulated river discharges. The model is fully described in the following papers: , , , , and .

CTRIP is available at a 0.5∘ spatial resolution. The coupling between ISBA and CTRIP occurs on a daily basis through the OASIS3-MCT coupler (Model Coupling Toolkit of the OASIS coupler) . ISBA provides updated runoff, drainage, groundwater and floodplain recharges to CTRIP, while the river routing model returns the water table depth or rise, floodplain fraction, and flood potential infiltration to the LSM.

LDAS-Monde is a sequential data assimilation system with a 24 h assimilation window. Each cycle is divided in two steps: forecast and analysis. Quantities produced during the forecast step (analysis step) are denoted with a superscript f (superscript a). The state of the studied system is described by x[p], the control vector that contains every prognostic variable of the ISBA LSM for a patch p and a given grid point. In this paper, we consider LAI and soil moisture from layers 2 (1–4 cm depth; SM2) to 7 (60–80 cm depth; SM7) in the control vector, with soil moisture in layer 1 being driven mostly by atmospheric forcings . As in many LDASs, LDAS-Monde performs DA for each grid point independently (no spatial covariances are considered).

The forecast step consists of propagating the state of the system from a time t to t+24 h using ISBA. Patches in each ISBA grid cell do not interact between each other. This implies that, for a patch p, the forecast of x[p], denoted by x[p]f(t+24h), only depends on the analysis at time t, x[p]a(t) and the ISBA LSM using the parametrization for patch p, denoted by M[p]. This yields 1x[p]f(t+24h)=M[p]x[p]a(t). The analysis step then corrects forecast estimates by assimilating observations of LAI and SSM.

The ISBA LSM is forced with the ERA5 atmospheric reanalysis developed by ECMWF. The ERA5 reanalysis is available with an hourly frequency at a 31 km horizontal spatial resolution. To be used, surface atmospheric variables such as air temperature, surface pressure, solid and liquid precipitations, incoming shortwave and longwave radiations values, and wind speed are interpolated to a 0.25∘ spatial resolution using bilinear interpolation. Replacing ECMWF's atmospheric ERA-Interim reanalysis with ERA5 has been shown to be beneficial in the context of LSV reanalyses with LDASs .

In this paper we assimilate observations from the SWI-001 and GEOLAND2 version 1 (GEOV1) LAI datasets, both being distributed by the Copernicus Global Land Service. These satellite-derived products have already been successfully assimilated into LDAS-Monde e.g..

The SWI-001 product consists of soil water indices obtained through a recursive exponential filter using backscatter observations from the ASCAT (Advanced SCATterometer) C-band radar . A 1 d timescale is used in the recursive filter in order to estimate the wetness of the first centimetres of the soil. This product is available daily at a 0.1∘ spatial resolution. The raw SWI-001 averaged over the 2008–2017 period can be seen in Fig. a.

Prior to the assimilation, the SWI-001 product needs to be rescaled to the model climatology to avoid introducing any bias in the LDAS system . We apply a linear rescaling to SWI-001 to match the observation mean and variance to the mean and variance of the modelled soil moisture in the second layer of soil (1–4 cm). Introduced by , this rescaling gives in practice very similar results to CDF (cumulative distribution function) matching. The linear rescaling is performed on a seasonal basis (with a 3-month moving window). and have highlighted the importance of allowing seasonal variability in the rescaling.

The GEOLAND2 version 1 LAI product is obtained through a neural network algorithm transforming observations of reflectance from SPOT-VGT and PROBA-V satellites into LAI. This dataset is available every 10 d with the finest spatial resolution being 1 km. The GEOV1 LAI averaged over the 2008–2017 period can be seen in Fig. b.

Following , both observation datasets are interpolated on the model grid (0.25∘ spatial resolution) where and when at least half of the observation grid points are available. As in previous LDAS-Monde studies, we use a 24 h assimilation window, and observations are assimilated at 09:00 UTC.

We consider independent datasets of evapotranspiration (ET), gross primary production (GPP) and river discharges to assess the validity of our approach and measure the influence of the EnSRF on the improvement of LSV reanalyses.

Satellite-derived estimates of ET come from the GLEAM v3.3b product . Daily estimates available for the period 1980–2018 at a 0.25∘ spatial resolution are fully driven by satellite observations and, as such, are independent of LDAS-Monde estimates. Figure c displays GLEAM ET averaged over the period 2008–2017 considered for validation in this paper.

Observations of GPP are derived from the FLUXCOM project. This dataset is obtained by merging upscaled measurements from eddy-covariance flux towers and satellite observations using machine learning. More details can be found in and . The FLUXCOM data are available at a 0.5∘ spatial resolution on a monthly basis for the period 1982–2013. Figure d shows FLUXCOM GPP averaged over the period 2008–2013 considered for validation in this paper.

River discharge output data from the CTRIP river routing model are compared to daily streamflow data obtained from the Global Runoff Data Centre (https://www.bafg.de/GRDC, last access: 16 January 2020). Due to the low resolution of CTRIP (0.5∘ spatial resolution), we only consider data for sub-basins with rather large drainage areas (greater than 10 000 km2) with a long enough time series (4 complete years or more over 2008–2017).

To assess the impact of EnSRF on LSV reanalyses and compare its skill with the routinely used SEKF, we have run LDAS-Monde over the Euro-Mediterranean region (longitude from 11.5∘ W to 62.5∘ E, latitude from 25.0∘ N to 75.5∘ N) at a 0.25∘ spatial resolution during the decade 2008–2017 for three different configurations: one model run without assimilation (i.e. open loop), one using the SEKF and another one using the EnSRF with a 20-member ensemble. This size of the ensemble is consistent with and . All three configurations start from the same initial state obtained after spinning up ISBA–CTRIP 20 times over 2008. This provides an initial state for which the system has reached equilibrium.

For the SEKF configuration, the Jacobian matrix Eq. () is obtained by finite differences using perturbed model runs. Following and subsequent studies, perturbations are taken proportional to the dynamic range (difference between the volumetric field capacity wfc and the wilting point wwilt) for the soil moisture variable. In practice, perturbations for SM are set to 10-4×wfc-wwilt. Regarding the fixed background error covariance, we prescribe a mean volumetric standard deviation (SD) of 0.04 m3 m-3 for SM in the second layer and 0.02 m3 m-3 for SM in deeper layers, both are then scaled by the dynamic range of SM. For LAI, perturbations are set to a fraction (0.001) of the modelled LAI following . LAI background error SD is set to 20 % of the LAI value for modelled values above 2.0 m2 m-2 and to a constant 0.4 m2 m-2 for modelled values below 2.0 m2 m-2. This SEKF configuration is the same as the one detailed in .

About the EnSRF configuration, the initial ensemble is obtained by perturbing the initial state using perturbations sampled from a multivariate Gaussian distribution with a zero mean and using the prescribed B covariance matrix used in the SEKF as the covariance matrix of that multivariate Gaussian distribution. Ensemble Kalman filters tend to underestimate variances and ensembles spreads. This brings about an artificially small spread leading ultimately to filter divergence if not counteracted. has shown that adding random perturbations to each ensemble member (additive inflation) at the start of each assimilation cycle can overcome this issue. It can also be used to represent model error. As in we use time-correlated model errors using a first-order auto-regressive model. We prescribe an associated Gaussian noise with zero mean and an SD of λwfc-wwilt for SM, with λ=0.5 for SM in layer 2 (1–4 cm depth), 0.2 for SM in layer 3 (4–10 cm depth), 0.05 for SM in layer 4 (10–20 cm depth) and 0.02 for SM in deeper layers. These values are in line with . For LAI, we prescribe a Gaussian noise with zero mean and an SD of 0.5 m2 -2. We also fix the time correlation to 1 d for SM in the second layer and 3 d for SM in deeper layers. This is similar to the work of and . For LAI, a rather small 1-day time correlation has to be used in order to avoid a collapse of the ensemble during the winter season due to the LAI threshold in ISBA.

For both SEKF and EnSRF configurations, we follow previous LDAS-Monde studies and set SSM observational errors to 0.05 m3 m-3 scaled to the dynamic range and LAI observational errors to 20 % of the observed LAI values see e.g.

As a check, we first verify that EnSRF estimates of SSM and LAI are closer to observations than their open-loop counterparts. We also compare the impact of EnSRF and SEKF on SM in layer 2 (1–4 cm depth; SM2) and LAI. This is achieved using scores such as biases, correlation coefficients (R), root mean square differences (RMSDs) and normalized root mean square differences (nRMSDs; RMSD divided by the averaged value of the studied variable).

The impact of assimilation on unobserved control variables (SM in deeper layers) is then assessed using a daily analysis increment. Moreover, we study the evolution of the ensemble correlations between unobserved and observed variables in the EnSRF configuration. They drive (as Jacobian values in the SEKF configuration) the influence of observations on unobserved control variables. We focus on SM in layer 4 (10–20 cm depth; SM4) and layer 6 (40–60 cm depth; SM6), as SM in layer 3 (4–10 cm depth) exhibits the same behaviour as SM4, and soil moisture in layer 5 (20–40 cm depth) and layer 7 (60–80 cm depth) have the same behaviour as SM6 (not shown).

Potential improvements in EnSRF and SEKF estimates of ET and GPP are measured using the same metrics as for SSM and LAI.

Finally the influence on river discharges for both DA approaches is measured by the Nash–Sutcliffe efficiency (NSE) score. 13NSE=1-∑t=1T(Qst-Qot)2∑t=1T(Qot-Q‾o)2, where Qst is the simulated or analysed river discharge at time t, Qto is the observed river discharge at the same time and Q‾o is the observed averaged river discharge. The NSE is a quantity between -∞ and 1. An NSE value of 1 means that the model or analysis perfectly matches observations. An NSE value of 0 means that the model or analysis has the same NSE as the observed averaged river discharge. Improvements or degradations caused by the SEKF or the EnSRF compared to the open loop is measured with the normalized information contribution index (NIC). 14NICNSE=100×NSEanalysis-NSEmodel1-NSEmodel

Figure  displays the open-loop, SEKF and EnSRF analyses and observed LAI 10 d time series averaged over Europe and the Mediterranean basin and spanning the period 2008–2017. It shows that the model simulation underestimates LAI compared to observations during winter and summer. The growing phase of vegetation occurs at a slower pace with averaged LAI reaching its maximum early August instead of late June to early July for observations. The senescence phase subsequently takes place later in the autumn compared to observations. Both DA systems efficiently correct model simulations for that latter phase. However, both SEKF and EnSRF fail to compensate for the slower LAI dynamics of the model during spring. This is in compliance with what and have observed over the Euro-Mediterranean region. During the growing phase, modelled LAI is more sensitive to atmospheric conditions than to initial LAI conditions. This implies that, while DA can artificially add LAI and biomass, its impact can be limited by the atmospheric forcing. During the senescence, LAI dynamics is driven by the rate of mortality, thus making DA more efficient.

As expected, both DA approaches produce estimates that are closer to the assimilated LAI observations than their open-loop counterpart. RMSDs are reduced from 0.880 m2 m-2 for the open loop to 0.671 m2 m-2 for SEKF and 0.694 m2 m-2 for EnSRF. Correlations with assimilated observations are increased from 0.593 for the model to 0.732 for SEKF and 0.723 for EnSRF. A full summary of statistics for LAI can be found in Table . We also note that the maximum LAI for EnSRF is smaller than the model or the SEKF maxima. The averaged bias for the open loop is rather small with -0.020 m2 m-2, but it hides a negative bias during winter and summer that is compensated for by a positive bias during autumn. DA approaches mostly correct the positive autumnal bias, thus making the averaged bias more negative, -0.116 m2 m-2 for the SEKF and -0.201 m2 m-2 for the EnSRF. The bias is more negative for the EnSRF than for the SEKF for every season. This is due in part to a systematic negative bias introduced by the EnSRF model perturbations. This bias can sometimes lead to degraded performances. As pointed out by , model perturbations can introduce a bias into the system in LDASs.

Figure  shows nRMSD calculated over 2008–2017 for the open loop (a) and the difference between nRMSD for the open loop and the estimates produced with SEKF (b) and EnSRF (c). On average nRMSD is reduced from 0.57 (open loop) to 0.42 (EnSRF) and 0.40 (SEKF). Both assimilation approaches display the same geographical patterns significantly reducing nRMSD over most parts of the Euro-Mediterranean region (in blue in Fig. ). For example, roughly 20 % of the domain has an nRMSD reduced by 0.25. We note that the largest nRMSD reductions occur in places where nRMSD is large. The main differences between the two methods occur in Ireland, western Great Britain, northwest Spain, the Alps, Scandinavia and Arctic regions, where the SEKF shows a greater positive impact than EnSRF, the latter even providing slightly degraded estimates compared to the open loop for 3 % of the total domain (in red in Fig. c).

The geographical patterns identified in Fig.  can be explained in part by the type of vegetation covering grid cells. We investigate the impact of DA for each of the four main vegetation types encountered in the Euro-Mediterranean region: deciduous forests, coniferous forests, C3 crops and grasslands. To that end, we consider only grid cells (GCs) in which at least 50 % of their surface is covered by one of these vegetation types. Figure  displays the spatial distribution of those grid cells: 1589 GCs for deciduous forests (5.7 % of the domain), 4223 GCs for coniferous forests (15.2 %), 1672 GCs for C3 crops (6.0 %) and 1725 GCs for grasslands (6.2 %). We calculate the averaged seasonal RMSD for the open loop and SEKF and EnSRF analyses for the entire domain (Fig. a) and for each dominant vegetation type (Fig. b–e). The biggest impact of assimilating LAI occurs in autumn for deciduous forests (Fig. e). For example, RMSD is reduced from 2.69 m2 m-2 for the open loop to 1.72 m2 m-2 for the SEKF and 1.45 m2 m-2 for the EnSRF. For C3 crops (Fig. c) both assimilation approaches reduce RMSD in a similar manner, the largest decrease happening between August and October. The SEKF and the EnSRF offer contrasting performances in the case of grasslands (Fig. d) as RMSDs are decreased by 0.18 m2 m-2 from the open-loop to SEKF estimates but by 0.09 m2 m-2 for EnSRF estimates. The largest RMSD reductions occur for both cases in April and September. This explains the reduced performance of the EnSRF compared to the SEKF over grasslands-dominated Ireland, western Great Britain and Arctic regions. For coniferous trees (Fig. b), the SEKF has a small positive impact on RMSDs, and the EnSRF has a slightly negative impact. This explains the rather poor performance of the EnSRF over Scandinavia. This also explains what happens in northwestern Spain and in the Alps. While not being dominated by one type of vegetation, coniferous trees and grasslands, the two types for which the EnSRF performs poorly, represent more than 70 % of the vegetation in those places.

The scale of reduction in RMSD for EnSRF analyses is directly connected to estimated variances and standard deviations from the ensemble. The bigger the ensemble variances are, the larger the weight of observations in the DA system is. Figure  displays the seasonal evolution of ensemble standard deviations averaged over the whole domain and for grid cells dominated by one type of vegetation. Ensemble standard deviations are clearly larger in summer than in winter peaking in July for C3 crops at 0.22 m2 m-2, in August for grasslands at 0.14 m2 m-2 and in September for coniferous forests at 0.07 m2 m-2. The maximum standard deviation is observed for deciduous forests and reaches 0.35 m2 m-2 also in September.

Standard deviations in the EnSRF relies heavily on the model perturbations. In the case of LAI, model perturbations applied to LAI in every vegetation patch are sampled from the same distribution. However, the behaviour of ensemble standard deviations varies greatly seasonally and for each type of vegetation. Standard deviations for coniferous trees are so low it leads to almost no impact of DA. Such behaviour can be explained by two caveats: first, ISBA-modelled LAI evolves over a prescribed threshold (1 m2 m-2 for coniferous forests, 0.3 m2 m-2 for other vegetation patches). Model perturbations can lead to LAI values below this threshold. To avoid model issues, estimated LAI is reset to that threshold when this is the case. It can lead to an artificially reduced ensemble standard deviation when modelled LAI is close to that threshold as in winter. Secondly, since LAI dynamics are smooth, reduced ensemble standard deviations due to the winter season still have an impact in spring through the ISBA LSM. An approach for model errors tailored for each vegetation patch could overcome the observed caveats.

This section studies the impact of assimilating jointly LAI and SSM on estimated SSM. We firstly recall that observed SSM is derived from the SWI-001 satellite product and is matched to the model climatology of soil moisture in the second layer of soil (1–4 cm depth) using a seasonal linear rescaling. This means that assimilating observed SSM mostly corrects the short-term variability of estimated SSM and does not modify its climatological seasonal cycle. Results from either SEKF or EnSRF experiments are in line with this statement. For example, the bias between observed and estimated SSM remains, on average over 2008–2017, below 0.002 m3 m-3 over all the domain (see also Table 1 all the averaged scores with observed SSM).

Figure  displays RMSD calculated over 2008–2017 for the open loop (a) and the difference between RMSD for the open loop and the estimates produced with SEKF (b) and EnSRF (c). On average, RMSD is reduced from 0.035 m3 m-3 (open loop) to 0.032 m3 m-3 (SEKF) and 0.027 m3 m-3 (EnSRF). RMSD for the open loop tends to be generally larger in wetter places than in drier places with the exception of southeastern Spain and parts of northern Africa where RMSDs can be larger than 0.050 m3 m-3. Both assimilation approaches significantly reduce RMSD in many places over the domain (in blue in Fig. b–c). The main reduction occurs for both approaches in the southern part of the Euro-Mediterranean region where grid cells consist of bare soil and bare rocks. In those places, vegetation is sparse, and SSM is the main source of information in assimilated observations, making its impact more straightforward. We also notice that the EnSRF tends to systematically produce estimates that are closer to observations than SEKF estimates. This is due to the model perturbations for the EnSRF and the prescribed background error covariance matrix in the SEKF. The prescribed model error for the EnSRF leads to ensembles with a bigger standard deviation than the one prescribed in the SEKF for SSM. This leads to a bigger weight to SSM observations in EnSRF than in SEKF, thus, making EnSRF estimates closer to SSM observations than SEKF estimates.

Assimilation also improves correlations with observed SSM from 0.544 for the open loop on average to 0.652 for SEKF and 0.760 for EnSRF. Figure  illustrates correlations for the open loop (a) and the difference between correlations for the open loop and SEKF (b) and EnSRF (c) outputs. From correlation results, similar conclusions are drawn as from RMSDs. In particular the main improvement occurs in northern Africa for both approaches. Finally we observe negative correlations between the open-loop and observed SSM (even with the seasonal linear rescaling) in arid places such as the Sahara and deserts in the Arabian Peninsula. This shows that the short-term variability of the observations is different from what we model with ISBA in this region. It raises the question of the quality of ISBA and/or SSM observations (after seasonal linear rescaling) in arid places. have shown that observed SSM derived from scatterometers can have poor quality in arid places. Further studies of such aspects are beyond the scope of this paper.

Examining Jacobians in the SEKF has provided interesting insights into the sensitivity of SSM and LAI on soil moisture in deeper layers see e.g.for coverage of the Euro-Mediterranean region between 2000 and 2012. In the EnSRF, the Jacobian is replaced by correlations sampled from the ensemble covariance matrix. Figure  shows maps of correlations between soil moisture in layer 2 (1–4 cm depth; SM2, which is used as a proxy for SSM) and SM in layer 4 (10–20 cm depth; SM4) and layer 6 (40–60 cm depth; SM6) and correlations between LAI and SM2, SM4 and SM6. Correlations are averaged by season (December–January–February, March–April–May, June–July–August and September–October–November) over the whole period 2008–2017.

The first two rows of Fig.  show the seasonal evolution of correlations between SM2 and SM4 and SM6. SM4 is highly correlated to SM2 (in blue), with R being above 0.5 for most places of the domain for each season. SM6 is also highly correlated to SM2, but it is to a lesser extent, meaning that correlations with SSM decrease in absolute value when we reach deeper soil layers. We also notice seasonal tendencies. For example, correlations with SM2 tend to be larger in western Europe during spring, while they reach their maximum during summer in Scandinavia. Negative correlations with SM2 (between -0.35 and -0.20) tend to appear during winter over Russia. It means that in those areas in winter, there is less liquid water in the surface when there is more liquid water in deeper layers. This is linked to snow and freezing as we only compare liquid soil moisture from the different layers of soil. We further notice that SM2 and SM6 are uncorrelated in summer over Spain and northern Africa. This decorrelation between surface and root-zone soil moisture occurs during very dry conditions, such as those which occurred in Spain and northern Africa during summer. The same phenomenon appears in very arid places such as in the Sahara. SM2 is not correlated to soil moisture in deeper layers such as SM4 or SM6 for each season. This implies that assimilating SSM in those areas will not modify soil moisture in deeper layers, as we will show in the next section.

The last three rows of Fig.  show the seasonal evolution of correlations between LAI and soil moisture in layers 2, 4 and 6. Soil moisture tends to be less correlated on average to LAI than to SSM; nevertheless the values reached are relatively large (between -0.5 and 0.5). It means that assimilating LAI has an impact on estimated soil moisture. In detail, correlations between LAI and SM6 are larger in absolute value than SM4 and SM2, meaning that LAI is more correlated to root-zone soil moisture than with SSM. We also observe seasonal geographical patterns. Positive correlations tend to appear in summer in northern Europe, where deciduous and coniferous forests are dominant, meaning more water in the soil leads to a greater LAI. On the contrary in spring and summer, negative correlations appear around the Mediterranean basin. This means a higher LAI leads to reduced soil moisture due to plant transpiration in part. has already highlighted this kind of behaviour for Jacobians for grassland places in southwest France.

Overall conclusions drawn from correlations are in accordance with those derived from the analyses of SEKF Jacobians drawn in over the Euro-Mediterranean region and over Burkina Faso. Nevertheless, we note that correlation can be influenced by the way we apply model error. Another type of model error, perturbing for example atmospheric forcing, may have led to different characteristics of the covariances between the ISBA variables.

Figure  displays soil moisture for layers 4 and 6 averaged over 2008–2017 from the open loop (left) and the averaged difference with SEKF estimates (central panels) and EnSRF estimates (right). We observe that the SEKF and the EnSRF overall have averaged SM4 values similar to the open loop. The main difference occurs in northern Africa and in the Arabian Peninsula, where the soil is estimated wetter than in SEKF, with a difference reaching 0.02 m3 m-3. This disparity over arid regions in due solely to a wet bias introduced by model error. In those places, EnSRF cannot correct this bias using observations of SSM or LAI. In other places, EnSRF can correct the bias potentially introduced by the model perturbations to unobserved control variables through the help of correlations. We also identify greater EnSRF SM4 estimates over places such as Poland and Spain, but the difference with the open loop is always below 0.01 m3 m-3.

Regarding SM6 estimates, both SEKF and EnSRF produce a drier soil layer than the model for most of the domain as shown in Fig. . We identify these patterns for every month without any seasonality (not shown). Also, EnSRF SM6 is wetter for regions where bare soil dominates in northern Africa than SM6 obtained with SEKF or the open loop. Again this is due solely to the wet bias introduced by model soil moisture perturbations as SM6 and SM2 are uncorrelated in those places. Then, we can observe for SM6 an abrupt change in the Arctic region for both SEKF and EnSRF compared to the open loop. This difference is due to modified hydraulic and thermal soil properties in ISBA for Arctic regions. This modification has been implemented by in order to include a dependency on soil organic carbon content.

Figure  shows analysis increments in SM4 for SEKF (top row) and EnSRF (bottom row) for May, July and September. We see that increments in SM4 tend to be negative in May and September in most parts of the domain and positive in July, particularly in northern Europe for SEKF. The SM4 analyses increments for SEKF and EnSRF tend to be similar, except for arid regions. This makes the SM4 estimates less dependent on the data assimilation method.

For analysis increments for SM6, SEKF increments are close to zero for every season (not shown). This implies that the drier estimates are solely due to the joint effect of the ISBA LSM and the updated LAI and soil moisture near the surface. For EnSRF, this joint effect also occurs, but analysis increments are not negligible (-0.01 m3 m-3 for the biggest values). The EnSRF SM6 analysis increments compensate for the wet bias from model error (not shown) and lead to similar SM6 estimates as the SEKF in most places as shown previously.

Overall SEKF and EnSRF provide similar estimates for soil moisture in deeper layers for most places but not necessarily through the same mechanisms.

We now evaluate the performance of our data assimilation systems using independent satellite-based datasets of ET and GPP.

The open loop tends to underestimate ET leading to an averaged negative bias of -0.328 kg m-2 d-1 reaching -0.8 kg m-2 d-1 in June and July. Both SEKF and EnSRF reduce this bias to -0.114 and -0.059 kg m-2 d-1, respectively. More statistics on ET can be found in Table 1. Figure  displays correlations between the GLEAM dataset and open-loop estimates (a) and the difference between correlations for the open loop and the estimates produced with SEKF (b) and EnSRF (c). Overall the correlation is increased on average from 0.789 to 0.803 (SEKF) and 0.823 (EnSRF). EnSRF provides estimates that are more correlated with this independent dataset for almost all grid cells; it improves correlation (between 0.05 and 0.1) especially over Spain, northern Africa or around the Caspian Sea, where correlations between the open loop and GLEAM were poorer than for the rest of the domain, showing its positive impact on ET. Similar conclusions can be drawn from geographical patterns observed for RMSD and nRMSD (not shown; see Table  for averaged results).

Figure  depicts the correlation between GPP from the FLUXCOM dataset and open-loop estimates (a) and the difference between correlations for the open loop and the estimates produced with SEKF (b) and EnSRF (c). As for ET, EnSRF provides GPP estimates that are more correlated to the FLUXCOM dataset than open-loop and SEKF estimates for almost everywhere, on average 0.817 compared to 0.784 for the model and 0.786 for SEKF. The biggest improvements are noticeable around the Caspian Sea (above 0.05), where correlations between the model and FLUXCOM GPP were poorer than for the rest of the domain. Also contrary to the SEKF, degradations are confined to only few places in Iraq, Iran and close to the Arctic Circle. Again similar conclusions can be drawn from geographical patterns observed for RMSD and nRMSD (not shown; see Table  for averaged results).

Overall the EnSRF exhibits moderate improvements for GPP and ET compared to SEKF.

We limit our evaluation to 92 stations over Europe with a model NSE above -1. The NIC of EnSRF compared to the open loop is displayed for those stations in Fig. . Most stations are located in France and Germany. Blue circles denote a positive impact (above 3 %) of EnSRF on estimated river discharges; red circles denote a negative one (below -3 %); and grey diamonds denote a neutral impact (between -3 % and 3 %). A positive NIC is observed for 61 stations and a negative NIC for only 11 stations. The rest of the stations (20) showed a neutral impact. The largest NIC values are seen for German stations. Such a positive influence for EnSRF contrasts with the rather neutral effect of SEKF on river discharges. In compliance with previous studies , we observe a significantly positive NIC of SEKF for only 15 stations and a negative NIC for 3 stations (not shown).

The rather systematic improvement of EnSRF estimates compared to the open loop may be due in part to the assimilation of SSM and LAI. It may also be due in part to a bias added by the EnSRF ensemble formulation (as observed for other LSVs) that compensates for an existing bias due to the coupling between ISBA and CTRIP. Further investigations have to be conducted to explore this question. Moreover, a negative NIC is observed for most of the Spanish stations, where anthropogenic effects (irrigation, importance of dams, etc.) can potentially modify soil moisture, streamflow and river discharges . Since CTRIP does not consider anthropogenic effects, this can explain poor performances of the LDAS–CTRIP system.

As seen in the previous section, the quality of EnSRF estimates highly depends on the specified model error. We have seen that our system would benefit from a more tailored approach. One way that has been followed in the LDAS community is to use perturbed atmospheric forcings to generate more physical model perturbations and to obtain an ensemble whose covariances are more physically based. This can be done by either perturbing precipitations only e.g., operating a more complex system of perturbations that includes correlations between precipitation, or shortwave and longwave radiation see among others. Another possibility is to perturb land parameters such as the soil texture or vegetation parameters. The main drawback of such approaches is that they tend to overcome underestimated ensemble variances by putting too much uncertainty on atmospheric forcings or model parameters that might be far better known than assumed. They can also induce a bias in model estimates as shown by.

The model error in ensemble Kalman filters aims to compensate for insufficiencies of the model and forcings, but it is difficult to prescribe as it aims to compensate something we do not know. One way to curb this issue is to estimate model error. describes a range of approaches to account for model biases in data assimilation systems. The last decade has also seen the development of techniques to estimate model error covariance matrices seefor a review of existing approaches. Approaches based on diagnostics developed in or on statistics of consecutive innovations seem affordable for LDASs from a computational point of view.

All these approaches help to estimate model deficiencies but do not necessarily provide the reasons for those caveats. For land surface models, they can come not only from possibly inadequate atmospheric or soil and vegetation parameters but also from inadequate model physics (missing processes, etc.). Finding the reasons for those is a complex task. An interesting step would be to assess the influence of atmospheric uncertainties on LSMs by using ensemble atmospheric forcings such as the 10-member atmospheric reanalysis included in ERA5 (available at a coarser spatial and temporal resolution though) or the 51 members of ECMWF ensemble medium-range forecasts. Such ideas have been explored over Spain in the case of multi-model and multi-forcing ensembles by .

Both SEKF and EnSRF in this paper do not consider covariances between patches and between grid cells. However, those covariances are likely to exists. For example, each patch of a given grid cell is forced with the same atmospheric forcing, errors in the forcing would result in correlated errors for the state of each patch. The same thing could be said for the state of two neighbouring grid cells since errors in atmospheric reanalyses are spatially correlated . Including those covariances could be beneficial to LSV reanalyses.

By construction, the SEKF cannot include these covariances by itself. Indeed the SEKF relies on the ISBA land surface model to calculate covariances between variables by building the Jacobian matrix of the model. Since each patch of each grid cell of the model does not interact with the others, the Jacobian between two variables of different patches is zero. The same occurs for variables between different grid cells. Therefore, if we want to include covariances between patches or between grid cells, they have to be prescribed in the fixed background error covariance matrix.

On the contrary, ensemble Kalman filters can include this information automatically as estimated covariances are built from the ensemble, thus making EnKFs more flexible than the SEKF. In our case, that would lead to a single state vector containing LAI and SM in the various layers of soil of each patch, multiplied by around 12 for the size of this state. and have shown that LDASs can use a small ensemble to provide good LSV estimates without experiencing the traditional undersampling issues or spurious ensemble covariances. However, including covariances between patches or between grid cells would make undersampling and spurious covariances more likely to occur due to the increased size of the state vector. Nevertheless these two potential issues can be overcome. Inflation aims to compensate undersampling by artificially inflating the ensemble spread. Approaches have been built to estimate inflation (under the form of a multiplicative coefficient). has proposed to add inflation as a parameter in the control vector leading to inflation being updated at each EnKF analysis. have successfully applied this approach to a soil hydrology problem. Other approaches based on consistency diagnostics developed by or reformulated EnKFs have gained popularity.

Long-range spatial spurious covariances can be filtered out using localization procedures either by artificially reducing distant spurious correlation or by assimilating observations locally ; LDAS-Monde could be seen as an extreme application of the second approach because of the 1-D nature of the ISBA LSM. Localization procedures are very efficient and are routinely used for a wide range of applications.

Unfortunately, the problem of potentially spurious covariances between patches remains as we would need to fix a criterion to determine which covariance has to be reduced. Recently have proposed a localization procedure based on augmented ensembles. Such formulation allows for a covariance localization not based on spatial characteristics, and it could be used to include covariances between patches in the LDAS-Monde EnSRF.