2.1 Ecohydrological model

The World-Wide Water (W3) model (van Dijk et al., 2013b) (available at http://wald.anu.science, last access: 20 January 2019) is a one-dimensional, grid-based distributed ecohydrological model that simulates water balance and water-related vegetation dynamics. It was adapted from the Australian Water Resources Assessment Landscape (AWRA-L) model (van Dijk, 2010; Frost et al., 2016). Precipitation is assumed to be the only water input into the system. The precipitation enters the grid cell through the vegetation and soil moisture stores and exits the grid cell through evapotranspiration, run-off, or groundwater discharge (Frost et al., 2016). Each grid cell contains a mix of land cover classes (hydrological response units; HRUs) and is conceptualized as a catchment that does not laterally exchange water with neighbouring cells. Different vegetation has different degrees of access to soil water. Soil and vegetation water and energy fluxes were simulated separately for deep-rooted and shallow-rooted vegetation to consider different rooting and water uptake behaviour. The soil water store was partitioned into three layers, namely, top, shallow, and deep soil to describe the plant-available water, approximately 0–5 cm, 0.05–1 m, and 1–10 m in depth, respectively. A simple groundwater model is used to simulate unconfined groundwater storage considering deep drainage from soil water, capillary rise, and groundwater evaporation and discharge. The unconfined groundwater and surface water stores were simulated at grid cell level.

A 0.25^∘ × 0.25^∘ global gridded Multi-Source Weighted-Ensemble Precipitation (MSWEP) data set derived by merging gauge, satellite, and reanalysis data (Beck et al., 2017) was used as the only water input in the system. The 0.5^∘ × 0.5^∘ WFDEI (WATCH Forcing Data methodology applied to ERA-Interim) meteorological forcing data set (Weedon et al., 2014) used in this study included radiation, air temperature, wind speed, and surface pressure, and these were resampled to be consistent with the resolution of precipitation at 0.25^∘. The soil water balance of the W3 model was simulated globally on a daily basis with a spatial resolution of 0.25^∘ × 0.25^∘.

2.2 Land cover types

The 2010 land cover types of each pixel were characterized by the MODIS (Moderate Resolution Imaging Spectroradiometer) global IGBP (International Geosphere-Biosphere Programme) land cover classifications (MCD12Q1) at ${\mathrm{5}}^{\prime }\times {\mathrm{5}}^{\prime }$ resolution (Channan et al., 2014). The number of pixels at ${\mathrm{5}}^{\prime }\times {\mathrm{5}}^{\prime }$ resolution for each land cover type in all the corresponding 0.25^∘ × 0.25^∘ grid cells were counted to determine the sub-pixel heterogeneity. If the land cover type is identical for the corresponding model grid cell, the land cover type of this model grid cell is considered to be homogeneous. Model grid cells with multiple land cover types and over 60 % grassland were defined as grassland-dominated mixed vegetation. Similarly, model grid cells with mostly forest were classified as forest-dominated pixels. Grid cells with multiple different land covers were classified as mixed land cover. The forest cover of each 0.25^∘ × 0.25^∘ grid cell was calculated with the percentage of forest (including evergreen, deciduous, and mixed forest) pixels to investigate the impact of woody vegetation on soil moisture estimation.

Figure 1Averaged relative error of satellite-observed water content in different land cover types for (a) SMOS-derived soil moisture; and (b) GRACE-derived total water storage.

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2.3 Satellite-observed water content

Satellite-observed near-surface soil moisture from SMOS and total water storage from GRACE were used in this study. GRACE tracked the water movement from space by measuring the changes in the distance between the twin satellites caused by surface mass variations (Tapley et al., 2004). The JPL RL05M mass concentration (mascon) GRACE solutions (Watkins et al., 2015) were used to constrain model-simulated total water storage (i.e. the integration of surface water, soil water at three layers and groundwater stores). The GRACE data were represented on a 0.25^∘ grid, but they represent the native resolution of 3^∘ × 3^∘ equal-area caps. In contrast with sensing the integrated water content, SMOS characterizes global temporal change in near-surface (0–5 cm) soil moisture from the microwave brightness temperature observations every 3 days (Kerr et al., 2010). The 0.25^∘ Level-3 global daily soil moisture retrievals from CADTS (Centre Aval de Traitement des Données SMOS, https://www.catds.fr, last access: 15 August 2018) (Jacquette et al., 2010; Kerr et al., 2013) for ascending and descending orbits were averaged over the overlapping area. The temporally and spatially varying uncertainties of GRACE and SMOS retrievals were provided as part of their respective products, and were used to investigate observation error variance–covariance matrices in the assimilation method. The relative error was calculated as the ratio of the uncertainty over the absolute value for both GRACE and SMOS retrievals for each grid cell at each time step. The average uncertainties for SMOS and GRACE observations were categorized based on land cover types to investigate the relative weighting between observations in the assimilation (Fig. 1).

2.4 International soil moisture network

In situ soil moisture observations at different depths available from the International Soil Moisture Network (ISMN) (Dorigo et al., 2011) were used to evaluate the performance of model-simulated soil moisture for the uppermost soil layer and root zone. An additional level of quality control was imposed here on the ISMN data to eliminate those sites with less than 2 years of data record, having persistently low or high values, or possessing inexplicable spikes or breaks in the time series. In total, 164 stations from 19 measurement networks provided near-surface (0–5 cm) soil moisture observation globally, while 197 stations from 15 networks provided root-zone soil moisture at 0–1 m (Fig. 2). Hourly observations were averaged over a 24 h period to give daily moisture measurements. Stations with multiple measurements for soil moisture within 1 m depth were aggregated to soil moisture at 0–1 m. The 98th and 2nd percentiles of the data records for each site were assumed to represent the field capacity and wilting point required for the calculation of relative wetness.

Figure 2Distribution of in situ near-surface and root-zone soil moisture sites from the International Soil Moisture Network (ISMN) overlaid on the background of MODIS IGBP (International Geosphere-Biosphere Programme) land cover classifications (MCD12Q1).

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2.5 Satellite-observed greenness

The MODIS 0.05^∘ monthly normalized difference vegetation index (NDVI) product (MOD13C2) (Didan and Huete, 2015) derived from atmospherically corrected reflectance in red and near-infrared wavelengths was used as a simple and robust indicator of vegetation greenness. The MOD13C2 NDVI data were aggregated to 0.25^∘ to be comparable with model simulations from January 2010 to December 2016. Areas of the Earth's surface that never exceeded a maximum NDVI value of 0.2 over this period were masked as barren land.

3.1 Data assimilation

Satellite-derived total water storage and near-surface soil moisture were jointly assimilated into the global W3 model from 2010 to 2016. Systematic differences between model and observations need to be removed to ensure optimal performance of the assimilation method (Evensen, 1994; Dee, 2005; Renzullo et al., 2014). Since the W3 model only specifies soil water storage in water depth (mm) rather than prescribing a physical thickness of the soil layers and porosity, the model-simulated soil water availability cannot be directly compared with SMOS soil moisture retrievals in volumetric fraction. To resolve the inconsistency between model and satellite observations in representing the near-surface soil water availability, both SMOS retrievals and W3-simulated top-layer soil water storage (θ_t) were converted to relative wetness (w_t) (0–1) with respect to the dry (θ_wt) and wet (θ_fc) extremes over the 7-year period, calculated as the 2nd and 98th percentiles, respectively (Eq. 1).

For total water storage, it was a simple matter of adding the W3 model-simulated total water storage averaged over 2004–2009 to the GRACE-observed water storage anomaly for absolute total water storage values.

Due to the disparity in temporal and spatial resolution and measurement depths between SMOS and GRACE, these contrasting satellite water content observations were assimilated using an ensemble-based Kalman smoother approach with a 1-month window, following the approach of Tian et al. (2017). Total water storage together with soil moisture data were used to constrain model-simulated water storage components formed as the state vector x, including vegetation water and soil water (top, shallow, and deep layers) for each hydrological response unit, surface water (rivers, lakes), and unconfined groundwater. The observation vector y consisted of the available daily SMOS surface soil moisture and the GRACE total water storage in a month at each grid. Model error variance P^f was derived from 100 ensemble members of the state variable, generated through the perturbation of precipitation, radiation, and air temperature data. The analysis states x^a were updated with the forecast states x^f and the weighted difference between the observations and forecasts at the end of every month (Eq. 2), i.e.

The matrix ${\mathbf{P}}^{\mathrm{f}}{\mathbf{H}}^T({\mathbf{HP}}^{\mathrm{f}}{\mathbf{H}}^T+\mathbf{R}{)}^{-\mathrm{1}}$ above, known as the Kalman gain, determines the degree of influence that observation y has on changing the model forecast state, x^f.

Spatially and temporally varying uncertainties from GRACE and SMOS products, characterized by R, were used in the assimilation to represent the observation error covariance matrix. Tian et al. (2017) applied an artificial weighting factor to the uncertainties of GRACE and SMOS data to compensate for the over-adjustment from SMOS due to the inconsistency in units between SMOS and GRACE data. In this study, the first part of the observation operator H converts SMOS soil moisture retrievals firstly into relative wetness (Eq. 1) and then into available water content (in millimetres) for the uppermost soil layer. The field capacity and wilting point from model simulations for the top 5 cm were applied to both soil wetness and uncertainties. No further weighting factor was required between GRACE and SMOS data after converting SMOS data to equivalent water height. Both ascending and descending SMOS soil moisture retrievals were used to improve the spatial coverage. The second part of the observation operator computes the monthly mean from the sum of daily water storage components in the state vector. The state variables for the next time step of the model forward run were initialized with the analysis states.

The open-loop run (without assimilation of any observation), the assimilation of soil moisture alone, and the assimilation of total water storage alone were also evaluated to examine different impacts of different satellite data on soil moisture profile adjustments. The same ensemble Kalman smoother was applied to the assimilation of SMOS alone (SMOS-only) and the assimilation of GRACE alone (GRACE-only) to compare with the joint assimilation. Since the uncertainty in SMOS data varies considerably between land cover types, another joint assimilation experiment (Joint-landcover) was conducted where SMOS uncertainties were increased by 50 % of the reported value over dense forest area (tree cover > 0.7), implemented to identify any possible underestimation of SMOS uncertainties in forest regions.

3.2 Evaluation of soil moisture estimates

Estimates of soil water content in the uppermost soil layer (0–5 cm) and root zone (0–1 m) after the joint assimilation were evaluated against in situ soil moisture observations from ISMN. The in situ stations within the corresponding model grid cell were aggregated to represent the soil moisture at 0.25^∘ scale. The in situ soil moisture monitoring sites were grouped based on the land cover type of the corresponding model grid cell. Both model-simulated and satellite-observed soil moisture were transformed to relative wetness to resolve differences in units and depths between model simulations and in situ observations (Eq. 1). The performance of soil moisture estimation was statistically evaluated with Pearson correlation (r) and root-mean-square error (RMSE) for the open-loop and different assimilation experiments.

3.3 Analysis of vegetation response to root-zone soil moisture

In this study, satellite-observed vegetation greenness was used as an independent evaluation of root-zone soil moisture estimates in water-limited regions. Thirty years of monthly potential evapotranspiration and precipitation data were used to derive the aridity index. The aridity was simply calculated by averaging the fraction of months that potential evapotranspiration exceeded precipitation in a year. The humid regions with aridity index less than 0.4 were masked out in the evaluation. The correlations between satellite-observed vegetation greenness and soil water storage from different sources were calculated for comparison. The deseasonalized NDVI and soil water storage were derived to investigate the impacts of data assimilation on simulating seasonal cycle and anomalies. The estimation of soil water availability used in the comparisons included SMOS soil moisture, GRACE total water storage, model-simulated root-zone soil moisture via the joint assimilation, and the precipitation-based soil moisture estimates from the antecedent precipitation index (API). The API was calculated using the MSWEP precipitation data with a constant decay coefficient of 0.9 (Hooke, 1979). The API was used as it better represents the cumulative effects of precipitation than individual rainfall events on vegetation response. The statistical improvement in correlation was used as an indicator of enhanced performance in simulating seasonal pattern and the deviation of monthly mean.

The soil water availability at the integrated depth that has the maximum correlation with NDVI best explains the changes in surface greenness at each grid cell, so-called vegetation-accessible storage (Tian et al., 2019). The correlations of monthly NDVI and soil moisture estimates integrated over different depths after joint assimilation were calculated. The soil water storage estimates were integrated at four depths: near-surface (0–5 cm), shallow-root zone (0–1 m), deep-root zone (0–10 m), and total water column. Annual trends of the accessible storage anomalies relative to monthly means were calculated to determine the area under soil water stress. Linear trend analysis was also applied to the annual average NDVI anomalies to investigate the consistency between vegetation greenness and soil water storage. The trends in accessible storage derived from the open-loop and joint assimilation were compared with the trends in NDVI to investigate the change in annual trend after data assimilation.

4.1 Near-surface and root-zone soil moisture estimation

SMOS soil wetness and W3 top-layer soil wetness from open-loop and data assimilation were compared with the in situ near-surface soil wetness observations from ISMN (Fig. 3). Satellite observations of soil moisture (SMOS) were generally better correlated with in situ soil moisture observations over non-forest areas than open-loop simulations (Fig. 3a). However, as the fraction of tree cover increases, the relative performance changes and model simulations tend to be better correlated with in situ measurements than SMOS observations. The joint assimilation of both SMOS and GRACE observations (Fig. 3b) shows improved correlation with in situ measurements compared with the model open-loop over the majority of the sites where SMOS observations better correlated with in situ measurements. This improvement is due to data assimilation bringing the model and SMOS soil moisture into better agreement for these sites, as illustrated in Fig. 3c for a grassland site. On the other hand, joint assimilation largely reduces the degradation on surface soil moisture over forest sites where SMOS retrievals are less accurate than model simulations (dark green dots in Fig. 3a and time series in Fig. 3d).

Figure 3Assessment of near-surface soil moisture estimation with ISMN in situ measurements from 2010 to 2015: (a) correlations of SMOS soil moisture retrievals with in situ measurements (y axis) compared against open-loop (x axis); (b) correlation of near soil moisture estimates after the joint assimilation with in situ measurements (y axis) compared against model open-loop (x axis). Each ISMN site is characterized by the fraction of tree cover within the corresponding 0.25^∘ cell. (c, d) Time series of simulated surface soil moisture before and after the joint assimilation over grassland and forest-dominated regions.

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The impact of data assimilation on W3 model performance is further illustrated in Fig. 4. For near-surface soil moisture (Fig. 4a), the assimilation of SMOS observations alone (SMOS-only) shows more sites with improved correlations and reduced RMSE against model open-loop. The assimilation of GRACE data alone had little impact on surface soil moisture estimation. Joint assimilation of SMOS and GRACE with SMOS observations down-weighted for ISMN sites in forest (high tree cover) areas (plot labelled “Joint-landcover”) was observed with fewer degradation sites than joint assimilation with original SMOS uncertainties (“Joint”).

Figure 4Performance of surface and root-zone soil moisture estimates from four data assimilation scenarios against open-loop: correlation (r) and root mean-squared error (RMSE) change after the assimilation (r^a−r^o, RMSE^a − RMSE^o; ^a: after assimilation, ^o: open-loop) in (a) surface soil moisture estimation; (b) root-zone soil moisture estimation. The four scenarios include SMOS-only as the assimilation of SMOS data alone, GRACE-only as the assimilation of GRACE data only, Joint as joint assimilation of SMOS and GRACE, and Joint-landcover as increasing SMOS uncertainty in forest regions in the joint assimilation. The points in the scatter plots are colour coded such that blue indicates ISMN sites where improvement was observed in both correlation and RMSE; green indicates sites where there was improvement in correlation, but not in RMSE; yellow indicates those sites where there was improved RMSE, but not correlation; and red indicates sites where assimilation resulted in degradation in both correlation and RMSE.

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Table 1Evaluation of near-surface and root-zone soil moisture estimation with ISMN in situ soil moisture observation across land cover types.

Land cover types: GS: grassland, OS: open shrubland, WS: woody savannas, SS: savannas, CP: cropland, CV: cropland/natural vegetation, EN: evergreen needleleaf forest, DB: deciduous broadleaf forest, MF: mix forest, GD: grassland-dominated mix types, FD: forest-dominated mix types, and ML: mixed land covers. NA: in situ observations not available.

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Data assimilation resulted in significant improvements in W3 root-zone soil moisture estimation over the majority of sites (Fig. 4b). In contrast to surface soil wetness, SMOS and GRACE observations both impacted deeper soil wetness estimation considerably. Simulation of soil wetness over the root zone (0–1 m) in the joint assimilation was less affected by forest cover compared to the near-surface soil wetness, as evident from the high degree of similarity between the “Joint” and “Joint-landcover” plots (Fig. 4b). This suggests no significant difference in performance as a result of down-weighting SMOS influence over forest regions.

Table 1 summarizes W3 model soil moisture estimation performance for both near-surface and root-zone for different land cover types. On average, the correlation with in situ observations increased for both surface and root-zone soil moisture estimates compared to model open-loop. The improvements in surface soil moisture estimates were mainly over croplands (i.e. CP and CV) and grassland-dominated areas (i.e. GS and GD), with changes in correlation, r^a−r^o, as high as 0.44 for cropland. Correlation in model surface soil moisture estimates over savannas and forest areas decreased relative to open-loop simulations. Data assimilation improved root-zone soil moisture estimates for most land cover types, with up to 0.38 increase over mix-type areas and an average change in correlation of 0.1 for croplands (from 0.59 to 0.69) and grass-dominated areas (from 0.54 to 0.64).

4.2 Relation between vegetation greenness and soil water availability

Monthly water storage integrated to different depths, from the uppermost soil layer to the total soil column, was compared with satellite-observed greenness. The response of vegetation greenness to water storage at different depths is illustrated for selected sites over six land cover types in Fig. 5. Significant differences in soil water variability were found between the joint assimilation and open-loop estimates in all sites (Fig. 5), in particular deep-root zone and total water column. The temporal pattern in greenness and water storage time series was characterized for open-loop and joint assimilation estimates by correlation, r^o and r^a, respectively. As an example, the grassland site in northern China responded more strongly to the availability of near-surface soil water (higher correlation) than deep soil water and total water storage (Fig. 5a). This suggests a shorter time lag between surface soil water availability and surface greenness. Stronger correlations between NDVI and near-surface soil water storage were found to have increased by 0.15 after assimilation (i.e. $r^{\mathrm{a}}-r^{\mathrm{o}}=\mathrm{0.15}$). Greenness of the savannas site in eastern Brazil and the cropland site in southern Australia showed a similar seasonal pattern (correlation) to water storage over all depths (Fig. 5b and c). The largest change in correlation as a result of joint assimilation was observed for the Brazil savannas site (Fig. 5b) ($r^{\mathrm{a}}-r^{\mathrm{o}}>\mathrm{0.4}$) for shallow and deep water storage. NDVI in shrublands and forest sites with deeper roots showed higher correlation with deep soil water and total water storage availability, such as the evergreen broadleaf forest in Nigeria, shrubland in northern Mexico, and deciduous broadleaf forest in southern Bolivia (Fig. 5d to f).

Figure 5Time series of vegetation responses (NDVI) to soil water storage over different integrated depths across land vegetation types before (r^o, red curves) and after the joint assimilation (r^a, blue curves). The location of each site is shown in Fig. 1.

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Figure 6Maximum change in correlation (r^a−r^o, r^a: joint assimilation, r^o: open-loop) of (a) the seasonal cycle of vegetation greenness and soil water storage over different integrated depths; (b) the anomalies of vegetation greenness and soil water storage over different integrated depths.

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Figure 7Vegetation response to different sources of soil water availability as indicated by the correlation between monthly NDVI and (a) antecedent precipitation index (API), (b) SMOS surface soil moisture retrievals, (c) GRACE total water storage change retrievals, and (d) vegetation-accessible water storage derived after the joint assimilation.

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Significant increases in correlation between W3 water storage and vegetation greenness resulted from the joint assimilation of SMOS and GRACE data. Figure 6a shows the maximum change in correlation between the seasonal cycle of NDVI and soil water storage at different integrated depths. Increases in correlations between the seasonality of NDVI and soil water storage after the joint assimilation were observed globally, most notably in the high latitudes of the Northern Hemisphere, where increases in correlation over 0.5 were widespread. This is due to the joint assimilation bringing the seasonality of soil water availability into better agreement with greenness. Significant increases in the correlation between NDVI anomalies and root-zone soil water anomalies by 0.2 were widely observed over the semi-arid and arid regions after the joint assimilation (Fig. 6b). The result shows that the deviations of root-zone soil water to monthly mean can be better simulated after the joint assimilation with improved consistency with vegetation greenness anomalies.

Figure 8Change in soil water availability and vegetation greenness from 2010 to 2016: linear trends of accessible water storage anomalies estimated from (a) model open-loop and (b) joint assimilation; (c) difference in trends between joint assimilation and model open-loop; (d) linear trends of NDVI anomalies.

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Having established that joint assimilation improved soil water estimation and the correlation with vegetation response globally, we explored the sources of the improvements. The correlations between NDVI and soil water content estimates from API, SMOS, GRACE, and W3 were computed globally (Fig. 7). API showed a correlation with NDVI of ∼0.5–0.6 over major dry lands and high-latitude regions, except for western and southern Australia and North America (Fig. 7a). Near-surface soil moisture estimates from SMOS showed a strong positive correlation with vegetation conditions over tropical grassland and savanna regions but a strong negative correlation over eastern America and Europe (Fig. 7b). Vegetation growth over tropical regions showed clear wet and dry seasonal patterns closely related to the variability of total water storage from GRACE (Fig. 7c). The correlation of derived accessible soil water storage (from joint assimilation) shows the strongest correlation with NDVI (Fig. 7d) in the semi-arid and arid regions compared to other water content estimates. The negative correlations over western Australia between vegetation conditions and precipitation and surface soil moisture were not observed in GRACE-observed total water storage and joint assimilation derived accessible storage. This indicates that the vegetation here mainly responds to the availability of deep soil moisture. The vegetation conditions were found to be less responsive to the soil moisture availability in Europe and North America since water is not the only limiting factor to the vegetation growth.

4.3 Trends in soil water availability and vegetation response

The soil water anomalies estimated from the W3 open-loop and joint assimilation from January 2010 to December 2016 were compared with the global vegetation greenness anomalies over the same period and clear differences in the magnitude of soil water storage change and high spatial variability were observed globally (Fig. 8a and b). For example, a decrease in soil water storage was simulated in open-loop simulations over southern Mexico and northeastern China. However, joint assimilation results showed an increase in soil water storage anomalies for these same regions. Differences in water storage anomaly change between open-loop and joint assimilation (Fig. 8c) could be over 10 mm yr⁻¹, and were most noticeable over Southeast Asia and Australia.

Clear decreasing trends in NDVI anomalies (more than 0.025 units per year) were observed over central and eastern Australia (Fig. 8d), while decreasing trends in soil water availability of over 10 mm yr⁻¹ were found in both model open-loop and joint assimilation estimates. A greater decrease in soil water storage was inferred in central and eastern Australia through joint assimilation than from the open-loop. Similarly, the deficit in accessible root-zone soil water storage estimated through joint assimilation aligned well with the dramatic decrease in vegetation greenness in eastern Brazil, southern India, and southern Africa. The joint assimilation resulted in estimated increases in soil water storage that were globally much more consistent with increased greenness than the open-loop simulations.