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1. Introduction
Soil moisture has been recognized as an essential climate variable by the Global Climate Observing System (GCOS) due to its important role in hydrological processes and its impact on global weather and climate through atmospheric feedbacks (Seneviratne et al. 2010; Mahfouf 2010). As the water source for evapotranspiration over land and an essential variable for vegetation growth, it is involved in the water, energy, and carbon cycles driving many land surface and atmospheric processes. The monitoring of soil moisture is thus essential in, for example, assessing possible drought development. This motivates the need for the development of long-term and large-scale data records of both surface and root-zone soil moisture.
Soil moisture can be derived from satellite-based brightness temperature or backscatter in the microwave spectrum (Kerr et al. 2010; Paloscia et al. 2013; Entekhabi et al. 2014). However, these microwave sensors have limited vertical penetration depth (top few centimeters of the soil), and the resulting products contain both temporal and spatial discontinuities. Alternatively, land surface models (LSMs) can simulate surface and root-zone soil moisture to obtain physically consistent estimates at all times and locations (Srinivasan et al. 2000). Data assimilation (DA) uses observations to constrain LSM estimates and enables us to obtain superior estimates of soil moisture by combining the advantages of both sources for soil moisture estimation. Numerous studies have shown the benefit of satellite-based soil moisture DA, either using backscatter or brightness temperatures (e.g., Loew et al. 2009; De Lannoy and Reichle 2016a,b; Lievens et al. 2017; Reichle et al. 2019) or soil moisture retrievals (e.g., Reichle and Koster 2005; Draper et al. 2012; Lievens et al. 2015; Kumar et al. 2014, 2019). The latter approach does not require an observation operator that converts the observations into the prognostic model space, leaving out an additional level of complexity to the DA system. However, it lacks the advantage of being physically consistent and inevitably suffers from biases between the retrieval and model estimates of soil moisture (Reichle and Koster 2004). In this paper, we assimilate soil moisture retrievals from the European Space Agency Climate Change Initiative Soil Moisture (ESA CCI SM; Dorigo et al. 2017) product. In this product, soil moisture retrievals from various active and passive microwave instruments have been harmonized and bias corrected to create a consistent merged long-term (over 30 years) soil moisture climate data record (Gruber et al. 2019).
Earlier studies have shown a positive impact of assimilating the ESA CCI SM product, e.g., for streamflow modeling in China (Liu et al. 2018) and estimating historical root-zone soil moisture records over India (Pal and Maity 2021). Blyverket et al. (2019) assimilated the ESA CCI SM, SMAP, and SMOS data over the contiguous United States using an ensemble optimal interpolation (EnOI) method to compare their respective performances. They found that out of the three resulting analyses, the one with assimilated ESA CCI SM data showed the smallest improvements in correlations with in situ soil moisture data. Over Europe, Albergel et al. (2017) found an improvement in the representation of above-ground biomass, gross primary production, and evapotranspiration by jointly assimilating the ESA CCI SM product and GEOV1 leaf area index (LAI) into a global land data assimilation system (LDAS-Monde). De Santis et al. (2021) found relatively minor improvements in predicting river flow by assimilating the ESA CCI SM product. Finally, Naz et al. (2020) assimilated the ESA CCI SM product into the community land model (CLM) over Europe, producing a high-resolution (3 km) reanalysis dataset for soil moisture. They found an improvement over in situ sites compared to the model-only simulation.
The studies above thus report mixed results, partly due to the use of different model and DA configurations. In this study, we assess the impact of such configurations on the performance of the DA system. Specifically, we consider three choices regarding the design of the DA system with its LSM and error parameterization. First, we focus on the chosen observation error (perturbation magnitude) and how this parameter affects the skill of the DA system and its internal diagnostics. Second, we consider two approaches for treating observation-minus-forecast bias: cumulative density function (CDF) matching through either the commonly used climatological rescaling (Reichle and Koster 2004) or seasonal monthly rescaling (Barbu et al. 2014). Third, we address the impact of the forcing input on the LSM by comparing two atmospheric reanalyses: the fifth-generation European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA5; Hersbach et al. 2020) and the NASA Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2; Gelaro et al. 2017). While comparisons between these datasets have been made previously for a variety of different applications (Olauson 2018; Seethala et al. 2021; Song and Wei 2021; Taszarek et al. 2021), this study presents, to our knowledge, the first assessment of the impact of ERA5 versus MERRA-2 forcing on Noah-MP soil moisture simulations with and without soil moisture DA. Additionally, we look into how external factors affect the in situ performance of the DA system. As in previous studies (e.g., Draper et al. 2012), we assess the impact of retrieval quality and land cover on the added value of DA using the ESA CCI SM product.
We assimilate the combined active–passive ESA CCI SM product into the Noah LSM with multiparameterization options (Noah-MP; Niu et al. 2011), which dynamically simulates both soil moisture and vegetation, over the European continent. We evaluate the model-only and DA performances for soil moisture against in situ measurements. However, the limited number of in situ sites does not represent the entire domain regarding soil texture, land cover, and climate. Therefore, we also evaluate the DA diagnostics (Reichle et al. 2017), which are available over the entire simulation domain.
Section 2 introduces the experiment setup and evaluation methods. Section 3 presents the results in view of the three design choices outlined above. The conclusions are summarized in section 4.
2. Methodology
a. Model configuration
Model simulations are performed using the Noah-MP model (Niu et al. 2011; Yang et al. 2011) version 4.01 with dynamic vegetation, implemented within the NASA Land Information System (LIS; Kumar et al. 2006). Noah-MP simulates soil moisture at depths of 0–10 cm (SM1), 10–40 cm (SM2), 40–100 cm (SM3), and 100–200 cm (SM4). We will refer to soil moisture in the top 10 cm as the surface soil moisture (sfsm, equivalent to SM1) and the top 100 cm as the root-zone soil moisture (rzsm). We derive the model rzsm as the weighted average of the top three layers, with the thickness of the layers serving as weights. We use a regular grid over the European continent (11.50°W–40.25°E, 29.75°–71.75°N) at a spatial resolution of 0.25°. Starting from a uniform initial condition, we spin up the LSM by looping three times from 2000 to 2010 to obtain a reliable climatology to initialize the year 2000. A 2-yr period from 1 January 2000 through 31 December 2001 then serves to spin up the 24 perturbed ensemble members (see section 2d). All experiments (see section 2e) are conducted from 1 January 2002 through 31 December 2019 using a model integration time step of 15 min and daily averaged model output at 0000 UTC.
The used land cover data are obtained from NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS; Friedl et al. 2002) while the Harmonized World Soil Database (HWSD; Nachtergaele et al. 2010) is used for soil texture information and NASA’s Shuttle Radar Topography Mission (SRTM; Farr et al. 2007) provides the elevation map. Land cover and soil texture are spatially transformed to the model grid using a tiling approach. Land cover is assumed to be constant over time as in most studies (unlike Maertens et al. 2021, for example).
b. Meteorological forcing
The Noah-MP LSM is forced by the latest two major climate reanalysis products in separate experiments (see section 2e): ERA5 (Hersbach et al. 2020) lowest model level forecasts with a resolution of 0.25° × 0.25°, and MERRA-2 (Gelaro et al. 2017) lowest model level analyses with a resolution of 0.5° × 0.625°. Both datasets are matched to the model grid using a bilinear interpolation approach. The MERRA-2 forcing includes a gauge-based precipitation correction similar to the one developed for MERRA-Land (Reichle et al. 2011; Reichle and Liu 2014). For both forcings, elevation-based atmospheric temperature corrections are applied in LIS.
c. Satellite retrievals
We use satellite retrievals from the combined active–passive ESA CCI SM product version 7.1 (Dorigo et al. 2017; Gruber et al. 2019) for assimilation into the Noah-MP LSM. This product merges soil moisture retrievals of multiple satellites by combining both active and passive microwave products after rescaling them to the Global Land Data Assimilation System Noah LSM (GLDAS Noah; Rodell et al. 2004), thereby obtaining a consistent long-term record. Passive products are retrieved using the Land Parameter Retrieval Model (LPRM; Owe et al. 2008) algorithm and include, for our study period, the Special Sensor Microwave Imager (SSM/I), the Tropical Rainfall Measuring Mission’s Microwave Imager (TMI), the Advanced Microwave Scanning Radiometer (AMSR)-E and AMSR-2, WindSat, the Soil Moisture Ocean Salinity mission (SMOS), and the Soil Moisture Active Passive mission (SMAP). Active products are retrieved using the TU Wien Water Retrieval Package (WARP; Wagner et al. 1999; Naeimi et al. 2009) algorithm and include the Active Microwave Instrument Wind Scatterometer (AMI-WS), and the Advanced Scatterometer (ASCAT)-A and ASCAT-B.
The ESA CCI SM product has a temporal resolution of one day on a 0.25° regular grid (same as the model grid). It is quality controlled, with retrievals masked out over rain forests, during frozen or snow-covered periods, or if flags of the retrieval algorithm are raised. Furthermore, we do not assimilate observations over grid cells for which the land cover is predominantly “urban and built-up land” or “snow or ice,” or where the topographic complexity (TC) exceeds 10%. TC is defined as the standard deviation of the elevation within a grid cell, normalized between 0% and 100%, and is provided with the ESA CCI SM product. We do assimilate retrievals over forested areas if they do not have a warning flag in the ESA CCI SM product.
For experiments using monthly CDF matching (see section 2e), we ensure a reliable rescaling for each location by omitting months with less than 100 observations across the 18 simulated years. For experiments using climatological CDF matching, we omit locations with less than 100 observations in at least three different years from the assimilation.
d. Data assimilation method
A one-dimensional ensemble Kalman filter (EnKF; Reichle et al. 2002; Evensen 2003) with 24 ensemble members is used for assimilation of the soil moisture retrievals into the Noah-MP LSM at 0000 UTC; the daily ESA CCI SM retrievals are centered around this time. CDF matching is applied to remove the differences in climatology between the model and the retrievals. Differences between the forecasted and observed sfsm, also called innovations, are mapped to updates in prognostic volumetric soil moisture content in the four LSM soil layers. The magnitude of the updates, also called increments, depends on the assumed error in the forecasts and observations.
Perturbations to meteorological fields and the model’s four soil moisture prognostic variables approximate the forecast errors. The settings for these perturbations are calibrated for the open loop through ensemble verification measures (De Lannoy et al. 2006). Settings for cross correlations of the errors are taken from Kumar et al. (2014). Note that the effective correlation of the forecast errors used in the Kalman filter is a combination of the correlations imposed via the perturbations and correlations from the dynamical coupling which is present in the model because of the physical interaction between the layers. As listed in Table 1, we perturb precipitation and downward shortwave radiation with multiplicative perturbations drawn from a lognormal distribution, whereas the downward longwave radiation and four soil moisture variables are perturbed with additive perturbations drawn from a normal distribution. This means that samples are drawn from a standard normal distribution (and truncated if their value exceeds 2.5) and multiplied by the standard deviation in Table 1. Forcing perturbations have a temporal correlation of 24 h, whereas the perturbations in the four prognostic variables are not temporally correlated. This temporal correlation relates to the time scale of the AR(1) process. No spatial correlations for the perturbations are enabled, and perturbations to the prognostic variables are not cross correlated to those of the forcings. We applied the correction described by Ryu et al. (2009) to remove unintended perturbation bias in the forecasts. This means that the ensemble average of an open loop will be the same as a deterministic forecast. The characterization of the random and systematic observation errors is treated as a design choice and is discussed below.
Overview of ensemble perturbations to forcing fields—downward shortwave radiation (SW), downward longwave radiation (LW), and precipitation (P)—and prognostic variables of soil moisture in the four soil layers (SMi, i = 1, …, 4). Additive (+) perturbations have a mean of 0 and are drawn from a normal distribution, while multiplicative (×) perturbations have a mean of 1 and are drawn from a lognormal distribution. We applied temporal correlations of the time series through a first-order autoregressive model. Perturbations to prognostic variables are uncorrelated to the forcing perturbations.
e. Performed experiments and impact assessments
Table 2 gives an overview of the experiments discussed in this paper. Two open loop (model-only) experiments OLx are performed, with x referring to the reanalysis dataset used to force the LSM, i.e., ERA5 for x = E and MERRA-2 for x = M. Similarly, the reference data assimilation experiments are denoted by DAx. These experiments use monthly CDF matching (see below) and an observation error (see below) of S = 0.025 m3 m−3 whereas other DA experiments use climatological CDF matching, denoted by
Overview of the performed experiments.
1) Impact of the observation error
The magnitude of the observation error S refers to the assumed observation error standard deviation. Several experiments DAE(S) are performed with S ∈ {0.006 25, 0.0125, 0.025, 0.05, 0.1, 0.2} (m3 m−3), leaving all other settings unchanged. The reference experiments DAE and DAM use a value of S = 0.025 m3 m−3, which was determined based on an optimization of innovation diagnostics (Reichle et al. 2002). This value is much smaller than the total error of the ESA CCI retrievals because anomaly observations are assimilated (after CDF matching) and the perturbations determined by S only reflect the error on the short-term and interannual signal in the observations.
2) Impact of the rescaling approach
Because the Kalman filter assumes unbiased observations and forecasts, we use a pixel-based CDF-matching approach to rescale the retrievals to the model climatology (Reichle and Koster 2004). In the reference experiments DAE and DAM, the CDF matching is done separately for each month of the year (Barbu et al. 2014) based on the 18 years of retrievals and model-only simulations. This approach was also used by Kumar et al. (2015), de Rosnay et al. (2020), and Aires et al. (2021), for example. In most other studies (e.g., Reichle and Koster 2005; Draper et al. 2012; Kumar et al. 2014; Lievens et al. 2015), however, the CDF matching is based on the entire time series of observations, here referred to as climatological CDF matching. We use this more common climatological rescaling approach in the
3) Impact of the meteorological forcing
Most land surface DA systems correct for short-term and interannual errors introduced by meteorological forcings. The only difference between experiments DAE and DAM is the reanalysis dataset used to force the Noah-MP LSM, as shown in Table 2.
f. Evaluation sites and skill metrics
Evaluation sites are acquired from two sources. First, the International Soil Moisture Network (ISMN; Dorigo et al. 2011, 2013, 2021) provides in situ measurements of soil moisture at various depths at individual points in the study domain. The data have been quality controlled, and we only use data points flagged as “good” for evaluation. Second, soil moisture observations from the SMAP/In Situ Core Validation Site Land Surface Parameters Matchup Data, Version 1, are available at 9-km grid-scale core validation sites as part of the SMAP Calibration/Validation Program (Cal/Val; Colliander et al. 2017). Figure 1a marks all 94 grid cells for which in situ sfsm is available for evaluation, after removing sites for locations where no DA takes place (e.g., mountainous areas). We aggregate the in situ data to daily resolution and require at least 200 daily observations over at least three different years per site before including it in the evaluation. When multiple sites are available within a 0.25° grid cell, skill metrics are computed for each site separately, after which the metric values are averaged to obtain a single value for the grid cell. This decreases the weight of areas with multiple sensors when computing the overall skill improvements over the domain. Similarly, there are 63 locations with in situ rzsm data (not shown). In situ sites are only used to assess rzsm if at least one sensor is present at a depth below 10 cm.
(a) Location of the ISMN in situ evaluation sites and the Cal/Val reference sites for sfsm, colored per network. The inset shows a close-up of the SMOSMANIA network in southern France. (b) The lines indicate the start and end dates for which sfsm information is available at individual sites, colored per network. Gaps in the data may be present between the start and end dates (not shown).
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
Figure 1b shows a considerable variation in the period in which in situ sfsm is available for evaluation. For example, the GTK network in Finland and the ORACLE network in central France cover periods in the first part of the simulations, whereas Cal/Val sites and data from the FMI network enable evaluation of later parts of the simulations. Some networks cover relatively long periods (e.g., SMOSMANIA), whereas others do not (e.g., GROW). The temporal coverage of the reference data matters. Indeed, we expect larger DA skill improvements at sites with data in later periods when the assimilated ESA CCI SM product has higher-quality retrievals. The supplemental material provides a detailed overview of the ISMN networks used and their references in Table S1.
g. Regional data assimilation diagnostics
Apart from evaluating over stations with in situ data, we also assess the DA system through internal diagnostics (Gelb et al. 1974). These diagnostics are based on statistics of the innovations, or observation-minus-forecast residuals, and are thus available at all times and locations for which soil moisture retrievals are assimilated (Reichle et al. 2017). Following previous studies (e.g., Reichle et al. 2002; De Lannoy and Reichle 2016a,b; Reichle et al. 2017), the DA diagnostics are used to explore whether the assumed errors of the system are consistent with the actual errors. If the DA system extracts the information from the observations optimally, the innovations ν should form a zero-mean white noise sequence in time for each location (Gelb et al. 1974; Reichle et al. 2017).
The normalized innovations
Increments are the state space equivalent of the innovations: we derive them for each of the four soil layers of the model. Like the innovations, they should follow a zero-mean white noise sequence in time. We will primarily focus on the relations between soil moisture increments of different soil layers and the impact of the three considered design choices on these relations.
3. Results and discussion
a. Model-only experiments
In this section, we compare the results of the two ensemble model-only experiments OLE and OLM. We do not assimilate retrievals in these runs but use the same perturbations to forcing fields and prognostic variables as the subsequent DA experiments (Table 1).
The map of time-average rzsm for the OLE experiment in Fig. 2a shows the expected patterns, with drier soils over southern Europe and northern Africa. Sandy soils, in Norway and Finland for example, are also substantially drier. The results for sfsm (not shown) are very similar, but with drier topsoil in northern Africa. Figure 2b shows the difference in the average rzsm between OLE and OLM (an artificial pattern is visible in this map due to the difference in resolution between both reanalyses). MERRA-2 yields drier soils in most regions of Europe, most pronounced over mountainous areas such as the Pyrenees and the Carpathians. Over northern Africa, the LSM forced by ERA5 generally yields drier soils, especially over the Atlas Mountain ranges. The bias over Scandinavia is small, with soils in OLE slightly drier. We observe that the soil moisture differences strongly relate to precipitation differences. Indeed, we observe higher average precipitation over most of Europe for the ERA5 reanalysis compared to MERRA-2 (Fig. S1). The magnitude of this difference is also linked to topography. An explanation for this may be that the ERA5 reanalysis is not rain gauge corrected over our study domain, and several studies (e.g., Bandhauer et al. 2022 over Europe) have found that the mean precipitation is overestimated. Over Scandinavia, the precipitation in both datasets is comparable, while MERRA-2 has more precipitation over northern Africa, in line with rzsm in Fig. 2b.
(a) Temporally averaged (2002–19) rzsm, 〈rzsm〉, in the OLE experiment. (b) Difference in 〈rzsm〉 between OLE and OLM: brown indicates higher values for OLE, and blue indicates higher values for OLM. (c) Difference in the spatial average for each day of the year, Δ〈rzsm〉doy, between OLE and OLM as a function of 〈rzsm〉doy for OLE. (d),(e) As in (a) and (b), but for the interquartile range IQRrzsm. (f) As in (c), but for the precipitation P.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
Figure 2d depicts the temporal variability of the rzsm through the interquartile range (IQR). There is a clear latitudinal effect, with southern Europe and Turkey showing the most variability in soil moisture over time and northern Europe the least. Mountainous areas such as the Pyrenees, the Alps, and the Carpathian Mountains show little variation in simulated soil moisture. Again, the maps for sfsm are very similar, but sfsm exhibits more variability than rzsm over northern Africa (not shown). The difference in rzsm variability between OLE and OLM is visualized in the map of Fig. 2e. Contrary to the map of the temporal average (Fig. 2b), most regions in Europe have a higher variability over time for OLM. This behavior can be understood by looking at the soil moisture dynamics in Fig. 2c, which compares the time series of spatially averaged rzsm for each day of the year across all simulation years, 〈rzsm〉doy. The difference Δ〈rzsm〉doy between OLE and OLM is shown as a function of 〈rzsm〉doy in the OLE experiment. This difference increases during summer, to reach its largest value during the driest period toward the end of summer. The difference between both runs then decreases again to reach its minimum during the wettest period at the end of winter. This means that soils dry out more during summer in the simulations forced by MERRA-2 than in simulations forced by ERA5, explaining the larger variability for the former observed in Fig. 2e. This effect is larger for rzsm than for sfsm (not shown). One important driver for the dynamics depicted in Fig. 2c is the precipitation P. Figure 2f portrays the difference Δ〈P〉doy between the ERA5 and MERRA-2 reanalyses for each day of the year, as a function of 〈P〉doy. The differences in precipitation between the two reanalyses can indirectly explain the differences in rzsm shown in Fig. 2c: 〈P〉doy is typically larger for ERA5 during light rainfall events, while 〈P〉doy is larger for MERRA-2 during heavy rainfall events. Note that the difference in color between Fig. 2c and Fig. 2f indicates a time delay between 〈P〉doy and 〈rzsm〉doy of about 6 months.
b. Number of assimilated observations
The number of assimilated soil moisture retrievals varies both in space and time for the DAE experiment. Figure 3a shows daily counts of assimilated observations over the study domain. Apart from a clear seasonal pattern, the number of assimilated retrievals increases over time as additional sensors are included in the combined active–passive ESA CCI SM product. This is most pronounced in the peaks of the summer months, when the number of retrievals increases from 12 500 in 2002 to 15 000 in 2019. The impact of adding MetOp-A ASCAT (January 2007) or AMSR2 (July 2012) is visible, for example (Dorigo et al. 2017). While the inclusion of some products (e.g., SMAP in April 2015) does not have a direct impact on the number of assimilated retrievals, it allows for a higher-quality daily averaging and should decrease the product uncertainty.
(a) Daily count of assimilated ESA CCI soil moisture retrievals over the study domain. (b) Total number of retrievals assimilated for each grid cell over the complete simulation period. No assimilation took place over white grid cells. Both figures correspond to the DAE experiment.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
The map for DAE in Fig. 3b shows that retrievals are never assimilated in mountainous areas such as the Alps, the Pyrenees, and the Carpathian Mountains as satellite retrievals in such areas are masked out (section 2c). Similarly, the map also shows fewer assimilated retrievals in areas with cold winters such as Northern Europe due to the masking of retrievals during frozen conditions. Drawing the map for the
c. Evaluation of the DA skill improvements
Figure 4a shows boxplots of Ranom for the model-only (OLE) and data assimilation (DAE) sfsm forced by ERA5, at the ISMN and SMAP Cal/Val sites. The mean difference between both Ranom distributions is significantly different from zero at the 5% level (paired two-sample t test, p = 0.0015), but the difference is small with mean Ranom = 0.52 for DAE and mean Ranom = 0.51 for OLE. Figure 4b shows the spatial pattern of the DA impact, with a skill improvement at sites in southern France (the SMOSMANIA network) and eastern Europe (the RSMN network) and a deterioration in Finland (GTK and FMI networks). As mentioned earlier, the SMOSMANIA and RSMN networks provide evaluation data toward the end of the simulation, when retrievals are more numerous and of higher quality, whereas the GTK network mostly consists of in situ information that can be used to evaluate the first half of the simulation (Fig. 1). We are thus not only comparing different regions but also different periods, which may be an additional explanation of the differences in skill improvements. Maps of the sfsm ubRMSD (not shown) display a similar spatial pattern, with mean values of 0.052 and 0.051 m3 m−3 for the OLE and DAE experiments, respectively. The evaluation of the rzsm (Figs. 4c,d) yields similar results as for the sfsm, with mean Ranom values of 0.51 and 0.49 for the OLE and DAE experiments, respectively (ubRMSD: 0.042 and 0.043 m3 m−3). Overall, the significant but small improvements found in our study align with Reichle et al. (2021) who show that the impact of soil moisture DA over Europe can be limited compared to other (drier) regions, or regions where the forcing data are presumably of lower quality.
(a) Comparing spatial distributions of sfsm Ranom for the OLE and DAE experiments relative to ISMN and Cal/Val evaluation data. (b) Change in anomaly correlation (ΔRanom) of sfsm: blue sites show an improvement in skill by the DA, whereas red sites show a degradation. The inset shows a close-up of the SMOSMANIA network in southern France. (c),(d) As in (a) and (b), but for the rzsm.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
In Fig. 5a, we visualize (through Ranom with the in situ data) the impact of model-only (OLE) F5 and observation skill on the skill improvement by the DAE system. For evaluation sites located in the top left of this figure, OLE outperforms the retrievals, whereas the retrievals outperform the model in the bottom right of the figure. No DA skill degradation is observed when the observations outperform the model, but this is the case only for a minority of the evaluation sites (18 out of 94). However, it is clear that improvements can still occur in other locations, where the retrievals perform worse than the model.
(a) Skill change (ΔRanom; DAE − OLE) for sfsm (color), as a function of OLE skill (vertical axis) and observation skill (horizontal axis). Blue indicates improvements and red indicates deteriorations. (b) Fraction of the evaluated grid cells occupied by forest, for all sites with improvements (blue boxplot) and deteriorations (red boxplot). The p value indicating the significance of the difference between the means of both distributions is shown on top (two-sample t test). (c) As in (a), but with the color replaced by the forest fraction. (d),(e) As in (b) and (c), but for the cropland fraction. (f),(g) As in (b) and (c), but for the mean rzsm.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
Linking the skill of the model and/or the retrievals, and thus the expected DA skill improvement, to environmental factors such as land cover would allow making a priori assumptions regarding locations where the DA is expected to have a substantial positive or negative impact. Figure 5b shows the distribution of forest fraction (based on the model land cover input) in the grid cells for sites showing skill improvement (blue boxplot) and sites with skill deterioration (red boxplot). A two-sample t test indicates that the means of the two distributions are different at the 5% significance level (p = 0.014). Locations with skill degradation are more likely located in (densely) forested areas, such as the ISMN sites in Finland. Figure 5c demonstrates that locations where retrievals outperform the model (OLE) indeed have a relatively low forest fraction, although exceptions occur.
Similarly, Figs. 5d and 5e reveal statistically significant (p = 0.009) skill improvement by DA at grid cells with larger cropland fractions. Model and satellite retrieval performance differences at such sites are generally smaller than over forested sites. This is consistent with the findings of Draper et al. (2012) and is linked to croplands being more suited for microwave remote sensing than forests, and the Noah-MP model not accounting for cropping practices such as irrigation. A map showing the spatial distributions of forests and croplands over our study domain can be found in the supplemental material (Fig. S2).
Previous studies over the contiguous United States (De Lannoy and Reichle 2016b; Kumar et al. 2019) show larger skill improvements over the east (wetter soils) than the west (drier soils) of the country. We therefore also examined the link between mean (modeled) rzsm and skill improvement (Figs. 5f,g) but found no statistically significant effect (p = 0.104).
1) Impact of the observation error
Figure 6 shows the distribution of sfsm and rzsm skill improvements ΔRanom (compared to OLE) at ISMN and SMAP Cal/Val sites for DAE(S) with different values of the observation error S. Superimposed on the boxplots are the individual evaluation sites, with blue colors indicating higher retrieval quality and red colors indicating lower retrieval quality (relative to the model skill). As discussed previously, higher satellite retrieval qualities result in larger skill improvements, but observations with lower skill than the model may still improve the DA results. Figure 6 displays a trade-off for both sfsm and rzsm when choosing the “optimal” value of the observation error S. If S is too small, the DA puts too much weight on the observations: while the best-performing sites show very strong improvements in this scenario, many sites also show strong deteriorations. As S increases, the DA remains closer to the OL and ΔRanom values converge toward zero. A larger value for S is thus a “safe” choice if the objective is to assimilate a product of low(er) quality (compared to the model) without harming the model simulations. The value S = 0.025 m3 m−3 results in the highest median skill improvement for both the sfsm (ΔRanom = 0.007) and the rzsm (ΔRanom = 0.008).
(a) Distribution of skill improvements in sfsm (horizontal axis) as a function of the observation error S (vertical axis). Individual evaluation sites are superimposed with an indication of the retrieval skills relative to OLE. (b) As in (a), but for the rzsm. Since the CCI product only represents surface soil moisture, no comparison between satellite retrievals and in situ rzsm measurements is shown.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
2) Impact of the rescaling approach
Skill improvements ΔRanom for DA with the monthly (DAE) and climatologically (
Relation between skill improvements of DAE and skill improvements of (a),(b)
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
3) Impact of the meteorological forcing
Figure 7c (sfsm) and Fig. 7d (rzsm) compare the skill improvements ΔRanom between DAE and DAM experiments. The DA skill changes, both improvements and degradations, are more moderate for DAM than for DAE, as indicated by the slope of the regression that is significantly smaller than 1, while the intercept is not significantly different from 0 (sfsm: average ΔRanom of 0.014 and −0.003 for DAE and DAM, respectively; rzsm: average ΔRanom of 0.015 and 0.012 for DAE and DAM, respectively). The OL simulations of sfsm have a larger Ranom when forced with MERRA-2 than when forced with ERA5 for about 79% of the stations. This may partly explain why the skill improvements are generally larger for DAE than for DAM, as they are compared to their respective OL experiments. Despite the smaller skill improvements, the DAM experiment still slightly outperforms DAE in terms of Ranom (not shown).
d. Statistics of the data assimilation innovations
By design, the temporal average of the innovations is small throughout the domain, with values ranging from −0.001 to 0.003 m3 m−3 (5th and 95th spatial percentiles, respectively) for DAE (Fig. S3), and similar values for
1) Impact of the observation error
Figure 8a shows the spatial distributions of the temporal standard deviation of the normalized innovations
(a) Spatial histograms of the normalized innovations
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
While our experiments with S = 0.025 m3 m−3 happen to simultaneously result in the best value for
2) Impact of the observation rescaling approach
Figure 8b shows the joint spatial
3) Impact of the meteorological forcing
The choice of meteorological forcing dataset does not have a significant impact on the
e. Statistics of the data assimilation increments
The results for the increments in each of the four soil layers are in line with those of the innovations, i.e., the
In this section, we will focus on the relation between increments of different layers. Figure 9a shows the bivariate distribution of individual increments, i.e., not aggregated over space or time, for layers 1 and 2 (relations between deeper layers look similar and are provided in Fig. S7). The increments between both layers are positively correlated, and two regimes can be discerned from the histogram: one of strong increment coupling between soil layers (close to the vertical zero line) and one of weak increment coupling (close to the horizontal zero line). For the latter, increments of layer 1 are relatively large but close to zero for layer 2. There are even some occasions where the increments of two different layers have an opposite sign (i.e., they contribute negatively to the correlation). The relatively low spatiotemporal increment correlation between the layers is in line with the assumed ensemble error correlation when perturbing the soil moisture forecasts (Table 1).
(a) Bivariate histogram of increments between layers 1 and 2 of the DAE experiment. The other panels show the difference between increment histograms of the DAE experiment and (b) DAE(S = 0.025), (c)
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
Before moving on to the other panels of Fig. 9, Fig. 10 links the different regimes in the bivariate increment distributions to other variables. The same two-dimensional bins between layers 1 and 2 as in Fig. 9a are shown, but the color now indicates the average value of some explanatory variables in that bin, rather than the count of increments. Figure 10a displays the vertical coupling strength (VCS), which is defined here as the anomaly correlation between the time series of sfsm (top layer) and rzsm (composite of the top three layers) in the model-only experiment OLE (Kumar et al. 2009). A map of the VCS over the study domain (Fig. S8) displays strong geographical differences, with the smallest values over Spain, Turkey, and Africa and a clear influence of the soil texture over the rest of Europe (e.g., a lower VCS over sandy soils). From Fig. 10a, we find that lower values of the VCS typically coincide with the weak increment coupling regime (large increments for the surface layer and near-zero increments for deeper layers), whereas higher values of the VCS typically coincide with the strong increment coupling regime (large increments for both surface and deeper layers). This is consistent with the findings of Kumar et al. (2009). The effect of other land surface variables, i.e., the evapotranspiration (ET), total runoff, rainfall, and rzsm, is visualized in Figs. 10b–e. The panels show that wetter soil and larger hydrological fluxes typically lead to stronger correlations between the increments of different layers. Note that all these variables have an important latitudinal dependence over our study domain. Indeed, the regions with little ET, runoff, rainfall, and rzsm are mostly located in northern Africa, southern Europe, and Turkey. These regions thus dominate the weak increment coupling regime.
As in Fig. 9a, but the colors now indicate the average value of different variables at the times and locations of the increments: (a) VCS, (b) ET, (c) total runoff, (d) rainfall rate, and (e) rzsm.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
1) Impact of the observation error
Figure 9b shows the difference between histograms of increments for the DAE(S) experiments with S = 0.025 m3 m−3 (as shown in Fig. 9a) and S = 0.05 m3 m−3. For the larger observation error S, the distribution shows more increments close to zero while the number of counts at the tails decreases. This is unsurprising, as we expect smaller DA updates for larger observation uncertainties.
2) Impact of the rescaling approach
The impact of rescaling the observations via monthly or climatological CDF matching is shown in Fig. 9c, which compares experiments DAE and
3) Impact of the meteorological forcing
Figure 9d shows that the DAM experiment has more increments in the weak increment coupling regime, whereas DAE has more increments in the strong coupling regime. This means that the correlations between layer 1 and deeper increments are larger with ERA5 meteorological forcings. As a result, we find more near-zero increments in the deeper layers for DAM and in the top layer for DAE. A possible explanation may be the higher number of heavy rainfall events in the ERA5 forcing compared to the MERRA-2 forcing (not shown), and the associated wetter rzsm for ERA5 (Fig. 2). Indeed, Figs. 10d and 10e show that heavy rainfall events and wetter rzsm are strongly linked to the strong coupling regime in the bivariate histograms.
Figure 11 offers a closer look at the impact of rainfall on the increment distribution. The top panel again shows a bivariate histogram, this time between the top soil layer increments for the DAE and the DAM experiments, respectively (Fig. S6 shows the histograms for all soil layers). Again, the distribution is centered around zero and decreases quickly for larger increments values. Most increments are located around the diagonal, resulting in a relatively high Pearson correlation of 0.72 between increments of both experiments. This correlation decreases for deeper layers, as shown in Fig. S6, indicating that the impact of choosing another forcing dataset is larger for the rzsm than for the sfsm. This can be linked to the fact that rzsm has a longer memory of distinct updates. A limited number of increments have opposite signs in the DAE and DAM experiments (top-left and bottom-right quadrants of Fig. 11a). An explanation for this may be rainfall events that are not be captured well in one or the other forcing dataset. Figure 11b shows that for increments close to the diagonal (the large majority), the average difference in rainfall rate ΔP between both forcing datasets is nearly zero. However, the small number of increments that have opposite signs in both experiments show large absolute values in ΔP, suggesting that the DA is correcting for a missed precipitation event in one of both forcing datasets.
(a) Bivariate distribution between increments of the DAE and DAM experiments for soil layer 1. (b) Same binning as in (a), but the color represents the average difference in rainfall ΔP between both meteorological forcings: brown indicates higher rainfall rates in DAE and blue indicates higher rainfall rates in DAM.
Citation: Journal of Hydrometeorology 24, 7; 10.1175/JHM-D-22-0141.1
4. Conclusions
The combined active–passive ESA CCI SM product v7.1 was assimilated into the Noah-MP land surface model over Europe and adjacent regions to produce consistent estimates of surface and root-zone soil moisture as well as other land surface variables (incl. dynamic vegetation). The data assimilation (DA) system was first evaluated using in situ soil moisture data. We found that the distributions of anomaly correlations Ranom across various in situ sites are similar for open loop (OL) and DA experiments. However, in some regions, the DA improves soil moisture estimates (e.g., eastern Europe), whereas in other regions it deteriorates the skill (Scandinavia). We found that DA often leads to degradation of skill over locations that are dominated by forests, whereas the largest improvements can be found over croplands. The DA typically introduces large improvements at sites where the Ranom between the ESA CCI SM retrievals and the in situ soil moisture is high compared to the Ranom between the model-only simulations and in situ soil moisture, but at most sites, the model outperforms the ESA CCI SM. This may be attributed to the fact that the reanalysis forcings over Europe have a high quality due to an abundance of observations from land stations, radiosondes, aircraft, etc., which help the model simulations.
A second assessment of the DA system used regional innovation and increment diagnostics. The bivariate distributions of increments in pairs of soil layers show regimes with strong and weak increment coupling between soil layers. A strong increment coupling is found in regions with high evapotranspiration, rainfall, and runoff values, i.e., outside of northern Africa, southern Europe, and Turkey.
In this study, we examined how the maximal amount of information from remotely sensed observations can be used by assessing the design choices of the DA system and tuning them for optimal performance. As such, we systematically examined the impact of three design choices for both the in situ and regional assessments outlined above:
-
The magnitude of the observation error S. This parameter has an important impact on the in situ soil moisture skill, with a trade-off between fostering large improvements at sites with high-quality retrievals (requiring small S) and limiting the deteriorations at sites with low-quality retrievals (requiring large S). A reference value of S = 0.025 m3 m−3 was found to have a temporal standard deviation of the normalized innovations close to the ideal value of
. This value for S also yielded the largest median improvement in terms of ΔRanom at the in situ sites. Additionally, we showed the impact of S on the distribution of the increments, which are narrower for larger S. A suggestion for future work is the exploration of temporally varying errors, as these may reflect the dataset properties more accurately and thus lead to better DA performance. -
The observation rescaling via monthly or climatological CDF matching. Although this choice does not significantly impact the in situ evaluation results, we found that innovations and increments follow the desired temporal white noise sequence much more closely if the observations are rescaled on a monthly basis. The increments, and thus possible water budget imbalances, are smaller in the DA experiment with monthly rescaling.
-
The choice of meteorological forcing dataset. Separate OL and DA experiments were performed using ERA5 and MERRA-2 atmospheric reanalyses as forcings. We found that the skill improvements in the experiments forced by MERRA-2 are smaller, at least in part because in this scenario the Ranom values of the model-only simulations are better at the validation sites to begin with. No clear effect of the forcing was visible in the statistics of the innovations. The increments showed a stronger propagation to deeper soil layers in the DA experiment forced by ERA5 than for that forced with MERRA-2. One possible explanation may be that the ERA5 reanalysis simulates more heavy rainfall events that result in wetter soils over mainland Europe (not for northern Africa), which thus result in increments belonging to the regime of strong vertical increment coupling.
It should be noted that each of the three design choices has been explored independently from one another, whereas in reality, we can expect to see interactions between them. For example, observation (and model) errors could be improved further by tuning them specifically for the meteorological forcing being used. The perturbations applied to the precipitation in particular (Table 1) would be chosen differently for land surface models forced by ERA5 and MERRA-2 in an optimal system.
In conclusion, our study demonstrates the potential benefits of assimilating the combined active–passive ESA CCI SM product into the Noah-MP LSM over Europe, with the optimization of key design choices leading to better estimates of soil moisture than can be achieved from satellite retrievals or models alone. This can in turn help in improving our understanding of the water, energy, and carbon cycles as these DA updates in soil moisture are linked to changes in other geophysical variables such as leaf area index and evapotranspiration.
Acknowledgments.
This work was funded by the Research Foundation Flanders (FWO, G0A7320N) and the Austrian Science Fund (FWF) as part of the CONSOLIDATION project, and by ESA as part of the CCN 1 to the ESA CCI+ Phase 1 CCI ECVS Soil Moisture (4000126684/19/I-NB). Computing resources were provided by the Flemish Super Computer Center (VSC). The authors thank Météo-France for providing the ERA5 reanalysis dataset in a suitable format for our DA system, and the reviewers for their constructive feedback.
Data availability statement.
The datasets presented in this paper are too large to be retained or publicly archived with available resources. Documentation and methods used to support this study are available from zdenko.heyvaert@kuleuven.be at KU Leuven.
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