3.1 Active products

Active products are retrieved using the TU Wien Water Retrieval Package (WARP) algorithm (Wagner et al., 1999; Naeimi et al., 2009), which is also used to generate the official operational ASCAT L2 soil moisture products for the Satellite Application Facility on Support to Operational Hydrology and Water Management of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT H SAF, http://hsaf.meteoam.it/soil-moisture.php, last access: 17 May 2019). The WARP algorithm is a change detection approach that retrieves soil moisture as the degree of saturation by scaling azimuthally corrected radar backscatter measurements between the historically lowest and highest observed values (at each individual grid location), which are assumed to represent completely dry and saturated conditions, respectively. The multi-antenna multi-incidence angle capability of the ERS and ASCAT scatterometers are exploited to correct for the (seasonally varying) backscatter contribution of vegetation (Vreugdenhil et al., 2016). A threshold-based decision tree algorithm is applied to incidence angle normalised backscatter measurements to detect and remove measurements that were taken under frozen or freezing/thawing conditions where no reliable soil moisture retrieval is possible (Naeimi et al., 2012). For a complete description of the model and how it is applied to ERS and ASCAT data see the Algorithm Theoretical Baseline Document (ATBD) D2.1 Version 04.4 – Soil Moisture Retrievals from Active Microwave Sensors (Chung et al., 2018b). Information as to which WARP algorithm versions have been used for the different ESA CCI SM versions can be found in Table 1.

3.2 Passive products

Passive products are retrieved using the Land Parameter Retrieval Model (LPRM) algorithm (Owe et al., 2008). LPRM is a forward model which is based on the radiative transfer model of Mo et al. (1982) and distinguishes itself from other soil moisture retrieval algorithms due to its applicability to a wide range of frequencies (i.e. 1–20 GHz) and by using an analytical solution based on the Microwave Polarization Difference Index for the derivation of the vegetation optical depth (VOD; Meesters et al., 2005). For C-band and higher-frequency sensors, the data is filtered for frozen conditions using Ka-band-based temperature (Holmes et al., 2009) and for radio frequency interference (RFI; de Nijs et al., 2015; Li et al., 2004). For SMOS L-band retrievals, the filtering is based on the RFI and modelled (by the European Centre for Medium Range Weather Forecasts) temperature data are provided alongside the brightness temperature input data (SMOS L3TB). Soil moisture retrievals of all sensors are masked out if the VOD exceeds a certain threshold that depends on the microwave frequency of the respective sensor. For a complete description of LPRM and how it is applied see the Algorithm Theoretical Baseline Document (ATBD) D2.1 Version 04.4 – Soil Moisture Retrievals from Passive Microwave Sensors (de Jeu et al., 2018) as well as van der Schalie et al. (2016) and van der Schalie et al. (2017). Information as to which LPRM algorithm versions have been used for the different ESA CCI SM versions can be found in Table 1.

3.3 GLDAS Noah

GLDAS Noah (Rodell et al., 2004) is used as a scaling reference in the COMBINED product to obtain a consistent climatology throughout the entire ESA CCI SM period (Liu et al., 2011, 2012, see the next sections) and as an instrumental product for triple collocation analysis in the ACTIVE, PASSIVE and COMBINED products to obtain the L2 input data uncertainties (Su et al., 2014). More specifically, GLDAS Noah version 2.1 (and previously, GLDAS Noah version 1), which provides data from 2000 to the present, is used for both rescaling and triple collocation analysis (see the next sections). In earlier periods, GLDAS Noah version 2.0, which provides data from 1948 to 2010, is used for triple collocation analyses for L2 products where there is no temporal overlap with GLDAS Noah v2.1 (or v1). However, all L2 data sets are rescaled (for the COMBINED product) against GLDAS Noah v2.1 (previously, v1) due to inconsistencies with GLDAS Noah v2.0, which originate from the historic forcing data that were used in this version.

GLDAS Noah (all versions) provides 3-hourly estimates of soil moisture and other land variables for four different depth layers on a 0.25^∘ regular grid. Top-layer (0–10 cm) soil moisture estimates at 00:00 UTC (coinciding with the resampled satellite input data) are used for rescaling and triple collocation analysis. Top-layer soil temperature (T_s) and snow water equivalent (SWE) estimates are used to mask out satellite measurements that were taken under conditions where no reliable soil moisture retrieval is possible (i.e. $T_{\mathrm{s}}<\mathrm{0}{}^{\circ }$ and SWE > 0 mm).

4.1 Harmonisation of L2 data

L2 input data sets from different missions are harmonised to a common climatology by matching the cumulative distribution function (CDF) of the individual data sets to that of a reference product, which was chosen to be the one that is expected to have the most stable climatology. For the active products this is ASCAT, as it is the direct successor instrument of ERS, with improved spatial resolution, temporal coverage and radiometric accuracy (Naeimi et al., 2009). For passive products it is AMSR-E due to its longer signal wavelength and higher spatial and temporal resolution (Liu et al., 2012). The CDF matching is realised by splitting the data sets into percentiles and rescaling these percentiles in a linear fashion (Liu et al., 2011).

For the harmonisation of the active products, a combined ERS-1/2 50 km (native) resolution time series is first simultaneously retrieved from well intercalibrated backscatter measurements from ERS-1 and ERS-2. Data gaps in these time series due to the on-board storage failure of ERS-2 in 2003 are filled with the experimental higher-resolution 25 km ERS-2-only soil moisture retrievals after rescaling (CDF matching) them against the combined ERS-1/2 data set. This complete ERS time series is then rescaled against ASCAT.

Passive products are harmonised as follows. WindSat and TMI retrievals are rescaled against AMSR-E, while AMSR2 is assumed to be properly intercalibrated with AMSR-E (which is most likely not always the case; see Parinussa et al., 2015 and Sect. 10). For SSM/I, only anomalies (calculated as deviations from the mean seasonal cycle) are rescaled against those of AMSR-E, while the mean seasonal cycle of SSM/I is fully replaced with that of AMSR-E due to its lack of consistency with other sensors (Liu et al., 2011, 2012). A merged SSM/I–TMI–AMSR-E time series is then created by selecting the best available sensor at a given time, assuming that the data quality negatively correlates with microwave frequency and the time since launch (Liu et al., 2012). Since TMI data are only available between ±37^∘ latitude, SSM/I retrievals are used in the remaining latitude bands, even though they are considered to be less reliable than those from the longer-wavelength TMI sensor. Finally, SMMR observations are rescaled against the merged SSM/I–TMI–AMSR-E time series. Note that, as there is no temporal overlap between SMMR and successive sensors, this step scales the observations of different periods and thus assumes that there is no trend from the SMMR period (1978–1987) to the combined TMI–SSM/I–AMSR-E period (1987–2011) (Liu et al., 2012).

4.2 Generation of the ACTIVE and the PASSIVE product

The ESA CCI SM v2 ACTIVE product is generated by concatenating ASCAT and the rescaled combined ERS time series. Since this product is provided in the ASCAT data space, i.e. as the degree of saturation, a porosity map derived from the Harmonized World Soil Database (HWSD; Nachtergaele and Batjes, 2012) is provided alongside the data in order to allow the soil moisture estimates to be converted to volumetric units if required.

Figure 2Merging periods and sensor selection of the ACTIVE (top), PASSIVE (middle) and COMBINED (bottom) ESA CCI SM v2, v3 and v4 products.

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The ESA CCI SM v2 PASSIVE product is generated by concatenating the rescaled SMMR data set, the harmonised and pre-concatenated AMSR-E–TMI–SSM/I time series and AMSR2. Note that in the ESA CCI SM v2 ACTIVE and PASSIVE products, measurements from different sensors are not merged. At all time steps, the presumed best-performing sensor operational at that date is selected, disregarding potentially available observations from the other sensors. Figure 2 illustrates the resulting sensor selection per time and latitude.

4.3 Harmonisation of the ACTIVE and the PASSIVE product

The ACTIVE and the PASSIVE products are harmonised by rescaling them against GLDAS Noah soil moisture simulations. The rationale for using a land surface model as a scaling reference for harmonisation is its supposedly long-term consistent climatology. For more details on the implications and caveats of this choice see Liu et al. (2011, 2012) and Sect. 10.

4.4 Generation of the COMBINED product

The harmonised ACTIVE and PASSIVE data sets are merged into the COMBINED product by following a decision tree that selects either one of the products alone or uses the arithmetic mean of both during a particular period based on the assumption that active retrievals tend to perform better in more densely vegetated areas, whereas passive retrievals tend to perform better in more sparsely vegetated areas (Liu et al., 2011, 2012). For each merging period (see Fig. 2) and at each quarter degree grid cell, the Pearson correlation coefficient between the ACTIVE and the PASSIVE product is calculated. At all locations and during each period where the correlation exceeds 0.65, the arithmetic mean between the ACTIVE and the PASSIVE product is used at time steps where both are available. If one data set does not provide a valid observation at a particular time step (due to L2 quality control and orbit characteristics), the observation of the respective other data set is used. At locations and in periods where the correlation threshold is not met, the ACTIVE data set is selected if the multi-year average AMSR-E-based VOD at that location is above a certain threshold and the PASSIVE data set is selected if the VOD is below that threshold. The threshold is taken as the average of multi-year average AMSR-E-based VOD estimates over all regions where the correlation between the ACTIVE and the PASSIVE products does exceed the aforementioned correlation threshold of 0.65 (i.e. where the ACTIVE and the PASSIVE product are expected to be of comparable quality). In regions and periods where ERS data are scarce due to the failure of the on-board storage (resulting in a temporal coverage below 15 %), passive observations are used to fill these gaps, even if the correlation and VOD threshold suggest the use of the ACTIVE product only.

In summary, the merging algorithm behind ESA CCI SM v2 COMBINED product is a ternary decision scheme that selects either active-microwave-based retrievals alone, passive-microwave-based retrievals alone or an unweighted average of the two based on their mutual correlation and average VOD conditions at a particular time and location.

6.1 Harmonisation of L2 data

The input data harmonisation is largely identical to that in ESA CCI SM v2 (see Sect. 4.1). ASCAT observations from MetOp-B, which were additionally included in v3, are treated as perfectly intercalibrated with those from MetOp-A and arithmetically averaged on days and at locations where both satellites provide collocated measurements. SMOS, which was additionally included in v3, is, as all the other products, rescaled (CDF matched) against AMSR-E.

6.2 Uncertainty estimation for (harmonised) L2 data

Following Gruber et al. (2017), estimates of the random error variances (i.e. uncertainties) of the L2 data sets, required for the parameterisation of the employed least squares merging scheme, are obtained through TCA. TCA simultaneously estimates uncertainties in three spatially and temporally collocated data sets with errors that are required to be mutually uncorrelated. This requirement is commonly assumed to be met when applying TCA to one active-microwave-based, one passive-microwave-based and one land surface model-based soil moisture data set (Scipal et al., 2008; Gruber et al., 2016b). Accordingly, uncertainties in all active and passive products (except for SMMR, which does not temporally overlap with any of the active data sets) are estimated as follows:

where the subscripts refer to the active (a), the passive (p) and the land surface model (m) time series; ${\mathit{\sigma }}_i^{\mathrm{2}}$ is the temporal variance of data set i; and σ_i,j is the temporal covariance between data sets i and j with $i,j\in [\mathrm{a},\mathrm{p},\mathrm{m}]$. Uncertainty estimates for each active (passive) data set are obtained by applying Eq. (3) to that data set in combination with the respective passive (active) data set with the longest temporal overlap and GLDAS Noah.

Note that the ${\mathit{\sigma }}_{{\mathit{\epsilon }}_i}^{\mathrm{2}}$ represent temporal mean data set uncertainties. Consequently, weights derived thereof (i.e. the P matrix in Eq. 2) are average weights for the period for which TCA was applied, although actual retrieval uncertainties (of individual sensors) may change over time (see Sect. 10). For more details on TCA we refer to Gruber et al. (2016b). Note also that, while errors of active and passive products are commonly assumed to be uncorrelated, significant correlations between the errors of different passive products may occur. Therefore, merging them into the PASSIVE product would require estimates of these error correlations in order to properly parameterise the full error covariance matrix in Eq. (2). Gruber et al. (2016a) proposed a modification of TCA which potentially allows the estimation of such error correlations, but this method has not yet been validated on a global scale and was found to be particularly susceptible to small sample sizes (sample sizes of products that are merged into the PASSIVE product are considered small in this context). Hence, lacking the ability to robustly estimate them, off-diagonal elements in the error covariance matrix are neglected in ESA CCI SM v3. The consequences of doing so are discussed in the next section and in Sect. 10.

6.3 Generation of the ACTIVE and the PASSIVE product

As in ESA CCI SM v2, the ACTIVE product is generated by concatenating the harmonised ERS and ASCAT time series because they do not have temporally overlapping observations which would allow for statistical merging. Consequently, their uncertainties, estimated from TCA, are merely appended to the product as auxiliary information and not used in the merging scheme.

Passive data sets are merged into the PASSIVE product as follows. Before October 2007 (i.e. before the launch of Coriolis, carrying WindSat), the low temporal coverage of the available sensors was assumed to render TCA-based error variance estimates too uncertain for a robust derivation of relative merging weights due to the susceptibility of TCA to small sample sizes (Zwieback et al., 2012). Consequently, SMMR, SSM/I, TMI and AMSR-E observations before October 2007 are concatenated in the same way as in ESA CCI SM v2, that is, by selecting the best available sensor at a particular time and location (see Fig. 2). Note that this was a relatively ad hoc albeit conservative assumption which has not yet been tested thoroughly but will be for future product versions (see Sect. 10).

All sensors available after this period (i.e. AMSR-E, WindSat, SMOS and AMSR2) are merged by employing the least squares estimator in Eq. (2) in the following manner: since the data sets are already harmonised, i.e. rescaled to a common climatology, the design matrix A is taken to be a column vector with all values being one. The error covariance matrices C required to calculate P (i.e. the relative weights for averaging the data sets) are constructed for each grid cell and for each merging period from the TCA-based uncertainty estimates of all sensors that are available during that particular period (see Fig. 2). As mentioned above, error cross-correlations are neglected. That is, off-diagonal elements in C are held zero, which may lead to biases in the estimated weights in case the errors of different passive data sets are significantly correlated (see Sect. 10). However, while this may reduce the efficiency (in uncertainty reduction) of the least squares estimator in several cases, it cannot lead to a substantial uncertainty increase (with respect to the individual L2 input products) because error correlations only pull the weights further towards the best product. If neglected, better products are still attributed with higher weights.

Note that the different sensors do not provide valid retrievals at every time step due to their orbit geometry and the L2 quality control (see Sect. 3). Consequently, if, during a particular merging period (see Fig. 2), a data set with significantly larger uncertainties has a higher temporal measurement coverage than the others, simply merging all available observations at each time step might result in a significantly larger overall uncertainty (of the merged time series) than that of the lower-uncertainty input time series alone. Therefore, to provide a trade-off between the best possible temporal measurement density and the lowest possible (average) uncertainty in merged time series, ESA CCI SM v3 imposes a minimum threshold for the cumulative weight of valid measurements available on a particular date, which has to exceed 1∕2N where N is the number of sensors in orbit and operational during that merging period. If this threshold is not met, no soil moisture estimate is provided for that day. For example, assume that for merging AMSR-E, WindSat and SMOS into the PASSIVE product, their weights as derived from their relative SNR at a particular location are 0.1, 0.05 and 0.85, respectively. Because N=3, the minimum-cumulative-weight threshold is 0.17. Therefore, if, on a particular day, only AMSR-E and WindSat observations are available, which have a cumulative weight of 0.15, no soil moisture estimate is provided. For more details on the choice and the implications of this threshold see Gruber et al. (2017).

6.4 Harmonisation of the ACTIVE and the PASSIVE product

As was the case with ESA CCI SM v2, in ESA CCI SM v3, before merging the ACTIVE and the PASSIVE products, their climatologies are harmonised by rescaling them against GLDAS Noah soil moisture simulations.

6.5 Uncertainty estimation for the (harmonised) ACTIVE and PASSIVE products

As mentioned in Sect. 6.2, TCA estimates represent the average retrieval uncertainties during the period in which TCA was applied. Since the uncertainties in the ACTIVE and PASSIVE products change significantly depending on which input data sets are used or merged at a particular point in time, uncertainties are estimated (from Eq. 3) separately for all periods with different sensor availabilities (see Fig. 2). In addition to TCA-based uncertainty estimates, significance levels (p  values) of the Pearson correlation between the ACTIVE data set, the PASSIVE data set and GLDAS Noah are calculated (separately for the same periods) in order to screen for unreliable TCA estimates (see the next section).

6.6 Generation of the COMBINED product

TCA estimates of soil moisture uncertainty are known to have limited reliability in certain regions such as deserts, high latitudes or areas with dense vegetation (Dorigo et al., 2010; Al-Yaari et al., 2014). Using these estimates to parameterise the covariance matrix in Eq. (2) could thus significantly alter the integrity of the least squares estimator. Therefore, following the approach of Gruber et al. (2017), p values are used to verify the reliability of TCA estimates and to fall back on the use of either active or passive retrievals alone, an unweighted average of the two, or to completely mask the grid cell during that period if uncertainty estimates and/or soil moisture retrievals are deemed unreliable. Specifically, the decision of whether to use the ACTIVE product alone, the PASSIVE product alone, an unweighted average of the two, the least squares estimate or to disregard the grid cell completely is based on the relative p value. combination as illustrated in Table 2. If the least squares estimator is used, a minimum-weight threshold of 0.25 (1∕2N where N=2, i.e. ACTIVE and PASSIVE) is again imposed on dates where only one of the data sets (ACTIVE or PASSIVE) provides a valid observation (see Sect. 6.3). More details and an evaluation of this classification scheme is provided in Gruber et al. (2017).

Table 2Merging scheme based on the one-tailed p value for the correlation between active (a), passive (p) and modelled (m) soil moisture with a 0.05 significance level (modified from Gruber et al., 2017).

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Figure 4Weights for merging the ACTIVE and PASSIVE products in the ESA CCI SM v3 algorithm (all sensor periods, a–h), weights for merging the ACTIVE and PASSIVE products in the ESA CCI SM v2 algorithm (latest period, i) and average VOD derived from AMSR-E (j).

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Figure 4 shows the relative weights during each merging period (see Fig. 2) which are used for merging the ESA CCI SM v3 ACTIVE and PASSIVE products based on the TCA uncertainty estimates and the p-value mask. As a reference, the weight distributions amongst the ACTIVE and PASSIVE product in the ESA CCI SM v2 algorithm (only during the last merging period) and average VOD conditions at each location are given. The main apparent feature is that weight distributions in all merging periods largely follow VOD patterns. While the ESA CCI SM v2 algorithm was specifically designed to do so, the fact that the uncertainty-based weights in the ESA CCI SM v3 algorithm do this as well (with a much better resolution) strengthens the evidence for the assumption that active products tend to perform better in more densely vegetated areas, whereas passive products tend to perform better in more sparsely vegetated regions. This behaviour forms the basis for the improved weight derivation in the ESA CCI SM v4 algorithm for regions where TCA estimates are deemed unreliable, which is discussed in the following section.

7.1 Direct merging of L2 observations into the COMBINED product

In ESA CCI SM v4, the COMBINED product is generated by directly merging L2 input data sets instead of the previously merged ACTIVE and PASSIVE products (as is the case in ESA CCI SM v2 and v3). This allows the estimation of temporally dynamic relative merging weights for each individual sensor based on which sensors provide valid observations on a particular day. For this purpose, all L2 input data sets are first directly scaled against GLDAS Noah to harmonise their climatology (as for the earlier versions, the SSM/I climatology is first replaced with that of AMSR-E). Uncertainties are then estimated (see below) for each individual product and used to construct error covariance matrices for all merging periods depending on the sensor availability during these periods (see Fig. 2). Finally, the data sets are merged into the COMBINED product, again using the minimum-weight threshold of 1∕2N on dates where not all input products available in that merging period provide valid measurements (see Sect. 6.3).

7.2 VOD-based uncertainty estimation

As was shown in Fig. 4, uncertainty estimates and hence merging weights largely follow VOD patterns. To obtain uncertainty estimates in regions where TCA estimates are not trusted, i.e. where not all three data sets used in TCA are significantly correlated, an empirical polynomial regression approach that predicts uncertainties from average VOD conditions at a particular location was introduced. Specifically, a polynomial function is fitted between mean VOD (estimated from AMSR-E C-band observations between 2002 and 2011) and TCA-based signal-to-noise ratio (SNR) estimates using VOD and SNR tuples from all grid cells where TCA estimates are assumed to be reliable, i.e. where all three data sets are significantly (p<0.05) correlated (see Fig. 6). Regression coefficients are calculated separately for each L2 input product and used to predict their SNR levels ($\widehat{{\text{SNR}}_i}$) from the mean VOD at grid cells (i) where the SNR could not be estimated from TCA:

where a_j are the polynomial coefficients and k is the degree of the polynomial function. k was chosen to be 3 for TMI and WindSat and 2 for all other sensors, which was empirically found to provide the best fit for the regression. Notice that regression coefficients are fitted between VOD and SNRs and not between VOD and uncertainties directly in order to account for varying signal variance across the grid cells that is used for the regression (Gruber et al., 2016b). SNRs are then converted into uncertainties as follows:

The overshooting in the regression curve of TMI for high-VOD values does not impact the final data product as grid cells with such high-VOD values are masked out by the L2 quality control process. The overshooting of WindSat for low VOD values affects a few grid cells in very dry regions and cannot be avoided by changing the polynomial order, as this would lead to overshooting in the more relevant VOD regions. SNR values at different grid cells and for particular VOD ranges sometimes show a significant variability around the corresponding estimate of the regression, which directly translates to uncertainties in the weight estimates that are used for the least squares merging. However, these uncertainties are assumed to be, on average, lower than the bias introduced by the p-value-based ternary decision of a weight of either 0, 0.5 or 1 as adopted in ESA CCI SM v2 and v3.

Figure 6Regression functions between VOD and SNRs (in decibel units) of all L2 products. Box plots show the median, the interquartile range and the 5 and 95 percentiles, respectively.

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Figure 7SNR (in decibel units) of all L2 input products with uncertainties estimated from TCA and the VOD regression.

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Figure 7 shows the combined TCA and VOD regression-based global SNR maps which are ultimately used to derive the merging weights for Eq. (2). Patterns generally follow common understanding. SNRs of active sensors are higher in more densely vegetated regions, whereas SNRs of passive sensors are higher in more sparsely vegetated areas (Dorigo et al., 2010; Liu et al., 2011, 2012; van der Schalie et al., 2018). SNRs of passive sensors largely depend on the microwave frequency (Liu et al., 2012; Parinussa et al., 2011, 2012). AMSR-E and AMSR2 (both C-band) SNRs are largely comparable and, in general, are higher than those for the higher-frequency (Ku-band) of SSM/I. SMOS (L-band) SNRs are, on average, relatively high and show a lower spatial variability as their longer wavelength makes the observations less sensitive to variation in vegetation.

Note that, as is the case in ESA CCI SM v3, SSM/I and TMI retrievals are never merged together or merged with AMSR-E, i.e. SSM/I data are only used at high latitudes where TMI data are not available, and neither of the two is used after AMSR-E becomes available (see Sect. 6.3). Nevertheless, their uncertainties are in many areas comparable with each other and with those of the other sensors, suggesting that they might add valuable information when included in the least squares merging scheme, which will be considered for future product versions (see Sect. 10).

7.3 P-value-based quality control

In ESA CCI SM v4, for the generation of both the PASSIVE and the COMBINED product, correlation significance levels are used to completely mask out individual L2 input products that are deemed unreliable at a particular location and during a particular merging period (in cases where more than one product is available for merging). For this purpose, the p-value mask that is used in the ESA CCI SM v3 product (see Sect. 6.6) was modified as shown in Table 3. All measurements from the target satellite product that is being tested for reliability are masked out if they do not correlate significantly with both soil moisture estimates from GLDAS Noah and the measurements from the second satellite product used for TCA, or if they correlate significantly with the reference satellite product but not with the model time series.

Table 3Merging scheme based on the one-tailed p value for the correlation between the model (m), the reference satellite (r), the target satellite (t) and soil moisture with a 0.05 significance level.

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The rationale behind the latter is that potential non-zero error correlations, arising, for example, from uncorrected vegetation variations (Zwieback et al., 2018), may lead to spurious correlations between the two products, even though they do not contain useful soil moisture information. Note, however, that the decisions in the p-value mask were empirically tuned to lead to a good performance (of the merged products) in terms of correlation against the ERA-Land soil moisture product. Consequently, decisions that are based on significance levels of the correlation against GLDAS Noah may be questionable, since the two models are most likely not fully independent. This issue is currently under investigation and will be addressed in future product versions (see Sect. 10).