2.1 GRACE and GRACE-FO data

To investigate fast temporal water storage changes, we use the daily gravity field solutions of the ITSG-Grace2018 model (Kvas et al., 2019) converted to a global time series of daily TWS anomalies. Compared to the standard monthly solutions, the limited satellite ground track coverage during 1 d does not allow for a stable global gravity field inversion; thus, additional information has to be introduced. The processing of the daily solutions is therefore carried out using a Kalman smoothing approach (similar to Kurtenbach et al., 2012), which introduces statistical information on the expected evolution of the gravity field over time in its process model. As a tradeoff, the resulting daily gravity field data are not fully independent daily solutions but exhibit some degree of correlation with previous time steps.

Daily gravity field data are given in the form of spherical harmonic coefficients (so-called Level 2 products) of the gravitational potential up to a degree of n=40, corresponding to a spatial resolution of 500 km. During the data processing, temporally high-frequency mass variations caused by tides (ocean, Earth, and pole tides), in addition to non-tidal atmospheric and ocean mass variations, are removed by subtracting the output of the geophysical background models from the observations (dealiasing; Dobslaw et al., 2017). Post-processing steps account for the effect of geocenter motion (adding the degree 1 harmonic coefficients given by Sun et al., 2016, on the basis of Swenson et al., 2008), replace the c₂₀ coefficient based on a time series from satellite laser ranging (Cheng and Ries, 2017), and subtract the influence of glacial isostatic adjustment (GIA), using the ICE6G-D model (Peltier et al., 2017). No extra spatial filtering is needed because the Kalman smoother effectively suppresses spatially correlated noise. After these processing steps, the resulting gravity field models are assumed to primarily contain water mass changes above and below the Earth's surface and can be converted to equivalent water heights on a global geographical grid of $\mathrm{1}{}^{\circ }\times \mathrm{1}{}^{\circ }$, according to the following:

where λ and ϑ symbolize the spherical coordinates, M and R are the mass and the radius of the Earth, ρ_w is the density of water $\left(\frac{\mathrm{1000}\mathrm{kg}}{{\mathrm{m}}^{\mathrm{3}}}\right)$, $k_n^{\prime }$ denote the load love numbers (Lambeck, 1988), c_nm are the spherical harmonic coefficients of the gravitational potential, and Υ(λ,ϑ) are the surface spherical harmonic functions. The degree and order of the spherical harmonic functions are denoted by n and m. For a reasonable overlap with all satellite-based SM products, we used the time period from April 2015 to December 2021 for our study, excluding the time span between the end of the mission GRACE (August 2017) and the start of the successor mission GRACE-FO (July 2018). Even though the Kalman smoother output provides a continuous daily time series without data gaps for the mission time periods, all days with insufficient GRACE observations were excluded from our analysis (i.e., days with an observation count of less than 10 000 observations per day as given on the website of the ITSG-Grace2018 product). On these days, the daily solutions are mainly informed by the process model of the Kalman filter and thus tend towards an a priori mean trend and annual signal. Calculation of the GRACE TWS data was done using the Gravity Recovery Object Oriented Programming System (GROOPS; Mayer-Gürr et al., 2021).

Limitations of the GRACE TWS data that are relevant for this study relate to the limited spatial resolution (i.e., 500 km for daily data, as stated above), which results in the TWS grid cell values not being independent from neighboring grid cells. This can lead to leakage effects (Longuevergne et al., 2013) of spatially localized mass variations that are small in their spatial extent but strong in magnitude, such as surface water storage change in lakes or reservoirs. Coastal areas should also be regarded with care because the limited spatial resolution prevents a strict separation between land and ocean signals in the GRACE data sets. While a mere dampening of the continental signal caused by a much lower mass variability on the ocean does not influence the correlations between the TWS and SM discussed in the present study, the so-called “leakage in” (Baur et al., 2009; i.e., spurious high-frequency ocean signal being leaked onto land areas) might have an influence on the comparison of TWS and SM in coastal areas. A more detailed discussion on this and a map (with areas that should be regarded with caution) is shown in Eicker et al. (2020, see Fig. 4 in their Supplement). Another issue that needs to be kept in mind when comparing TWS with SM data is the fact that the GRACE TWS observations represent the fully integrated vertical water column, which includes SM but is not limited to it. On the one hand, this is a challenge, as the two quantities (TWS and SM) are not directly comparable. One the other hand, it is the particular strength of the TWS observations to be sensitive to water storage dynamics that otherwise are not observable by remote sensing, such as those in deep soil layers down to the groundwater. To explore what we might learn from such differences (TWS versus SM), regarding hydrological process dynamics in the subsurface, is one motivation for this study.

2.2 Soil moisture data sets

Active or passive microwave remote sensing can observe SM in the top few centimeters of the soil, exploiting the fact that the dielectric constant of the soil changes with varying soil water content. Several dedicated instruments are currently in operation on different satellite missions. Active microwave sensors (radars) transmit an electromagnetic pulse to the Earth and measure the pulse's backscattered energy from the surface of the Earth, whereas passive microwave sensors (radiometers) observe the radiation naturally emitted by the Earth's soil, which is expressed as the brightness temperature (Robinson et al., 2008). The observed parameters (backscattered energy and brightness temperature) of both techniques depend on the dielectric constant of the soil, which allows the measurement of SM.

In our study, we use satellite-derived SSM products from the missions SMOS, SMAP, and from the combination data product ESA CCI, as well as RZSM products from SMOS and SMAP. Both SMOS and SMAP provide so-called Level 3 (L3) and Level 4 (L4) data, with L3 referring to the original satellite observations acquired over a 24 h period given as a multi-orbit global map of retrieved soil moisture (L3 data do not have complete global coverage), while L4 relates to post-processed data products. The way of post-processing differs between the two satellite missions and will be detailed below. The overlapping time span of all missions between April 2015 (start of the SMAP mission) and December 2021 was selected. In addition, it should be mentioned that the orbit direction (ascending/descending orbit) differs across the L3 products and therefore also the overpass time. In this study, the early morning overpass is chosen for the L3 satellite SM products. This is suggested for passive measurement methods, as the temperature difference between the soil surface and the vegetation canopy in the morning and night, in addition to the thermal difference between various types of land cover, within a pixel is reduced; this results in a minimization of SM retrieval errors and better reliability (Owe et al., 2008; Entekhabi et al., 2014; Lei et al., 2015; Montzka et al., 2017).

3.1 Spatial mask

The type of land cover can lead to limitations for observing SM. In densely vegetated areas such as tropical rainforests, the observed emissivity by passive satellites or the backscattered energy by active satellites is primarily caused by the vegetation (Ulaby and Long, 2014; Owe et al., 2001). In deserts, the SM signal may be unreliable, as the variability in the water in the upper soil is low (Dorigo et al., 2010). The problem of reduced sensitivity in deserts also accounts for the satellite gravimetry observations from GRACE and GRACE-FO, as their signal-to-noise ratio is low, and the noise floor of GRACE strongly dominates the time series. Other surface characteristics that limit the measurements of satellite SM are snow cover and frozen soil, since the dielectric constant of snow and frozen water varies significantly from the one of liquid water (Wagner, 1998).

Therefore, three spatial masks have been defined to identify problematic regions for observing SM. These are dense vegetation, regions with snow and frozen ground throughout large parts of the year, and areas with low SM (e.g., deserts), as seen in Fig. 2. To indicate dense vegetation, in our study we use the tropical rainforest mask that is also applied in the ESA CCI data set. Also, for regions with a large fraction of snow cover and frozen soil, the same method used for the ESA CCI mask is applied. It uses soil temperature (T_S) and snow water equivalent (SWE) estimates from the Global Land Data Assimilation System Noah (GLDAS Noah) to flag satellite observations that were taken under the conditions of frozen soil (T_S < 0 ^∘C) and snow cover (SWE > 0 mm; Gruber et al., 2019). Grid cells in which more than 40 % of all observations are influenced by these conditions were included in the mask. We classify dry (desert) regions based on the SM signal variability, i.e., the root mean square (rms) of the daily SM time series in each grid cell. As a threshold value for low variability, we use twice the mean rms of a test region in the Sahara desert, where no major day-to-day SM variations can be expected. To define the mask with this criterion, we used the SMOS L3 data product. Using the other SM data products led to very similar results. In some regions, the low SM variability mask overlaps with the snow cover and frozen ground mask. The low SM variability areas are excluded from further analyses because no discernible signals of both SM and TWS can be expected. As we want to use the maximum of the available information of both data sets for the first analysis of this kind performed in the present study, values in the region of the other two masks (dense vegetation and snow cover and frozen ground) are considered in the analyses but will be discussed with care to recognize the limitations of SM retrieval.

Figure 2Spatial masks applied in this study for low SM variability (red), dense vegetation (green), and snow cover and frozen ground (blue). In the other areas (beige; here denoted as the area suited for analysis), reasonable satellite-based SM signals can be expected.

4.1 Time series comparison for an example location

The comparison of time series between TWS from ITSG-Grace2018 and SM from various products is first shown for one exemplary grid cell. We chose one cell, with marked short-term and seasonal SM variations, close to the city of Kota (25^∘ N, 75^∘ E), located in the southeast of the Indian state of Rajasthan and characterized by a hot semi-arid climate, with a monsoon season from July to September. The location of this grid cell is indicated in the maps in Fig. 4 (blue circle). Figure 3 (top) shows daily TWS in this grid cell in comparison to SSM derived from satellite observations only. While TWS exhibits a comparatively smooth behavior for short timescales and a dominant seasonal signal, the SSM time series are of considerably higher variability at short timescales. One reason is the noise of the satellite SM observations themselves (e.g., Karthikeyan et al., 2017). On the other hand, this variability can partly represent a real signal, as near-surface SM exhibits quick wetting and drying dynamics from individual precipitation events and from subsequent evaporation. In contrast, the much larger integration depth of the GRACE observations down to groundwater results in integral water storage with much slower dynamics. Furthermore, it has to be noted that, for an integration depth of the SSM products of a few centimeters, the overall amplitudes of SM experience a change of the order of 40 vol. % (shown in Fig. 3) that corresponds to water storage changes that are 1 order of magnitude smaller than those of the GRACE-based TWS. An investigation into whether the fast-changing surface signals can also be detected in the GRACE data will be pursued in Sect. 4.3 for high-pass filtered time series. Comparing the time series of the three SSM products for this particular location, SMAP L3 and the multi-satellite combination product ESA CCI time series appear less noisy than the SMOS L3 time series, which is in good agreement with findings of, e.g., Montzka et al. (2017), Cui et al. (2017), Xu and Frey (2021), and Kim et al. (2021).

While there is a general correspondence in the dynamics of TWS and SSM regarding the dominating seasonal signal (strong rise in water storage and SM during the monsoon season followed by a quick decline), a time shift can be identified between both quantities. The seasonal maxima and minima of the GRACE time series occur approximately 1–2 months later than those of SSM. This can again be attributed to the slower and delayed water storage change in the deeper layers seen by GRACE, in which a change from dry to wet conditions (or vice versa) takes much longer to evolve than in the layers close to the surface. In addition to the main seasonal maximum, a minor secondary maximum can be identified each year in the period from November to January in the SSM time series, and it is particularly well visible in the SMAP L3 data (yellow line). For the TWS data, minor peaks or a less steep TWS recession can be observed during this period, although a more general statement is hindered by the gaps in the TWS time series. Further discussion on this feature follows in the next paragraph.

Figure 3Time series of TWS from ITSG-Grace2018 and satellite SM for an exemplary grid cell around Kota, Rajasthan, in India (25^∘ N, 75^∘ E). Linear trend components have been subtracted from all time series. (a) TWS ITSG-Grace2018 vs. SSM from SMOS L3, SMAP L3, and ESA CCI. (b) TWS ITSG-Grace2018 vs. SSM from SMAP L4 and RZSM from SMOS L4 and SMAP L4. (c) Time series of the average year between TWS and all SM products.

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Figure 3 (middle) compares the TWS time series and the L4 SM products. For SMAP, both the surface (SSM) and the root zone (RZSM) products are the result of the data assimilation procedure described in Sect. 2.2.2. The SMAP L4 RZSM time series has a smaller variability compared to the SSM data at both short-term and at seasonal timescales. This is also the case for the L4 RZSM product of SMOS, in which the seasonal variability is dampened even more strongly. The secondary maximum in November–January obvious in the L3 products is still visible in the L4 RZSM data set of SMOS, since the physical extrapolation of the SSM data into deeper layers is applied for the SMOS L4 product. In contrast, the assimilation applied to SMAP L4 removes this second seasonal maximum for both the SSM and the RZSM data sets. This indicates that the signal seen in the direct satellite SM data is not represented by the forcing data of the underlying model (i.e., precipitation) and thus fades out in the L4 SMAP product. This shows how strongly SMAP L4 is influenced by the underlying model and the climate data used as model forcing. The secondary SM peak might thus be caused by extensive irrigation after the end of the monsoon season. The results corroborate a possible deficiency of the SMAP L4 product (i.e., that it is mainly driven by precipitation input in the data assimilation framework and thus does not represent the impact of irrigation). The combination of (near-surface) soil moisture products and TWS observations may thus shed light on how human activities and irrigation practices in particular translate into water storage changes in deeper soil zones. While the focus of this study is on shorter-term storage changes, overlapping trend signals in the unsaturated zone and in the groundwater that may be caused by these activities may be difficult to disentangle. However, a detailed analysis of this particular phenomenon is beyond the scope of this study.

The described characteristics of the different products are also confirmed when investigating the average year (i.e., the mean value for each day of the year shown in Fig. 3 at the bottom). Even though the short overlapping time span does not allow for the computation of a stable climatology, the increase in the seasonal signal with SM during the monsoon phase between July and September can clearly be identified. The SSM products exhibit a larger seasonal amplitude than the dampened RZSM counterparts. Furthermore, the time shift between SSM and TWS is generally larger than for the RZSM products. Here it can be concluded that the dynamics of RZSM are closer to the variability in the integral TWS signal that represents the entire water column, even though the RZSM data still miss the even slower processes in deeper soil layers and in groundwater.

4.2 Global analysis

The correspondence of the daily time series of TWS from ITSG-Grace2018 with the various SM products is analyzed globally for each 1^∘ continental grid cell and displayed as global maps of the correlation coefficient in Fig. 4. Desert areas, according to the definition provided in Sect. 3.1, are excluded, as the GRACE signal is dominated by noise in these regions, and no reasonable comparison is possible. Additionally, Fig. 5 shows the cumulative distribution functions (CDFs) of cell-based correlation values, both globally and separately, for the major land cover types shown in Fig. 2.

Figure 4Comparison of the correlation coefficient between all SM products and ITSG-Grace2018. Desert regions are masked out due to low water variability. In all maps, the location of the exemplary time series in India (see Fig. 3) is marked with a blue circle.

The global patterns of regions with comparably large correlations between GRACE TWS and SM are similar for all SM products. These regions are particularly found in humid climate zones and in seasonally dry climates (parts of tropical South America, Southeast Asia, southeastern USA, northern Australia, and the outer tropics in Africa). The absolute correlation values differ markedly between the SM products. The smallest correlations are found for the satellite-only L3 SSM data products (Fig. 4a–c). While maximum values in individual grid cells can reach up to 0.92 (SMOS) and 0.93 (SMAP), the median values amount to 0.23 (SMOS) and 0.27 (SMAP) only. SMOS L3 SSM has negative correlations (Fig. 5), particularly in the northern latitudes that are at least partly influenced by snow cover and frozen ground (Fig. 5c), and has fewer large positive correlations in grid cells that are potentially well suited for SM remote sensing (i.e., that are not influenced by snow, ice, or dense vegetation; Fig. 5b). The latter might be attributed to a larger noise level in the SMOS than in the SMAP time series. The combination data product ESA CCI (black curve in Fig. 5b) generally shows larger correlation values than both the single mission products (except in the northern latitudes), particularly in South America, Africa, and Australia (Fig. 4c). Please note that the masking of, e.g., rainforest areas in the CCI product leads to an overall smaller number of grid cells for the comparison than for SMOS or SMAP. The overall larger correlation of ESA CCI implies that the ensemble product weighs down the spurious contributions of individual data sets. Nevertheless, the interpretation needs to be done with caution, as TWS cannot be directly taken as a benchmark for SSM, and the limitations of the GRACE data product outlined in Sect. 2.1 might additionally hamper the comparison.

Figure 5Cumulative distribution functions (CDFs) of cell-based correlation values. (a) Showing the CDFs of all grid cells globally. (b, c, d) Showing the grid cells for the major land cover types, as defined in Fig. 2. In the upper left corner, the number of grid cells used for the creation of the individual CDFs is shown.

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The effect of using a land surface model with data assimilation for generating the SMAP L4 SSM product is a strong increase in the correspondence of the temporal dynamics of this SM data set with GRACE-based TWS (Fig. 4d). The CDF in Fig. 5a (red line) reveals the most common correlation values in the range of 0.4–0.7, with a median of 0.52. This increase in the correlation for the L4 SSM data indicates that constraining the SM dynamics by a deterministic modeling approach and by independently observed forcing data, such as precipitation rates and air temperature, leads to a model-dominated product with considerably less noise than the L3 SSM product. For the L4 RZSM products of both SMOS and SMAP, their larger integration depth leads to another increase in the agreement with TWS compared to the respective surface products (Fig. 4e, f). This again indicates that reflecting the slower and delayed water transport processes in deeper soil layers in the L4 RZSM products causes their dynamics to be more similar to the integrative GRACE-based TWS, in particular with respect to the temporal phase (also see the time shift analysis below). This applies in particular to the grid cells that are reasonably suited for satellite-based SM monitoring for which the CDFs are shifted strongly to higher correlation values compared to the L3 data, with the most common values of around 0.7 (SMOS) and 0.8 (SMAP; Fig. 5b). In contrast, for SMOS L4 RZSM in high northern latitudes, correlations with TWS become even more negative than for SMOS L3 SSM (see the time shift analysis below). Xu et al. (2021a) have already shown that the SMAP L4 RZSM product outperforms the SMOS L4 product in terms of agreement with in situ measurements from the International Soil Moisture Network, particularly in the Northern Hemisphere.

The different integration volumes and the different processes acting on SM and TWS cause a time shift between their respective dynamics (e.g., Fig. 3). We use a cross-correlation analysis (see Appendix A1) for each grid cell to investigate the time shift on a global scale. Regarding the maps in Fig. 6, a negative time shift (blue colored grid cells) indicates a delay of the GRACE signal; i.e., the maximum of the dominant seasonal signal of TWS occurs later in the year than the maximum of SM. In the Arctic regions, mostly positive shifts (in some cases more than +120 d) are seen, in particular for the two SMOS products (see also the CDFs in Fig. 7). Snow accumulation leads to an increase and a maximum of TWS during the winter season, whereas the maximum of SM is reached during the melting season several months later, resulting in a delay of SM versus TWS. This effect becomes even more pronounced when the further delay by SM storage in deeper layers is considered in the L4 root zone products of SMAP and, in particular, SMOS. Negative correlation coefficients of TWS and SM time series are a consequence of the inverse seasonal dynamics of the two storage terms (Fig. 5). The least positive time shifts in the northern latitude regions are visible in the ESA CCI data set, which already masks out the data in the time series when observations were taken under the conditions of frozen soil and snow cover (see Sect. 3.1). Positive time shifts are also seen in some tropical forest regions (e.g., the Amazon and Congo rainforests), where the dense vegetation cover hampers the SM retrieval. This is particularly evident in the SSM L3 products (SMOS and SMAP) and persists in the SMOS RZSM, while the data assimilation introduced for SMOS L4 strongly reduces this effect. The positive time shifts can thus be attributed to artifacts in the SM data rather than to a hydrological signal.

Figure 6Time shift between SM and TWS time series per grid cell. Negative numbers imply that TWS is delayed in comparison to SM.

Figure 7Cumulative distribution functions (CDFs) of the cell-based time shift. (a) Showing the CDFs of all grid cells globally. (b, c, d) Showing the CDFs for grid cells for the major land cover types which are shown in Fig. 2. In the upper left corner, the number of grid cells used for the creation of the individual CDFs is shown.

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In grid cells that are neither influenced by snow cover nor by dense vegetation (Fig. 7b), the time shifts are primarily negative, indicating the delayed dynamics of TWS compared to SM. For the majority of the products, the time shifts are negative and can reach up to −90 d and beyond. A comparison of the different products reveals that the time shifts decrease (i.e., become less negative) the closer the SM products conceptively resemble TWS. The three surface SM products from ESA CCI, SMAP L3, and SMOS L3 show the highest negative time shifts (up to −60 to −90 d in Fig. 6), with median values of −35 d (both ESA CCI and SMAP L3) and −32 d (SMOS L3). The time shifts are smaller for SMAP L4 (SSM; median of −17 d) and even smaller for the RZSM products, with median values of −5 d (SMAP L4 RZSM) and −13 d (SMOS L4 RZSM). This supports the assumption that adding the SM dynamics of deeper soil layers to SSM increases the resemblance to the integrated TWS signal. For SMOS L4 SM, the extrapolation into deeper soil layers even leads to a change from a negative time shift to a positive time shift (i.e., TWS dynamics preceding those of SMOS L4 RZSM) in 17 % of the land areas, e.g., in parts of South America, Asia, and Australia. This points out possible deficiencies in the depth-scaling algorithm for SMOS L4 in some regions in terms of the way that it represents the transport and storage processes from the surface to deeper soil layers with too many delays and that the rates of reduction in the water storage in the deeper layers by evapotranspiration and percolation and/or runoff may be underestimated, thus leaving too much water in the storage for a time period that is too long. While the limitations of the GRACE observations can also be expected to cause some discrepancy between the two data types, there is no known deficit in the GRACE data that may spuriously pull their dynamics to an earlier stage.

4.3 Sub-monthly variations (high-pass filtered data)

The exemplary comparison of the TWS and SM time series in Fig. 3 suggests that fast-changing SM signals might be masked in the TWS time series by the dominating slower dynamics of the deeper layers in the unsaturated zone and in groundwater. Therefore, we isolate the water storage changes on sub-monthly timescales by applying a high-pass filter (third-order Butterworth filter) with a 30 d cutoff frequency (see Appendix B for details). Exemplary high-pass filtered time series for 1.5 years of SMAP L4 RZSM and TWS from ITSG-Grace2018 are shown in Fig. 8 for the same grid cell as in Fig. 3. The overall correlation of the two time series amounts to ρ=0.33, but it varies strongly with signal strength. While the GRACE time series is dominated by noise and only a very small correlation to RZSM of ρ=0.17 was found in dry months (October to June) with very small high-frequency water storage fluctuations, the correlation is higher in the monsoon season (July to September) with ρ=0.45. Additional high-pass filtered time series for grid cells belonging to different climate zones are presented in Appendix C.

Figure 8High-pass filtered time series of TWS from ITSG-Grace2018 and RZSM from SMAP L4 for an exemplary grid cell in India (25^∘ N, 75^∘ E).

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The correlations of the high-pass filtered TWS and SM time series (Fig. 9) are considerably smaller than those of the unfiltered time series. This can be expected, as the seasonal storage variations that often cause high correlation values for the unfiltered time series are not present anymore in the filtered ones. Nevertheless, correlations of the sub-monthly signals are generally positive, with only a few grid cells showing negative correlations. Non-significant correlations are stippled in Fig. 9 (for more information on significance testing, see Appendix A2). Again, it can be observed that RZSM products have a stronger correlation with TWS than their SSM counterparts. While the numbers are very small for the SSM of SMOS L3 (maximum value of ρ_max=0.33 and significantly positive correlations in only 26 % of land areas covered by the data product, with desert areas excluded), they are larger for SMAP L3 SSM products (ρ_max=0.37 and 43 % significantly positive). Again, the larger noise floor of the SMOS data set most likely dominates the high-pass filtered time series. The share of grid cells with significantly positive correlations increases for the combination data product ESA CCI (ρ_max=0.38 and 58 % significantly positive) and even more for the data-assimilated product of SMAP L4 SSM (ρ_max=0.40 and 71 % significantly positive). The former reveals the positive effect of combining several SSM data sets, which very likely results in a reduction in the high-frequency noise, and the latter indicates the influence of the forcing data of the underlying land surface model. In particular, it can be argued that model forcing with observation-based rainfall data causes major SSM increases to be closer in time and magnitude to the water storage increases that are seen by the GRACE observations. For the root zone, the percentage of the significantly positive grid cells is still low for SMOS L4 (37 %), with only a few larger areas in western Brazil, the south of Africa, and India, but the magnitude of the correlations has increased (ρ_max=0.50). For SMAP L4 RZSM, the values are significantly positive in the largest parts of the continents (77 %), with exceptions only in the very high latitudes and some small spots in dry regions in Africa, Australia, and Asia. In large regions (particularly in the southeastern United States, large parts of South America's southeastern region, the Ganges–Brahmaputra basin and China, and northern Australia), the correlations are in the range of 0.5, reaching maximum values of ρ_max=0.62. Overall, even though correlations are rather low for the high-pass filtered signals (with the exception of SMAP L4), they are significantly positive in large parts of the continents, hinting at the fact that satellite gravimetry and SM remote sensing are sensitive to the same hydrological dynamics, even for timescales shorter than 1 month.

Figure 9Correlation coefficients of high-pass filtered SM and TWS time series. Grid cells with non-significant correlations are stippled. In the lower-right map (f), the location of the exemplary time series in India (see Fig. 8) is circled in blue.

Finally, by computing the cross-correlation function for the high-pass filtered signals, we determine, for each grid cell, the time shift in the TWS versus the SM time series that leads to the highest correlation (Fig. 10). Time shifts larger than ±15 d are masked out because they have no physical meaning, given that a high-pass filter of 30 d was used. The remaining regions with valid results noticeably overlap with the regions in which some correspondence of TWS and SM dynamics has already been found in the correlation analysis with an unshifted time series (Fig. 9). The time shifts found for the high-pass filtered time series are considerably smaller than those found for the full unfiltered signal. Time shifts tend to be negative, with up to −3 d for all SSM products (i.e., TWS is lagging behind SSM). For the RZSM products, however, the time shifts are less negative or close to zero (SMAP L4) or even positive (SMOS L4). The negative time shifts illustrate that GRACE observations represent the depth-integrated water storage dynamics in the subsurface that are delayed relative to SSM, even at sub-monthly timescales. This is corroborated by the observation that the time shifts mostly vanish when deeper layers are included in the SM product (SMAP L4; i.e., when the SM product becomes conceptually closer to the storage that is represented by the TWS observations). The positive time shifts for the SMOS L4 relative to TWS in most parts of the world indicate that the depth-scaling approach used for SMOS L4 may represent transport and storage processes from the surface to deeper soil layers with too much delay, which is similar to the results obtained with the full unfiltered signal. Even for the short timescales considered here with the high-pass filtered signal, some processes such as daily evapotranspiration or runoff that cause water to be removed from the storage may be underestimated.

Figure 10Time shift between high-pass filtered soil moisture and total water storage time series per grid cell. Negative numbers imply that the TWS is delayed in comparison to the SM.