A Comparison of Global and Regional GRACE Models for Land Hydrology
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DOI: 10.1007/s10712-008-9049-8
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- Klees, R., Liu, X., Wittwer, T. et al. Surv Geophys (2008) 29: 335. doi:10.1007/s10712-008-9049-8
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Abstract
When using GRACE as a tool for hydrology, many different gravity field model products are now available to the end user. The traditional spherical harmonics solutions produced from GRACE are typically obtained through an optimization of the gravity field data at the global scale, and are generated by a number of processing centers around the world. Alternatives to this global approach include so-called regional techniques, for which many variants exist, but whose common trait is that they only use the gravity data collected over the area of interest to generate the solution. To determine whether these regional solutions hold any advantage over the global techniques in terms of overall accuracy, a range of comparisons were made using some of the more widely used regional and global methods currently available. The regional techniques tested made use of either spherical radial basis functions or single layer densities (i.e., mascons), with the global solutions having been obtained from the various major processing centers. The solutions were evaluated using a range of computed statistics over a selection of major river basins, which were globally distributed and ranged in size from 1 to 6 million km^{2}. For one of the basins tested, the Zambezi, additional validation tests were conducted through comparisons against a custom designed regional hydrology model of the region. We could not prove that current regional models perform better than global ones. Monthly mean water storage variations agree at the level of 0.02 m equivalent water height. The differences in terms of monthly mean water storage variations between regional and global solutions are comparable with the differences among only global or regional solutions. Typically they reach values of 0.02 m equivalent water heights, which seems to be the level of accuracy of current GRACE solutions for river basins above 1 million km^{2}. The amplitudes of the seasonal mass variations agree at the sub-centimetre level. Evident from all of the comparisons shown is the importance that the choice of regularization, or spatial filtering, can have on the solution quality. This was found to be true for global as well as regional techniques.
Keywords
GRACE Global gravity models Regional gravity models Land hydrology1 Introduction
The Gravity Recovery and Climate Experiment (GRACE) satellite mission is managed by the US National Aeronautics and Space Administration (NASA) and the German Aerospace Centre (DLR) (e.g., Tapley et al. 2004). Its goal is to map the Earth’s time-varying gravity field with a temporal resolution of 1 month or better and a spatial resolution of about 400 km. The mission was launched in March 2002 and is expected to provide data until at least 2010. Temporal gravity variations at these spatial and temporal scales are mainly caused by mass redistribution in the atmosphere and oceans, tides, postglacial rebound, and terrestrial water cycling. Through the data pre-processing, the contributions of tides, atmosphere, and oceans are largely removed using models of the underlying geophysical processes. Therefore, monthly gravity models mainly reflect changes in terrestrial water storage, as well as the change in snow/ice mass of the polar ice sheets and mountain glaciers, with respect to a long-term mean.
Monthly gravity field solutions are computed at the University of Texas at Austin Center for Space Research (CSR), the GeoForschungsZentrum Postsdam (GFZ) and the Jet Propulsion Laboratory (JPL) (see http://podaac.jpl.nasa.gov/grace or http://isdc.gfz-potsdam.de/grace), the Centre National d’Etudes Spatiales (CNES) (Lemoine et al. 2007), and the Delft Institute of Earth Observation and Space Systems (DEOS) at Delft University of Technology (Liu 2008), among others. These solutions are expressed in the form of spherical harmonic coefficients up to some maximum degree, representing monthly average values, although temporal sampling and averaging intervals are not completely uniform. The analysis centres follow different data pre-processing, processing, and post-processing strategies, which cause differences in the monthly sets of spherical harmonic coefficients.
Some analysis centres such as DEOS (e.g., Klees et al. 2007a), the Institute of Theoretical Geodesy (ITG) at the University of Bonn (e.g., Eicker 2008), the Goddard Space Flight Center (GSFC) (e.g., Rowlands et al. 2005; Luthcke et al. 2006), and others, compute solutions for specific areas of interest using spherical radial basis functions (SRBFs) or single layer densities (mascons) as an alternative to the spherical harmonic representation of surface mass change. These so-called regional solutions use overflight data exclusively over the region of interest. They are attractive for two reasons: (1) they require only a limited set of GRACE data to be processed and a relatively small number of basis functions, and (2) they are expected to exploit the resolution of the GRACE observations better than the spherical harmonic basis functions. Again, each analysis centre uses its own data retrieval procedure.
The main objectives of the paper are (1) to quantify the differences between the latest release of monthly spherical harmonic models of terrestrial water mass change, (2) to quantify the differences between monthly spherical harmonic models and monthly regional (SRBF and mascon) models, and (3) to investigate whether regional models provide more accurate estimates of water storage variations and better spatial resolutions than global models.
The paper is organized as follows: in Section 2, we briefly describe the GRACE gravity models, the main target areas, and the hydrological data used for GRACE model validation. The main results are presented in Section 3, which consist of a series of comparisons between regional and global GRACE models for different target areas, as well as a validation of these models. The latter consists of two parts: (1) we compare the GRACE models with the output of a regional hydrological model for the Zambezi River basin developed at Delft University of Technology; (2) we use the driest part of the Sahara desert as a validation area, with the assumption that the monthly mean mass change over this area is close to zero. In Section 4 we discuss the importance of a proper regularization or post-processing filtering of the regional GRACE solutions. The main results of the study are summarized and some conclusions are drawn in Section 5.
2 GRACE Gravity Models, Target Areas, and Hydrological Models
2.1 GRACE Gravity Models
We compare monthly global GRACE models provided by the CSR (GRACE Level-2 products, version CSR-RL04), GFZ (GRACE Level-2 products, version GFZ-RL04), JPL (GRACE Level-2 products, version JPL-RL04), CNES, and DEOS. The cut-off degree for most of the models is 120 with the exception of the CNES models, which is 50. The models are analyzed for the period February 2003 to February 2006. To allow for a fair comparison, we apply the same filters to all models in order to remove correlated noise in the spherical harmonic coefficients. We use the destriping technique of Swenson and Wahr (2006) in combination with a 400 km halfwidth Gaussian smoothing. This filter is referred to as DS400. The decision to apply the DS400 also to the CNES models has been made after a comparison with the unsmoothed CNES models. This comparison reveals that the unsmoothed CNES models still suffer from significant noise artefacts and perform worse compared with the DS400-filtered CNES models. The models are complemented by a global DEOS solution, which is filtered with an anisotropic non-symmetric (ANS) filter. The ANS filter has been designed to minimize the global mean of the mean-square error (Klees et al. 2008). The filter exploits full signal and noise variance–covariance information in an iterative least-squares approach. The corresponding model is referred to as DEOS-ANS, whereas the DEOS model that uses the DS400 filter is referred to as DEOS.
Two types of regional solutions are included in the study, which differ in terms of the parameterization used to model water mass change over the target area. The DEOS-SRBF solutions use Poisson wavelets (Holschneider et al. 2003; Holschneider and Iglewska-Nowak 2007) on an order-35 Reuter grid (Freeden et al. 1998), for a total of 1,542 basis functions. The order of the Reuter grid is an indication of the spatial resolution: order 35 corresponds to a cutoff spherical harmonic degree of 35. The optimal bandwidth of the Poisson wavelets was estimated in an iterative least-squares approach using Generalized Cross Validation (Golub et al. 1979). The approach is very similar to the one of Klees et al. (2007a) with the only difference being that no local refinement needs to be applied. The latter is justified by the relatively homogeneous coverage of the target area with satellite data. The solutions were regularized using the inverse of the ANS signal covariance matrix as a regularization matrix. This is equivalent to using the ANS post-processing filter, as shown in (Klees et al. 2008). The DEOS-MASCON solutions represent the time-varying gravity field as the potential of a single layer. The single layer density is modelled as a piecewise constant function over blocks of 4 × 4 deg. This is the same parameterization as that currently being used in the mascon solutions of GSFC (Rowland et al. 2005). The main difference between the DEOS-MASCON solutions and the GSFC solutions is that the latter use (1) a short arc analysis technique to relate GRACE range-rate data to the unknown mascons, and (2) an exponential signal covariance function in space and time to stabilize the solution and to enhance the spatio-temporal resolution. The DEOS-MASCON solutions are regularized in the same way as the DEOS-SRBF and the DEOS-ANS solutions.
The global and regional DEOS models use linear combinations of range measurements as observations in the functional model, which can be interpreted as average range accelerations. They are linearly related to the spherical harmonic coefficients, which express time variations in the gravity field. Assuming the noise in range observations is white, the noise in linear range combinations is colored, indicating that there are noise correlations in successive linear range combinations. These noise correlations were properly taken into account in the least-squares estimation procedure.
In all models to be studied the coefficients of degree 1 have been forced to zero and the coefficients of degree 2 were estimated together with the other spherical harmonic coefficients. The only exception are the CNES models, which use LAGEOS 1/2 satellite laser ranging data to fix the degree 2 coefficients.
2.2 Target Areas
The focus will be on three target areas: Zambezi (1.4 million km^{2}), La Plata (3.0 million km^{2}), and Sahara desert (3.0 million km^{2}). Moreover, some results will also be presented for the Amazon (6.9 million km^{2}), Mississippi (4.8 million km^{2}), and Ob (3.0 million km^{2}) drainage systems.
The La Plata River basin is the fifth largest river basin in the world (see Fig. 1) covering an area of about 3.0 million km^{2}. The area is of interest because we expect that the GRACE estimates of the La Plata monthly mean water storage variations suffer from leakage of the Amazon River basin, the Tocantins catchment basin, and the San Francisco catchment basin, all of them being located to the north and north-east of the La Plata River basin. Leakage is caused by the application of a spatial filter (DS400 or ANS). Because the filter function is actually non-zero outside the target area (though its amplitude decreases quickly with increasing distance from the target area), mass variations outside the target leak into the target area, leading to a wrong estimate of the mean mass variation over the target area (see e.g., Klees et al. 2007b).
The part of the Sahara desert being used in this study comprises only the driest part of the desert. In particular, the Nile River basin in the eastern part and the Atlas mountain range in the western part of the Sahara desert have been excluded (see Fig. 1). The area extends over about 3.5 million km^{2} and will be referred to as Sahara desert for reasons of simplicity. When accepting that the monthly mean mass variations over this area are almost zero, then the GRACE estimates represent residual noise artefacts and/or leakage from surrounding areas, in particular from the Mediterranean Sea, the Intertropical Convergence Zone, and the Nile River basin. This would make the area well suited to validate the global and regional GRACE models.
2.3 LEW Regional Hydrological Model
For the Zambezi River basin, the Lumped Elementary Watershed (LEW) regional hydrological model is used as reference for the GRACE models. The LEW approach has been presented in a previous study by Winsemius et al. (2006) (see also Klees et al. 2007a, b). The LEW approach incorporates the redistribution of surface runoff in downstream located model units, called LEW’s, that represent e.g., a wetland, lake or man-made reservoir. The model has been forced by data from the Climate Research Unit (CRU) (New et al. 2002) and monthly runoff data from several data sources, including the Global Runoff Data Centre and the Zambian Department of Water Affairs. The LEW water storage estimates have been generated using rainfall estimates from the Famine Early Warning System (FEWS) (Herman et al. 1997). These estimates were lumped over the LEWs to provide a time series from February 2001 to February 2006. The first 2 years of simulation (February 2001 to February 2003) have been taken as a warm-up period to stabilize the state variables of the LEW model structures.
- 1.
D (mm/month), which determines the amount of the monthly rainfall that is intercepted by vegetation and top-soil. D was allowed to vary around the calibrated value by 50% (uniformly distributed) with a fixed minimum of 30 mm/month;
- 2.
S_{u,max} (mm), determining the maximum soil moisture capacity. S_{u,max} was allowed to vary with 25% with a fixed minimum of 0 (a negative soil moisture storage does not exist);
- 3.
B (−), describing the spatial variability of the soil moisture capacity. B was allowed to vary with 50% with a fixed minimum of 0.
In this manner, 4.4% of all 10,000 Monte–Carlo simulations were retained and used as a proxy for the model parameter uncertainty. These models were then used to provide simulations with perturbed rainfall. The resulting time-variable storage estimations, lumped over the whole basin, are used in the following sections to provide confidence bounds for comparisons with the different GRACE models.
3 Comparison and Validation
3.1 Sahara
A further analysis of the 3-year time series reveals that the CNES time series is the only one with a statistically significant yearly cycle. The amplitude is 0.02 ± 0.006 m. This yearly cycle is likely the effect of leakage from surrounding areas, e.g., the intertropical convergence zone, the Mediterranean Sea, or the Nile River system. The maximum of the yearly cycle is attained around December/January each year, which indicates a dominant influence from the intertropical convergence zone. The yearly amplitudes of the other global and regional models do not differ statistically from zero. A representative example is the DEOS time series with an amplitude of 0.007 ± 0.004 m.
3.2 Zambezi
Zambezi River basin: fit of a yearly sinusoidal through a time series spanning the period from February 2003 to February 2006
Model | Amplitude (m) | Phase (months) | \(\hat{\sigma}\) (m) | R^{2} |
---|---|---|---|---|
CNES | 0.112 ± 0.008 | −0.1 ± 0.2 | 0.039 | 0.82 |
CSR | 0.111 ± 0.008 | −0.2 ± 0.1 | 0.039 | 0.80 |
GFZ | 0.102 ± 0.009 | −0.2 ± 0.1 | 0.042 | 0.76 |
JPL | 0.098 ± 0.006 | −0.3 ± 0.1 | 0.029 | 0.85 |
DEOS | 0.088 ± 0.006 | −0.3 ± 0.2 | 0.030 | 0.81 |
DEOS-ANS | 0.099 ± 0.010 | −0.2 ± 0.2 | 0.042 | 0.72 |
DEOS-SRBF | 0.118 ± 0.010 | −0.2 ± 0.2 | 0.040 | 0.81 |
DEOS-MASCON | 0.107 ± 0.009 | −0.3 ± 0.2 | 0.044 | 0.72 |
The annual amplitude of the LEW model is 0.129 ± 0.007 m; about 11% of the signal variance cannot be explained by the yearly cycle. The RMS of the un-modelled part is 0.031 m, which is about 20% of the peak amplitude. GRACE underestimates the annual signal amplitude over the period February 2003 to February 2006; the differences with respect to the LEW model range from −0.041 m (DEOS) to −0.011 m (DEOS-SRBF).
3.3 Intertropical Convergence Zone
3.4 La Plata
The plots for South America (cf. Fig. 4) are dominated by the strong mass redistribution signal in the Orinoco and Amazon river basins, which is the reason why the mass change patterns provided by the various GRACE solutions seem to be very similar. However, a closer look reveals that the amplitudes of the DEOS solution for Orinoco and Amazon are significantly smaller than the amplitudes provided by the other models. Also visible are the more pronounced differences among the models for the La Plata River basin compared with other river basins like the Zambezi, Amazon, and Ob River basins. When changing the color bar to emphasize mass variations outside the Amazon and Orinoco River basins (not shown here), we observe that all geographic plots show bumpy patterns and some East–West smearing effects, which may represent residual noise and, as far as the global models CSR, GFZ, JPL, DEOS, and CNES are concerned, the effect of the DS400 filter.
La Plata River basin: fit of a yearly sinusoidal through the time series spanning the period from February 2003 to February 2006
Model | Amplitude (m) | Phase (months) | \(\hat{\sigma}\) (m) | R^{2} |
---|---|---|---|---|
CNES | 0.032 ± 0.004 | 0.7 ± 0.2 | 0.018 | 0.59 |
CSR | 0.033 ± 0.004 | 0.5 ± 0.2 | 0.018 | 0.62 |
GFZ | 0.032 ± 0.005 | 0.4 ± 0.3 | 0.021 | 0.51 |
JPL | 0.029 ± 0.005 | 2.6 ± 0.3 | 0.021 | 0.44 |
DEOS | 0.029 ± 0.005 | 3.8 ± 0.3 | 0.021 | 0.47 |
DEOS-ANS | 0.020 ± 0.005 | 4.4 ± 0.2 | 0.020 | 0.27 |
DEOS-SRBF | 0.027 ± 0.005 | 4.3 ± 0.3 | 0.023 | 0.32 |
DEOS-MASCON | 0.032 ± 0.005 | 4.3 ± 0.2 | 0.018 | 0.61 |
Amazon River basin: fit of a yearly sinusoidal through the time series from February 2003 to February 2006
Model | Amplitude (m) | Phase (months) | \(\hat{\sigma}\) (m) | R^{2} |
---|---|---|---|---|
CNES | 0.145 ± 0.007 | −0.15 ± 0.10 | 0.034 | 0.90 |
CSR | 0.149 ± 0.009 | −0.15 ± 0.11 | 0.040 | 0.88 |
GFZ | 0.142 ± 0.008 | −0.19 ± 0.10 | 0.034 | 0.90 |
JPL | 0.122 ± 0.006 | 0.32 ± 0.09 | 0.025 | 0.93 |
DEOS | 0.104 ± 0.006 | −0.29 ± 0.10 | 0.025 | 0.90 |
DEOS-ANS | 0.115 ± 0.006 | 0.09 ± 0.10 | 0.025 | 0.91 |
DEOS-SRBF | 0.121 ± 0.005 | 0.05 ± 0.08 | 0.024 | 0.93 |
DEOS-MASCON | 0.098 ± 0.005 | −0.31 ± 0.10 | 0.022 | 0.90 |
We explain these larger differences among GRACE models for the La Plata river basin with complex hydrological cycle, which makes the results sensitive to the differences in data processing and post-processing. Berbery and Barros (2002) have shown that there are different precipitation regimes within the La Plata river basin. Each of these different regimes has a well-defined annual cycle but with different phases. Correspondingly, the mean annual cycle over the basin is rather small. The limited spatial resolution of the filtered GRACE solutions does not allow to distinguish between the different precipitation regimes. The significant spatio-temporal variability inside the La Plata river basin is supported by the very low value of the signal variance that can be explained by the yearly sinusoidal for the DEOS-ANS solutions (27%), because the spatial resolution of DEOS-ANS is usually better than that of the other global models due to a better performance of the ANS filter compared with the DS400 filter (Klees et al. 2008). Another reason for the larger differences is leakage from outside the river basin, in particular from the southernmost extension of the monsoon system, which is close to the northern boundary of the river basin. The larger differences could also be attributed to residual noise artefacts, due to the relatively small amplitude of monthly mean water mass change over the La Plata River basin (Klees et al. 2008).
3.5 Amazon, Mississippi, and Ob
Mississippi River basin: fit of a yearly sinusoidal through the time series from February 2003 to February 2006
Model | Amplitude (m) | Phase (months) | \(\hat{\sigma}\) (m) | R^{2} |
---|---|---|---|---|
CNES | 0.041 ± 0.007 | 0.82 ± 0.32 | 0.032 | 0.37 |
CSR | 0.045 ± 0.005 | 0.90 ± 0.19 | 0.020 | 0.70 |
GFZ | 0.043 ± 0.005 | 0.92 ± 0.20 | 0.020 | 0.71 |
JPL | 0.047 ± 0.005 | 0.55 ± 0.18 | 0.020 | 0.73 |
DEOS | 0.044 ± 0.003 | 0.38 ± 0.16 | 0.017 | 0.77 |
DEOS-ANS | 0.043 ± 0.004 | 0.59 ± 0.20 | 0.018 | 0.75 |
DEOS-SRBF | 0.048 ± 0.005 | 0.56 ± 0.22 | 0.025 | 0.64 |
DEOS-MASCON | 0.034 ± 0.004 | 0.59 ± 0.22 | 0.016 | 0.71 |
Ob River basin: fit of a yearly sinusoidal through the time series from February 2003 to February 2006
Model | Amplitude (m) | Phase (months) | \(\hat{\sigma}\) (m) | R^{2} |
---|---|---|---|---|
CNES | 0.050 ± 0.004 | 0.89 ± 0.18 | 0.021 | 0.74 |
CSR | 0.058 ± 0.005 | 0.75 ± 0.18 | 0.026 | 0.73 |
GFZ | 0.055 ± 0.004 | 0.91 ± 0.16 | 0.020 | 0.80 |
JPL | 0.044 ± 0.002 | 0.73 ± 0.12 | 0.013 | 0.86 |
DEOS | 0.052 ± 0.004 | 0.72 ± 0.15 | 0.018 | 0.82 |
DEOS-ANS | 0.050 ± 0.004 | 0.72 ± 0.15 | 0.016 | 0.83 |
DEOS-SRBF | 0.049 ± 0.004 | 0.81 ± 0.15 | 0.017 | 0.82 |
DEOS-MASCON | 0.044 ± 0.003 | 1.70 ± 0.16 | 0.015 | 0.82 |
4 The Effect of Filtering
A direct comparison of the DEOS time series with the DEOS-ANS time series shows the effect of filtering. Figures 2 and 4 indicate that the use of an ANS filter (DEOS-ANS) provides a smoother solution and, at the same time, improved spatial resolution and higher amplitudes than the DS400 filter. This is clearly visible in the South African intertropical convergence zone, on Madagascar island, in the Orinoco River basin, and in the La Plata River basin. For instance, the DEOS-ANS solution is the only global solution which resolves the mass change signal on Madagascar island for April 2004, whereas this signal is hidden in all global solutions that use the DS400 filter due to some pronounced smearing effects. This improved spatial resolution of the DEOS-ANS solution is due to the optimal filter, which exploits information about noise and signal variances and covariances. Leakage is more pronounced in the DS400 solutions and the application of a DS400 filter yields over-smoothed solutions. The superior performance of the DEOS-ANS models is also supported by a smaller RMS signal for the Sahara region (cf. Fig. 6). The ANS filter is extensively discussed and analyzed in Klees et al. (2008).
Regional solutions are attractive, because they require a parameterization of only the target area and the surroundings, only use overflight data, and allow for a more flexible adaptation of the parameterization to the signal over the target area. Global solutions have to be filtered in order to remove the high-frequency correlated noise. Filtering is mostly done as a post-processing operation (e.g., DS400); the ANS-filtered solution used in the DEOS-ANS, DEOS-SRBF, and DEOS-MASCON time series can also be interpreted as a regularized least-squares solution of GRACE K-band ranging data. One of the objectives of this study was to determine whether regularization (or post-processing filtering) is also needed when computing regional solutions. This question is justified, because one could argue that regional solutions do not require (additional) regularization, as long as the parameterization is suitably chosen. Note that selecting the number and halfwidth of SRBFs can always be interpreted as a regularization by parameterization. When mascons are used, the choice of the size of the block, represented by a mascon, is nothing else but a regularization by parameterization. On the other hand, when choosing an insufficient number of SRBFs (or too large of blocks for each mascon), the resolution of the solution may be suboptimal, leading to a loss of information. This is equivalent to over-smoothing. Alternatively, one may select a larger number of SRBFs with a smaller halfwidth and adjust for the instability of the normal equations by adding a regularization matrix. If the latter is chosen equal to the inverse of the signal variance–covariance matrix (as has been done for the DEOS-SRBF and DEOS-MASCON solutions presented in this study), the solution will be the same as when applying the optimal ANS filter as a post-processing operation.
5 Summary and Conclusions
We analyzed a range of global and regional GRACE solutions to quantify the differences between them and to answer the question whether regional GRACE solutions are to be preferred to global ones. The main result of the study is that current regional modelling techniques do not perform better than global ones for the river basins investigated in this study, as long as a proper spatial filter is applied. This could be different for high-latitude target areas, because more data are available there than for equatorial regions. This data coverage may result in a better signal-to-noise ratio for particular areas, which can be better exploited using a regional parameterization. This is a subject currently being investigated.
More important than the question of a regional or global parameterization is the application of a proper regularization or a suitable post-processing filter. For instance, Klees et al. (2008) have shown that the ANS filter performs significantly better than the DS400 filter. The latter performs well at the mid-latitudes, but has some weaknesses at the equatorial regions and the higher latitudes (cf. Swenson and Wahr 2006). The differences between the DEOS solutions (which were filtered with the DS400 filter) and the DEOS-ANS solutions are significant. Moreover, the regional DEOS solutions perform worse if other filters or regularization matrices are used. This includes the exponential signal covariance function, which is being used in the regional mascon solutions of the Goddard Space Flight Centre (GSFC) (e.g., Rowlands et al. 2005) as several tests with this regularization matrix (not presented here) have shown.
When we take the differences between GRACE models as a lower bound for the accuracy, we believe that 0.02 m equivalent water height is currently a reasonable estimate of accuracy of GRACE estimates of monthly mean water storage variations over river basins above 1 million km^{2}. The amplitude of the annual signal can be estimated with an accuracy of several millimetres equivalent water height. We could not find a relation between the accuracy and the size of the river basin, even though river basins which varied significantly in size, i.e., between 1 million km^{2} (Zambezi) and 6 million km^{2} (Amazon), were examined. In general, the annual signal accounts for 70–80% of the total signal variance, with only the La Plata River basin showing exceptions in both directions. For the La Plata River basin, between 40 and 70% of the signal cannot be explained by the annual cycle, which may be seen as an indicator of strong out-of-phase mass variations outside the river basin (leakage) or significant variability at shorter spatio-temporal scales inside the river basin.
A comparison of the various GRACE solutions with the output of the LEW regional hydrological model for the Zambezi River basin does not allow us to conclude which model is to be preferred for this particular target area. The monthly mean mass change estimates derived from the filtered CSR solutions are closer to the unfiltered LEW model than the other ones; on the other hand, the GFZ models show the highest spatial correlation coefficient, though the correlation coefficients of the other GRACE models are not much smaller. Moreover, the RMS differences over blocks of 4 × 4 deg are significantly larger than the RMS differences of the mean over the Zambezi River basin; this is the effect of residual noise, which is left after filtering. Moreover, during periods of maximum mass surplus, the GRACE models are outside the 5–95% quantile band of the LEW model, which can be attributed to leakage effects.
The Sahara test also has its shortcomings because the signal is close to zero and no information about annual or shorter period signals is provided. Nevertheless, the analysis of the Sahara data has revealed significant differences between the GRACE solutions. In particular, the CNES solutions suffer from strong leakage effects, which lead to a statistically significant annual amplitude of 0.02 m equivalent water height, whereas the other GRACE solutions show random signals with a RMS value around or even below 0.01 m.
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