The GRACE satellites provide signals of total terrestrial water storage (TWS) variations over large spatial domains at seasonal to inter-annual timescales. While the GRACE data have been extensively and successfully used to assess spatio-temporal changes in TWS, little effort has been made to quantify the relative contributions of snowpacks, soil moisture, and other components to the integrated TWS signal across northern latitudes, which is essential to gain a better insight into the underlying hydrological processes. Therefore, this study aims to assess which storage component dominates the spatio-temporal patterns of TWS variations in the humid regions of northern mid- to high latitudes.
To do so, we constrained a rather parsimonious hydrological model with multiple state-of-the-art Earth observation products including GRACE TWS anomalies, estimates of snow water equivalent, evapotranspiration fluxes, and gridded runoff estimates. The optimized model demonstrates good agreement with observed hydrological spatio-temporal patterns and was used to assess the relative contributions of solid (snowpack) versus liquid (soil moisture, retained water) storage components to total TWS variations. In particular, we analysed whether the same storage component dominates TWS variations at seasonal and inter-annual temporal scales, and whether the dominating component is consistent across small to large spatial scales.
Consistent with previous studies, we show that snow dynamics control seasonal TWS variations across all spatial scales in the northern mid- to high latitudes. In contrast, we find that inter-annual variations of TWS are dominated by liquid water storages at all spatial scales. The relative contribution of snow to inter-annual TWS variations, though, increases when the spatial domain over which the storages are averaged becomes larger. This is due to a stronger spatial coherence of snow dynamics that are mainly driven by temperature, as opposed to spatially more heterogeneous liquid water anomalies, that cancel out when averaged over a larger spatial domain. The findings first highlight the effectiveness of our model–data fusion approach that jointly interprets multiple Earth observation data streams with a simple model. Secondly, they reveal that the determinants of TWS variations in snow-affected northern latitudes are scale-dependent. In particular, they seem to be not merely driven by snow variability, but rather are determined by liquid water storages on inter-annual timescales. We conclude that inferred driving mechanisms of TWS cannot simply be transferred from one scale to another, which is of particular relevance for understanding the short- and long-term variability of water resources.
Since the start of the mission in 2002, measurements from the Gravity Recovery and Climate Experiment (GRACE) provide unprecedented estimates of changes in the terrestrial water storage (TWS) across large spatial domains (Tapley et al., 2004; Wahr et al., 2004). Due to their global coverage and independence from surface conditions, the data represent a unique opportunity to quantify spatio-temporal variations of the Earth's water resources (Alkama et al., 2010; Werth et al., 2009). Therefore, GRACE data have been widely used to diagnose patterns of hydrological variability (Seo et al., 2010; Rodell et al., 2009; Ramillien et al., 2006; Feng et al., 2013), to validate and improve model simulations (Döll et al., 2014; Güntner, 2008; Werth and Güntner, 2010; Chen et al., 2017; Eicker et al., 2014; Girotto et al., 2016; Schellekens et al., 2017), and to enhance our understanding of the water cycle on regional to global scales (Syed et al., 2009; Felfelani et al., 2017).
Despite the high potential of GRACE data for hydrological applications (Döll et al., 2015; Werth et al., 2009), the measured signal vertically integrates over all water storages on and within the land surface, which challenges the interpretation of the driving mechanism behind TWS variations. To facilitate insight into the underlying processes, hydrological models are frequently used to separate the measured TWS into its different components such as groundwater, soil moisture, and snowpacks (Felfelani et al., 2017). However, as a consequence of uncertain model structure, forcing, and parametrization, model-based partitioning is ambiguous (Güntner, 2008) and may lead to diverging conclusions, especially on regional scale (Long et al., 2015; Schellekens et al., 2017).
While the uncertainties of catchment-scale hydrological models are commonly reduced by calibrating the model parameters against discharge measurements, the majority of macro-scale models rely on a priori parametrization. So far, only a few models used to assess hydrological processes on continental to global scales are constrained by observations, and if so, they are mainly calibrated against the observed discharge of large river basins (Long et al., 2015; Döll et al., 2015). Recently, several studies showed the benefits of additionally including GRACE TWS data in model calibration (Werth and Güntner, 2010; Xie et al., 2012; Chen et al., 2017) or by means of data assimilation (Eicker et al., 2014; Forman et al., 2012; Kumar et al., 2016). However, although these approaches improve model simulations, they do not reduce the uncertainty in the partitioning of TWS due to the parameter equifinality problem (Güntner, 2008). Therefore, it is desirable to include multiple observations, ideally of several hydrological storages and fluxes, to constrain model results (Syed et al., 2009).
Nowadays, the increasing number and quality of Earth-observation-based products provides valuable information on a variety of hydrological variables over large scales, and thus facilitates the constraint of model simulations with multiple data streams simultaneously. While this can provide a more robust understanding of how variations in water storages translate into the observed TWS (Werth and Güntner, 2010), it is very challenging in practice and has rarely been implemented.
On the one hand, this is due to the limitations and inherent uncertainties of each Earth-observation-based product that need to be considered when comparing simulations and observations. For example, satellite-based soil moisture retrievals only capture the upper 5 cm of soil under snow-free conditions and therefore are difficult to compare to modelled soil water (Lettenmaier et al., 2015), while large-scale observations of snow mass based on passive microwave sensors are known to suffer from uncertainties in deep and wet snow conditions (Niu et al., 2007), and multispectral sensors solely provide estimates of snow cover in the absence of clouds (Lettenmaier et al., 2015).
On the other hand, the application of multi-criteria calibration approaches is limited by the increasing complexity of most macro-scale hydrological models over time (Döll et al., 2015). This high model complexity is not only associated with conceptual issues related to over-parametrization (Jakeman and Hornberger, 1993) and large computational demand, but has also been shown to not necessarily improve model performance (Orth et al., 2015). Therefore, it is desirable to implement a rather parsimonious model structure (Sorooshian et al., 1993), especially in multi-criteria model–data fusion approaches.
Applying multiple observational constraints is particularly beneficial in regions where hydrological dynamics are poorly understood and thus their representation in models varies widely. This is the case for snow-dominated regions as the northern high latitudes (Schellekens et al., 2017), which are among the areas most prone to the impacts of climate change (Tallaksen et al., 2015). These regions have been experiencing the strongest surface warming over the last century globally (IPCC, 2014), a trend which is expected to be exacerbated in the future and to significantly change hydrological patterns (AMAP, 2017). Therefore, solid understanding of present hydrological processes and variations is crucial, yet the effect of complex snow dynamics on other storages and water resources is relatively unknown (van den Hurk et al., 2016; Kug et al., 2015). While it has been shown that snow mass is the primary component of seasonal variations of TWS in large northern basins (Niu et al., 2007; Rangelova et al., 2007), it is not known what drives the TWS variations on inter-annual or longer timescales in these regions. Moreover, most analysis has so far focused on individual river basins and do not provide a comprehensive picture over large spatial scales.
Experiment design and considered time periods for forcing and analysis (grey) as well as model calibration and evaluation (orange).
In this study, we therefore aim to investigate the contributions of snow compared to other (liquid) water reservoirs to spatio-temporal variations of TWS in the northern mid- to high latitudes. To do so, we establish a model–data fusion approach that integrates multiple Earth-observation-based data streams including GRACE TWS along with estimates of snow water equivalent (SWE), evapotranspiration, and runoff into a rather simple hydrological model. This model is designed as a combination of standard model formulations yet aims to maintain low complexity in order to facilitate multi-criteria calibration and to focus on variables that can be constrained by observations.
First, we explain the applied methods, including the implemented model, the data used, and the multi-criteria calibration approach. The following section presents and discusses the results obtained with the optimized model. In the results, we describe the calibrated model parameters and evaluate the model performance with respect to observed patterns of TWS and SWE. Subsequently, the relative contributions of snow and liquid water storages to TWS variations are assessed on seasonal and inter-annual scales. Thereby we first focus on spatially integrated values across the study domain, and secondly on the composition on local grid scale. Finally, we summarize our findings and draw the conclusions.
The following section provides an overview on the experimental set-up, followed by a more detailed description of the model, the input data, and the methods for model calibration and analysis.
To assess the composition of TWS variations in northern mid- to high
latitudes, we optimized a simple hydrological model on daily time steps at a
1
Forced with global observation-based climate data, the model parameters were constrained for a subset of the study domain by multiple Earth observation data products using a multi-criteria calibration approach. These products include terrestrial water storage anomalies as seen by the GRACE satellites (Watkins et al., 2015; Wiese, 2015), measurements of snow water equivalent obtained in the GlobSnow project (Luojus et al., 2014), evapotranspiration fluxes based on FLUXCOM (Tramontana et al., 2016), and runoff estimates for Europe from E-RUN based on E-OBS (Gudmundsson and Seneviratne, 2016). Once the model parameters were calibrated, we evaluated the model against the same data, taking into account the entire study domain. Finally we applied the calibrated model to quantify the contributions of snow and liquid water storages to the integrated TWS. Thereby we considered different spatial domains (local grid cell and spatially aggregated) and temporal scales (mean seasonal and inter-annual variations).
Due to the differences in the temporal coverage of the observational data streams, model calibration and evaluation were conducted for the period 2002–2012, while analysis of TWS components covers the whole period of 2000–2014.
An overview on the experiment design and the selected time periods is provided by Fig. 1, while the following sections give a detailed description of the individual steps.
We designed a conceptual hydrological model with low complexity and a total
number of 10 adjustable parameters. The model considers major hydrological
fluxes such as snowmelt, sublimation, infiltration, evapotranspiration, and
(delayed) runoff and includes water storages in the snowpack, in the soil,
and due to delay in runoff (Fig. 2). It is forced by precipitation (
Schematic structure of the model with calculation of TWS. Boxes denote
the water storages (mm): snow water equivalent SWE, soil moisture SM, retained
water RW, liquid water
In the first step, precipitation
Similar to the WaterGAP model (Döll et al., 2002), incoming water
from rain and snowmelt is allocated to soil moisture (SM) and land runoff (
As land runoff results from an effective soil water recharge formulation,
the calculated runoff is essentially all the water that cannot be stored in
the soil. Thus, it implicitly contains both surface and subsurface runoff
as well as the percolation to deeper water storages such as groundwater, as
well as contributions from surface water bodies. To account for runoff
contributions from slow-varying storages, we calculate runoff from each grid
cell (
Finally, the sum of liquid water storage and snow is taken as the modelled
terrestrial water storage (TWS
As meteorological forcing we used globally available, daily cumulated
gridded precipitation sums (mm day
Precipitation values originate from the 1
Rather than using a single data stream, e.g. discharge measurements at the
outlet of large continental catchments as used in traditional large-scale
hydrological studies, we calibrated the model against multiple
observation-based data streams on the grid scale. The integrated datasets
include terrestrial water storage anomalies (TWS
TWS
To gain confidence in the partitioning of the integrated TWS, we additionally used SWE estimates from the European Space Agency's (ESA) GlobSnow SWE v2.0 product (Luojus et al., 2014). The dataset provides daily SWE values (mm) for the non-alpine Northern Hemisphere based on assimilating passive microwave satellite data and observed snow depth from weather stations by applying a semi-empirical snow emission model. Compared to data from stand-alone remote sensing approaches, GlobSnow SWE shows superior performance, even though validation against ground-based measurements still reveals a systematic underestimation of SWE under deep snow conditions due to a change in the microwave behaviour of the snowpack (Derksen et al., 2014; Takala et al., 2011; Luojus et al., 2014).
The ET product is based on FLUXCOM (
Similar to TWS that represents the vertically integrated water storage, observations of river discharge spatially integrate hydrological processes within a basin. Thus, they provide an invaluable tool for model validation at large scales. However, it is desirable to apply gridded products to evaluate model performance at local (grid) scale. Therefore, we used the observation-based gridded runoff product E-RUN version 1.1 (Gudmundsson and Seneviratne, 2016) as a constraint for runoff processes. This dataset is based on observed river flow from 2771 small European catchments that was spatially disaggregated to upstream grid cells using a machine learning approach. The data provide mean monthly runoff rates per unit area for each grid, so that river routing is not necessary to directly compare runoff estimates with modelled runoff. Similar to the ET data, gridded runoff estimates show high accuracy for the mean seasonal cycle across Europe, and poorer agreement regarding monthly time series and inter-annual variations (Gudmundsson and Seneviratne, 2016).
Table 1 summarizes the main features of the data
used in this study. If required, the data streams were resampled from their
original resolution to a consistent 1
Overview on data applied for meteorological forcing and multi-criteria calibration and model evaluation (NH: Northern Hemisphere).
Adjustable model parameters, their meaning, calibration range (theoretical range in brackets), optimized value including estimated uncertainty, and the corresponding equation in S1.
In this study, calibration is intended to identify the set of 10 model parameters (Table 2) that achieves the best fit between simulations and observations for all grid cells while regarding all observational data simultaneously. Thereby, we aimed to exploit the strength of each data stream, while considering known uncertainties and biases. For this purpose, we defined a cost function that takes into account the weakness of each observed variable and evaluates the overall model fit with one value of total cost (see subsequent section). To minimize total costs and thus find the optimal parameter values, we applied the covariance matrix evolution strategy (CMAES) (Hansen and Kern, 2004) search algorithm. The CMAES, as an evolutionary algorithm, is a stochastic, derivative-free method for non-linear, non-convex optimization problems. Compared to gradient-based approaches, it performs better on rough response surfaces with discontinuities, noise, local optima, and/or outliers and is a reliable tool even for global optimization (Hansen and Kern, 2004). Additionally, the CMAES guided search in the parameter space makes the algorithm less computationally demanding than other global optimization approaches, which enumerate a large number of possible solutions (e.g. Monte Carlo–Markov chain methods) (Bayer and Finkel, 2007).
In order to keep computational demands low and to avoid overfitting by a very small sample size, we perform calibration for a subset of 1000 randomly chosen grid cells. Within this iterative process, the model simulations are carried out on daily time steps, while costs are calculated based on monthly values. Further, each model run includes an initialization based on 10 random years that were selected a priori.
To objectively describe the goodness of fit, we defined a cost function
based on model efficiency (Nash and Sutcliffe, 1970), but with
explicit consideration of the uncertainty
The costs of each observed variable and its modelled counterpart are then
added equally to derive a single value of total cost (Eq. 2). Since a
perfect simulation would yield a total cost of 0, calibration aims to find
the global minimum of cost
As ET
For SWE, we applied an absolute uncertainty of 35 mm based on reported
differences to ground measurements (Liu et al., 2014; Luojus et al.,
2014). Since GlobSnow SWE saturates above approx. 100 mm (Luojus et al.,
2014), we do not penalize model simulations when both SWE
For maps of the temporal average uncertainties see Sect. S2.
Once the parameters were optimized, we applied the model for the entire
study domain and evaluated its performance regarding all grid cells (6050)
in terms of Pearson correlation coefficient
In order to benchmark our model against current state-of-the-art hydrological models, we compared its simulations with the multi-model ensemble of the global hydrological and land surface models of the eartH2Observe dataset (Schellekens et al., 2017). This ensemble includes HTESSEL-CaMa (Balsamo et al., 2009), JULES (Best et al., 2011; Clark et al., 2011), LISFLOOD (van der Knijff et al., 2010), ORCHIDEE (Krinner et al., 2005; Ngo-Duc et al., 2007; d'Orgeval et al., 2008), SURFEX-TRIP (Alkama et al., 2010; Decharme et al., 2013), W3RA (van Dijk and Warren, 2010; van Dijk et al., 2014), WaterGAP3 (Flörke et al., 2013; Döll et al., 2009), PCR-GLOBWB (van Beek et al., 2011; Wada et al., 2014), and SWBM (Orth et al., 2013). For consistency, we processed the model estimates in the same manner as our model simulations to directly compare modelled SWE and TWS to observations from GlobSnow and GRACE, respectively. While each model provides simulated SWE, they vary in the representation of other storage components. We calculated modelled TWS for each model by summing up the available water storage components. Thus, the variables contributing to modelled TWS vary between the models, which impedes detailed comparison. Additionally, we calculated the multi-model mean of SWE and TWS simulations.
Finally, the contribution of snow and liquid water to seasonal and
inter-annual TWS variability was quantified across spatial scales. For this,
we ran the model with optimized parameters for the entire study domain
from 2000 to 2014 and translated simulated storages as anomalies to the
time-mean baseline. As in the model evaluation, the MSC and IAV of SWE
From Eq. (3) and the assumption that
The following sections present and discuss the results obtained with the calibrated model. First, we review the calibration approach and the optimized parameter values. Then the model is validated with respect to its overall performance at grid scale, as well as the reproduction of average seasonal (MSC) and inter-annual (IAV) dynamics. Subsequently, we assess the driving component of spatially integrated TWS variations and the relative contributions of snow and liquid water to TWS variability on local scale. Finally, we summarize the results across spatio-temporal scales.
Optimization of the model identifies the parameter values listed in Table 2
as being most suitable regarding all data constraints simultaneously. The CMAES
search algorithm converged after 3272 function evaluations as no further
improvement of costs
In detail, snowfall is reduced by
Further, each grid is assumed to be completely covered by snow if
The maximum soil water holding capacity is set to 515 mm after calibration,
a comparatively high value that is likely to include storages in surface
water bodies such as lakes and wetlands within our study domain. The
optimized value of
Regarding evapotranspiration, the alpha coefficient (et
Finally, the calibrated recession timescale that delays land runoff is
13 days (
The uncertainty in the optimized parameter vector was estimated by quantifying each parameter's standard error as the square root of the product between the diagonal elements of the parameters' covariance matrix (calculated from the Jacobian matrix) and the sum of residual squares according to Omlin and Reichert (1999) and Draper and Smith (1981). The resulting relative parameter uncertainty is particularly instructive for comparing how well individual parameters could be constrained.
Most parameters were well constrained (Table 2), suggesting that our
model–data fusion method, fed by multiple observation streams, succeeded in
reducing the initial theoretical parameter ranges (up to 500 %) to much
narrower ranges. Nonetheless, some parameters have a larger uncertainty
range than others (e.g.
We adopted the calibrated parameter values as global constants for model simulations over the entire study domain. Even though the globally uniform parameters may not provide perfect simulation for all grids over a large study domain, this approach represents a compromise between a priori parametrization of the model and its calibration at local or regional (e.g. basin) scale. While local and regional model calibration enables good adaption to geographic characteristics, it easily leads to overfitting of the model and thus propagates the constraints' inherent errors and uncertainties in the modelling result. As these uncertainties often vary in space, globally uniform parameter values diminish overfitting uncertainties. In addition, calibration for several independent grids is computationally demanding and subsequently requires a parameter regionalization approach (He et al., 2011). Since such approaches are not commonly accepted (Sood and Smakhtin, 2015; Bierkens et al., 2015), macro-scale models mostly apply a priori parameters based on empirical values or on expert knowledge, which may yet lead to suboptimal simulations (Beck et al., 2016; Sood and Smakhtin, 2015).
For model validation, we used the optimized parameter values to simulate
hydrological fluxes and states of the 2002–2012 period over the entire
study domain and evaluated the model results against the observation-based
data of TWS, SWE, ET, and
In general, all observed patterns are reproduced very well, taking into
account the specific data weaknesses. We achieve a “near-perfect”
correlation of 0.99 and 0.94 for mean seasonal variations of ET and
Pearson correlation coefficient
Overall, the model performs well compared to the observations of monthly
time series of SWE and TWS (Fig. 3). More than half of the grid cells obtain
correlation values higher than 0.74 between SWE
Spatially averaged mean seasonal cycle (MSC) of the period 2002–2012
as well as inter-annual variability (IAV, difference between monthly values and
the MSC) for
Similar to SWE, more than half of the grid cells show a strong correlation
of 0.71 between TWS
Since the aim of this study is to analyse the composition of TWS across temporal scales, we additionally evaluated average (spatially integrated) MSC and IAV of SWE and TWS (Fig. 4). While the mean seasonal variations of both observational data streams are relatively robust and have been used for model evaluation before (Alkama et al., 2010; Döll et al., 2014; Schellekens et al., 2017; Zhang et al., 2017), their inter-annual variations are more uncertain and contain considerable noise. This clearly reduces the information content in the observational data, so that we evaluate the IAV in more qualitative terms.
As with the comparison at grid scale, the spatially averaged SWE
Similar to SWE, the spatial average of TWS shows high correlation of 0.91 for
seasonal variations, with positive anomalies from December to May–June and
negative anomalies during summer and autumn months (Fig. 4b). Even though
the modelled amplitude is slightly larger than the observed one, it stays
within the uncertainty range of TWS
In terms of inter-annual variations, the variance in monthly TWS
Compared to the model ensemble of the eartH2Observe dataset, we achieve an equally good or better performance for the spatially integrated SWE and TWS on both MSC and IAV scales (Figs. 5 and S6). Besides, the majority of the model ensemble obtains similar spatial patterns of performance criteria for SWE as well as for TWS (not shown).
The average observed MSC of SWE is captured with a correlation in the range
of 0.79 (PCR-GLOBWB) to 0.99 (ORCHIDEE), whereby only ORCHIDEE shows a
better correlation than our model (
Pearson correlation for the spatially integrated SWE
Regarding average seasonal TWS variations, our model performs as well as the
model ensemble (
Although our modelling framework assimilates information from more data streams compared to the model simulations in the EartH2Observe ensemble, e.g. GRACE and GlobSnow data, we only used a subset of 1000 random grid cells to constrain the model parameters. Despite this, our model performs better than the EartH2Observe ensemble over the whole domain (6050 grids). This improvement in model performance is also consistent among several modelled variables and not limited to storage components only. This suggests that remote sensing data, with larger spatial coverage than site measurements, have large potential to improve hydrological simulations over a large domain. In addition, remote sensing data also hold potential beyond their use as an observational constraint and can provide information on identifying and formulating functional relationships across several spatial and temporal scales, which should be addressed in future efforts.
All in all, we conclude that our simple model with a global uniform parameter set achieves considerably good performance regarding observed patterns, especially compared to well-established, more complex models, and with respect to its simplicity and given uncertainties of forcing and calibration data. Thus, we found the model results to be suitable to analyse the composition of TWS across spatial and temporal scales.
To assess the average composition of seasonal and inter-annual TWS
variations, we spatially integrated modelled TWS anomalies as well as
modelled anomalies of snow (SWE) and liquid water storages (
Spatially averaged mean seasonal cycle (MSC) of the period 2000–2014
as well as inter-annual variability (IAV, difference between monthly values and
the MSC) for modelled TWS, SWE, and
Regarding the MSC, all water storages show a clear seasonal pattern. The
maximum TWS
On IAV scales, the pattern seems less homogeneous
(Fig. 6). In contrast to the MSC,
Besides, Güntner et al. (2007) demonstrated a shift from
short-term storages with high seasonality such as SWE on MSC scales towards
storages with longer delay times on IAV scales. Although modelled
Based on CR (Eq. 3), Fig. 7 shows the relative
contribution of SWE
Accordingly, variations in the MSC of TWS
Relative contribution based on CR (Eq. 3) of modelled snow (SWE) and
liquid water (
This obtained pattern confirms earlier studies that showed the dominance of
snow in northern latitudes in North America (Rangelova et al.,
2007), and prevailing soil moisture dynamics further south, e.g. in the
Mississippi basin (Ngo-Duc et al., 2007; Güntner et al., 2007).
Besides, the north extent of dominating
Opposed to the MSC, the variability of
Relative contribution based on CR (Eq. 3) of modelled snowfall and
rainfall to total precipitation (
Apart from that, and since we already showed a link between average TWS
Relative contribution of snow (SWE) and liquid water (
Figure 9 summarizes the above-presented contributions to TWS
Regarding (1), Fig. 9 emphasizes again that seasonal variations of TWS
Concerning IAV scales, we found that the determination of TWS
Proportion of total positive (grey) and negative (orange) covariances
among grid cells for inter-annual variations of
For inter-annual variations of SWE
In order to ensure that these results are not artificially caused by the forcing data, we did the same analysis running the model with rain and snowfall estimates of the WFDEI product (Weedon et al., 2014). Since we observed the same patterns, we assume our findings to be robust (Sect. S7.1).
Although the model of this study reproduces observed hydrological patterns well and achieves comparable results to state-of-the-art models, its low complexity and the applied calibration approach are associated with limitations in terms of process understanding and predictive power.
First of all, the simple structure only allows inferences on represented processes, which likely include effects of fluxes and storages not considered explicitly. For example, the model does not resolve individual liquid water storages such as deep groundwater and surface water explicitly. As discussed previously, our delayed land runoff comprises various (intermediate) storages and delay times, and thus cannot be associated with one distinct storage component. Even though soil moisture is distinguished from these slowly varying reservoirs, its quantity and pattern have not been directly validated. Future research is required to increase confidence by including remote-sensing-based data of soil moisture in calibration and/or validation. However, these satellite data still have limited value as the microwave signals can only capture moisture in the upper 5 cm of soil and do not provide estimates under snow cover and dense vegetation (Döll et al., 2015; Lettenmaier et al., 2015). Therefore, a multi-layer soil scheme is needed to compare model outputs to satellite-derived soil moisture estimates, as was successfully demonstrated by Albergel et al. (2017) for example.
Further, the model does not include any human-induced changes in water
storages, which yet contribute to observed TWS variability in many regions
(Döll et al., 2015; Rodell et al., 2015). Other simplified or ignored
hydrological processes include the coincident occurrence of rain and snowfall, liquid water capacity of snow, interception, freeze–thaw dynamics
within the soil, capillary rise, and other surface-groundwater interactions,
the effect of vegetation or other surface properties, and lateral
flow from one grid cell to another. In the downstream areas of
large basins especially, the latter represents a potential input that may significantly
affect total TWS (Kim et al., 2009) and thus may contribute to
the discrepancy between TWS
With regards to model parameters, we apply a global uniform parameter set and do not regionalize the parameters according to spatially distributed physio-geographical characteristics. In contrast, most macro-scale hydrological models include spatially distributed soil properties to define parameters related to infiltration, soil water holding capacity, and percolation, as well as vegetation types to assess the effects of different plant functional types on evapotranspiration and canopy storage (Sood and Smakhtin, 2015). Our model only implicitly considers the effects of vegetation, for example on ET, but not its spatial variability, as the associated impacts are included in the observational constraint. Spatial variability of model parameters might affect the relative contributions of different storage components to TWS variability at different spatial scales. However, the comparison with eartH2Observe models, which generally involve spatial heterogeneity in model parameters, suggests that the main conclusions remain unchanged. Additionally, we want to highlight that the spatial distribution of model parameters depends on assumptions and some degree of simplification as well and thus does not necessarily improve model performance compared to a global uniform parameter set obtained from multiple observational data. Further, as we encountered issues with parameter equifinality, especially between modelled snowmelt and sublimation, future efforts should include a stronger utilization of runoff data in the calibration and validation process. This would help to better constrain water fluxes to the atmosphere and liquid water fluxes, which can contribute to the runoff.
Finally, though the implemented cost function explicitly accounts for the uncertainty of the calibration data and additional uncertainties of other input data, their processing and characteristics remain partly unaddressed.
In this study, we assessed the relative contributions of snowpack versus soil and retained water variations to the variability of total terrestrial water storage (TWS) for northern mid- to high latitudes. To do so, we constrained a parsimonious hydrological model with multi-criteria calibration against multiple Earth observation data streams, including TWS from GRACE satellites and snowpack estimates from GlobSnow. The optimized model showed considerably good agreement with observed patterns of hydrological fluxes and states, and was found to perform comparably to or better than simulations from state-of-the-art macro-scale hydrological models. This underlines the potential of simple hydrological models tied to observational data streams as powerful tools to diagnose and understand large-scale water cycle patterns. Further, it highlights the benefits of considering multiple complementary data constraints to overcome their individual shortcomings.
Consistent with previous studies, we found that seasonal TWS variations are dominated by the development of snowpacks during winter months in most places of the mid- to high northern latitudes. In contrast to this seasonal pattern, our study reveals that not snow but anomalies in liquid water storages, mainly comprising soil moisture, drive inter-annual TWS variations in almost the entire spatial domain. This counter-intuitive pattern was found to relate to larger rainfall anomalies compared to snowfall anomalies.
Apart from the timescale-dependent dominant controls on TWS variations, we additionally observed different behaviour across spatial scales. In terms of seasonal variations, the spatially integrated contribution reflects the average of the spatial domain. However, and more interestingly, the relative contribution of snowpack variations to total TWS inter-annual anomalies appears to be larger when spatially integrated than at local scale. We found this pattern results from stronger spatial coherence of snowpack anomalies compared to anomalies in other storages, such that the latter cancel out more strongly than the former when calculating an average across large spatial domains. The stronger spatial coherence of snowpack anomalies seems to be driven by the nature of spatially coherent temperature anomalies that determine snow accumulation and melt. These findings imply that patterns from large-scale integrated signals should not be associated with locally operating processes, since spatial covariations of climatic variables can confound the picture.
Overall, our study underlines the benefits of GRACE TWS as a model constraint, and moreover, stresses the importance of temporal and spatial scale when assessing the determinants of TWS variability. Clearly, insights obtained at one scale cannot be transferred to another, as is often (unintentionally) done. Hence, TWS variations in northern latitudes seem to be not merely subject to snow variability, but rather are driven by soil moisture on inter-annual scales – which may be of considerable importance when assessing long-term water availability in the context of climate changes.
The hydrological model and all simulation results from this
study can be obtained from the corresponding author on request. Due to the large
size and quantity of the data, along with potentially few users of the “same”
simulation results in the foreseeable future, it is not hosted on any public platform.
The forcing and calibration data is publicly available as specified with the
corresponding citation. For ET
The supplement related to this article is available online at:
TT, SK, and MJ designed the research in extensive collaboration with NC, AE, and MF. CN processed and integrated runoff estimates from E-RUN in model calibration. NC contributed to parameter estimation and uncertainty analysis. TT conducted the analysis. All co-authors contributed to the preparation of the paper.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Integration of Earth observations and models for global water resource assessment”. It does not belong to a conference.
This research was carried out within the initiative for the development of the SINDBAD (Strategies to Integrate Data and Biogeochemical models) framework. The article processing charges for this open-access publication were covered by the Max Planck Society. Edited by: Jean-Christophe Calvet Reviewed by: Vincent Humphrey and one anonymous referee