Terrestrial water storage (TWS) exerts a key control in global water, energy,
and biogeochemical cycles. Although certain causal relationship exists
between precipitation and TWS, the latter quantity also reflects impacts of
anthropogenic activities. Thus, quantification of the spatial patterns of TWS
will not only help to understand feedbacks between climate dynamics and
the hydrologic cycle, but also provide new insights and model calibration
constraints for improving the current land surface models. This work is the
first attempt to quantify the spatial connectivity of TWS using the complex
network theory, which has received broad attention in the climate modeling
community in recent years. Complex networks of TWS anomalies are built using
two global TWS data sets, a remote sensing product that is obtained from the
Gravity Recovery and Climate Experiment (GRACE) satellite mission, and a
model-generated data set from the global land data assimilation system's
NOAH model (GLDAS-NOAH). Both data sets have 1
Terrestrial water storage (TWS) is defined as vertically integrated water of all forms above and below the Earth's surface (e.g., surface water, soil moisture, groundwater, and snow and ice) (Famiglietti, 2004). It is not only a key control of global water, energy, and biogeochemical cycles but also provides an integrated indicator of water availability and uses (Houborg et al., 2012; Lettenmaier and Famiglietti, 2006; Long et al., 2013; Voss et al., 2013; Guentner et al., 2007). Global TWS has been the subject of modeling studies for decades; however, validation of modeling results has been challenging historically because of limited availability of in situ data. Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided an unprecedented opportunity to study TWS remotely. GRACE detects temporal variations of the Earth's gravity field which, over land, are mainly caused by short-term variations or TWS anomalies (TWSA). Numerous studies conducted in the past decade have confirmed the remarkable capability of GRACE in tracking continental- and regional-scale TWS changes (e.g., Famiglietti et al., 2011; Sun et al., 2010; Yeh et al., 2006; Long et al., 2013, 2014; Rodell et al., 2009; Swenson and Wahr, 2003; Han et al., 2005). So far, the monthly TWSA grids derived from GRACE have been used as an independent source of information for hydrologic model validation (Ramillien et al., 2008; Syed et al., 2008; Chen et al., 2005), calibration (Sun et al., 2012; Werth et al., 2009; Lo et al., 2010; Sun et al., 2010; Döll et al., 2014), and data fusion (Zaitchik et al., 2010; Houborg et al., 2012; Sun, 2013; Forman et al., 2012; Li and Rodell, 2015).
The global GRACE data set accumulated over the last decade is an important type of big data that can be mined for discovering information of global water/energy dynamics, and for helping to illuminate connections among major river basins and within the river basins themselves. Such information will be complementary to existing physically based TWS modeling efforts and will potentially provide calibration constraints (e.g., Guentner et al., 2007; Rodell et al., 2004). In this study, the complex network theory is adopted to construct a global TWSA network using GRACE data. The interannual spatial patterns of TWSA are then quantified through analyses of network topologies.
Complex network theory has long been used by scientists in various disciplines to study intricate connections in natural and social phenomena (Jackson, 2008; Newman and Girvan, 2004; Rubinov and Sporns, 2010). In recent years, the field of complex climate networks (CCN), which involves applications of traditional complex network analyses to climate systems (Tsonis and Roebber, 2004; Tsonis et al., 2006), has attracted significant attention. In typical CCN applications, cells of a gridded data set are deemed as nodes of a complex network, and links (or edges) between nodes are established on the basis of statistical similarity of the time series associated with the cells. After a climate network is constructed, various descriptive measures derived from the classical complex network theory are then applied to quantify network topologies (Donges et al., 2009b; Tsonis et al., 2006; Steinhaeuser et al., 2011). One of the main findings from the previous CCN studies is that climate networks manifest a “small-world” network property, akin to networks appear in many other fields (e.g., social networks). In CCN, this can be contributed to the existence of long-range connections that stabilize the climate system and enhance energy transfers within it (Donges et al., 2009a, b, 2011). TWS is closely intertwined with soil–vegetation–atmosphere interactions and is thus expected to show similar spatiotemporal patterns as observed from climate networks (e.g., precipitation network); however, it is well known that climate only plays a partial role in TWS changes. Land use changes and other anthropogenic activities (e.g., deforestation, aquifer mining, and water structures) increasingly stress water availability in many parts of the world and have been shown to produce global-scale impacts on the terrestrial water cycle (Vörösmarty and Sahagian, 2000). Such aspects are usually difficult to be fully captured and quantified without extensive monitoring data. The global coverage of GRACE TWSA, thus, becomes especially important.
Different from the global circulation model outputs analyzed by many previous
CCN studies, GRACE TWSA is a remote sensing product, subjected to errors and
uncertainties caused by instrumentation and data processing. As a result, the
actual spatial resolution of GRACE TWSA is not 1
A network is commonly represented by a graph
Several methods have been used in the CCN literature to determine
Obviously, all methods involve a certain degree of subjectivity. The selection
of
The outcome of the network construction process is a Boolean-valued, symmetric
The degree of centrality of a node,
A classic measure of network integration is the average distance between node
The GRACE TWSA data set used in this study was downloaded from the Tellus site of the Jet Propulsion Laboratory (JPL;
Outputs from GLDAS's NOAH model were obtained from NASA
(
Monthly time series contain high-frequency noise. Because the main interest
in this study is on interannual correlations of TWSA, the high-frequency
noise in each TWSA time series is removed. Several methods have been used
for such a purpose; the z-score method has been employed in the CCN literature
to remove seasonal variability (Donges et al., 2009b; Steinbach et al., 2003;
Tsonis et al., 2006). It entails normalizing each monthly data point using
the mean and standard deviation calculated for the corresponding month and
over the entire record length. The least squares method, which is extensively
used in the GRACE literature (e.g., Yeh et al., 2006; Crowley et al., 2006),
models the intra-annual variability using Fourier series (two annual
sine/cosine terms and two semi-annual sine/cosine terms) and then removes the
variability, together with a slowly moving trend. Our numerical tests show
the two methods give very similar results. Lags existing between time series
may weaken linear correlation. Thus, to examine the effect of temporal lags,
the same interannual correlation analysis is repeated using a temporal window
of 36 months (i.e., the maximum correlation observed within
The number of possible edges represented by the TWS data sets is more than
100 million for
Patterns of connection inferred from GRACE TWSA for six river basins, in which connection pattern is based on correlation between the basin centroid and all other cells in the grid.
GRACE connection patterns after cutoff threshold
Sensitivity of connection patterns to cutoff threshold, demonstrated using Mississippi River basin's centroid. Left column panels: GRACE results; right column panels: GLDAS results.
Figure 1a shows edge-density functions constructed using GRACE and GLDAS TWS
data, both are monotonically decreasing (i.e., fewer connected
edges at higher
A basin analysis is useful for helping visualize the TWSA connection patterns
at the basin level. As some examples, Figure 2 shows the results for six
river basins around the world. To generate a plot in Fig. 2, a cell is first
fixed, and all its edges are colored according to the actual
Extensive teleconnection is an advantage from a forecasting perspective because climate indices, such as El Niño–Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO), can be used as possible indicators of future changes. For those basins without strong teleconnection, water resources planning must rely mainly on regional data. Such distinction sheds light on the significance of GRACE data to long-term basin planning and natural hazard mitigation strategies, as we will elaborate on in the following sections.
As a sensitivity study, Fig. 4 (left column panels) shows the results of basin
analysis for the Mississippi Basin, the largest basin in North America, using
different thresholds corresponding to
Using the selected cutoff
Area-weighted connectivity map obtained using
The supernode regions shown in Fig. 5a reflect the superposed effects of climate variations and anthropogenic activities. These can be explained in terms of global precipitation and atmospheric circulation patterns. In general, the poorly connected regions have stronger precipitation variations over shorter spatial scales, leading to the emergence of high-precipitation gradients which, in turn, are responsible for regional extreme events that are more localized in time and space (Scarsoglio et al., 2013). Those with high connectivity tend to be directly influenced by ocean and climatic oscillations (e.g., ENSO and NAO). Kahya and Dracup (1993) studied streamflow variations in the contiguous USA and identified northeast, northcentral, Pacific northwest, and Gulf of Mexico states as regions with potentially significant streamflow responses to ENSO forcing. These four regions can be easily identified on Fig. 5a, among which the Gulf of Mexico region shows the weakest connection. Similarly, Chiew et al. (1998) reported that the ENSO can be used to help forecast spring runoff in southeast Australia and summer runoff in the northeast and east coasts of Australia. This teleconnection pattern is also indicated clearly by Fig. 5a.
At the global scale, Dai et al. (2009) studied the monthly streamflow records
of the world's 925 largest ocean-reaching rivers from 1948 to 2004. They
concluded that (a) the interannual variations of streamflows are correlated
with the ENSO events for discharge into the Atlantic, Pacific, Indian, and
the global oceans as a whole and (b) the effects of anthropogenic activities
on annual streamflow are likely to be small compared to those of climate
variations; however, anthropogenic activities can create more disturbances in
arid and semi-arid regions, where the discharge magnitudes are low (e.g.,
Indus, Yellow, and Tigris–Euphrates river basins). To elaborate the latter
point further, Fig. A1 in Appendix A plots the proportion of total renewable
water resources withdrawn by country for human uses in the agricultural,
municipal, and industrial sectors, using long-term data compiled by the Food
Agricultural Organization of United Nations. Figure A1 indicates that the
Middle East and northern African countries show the highest withdraw
proportions. In a recent GRACE study focusing on northcentral Middle East,
Voss et al. (2013) reported that GRACE data show an “alarming rate” of
decrease in TWS of approximately 143.6 km
Having elaborated the close relationship between GRACE TWSA and climate patterns, it is important to point out that the TWS also includes effects of soil moisture and groundwater storage (mostly unconfined aquifers) changes that may not synchronize with climate patterns.
Figure 5b shows the same area-weighted connectivity map, but constructed using the GLDAS-NOAH outputs. Although GLDAS-NOAH shows many of the similar patterns detected by GRACE, it also indicates stronger connectivity in the Arabian Peninsula, northern Africa, and in middle South America, and much weaker connectivity in southern Africa. These discrepancies may be caused by GLDAS-NOAH's parameterization and other errors. The other main reason is the lack of representation of the deeper groundwater storage in GLDAS. The discrepancies highlighted here provide additional spatial calibration constraints for land surface models. In areas dominated by shallow TWS components, GLDAS needs to show similar patterns as those derived from GRACE, whereas discrepancies are only expected in areas dominated by deep TWS components and/or impacted by significant anthropogenic activities. We emphasize here the connectivity maps shown in Fig. 5 are for TWSA. Thus, the high-precipitation areas (e.g., Amazon Basin) do not necessarily exhibit high anomaly connectivity after removing the intra-annual variability.
Effect of lagged correlation on GRACE area-weighted connectivity,
where the window of lagged correlation is [
So far, all results have been based on zero-lag correlations. The effect of
temporal lag on connectivity is examined in Fig. 6, in which the connectivity
map is built using the maximum (absolute) correlation found between
Figure 7a shows maps of the physical-based average nodal connection length
The average nodal connection length map constructed using GLDAS data suggests much wider connections, although most are local. Again this can be attributed to model parameterization schemes, forcing resolution, and spatial correlation constraints, as discussed before.
Map of average node connection lengths derived based on
The probability distribution of the average connection length,
In this work, the complex network theory is applied to analyzing spatial connection patterns in TWS. A comparative study is conducted using two global TWS data sets derived from GRACE and GLDAS, respectively, with an emphasis on interannual variability. Both data sets are large and have more than 100 million potential connections. An edge-density method is adopted to define an appropriate network pruning threshold. The constructed networks are further analyzed using the degree of centrality and connection length measures.
Distribution of average edge lengths in GRACE and GLDAS networks,
where
Our results show that complex networks and GRACE TWSA can be used to identify global TWSA hotspots or supernode regions. The area-weighted connectivity is a local measure that reveals nodes with a large number of connections (edges), whereas the connection length helps identify the dominating type of connections (i.e., local connections vs. teleconnections). In terms of connectivity, the largest cluster of supernodes appears in the Middle East region, while other prominent ones are found in Pacific northwest and eastern USA, southern Africa, southern South America, and eastern Australia. In terms of connection lengths, the Middle East region is dominated by local connections, whereas regions such as Pacific northwest, northcentral, Colorado River, and northeastern regions of the USA, southern Africa, and eastern Australia all have strong bimodal connections.
While many of the TWSA network features found here can be explained by established climate teleconnection theories, the TWS, as an integrated indicator of global water storage, is unique in its own way. It shows the impact of both climate and anthropogenic activities. Knowledge of both the strength and type of TWS connectivity can help identify useful TWS predictors and provide insight to further improve current land surface models.
GLDAS outputs have been used extensively in validating GRACE results at various scales. Less focused is the consistency of spatial correlation represented by GLDAS and GRACE data. Results from this study statistically quantify the similarity and discrepancies between the two data sets. In this case, the observed discrepancies may be attributed to missing surface and groundwater components in the GLDAS model, or to GRACE uncertainties (Syed et al., 2008; Li and Rodell, 2015). Although data assimilation has been used to reduce discrepancies in land surface models, the geometrical, spatial connection patterns have not been used before. A main conclusion from this work is that network connectivity measures should be incorporated as an additional model calibration and validation criterion when developing the future generation of GLDAS models.
Proportion of total renewable water resources used by country (data
source: Food Agricultural Organization (FAO) of the United Nations;
According to FAO, the proportion of total renewable water resources withdrawn
is defined as the total volume of fresh groundwater and surface water
withdrawn from their sources for human use (in the agricultural, municipal,
and industrial sectors), expressed as a percentage of the total actual
renewable water resources. The data used in Fig. A1 are compiled from 2005
data published by FAO
Degree centrality inferred from GRACE TWSA for six river basins,
based on the maximum correlation between each basin centroid and all other
cells in the grid, and within a window of [
Figure B1 shows the maximum correlations for the six basins chosen in Fig. 2, and Fig. B2 shows the corresponding phase lags. Recall these plots show the correlation between each basin centroid and all other cells in the TWSA data set. The phase lag plot (normalized by 18 months) shows that each river basin is in phase with most cells in itself and the immediate surrounding regions, but there can be significant phase shifts between each river basin and other river basins.
Phase lag of maximum correlations obtained for the six river basins
shown in Fig.
The authors are very grateful to the editor and two anonymous reviewers for their constructive comments. Edited by: J. Davidsen Reviewed by: two anonymous referees