The filling and emptying of the study basins at the regional-scale over the course of an individual WY results in a hysteretic relationship between storage and runoff (Fig. 3a). The hysteresis loops begin at the onset of the wet season in October, with TWSA increasing (Figs. 3a, 4a–c) as precipitation is stored as snow and soil moisture. An increase in storage that is not offset by an increase in discharge indicates a predominance of snow inputs and the freezing of soil water. The lower branch of the hysteresis plot (storage increase unmatched by runoff) can be used to estimate cumulative snow water equivalent and soil moisture in the basin. This is the water that later contributes to streamflow and groundwater recharge in the spring.

The hysteresis shifts direction from February–April (inflection 1, Fig. 3a), and represents each watershed's transition from storage to release. This response is evident (Figs. 3a, 4a–c, and 5), as each hysteresis loop contains a vertical branch of the curve during which storage is relatively constant, but streamflow increases rapidly. This timing also represents the groundwater recharge branch of the loop. As snow melts and the ground thaws, runoff is generated, recharge into soils occurs, and basins tend to be at peak storage during this branch. Storage losses and additional precipitation inputs during this period are re-organized internally. A second shift (inflection 2, Fig. 3a) occurs from April-June when peak TWSA begins to decrease, representing spring snowmelt and a switch from precipitation that falls primarily as snow to rain; these combine to contribute to peak R.

Once peak R values are reached, the loop shifts direction a third time (inflection 3, Fig. 3a), receding on both axes as contributions from snowmelt diminish while presumably groundwater sustains streams and provides a source for irrigated agriculture. During this period, the relationship between TWSA and discharge is more linear, corresponding to baseflow-driven runoff processes in which each monthly change in storage causes a proportional change in the generation of streamflow.

The hysteresis plots of TWSA-R for an individual water year demonstrate that the timing and quantity of precipitation governs the size of a hysteresis loop for an individual WY (Figs. 3a, 4a–c, 5). For instance, wet years (e.g., 2008) have bigger loops, while dry years (e.g., 2005) are more compressed along both axes. However, the general shape of the loops is distinct for each basin. Plotting multiple WYs provides a family of curves for each basin that helps describe how climate, topography, and geology govern the timing and magnitude of the relationship between TWSA and R (Figs. 3a, 5).

The TWSAsub hysteresis curve contracts horizontally when the snow signal is removed from TWSA values for both the Upper Columbia and The Dalles (Figs. 3b, 4d–f), which collapses the loops and takes a form similar to a plot-scale hysteresis of soil. In the initial stages of the WY, the direction of the curve changes directions 2–3 times along the TWSA axis. Similar hysteresis fluctuations have also been documented at the more local scale as the soil profile moves towards saturation (Penna et al., 2011). Peak TWSAsub occurs in June, which corresponds to the spring melt of mountain snowpack and the end of the wet season (Figs. 4d–f). In contrast to the near linear relationship between TWSAsub and R in the Upper Columbia and The Dalles, the Snake River retains a more complex relationship. In this watershed the hysteresis curve still retains a loop, but the timing of maximum TWSAsub is also earlier, reaching its peak during March and April (Fig. 4e). It is also noteworthy that in the Snake River the TWSAsub-R hysteresis loop temporally progresses in the opposite direction, but stays in phase with precipitation inputs.

The hysteresis loops describing the temporal relationship between GWSA and R are equally informative, with one distinct difference – they temporally progress in opposite directions of the hysteresis loops of TWSA and R (Fig. 3). For all three watersheds, GWSA decreases from October–February/March (Fig. 4h–j), which is out of phase with the onset of the wet season. GWSA does not shift towards positive gains until early spring and the initial stages of melt before reaching its maximum in June. From June–September, GWSA decreases minimally across all years during the runoff recession limb, indicating groundwater contributions to streamflow. This decreasing GWSA signal does not stand out in Fig. 2, as during WY 2011 the GSWA increased from 12.8 in June to 71.2 mm in September due a large snowpack that melted several months later than normal. This considerable anomaly muted the overall GWSA recession from June–September that is found in all other water years (supplementary data and the interactive visualizations described subsequently).

The 33 point-specific well data located across the CRB show considerable individual variability throughout a water year, and the mean of the normalized standard deviations of well levels was close to zero for all months. The temporal variability for the well data provides no discernable correlation with the derived GWSA signal (Fig. A1).

Of the three study basins, the Upper Columbia is the most hydrologically active, showing the largest annual range for TWSA, TWSAsub, GWSA, and R (Fig. 6). The TWS-R hysteresis loops are more open (Fig. 4), corresponding to the fluxes of water moving through watershed. When SWE is removed and subsurface water is highlighted, the TWSAsub-R hysteresis loops collapse horizontally and more closely resemble the hystereses associated with soil (Figs. 4d). However the inter-annual range (WYmax-WYmin) for TWSAsub in the Upper Columbia is considerably greater than the other two basins (median range = 234 mm; Fig. 6). As the hysteresis reverses directions for GWSA-R, the loops shift to a more open shape (Figs. 4d), but the inter-annual range remains similar.

In contrast to the rapid response of the Upper Columbia, the Snake River receives ∼ 60 % less annual precipitation, but has an annual TWSA range that is only 22 % less (median annual range = 192 mm; R=7 mm; Figs. 4, 5, and 6). However, the TWSA hysteresis loops for the Snake River are collapsed vertically (Fig. 4b). In the more arid Snake River, removing the snow signal does not collapse the TWSAsub-R hysteresis loops (TWSAsub= 89 mm). Similarly, the GWSA loops suggest that subsurface moisture plays a more prominent role in the Snake River.

The climate, topography, and geology of the Columbia River at The Dalles are an integration of the Upper Columbia and Snake River, seen in the shape of the hysteresis loops (Figs. 4, 5, 6; median annual range TWSA = 195 mm; R= 27 mm). The period from February–June more closely resembles the Snake River basin, with gradual increases in TWSA and sharp increases in R. The slope of the recession from June–September has the same general shape for The Dalles as the Upper Columbia (Figs. 4a, c), presumably from snowmelt-generated runoff.

Interactive visualizations that compliment all of the hysteresis figures are online at: https://public.tableau.com/profile/sprolese#!/vizhome/GRACE_hystereses/WSADash.

We next present how TWSA was applied prognostically to predict streamflow. Using the double-pass calibration and validation approach, TWSAMar provided the best overall predictive capabilities for Rseason with a mean NSE (NSE‾) and mean R2 (R2‾) of 0.75 and 0.91, respectfully (Fig. 7a, Table 1), for all three basins. The Dalles had the highest NSE and R2, and lowest RMSE values (0.98, 0.98, 6 mm; Table 1). The results in the Upper Columbia were also robust (0.82, 0.86, 33 mm; Table 1), while the Snake River performed with less skill (0.46, 0.59, and 14 mm, Table 1). Applying TWSAApril also provided similar results, but with a lower degree of skill in predicting R (NSE‾= 0.57, R2‾= 0.69). TWSAApr provided improved predicted capabilities in the Upper Columbia (0.87, 0.88, and 28 mm, Table 1), but inferior results in the other two watersheds. TWSAFeb had a low degree of skill in predicting R in all three watersheds (Table A3).

TWSAMar and TWSAApril also served as a good predictor of monthly runoff in July and August for the Upper Columbia and to a lesser degree in The Dalles (Tables 1 and A3). In the Snake River, TWSA did not serve as a good predictor for R in an individual month.

Snowpack and soil moisture play a considerable role in the hydrology of the CRB and are commonly used to help predict water demand and availability later in the year (Koster et al., 2010). We compared the capabilities of the modeled snow (SWE) and soil moisture (SM) products to predict R to the skill of measured GRACE TWSA data (Table 1). In the Upper Columbia and The Dalles, TWSAMar predicts seasonal and monthly runoff (July and August) with considerably more skill than SWE or SM (Fig. 7, Table 1). In the Snake River, SMMar has a higher degree of skill than TWSAMar in predicting Rseason and RAug. SWEMar provided inferior results in all three watersheds, but with some predictive skill in the Upper Columbia and The Dalles (NSE of 0.24 and 0.46 respectively, Table 1). In all three watersheds, TWSAsub provided extremely poor predictions (Tables 1 and A3).

When the results of the empirical model using two independent sets of data proved robust for some of the storage metrics, the observed data were tested against the simulated data from the complete, but limited data record. The performance of the empirical model improved using the complete data set (Tables 2 and A4), with the same general results. TWSAMar provided the best model fit for seasonal runoff in the Upper Columbia (NSE = 0.93, RMSE = 19.8 mm) and The Dalles (NSE = 0.98, RMSE = 5.7 mm). In the Snake River, predictive capabilities improved more dramatically (NSE = 0.83, RMSE = 7.4 mm), but soil moisture still served as a better predictor of seasonal streamflow (NSE = 0.93, RMSE = 5.2 mm). Similarly, TWSAMar provided the best model fit for runoff in August, one of the drier months when demand is at its peak (Tables 2 and A4).

Decades of data collection and monitoring at individual gage sites indicate that watersheds collect, store and release water. Using one integrated measurement from the GRACE satellites, our results show these same processes at the regional scale in the hysteresis loops of storage (TWSA) and runoff (R). While hysteretic processes have previously been identified in local-scale measurements (McDonnell, 2003; McGlynn and McDonnell, 2003), only recently has streamflow-storage hysteresis been identified at the regional scale (Riegger and Tourian, 2014).

Our work builds on Riegger and Tourian's (2014) results, and employs GRACE data to describe how regional watersheds function as integrated, non-linear systems governed by climate, topography, and geology. Climate controls the size of the hysteresis loops by providing a first-order control on hydrologic inputs and the storage of solid water, which in turn governs the ranges of TWSA and R. However, runoff response to precipitation and snowmelt does not act independently from topography and geology (Jefferson et al., 2008; Tague et al., 2008), which controls how liquid water is stored and routed through a watershed, even at the regional scale. The climatic, topographic, and geological characteristics of each watershed provide an explanation of the S-R relationship that govern the shape and size of its respective hysteresis curve. GRACE offers a single, integrated measurement of changes in water storage through and across a watershed that can be applied to predict regional streamflow using an empirical model. Where these predictive capabilities succeed and fail help better describe the climatic, topographic, and geological characteristics in each watershed.

For example, in the Upper Columbia, steep topography and wet climate fills subsurface storage quickly before reaching a threshold in April or May. This transition represents the watershed's transition from winter storage to spring runoff. After this watershed-scale threshold is reached, the steep topography moves snowmelt and rain quickly through the terrestrial system and into the river channel until cresting in June (Figs. 4, 5, and 6), followed by declines in TWSA and R from June-September. These large fluxes of water create a more open hysteresis loop, expanding non-linearly on both the horizontal and vertical axes.

The Upper Columbia also has the broadest range of annual TWSAsub and GWSA during the study period (Figs. 5 and 6), despite having limited aquifer capacity. Conceptually, this demonstrates that the upper limit of storage is greater than in the Snake River or The Dalles, but that it also loses the most water. Its minimums at the end of the WY are also the lowest (median TWSASep=-98 mm; Figs. 5 and 6). This range across TWSA, TWSAsub, and GWSA supports the conceptual model that the watershed fills during the wet season, and is then drained more quickly due to steep topography and limited water storage. The predictive capability of TWSA also strongly suggests that the components and temporal relationships of storage across this watershed are interconnected, and that incorporating April snowpack improves the model results.

In contrast, the arid Snake River basin provides a very different family of hysteresis curves (Figs. 4, 5) that identify groundwater and soil moisture as primary components of watershed function. The curves are compressed vertically (R) as compared to the Upper Columbia, and are more constrained horizontally (Fig. 6). The onset of spring melt runoff in February does not deplete TWSA for the Snake River. Instead, TWSA continues to increase until May, when peak runoff occurs. As TWSA decreases to the end of the water year in September, the median TWSASep measurement (-78 mm) is 20 mm greater than in the Upper Columbia. This indicates that the lower drainage threshold of the Snake River watershed is relatively greater than the Upper Columbia, potentially explained by a less severe topography and higher aquifer capacity.

The TWSAsub hysteresis curves in the Snake River retain a similar shape to the TWSA signal. While they reverse direction they do stay temporally connected to the onset of the wet season in October, indicating that subsurface moisture is a central control on the filling of the watershed through May. The capabilities of SM to empirically predict R better than TWSA further highlight the importance of subsurface water in this watershed. The intra-annual range of GWSA in the Snake River is also more limited than in the more hydrologically responsive Upper Columbia. This more limited range of data supports the conceptual model of a watershed that retains comparatively more winter precipitation in soils and aquifers throughout the spring season, and that sustains flow later in the year and until the onset of melt the following winter.

The greater Columbia River Basin upstream from The Dalles integrates the climatic, topographic, and geologic characteristics of the Snake River and Upper Columbia as well as other areas within the CRB. The western slope of the Cascades (Fig. 1), which is outside of the Upper Columbia, accumulates up to several meters of SWE each winter. Due east of the Cascades, a broad basalt plain that provides aquifer storage helps dampen the snowmelt pulse in the spring. The hysteresis loops for The Dalles reflect these combined characteristics.

Storage at The Dalles increases along the horizontal axis (TWSA) until peak storage is reached in March or April (Figs. 3, 4, and 5). This TWSA threshold of approximately 100 mm responds with an increase in R that continues through June. In July, the hysteresis begins to recede along both axes closing out the loop. GWSA has the most limited range, potentially explained by the extensive basalt aquifer moderating the relationship between storage and runoff. In The Dalles, TWSASep has a median value of -88 mm (Fig. 6), between the lower drainage thresholds of the Upper Columbia and Snake River watersheds; indicating an integration of the contributing climate, topography, and geology.

Conceptually TWSAsub represents changes in the amount of water stored as soil moisture and groundwater, where as GWSA represents water changes greater than 2000 mm below the soil surface. The goals of evaluating these metrics were to see if monthly changes in soil moisture were linked to changes in groundwater storage, and the role of snowpack in the S-R relationship.

The TWSAsub hysteresis curves in the Upper Columbia and The Dalles collapse into a more linear relationship that is more commonly associated with the S-R relationship of a soil matrix (Fig. 3 and 4). These stand in contrast to the Snake River where the TWSAsub-R hystereses retain a loop, indicating a more complex relationship between storage and runoff. The hydrological processes that create these differences warrant investigation, but lie outside the scope of this study.

Although the annual fluctuations of SM are similar in all three basins (Fig. 2), its impact in the Upper Columbia is more pronounced. This watershed has poor groundwater storage, and relies on soils to provide seasonal storage of rain and snowmelt. In the Upper Columbia once the SM signal is removed, the intra-annual range of GWSA shifts to considerably lower values (Fig. 6). Shifts of similar magnitudes in GWSA are not found in the Snake River and The Dalles. These watersheds have excellent groundwater storage and are less reliant on soils to provide seasonal storage of rain and snowmelt. Fluctuations in reservoir levels are minimal with regards to the water fluxes in this region, and have minimal impact on calculations of GWSA.

The GWSA-R hystereses are represented by loops that show an out-of-phase relationship between precipitation and groundwater recharge from the start of the wet season in October until February or March. The TWSAsub and GWSA hysteresis plots demonstrate that in the Upper Columbia and The Dalles changes in monthly soil moisture are not always temporally aligned with GWSA. This can be explained by the physical reality that soil moisture and groundwater are not always interconnected, and that there is not a fixed depth (i.e., 2000 mm) that separates the two components of water storage.

GRACE-derived calculations of GWSA also provide insights into the hydrological processes governing groundwater recharge and depletion, as evidenced in the GWSA hysteresis loops. The GWSA-R curves show an out-of-phase relationship between precipitation and groundwater recharge from the start of the wet season in October until February or March.

This response in all of the GWSA-R hystereses suggests that even at the watershed scale groundwater recharge requires soils and geologic materials to fill to a certain moisture threshold and for the onset of snowmelt (Figs. 3a, 4a–c, 5, and web-based interactive visualizations https://public.tableau.com/profile/sprolese#!/vizhome/GRACE_hystereses/WSADash). This also suggests that snowmelt inputs to groundwater are considerable. In the CRB this is critical as current climate trends are projected to reduce snowpack accumulation and exacerbate melt in the region (Wu et al., 2012; Rupp et al., 2013; Sproles et al., 2013).

Additionally, our analysis identifies summer as the time of peak groundwater storage in all three regional watersheds. This finding is of value for groundwater management and policy decisions, as peak groundwater levels in June correspond to the timing of groundwater pump tests that are used to develop groundwater withdrawal regulations (Jarvis, 2011, 2014). Our data suggest that groundwater pump tests should not be limited to an individual month, and should also include periods of reduced storage particularly during the winter months. The inclusion of multiple pump tests throughout the year could be particularly relevant as the population and water demand is projected to increase in the region.

The point-specific well data are not conclusive and show considerable variability with no consistent pattern regarding the timing of recharge and peak groundwater levels. This is presumably a function of how site characteristics (i.e., usage, depth, location, elevation) are extremely variable across a region. Rather than excluding these results or selecting individual wells that match GRACE data, we discuss the results from all 33 wells to help demonstrate the high variability that exists from well to well, and that measurements of groundwater changes at a fixed location do not represent watershed-scale characteristics (Jarvis, 2011, 2014). The disconnect between sites also highlights the concept brought forward by Spence (2010), that storage is not uniform across a watershed, and functions as a series of discontinuous processes at the watershed scale.

We applied these climatic, topographic, and geologic insights to develop and test the hypothesis that spring TWSA could predict R later in the year, based on two observations: first, the shapes of the hysteresis curves for each basin are similar (Figs. 4a–c, 5), but vary by magnitude of annual TWSA. Second, peak TWSA occurs before the peak runoff. We show that the integrated GRACE signal is a good baseline measurement to empirically predict seasonal streamflow across a range of water years with regards to precipitation and streamflow. In essence, our data suggest that the water stored across and through the Columbia River Basin in March describes the water available for the remainder of the water year.

In the CRB and in the northwestern United States, peak snowpack occurs in March or April, and is commonly used as a metric for predicting spring runoff. Despite the importance of snowpack to the hydrologic cycle of the region, measurements of TWSAMar from GRACE provide a better prediction of Rseason, RJuly, and RAug than model-derived estimates of snowpack. GRACE TWSAMar also provided a better prediction for runoff than soil moisture, except for the Snake River watershed. There SMMar provided a better indicator of runoff for the rest of the year. TWSAFeb provided inferior predictive capacity, as the annual maximum TWSA values have not been reached.

These results are promising with regards to using GRACE as a predictive tool for water resources in both wet and dry years. Our limited data record represents a wide-range of conditions with regards to climate and streamflow, which is captured in our empirical models and is shown in the box plots to the right of Figs. 7a–b. These same results also indicate that R is insensitive to TWSAMar values below 100 mm in the Upper Columbia and at The Dalles and below 85 mm in the Snake River watershed. This limitation is not the empirical model, which works well, but that the basins have a limited response (i.e., Rseason in the Snake River only changes about 60 mm, from around 20 to 85 mm). Given these responses the model works, and provides a lower threshold that describes with some certainty the amount of runoff that will be available for operations for the remainder of the year.

We recognize that all three of these regional watersheds are managed through a series of dams and reservoirs that create an altered runoff signal. Water resources managers use point-specific and model-based estimates of water storage in the region to optimize their operations for the water year. Additionally, in the fertile plains of the Snake River and lower CRB, broad-scale agriculture relies on both ground- and surface water for irrigation. Water withdrawals would be implicit in the TWSA signal and reduce R. However, a more detailed analysis of withdrawals lies outside the scope of this study.

Regardless of the length of record or anthropogenic influence, climate, topography, and geology still provide the first-order controls on water storage that are found in the hysteresis loops. GRACE encapsulates these hydrologic processes through measurements of TWSA. The hysteresis loops expand and contract accordingly during wet and dry years, as the intra-annual relationship between TWSA and Q represents the fluxes of water into and out of the watershed. Despite intra-annual differences, a family of hysteresis curves can describe each of the sub-regional watersheds. The predicative capability using TWSA, the vertical sum of water, as compared to snowpack and soil moisture further highlights the integrated nature of water storage in regional hydrology. These predictive capabilities highlight the potential of GRACE to improve upon seasonal forecast predictions and regional hydrological models.

Where previous approaches to modeling watershed behavior have focused on separate storage compartments, new approaches should include the magnitude and direction of hysteresis (Spence, 2010). This integrated approach would provide new ways forward to classify watersheds not only by runoff, but also on the first-order controls that govern the non-linear hydrological processes.

Even though GRACE is somewhat of a blunt instrument with regards to temporal (monthly) and spatial (1∘) resolution, this emerging technology provides a new dimension to regional watershed analysis by providing an integrated measurement of water stored across and through the Earth. These measurements continue to prove their value in retrospective analysis of regional hydrology (Rodell et al., 2009; Castle et al., 2014). However, the hysteresis loops presented by Riegger and Tourian (2014) and further developed in this paper demonstrate the ability of GRACE data to help develop a process-based understanding of how regional watersheds function as simple, dynamic systems. As the temporal record of GRACE continues to increase, its value as both a diagnostic and predictive tool will continue to grow. In the mean time, these data have value in augmenting existing management strategies.

Perhaps one of the most important facets of GRACE data is that it does not distinguish political boundaries. It is not linked to a specific in situ monitoring agency with limited data access and has the capacity to bridge sparse and inconsistent on-the-ground hydrologic monitoring networks that exist in many regions of the world. Previous GRACE-based analysis has shown its value in highlighting negative trends in terrestrial water storage in trans-boundary watersheds (Voss et al., 2013; Castle et al., 2014), and resulting regional conflict exacerbated by water shortages (Gleick, 2014b). GRACE provides an objective measurement of a region's water resources that can provide valuable insights into potential shortages or surpluses of water resources, and simple empirical predictions of seasonal and monthly runoff that are easily deployable in places with limited data.