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Abstract Drought intensity is commonly characterized using meteorologically‐based metrics that do not provide insight into water deficits within deeper hydrologic systems. In contrast, global positioning system (GPS) displacements are sensitive to both local and regional hydrologic‐storage fluctuations. While a few studies have leveraged this sensitivity to produce geodetic drought indices, hydrologic drought characterization using GPS is not commonly accounted for in drought assessment and management. To motivate this application, we produce a new geodetic drought index (GDI) and quantify its ability to characterize hydrologic drought conditions in key surface and sub‐surface hydrologic reservoirs/pools across California. In northern California, the GDI exhibits a strong regional association with surface‐reservoir storage at the 1‐month time scale (correlation coefficient: 0.83) and groundwater levels at the 3‐month time scale (correlation coefficient: 0.87), along with moderate associations with stream discharge at the daily (instantaneous) time scale (correlation coefficient: 0.50). Groundwater in southern California is best characterized with a 12‐month GDI (correlation coefficient: 0.77), and surface‐reservoir storage is optimized with the 3‐month GDI (correlation coefficient: 0.72). Two sigma uncertainties are ±0.03. Differences between northern and southern California reveal that the GDI is sensitive to unique aquifer and drainage basin characteristics. In addition to capturing long‐term hydrologic trends, rapid changes in the GDI initiate during clusters of large atmospheric river events that closely mirror fluctuations in traditional hydrologic and meteorological observations. We show that GPS‐based hydrologic drought indices provide a significant opportunity to improve drought assessment, in California and beyond, by improving our understanding of the hydrologic cycle. 

Abstract Storage-discharge relationships and dynamic changes in storage connectivity remain key unknowns in understanding and predicting watershed behavior. In this study, we use Global Positioning System measurements of load-induced Earth surface displacement as a proxy for total water storage change in four climatologically diverse mountain watersheds in the western United States. Comparing total water storage estimates with stream-connected storage derived from hydrograph analysis, we find that each of the investigated watersheds exhibits a characteristic seasonal pattern of connection and disconnection between total and stream-connected storage. We investigate how the degree and timing of watershed-scale connectivity is related to the timing of precipitation and seasonal changes in dominant hydrologic processes. Our results show that elastic deformation of the Earth due to water loading is a powerful new tool for elucidating dynamic storage connectivity and watershed discharge response across scales in space and time. 

Abstract Atmospheric rivers (ARs) deliver significant and essential precipitation to the western United States (US) with consequential interannual variability. The intensity and frequency of ARs strongly influence reservoir levels, mountain snowpack, and groundwater recharge, which are key drivers of water‐resource availability and natural hazards. Between October 2022 and April 2023, western states experienced exceptionally heavy precipitation from several families of powerful ARs. Using observations of surface‐loading deformation from Global Navigation Satellite Systems, we find that terrestrial water‐storage gains exceeded 100% of normal within vital California watersheds. Independent water‐storage solutions derived from different data‐analysis and inversion methods provide an important measure of precision. The sustained storage increases, which we show are closely associated with ARs at daily‐to‐weekly timescales, alleviated both meteorological and hydrological drought conditions in the region, with a lag in hydrological‐drought improvements. Quantifying water‐storage recovery associated with extreme precipitation after drought advances understanding of an increasingly variable hydrologic cycle. 

Abstract Geodetic methods can monitor changes in terrestrial water storage (TWS) across large regions in near real‐time. Here, we investigate the effect of assumed Earth structure on TWS estimates derived from Global Navigation Satellite System (GNSS) displacement time series. Through a series of synthetic tests, we systematically explore how the spatial wavelength of water load affects the error of TWS estimates. Large loads (e.g., >1,000 km) are well recovered regardless of the assumed Earth model. For small loads (e.g., <10 km), however, errors can exceed 75% when an incorrect model for the Earth is chosen. As a case study, we consider the sensitivity of seasonal TWS estimates within mountainous watersheds of the western U.S., finding estimates that differ by over 13% for a collection of common global and regional structural models. Errors in the recovered water load generally scale with the total weight of the load; thus, long‐term changes in storage can produce significant uplift (subsidence), enhancing errors. We demonstrate that regions experiencing systematic and large‐scale variations in water storage, such as the Greenland ice sheet, exhibit significant differences in predicted displacement (over 20 mm) depending on the choice of Earth model. Since the discrepancies exceed GNSS observational precision, an appropriate Earth model must be adopted when inverting GNSS observations for mass changes in these regions. Furthermore, regions with large‐scale mass changes that can be quantified using independent data (e.g., altimetry, gravity) present opportunities to use geodetic observations to refine structural properties of seismologically derived models for the Earth's interior structure. 

Abstract We installed a purpose‐built network of co‐located Global Navigation Satellite System (GNSS) stations and meteorological instrumentation to investigate water storage in a high‐mountain watershed along the Idaho‐Montana border. Twelve GNSS stations are distributed across the Selway‐Lochsa watersheds at approximately 30–40 km spacing, filling a critical observational gap between localized point measurements and regional geodetic and satellite data sets. The unique coupling of geodetic and hydrologic observations in this network enables direct comparison between co‐located GNSS measurements of the elastic response of the solid Earth and local changes in measured water storage. This network is specifically designed to address questions of hydrologic storage and movement at the mountain watershed scale. Here, we describe technical details of the network and its deployment; introduce new hydrologic, meteorologic, and geodetic data sets recorded by the network; process and analyze the source data (e.g., time series of daily three‐dimensional GNSS site positions, removal of non‐hydrologic signals); and characterize basic empirical relationships between water storage, water movement, and GNSS‐inferred surface displacement. The network shows preliminary evidence for spatial differences in displacement resulting from a range of snow loads across elevations, but longer and more complete data records are needed to support these initial findings. We also provide examples of additional scientific applications of this network, including estimations of snow depth and snow water equivalent from GNSS multipath reflectometry. Finally, we consider the challenges, limitations, and opportunities of deploying GNSS and weather stations at high elevations with heavy snowpack and offer ideas for technical improvements. 

The data provided here accompany the publication "Drought Characterization with GPS: Insights into Groundwater and Reservoir Storage in California" [Young et al., (2024)] which is currently under review with Water Resources Research. (as of 28 May 2024)Please refer to the manuscript and its supplemental materials for full details. (A link will be appended following publication)File formatting information is listed below, followed by a sub-section of the text describing the Geodetic Drought Index Calculation. The longitude, latitude, and label for grid points are provided in the file "loading_grid_lon_lat".Time series for each Geodetic Drought Index (GDI) time scale are provided within "GDI_time_series.zip".The included time scales are for 00- (daily), 1-, 3-, 6-, 12- 18- 24-, 36-, and 48-month GDI solutions.Files are formatted following...Title: "grid point label L****"_"time scale"_monthFile Format: ["decimal date" "GDI value"]Gridded, epoch-by-epoch, solutions for each time scale are provided within "GDI_grids.zip".Files are formatted following...Title: GDI_"decimal date"_"time scale"_monthFile Format: ["longitude" "latitude" "GDI value" "grid point label L****"]2.2 GEODETIC DROUGHT INDEX CALCULATION We develop the GDI following Vicente-Serrano et al. (2010) and Tang et al. (2023), such that the GDI mimics the derivation of the SPEI, and utilize the log-logistic distribution (further details below). While we apply hydrologic load estimates derived from GPS displacements as the input for this GDI (Figure 1a-d), we note that alternate geodetic drought indices could be derived using other types of geodetic observations, such as InSAR, gravity, strain, or a combination thereof. Therefore, the GDI is a generalizable drought index framework. A key benefit of the SPEI is that it is a multi-scale index, allowing the identification of droughts which occur across different time scales. For example, flash droughts (Otkin et al., 2018), which may develop over the period of a few weeks, and persistent droughts (>18 months), may not be observed or fully quantified in a uni-scale drought index framework. However, by adopting a multi-scale approach these signals can be better identified (Vicente-Serrano et al., 2010). Similarly, in the case of this GPS-based GDI, hydrologic drought signals are expected to develop at time scales that are both characteristic to the drought, as well as the source of the load variation (i.e., groundwater versus surface water and their respective drainage basin/aquifer characteristics). Thus, to test a range of time scales, the TWS time series are summarized with a retrospective rolling average window of D (daily with no averaging), 1, 3, 6, 12, 18, 24, 36, and 48-months width (where one month equals 30.44 days). From these time-scale averaged time series, representative compilation window load distributions are identified for each epoch. The compilation window distributions include all dates that range ±15 days from the epoch in question per year. This allows a characterization of the estimated loads for each day relative to all past/future loads near that day, in order to bolster the sample size and provide more robust parametric estimates [similar to Ford et al., (2016)]; this is a key difference between our GDI derivation and that presented by Tang et al. (2023). Figure 1d illustrates the representative distribution for 01 December of each year at the grid cell co-located with GPS station P349 for the daily TWS solution. Here all epochs between between 16 November and 16 December of each year (red dots), are compiled to form the distribution presented in Figure 1e. This approach allows inter-annual variability in the phase and amplitude of the signal to be retained (which is largely driven by variation in the hydrologic cycle), while removing the primary annual and semi-annual signals. Solutions converge for compilation windows >±5 days, and show a minor increase in scatter of the GDI time series for windows of ±3-4 days (below which instability becomes more prevalent). To ensure robust characterization of drought characteristics, we opt for an extended ±15-day compilation window. While Tang et al. (2023) found the log-logistic distribution to be unstable and opted for a normal distribution, we find that, by using the extended compiled distribution, the solutions are stable with negligible differences compared to the use of a normal distribution. Thus, to remain aligned with the SPEI solution, we retain the three-parameter log-logistic distribution to characterize the anomalies. Probability weighted moments for the log-logistic distribution are calculated following Singh et al., (1993) and Vicente-Serrano et al., (2010). The individual moments are calculated following Equation 3. These are then used to calculate the L-moments for shape (), scale (), and location () of the three-parameter log-logistic distribution (Equations 4 – 6). The probability density function (PDF) and the cumulative distribution function (CDF) are then calculated following Equations 7 and 8, respectively. The inverse Gaussian function is used to transform the CDF from estimates of the parametric sample quantiles to standard normal index values that represent the magnitude of the standardized anomaly. Here, positive/negative values represent greater/lower than normal hydrologic storage. Thus, an index value of -1 indicates that the estimated load is approximately one standard deviation dryer than the expected average load on that epoch. *Equations can be found in the main text. 

Abstract Hydrogeodesy, a relatively new field within the earth sciences, is the analysis of the distribution and movement of terrestrial water at Earth's surface using measurements of Earth's shape, orientation, and gravitational field. In this paper, we review the current state of hydrogeodesy with a specific focus on Global Navigation Satellite System (GNSS)/Global Positioning System measurements of hydrologic loading. As water cycles through the hydrosphere, GNSS stations anchored to Earth's crust measure the associated movement of the land surface under the weight of changing hydrologic loads. Recent advances in GNSS‐based hydrogeodesy have led to exciting applications of hydrologic loading and subsequent terrestrial water storage (TWS) estimates. We describe how GNSS position time series respond to climatic drivers, can be used to estimate TWS across temporal scales, and can improve drought characterization. We aim to facilitate hydrologists' use of GNSS‐observed surface deformation as an emerging tool for investigating and quantifying water resources, propose methods to further strengthen collaborative research and exchange between geodesists and hydrologists, and offer ideas about pressing questions in hydrology that GNSS may help to answer. 

These datasets accompany a publication in Geophysical Research Letters by Martens et al. (2024), entitled: "GNSS Geodesy Quantifies Water-Storage Gains and Drought Improvements in California Spurred by Atmospheric Rivers." Please refer to the manuscript and supporting information for additional details.Dataset 1: Seasonal Changes in TWS based on the Mean and Median of the Solution SetWe estimate net gains in water storage during the fall and winter of each year (October to March) using the mean TWS solutions from all nine inversion products, subtracting the average storage for October from the average storage for March in the following year. One-sigma standard deviations are computed as the square root of the sum of the variances for October and for March. The variance in each month is computed based on the nine independent estimates of mean monthly storage (see “GNSS Analysis and Inversion” in the Supporting Information).The dataset includes net gains in water storage for both the Sierra Nevada and the SST watersheds (see header lines). For each watershed, results are provided in units of volume (km³) and in units of equivalent water height (mm). Furthermore, for each watershed, we also provide the total storage gains based on non-detrended and linearly detrended time series. In columns four and five, respectively, we provide estimates of snow water equivalent (SWE) from SNODAS (National Operational Hydrologic Remote Sensing Center, 2023) and water-storage changes in surface reservoirs from CDEC (California Data Exchange Center, 2023). In the final column, we provide estimates of net gains in subsurface storage (soil moisture plus groundwater), which are computed by subtracting SWE and reservoir storage from total storage.For each data block, the columns are: (1) time period (October of the starting year to March of the following year); (2) average gain in total water storage constrained by nine inversions of GNSS data; (3) one-sigma standard deviation in the average gain in total water storage; (4) gain in snow water equivalent, computed by subtracting the average snow storage in October from the average snow storage in March of the following year; (5) gain in reservoir storage (CDEC database; within the boundaries of each watershed), computed by subtracting the average reservoir storage in October from the average reservoir storage in March of the following year; and (6) average gain in subsurface water storage, estimated as the average gain in total water storage minus the average gain in snow storage minus the gain in reservoir storage.For the period from October 2022 to March 2023, we also compute mean gains in total water storage using daily estimates of TWS. Here, we subtract the average storage for the first week in October 2022 (1-7 October) from the average storage for the last week in March 2023 (26 March – 1 April). The one-sigma standard deviation is computed as the square root of the sum of the variances for the first week in October and the last week in March. The variance in each week is computed based on the nine independent estimates of daily storage over seven days (63 values per week). The storage gains for 2022-2023 computed using these methods are distinguished in the datafile by an asterisk (2022-2023*; final row in each data section).Dataset 1a provides estimates of storage changes based on the mean and standard deviation of the solution set. Dataset 1b provides estimates of storage changes based on the median and inter-quartile range of the solution set.Dataset 2: Estimated Changes in TWS in the Sierra NevadaChanges in TWS (units of volume: km³) in the Sierra Nevada watersheds. The first column represents the date (YYYY-MM-DD). For monthly solutions, the TWS solutions apply to the month leading up to that date. The remaining nine columns represent each of the nine solutions described in the text. “UM” represents the University of Montana, “SIO” represents the Scripps Institution of Oceanography, and “JPL” represents the Jet Propulsion Laboratory. “NGL” refers to the use of GNSS analysis products from the Nevada Geodetic Laboratory, “CWU” refers to Central Washington University, and “MEaSUREs” refers to the Making Earth System Data Records for Use in Research Environments program. The time series have not been detrended.We highlight that we have added changes in reservoir storage (see Dataset 8) back into the JPL solutions, since reservoir storage had been modeled and removed from the GNSS time series prior to inversion in the JPL workflow (see “Detailed Description of Methods” in the Supporting Information). Thus, the storage values presented here for JPL differ slightly from storage values pulled directly from Dataset 6 and integrated over the area of the Sierra Nevada watersheds.Dataset 3: Estimated Changes in TWS in the Sacramento-San Joaquin-Tulare BasinSame as Dataset 2, except that data apply to the Sacramento-San Joaquin-Tulare (SST) Basin.Dataset 4: Inversion Products (SIO)Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the Scripps Institution of Oceanography (SIO) using the methods described in the Supporting Information.Dataset 5: Inversion Products (UM)Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the University of Montana (UM) using the methods described in the Supporting Information.Dataset 6: Inversion Products (JPL)Inversion solutions (NetCDF format) for TWS changes across the western US from January 2006 through March 2023. The products were produced at the Jet Propulsion Laboratory (JPL) using the methods described in the Supporting Information.Dataset 7: Lists of Excluded StationsStations are excluded from an inversion for TWS change based on a variety of criteria (detailed in the Supporting Information), including poroelastic behavior, high noise levels, and susceptibility to volcanic deformation. This dataset provides lists of excluded stations from each institution generating inversion products (SIO, UM, JPL).Dataset 8: Lists of Reservoirs and LakesLists of reservoirs and lakes from the California Data Exchange Center (CDEC) (California Data Exchange Center, 2023), which are shown in Figures 1 and 2 of the main manuscript. In the interest of figure clarity, Figure 1 depicts only those reservoirs that exhibited volume changes of at least 0.15 km³ during the first half of WY23.Dataset 8a includes all reservoirs and lakes in California that exhibited volume changes of at least 0.15 km³ between October 2022 and March 2023. The threshold of 0.15 km³ represents a natural break in the distribution of volume changes at all reservoirs and lakes in California over that period (169 reservoirs and lakes in total). Most of the 169 reservoirs and lakes exhibited volume changes near zero km³. Datasets 8b and 8c include subsets of reservoirs and lakes (from Dataset 8a) that fall within the boundaries of the Sierra Nevada and SST watersheds.Furthermore, in the JPL data-processing and inversion workflow (see “Detailed Description of Methods” in the Supporting Information), surface displacements induced by volume changes in select lakes and reservoirs are modeled and removed from GNSS time series prior to inversion. The water-storage changes in the lakes and reservoirs are then added back into the solutions for water storage, derived from the inversion of GNSS data. Dataset 8d includes the list of reservoirs used in the JPL workflow.Dataset 9: Interseismic Strain Accumulation along the Cascadia Subduction ZoneJPL and UM remove interseismic strain accumulation associated with locking of the Cascadia subduction zone using an updated version of the Li et al. model (Li et al., 2018); see Supporting Information Section 2d. The dataset lists the east, north, and up velocity corrections (in the 4^th, 5^th, and 6^th columns of the dataset, respectively) at each station; units are mm/year. The station ID, latitude, and longitude are listed in columns one, two, and three, respectively, of the dataset.Dataset 10: Days Impacted by Atmospheric RiversA list of days impacted by atmospheric rivers within (a) the HUC-2 boundary for California from 1 January 2008 until 1 April 2023 [Dataset 10a] and (b) the Sierra Nevada and SST watersheds from 1 October 2022 until 1 April 2023 [Dataset 10b]. File formats: [decimal year; integrated water-vapor transport (IVT) in kg m^-1 s^-1; AR category; and calendar date as a two-digit year followed by a three-character month followed by a two-digit day]. The AR category reflects the peak intensity anywhere within the watershed. We use the detection and classification methods of (Ralph et al., 2019; Rutz et al., 2014, 2019). See also Supporting Information Section 2i.Dataset 10c provides a list of days and times when ARs made landfall along the California coast between October 1980 and September 2023, based on the MERRA-2 reanalysis using the methods of (Rutz et al., 2014, 2019). Only coastal grid cells are included. File format: [year, month, day, hour, latitude, longitude, and IVT in kg m^-1 s^-1]. Values are sorted by time (year, month, day, hour) and then by latitude. See also Supporting Information Section 2g.