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In the recent past, the Gravity Recovery and Climate Experiment (GRACE) satellite mission and its successor GRACE Follow‐On (GRACE‐FO), have become invaluable tools for characterizing drought through measurements of Total Water Storage Anomaly (TWSA). However, the existing approaches have often overlooked the uncertainties in TWSA that stem from GRACE orbit configuration, background models, and intrinsic data errors. Here we introduce a fresh view on this problem which incorporates the uncertainties in the data: the Probabilistic Storage‐based Drought Index (PSDI). Our method leverages Monte Carlo simulations to yield realistic realizations for the stochastic process of the TWSA time series. These realizations depict a range of plausible drought scenarios that later on are used to characterize drought. This approach provides probability for each drought category instead of selecting a single final category at each epoch. We have compared PSDI with the deterministic approach (Storage‐based Drought Index, SDI) over major global basins. Our results show that the deterministic approach often leans toward an overestimation of storage‐based drought severity. Furthermore, we scrutinize the performance of PSDI across diverse hydrologic events, spanning continents from the United States to Europe, the Middle East, Southern Africa, South America, and Australia. In each case, PSDI emerges as a reliable indicator for characterizing drought conditions, providing a more comprehensive perspective than conventional deterministic indices. In contrast to the common deterministic view, our probabilistic approach provides a more realistic characterization of the TWS drought, making it more suited for adaptive strategies and realistic risk management. Plain Language Summary Total Water Storage (TWS) is defined as the sum of water stored as surface water (e.g., lakes and rivers), groundwater, soil moisture, snow, ice, and vegetation biomass. Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided unique TWS change measurements with many applications in hydrology, including characterizing drought events. Scientists have been using satellites like GRACE and its successor, GRACE‐FO, to understand drought by measuring the Total Water Storage Anomaly (TWSA). However, previous methods didn't consider uncertainties from satellite orbits, models, and data errors. This study offers a novel probabilistic approach for characterizing drought, Probabilistic Storage‐based Drought Index (PSDI), which acknowledges the uncertainties in the GRACE TWS change. We use simulations to create different drought scenarios, offering probabilities for each category instead of one fixed category. Comparing PSDI to traditional methods, we found that traditional methods tend to overestimate drought severity. We tested PSDI across different regions, and it consistently proved to be a reliable way to understand drought conditions, offering a more comprehensive perspective. Our probabilistic approach offers a more realistic view of TWS drought, making it suitable for adaptive strategies and risk management. Key Points A novel probabilistic framework is introduced to characterize drought using Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On observations and propagating their stochastics Our study suggests a tendency of deterministic approaches to overestimate storage‐based drought severity The probabilistic approach captures global hydrological droughts while delivering more realistic results suited for risk management

The Global Runoff Data Center (GRDC) data set has faced a decline in the number of active gauges since the 1980s, leaving only 14% of gauges active as of 2020. We develop the Remote Sensing-based Extension for the GRDC (RSEG) data set that can ingest legacy gauge discharge and remote sensing observations. We employ a stochastic nonparametric mapping algorithm to extend the monthly discharge time series for inactive GRDC stations, benefiting from satellite imagery- and altimetry-derived river width and water height observations. After a rigorous quality assessment of our estimated discharge, involving statistical validation, tests and visual inspection, results in the extension of discharge records for 3377 out of 6015 GRDC stations. The quality of discharge estimates for the rivers with a large or medium mean discharge is quite satisfactory (average KGE value > 0.5) however for river reaches with a low mean discharge the average KGE value drops to 0.33.The RSEG data set regains monitoring capability for 83% of total river discharge measured by GRDC stations, equivalent to 7895 km 3 /month.

Against the backdrop of global change, in terms of both climate and demography, there is a pressing need for monitoring of the global water cycle. The publicly available global database is very limited in its spatial and temporal coverage worldwide. Moreover, the acquisition of in situ data and their delivery to the database have been in decline since the late 1970s, be it for economical or political reasons. Given the insufficient monitoring from in situ gauge networks, and with no outlook for improvement, spaceborne approaches have been under investigation for some years now. Satellite-based Earth observation with its global coverage and homogeneous accuracy has been demonstrated to be a potential alternative to in situ measurements. This paper presents HydroSat as a database containing geometric quantities of the global water cycle from geodetic satellites. HydroSat provides time series and their uncertainty in water level from satellite altimetry, surface water extent from satellite imagery, terrestrial water storage anomaly represented in equivalent water height from satellite gravimetry, lake and reservoir water volume anomaly from a combination of satellite altimetry and imagery, and river discharge from either satellite altimetry or imagery. The spatial and temporal coverage of these datasets varies and depends on the availability of geodetic satellites. These products, which are complementary to existing products, can contribute to our understanding of the global water cycle within the Earth system in several ways. They can be incorporated for hydrological modeling, they can be complementary to current and future spaceborne observations, and they can define indicators of the past and future state of the global freshwater system. HydroSat is publicly available through http://hydrosat.gis.uni-stuttgart.de (last access: 18 May 2022​​​​​​​). Moreover, a snapshot of all the data (taken in April 2021) is available in GFZ Data Services at https://doi.org/10.5880/fidgeo.2021.017 (Tourian et al., 2021).

Our knowledge of the spatio-temporal variation of river hydrological parameters is surprisingly poor. In situ gauge stations are limited in spatial and temporal coverage, and their number has been decreasing during the past decades. On the other hand, remote sensing techniques have proven their ability to measure different parameters within the Earth system. Satellite imagery, for instance, can provide variations in river area with appropriate temporal sampling. In this study, we develop an automatic algorithm for water body area monitoring based on maximum a posteriori estimation of Markov random fields. The algorithm considers pixel intensity, spatial correlation between neighboring pixels, and temporal behavior of the water body to extract accurate water masks. We solve this optimization problem using the graph cuts technique. We also measure the uncertainty associated with the determined water masks. Our method is applied over three different river reaches of Niger and Congo rivers with different hydrological characteristics. We validate the obtained river area time series by comparing with in situ river discharge and satellite altimetric water level time series. Along the Niger River, we obtain correlation coefficients of 0.85–0.96 for river reaches and 0.65 for the Congo River, which is demonstrably an improvement over other river mask retrieval algorithms.

The Congo Basin is of global significance for biodiversity and the water and carbon cycles. However, its freshwater availability and distribution remain relatively unknown. Using satellite data, here we show that currently the Congo Basin’s Total Drainable Water Storage lies within a range of 476 km 3 to 502 km 3 , unevenly distributed throughout the region, with 63% being stored in the southernmost sub-basins, Kasaï (220–228 km 3 ) and Lualaba (109–169 km 3 ), while the northern sub-basins contribute only 173 ± 8 km 3 . We further estimate the hydraulic time constant for draining its entire water storage to be 4.3 ± 0.1 months, but, regionally, permanent wetlands and large lakes act as resistors resulting in greater time constants of up to 105 ± 3 months. Our estimate provides a robust basis to address the challenges of water demand for 120 million inhabitants, a population expected to double in a few decades.

The proposed Surface Water and Ocean Topography (SWOT) mission aims to improve spaceborne estimates of river discharge through its measurements of water surface elevation, river width and slope. SWOT, however, will not observe baseflow depth, which limits its value in estimating river discharge especially for those rivers with heterogeneous channel geometry. In this study, we aim to obtain river depths from spaceborne observations together with in situ data of river discharge. We first obtain SWOT-like observables from current satellite techniques. We obtain river water level and slope time series from multi-mission altimetry and effective river width from satellite imagery (MODIS). We then employ a Gauss–Helmert adjustment model to estimate average river depth for 16 defined reaches along the Po River in Italy, for which we use our spaceborne observations in two recognized models for discharge estimation. The average river depth estimates along the Po River are validated against surveyed cross-section information, which shows a generally good agreement in the range of ∼10% relative root mean squared error. Furthermore, we analyzed the sensitivity of error in the estimated river depth to errors of individual parameters. We show that the estimated river depth is less influenced by errors of river width and river discharge, while it is strongly influenced by errors in water level. This result gives a perspective to the SWOT mission to infer river depth by coarse estimates of river width and discharge.

We study users’ adoption and consumption of entertainment products in three chapters. Using unique data collected from online video gaming platforms on users’ playing times, we study how consumers make decisions to adopt and play video games.In the first chapter, we investigate the factors that influence an individual’s adoption of a video game. Specifically, we study how the adoption of a video game in a franchise is influenced by the adoption of previous games in that franchise and users’ experiences with those games. We also introduce some measures of dissimilarity between a video game and its franchise. The results show that being franchised does not affect the time of adoption in general. However, users who have adopted the last game in the franchise and have better experience with the franchise adopt the new game faster. We also find that a game’s changes in genres are more favored by general users. However, users who have adopted the last game in the franchise adopt the new game later when there are some changes in genres.In the second chapter, we investigate the effects of esports events and product update on players’ decisions to play a video game using individual player’s gaming history data of Dota 2. To study individual video game playing decisions in continuous time, we develop a continuous-time discrete choice structural model of product usage. Counterfactual analysis results show that decreasing the frequency of esports events and decreasing the frequency of product updates can both increase the total game playing time of players. In addition, joint scheduling of product updates and esports events can increase product usage further. Considering these findings, product managers in the video game industry might want to decrease product update frequency and allocate budgets to host less esports events. They should also consider joint scheduling of product updates and esports events to take advantage of the synergy between these marketing actions.In the third chapter, we investigate the interdependencies in consumers’ video game consumption, specifically how esports events of two particular video games affect the consumption of those video games as well as other video games in the same genres (i.e., product categories) and other genres. Players may consume more than one video game in a specific time window. Standard choice models are not appropriate to model contexts entailing this phenomenon called multiple discreteness. Multiple discreteness is a characteristics of consumption behavior as the choice of multiple, but not necessarily all alternatives simultaneously (Bhat, 2008). To address these challenges, we extend the model developed by Bhat (2005, 2008) called multiple discrete-continuous extreme value (MDCEV) model. The results show that esports events of Dota 2 and CS:GO do not increase the baseline preference for these video games during these events or after these events. We also find that the impact of esports events spillover to other genres, depending on the interdependencies in consumers’ consumption. Platform managers and video game developers can utilize the methodology in this paper to predict the probable impacts of their marketing actions on consumers’ consumption.

Increasing climatic and human pressures are changing the world's water resources and hydrological processes at unprecedented rates. Understanding these changes requires comprehensive monitoring of water resources. Hydrogeodesy, the science that measures the Earth's solid and aquatic surfaces, gravity field, and their changes over time, delivers a range of novel monitoring tools that are complementary to traditional hydrological methods. It encompasses geodetic technologies such as Altimetry, Interferometric Synthetic Aperture Radar (InSAR), Gravimetry, and Global Navigation Satellite Systems (GNSS). Beyond quantifying these changes, there is a need to understand how hydrogeodesy can contribute to more ambitious goals dealing with water‐related and sustainability sciences. Addressing this need, we combine a meta‐analysis of over 3,000 articles to chart the range, trends, and applications of satellite‐based hydrogeodesy with an expert elicitation that systematically assesses the potential of hydrogeodesy. We find a growing body of literature relating to the advancements in hydrogeodetic methods, their accuracy and precision, and their inclusion in hydrological modeling, with a considerably smaller portion related to understanding hydrological processes, water management, and sustainability sciences. The meta‐analysis also shows that while lakes, groundwater and glaciers are commonly monitored by these technologies, wetlands or permafrost could benefit from a wider range of applications. In turn, the expert elicitation envisages the potential of hydrogeodesy to help solve the 23 Unsolved Questions of the International Association of Hydrological Sciences and advance knowledge as guidance toward a safe operating space for humanity. It also highlights how this potential can be maximized by combining hydrogeodetic technologies simultaneously, exploiting artificial intelligence, and accurately integrating other Earth science disciplines. Finally, we call for a coordinated way forward to include hydrogeodesy in tertiary education and broaden its application to water‐related and sustainability sciences in order to exploit its full potential. Plain Language Summary Increasing climatic and human pressures are changing the world's water resources and hydrological processes at unprecedented rates. Understanding these changes requires comprehensive monitoring of water resources. Hydrogeodesy, the science that measures the Earth's solid and aquatic surfaces, gravity field, and their changes over time, delivers a range of novel monitoring tools complementary to traditional hydrological methods. It encompasses technologies such as Altimetry, Interferometric Synthetic Aperture Radar (InSAR), Gravimetry, and Global Navigation Satellite Systems (GNSS). Beyond quantifying these changes, we need to understand the potential of hydrogeodesy to contribute to more ambitious goals of water‐related and sustainability sciences. Addressing this need, we combine a meta‐analysis of over 3,000 articles to chart the range, trends, and applications of hydrogeodesy with an expert elicitation that systematically assesses this potential. We find a growing body of literature relating to advancements in hydrogeodetic methods, their accuracy and precision, and their inclusion in hydrological modeling. The expert elicitation envisages the large potential to solve hydrological problems and sustainability challenges. It also highlights how this potential can be maximized by combining several hydrogeodetic technologies, exploiting artificial intelligence, and accurately integrating other Earth science disciplines. Key Points This is a community view on hydrogeodesy, the science that measures the Earth's solid and aquatic surfaces, gravity field, and their changes Hydrogeodesy encompasses geodetic technologies such as Altimetry, Interferometric Synthetic Aperture Radar, Mass gravimetry, and Global Navigation Satellite Systems We study the evolution of hydrogeodesy and its role within current hydrological, sustainability science, and management frameworks

The SWOT satellite mission is the first to conduct a global survey of the Earth's surface waters, measuring water surface height, river width, and water surface slope, based on which river discharge is estimated. At mid‐latitudes, the repeat orbit design of SWOT only allows a sampling of twice per repeat cycle, which is considered too low for most hydrological applications. To address the spatiotemporal limitations of SWOT, we develop a method that assimilates SWOT observations across continuous reaches within a single‐branch river network to obtain daily discharge estimates. Our model‐free assimilation method provides a linear dynamic system that includes a process model based on a physically based spatiotemporal discharge correlation model and observation equations utilizing SWOT products. We solve this dynamic system using a simple Kalman filter in the time domain, assimilating SWOT observations and incorporating the physically based prior to estimate daily discharge. Since SWOT discharge products were not yet available during the period of this research, we used synthetic SWOT data sets, introducing random and systematic errors through Monte Carlo simulation. The validation of the estimated discharge against true discharge over all test cases leads to a median correlation as high as 0.95, a median NSE for residuals (mean‐removed discharge) as high as 0.81, and a median relative bias as low as 5%, respectively. These promising results suggest that daily discharge for continuous reaches in a river network can be obtained through our data assimilation framework.

River discharge is a crucial measurement, indicating the volume of water flowing through a river cross-section at any given time. However, the existing network of river discharge gauges faces significant issues, largely due to the declining number of active gauges and temporal gaps. Remote sensing, especially radar-based techniques, offers an effective means to this issue. This study introduces the Satellite Altimetry-based Extension of the global-scale in situ river discharge Measurements (SAEM) data set, which utilizes multiple satellite altimetry missions and estimates discharge using the existing worldwide networks of national and international gauges. In SAEM, we have explored 47 000 gauges and estimated height-based discharge for 8730 of them, which is approximately 3 times the number of gauges of the largest existing remote-sensing-based data set. These gauges cover approximately 88 % of the total gauged discharge volume. The height-based discharge estimates in SAEM demonstrate a median Kling–Gupta efficiency (KGE) of 0.48, outperforming current global data sets. In addition to the river discharge time series, the SAEM data set comprises three more products, each contributing a unique facet to better usage of our data. (1) A catalog of virtual stations (VSs) is defined by certain predefined criteria. In addition to each station's coordinates, this catalog provides information on satellite altimetry missions, distance to the discharge gauge, and relevant quality flags. (2) The altimetric water level time series of those VSs are included, for which we ultimately obtained good-quality discharge data. These water level time series are sourced from both existing Level-3 water level time series and newly generated ones within this study. The Level-3 data are gathered from pre-existing data sets, including Hydroweb.Next (formerly Hydroweb), the Database of Hydrological Time Series of Inland Waters (DAHITI), the Global River Radar Altimetry Time Series (GRRATS), and HydroSat. (3) SAEM's third product is rating curves for the defined VSs, which map water level values into discharge values, derived using a nonparametric stochastic quantile mapping function approach. The SAEM data set can be used to improve hydrological models, inform water resource management, and address nonlinear water-related challenges under climate change. The SAEM data set is available from https://doi.org/10.18419/darus-4475 (Saemian et al., 2024).