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Global hydrological models enhance our understanding of the Earth system and support the sustainable management of water, food and energy in a globalized world. They integrate process knowledge with a multitude of model input data (e.g., precipitation, land cover and soil properties and location and extent of surface water bodies) that describe the state of the Earth. However, they do not fully utilize observations of model output variables (e.g., streamflow and water storage) to decrease model output uncertainty by, e.g., parameter estimation. For the pilot region Mississippi River basin, we assessed the suitability of three ensemble-based multi-variable calibration approaches for identifying both optimal and behavioral parameter sets for the global hydrological model WaterGAP, utilizing observations of streamflow (Q) and total water storage anomaly (TWSA). The common first steps in all approaches are 1) the definition of spatial units for which calibration parameters are uniformly adjusted (CDA units), combined with the selection of observation data, 2) the identification of potential calibration parameters and their a-priori probability distributions and 3) sensitivity analyses to select the most influential model parameters per CDA unit that will be adjusted by calibration. In the estimation of model output uncertainty, we considered the uncertainties of the Q and TWSA observations. We found that the Pareto-optimal calibration (POC) approach, which utilizes the Borg multi-objective evolutionary search algorithm to find Pareto-optimal parameter sets, is best suited for identifying a single “optimal” parameter set for each CDA unit. This parameter set leads to an improved fit to the monthly time series of both Q and TWSA as compared to the standard WaterGAP variant, which is only calibrated against mean annual Q, and can be used to compute the best estimate of WaterGAP output. The Generalized Likelihood Uncertainty Estimation (GLUE) approach is less suitable than POC to identify the optimal parameter set but enables the estimation of model output uncertainties that are due to the equifinality of parameter sets and the observation uncertainty. The potential advantages of the ensemble Kalman filter calibration and data assimilation (EnCDA) approach, in which both parameter sets and water storages are updated, could not be realized, likely due to the high computational burden of this approach, This limited the EnCDA ensemble size to 32, while 20,000 ensemble members could be evaluated in the case of POC and GLUE. Partitioning the whole Mississippi River basin into five CDA units (sub-basins) instead of only one improved model performance during the calibration and validation periods. Very diverse parameter sets were found to lead to similarly good fits to observations, but the range of values of three parameters could be narrowed by calibration. Model structure uncertainties, in particular regarding the operation of man-made reservoirs, the location and extent of small wetlands, and the (lacking) representation of losing river conditions in WaterGAP, are suspected to be the main reasons for the low coverage of the observation uncertainty bands by the GLUE-derived model output uncertainty bands. Model structure uncertainties are also the likely reason for major trade-offs between optimal fit to Q and TWSA. Calibration against GRACE TWSA only, in regions without Q observations, may worsen the Q simulation as compared to the uncalibrated model variant. We plan to add additional remotely-sensed observations in the multi-variable calibration of WaterGAP and suggest considering parameter uncertainty in multi-model ensemble studies of the global freshwater system.

We describe the new Global Land Water Storage data set (GLWS2.0), which contains total water storage anomalies (TWSA) over the global land with a spatial resolution of 0.5°, covering the time frame 2003 to 2019 without gaps, and including an uncertainty quantification. GLWS is produced by assimilating 4° gridded GRACE and GRACE-FO-derived TWSA into the WaterGAP global hydrological model using the Parallel Data Assimilation Framework (PDAF). The resulting data set represents thus an optimal synthesis of GRACE data, the hydrological model and implicitly all data sets that went into the model. This synthesis seeks to fit GRACE and GRACE-FO TWSA grids within error bars (from propagating full level-2 error variance covariance matrices), and at the same time it solves the horizontal and vertical water balances as represented in the hydrological model, again within error bars. To this end, the uncertainty of the hydrological model simulation is represented via a 32-member ensemble, where we account for the uncertainty of the precipitation and temperature data and for the uncertainty of some model calibration parameters. As a result, when no GRACE (-FO) data is available, GLWS represents the mean of an ensemble where each member is dynamically consistent with the model. It is important to understand that this mean depends on the ensemble and the previous GRACE estimates, and thus differs from published WaterGAP standard runs even if there is no GRACE data within a particular month. Due to the dynamical constraints, the assimilation-derived GLWS data set does not represent a simple downscaling of the GRACE data, i.e. spatial smoothing of GLWS does not necessarily correspond to GRACE (-FO) TWSA. GLWS indeed contains all water storages that are represented in WaterGAP (e.g. groundwater), but here we will focus only on TWSA. The main updates with respect to the release 1 were the use of an updated version of WaterGAP as well as minor bug fixes in the assimilation. GLWS1.0 and GLWS2.0 have already been provided to several research groups within the DFG GlobalCDA research unit and beyond for evaluation purposes. In this presentation we describe the methods and data sets that went into GLWS2.0, and the validation of the resulting 0.5° TWSA grids from a geodesy applications perspective, including comparisons to GRACE and GRACE-FO data and to GNSS-derived site displacements. We will also show some extended experiments with jointly assimilating river discharge data, model parameter estimation, and the integration of machine-learning based model prediction in our assimilation approach.

Global hydrological models simulate water storages and fluxes of the water cycle, motivated to assess water problems such as water scarcity, high flows and more generally the impact of anthropogenic change on the global water system. However, the models include many uncertainties due to the model inputs (e.g. climate forcing data), model parameters, and model structure which can lead to disagreements when simulation results are compared to observations. To reduce and quantify these uncertainties, some of the models are calibrated against in-situ streamflow observations or compared against total water storage anomalies (TWSA) derived from the Gravity Recovery And Climate Experiment (GRACE) satellite mission. In recent years, TWSA data are integrated into some models via data assimilation to directly improve the realism of the models.In this study, we present our framework for jointly assimilating satellite and in-situ observations into the WaterGAP Global Hydrological Model (WGHM). In addition to GRACE TWSA maps, for the first time here we experimentally jointly assimilate in-situ streamflow observations from gauge stations. This is in preparation for the Surface Water and Ocean Topography (SWOT) satellite, which will be launched this year and is expected to allow the derivation of streamflow observations globally for rivers wider than 50-100m. GRACE assimilation strongly improves the TWSA simulations in the Mississippi River Basin, e.g. the correlation increases to 91%, with which our results are consistent with previous studies. However, we find in this case that the streamflow simulation deteriorates, for example, correlation reduces from 92% to 61% at the most downstream gauge station. In contrast, jointly assimilating GRACE data and streamflow observations from GRDC gauge stations improves the streamflow observations by up to 33% in terms of e.g. RMSE and correlation while maintaining the good TWSA simulations. In view of the upcoming SWOT mission, our data suggest that the SWOT data will help to further improve the structure and simulations of global hydrological models.

Global hydrological models simulate water storages and fluxes of the water cycle which is important for e.g. water management decisions and drought/flood predictions. However, the models include many uncertainties due to the model inputs (e.g. climate forcing data), model parameters, and model structure resulting in disagreements with observations. To reduce these uncertainties, the models are typically calibrated against in-situ discharge observations or GRACE-derived total water storage anomalies (TWSA) are integrated into the model by data assimilation.In this study, we introduce a framework for jointly assimilating multiple observations into the WaterGAP 2.2d model over the Mississippi River Basin for 2003-2018. We do not only assimilate GRACE-derived TWSA but also in-situ discharge observations from gauge stations. In addition, we vary the number as well as the location of the considered discharge stations to derive information about e.g. the influence of assimilating down- or upstream stations.Our results show a strong influence of the GRACE data and that the assimilation of multiple discharge stations resembles the results of a traditional calibration approach. We expect the most downstream stations to have a larger impact on the assimilation results than the more upstream stations (as the downstream stations already include the information of the upstream stations). The gained insights of this study show a great potential to better assess and understand the global freshwater system and become even more relevant in view of the Surface Water and Ocean Topography (SWOT) satellite. SWOT will be launched in 2022 and is expected to allow the derivation of discharge observations globally for rivers wider than 50-100m.

The frequency and severity of drought increase in many regions of the world, which emphasizes the need for sufficient research to better monitor and trigger management plans. An important role hereby plays hydrological drought, because it affects water supply and crop yields that are necessary to ensure food security. Typically, hydrological drought detection is based on in-situ observations of fluxes or storages at the surface. However, this neglects the fact that drought might occur in multiple storages with different timing and severity. The use of subsurface storage, e.g. groundwater, is rare because the available in-situ well level monitoring is irregularly distributed in space and time and access might be restricted, for example due to national security reasons or problems in converting them to storage estimates.The satellite mission Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE-FO offer a great possibility to observe the total water storage, i.e. the sum of surface and subsurface storages, on a global scale from space. However, GRACE is restricted to monthly data on a spatial resolution of about 300 km and the vertical sum of the storages. Hydrological models present another possibility to derive global storage information with a finer spatial (~50km), temporal and vertical resolution than GRACE but they do not perfectly represent the reality because they are underlying assumptions and are affected by uncertainty of forcing data. Therefore, to enable downscaling of GRACE while improving the models realism, the GRACE measurements are assimilated into a hydrological model.In previous works we used a framework that assimilates GRACE into the WaterGAP Global Hydrological Model (WGHM) regionally or basin-wise. In this work we present a new framework that globally assimilates GRACE on a 4 degree grid with full uncertainty information from 2003 to 2018. The framework enables to assimilate about 95% of the global WGHM land surface except Greenland. With regard to vertical and spatial resolution the performance of model, observation and assimilation is compared. Global GRACE based drought indicators are applied and its development in the different compartments of surface water, soil and groundwater is analyzed to identify new insights into the propagation of drought. We expect that by including GRACE we derive new information especially for groundwater droughts, which might reveal time lags and a different severity as compared to surface water droughts for some regions.

When customers deliberately change the channel through which they do business with a firm, is that an indication of behavior change, and thus, future revenue? This research investigates the causal effects of customer channel migration to direct, company-managed or indirect, independent agent-managed online and offline channels using data from a leading international airline. In a quasi-experimental design via Mahalanobis-metric matching and conditional difference-in-differences estimation, the authors show that channel migration affects customer relationship breadth and depth: (1) Customers migrating from indirect to direct channels exhibit lower levels of relationship depth (revenue), (2) customers migrating from offline to online channels exhibit higher levels of relationship breadth (cross-buying), and (3) customers migrating from indirect offline to direct online channels exhibit higher levels of relationship depth (sales) and breadth (cross-buying). These findings expand our understanding of customer channel migration in service industries and suggest reconsidering and evaluating service firms’ strategies for direct channels as a lever for short-term revenue increase. Improving service firm’s direct channel relationship depth and breadth, pricing structure in direct channels must be adapted to compensate for lower sales figures per customer. In addition, direct channels services should be optimized to achieve higher conversion rates.