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This study proposes a new mathematical approach to downscale monthly terrestrial water storage anomalies (TWSA) from the Gravity Recovery and Climate Experiment (GRACE) and estimates groundwater storage anomalies (GWSA) at a daily temporal resolution and a spatial resolution of 0.25° × 0.25°, simultaneously. The method combines monthly 3° GRACE gravity models and daily 0.25° hydrological model outputs and their uncertainties in the spectral domain by minimizing the mean-square error (MSE) of their estimator to enhance the quality of both low and high frequency signals in the estimated TWSA and GWSA. The Global Land Data Assimilation System (GLDAS) was the hydrological model considered in this study. The estimator was tested over Alberta, Saskatchewan, and Manitoba (Canada), especially over the Province of Alberta, using data from 65 in-situ piezometric wells for 2003. Daily minimum and maximum GWS varied from 14 mm to 32 mm across the study area. A comparison of the estimated GWSA with the corresponding in-situ wells showed significant and consistent correlations in most cases, with r = 0.43–0.92 (mean r = 0.73). Correlations were >0.70 for approximately 70% of the wells, with root mean square errors <24 mm. These results provide evidence for using the proposed spectral combination estimator in downscaling GRACE data on a daily basis at a spatial scale of 0.25° × 0.25°., This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Groundwater is an essential natural resource for domestic, industrial and agricultural uses worldwide. Unfortunately, climate change, excess withdrawal, population growth and other human impacts can affect its dynamics and availability. These excessive demands can lead to lower groundwater levels and depletion of aquifers, and potentially to increased water scarcity. Despite the abundance of lakes and rivers in many parts of Canada, the potential depletion of groundwater remains a major concern, particularly in the southern Prairie. Groundwater is traditionally monitored through in-situ piezometric wells, which are scarcely distributed in Canada and many parts of the world. Consequently, its quantities, distribution and availability are not well known, both spatially and temporally. Fortunately, the launch of the twin satellite systems of Gravity Recovery And Climate Experiment (GRACE) in 2002 and its successor, GRACE Follow-On in 2018 (GRACE-FO) opened up new ways to study groundwater changes. These platforms measure the variations of the Earth's gravity field, which in turn can be related to terrestrial water storage (TWS). The main objective of this thesis is to improve the estimation and spatial resolution of TWS and related groundwater storage changes (GWS), using GRACE and GRACE-FO data. This challenge was addressed through four specific objectives, where original approaches were developed in each case. The first objective was to understand and better take into account the uncertainties associated with the hydrological models (the Global Land Data Assimilation System (GLDAS), and the Water Global Assessment Prognosis hydrological model (WGHM)), generally used in the processing of GRACE or GRACE-FO data. The thesis proposes a new approach based on the Gauss-Markov model to estimate the optimal hydrological parameters from GLDAS, considering six different surface schemes. The Förstner estimator and the best quadratic unbiased estimator of the variance, Les eaux souterraines sont une ressource naturelle essentielle pour un usage domestique, industriel ou agricole dans le monde entier (Megdal, 2018). Malheureusement, le changement climatique, les prélèvements excessifs, et d'autres impacts humains peuvent affecter sa dynamique et sa disponibilité. Ces demandes excessives peuvent entraîner une baisse du niveau des nappes phréatiques et même l'épuisement des aquifères, pouvant entraîner une pénurie d'eau accrue (Zhao et al., 2019). Les systèmes d'eaux souterraines sont menacés dans certaines des zones les plus densément peuplées du monde (Herrara-García et al., 2021). Dans un contexte de croissance démographique rapide, d'augmentation de la demande alimentaire, d'agriculture intensive, de changement climatique, de pénurie des ressources en eau de surface et de fortes pressions qui s'exercent sur les aquifères, la gestion durable des ressources en eaux souterraines est devenue une préoccupation mondiale majeure (Long et al., 2020). Ces ressources doivent être adéquatement suivies et gérées pour assurer un équilibre des besoins en eau domestique, industrielle et d'irrigation pour un développement durable (Wu et al., 2019). Malgré l'abondance de lacs et de rivières dans de nombreuses régions du Canada, l'épuisement possible des eaux souterraines demeure une grande préoccupation dans l'Ouest canadien, en particulier dans les Prairies canadiennes. Cette vaste région (1,982 million de km2) est composée de trois provinces (Manitoba, Saskatchewan et Alberta), où le tiers de la population dépend de l'approvisionnement en eau souterraine (Larocque et Broda, 2016). La région est particulièrement bien connue pour ses activités agricoles intensives, qui exigent des quantités substantielles d'eau de surface et d'eau souterraine pour l'irrigation (Kromm, 1993). D'autres activités industrielles, telles que l'exploitation minière, consomment également des quantités considérables d'eau. Le réchauffement climatique et les activités huma

Temporal variations in the Earth’s gravity field can be used for monitoring of lithospheric deformations. The network of continuously operating gravity stations is required for this purpose but a global coverage by such network is currently extremely sparse. Temporal variations in long-wavelength part of the Earth’s gravity field have been, however, observed by two satellite missions, namely the Gravity Recovery And Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO). These satellite gravity observations can be used to study long-wavelength deformations of the lithosphere. Consequently, considering the lithosphere as a spherical elastic shell and solving the partial differential equation of elasticity for it, the stress, strain and displacement inside the lithosphere can be estimated. The lower boundary of this shell is assumed to be stressed by mantle convection, which has a direct relation to the Earth’s gravity field according to Runcorn’s theory. Changes in gravity field lead to changes in the sublithospheric stress and the stress propagated throughout the lithosphere. In this study, we develop mathematical models in spherical coordinates for describing the stress propagation from the sublithosphere through the lithosphere. We then organize a system of observation equations for finding a special solution to the boundary-value problem of elasticity in the way that provides a stable solution. In contrast, models presented in previously published studies are ill-posed. Furthermore, we use constants of the solution determined from the boundary stresses to determine the strain and displacements leading to these stresses, while in previous studies only the stress has been considered according to rheological properties of the lithosphere. We demonstrate a practical applicability of this theoretical model to estimate the stress–strain redistribution caused by the Sar-e-Pol Zahab 2018 earthquake in Iran by using the GRACE-FO monthly solutions.