Regularization of the Gravity Field Inversion Process with High-Dimensional Vector Autoregressive Models

Earth’s gravitational field provides invaluable insights into the changing nature of our planet. It reflects mass change caused by geophysical processes like continental hydrology, changes in the cryosphere or mass flux in the ocean. Satellite missions such as the NASA/DLR operated Gravity Recovery and Climate Experiment (GRACE), and its successor GRACE Follow-On (GRACE-FO) continuously monitor these temporal variations of the gravitational attraction. In contrast to other satellite remote sensing datasets, gravity field recovery is based on geophysical inversion which requires a global, homogeneous data coverage. GRACE and GRACE-FO typically reach this global coverage after about 30 days, so short-lived events such as floods, which occur on time frames from hours to weeks, require additional information to be properly resolved. In this contribution we treat Earth’s gravitational field as a stationary random process and model its spatio-temporal correlations in the form of a vector autoregressive (VAR) model. The satellite measurements are combined with this prior information in a Kalman smoother framework to regularize the inversion process, which allows us to estimate daily, global gravity field snapshots. To derive the prior, we analyze geophysical model output which reflects the expected signal content and temporal evolution of the estimated gravity field solutions. The main challenges here are the high dimensionality of the process, with a state vector size in the order of 103 to 104, and the limited amount of model output from which to estimate such a high-dimensional VAR model. We introduce geophysically motivated constraints in the VAR model estimation process to ensure a positive-definite covariance function.

Capturing watershed water balance with a physically-based two-hydrological-variable model: Application to the Little Washita basin

<p>Hydrological processes import across scales is known to constitute a key challenge to improve their representation in large-scale land surface models. Since these models describe continental hydrology with vertical one dimensional infiltration and evapotranspiration, the challenge mainly resides in the dimensionality reduction of the processes. Departing from the catchment three-dimensional scale, previous work has shown that an equivalent two-dimensional hillslope model is able to simulate long term watershed water balance with good accuracy. This work has been done on the Little Washita basin (Ok, USA) using the integrated code HydroGeoSphere. Following this framework, we show that hillslope hydrology can be described by using realistic simplifying assumptions, such as linear water table profile. These assumptions allow the writing of an analytical model relying on two hydrological variables: the seepage face extension, which describe the intersection length between the water table and the land surface, and the water table slope. The last step of the work will be to use these key variables and this simplified description of the driving processes for importing small-scale hydrological processes into large-scale models.</p>

SLR analysis employing consistent weather-driven corrections for atmospheric refraction, geophysical displacements, and gravity field variations

<p>Satellite Laser Ranging (SLR) observations are affected by weather variations. Mass redistributions within Earth‘s fluid envelope (the atmosphere, the oceans, and the continental hydrology) which are partly induced by the perpetual variability of weather, have an impact on (i) the orbits of satellites by inducing gravity field variations, and (ii) the locations of the ground stations by inducing elastic geophysical loading deformations. The SLR range observations between stations and satellites are also dependent on atmospheric conditions (mainly pressure, temperature, and humidity), induced by refraction. This work discusses the benefits that stem from applying consistently derived reduction models for transient gravity field variations, mass loading and atmospheric refraction effects in SLR data analysis. The models are driven from ECMWF‘s latest high-resolution reanalysis, the ERA5. SLR range observations to LAGEOS-1 and -2 serve as the geodetic data input. The software suite EPOSOC is employed to assess the effect of the application of the aforementioned reduction models and to quantify the benefits.</p>

Rapid extreme meteorological events detected by daily regional GRACE solutions

<p>We investigate the possibility to use the Low-Earth Orbiter mission well known as GRACE to detect sudden regional variations of water mass storage caused by heavy precipitation and flooding episodes caused by the passage of tropical hurricanes of categories 4-5 (from day to a week). For this purpose, daily water mass solutions are produced from along-track GRACE geopotential anomalies to catch the signatures of these intense meteorological events. These geopotential variations are derived from accurate inter-satellite K-Band Range Rate (KBRR) measurements made along the 5-second orbits by imposing the total energy conservation to the twin GRACE vehicles. The determination of these surface sources is made over a regional network of juxtaposed triangular tiles of quasi-constant areas, and they are refreshed by a Kalman filtering for integrating progressively daily geopotential observations. These latter data have been previously reduced from known gravitational effects of atmosphere and oceanic masses (including periodic tides) for isolating the continental hydrology contribution. Our estimates of regional hydrological impacts are also compared to the ones obtained by synthesis of daily degree-40 Stokes coefficients provided by ITSG, Graz.</p>

Self-validating deep learning of continental hydrology through satellite gravimetry and altimetry

<p>Space-borne observations of terrestrial water storage (TWS) are an essential ingredient for understanding the Earth's global water cycle, its susceptibility to climate change, and for risk assessments of ecosystems, agriculture, and water management. However, the complex distribution of water masses in rivers, lakes, or groundwater basins remains elusive in coarse-resolution gravimetry observations. We combine machine learning, numerical modeling, and satellite altimetry to build and train a downscaling neural network that recovers simulated TWS from synthetic space-borne gravity observations. The neural network is designed to adapt and validate its training progress by considering independent satellite altimetry records. We show that the neural network can accurately derive TWS anomalies in 2019 after being trained over the years 2003 to 2018. Specifically for validated regions in the Amazonas, we highlight that the neural network can outperform the numerical hydrology model used in the network training.</p><p>https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020GL089258</p>

Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry

Since its launch in March 2002, the Gravity Recovery And Climate Experiment (GRACE) mission has been mapping the time variations of the Earth’s gravity field with a precision of 2–3 cm in terms of geoid height at the surface resolution of 300–400 km. The unprecedented precision of this twin satellite system enables to detect tiny changes of gravity that are due to the water mass variations inside the fluid envelops of our planet. Once they are corrected from known gravitational contributions of the atmosphere and the oceans, the monthly and (bi)weekly GRACE solutions reveal the continental water storage redistributions, and mainly the dominant seasonal cycle in the largest drainage river basins such as Amazon, Congo, Mississippi. The potential differences measured between the twin GRACE satellites represent the sum of integrated surface waters (lakes and rivers), soil moisture, snow, ice and groundwater. Once they are inverted for estimating surface water mass densities, GRACE solutions are also used to establish the long-term mass balance of the ice sheets impacted by global warming, for quantifying the interannual variations of the major aquifers, as well as for surveying the hydrological signatures of intense meteorological events lasting a few days such as tropical hurricanes. This chapter describes GRACE gravity products and the different data processings used for mapping continental water storage variations, it also presents the most remarkable results concerning global continental hydrology and climate changes.

Interannual variations of degree 2 from geodetic observations and surface processes

Summary Geodetic observations from space continuously record surface deformation and global mass redistribution with an increasing accuracy. In parallel, surficial processes (oceanic, atmospheric, and hydrological loading) are more and more precisely modeled.We propose a confrontation of the geodetic Global Positioning System (GPS) and gravity-field satellite laser ranging (SLR) observations at decadal and interannual time scales, in terms of resolution, correlation and comparison with surficial loading models. We focus on the largest global scale signals of degree 2. At interannual periods, surface deformations retrieved from GPS time-series do not exceed 0.8 mm. Our analysis does not reveal the presence of a dominant signal at a specific period, except perhaps for a signal of approximately 3 yr likely connected to the loading response to El Nio / Southern Oscillations. Contrary to the results of previous studies, we do not find in GPS time-series a clear 6-yr oscillation associated with a degree-2 order-2 pattern. Interannual variations in the degree-2 Stokes coefficients of the gravity field do not exceed 2 × 10−11. We do not detect a dominant gravity signal at one specific period but instead a broad spectrum of frequencies. The comparison between the degree 2 deformations built from GPS time-series with a prediction from SLR derived gravity variations reveals some correlations, though their differences remain important. This highlights the present day limitations of these techniques in their ability to characterize global scale interannual variations. Hydrological loading models show some correlations with both GPS and SLR signals, but we cannot firmly establish that continental hydrology is dominantly responsible for the observed variations. Given the current limits in the resolution of both gravity and surface deformation and in the modelling of surface processes, we conclude that it will be a challenge to retrieve a geodetic signal of sub-decadal period originating in the Earth’s core.

Recovery of Rapid Water Mass Changes (RWMC) by Kalman Filtering of GRACE Observations

We demonstrate a new approach to recover water mass changes from GRACE satellite data at a daily temporal resolution. Such a product can be beneficial in monitoring extreme weather events that last a few days and are missing by conventional monthly GRACE data. The determination of the distribution of these water mass sources over networks of juxtaposed triangular tiles was made using Kalman Filtering (KF) of daily GRACE geopotential difference observations that were reduced for isolating the continental hydrology contribution of the measured gravity field. Geopotential differences were obtained from the along-track K-Band Range Rate (KBRR) measurements according to the method of energy integral. The recovery approach was validated by inverting synthetic GRACE geopotential differences simulated using GLDAS/WGHM global hydrology model outputs. Series of daily regional and global KF solutions were estimated from real GRACE KBRR data for the period 2003–2012. They provide a realistic description of hydrological fluxes at monthly time scales, which are consistent with classical spherical harmonics and mascons solutions provided by the GRACE official centers but also give an intra-month/daily continuity of these variations.

Fast determination of surface water mass changes using regional orthogonal functions

<p>Approaches based on Stokes coefficient filtering and « mass concentration » representations have been proposed for recovering changes of the surface water mass density from along-track accurate GRACE K-Band Range Rate (KBRR) measurements of geopotential change. The number of parameters, i.e. surface triangular tiles of water mass, to be determined remains large and the choice of the regularization strategy as the gravimetry inverse problem is non unique. In this study, we propose to use regional sets of orthogonal surface functions to image the structure of the surface water mass density variations. Since the number of coefficients of the development is largely smaller than the number of tiles, the computation of daily GRACE solutions for continental hydrology, e.g. obtained by Extended Kalman Filtering (EKF), is greatly fastened and eased by the matrix dimensions and conditioning. The proposed scheme of decomposition is applied to the African continent where it enables to very localized sources of (sub-)monthly water mass amplitudes.</p>

Geocenter Motion from a Combination of GRACE Mascon and SLR Data

<p>GRACE and GRACE Follow-On (FO) Level 2 data provide quasi-monthly, band-limited estimates of Stokes (geopotential, spherical harmonic) coefficients mostly reflecting surface mass variability due to non-tidal atmosphere, ocean, and continental hydrology.    <br>Although space gravimetry does not directly provide CM-related degree-1 Stokes coefficients, GRACE data have been successfully used over the years to complement time series of station positions from global space-geodetic (SG) network when inverting for Center-of-Mass to Center-of-Network (CM-CN) displacements (Wu et al, 2006).</p><p>Surficial mass variability observed through GRACE/GRACE-FO can be conveniently converted into load-induced (ENU) deformations at SG observing sites by adopting a spectral (i.e. load Love-number based) formalism and assuming Earth’s response is fully elastic and isotropic. GRACE-derived elastic displacements at observing sites would represent, if accurate, band-limited (degree 2 to 96, or higher if Mascon solutions are adopted) load-induced deformations that can be removed from SG-derived station displacements  in order to more accurately recover degree-1 surface deformation signature (and therefore geocenter motion). </p><p>In this study, we adopt GRACE JPL Mascon RL06 data in conjunction with Preliminary Reference Earth Model-derived load Love numbers to infer elastic displacement at SG sites and remove them from SLR inherently geocentric time series of station positions.<br>In so doing, the residual SLR station displacements, consistently expressed in a geocentric frame, would in principle reflect a degree-1 deformation signature that can be recovered via either surface deformation (Chanard et al, 2018) or translational approach.</p><p>We will compare the SLR/GRACE (CM-CN) determined in this study to standard estimates of geocenter motion such as ILRS’s and JTRF2014’s estimated via translational approach and spectrally inverted solutions (CM-CF).</p><p>References<br>Chanard K et al, (2018). JGR-Sol Ea doi:10.1002/2017JB015245 <br>Wu X et al, (2006). JGR-Sol Ea doi:10.1029/2005JB004100. </p>