Nico Sneeuw

Abstract

The Copernicus Sentinel-3 Surface Topography Mission (STM) Land Altimetry provides valuable surface elevation information over inland waters, sea ice, and land ice, thanks to its synthetic aperture radar (SAR) altimeter and its orbit that covers high-latitude polar regions. To ensure that these measurements are reliable and to maximise the return on investment, adequate validation of the geophysical retrieval methods, processing algorithms, and corrections must be performed using independent observations. The EU-ESA project St3TART (started July 2021) aims to generalise the concept of Fiducial Reference Measurements (FRMs) for the Copernicus Sentinel-3 STM. This work has gathered existing data, made new observations during field campaigns, and ensured that these observations meet the criteria of FRM standards so that they can be used to validate Sentinel-3 STM Land Altimetry products operationally. A roadmap for the operational provision of the FRM, including the definition, consolidation, and identification of the most relevant and cost-effective methods and protocols to be maintained, supported, or implemented, has been developed. The roadmap includes guidelines for SI traceability, definitions of FRM measurement procedures, processing methods, and uncertainty budget estimations.

Abstract

The spherical shell and spherical zonal band are two elemental geometries that are often used as benchmarks for gravity field modeling. When applying the spherical shell and spherical zonal band discretized into tesseroids, the errors may be reduced or cancelled for the superposition of the tesseroids due to the spherical symmetry of the spherical shell and spherical zonal band. In previous studies, this superposition error elimination effect (SEEE) of the spherical shell and spherical zonal band has not been taken seriously, and it needs to be investigated carefully. In this contribution, the analytical formulas of the signal of derivatives of the gravitational potential up to third order (e.g., V, \$\$V\_\z\\$\$, \$\$V\_\zz\\$\$, \$\$V\_\xx\\$\$, \$\$V\_\yy\\$\$, \$\$V\_\zzz\\$\$, \$\$V\_\xxz\\$\$, and \$\$V\_\yyz\\$\$) of a tesseroid are derived when the computation point is situated on the polar axis. In comparison with prior research, simpler analytical expressions of the gravitational effects of a spherical zonal band are derived from these novel expressions of a tesseroid. In the numerical experiments, the relative errors of the gravitational effects of the individual tesseroid are compared to those of the spherical zonal band and spherical shell not only with different 3D Gauss--Legendre quadrature orders ranging from (1,1,1) to (7,7,7) but also with different grid sizes (i.e., \$\$5^\\backslashcirc \\backslashtimes 5^\\backslashcirc \\$\$, \$\$2^\\backslashcirc \\backslashtimes 2^\\backslashcirc \\$\$, \$\$1^\\backslashcirc \\backslashtimes 1^\\backslashcirc \\$\$, \$\$30^\\backslashprime \\backslashtimes 30^\\backslashprime \\$\$, and \$\$15^\\backslashprime \\backslashtimes 15^\\backslashprime \\$\$) at a satellite altitude of 260 km. Numerical results reveal that the SEEE does not occur for the gravitational components V, \$\$V\_\z\\$\$, \$\$V\_\zz\\$\$, and \$\$V\_\zzz\\$\$of a spherical zonal band discretized into tesseroids. The SEEE can be found for the \$\$V\_\xx\\$\$and \$\$V\_\yy\\$\$, whereas the superposition error effect exists for the \$\$V\_\xxz\\$\$and \$\$V\_\yyz\\$\$of a spherical zonal band discretized into tesseroids on the overall average. In most instances, the SEEE occurs for a spherical shell discretized into tesseroids. In summary, numerical experiments demonstrate the existence of the SEEE of a spherical zonal band and a spherical shell, and the analytical solutions for a tesseroid can benefit the investigation of the SEEE. The single tesseroid benchmark can be proposed in comparison to the spherical shell and spherical zonal band benchmarks in gravity field modeling based on these new analytical formulas of a tesseroid.

Abstract

Inland satellite altimetry has gained traction over the past decade and is now routinely used to monitor the water levels of rivers, lakes and reservoirs. The accuracy of such inland water height measurements, at least from radar altimetry is still relatively poor from a geodetic viewpoint, namely in the range of several decimeter. Accuracies from spaceborne laser altimetry, in particular from the ICESat-2 mission, are at cm-level, however, and further progress in the radar altimetry domain is expected from swath-based altimetry by the SWOT mission, (to be) launched December 2022. With accuracies down to cm-level one needs to reconsider the height system definition of inland lake surfaces as obtained from satellite altimetry. Conventionally one subtracts a global geoid model from the altimetry-derived ellipsoidal height to obtain an orthometric height. Without wind stress, seiches and other time-variable height disturbances the lake water surfaces will conform to equipotential surfaces in the Earth's gravity field. Thus lake surfaces are surfaces of constant dynamic height, from which follows that a lake surface cannot be a surface of constant orthometric or normal height. Because equipotential surfaces are inherently non-parallel, two points at a lake surface can and will have different orthometric height. Although being well-understood in physical geodesy, we will here model this effect and quantify it for various case studies. We demonstrate that the effects can be as large as a few dm for large lakes at high altitudes, which is an order of magnitude that is relevant in terms of satellite altimetry error levels.

Abstract

The GRACE and GRACE-FO satellite missions provide mass variations as a fundamentally new observation type for a broad spectrum of novel applications in Earth science disciplines, including oceanography, geophysics, hydrology, and hydrometeorology. Despite all the key findings in hydrology, the utility of GRACE-derived Terrestrial Water Storage Anomaly (TWSA) and its time derivative Terrestrial Water Storage Flux (TWSF) have mainly been limited to large catchments due to their coarse spatial resolution. Here, we propose a method to downscale TWSF by incorporating available finer-resolution data. We determine the downscaled TWSF and its uncertainty within a proposed Bayesian framework by incorporating the fine-scale data of TWSF and Soil Moisture Change (SMC) from different available sources. For the Bayesian ingredients, we rely on GRACE data to obtain the prior and rely on copula models to obtain nonparametric likelihood functions based on the statistical relationship between GRACE TWSF with fine-scale TWSF data and SMC. We apply our method to the Amazon Basin and assess the performances of our products from various fine-scale input datasets of TWSFs and SMCs. Given the lack of ground truth for TWSF, we validate our results against space-based Surface Water Storage Change (SWSC) in the Amazon river system and also against the Vertical Crustal Displacements Rate (VCDR) observed by the Global Positioning System (GPS). Overall, the results show that the proposed method is able to estimate a downscaled TWSF, which is informed by GRACE and fine-scale data. Validation shows that our downscaled products are better anticorrelated with VCDR (−0.81) than fine-scale TWSF (−0.73) and show a mean relative RMSE of 26% with SWSC versus 70% for fine-scale TWSF. The proposed methodology can be extended to other coarse scale datasets, which are crucial for hydrological application at regional and local scales.

Abstract

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 476þinspacekm3 to 502þinspacekm3, unevenly distributed throughout the region, with 63\% being stored in the southernmost sub-basins, Kasaï (220--228þinspacekm3) and Lualaba (109--169þinspacekm3), while the northern sub-basins contribute only 173þinspace±þinspace8þinspacekm3. We further estimate the hydraulic time constant for draining its entire water storage to be 4.3þinspace±þinspace0.1 months, but, regionally, permanent wetlands and large lakes act as resistors resulting in greater time constants of up to 105þinspace±þinspace3 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.

Abstract

The Arctic is undergoing dramatic climate and environmental changes. The long-term alterations in river discharges from the boreal catchments, which serve as vital links between the ocean and land, are having a profound impact on various environmental factors, particularly ocean circulation and sea-ice content. However, comprehensive and continuous monitoring of Arctic river discharge at seasonal or higher temporal resolutions remains challenging. In this study, we propose a new approach to estimate runoff by generating monthly runoff time series at the basin scale. Our method is based on changes in water storage observed by the gravimetric satellites Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission since 2002. The method utilizes an empirical runoff-storage (R-S) relationship, offering simplicity and low computational burden while maintaining good accuracy in estimating runoff. To validate our method, we utilize in-situ runoff measurements from the seven largest boreal drainage basins spanning the period from 2002 to 2019, encompassing a total of 18 years. We divide these 18 years of observations into two phases: a training phase (8 years) and a testing phase (10 years). The results indicate that the R-S method established during the training phase yields monthly Nash-Sutcliffe efficiency (NSE) values ranging from 0.65 to 0.92 when compared to in-situ runoff measurements. Moreover, the method demonstrates a consistent performance in estimating runoff during the testing phase (monthly NSE: 0.67–0.84). With the exception of the Ob and Mackenzie basins, which exhibit distinct climatic conditions and hydrological networks, the R-S models are interchangeable across basins. This makes it suitable for both temporal and spatial extrapolation to fill data gaps, provided that accurate water and snow storage data are available. All in all, our method enables the reconstruction of monthly surface runoff across the entire boreal basins between 2002 and 2019. The results indicate an average annual runoff of 3200 ± 160 Gt over the study area of 1.58 × 107 km2. To evaluate the accuracy of our estimates, we compare the total runoff estimates obtained using the R-S method with those from 12 model estimates. Our estimates exhibit the highest correlation with available in-situ runoff measurements and yield monthly NSE values >0.57 for five out of the twelve model estimates. This study presents a convenient method to address the urgent need for comprehensive, continuous, and monthly temporal resolution of runoff estimates throughout the entire boreal region.

Abstract

Prevalent north--south striping (NSS) noise in the spherical harmonic coefficient products of the satellite missions gravity recovery and climate experiment greatly impedes the interpretation of signals. The overwhelming NSS noise always leads to excessive smoothing of the data, allowing a large room for improvement in the spatial resolution if this particular NSS noise can be mitigated beforehand. Here, we put forward a new spatial filter that can effectively remove NSS noise while remaining orthogonal to physical signals. This new approach overcomes the limitations of the previous method proposed by Swenson and Wahr (2006), where signal distortion was large and high-order coefficients were uncorrectable. The filter is based on autocorrelation in the longitude direction and cross-correlation in the latitude direction. The NSS-type noise identified by our method is mainly located in coefficients of spherical harmonic order larger than about 20 and degree beyond 30, spatially between latitudesþinspace±þinspace60°. After removing the dominating NSS noise with our method, a weaker filter than before is added to handle the residual noise. Thereby, the spatial resolution can be increased and the amplitude damping can be reduced. Our method can coincidentally reduce outliers in time series without significant trend bias, which underpins its effectiveness and reliability.

Abstract

A harmonic scalar field has a Laplacian (i.e., both source-free and curl-free) gradient vector field and vice versa. Despite the good performance of spherical harmonic series on modeling the gravitational field generated by spheroidal bodies (e.g., the Earth), the series may diverge inside the Brillouin sphere enclosing all field-generating mass. Divergence may realistically occur when determining the gravitational fields of asteroids or comets that have complex shapes, which is known as the complex-boundary value problem (CBVP). To overcome this weakness, we propose a new spatial-domain numerical method based on the equivalence transformation which is well known in the fluid dynamics community: a potential-flow velocity field and a gravitational force vector field are equivalent in a mathematical sense, both referring to a Laplacian vector field. The new method abandons the perturbation theory based on the Laplace equation, and, instead, derives the governing equation and the boundary condition of the potential flow from the conservation laws of mass, momentum and energy. Correspondingly, computational fluid dynamics (CFD) techniques are introduced as a numerical solving scheme. We apply this novel approach to the gravitational field of the comet 67P/Churyumov--Gerasimenko which has an irregular shape. The method is validated in a closed-loop simulation by comparing the result with a direct integration of Newton's formula. Both methods are consistent with a relative magnitude discrepancy at the percentage level and with a small directional difference root-mean-square value of \$\$0.78^\\backslashcirc \\$\$. Moreover, the Laplacian property of the potential flow's velocity field is proved mathematically. From both theoretical and practical points of view, the new numerical method is able to overcome the divergence problem and, hence, has a good potential for solving CBVPs.

Abstract

In this paper, the three kind of solutions of TLS problem, the common solution by singular value decomposition (SVD), the iteration solution and Partial-EIV model are firstly reviewed with respect to their advantages and disadvantages. Then a newly developed Converted Total Least Squares (CTLS) dealing with the errors-in-variables (EIV) model is introduced. The basic idea of CTLS has been proposed by the authors in 2010, which is to take the stochastic design matrix elements as virtual observations, and to transform the TLS problem into a traditional Least Squares problem. This new method has the advantages that it cannot only easily consider the weight of observations and the weight of stochastic design matrix, but also deal with TLS problem without complicated iteration processing, if the suitable approximates of parameters are available, which enriches the TLS algorithm and solves the bottleneck restricting the application of TLS solutions. CTLS method, together with all the three TLS models reviewed here has been successfully integrated in our coordinate transformation programs and verified with the real case study of 6-parameters Affine coordinate transformation. Furthermore, the comparison and connection of this notable CLTS method and estimation of Gauss-Helmert model are also discussed in detail with applications of coordinate transformations.

Abstract

© Springer International Publishing Switzerland 2016. Ocean tides cause notable aliasing errors in the gravity field from single pair space-borne gravimetry missions like GRACE. Several studies into future gravity missions have shown that constellations with two or more GRACE-like tandems lead to a significant reduction of aliasing error from all kinds of high-frequency signal sources. Despite such reduction, tidal aliasing will remain an error source. We here investigate the efficiency of tidal error de-aliasing in the post-processing mode for such future double-pair missions. To that purpose, we analyze how a certain satellite mission samples each tidal constituent. Given the repeat orbit patterns and the observation time span, we examine and model the alias periods and amplitudes constituent by constituent based on data-driven analysis. Results show that a double-pair formation has indeed better de-aliasing properties than a single-pair formation in terms of distribution and amplitude of ocean tide aliasing error. After least-squares (LS) spectral estimation of the tidal aliases at the derived alias periods, the aliasing error is reduced significantly.