Nico Sneeuw

Zusammenfassung

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 7895þinspacekm3/month.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

Abstract The number of active gauges with open-data policy for discharge monitoring along rivers has decreased over the last decades. Therefore, spaceborne measurements are investigated as alternatives. Among different techniques for estimating river discharge from space, developing a rating curve between the ground-based discharge and spaceborne river water level or width is the most straightforward one. However, this does not always lead to successful results, since the river section morphology often cannot simply be modeled by a limited number of parameters. Moreover, such methods do not deliver a proper estimation of the discharge’s uncertainty as a result of the mismodeling and also the coarse assumptions made for the uncertainty of inputs. Here we propose a nonparametric model for estimating river discharge and its uncertainty from spaceborne river width measurements. The model employs a stochastic quantile mapping scheme by, iteratively: 1) generating realizations of river discharge and width time series using Monte Carlo simulation, 2) obtaining a collection of quantile mapping functions by matching all possible permutations of simulated river discharge and width quantile functions, 3) adjusting the measurement uncertainties according to the point cloud scatter. We validate our method over 14 different river reaches along the Niger, Congo, Po rivers and several river reaches in the Mississippi river basin. Our results show that the proposed algorithm can mitigate the effect of measurement noise and also possible mismodelling. Moreover, the proposed algorithm delivers a meaningful uncertainty for the estimated discharge and allows us to calibrate the error bars of in situ discharge measurements.

Zusammenfassung

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.