No abstract

No abstract

Limitations of satellite radar altimetry for operational hydrology include its spatial and temporal sampling as well as measurement problems caused by local topography and heterogeneity of the reflecting surface. In this study, we develop an approach that eliminates most of these limitations to produce an approximately 3 day temporal resolution water level time series from the original typically (sub)monthly data sets for the Po River in detail, and for Congo, Mississippi, and Danube Rivers. We follow a geodetic approach by which, after estimating and removing intersatellite biases, all virtual stations of several satellite altimeters are connected hydraulically and statistically to produce water level time series at any location along the river. We test different data-selection strategies and validate our method against the extensive available in situ data over the Po River, resulting in an average correlation of 0.7, Root-Mean-Square Error of 0.8 m, bias of 20.4 m, and Nash-Sutcliffe Efficiency coefficient of 0.5. We validate the transferability of our method by applying it to the Congo, Mississippi, and Danube Rivers, which have very different geomorphological and climatic conditions. The methodology yields correlations above 0.75 and Nash-Sutcliffe coefficients of 0.84 (Congo), 0.34 (Mississippi), and 0.35 (Danube). Maillard et al., 2015]. Such studies were motivated to a large extent by the premise that satellite altimetry may fill the gap left by the decline of gauge stations database. Surprisingly, other hydrological data like discharge are available in the open domain globally to a larger extent than in situ water level data. Since it cannot realistically be expected that the distribution and availability of global in situ water level stations will be improved in the future, of course with regional exceptions, research on the use of geodetic satellite data needs to be expanded. It is expected that time series from individual altimetric missions over most rivers are of poor quality, due to the neighboring topography and the heterogeneity of the reflecting surface. Therefore, the time series from individual missions often carry uncertainties and contain data outages, which limit the operational use of altimetry for improving the global river water level databases. As a result, these limitations inhibit also the operational use of altimetric water level into hydrological and hydrodynamic models [Alsdorf et al., 2007].

The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of R (or R 2 ) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity ®eld missions.

The performance of hydrological and hydrometeorological water-balance-based methods to estimate monthly runoff is analyzed. Such an analysis also allows for the examination of the closure of water budgets at different spatial (continental and catchment) and temporal (monthly, seasonal, and annual) scales. For this analysis, different combinations of gridded observations [Global Precipitation Climatology Centre (GPCC), Global Precipitation Climatology Project (GPCP), Climate Prediction Center (CPC), Climatic Research Unit (CRU), and University of Delaware (DEL)], atmospheric reanalysis models [Interim ECMWF Re-Analysis (ERA-Interim), Climate Forecast System Reanalysis (CFSR), and Modern-Era Retrospective Analysis for Research and Applications (MERRA)], partially model-based datasets [Global Land Surface Evaporation: The Amsterdam Methodology (GLEAM), Moderate Resolution Imaging Spectroradiometer (MODIS) Global Evapotranspiration Project (MOD16), and FLUXNET Multi-Tree Ensemble (FLUXNET MTE)], and Gravity Recovery and Climate Experiment (GRACE) satellite-derived water storage changes are employed. The derived ensemble of hydrological and hydrometeorological budget–based runoff estimates, together with results from different land surface hydrological models [Global Land Data Assimilation System (GLDAS) and the land-only version of MERRA (MERRA-Land)] and a simple predictor based on the precipitation–runoff ratio, is compared with observed monthly in situ runoff for 96 catchments of different sizes and climatic conditions worldwide. Despite significant shortcomings of the budget-based methods over many catchments, the evaluation allows for the demarcation of areas with consistently reasonable runoff estimates. Good agreement was particularly observed when runoff followed a dominant annual cycle like the Amazon. This holds true also for catchments with an area far below the spatial resolution of GRACE, like the Rhine. Over catchments with low or nearly constant runoff, the budget-based approaches do not provide realistic runoff estimates because of significant biases in the input datasets. In general, no specific data combination could be identified that consistently performed over all catchments. Thus, the performance over a specific single catchment cannot be extrapolated to other regions. Only in few cases do specific dataset combinations provide reasonable water budget closure; in most cases, significant imbalances remain for all the applied datasets.