High-dimensional experiments for the downward continuation using the LRFMP algorithm

Time-dependent gravity data from satellite missions like GRACE-FO reveal mass redistribution in the system Earth at various time scales: long-term climate change signals, inter-annual phenomena like El Nino, seasonal mass transports and transients, e. g. due to earthquakes. For this contemporary issue, a classical inverse problem has to be considered: the gravitational potential has to be modelled on the Earth's surface from measurements in space. This is also known as the downward continuation problem. Thus, it is important to further develop current mathematical methods for such inverse problems. For this, the (Learning) Inverse Problem Matching Pursuits ((L)IPMPs) have been developed within the last decade. Their unique feature is the combination of local as well as global trial functions in the approximative solution of an inverse problem such as the downward continuation of the gravitational potential. In this way, they harmonize the ideas of a traditional spherical harmonic ansatz and the radial basis function approach. Previous publications on these methods showed proofs of concept. Here, we consider the methods for high-dimensional experiments settings with more than 500 000 grid points which yields a resolution of 20 km at best on a realistic satellite geometry. We also explain the changes in the methods that had to be done to work with such a large amount of data. The corresponding code (updated for big data use) is available at https://doi.org/10.5281/zenodo.8223771 under the licence CC BY-NC-SA 3.0 Germany

Analyzing the Lake Urmia restoration progress using ground-based and spaceborne observations

Lake Urmia, located in the North West of Iran, was once the most extensive permanent hypersaline lake in the world. Unsustainable water management in response to increasing demand together with climatic extremes have given rise to the lake's depletion during the last two decades. The Urmia Lake Restoration Program (ULRP) was established in 2013 and aims to restore the lake within a 10-year program. This study aims to monitor these restoration endeavours using spaceborne and ground-based observations. We analyzed the in-situ water level, the surface water extent, and the water volume of the lake. The water storage change of the Urmia Lake catchment is quantified using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On satellite observations, which gives us a holistic view of hydrological components. Our analysis shows a positive trend of 14.5 cm/yr, 204 km2/yr, and 0.42 km3/yr in the time series of lake water level, lake water area, and water volume from 2015 to 2019 which indicates a short-lived stabilization of Lake Urmia. This has been achieved mainly due to an increase of 0.35 km3/yr in inflow from rivers to the lake, predominantly driven by anomalous precipitation events in 2016 and early 2019. However, the long-term trend from 2003 to 2019 still shows negative values of −22 cm/yr, −200 km2/yr, and −0.72 km3/yr for the water level, the surface area, and the water volume of the lake, respectively. The stabilization seems to be fragile however, since most of the increase in the water volume of the lake has spread over the large shallow southern region with high evaporation potential during hot seasons. Furthermore, due to the high correlation between the lake water level and precipitation, the recovery observed in 2016 and the first half of 2019 might not continue in case of a long drought period

Basin-scale runoff prediction: An Ensemble Kalman Filter framework based on global hydrometeorological data sets

In order to cope with the steady decline of the number of in situ gauges worldwide, there is a growing need for alternative methods to estimate runoff. We present an Ensemble Kalman Filter based approach that allows us to conclude on runoff for poorly or irregularly gauged basins. The approach focuses on the application of publicly available global hydrometeorological data sets for precipitation (GPCC, GPCP, CRU, UDEL), evapotranspiration (MODIS, FLUXNET, GLEAM, ERA interim, GLDAS), and water storage changes (GRACE, WGHM, GLDAS, MERRA LAND). Furthermore, runoff data from the GRDC and satellite altimetry derived estimates are used. We follow a least squares prediction that exploits the joint temporal and spatial auto- and cross-covariance structures of precipitation, evapotranspiration, water storage changes and runoff. We further consider time-dependent uncertainty estimates derived from all data sets. Our in-depth analysis comprises of 29 large river basins of different climate regions, with which runoff is predicted for a subset of 16 basins. Six configurations are analyzed: the Ensemble Kalman Filter (Smoother) and the hard (soft) Constrained Ensemble Kalman Filter (Smoother). Comparing the predictions to observed monthly runoff shows correlations larger than 0.5, percentage biases lower than ± 20%, and NSE-values larger than 0.5. A modified NSE-metric, stressing the difference to the mean annual cycle, shows an improvement of runoff predictions for 14 of the 16 basins. The proposed method is able to provide runoff estimates for nearly 100 poorly gauged basins covering an area of more than 11,500,000 km2 with a freshwater discharge, in volume, of more than 125,000 m3/s