Simulation-based inference (SBI) is an established approach for performing Bayesian inference on scientific simulators. SBI so far works best on low-dimensional parametric models. However, it is difficult to infer function-valued parameters, which frequently occur in disciplines that model spatiotemporal processes such as the climate and earth sciences. Here, we introduce an approach for efficient posterior estimation, using a Fourier Neural Operator (FNO) architecture with a flow matching objective. We show that our approach, FNOPE, can perform inference of function-valued parameters at a fraction of the simulation budget of state of the art methods. In addition, FNOPE supports posterior evaluation at arbitrary discretizations of the domain, as well as simultaneous estimation of vector-valued parameters. We demonstrate the effectiveness of our approach on several benchmark tasks and a challenging spatial inference task from glaciology. FNOPE extends the applicability of SBI methods to new scientific domains by enabling the inference of function-valued parameters.

Ground-penetrating radar is an extensively used geophysical tool in cryosphere sciences (ice sheets and glaciers) with sounding depths of several kilometers due to the small radio-wave attenuation in ice sheets. Detection of the ice thickness and internal ice stratigraphy with commercial radars has become standard. However, there is still an observational gap in determining dielectric and mechanical ice-fabric anisotropy and basal properties using these systems. Recently, ground-based phase coherent radar has been showed its potential to fill this gap. However, this requires that the corresponding ground-based radars cover profiles several tens of kilometers in length. We address this challenge by modifying an autonomous rover to collect phase-coherent, quad-polarimetric radar data geolocated with real-time kinematic positioning. In a proof-of-concept study in Antarctica, we demonstrate that this allows the collection of quad-polarimetric data along a 23 km profile, mapping anisotropic ice-fabric properties at <100 m intervals across the transition of grounded to floating ice. This study shows the possibility of collecting data that will refine ice-flow models by providing missing rheological parameters. This work also demonstrates the versatility of the autonomous ground vehicle with its ability to tow more than 200 kg payload, with a battery run time of over six hours, and with a modular design that enables future integration of different radars or other geophysical sensors.

In this paper, a new digital elevation model (DEM) is derived for the ice sheet in western Dronning Maud Land, Antarctica. It is based on differential interferometric synthetic aperture radar (SAR) from the European Remote Sensing 1/2 (ERS-1/2) satellites, in combination with ICESat's Geoscience Laser Altimeter System (GLAS). A DEM mosaic is compiled out of 116 scenes from the ERS-1 ice phase in 1994 and the ERS-1/2 tandem mission between 1996 and 1997 with the GLAS data acquired in 2003 that served as ground control. Using three different SAR processors, uncertainties in phase stability and baseline model, resulting in height errors of up to 20 m, are exemplified. Atmospheric influences at the same order of magnitude are demonstrated, and corresponding scenes are excluded. For validation of the DEM mosaic, covering an area of about 130 000 km2on a 50-m grid, independent ICESat heights (2004-2007), ground-based kinematic GPS (2005), and airborne laser scanner data (ALS, 2007) are used. Excluding small areas with low phase coherence, the DEM differs in mean and standard deviation by 0.5 + / - 10.1, 1.1 + / - 6.4, and 3.1 +/ - 4.0 m from ICESat, GPS, and ALS, respectively. The excluded data points may deviate by more than 50 m. In order to suppress the spatially variable noise below a 5-m threshold, 18% of the DEM area is selectively averaged to a final product at varying horizontal spatial resolution. Apart from mountainous areas, the new DEM outperforms other currently available DEMs and may serve as a benchmark for future elevation models such as from the TanDEM-X mission to spatially monitor ice sheet elevation.