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Supraglacial lakes play a central role in storing melt water, enhancing surface melt, and ultimately in driving ice flow and ice shelf melt through injecting water into the subglacial environment and facilitating fracturing. Here, we…
Satellite-based remote sensing missions have revolutionized our understanding of the Ocean state and dynamics. Among them, space-borne altimetry provides valuable Sea Surface Height (SSH) measurements, used to estimate surface geostrophic…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
The proper determination of soil moisture on different scales is important for applications in a variety of fields. We aim to develop a high-level soil moisture product with high temporal and spatial resolution by assimilating the…
Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level…
Surface ablation measurements of glaciers are critical for understanding mass change over time. Mass-balance stakes are commonly used for localized measurements, with the exposed length typically measured manually at infrequent intervals.…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
Graph transformers have demonstrated remarkable capability on complex spatio-temporal tasks, yet their depth is often limited by oversmoothing and weak long-range dependency modeling. To address these challenges, we introduce GRIT-LP, a…
Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…
We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…
Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods…
Accurate prediction of water temperature in streams is critical for monitoring and understanding biogeochemical and ecological processes in streams. Stream temperature is affected by weather patterns (such as solar radiation) and water…
Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction (NWP). There is a growing interest for physical models…
Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…
A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient…
We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…
Modeling time series is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly non-uniform sampling of measurements from different sensors with different levels of accuracy, as…