Reducing Numerical Artifacts by Sacrificing Well-Balance for Rotating Shallow-Water Flow

We consider the problem of rotational shallow-water flow for which non-trivial rotating steady-state solutions are of great importance. In particular, we investigate a high-resolution central-upwind scheme that is well-balanced for a subset of these stationary solutions and show that the well-balanced design is the source of numerical artifacts when applied to more general problems. We propose an alternative flux evaluation that sacrifices the well-balanced property and demonstrate that this gives qualitatively better results for relevant test cases and real-world oceanographic simulations.acceptedVersio

Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme

In this work, we take a modern high-resolution finite-volume scheme for solving the rotational shallow-water equations and extend it with features required to run real-world ocean simulations. Our contributions include a spatially varying north vector and Coriolis term required for large scale domains, moving wet-dry fronts, a static land mask, bottom shear stress, wind forcing, boundary conditions for nesting in a global model, and an efficient model reformulation that makes it well-suited for massively parallel implementations. Our model order is verified using a grid convergence test, and we show numerical experiments using three different sections along the coast of Norway based on data originating from operational forecasts run at the Norwegian Meteorological Institute. Our simulation framework shows perfect weak scaling on a modern P100 GPU, and is capable of providing tidal wave forecasts that are very close to the operational model at a fraction of the cost. All source code and data used in this work are publicly available under open licenses.publishedVersio

Massively parallel implicit equal-weights particle filter for ocean drift trajectory forecasting

Forecasting of ocean drift trajectories are important for many applications, including search and rescue operations, oil spill cleanup and iceberg risk mitigation. In an operational setting, forecasts of drift trajectories are produced based on computationally demanding forecasts of three-dimensional ocean currents. Herein, we investigate a complementary approach for shorter time scales by using the recently proposed two-stage implicit equal-weights particle filter applied to a simplified ocean model. To achieve this, we present a new algorithmic design for a data-assimilation system in which all components – including the model, model errors, and particle filter – take advantage of massively parallel compute architectures, such as graphical processing units. Faster computations can enable in-situ and ad-hoc model runs for emergency management, and larger ensembles for better uncertainty quantification. Using a challenging test case with near-realistic chaotic instabilities, we run data-assimilation experiments based on synthetic observations from drifting and moored buoys, and analyze the trajectory forecasts for the drifters. Our results show that even sparse drifter observations are sufficient to significantly improve short-term drift forecasts up to twelve hours. With equidistant moored buoys observing only 0.1% of the state space, the ensemble gives an accurate description of the true state after data assimilation followed by a high-quality probabilistic forecast

Comparison of Ensemble-Based Data Assimilation Methods for Sparse Oceanographic Data

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term predictions of drift trajectories are essential to efficiently define search areas, but in-situ buoy observations provide only very sparse point measurements, while the mission is ongoing. Statistically optimal forecasts, including consistent uncertainty statements, rely on Bayesian methods for data assimilation to make the best out of both the complex mathematical modeling and the sparse spatial data. To identify suitable approaches for data assimilation in this context, we discuss localisation strategies and compare two state-of-the-art ensemble-based methods for applications with spatially sparse observations. The first method is a version of the ensemble-transform Kalman filter, where we tailor a localisation scheme for sparse point data. The second method is the implicit equal-weights particle filter which has recently been tested for related oceanographic applications. First, we study a linear spatio-temporal model for contaminant advection and diffusion, where the analytical Kalman filter provides a reference. Next, we consider a simplified ocean model for sea currents, where we conduct state estimation and predict drift. Insight is gained by comparing ensemble-based methods on a number of skill scores including prediction bias and accuracy, distribution coverage, rank histograms, spatial connectivity and drift trajectory forecasts

Efficient Forecasting of Drift Trajectories using Simplified Ocean Models and Nonlinear Data Assimilation on GPUs

This thesis presents research on efficient, massively parallel methods and algorithms related to short-term forecasting of drift trajectories in the ocean. The topic has clear societal applications and is an important tool for, e.g.,search-and-rescue operations at sea, planning of oil-spill cleanup, and collision detection between icebergs and offshore installations. In this work, we investigate computational techniques that can be used complementary to the operational methods already in place today. The traditional approach is to use complex ocean models, of which it is only feasible to run a small ensemble. Due to large uncertainties in initial conditions for oceanographic simulations, however, we propose to use simplified ocean models that capture the relevant physics on short time horizons. We base our simplified ocean models on the rotational shallow-water equations, simulated using an explicit, high-resolution, finite-volume scheme. Since such schemes can be implemented to run efficiently on the graphics processing unit (GPU), we can afford to run a large ensemble of simplified ocean models. Furthermore, we investigate nonlinear data-assimilation techniques, such as particle filters, that enable us to use available observations of the ocean state to reduce the uncertainty in the ensemble. Our hope is that this approach, possibly in combination with the operational methods, can give a more complete picture of the uncertainties in the forecasted drift trajectories. The thesis consists of an introductory part plus five scientific papers. The first two papers assess enabling technologies and methods needed for our approach to forecasting of drift trajectories. This includes evaluating numerical schemes for their suitability to capture oceanographic shallowwater flow, and assessing programming environments for GPU computing. The third paper presents a massively parallel algorithm for applying the recently proposed implicit equal-weights particle filter to a shallowwater model for forecasting of drift trajectories. In the fourth paper, we present a framework for running efficient oceanographic simulations using a modern finite-volume scheme initiated from operational ocean circulation forecasts. Finally, the fifth paper explores the possibility of using a very large ensemble with 10 000 members along with a basic particle filter method for ensemble prediction of drift trajectories

A CUDA Back-End for the Equelle Compiler.

As parallel and heterogeneous computing becomes more and more a necessity for implementing high performance simulators, it becomes increasingly harder for scientists and engineers without experience in high performance computing to achieve good performance. Even for those who knows how to write efficient code the process for doing so is time consuming and error prone, and maintaining and implementing changes in such code requires huge effort. By providing tools for automated utilization of parallel hardware, such efforts could be restricted and experts in numerical methods could spend their time on expressing better methods rather than on implementation details.In this thesis we present a CUDA back-end for the Equelle compiler. Equelle is a domain-specific language designed for writing simulators of partial differential equations, and is under development at SINTEF ICT. The language provides natural syntax for describing finite volume methods, and lets the compiler take care of high performance. The back-end presented in this thesis allows programs written in Equelle be compiled to execute on graphics processing units (GPUs), without requiring the user to have any knowledge in GPU programming.We have verified correctness of the CUDA back-end by applying it to Equelle simulators for the shallow water equations and both explicit and implicit methods for the heat equation. Good performance have been shown for all three simulators, and we discuss what should be done next to achieve even higher performance

Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme

In this work, we take a modern high-resolution finite-volume scheme for solving the rotational shallow-water equations and extend it with features required to run real-world ocean simulations. Our contributions include a spatially varying north vector and Coriolis term required for large scale domains, moving wet-dry fronts, a static land mask, bottom shear stress, wind forcing, boundary conditions for nesting in a global model, and an efficient model reformulation that makes it well-suited for massively parallel implementations. Our model order is verified using a grid convergence test, and we show numerical experiments using three different sections along the coast of Norway based on data originating from operational forecasts run at the Norwegian Meteorological Institute. Our simulation framework shows perfect weak scaling on a modern P100 GPU, and is capable of providing tidal wave forecasts that are very close to the operational model at a fraction of the cost. All source code and data used in this work are publicly available under open licenses

Coastal ocean forecasting on the GPU using a two-dimensional finite-volume scheme

In this work, we take a modern high-resolution finite-volume scheme for solving the rotational shallow-water equations and extend it with features required to run real-world ocean simulations. Our contributions include a spatially varying north vector and Coriolis term required for large scale domains, moving wet-dry fronts, a static land mask, bottom shear stress, wind forcing, boundary conditions for nesting in a global model, and an efficient model reformulation that makes it well-suited for massively parallel implementations. Our model order is verified using a grid convergence test, and we show numerical experiments using three different sections along the coast of Norway based on data originating from operational forecasts run at the Norwegian Meteorological Institute. Our simulation framework shows perfect weak scaling on a modern P100 GPU, and is capable of providing tidal wave forecasts that are very close to the operational model at a fraction of the cost. All source code and data used in this work are publicly available under open licenses

Data Assimilation for Ocean Drift Trajectories Using Massive Ensembles and GPUs

In this work, we perform fully nonlinear data assimilation of ocean drift trajectories using multiple GPUs. We use an ensemble of up to 10000 members and the sequential importance resampling algorithm to assimilate observations of drift trajectories into the underlying shallow-water simulation model. Our results show an improved drift trajectory forecast using data assimilation for a complex and realistic simulation scenario, and the implementation exhibits good weak and strong scaling