LAPS v1.0.0: Lagrangian Advection of Particles at Sea, a Matlab program to simulate the displacement of particles in the ocean

We develop a Matlab program named LAPS (Lagrangian Advection of Particles at Sea) to simulate the advection of suspended particles in the global ocean with a minimal user effort to install, set and run the simulations. LAPS uses the 3D sea current velocity fields provided by ECCO2 to track the fate of suspended particles injected in the ocean, at specific places and times, during a period of time. LAPS runs with a short configuration file set by the user and returns the distribution of the particles at the end of the advection. A continuous tracking option is also available to record the complete trajectory of the particles throughout the entire period of advection. The effect of water waves, or Stokes drift, which alter sea surface current velocities, can also be taken into account. The principle and usage of the program is detailed and then applied to three case studies. The first two cases studies are applied to suspended sediment transport. We show how LAPS simulations can be used to investigate the spatio-temporal distribution of fine particles observed by satellites in the upper ocean. We also estimated sediment deposit areas on the seafloor as a function of sediment grain sizes. The third case study simulates the dispersion of microplastic particles during a tropical cyclone, and shows how the Stokes drift, which is significant during storm events, alters the particles trajectories compared to the case where the Stokes drift is neglected.

Neural UpFlow

We present a novel up-resing technique for generating high-resolution liquids based on scene flow estimation using deep neural networks. Our approach infers and synthesizes small- and large-scale details solely from a low-resolution particle-based liquid simulation. The proposed network leverages neighborhood contributions to encode inherent liquid properties throughout convolutions. We also propose a particle-based approach to interpolate between liquids generated from varying simulation discretizations using a state-of-the-art bidirectional optical flow solver method for fluids in addition with a novel key-event topological alignment constraint. In conjunction with the neighborhood contributions, our loss formulation allows the inference model throughout epochs to reward important differences in regard to significant gaps in simulation discretizations. Even when applied in an untested simulation setup, our approach is able to generate plausible high-resolution details. Using this interpolation approach and the predicted displacements, our approach combines the input liquid properties with the predicted motion to infer semi-Lagrangian advection. We furthermore showcase how the proposed interpolation approach can facilitate generating large simulation datasets with a subset of initial condition parameters.

Hurricane Irma Simulation at South Florida Using the Parallel CEST Model

In this study, a parallel extension of the Coastal and Estuarine Storm Tide (CEST) model is developed and applied to simulate the storm surge tide at South Florida induced by hurricane Irma occurred in 2017. An improvement is also made to the existing advection algorithm in CEST. This is achieved through the introduction of high-order, monotone Semi-Lagrangian advection. Distributed memory parallelization is developed via the Message Passing Interface (MPI) library. The parallel CEST model can therefore be run efficiently on machines ranging from multicore laptops to massively High Performance Computing (HPC) system. The principle advantage of being able to run the CEST model on multiple cores is that relatively low run-time is possible for real world storm surge simulations on grids with high resolution, especially in the locality where the hurricane makes landfall. The computational time is critical for storm surge model forecast to finish simulations in 30 min, and results are available to users before the arrival of the next advisory. In this study, simulation of hurricane Irma induced storm surge was approximately 22 min for 4 day simulation, with the results validated by field measurements. Further efficiency analysis reveals that the parallel CEST model can achieve linear speedup when the number of processors is not very large.

A Fast Linear Semi-Lagrangian Advection Scheme Coupled with Spectral (bin) Microphysics to Simulate an Idealized Super Cell Storm in WRF

A new, computationally efficient Semi-Lagrangian advection (SLA) scheme was used to simulate an idealized supercell storm using WRF coupled with Spectral (bin) Microphysics (SBM). SLA was developed to make complicated microphysical schemes more computationally accessible to cloud resolving models. The SLA is a linear combination of Semi-Lagrangian schemes of the first and the second order. It has relatively low numerical diffusion, a high level of mass conservation accuracy, and preserves the sum of multiple advected variables. In addition to idealized tests, comparisons were made with standard WRF higher-order, non-linear advection schemes. Tests of the SLA were performed using different weighting coefficients of γ for the combination of the first and second order components. The results of SLA on grids of 1 km, 500 m, and 250 m agree well with those of the standard WRF advection schemes, with results most similar to simulations with 250 m grid spacing. At the same time, the advection CPU time required by the SLA was 2.2 to 3 times shorter than the WRF advection schemes. The speed-up occurred in part because of the utilization of the same advection matrix for the advection of all hydrometeor mass bins. The findings of this work support the hypothesis that cloud microphysical simulation is more sensitive to the choice of microphysics than to the choice of advection schemes, thereby justifying the use of computationally efficient lower order linear schemes.

Long Time Steps for Advection: MPDATA with implicit time stepping

<p>Semi-Lagrangian advection schemes are accurate and efficient and retain accuracy and stability even for large Courant numbers but are not conservative. Flux-form semi-Lagrangian is conservative and in principle can be used to achieve large Courant numbers. However this is complicated and would be prohibitively expensive on grids that are not logically rectangular. </p><p>Strong winds or updrafts can lead to localised violations of Courant number restrictions which can cause a model with explicit Eulerian advection to crash. Schemes are needed that remain stable in the presence of large Courant numbers. However accuracy in the presence of localised large Courant numbers may not be so crucial.</p><p>Implicit time stepping for advection is not popular in atmospheric science because of the cost of the global matrix solution and the phase errors for large Courant numbers. However implicit advection is simple to implement (once appropriate matrix solvers are available) and is conservative on any grid structure and can exploit improvements in solver efficiency and parallelisation. This talk will describe an implicit version of the MPDATA advection scheme and show results of linear advection test cases. To optimise accuracy and efficiency, implicit time stepping is only used locally where needed. This makes the matrix inversion problem local rather than global. With implicit time stepping MPDATA retains positivity, smooth solutions and accuracy in space and time.</p>

Semi-Lagrangian advection models for quasi-uniform nodes on the sphere

<p>Radial basis functions enable the use of unstructured quasi-uniform nodes on the sphere. Iteratively generated nodes such as the minimum energy nodes may not converge due to exponentially increasing local minima as the number of nodes grows. By contrast, deterministic nodes, such as those made with a spherical helix, are fast to generate and have no arbitrariness. It is noteworthy that the spherical helix nodes are more uniform on the sphere than the minimum energy nodes. Semi-Lagrangian and Eulerian models are constructed using radial basis functions and validated in a standard advection test of a cosine bell by the solid body rotation. With Gaussian radial basis functions, the semi-Lagrangian model found produces significantly smaller error than the Eulerian counterpart in addition to approximately three times longer time step for the same error. Moreover, the ripple-like noise away from the cosine bell found in the Eulerian model is significantly reduced in the semi-Lagrangian model. It is straightforward to parallelize the matrix–vector multiplication in the time integration. In addition, an iterative solver can be applied to calculate the inverse of the interpolation matrix, which can be made sparse.</p>

Development of a semi-Lagrangian advection scheme for the NEMO ocean model (3.1)

As resolutions of ocean circulation models increase, the advective Courant number – the ratio between the distance travelled by a fluid parcel in one time step and the grid size – becomes the most stringent factor limiting model time steps. Some atmospheric models have escaped this limit by using an implicit or semi-implicit semi-Lagrangian formulation of advection, which calculates materially conserved fluid properties along trajectories which follow the fluid motion and end at prescribed grid points. Unfortunately, this formulation is not straightforward in ocean contexts, where the irregular, interior boundaries imposed by the shore and bottom orography are incompatible with traditional trajectory calculations. This work describes the adaptation of the semi-Lagrangian method as an advection module for an operational ocean model. We solve the difficulties of the ocean's internal boundaries by calculating parcel trajectories using a time-exponential formulation, which ensures that all parcel trajectories remain inside the ocean domain despite strong accelerations near the boundary. Additionally, we derive this method in a way that is compatible with the leapfrog time-stepping scheme used in the NEMO-OPA (Nucleus for European Modelling of the Ocean, Océan Parallélisé) ocean model, and we present simulation results for a simplified test case of flow past a model island and for 10-year free runs of the global ocean on the quarter-degree ORCA025 grid.

A Lagrangian Advection Scheme for Solving Cloud Droplet Diffusion Growth

Cloud drop diffusion growth is a fundamental microphysical process in warm clouds. In the present work, a new Lagrangian advection scheme (LAS) is proposed for solving this process. The LAS discretizes cloud drop size distribution (CDSD) with movable bins. Two types of prognostic variable, namely, bin radius and bin width, are included in the LAS. Bin radius is tracked by the well-known cloud drop diffusion growth equation, while bin width is solved by a derived equation. CDSD is then calculated with the information of bin radius, bin width, and prescribed droplet number concentration. The reliability of the new scheme is validated by the reference analytical solutions in a parcel cloud model. Artificial broadening of CDSD, understood as a by-product of numerical diffusion in advection algorithm, is strictly prohibited by the new scheme. The authors further coupled the LAS into a one-and-half dimensional (1.5D) Eulerian cloud model to evaluate its performance. An individual deep cumulus cloud studied in the Cooperative Convective Precipitation Experiment (CCOPE) campaign was simulated with the LAS-coupled 1.5D model and the original 1.5D model. Simulation results of CDSD and microphysical properties were compared with observational data. Improvements, namely, narrower CDSD and accurate reproduction of particle mean diameter, were achieved with the LAS-coupled 1.5D model.