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The relative importance of atmospheric advection and local land–atmosphere coupling to Australian precipitation is uncertain. Identifying the evaporative source regions and level of precipitation recycling can help quantify the importance of local and remotemarine and terrestrial moisture to precipitation within the different hydroclimates across Australia. Using a three-dimensional Lagrangian back-trajectory approach, moisture from precipitation events across Australia during 1979–2013 was tracked to determine the source of moisture (the evaporative origin) and level of precipitation recycling. We show that source regions vary markedly for precipitation falling in different regions. Advected marine moisture was relatively more important than terrestrial contributions for precipitation in all regions and seasons. For Australia as a whole, contributions from precipitation recycling varied from ∼11% in winter up to ∼21% in summer. The strongest land–atmosphere coupling was in the northwest and southeast where recycled local land evapotranspiration accounted for an average of 9% of warm-season precipitation. Marine contributions to precipitation in the northwest of Australia increased in spring and, coupled with positive evaporation trends in the key source regions, suggest that the observed precipitation increase is the result of intensified evaporation in the Maritime Continent and Indian and Pacific Oceans. Less clear were the processes behind an observed shift in moisture contribution from winter to summer in southeastern Australia. Establishing the climatological source regions and the magnitude of moisture recycling enables future investigation of anomalous precipitation during extreme periods and provides further insight into the processes driving Australia’s variable precipitation.

Ocean surface waves have been demonstrated to be an important component of coupled Earth System Models (ESMs), influencing atmosphere‐ocean momentum transfer; ice floe breakage; CFC, carbon, and energy uptake; and mixed‐layer depth. Modest errors in sea state properties do not strongly affect the impacts of these parameterizations. The modest data and accuracy needed contrast sharply with the high computational costs of spectral wave models in next‐generation ESMs, which can very easily exceed the cost of the ocean model component. We establish an alternative, cost‐efficient prototype wave modeling framework for air‐sea and ice‐ocean interactions, enabling the routine use of sea state‐dependent air‐sea coupling in future ESMs. In contrast to spectral models, the Particle‐in‐Cell for Efficient Swell (PiCLES) wave model is customized for coupled atmosphere‐ocean‐sea ice modeling. Combining Lagrangian wave growth solutions with the Particle‐In‐Cell method leads to a model that periodically projects wave information onto any convenient grid and scales in an embarrassingly parallel manner. The set of equations solves for the growth and propagation of a parametric wave spectrum's peak wavenumber vector and total wave energy, which reduces the state vector size by a factor of 50–200 compared to the standard resolution of spectral models. PiCLES's current computational costs in idealized wind‐sea simulations are about one order of magnitude faster than established wave models used in ESMs, with sufficient accuracy in bulk sea‐state variables relevant for coupling. PiCLES is compared to WAVEWATCH III in efficiency and accuracy in idealized cases. Plain Language Summary Today's climate models have a higher resolution than those of 30 years ago. Because they better resolve the near‐surface atmosphere and ocean, surface water waves are important. However, including today's wave models in climate models is costly. Here, we present an alternative wave model that is faster and is designed to be coupled with climate models. The Particle‐in‐CelL for Efficient Swell (PiCLES) wave model uses efficient numerics and modern coding practices that have yet to be used for surface waves. PiCLES is 10 times faster than conventional wave models used in climate models because it is simpler and uses fewer variables. It provides precisely the output variables needed for modeling the interaction of waves with the atmosphere and ocean. Key Points This paper describes an efficient wave model for the dominant, non‐local wind sea, called PiCLES The Particle‐in‐Cell method allows for an integration of wave growth and propagation along Lagrangian rays with gridded output when needed PiCLES is written in a modern programming language and can easily incorporate ML/AI‐driven coupling in Earth system and prediction models

This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge–Ampère equation on general triangular grids. This is done by establishing an equivalent (in the viscosity sense) Hamilton–Jacobi–Bellman formulation of the Monge–Ampère equation. A significant benefit of the reformulation is the removal of the convexity constraint from the admissible space as convexity becomes a built-in property of the new formulation. Moreover, this new approach allows one to tap the wealthy numerical methods, such as semi-Lagrangian schemes, for Hamilton–Jacobi–Bellman equations to solve Monge–Ampère-type equations. It is proved that the considered numerical methods are monotone, pointwise consistent, and uniformly stable. Consequently, its solutions converge uniformly to the unique convex viscosity solution of the Monte–Ampère Dirichlet problem. A superlinearly convergent Howard's algorithm, which is a Newton-type method, is utilized as the nonlinear solver to take advantage of the monotonicity of the scheme. Numerical experiments are also presented to gauge the performance of the proposed numerical method and the nonlinear solver.

We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman (HJB) equations on networks. The scheme is explicit, consistent, and stable for large time steps. We prove a convergence result and two error estimates. For an HJB equation with space-independent Hamiltonian, we obtain a first order error estimate. In the general case, we provide, under a hyperbolic CFL condition, a convergence estimate of order one half. The theoretical results are discussed and validated in a numerical tests section.

In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the nonnegativity of the solution, conserves the mass, and, as the discretization parameters tend to zero, has limit measure-valued trajectories which are shown to solve the equation. The main assumptions to obtain a convergence result are that the coefficients are continuous and satisfy a suitable linear growth property with respect to the space variable. In particular, we obtain a new proof of existence of solutions for such equations. We apply our results to some nonlinear examples, including Mean Field Games systems and variations of the Hughes model for pedestrian dynamics.

Inconsistencies may arise in numerical weather prediction models—that are based on semi-Lagrangian advection—when the governing dynamical and the kinematic trajectory equations are discretized in a dissimilar manner. This study presents consistent trajectory calculation approaches, both in the presence and absence of off-centering in the discretized dynamical equations. Both uniform and differential off-centering in the discretized dynamical equations have been considered. The proposed consistent trajectory calculations are evaluated using numerical experiments involving a nonhydrostatic two-dimensional theoretical mountain case and hydrostatic global forecasts. The experiments are carried out using the Global Environmental Multiscale model. Both the choice of the averaging method for approximating the velocity integral in the discretized trajectory equations and the interpolation scheme for calculating the departure positions are found to be important for consistent trajectory calculations. Results from the numerical experiments confirm that the proposed consistent trajectory calculation approaches not only improve numerical consistency, but also improve forecast accuracy.

In this work we propose a fully discrete semi-Lagrangian scheme for a first order mean field game system. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.

Currently, there is a lack of investigating moisture sources for precipitation over the upstream catchment of the Three Gorges Dam (UCTGD), the world’s largest dam. Using the dynamical recycling model (DRM), trajectory frequency method (TFM), and the Climate Forecast System Reanalysis (CFSR), this study quantifies moisture sources and transport paths for UCTGD summer precipitation from 1980 to 2009 based on two categories of sources: region-specific and source-direction. Overall, the land and oceanic sources contribute roughly 63% and 37%, respectively, of the moisture to UCTGD summer precipitation. UCTGD and the Indian Ocean are the most important land and oceanic sources, respectively, in which the southern Indian Ocean with over 10% of moisture contribution was overlooked previously. Under the influence of the Asian monsoon and prevailing westerlies, the land contribution decreases to 57.3% in June, then gradually increases to 68.8%. It is found that for drought years with enhanced southwest monsoon, there is a weakening of the moisture contribution from the C-shaped belt along the Arabian Sea, South Asia, and UCTGD, and vice versa. TFM results show three main moisture transport paths and highlight the importance of moisture from the southwest. Comparison analysis indicates that, generally, sink regions are more affected by land evaporation with their locations more interior to the center of the mainland. Furthermore, correlations between moisture contributions and indices of general circulation and sea surface temperature are investigated, suggesting that these indices affect precipitation by influencing moisture contributions of the subregions. All of these are useful for comprehending the causes of summer UCTGD precipitation.

This review paper presents an overview of Vortex Methods for flow simulation and their different sub-approaches, from their creation to the present. Particle methods distinguish themselves by their intuitive and natural description of the fluid flow as well as their low numerical dissipation and their stability. Vortex methods belong to Lagrangian approaches and allow us to solve the incompressible Navier-Stokes equations in their velocity-vorticity formulation. In the last three decades, the wide range of research works performed on these methods allowed us to highlight their robustness and accuracy while providing efficient computational algorithms and a solid mathematical framework. On the other hand, many efforts have been devoted to overcoming their main intrinsic difficulties, mostly relying on the treatment of the boundary conditions and the distortion of particle distribution. The present review aims to describe the Vortex methods by following their chronological evolution and provides for each step of their development the mathematical framework, the strengths and limits as well as references to applications and numerical simulations. The paper ends with a presentation of some challenging and very recent works based on Vortex methods and successfully applied to problems such as hydrodynamics, turbulent wake dynamics, sediment or porous flows.

The core Argo array has operated with the design goal of uniform spatial distribution of 3° in latitude and longitude. Recent studies have acknowledged that spatial and temporal scales of variability in some parts of the ocean are not resolved by 3° sampling and have recommended increased core Argo density in the equatorial region, boundary currents, and marginal seas with an integrated vision of other Argo variants. Biogeochemical (BGC) Argo floats currently observe the ocean from a collection of pilot arrays, but recently funded proposals will transition these pilot arrays to a global array. The current BGC Argo implementation plan recommends uniform spatial distribution of BGC Argo floats. For the first time, we estimate the effectiveness of the existing BGC Argo array to resolve the anomaly from the mean using a subset of modeled, full-depth BGC fields. We also study the effectiveness of uniformly distributed BGC Argo arrays with varying float densities at observing the ocean. Then, using previous Argo trajectories, we estimate the Argo array’s future distribution and quantify how well it observes the ocean. Finally, using a novel technique for sequentially identifying the best deployment locations, we suggest the optimal array distribution for BGC Argo floats to minimize objective mapping uncertainty in a subset of BGC fields and to best constrain BGC temporal variability.