Visualize a tripolar grid

This example demonstrates how to generate a tripolar grid using the OrthogonalSphericalShellGrids package and how to visualize the grid using the GLMakie package. The example is structured into several key sections, each performing a specific task in the process of creating and visualizing the grid.

We begin by importing the required Julia packages. OrthogonalSphericalShellGrids is used for generating the tripolar grid, a type of grid used in geophysical and oceanographic modeling due to its ability to handle polar singularities effectively. GLMakie is used for visualization purposes, allowing the creation of figures and plots to visualize the grid.

using OrthogonalSphericalShellGrids
using OrthogonalSphericalShellGrids: Face, Center
using OrthogonalSphericalShellGrids: get_cartesian_nodes_and_vertices
using GLMakie

Grid generation

The grid is generated via OrthogonalSphericalShellGrids.TripolarGrid method by specifying the grid size and the latitude of the "north" singularities. Here, we use a lateral resolution of 6 degrees (60 x 30 grid points in the horizontal) and we configure the North hemisphere singularities to be at 60 degrees latitude. This setup creates a grid that covers the globe with a specific focus on handling the complexities near the North pole.

grid = OrthogonalSphericalShellGrids.TripolarGrid(size = (60, 30, 1),
                                                  north_poles_latitude = 60)

60×30×1 OrthogonalSphericalShellGrid{Float64, Oceananigans.Grids.Periodic, Oceananigans.Grids.RightConnected, Oceananigans.Grids.Bounded} on Oceananigans.Architectures.CPU with 4×4×4 halo and with precomputed metrics
├── centered at (λ, φ) = (70.0, 2.6549)
├── longitude: Oceananigans.Grids.Periodic  extent 359.895 degrees       variably spaced with min(Δλ)=0.286186, max(Δλ)=6.22702
├── latitude:  Oceananigans.Grids.RightConnected  extent 175.667 degrees variably spaced with min(Δφ)=0.517693, max(Δφ)=5.86207
└── z:         Bounded  z ∈ [0.0, 1.0]                                   regularly spaced with Δz=1.0

Retrieving the nodes

The lines retrieve Cartesian coordinates for two types of grid nodes: Face–Face nodes and Center–Centernodes. This is done using thegetcartesiannodesandverticesmethod, which converts the grid's spherical coordinates into Cartesian coordinates for easier manipulation and visualization. The coordinates are stored in variablesxF,yF,zFfor Face-Face nodes, andxC,yC,zC` for Center-Center nodes.

cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Face(), Face(), Center())
xF, yF, zF = cartesian_nodes

cartesian_nodes, _ = get_cartesian_nodes_and_vertices(grid, Center(), Center(), Center())
xC, yC, zC = cartesian_nodes

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Visualization

Finally, we can visualize the grid using two types of visual elements: surfaces and wireframes. Surfaces are plotted slightly smaller (at a scale of 0.99 instead of 1) than the wireframes to create a layered effect, enhancing the visual distinction between the grid's structure and its outline. The Face-Face nodes are visualized with blue surfaces and black wireframes, while the Center-Center nodes are visualized with blue surfaces and wireframes.

fig = Figure(size=(1200, 600))
axN = Axis3(fig[1, 1]; aspect=(1, 1, 1), elevation = +0.9, azimuth = 7, height=1500)
axS = Axis3(fig[1, 2]; aspect=(1, 1, 1), elevation = -0.9, azimuth = 7, height=1500)

for ax in (axN, axS)
    scale_factor = 0.99

    surface!(ax, xF .* scale_factor, yF .* scale_factor, zF .* scale_factor, color = :blue)
    wireframe!(ax, xF, yF, zF, color = :black)

    surface!(ax, xC .* scale_factor, yC .* scale_factor, zC .* scale_factor, color = :blue)
    wireframe!(ax, xC, yC, zC, color = :blue)

    scatter!(ax, 0, 0, +1, color=:red, markersize=15)
    scatter!(ax, 0, 0, -1, color=:red, markersize=15)

    hidedecorations!(ax)
    hidespines!(ax)
end

save("tripolar_grid_nodes.png", fig, px_per_unit = 2)

MESA: error: ZINK: vkCreateInstance failed (VK_ERROR_INCOMPATIBLE_DRIVER)
glx: failed to create drisw screen

Above there are two views of the grid: Northern hemisphere on the left, Southern hemisphere on the right. The actual North and South poles are the red dots. On the left we see how the Northern hemisphere does not have a gridline convergence singularity at the actual North Pole but instead the singularity has moved to the two fictitious poles shifted at latitude 60; on the right the Southern hemisphere still has a gridline convergence singularity at the actual South Pole.

This tripolar configuration is typically used in ocean modeling so that the gridline convergence singularity in the Arctic ocean is moved away and into the land mases of Russia and Canada; the South pole singularity is already within the land mass of Antarctica so things are all good there!

This page was generated using Literate.jl.