ClimaCore.jl

ClimaCore.jl is the spatial discretization library of the CliMA Earth system model. It provides the grids, fields, and differential operators on which ClimaAtmos.jl and ClimaLand.jl build their governing equations, and it runs on CPUs and on NVIDIA GPUs.

What ClimaCore provides

• Spectral elements in the horizontal, staggered finite differences in the vertical. Horizontal grids are continuous (CG) or discontinuous (DG) Galerkin spectral elements on Gauss–Lobatto–Legendre nodes. The vertical grid is a staggered finite-difference grid with the vertical velocity on cell faces and all other variables on cell centers. An unstaggered vertical grid always carries computational modes; the staggering suppresses them, which matters most at the large aspect ratios of atmospheric grids, where the horizontal spacing exceeds the vertical spacing by orders of magnitude [1]. See Spectral elements: CG and DG.
• One tendency for CG and DG. The discretization is a property of the space. Element-local tendencies are completed by direct stiffness summation on CG spaces and by interface numerical fluxes on DG spaces, so model code can use CG and DG interchangeably (tutorial).
• Portable performance. Broadcast expressions over fields compile to CPU loops or CUDA kernels. The CliMA atmosphere built on ClimaCore runs at more than one simulated year per day at 25–50 km horizontal resolution on a few dozen GPUs, with weak-scaling efficiency above 92% on GPUs and above 98% on CPUs, on supercomputers and on cloud GPU instances [2]. (Performance and portability).
• Differentiable in forward mode. ForwardDiff dual numbers propagate through fields, broadcasts, and operators, and grid metric terms are computed by automatic differentiation of the mesh coordinates.
• Geometries from a single column to the cubed sphere. Columns, x–z slices, Cartesian boxes and planes, and the equiangular cubed sphere, with terrain-following vertical coordinates. The operators serve both large-eddy-simulation boxes and global climate simulations [2, 3].
• Time stepping by ClimaTimeSteppers.jl. Fields and FieldVectors are the state vectors of its explicit and implicit-explicit Runge–Kutta methods.

Where to start

Quick example

A one-dimensional column, a field on it, and a vertical derivative.

import ClimaComms
ClimaComms.@import_required_backends
import ClimaCore: Domains, Meshes, Spaces, Fields, Geometry, Operators

FT = Float64

# Build a 1D column: interval domain -> mesh -> finite-difference space
domain = Domains.IntervalDomain(
    Geometry.ZPoint{FT}(0),
    Geometry.ZPoint{FT}(2π),
    boundary_names = (:bottom, :top),
)
mesh = Meshes.IntervalMesh(domain; nelems = 128)
space = Spaces.CenterFiniteDifferenceSpace(ClimaComms.device(), mesh)

# Define a field over the space and differentiate it with a composed operator
z = Fields.coordinate_field(space).z
θ = sin.(z)
grad = Operators.GradientC2F(
    bottom = Operators.SetValue(FT(0)),
    top = Operators.SetValue(FT(0)),
)
∂θ = @. Geometry.WVector(grad(θ))   # face-valued vertical gradient (≈ cos(z))

ClimaCore.Geometry.WVector{Float64}-valued Field:
  components: 
    data: 
      1: [0.9999, 0.998695, 0.995085, 0.989077, 0.980687, 0.969934, 0.956844, 0.94145, 0.923787, 0.903899  …  0.903899, 0.923787, 0.94145, 0.956844, 0.969934, 0.980687, 0.989077, 0.995085, 0.998695, 0.9999]

Related packages

• ClimaComms.jl selects the compute device (CPU or GPU) and the communication context (single process or MPI) from environment variables.
• ClimaTimeSteppers.jl advances ClimaCore fields in time.
• ClimaAtmos.jl documents the atmosphere model built on these operators, including its governing equations and their semi-discrete form.
• The shared CliMA developer guides, vendored at docs/dev-guides/, hold the engineering standards contributors follow.