diff --git a/Manifest.toml b/Manifest.toml index ff43819..5752fb0 100644 --- a/Manifest.toml +++ b/Manifest.toml @@ -2,7 +2,7 @@ julia_version = "1.9.2" manifest_format = "2.0" -project_hash = "919dab67366ad3399e882328af9dc0cc9ff8b04f" +project_hash = "c88ef8733706dadcee8b23c8aa1dbaecea03d700" [[deps.AbstractFFTs]] deps = ["LinearAlgebra"] @@ -127,6 +127,12 @@ git-tree-sha1 = "0eee5eb66b1cf62cd6ad1b460238e60e4b09400c" uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2" version = "0.2.4" +[[deps.CommonSubexpressions]] +deps = ["MacroTools", "Test"] +git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7" +uuid = "bbf7d656-a473-5ed7-a52c-81e309532950" +version = "0.3.0" + [[deps.Compat]] deps = ["UUIDs"] git-tree-sha1 = "e460f044ca8b99be31d35fe54fc33a5c33dd8ed7" @@ -187,6 +193,28 @@ version = "1.0.0" deps = ["Printf"] uuid = "ade2ca70-3891-5945-98fb-dc099432e06a" +[[deps.DiffResults]] +deps = ["StaticArraysCore"] +git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621" +uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5" +version = "1.1.0" + +[[deps.DiffRules]] +deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"] +git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272" +uuid = "b552c78f-8df3-52c6-915a-8e097449b14b" +version = "1.15.1" + +[[deps.Distances]] +deps = ["LinearAlgebra", "Statistics", "StatsAPI"] +git-tree-sha1 = "b6def76ffad15143924a2199f72a5cd883a2e8a9" +uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7" +version = "0.10.9" +weakdeps = ["SparseArrays"] + + [deps.Distances.extensions] + DistancesSparseArraysExt = "SparseArrays" + [[deps.Distributed]] deps = ["Random", "Serialization", "Sockets"] uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b" @@ -233,6 +261,16 @@ version = "1.16.1" [[deps.FileWatching]] uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" +[[deps.ForwardDiff]] +deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"] +git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad" +uuid = "f6369f11-7733-5829-9624-2563aa707210" +version = "0.10.36" +weakdeps = ["StaticArrays"] + + [deps.ForwardDiff.extensions] + ForwardDiffStaticArraysExt = "StaticArrays" + [[deps.Future]] deps = ["Random"] uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820" @@ -311,9 +349,9 @@ version = "0.4.33" [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] -git-tree-sha1 = "a7e91ef94114d5bc8952bcaa8d6ff952cf709808" +git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca" uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210" -version = "1.4.2" +version = "1.5.0" [[deps.JSON3]] deps = ["Dates", "Mmap", "Parsers", "PrecompileTools", "StructTypes", "UUIDs"] @@ -389,9 +427,9 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[deps.LogExpFunctions]] deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"] -git-tree-sha1 = "c3ce8e7420b3a6e071e0fe4745f5d4300e37b13f" +git-tree-sha1 = "7d6dd4e9212aebaeed356de34ccf262a3cd415aa" uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688" -version = "0.3.24" +version = "0.3.26" [deps.LogExpFunctions.extensions] LogExpFunctionsChainRulesCoreExt = "ChainRulesCore" @@ -446,9 +484,9 @@ version = "5.3.1+0" [[deps.MacroTools]] deps = ["Markdown", "Random"] -git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2" +git-tree-sha1 = "9ee1618cbf5240e6d4e0371d6f24065083f60c48" uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" -version = "0.5.10" +version = "0.5.11" [[deps.Markdown]] deps = ["Base64"] @@ -478,6 +516,12 @@ git-tree-sha1 = "4263c4220f22e20729329838bf7e94a49d1ac32f" uuid = "85f8d34a-cbdd-5861-8df4-14fed0d494ab" version = "0.12.17" +[[deps.NaNMath]] +deps = ["OpenLibm_jll"] +git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4" +uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3" +version = "1.0.2" + [[deps.NetCDF_jll]] deps = ["Artifacts", "Bzip2_jll", "HDF5_jll", "JLLWrappers", "LibCURL_jll", "Libdl", "XML2_jll", "Zlib_jll", "Zstd_jll"] git-tree-sha1 = "10c612c81eaffdd6b7c28a45a554cdd9d2f40ff1" @@ -489,10 +533,10 @@ uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" version = "1.2.0" [[deps.Oceananigans]] -deps = ["Adapt", "CUDA", "Crayons", "CubedSphere", "Dates", "DocStringExtensions", "FFTW", "Glob", "IncompleteLU", "InteractiveUtils", "IterativeSolvers", "JLD2", "KernelAbstractions", "LinearAlgebra", "Logging", "MPI", "NCDatasets", "OffsetArrays", "OrderedCollections", "PencilArrays", "PencilFFTs", "Pkg", "Printf", "Random", "Rotations", "SeawaterPolynomials", "SparseArrays", "Statistics", "StructArrays"] -git-tree-sha1 = "f4bebf2d3e79f81fe516afb3fd71ec829cd8e36f" +deps = ["Adapt", "CUDA", "Crayons", "CubedSphere", "Dates", "Distances", "DocStringExtensions", "FFTW", "Glob", "IncompleteLU", "InteractiveUtils", "IterativeSolvers", "JLD2", "KernelAbstractions", "LinearAlgebra", "Logging", "MPI", "NCDatasets", "OffsetArrays", "OrderedCollections", "PencilArrays", "PencilFFTs", "Pkg", "Printf", "Random", "Rotations", "SeawaterPolynomials", "SparseArrays", "Statistics", "StructArrays"] +git-tree-sha1 = "996eb159d0a1380d09beb7190ed0807d51ba0924" uuid = "9e8cae18-63c1-5223-a75c-80ca9d6e9a09" -version = "0.86.0" +version = "0.87.1" [[deps.OffsetArrays]] deps = ["Adapt"] @@ -572,9 +616,9 @@ version = "0.3.2" [[deps.PrecompileTools]] deps = ["Preferences"] -git-tree-sha1 = "9673d39decc5feece56ef3940e5dafba15ba0f81" +git-tree-sha1 = "03b4c25b43cb84cee5c90aa9b5ea0a78fd848d2f" uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a" -version = "1.1.2" +version = "1.2.0" [[deps.Preferences]] deps = ["TOML"] @@ -588,9 +632,9 @@ uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7" [[deps.ProgressBars]] deps = ["Printf"] -git-tree-sha1 = "9d84c8646109eb8bc7a006d59b157c64d5155c81" +git-tree-sha1 = "b437cdb0385ed38312d91d9c00c20f3798b30256" uuid = "49802e3a-d2f1-5c88-81d8-b72133a6f568" -version = "1.5.0" +version = "1.5.1" [[deps.Quaternions]] deps = ["LinearAlgebra", "Random", "RealDot"] @@ -641,6 +685,12 @@ git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7" uuid = "ae029012-a4dd-5104-9daa-d747884805df" version = "1.3.0" +[[deps.RootSolvers]] +deps = ["DocStringExtensions", "ForwardDiff"] +git-tree-sha1 = "9fb3462240d2898be5d4acf8925e47f70ec64d07" +uuid = "7181ea78-2dcb-4de3-ab41-2b8ab5a31e74" +version = "0.3.5" + [[deps.Roots]] deps = ["ChainRulesCore", "CommonSolve", "Printf", "Setfield"] git-tree-sha1 = "ff42754a57bb0d6dcfe302fd0d4272853190421f" @@ -752,6 +802,12 @@ deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" version = "1.9.0" +[[deps.StatsAPI]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "45a7769a04a3cf80da1c1c7c60caf932e6f4c9f7" +uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" +version = "1.6.0" + [[deps.Strided]] deps = ["LinearAlgebra", "StridedViews", "TupleTools"] git-tree-sha1 = "137303f5e0a39f966b462c53ae2c5c6e34c4828b" diff --git a/Project.toml b/Project.toml index 633b53c..c6f556f 100644 --- a/Project.toml +++ b/Project.toml @@ -6,10 +6,10 @@ version = "0.1.0" [deps] KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c" Oceananigans = "9e8cae18-63c1-5223-a75c-80ca9d6e9a09" +RootSolvers = "7181ea78-2dcb-4de3-ab41-2b8ab5a31e74" Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665" [compat] -Oceananigans = "0.86" KernelAbstractions = "0.9" Roots = "2" diff --git a/docs/Manifest.toml b/docs/Manifest.toml index 03cb182..56447ea 100644 --- a/docs/Manifest.toml +++ b/docs/Manifest.toml @@ -2,16 +2,97 @@ julia_version = "1.9.2" manifest_format = "2.0" -project_hash = "c8b9437d4b095fc9a3fcf7a39d8c1fad8f05210e" +project_hash = "c17176d00ba2b8c3e38a54d717165bc946d88851" [[deps.ANSIColoredPrinters]] git-tree-sha1 = "574baf8110975760d391c710b6341da1afa48d8c" uuid = "a4c015fc-c6ff-483c-b24f-f7ea428134e9" version = "0.0.1" +[[deps.AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.5.0" +weakdeps = ["ChainRulesCore", "Test"] + + [deps.AbstractFFTs.extensions] + AbstractFFTsChainRulesCoreExt = "ChainRulesCore" + AbstractFFTsTestExt = "Test" + +[[deps.AbstractLattices]] +git-tree-sha1 = "f35684b7349da49fcc8a9e520e30e45dbb077166" +uuid = "398f06c4-4d28-53ec-89ca-5b2656b7603d" +version = "0.2.1" + +[[deps.AbstractTrees]] +git-tree-sha1 = "faa260e4cb5aba097a73fab382dd4b5819d8ec8c" +uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" +version = "0.4.4" + +[[deps.Adapt]] +deps = ["LinearAlgebra", "Requires"] +git-tree-sha1 = "76289dc51920fdc6e0013c872ba9551d54961c24" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "3.6.2" +weakdeps = ["StaticArrays"] + + [deps.Adapt.extensions] + AdaptStaticArraysExt = "StaticArrays" + +[[deps.Animations]] +deps = ["Colors"] +git-tree-sha1 = "e81c509d2c8e49592413bfb0bb3b08150056c79d" +uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340" +version = "0.4.1" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.1" + +[[deps.ArrayInterface]] +deps = ["Adapt", "LinearAlgebra", "Requires", "SparseArrays", "SuiteSparse"] +git-tree-sha1 = "f83ec24f76d4c8f525099b2ac475fc098138ec31" +uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9" +version = "7.4.11" + + [deps.ArrayInterface.extensions] + ArrayInterfaceBandedMatricesExt = "BandedMatrices" + ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices" + ArrayInterfaceCUDAExt = "CUDA" + ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore" + ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore" + ArrayInterfaceTrackerExt = "Tracker" + + [deps.ArrayInterface.weakdeps] + BandedMatrices = "aae01518-5342-5314-be14-df237901396f" + BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0" + CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" + GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527" + StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" + Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c" + [[deps.Artifacts]] uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +[[deps.Automa]] +deps = ["TranscodingStreams"] +git-tree-sha1 = "ef9997b3d5547c48b41c7bd8899e812a917b409d" +uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b" +version = "0.8.4" + +[[deps.AxisAlgorithms]] +deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"] +git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7" +uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950" +version = "1.0.1" + +[[deps.AxisArrays]] +deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"] +git-tree-sha1 = "16351be62963a67ac4083f748fdb3cca58bfd52f" +uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9" +version = "0.4.7" + [[deps.Base64]] uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" @@ -20,28 +101,212 @@ git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d" uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35" version = "0.1.7" +[[deps.Bzip2_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2" +uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0" +version = "1.0.8+0" + +[[deps.CEnum]] +git-tree-sha1 = "eb4cb44a499229b3b8426dcfb5dd85333951ff90" +uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82" +version = "0.4.2" + +[[deps.CRC32c]] +uuid = "8bf52ea8-c179-5cab-976a-9e18b702a9bc" + +[[deps.CRlibm]] +deps = ["CRlibm_jll"] +git-tree-sha1 = "32abd86e3c2025db5172aa182b982debed519834" +uuid = "96374032-68de-5a5b-8d9e-752f78720389" +version = "1.0.1" + +[[deps.CRlibm_jll]] +deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] +git-tree-sha1 = "e329286945d0cfc04456972ea732551869af1cfc" +uuid = "4e9b3aee-d8a1-5a3d-ad8b-7d824db253f0" +version = "1.0.1+0" + +[[deps.Cairo]] +deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"] +git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b" +uuid = "159f3aea-2a34-519c-b102-8c37f9878175" +version = "1.0.5" + +[[deps.CairoMakie]] +deps = ["Base64", "Cairo", "Colors", "FFTW", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "Makie", "PrecompileTools", "SHA"] +git-tree-sha1 = "30562a68ded3dabe80109caf6b4de73a48ac27bc" +uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" +version = "0.10.8" + +[[deps.Cairo_jll]] +deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] +git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" +uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" +version = "1.16.1+1" + +[[deps.Calculus]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad" +uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9" +version = "0.5.1" + +[[deps.ChainRulesCore]] +deps = ["Compat", "LinearAlgebra", "SparseArrays"] +git-tree-sha1 = "e30f2f4e20f7f186dc36529910beaedc60cfa644" +uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" +version = "1.16.0" + [[deps.CodecZlib]] deps = ["TranscodingStreams", "Zlib_jll"] git-tree-sha1 = "02aa26a4cf76381be7f66e020a3eddeb27b0a092" uuid = "944b1d66-785c-5afd-91f1-9de20f533193" version = "0.7.2" +[[deps.ColorBrewer]] +deps = ["Colors", "JSON", "Test"] +git-tree-sha1 = "61c5334f33d91e570e1d0c3eb5465835242582c4" +uuid = "a2cac450-b92f-5266-8821-25eda20663c8" +version = "0.4.0" + +[[deps.ColorSchemes]] +deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"] +git-tree-sha1 = "d9a8f86737b665e15a9641ecbac64deef9ce6724" +uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4" +version = "3.23.0" + +[[deps.ColorTypes]] +deps = ["FixedPointNumbers", "Random"] +git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4" +uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f" +version = "0.11.4" + +[[deps.ColorVectorSpace]] +deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"] +git-tree-sha1 = "600cc5508d66b78aae350f7accdb58763ac18589" +uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4" +version = "0.9.10" + +[[deps.Colors]] +deps = ["ColorTypes", 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DataDeps = "124859b0-ceae-595e-8997-d05f6a7a8dfe" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" Glob = "c27321d9-0574-5035-807b-f59d2c89b15c" diff --git a/docs/make.jl b/docs/make.jl index 86d64a9..a75c5ff 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -14,15 +14,21 @@ ENV["DATADEPS_ALWAYS_ACCEPT"] = "true" ##### const EXAMPLES_DIR = joinpath(@__DIR__, "..", "examples") -const OUTPUT_DIR = joinpath(@__DIR__, "src/literated") +const OUTPUT_DIR = joinpath(@__DIR__, "src/generated") -to_be_literated = [] +example_scripts = [ + "freezing_bucket.jl", +] -for file in to_be_literated - filepath = joinpath(EXAMPLES_DIR, file) +for filename in example_scripts + filepath = joinpath(EXAMPLES_DIR, filename) Literate.markdown(filepath, OUTPUT_DIR; flavor = Literate.DocumenterFlavor()) end +example_pages = [ + "Freezing bucket" => "generated/freezing_bucket.md", +] + ##### ##### Build and deploy docs ##### @@ -35,6 +41,7 @@ format = Documenter.HTML( pages = [ "Home" => "index.md", + "Examples" => example_pages, "Library" => [ "Contents" => "library/outline.md", diff --git a/examples/diffusive_ice_column_model.jl b/examples/diffusive_ice_column_model.jl index bc6ff05..18e399b 100644 --- a/examples/diffusive_ice_column_model.jl +++ b/examples/diffusive_ice_column_model.jl @@ -1,4 +1,4 @@ -using ClimaSeaIce.EulerianThermodynamicSeaIceModels: EulerianThermodynamicSeaIceModel, MolecularDiffusivity +using ClimaSeaIce.EnthalpyMethodSeaIceModels: EnthalpyMethodSeaIceModel, MolecularDiffusivity using Oceananigans using Oceananigans.Units using Oceananigans.Operators: Δzᶜᶜᶠ @@ -6,7 +6,7 @@ using Oceananigans.Grids: znode using GLMakie ##### -##### Set up a EulerianThermodynamicSeaIceModel +##### Set up a EnthalpyMethodSeaIceModel ##### # Build a grid with 10 cm resolution @@ -49,7 +49,7 @@ top_T_bc = ValueBoundaryCondition(air_ice_temperature) bottom_T_bc = ValueBoundaryCondition(ice_ocean_temperature) T_bcs = FieldBoundaryConditions(top=top_T_bc, bottom=bottom_T_bc) -model = EulerianThermodynamicSeaIceModel(; grid, closure, boundary_conditions=(; T=T_bcs)) +model = EnthalpyMethodSeaIceModel(; grid, closure, boundary_conditions=(; T=T_bcs)) # Initialize and run set!(model, T=initial_ice_ocean_temperature) diff --git a/examples/freezing_bucket.jl b/examples/freezing_bucket.jl new file mode 100644 index 0000000..24e7bd0 --- /dev/null +++ b/examples/freezing_bucket.jl @@ -0,0 +1,69 @@ +using Oceananigans +using Oceananigans.Units +using ClimaSeaIce + +# # Setting up a model of a bucket of water freezing from the top down +# +# We'll model a slab of ice in a bucket with one grid point, which +# requires only a zero-dimensional grid. + +grid = RectilinearGrid(size=(), topology=(Flat, Flat, Flat)) + +## Set the temperature at the top of the bucket to ``Tᵤ = -10ᵒC``. +model = SlabSeaIceModel(grid; top_thermal_boundary_condition=PrescribedTemperature(-10)) + +## We'll freeze the bucket for 10 straight days +simulation = Simulation(model, Δt=10minute, stop_time=10days) + +## Initialize the ice thickness to 1 cm +set!(model, h=0.01) + +# # Collecting data and running the simulation +# +# Before running the simulation, we set up a `Callback` to create +# a timeseries of the ice thickness saved at every time step. + +## Container to hold the data +timeseries = [] + +## Callback function to collect the data from the `sim`ulation +function accumulate_timeseries(sim) + h = sim.model.ice_thickness + push!(timeseries, (time(sim), first(h))) +end + +## Add the callback to `simulation` +simulation.callbacks[:save] = Callback(accumulate_timeseries) + +# Now we're ready to hit the Big Red Button (it should run pretty quick): +run!(simulation) + +# # Visualizing the result +# +# It'd be a shame to run such a "cool" simulation without looking at the +# results. We'll visualize it with Makie. + +using CairoMakie + +# `timeseries` is a `Vector` of `Tuple`. So we have to do a bit of processing +# to build `Vector`s of time `t` and thickness `h`. It's not much work though: +t = map(ts -> ts[1], timeseries) +h = map(ts -> ts[2], timeseries) + +# Just for fun, we also compute the velocity of the ice-water interface: +dhdt = @. (h[2:end] - h[1:end-1]) / simulation.Δt + +# All that's left, really, is to put those `lines!` in an `Axis`: +set_theme!(Theme(fontsize=24, linewidth=4)) + +fig = Figure(resolution=(1200, 600)) + +axh = Axis(fig[1, 1], xlabel="Time (days)", ylabel="Ice thickness (cm)") +axd = Axis(fig[1, 2], xlabel="Ice thickness (cm)", ylabel="Freezing rate (μm s⁻¹)") + +lines!(axh, t ./ day, 1e2 .* h) +lines!(axd, 1e2 .* h[1:end-1], 1e6 .* dhdt) + +current_figure() # hide +fig + diff --git a/examples/ice_ocean_column_model.jl b/examples/ice_ocean_column_model.jl deleted file mode 100644 index 303ba09..0000000 --- a/examples/ice_ocean_column_model.jl +++ /dev/null @@ -1,112 +0,0 @@ -using ClimaSeaIce.EulerianThermodynamicSeaIceModels: EulerianThermodynamicSeaIceModel, MolecularDiffusivity, temperature_flux -using Oceananigans -using Oceananigans.Units -using Oceananigans.Operators: Δzᶜᶜᶠ -using Oceananigans.TurbulenceClosures: CATKEVerticalDiffusivity -using Oceananigans.Grids: znode -using GLMakie - -##### -##### Set up an Ocean column model -##### - -ocean_grid = RectilinearGrid(size=20, z=(-100, 0), topology=(Flat, Flat, Bounded)) -equation_of_state = LinearEquationOfState(thermal_expansion=2e-4, haline_contraction=8e-5) - -# Set up boundary conditions ready for coupling (on the CPU) -top_T_flux = zeros(1, 1) -top_S_flux = zeros(1, 1) -T_bcs = FieldBoundaryConditions(top=FluxBoundaryCondition(top_T_flux)) -S_bcs = FieldBoundaryConditions(top=FluxBoundaryCondition(top_S_flux)) - -ocean_model = HydrostaticFreeSurfaceModel(grid = ocean_grid, - closure = CATKEVerticalDiffusivity(), - tracers = (:T, :S, :e), - buoyancy = SeawaterBuoyancy(; equation_of_state), - boundary_conditions = (; T=T_bcs, S=S_bcs)) - - -# Ocean initial condition -α = equation_of_state.thermal_expansion -g = ocean_model.buoyancy.model.gravitational_acceleration -N² = 1e-6 -dTdz = - α * g * N² -T₀ = 0.1 # Temperature at surface -Tᵢ(x, y, z) = T₀ + dTdz * z -Sᵢ(x, y, z) = 35 -set!(ocean_model, T=Tᵢ, S=Sᵢ) - -##### -##### Set up a EulerianThermodynamicSeaIceModel -##### - -# Build a grid with 10 cm resolution -ice_grid = RectilinearGrid(size=20, z=(-1, 0), topology=(Flat, Flat, Bounded)) - -# Set up a simple problem and build the ice model -ice_closure = MolecularDiffusivity(ice_grid, κ_ice=1e-5, κ_water=1e-6) - -##### -##### Create temperature boundary conditions -##### - -# Atmopshere-ice surface temperature parameters -initial_air_ice_temperature = -5 -air_ice_temperature_fluctuation_amplitude = 5 -air_ice_tendency = -0.5 / day # ᵒC s⁻¹ - -parameters = (Tᵢ = initial_air_ice_temperature, - Tₐ = air_ice_temperature_fluctuation_amplitude, - dTdt = air_ice_tendency) - -@inline air_ice_temperature(x, y, t, p) = p.dTdt * t + p.Tₐ * sin(2π*t / day) + p.Tᵢ -top_T_bc = ValueBoundaryCondition(air_ice_temperature; parameters) -T_bcs = FieldBoundaryConditions(top=top_T_bc) - -ice_model = EulerianThermodynamicSeaIceModel(grid = ice_grid, - closure = ice_closure, - boundary_conditions=(; T=T_bcs)) - - -κ = 1e-5 -Δz = Δzᶜᶜᶠ(1, 1, 1, ice_grid) -Δt = 0.1 * Δz^2 / κ - -ice_simulation = Simulation(ice_model; Δt, stop_iteration=10) - -@inline is_ocean(i, j, k, grid, ϕ) = @inbounds ϕ[i, j, k] == 1 - -function fix_liquid_temperature!(ϕ_ice_model, T_ice_model, grid, T_ocean_model) - Nz = size(grid, 3) - - i = j = 1 - @inbounds for k = 1:Nz - T_ice_model[i, j, k] = ifelse(is_ocean(i, j, k, grid, ϕ_ice_model), - T_ocean_model[i, j], - T_ice_model[i, j, k]) - end - - return nothing -end - -function set_liquid_state!(ice_simulation) - ice_model = ice_simulation.model - - # Extract ocean temperature at top grid point - ocean_Nz = size(ocean_model.grid, 3) - ocean_temperature = interior(ocean_model.tracers.T, :, :, ocean_Nz) - - # Eventually this will launch a kernel on the GPU - ϕ = ice_model.state.ϕ - T = ice_model.state.T - fix_liquid_temperature!(ϕ, T, ice_model.grid, ocean_temperature) - - - return nothing -end - -ice_simulation.callbacks[:ocean_state] = Callback(set_liquid_state!) - -#= -ocean_simulation = Simulation(ocean_model; Δt) -=# diff --git a/examples/idealized_boundary_conditions.jl b/examples/idealized_boundary_conditions.jl deleted file mode 100644 index 37bdd31..0000000 --- a/examples/idealized_boundary_conditions.jl +++ /dev/null @@ -1,35 +0,0 @@ -using Oceananigans.Units -using GLMakie - -# This file creates idealized ice-interface temperatures -# for driving an ice column model. - -# Information about the diurnal temperature fluctuations and cooling trends at the atmosphere boundary -top_T_initial = -5 -top_T_amplitude = 5 -top_T_slope = -0.5 / day # ᵒC s⁻¹ - -# Information about ocean cooling -bottom_T_initial = 0 -bottom_T_slope = -0.5 / day # ᵒC s⁻¹ - -# Information about time steps -dt = 1000 -tf = 864000 -time = 0:dt:tf - -# Calculate BCs -top_T_BC = @. top_T_slope * time + top_T_amplitude * sin(2π*time/day) + top_T_initial -bottom_T_BC = @. bottom_T_slope * time + bottom_T_initial - -# Plot boundary conditions - -set_theme!(Theme(fontsize=24, linewidth=3)) -fig = Figure() -ax = Axis(fig[1, 1], title="Boundary Conditions", xlabel="Time (s)", ylabel="Temperature (ᵒC)") -lines!(ax, time, top_T_BC, label="Air-ice surface temperature") -lines!(ax, time, bottom_T_BC, label="Ice-ocean temperature") -axislegend(ax) - -display(fig) - diff --git a/examples/melting_in_march.jl b/examples/melting_in_march.jl new file mode 100644 index 0000000..1bc7444 --- /dev/null +++ b/examples/melting_in_march.jl @@ -0,0 +1,73 @@ +using Oceananigans +using Oceananigans.Units +using ClimaSeaIce +using GLMakie + +# Generate a 0D grid for a single column slab model +grid = RectilinearGrid(size=(), topology=(Flat, Flat, Flat)) + +# Build a model of an ice slab that has internal conductive fluxes +# and that emits radiation from its top surface. +solar_insolation = -500 # W m⁻² +outgoing_radiation = RadiativeEmission() + +# Define a FluxFunction representing a sensible heat flux +parameters = ( + transfer_coefficient = 1e-3, # Unitless + atmosphere_density = 1.225, # kg m⁻³ + atmosphere_heat_capacity = 1004, # + atmosphere_temperature = -5, # ᵒC + atmosphere_wind_speed = 5 # m s⁻¹ +) + +@inline function sensible_heat_flux(i, j, grid, Tᵤ, clock, fields, parameters) + Cₛ = parameters.transfer_coefficient + ρₐ = parameters.atmosphere_density + cₐ = parameters.atmosphere_heat_capacity + Tₐ = parameters.atmosphere_temperature + uₐ = parameters.atmosphere_wind_speed + + # Flux is positive (cooling by fluxing heat up away from upper surface) + # when Tₐ < Tᵤ: + return Cₛ * ρₐ * cₐ * uₐ * (Tᵤ - Tₐ) +end + +aerodynamic_flux = FluxFunction(sensible_heat_flux; parameters) + +top_thermal_flux = (outgoing_radiation, solar_insolation, aerodynamic_flux) +model = SlabSeaIceModel(grid; top_thermal_flux) +set!(model, h=1) + +simulation = Simulation(model, Δt=10minute, stop_time=1day) + +# Accumulate data +timeseries = [] + +function accumulate_timeseries(sim) + T = model.top_temperature + h = model.ice_thickness + push!(timeseries, (time(sim), first(h), first(T))) +end + +simulation.callbacks[:save] = Callback(accumulate_timeseries) + +run!(simulation) + +# Extract and visualize data + +t = [datum[1] for datum in timeseries] +h = [datum[2] for datum in timeseries] +T = [datum[3] for datum in timeseries] + +set_theme!(Theme(fontsize=24, linewidth=4)) + +fig = Figure(resolution=(1000, 800)) + +axT = Axis(fig[1, 1], xlabel="Time (days)", ylabel="Top temperature (ᵒC)") +axh = Axis(fig[2, 1], xlabel="Time (days)", ylabel="Ice thickness (m)") + +lines!(axT, t / day, T) +lines!(axh, t / day, h) + +display(fig) + diff --git a/examples/perpetual_night.jl b/examples/perpetual_night.jl new file mode 100644 index 0000000..ef7a850 --- /dev/null +++ b/examples/perpetual_night.jl @@ -0,0 +1,47 @@ +using Oceananigans +using Oceananigans.Units +using ClimaSeaIce +using ClimaSeaIce.ThermalBoundaryConditions: RadiativeEmission +using GLMakie + +# Generate a zero-dimensional grid for a single column slab model +grid = RectilinearGrid(size=(), topology=(Flat, Flat, Flat)) + +# Build a model of an ice slab that has internal conductive fluxes +# and that emits radiation from its top surface. +model = SlabSeaIceModel(grid; top_thermal_flux=RadiativeEmission()) +set!(model, h=0.01) + +simulation = Simulation(model, Δt=1hour, stop_time=40days) + +# Accumulate data +timeseries = [] + +function accumulate_timeseries(sim) + T = model.top_temperature + h = model.ice_thickness + push!(timeseries, (time(sim), first(h), first(T))) +end + +simulation.callbacks[:save] = Callback(accumulate_timeseries) + +run!(simulation) + +# Extract and visualize data + +t = [datum[1] for datum in timeseries] +h = [datum[2] for datum in timeseries] +T = [datum[3] for datum in timeseries] + +set_theme!(Theme(fontsize=24, linewidth=4)) + +fig = Figure(resolution=(1000, 800)) + +axT = Axis(fig[1, 1], xlabel="Time (days)", ylabel="Top temperature (ᵒC)") +axh = Axis(fig[2, 1], xlabel="Time (days)", ylabel="Ice thickness (m)") + +lines!(axT, t / day, T) +lines!(axh, t / day, h) + +display(fig) + diff --git a/src/ClimaSeaIce.jl b/src/ClimaSeaIce.jl index 252fb18..3ba44d9 100644 --- a/src/ClimaSeaIce.jl +++ b/src/ClimaSeaIce.jl @@ -1,8 +1,140 @@ module ClimaSeaIce -include("EulerianThermodynamicSeaIceModels.jl") -include("PrognosticThicknessThermodynamicsModels.jl") +import Oceananigans.TimeSteppers: time_step! -using .EulerianThermodynamicSeaIceModels: EulerianThermodynamicSeaIceModel +export + MeltingConstrainedFluxBalance, + PrescribedTemperature, + RadiativeEmission, + ConductiveFlux, + FluxFunction, + SlabSeaIceModel + +##### +##### A bit of thermodynamics to start the day +##### + +struct LinearLiquidus{FT} + freshwater_melting_temperature :: FT + slope :: FT +end + +""" + LinearLiquidus(FT=Float64, + slope = 0.054, # psu / ᵒC + freshwater_melting_temperature = 0) # ᵒC + +Return a linear model for the dependence of the melting temperature of +saltwater on salinity, + +```math +Tₘ(S) = T₀ - m S , +``` + +where ``Tₘ(S)`` is the melting temperature as a function of salinity ``S``, +``T₀`` is the melting temperature of freshwater, and ``m`` is the ratio +between the melting temperature and salinity (in other words the linear model +should be thought of as defining ``m`` and could be written ``m ≡ (T₀ - Tₘ) / S``. +The signs are arranged so that ``m > 0`` for saltwater). + +The defaults assume that salinity is given in practical salinity units `psu` and +temperature is in degrees Celsius. + +Note: the function `melting_temperature(liquidus, salinity)` returns the +melting temperature given `salinity`. +""" +function LinearLiquidus(FT::DataType=Float64; + slope = 0.054, # psu / ᵒC + freshwater_melting_temperature = 0) # ᵒC + + return LinearLiquidus(convert(FT, freshwater_melting_temperature), + convert(FT, slope)) +end + +@inline function melting_temperature(liquidus::LinearLiquidus, salinity) + return liquidus.freshwater_melting_temperature - liquidus.slope * salinity +end + +struct PhaseTransitions{FT, L} + ice_density :: FT + ice_heat_capacity :: FT + liquid_density :: FT + liquid_heat_capacity :: FT + reference_latent_heat :: FT + reference_temperature :: FT + liquidus :: L +end + +""" + PhaseTransitions(FT=Float64, + ice_density = 917, # kg m⁻³ + ice_heat_capacity = 2000, # J / (kg ᵒC) + liquid_density = 999.8, # kg m⁻³ + liquid_heat_capacity = 4186, # J / (kg ᵒC) + reference_latent_heat = 334e3 # J kg⁻³ + liquidus = LinearLiquidus(FT)) # default assumes psu, ᵒC + +Return a representation of transitions between the solid and liquid phases +of salty water: in other words, the freezing and melting of sea ice. + +The latent heat of fusion ``ℒ(T)`` (more simply just "latent heat") is +a function of temperature ``T`` via + +```math +ρᵢ ℒ(T) = ρᵢ ℒ₀ + (ρℓ cℓ - ρᵢ cᵢ) * (T - T₀) +``` + +where ``ρᵢ`` is the `ice_density`, ``ρℓ`` is the liquid density, +``cᵢ`` is the heat capacity of ice, and ``cℓ`` is the heat capacity of +liquid, and ``T₀`` is a reference temperature, all of which are assumed constant. + +The default `liquidus` assumes that salinity has practical salinity units (psu) +and that temperature is degrees Celsius. +""" +@inline function PhaseTransitions(FT=Float64, + ice_density = 917, # kg m⁻³ + ice_heat_capacity = 2000, # J / (kg ᵒC) + liquid_density = 999.8, # kg m⁻³ + liquid_heat_capacity = 4186, # J / (kg ᵒC) + reference_latent_heat = 334e3, # J kg⁻³ + reference_temperature = 0, # ᵒC + liquidus = LinearLiquidus(FT)) + + return PhaseTransitions(convert(FT, ice_density), + convert(FT, ice_heat_capacity), + convert(FT, liquid_density), + convert(FT, liquid_heat_capacity), + convert(FT, reference_latent_heat), + convert(FT, reference_temperature), + liquidus) +end + +@inline function latent_heat(thermo::PhaseTransitions, T) + T₀ = thermo.reference_temperature + ℒ₀ = thermo.reference_latent_heat + ρᵢ = thermo.ice_density + ρℓ = thermo.liquid_density + cᵢ = thermo.ice_heat_capacity + cℓ = thermo.liquid_heat_capacity + + return ρᵢ * ℒ₀ + (ρℓ * cℓ - ρᵢ * cᵢ) * (T - T₀) +end + +struct ForwardEulerTimestepper end + +include("ThermalBoundaryConditions/ThermalBoundaryConditions.jl") + +using .ThermalBoundaryConditions: + IceWaterThermalEquilibrium, + MeltingConstrainedFluxBalance, + RadiativeEmission, + FluxFunction, + PrescribedTemperature + +include("EnthalpyMethodSeaIceModels.jl") +include("SlabSeaIceModels.jl") + +using .EnthalpyMethodSeaIceModels: EnthalpyMethodSeaIceModel +using .SlabSeaIceModels: SlabSeaIceModel, ConductiveFlux end # module diff --git a/src/EulerianThermodynamicSeaIceModels.jl b/src/EnthalpyMethodSeaIceModels.jl similarity index 79% rename from src/EulerianThermodynamicSeaIceModels.jl rename to src/EnthalpyMethodSeaIceModels.jl index 6bebf50..78f6a61 100644 --- a/src/EulerianThermodynamicSeaIceModels.jl +++ b/src/EnthalpyMethodSeaIceModels.jl @@ -1,4 +1,4 @@ -module EulerianThermodynamicSeaIceModels +module EnthalpyMethodSeaIceModels using Oceananigans.BoundaryConditions: fill_halo_regions!, @@ -21,14 +21,14 @@ import Oceananigans.Fields: set! import Oceananigans.TimeSteppers: time_step!, update_state! import Oceananigans.Simulations: reset! -mutable struct EulerianThermodynamicSeaIceModel{Grid, - Tim, - Clk, - Clo, - State, - Cp, - Fu, - Tend} <: AbstractModel{Nothing} +mutable struct EnthalpyMethodSeaIceModel{Grid, + Tim, + Clk, + Clo, + State, + Cp, + Fu, + Tend} <: AbstractModel{Nothing} grid :: Grid timestepper :: Tim # unused placeholder for now clock :: Clk @@ -40,27 +40,27 @@ mutable struct EulerianThermodynamicSeaIceModel{Grid, tendencies :: Tend end -const ETSIM = EulerianThermodynamicSeaIceModel +const ETSIM = EnthalpyMethodSeaIceModel function Base.show(io::IO, model::ETSIM) clock = model.clock - print(io, "EulerianThermodynamicSeaIceModel(t=", prettytime(clock.time), ", iteration=", clock.iteration, ")", '\n') + print(io, "EnthalpyMethodSeaIceModel(t=", prettytime(clock.time), ", iteration=", clock.iteration, ")", '\n') print(io, " grid: ", summary(model.grid)) end const reference_density = 999.8 # kg m⁻³ """ - EulerianThermodynamicSeaIceModel(; grid, kw...) + EnthalpyMethodSeaIceModel(; grid, kw...) Return a thermodynamic model for ice sandwiched between an atmosphere and ocean on an Eulerian grid. """ -function EulerianThermodynamicSeaIceModel(; grid, - closure = default_closure(grid), - ice_heat_capacity = 2090.0 / reference_density, - water_heat_capacity = 3991.0 / reference_density, - fusion_enthalpy = 3.3e5 / reference_density, - boundary_conditions = NamedTuple()) +function EnthalpyMethodSeaIceModel(; grid, + closure = default_closure(grid), + ice_heat_capacity = 2090.0 / reference_density, + water_heat_capacity = 3991.0 / reference_density, + fusion_enthalpy = 3.3e5 / reference_density, + boundary_conditions = NamedTuple()) # Prognostic fields: temperature, enthalpy, porosity field_names = (:T, :H, :ϕ) @@ -74,7 +74,7 @@ function EulerianThermodynamicSeaIceModel(; grid, tendencies = (; H=CenterField(grid)) clock = Clock{eltype(grid)}(0, 0, 1) - return EulerianThermodynamicSeaIceModel(grid, + return EnthalpyMethodSeaIceModel(grid, nothing, clock, closure, @@ -99,7 +99,7 @@ function set!(model::ETSIM; T=nothing, H=nothing) if setting_enthalpy set!(model.state.H, H) - update_temperature!(model) + compute_temperature!(model) end return nothing @@ -116,7 +116,7 @@ prognostic_fields(model::ETSIM) = (; model.state.H) ##### Time-stepping ##### -function update_porosity!(model) +function compute_porosity!(model) T = model.state.T ϕ = model.state.ϕ grid = model.grid @@ -137,7 +137,7 @@ end end end -function update_temperature!(model) +function compute_temperature!(model) H = model.state.H T = model.state.T c = model.ice_heat_capacity @@ -171,13 +171,13 @@ function update_state!(model::ETSIM) grid = model.grid arch = grid.architecture args = (model.clock, fields(model)) - update_temperature!(model) - update_porosity!(model) - update_diffusivity!(model.closure, model) + compute_temperature!(model) + compute_porosity!(model) + compute_diffusivity!(model.closure, model) return nothing end -function time_step!(model, Δt; callbacks=nothing) +function time_step!(model::ETSIM, Δt; callbacks=nothing) grid = model.grid arch = grid.architecture Ψ = model.state @@ -219,13 +219,12 @@ struct MolecularDiffusivity{C} κ :: C end - function MolecularDiffusivity(grid; κ_ice=1e-5, κ_water=1e-6) κ = CenterField(grid) return MolecularDiffusivity(κ_ice, κ_water, κ) end -function update_diffusivity!(closure::MolecularDiffusivity, model) +function compute_diffusivity!(closure::MolecularDiffusivity, model) κ = closure.κ κ_ice = closure.κ_ice κ_water = closure.κ_water diff --git a/src/PrognosticThicknessThermodynamicsModels.jl b/src/PrognosticThicknessThermodynamicsModels.jl deleted file mode 100644 index 467aba2..0000000 --- a/src/PrognosticThicknessThermodynamicsModels.jl +++ /dev/null @@ -1,15 +0,0 @@ -module PrognosticThicknessThermodynamicsModels - -abstract type AbstractPrognosticThicknessThermodynamicsModel end - -mutable struct ZeroLayerThermodynamicSeaIceModel{G, H, A, L, KS, KI} <: AbstractPrognosticThicknessThermodynamicsModel - horizontal_grid :: G - thicknesses :: H - previous_thicknesses :: H - albedo :: A - latent_heat_of_fusion :: L - snow_diffusivity :: KS - ice_diffusivity :: KI -end - -end # module diff --git a/src/SlabSeaIceModels.jl b/src/SlabSeaIceModels.jl new file mode 100644 index 0000000..bea3ee0 --- /dev/null +++ b/src/SlabSeaIceModels.jl @@ -0,0 +1,256 @@ +module SlabSeaIceModels + +using ClimaSeaIce: + PhaseTransitions, + latent_heat, + ForwardEulerTimestepper, + melting_temperature + +using ClimaSeaIce.ThermalBoundaryConditions: + MeltingConstrainedFluxBalance, + IceWaterThermalEquilibrium, + PrescribedTemperature, + FluxFunction, + SurfaceTemperatureDependent, + bottom_temperature, + top_temperature, + top_flux_imbalance, + bottom_flux_imbalance + +# using RootSolvers: find_zero + +using Oceananigans.Fields: Field, Center, ZeroField, ConstantField +using Oceananigans.TimeSteppers: Clock, tick! + +# Simulations interface +import Oceananigans: fields, prognostic_fields +import Oceananigans.Fields: field, set! +import Oceananigans.TimeSteppers: time_step!, update_state! +import Oceananigans.Simulations: reset!, initialize! +import Oceananigans.OutputWriters: default_included_properties + +# TODO: move to Oceananigans +field(loc, a::Number, grid) = ConstantField(a) + +struct SlabSeaIceModel{GR, CL, TS, IT, ST, IS, STF, TBC, CF, P} + grid :: GR + clock :: CL + timestepper :: TS + # State + ice_thickness :: IT + top_temperature :: ST + ice_salinity :: IS + # Boundary conditions + external_thermal_fluxes :: STF + thermal_boundary_conditions :: TBC + # Internal flux + internal_thermal_flux :: CF + # Melting and freezing stuff + phase_transitions :: P +end + +const SSIM = SlabSeaIceModel + +initialize!(::SSIM) = nothing +default_included_properties(::SSIM) = tuple(:grid) + +fields(model::SSIM) = (h = model.ice_thickness, + Tᵤ = model.top_temperature, + Sᵢ = model.ice_salinity) + +# TODO: make this correct +prognostic_fields(model::SSIM) = fields(model) + +struct ConductiveFlux{K} + conductivity :: K +end + +ConductiveFlux(FT::DataType=Float64; conductivity) = ConductiveFlux(convert(FT, conductivity)) + +@inline function slab_internal_thermal_flux(conductive_flux::ConductiveFlux, + top_temperature, + bottom_temperature, + ice_thickness) + + k = conductive_flux.conductivity + Tu = top_temperature + Tb = bottom_temperature + h = ice_thickness + + return - k * (Tu - Tb) / h +end + +@inline function slab_internal_thermal_flux(i, j, grid, + top_temperature::Number, + clock, fields, parameters) + flux = parameters.flux + bottom_bc = parameters.bottom_thermal_boundary_condition + liquidus = parameters.liquidus + Tu = top_temperature + Tb = bottom_temperature(i, j, grid, bottom_bc, liquidus) + h = @inbounds fields.h[i, j, 1] + return slab_internal_thermal_flux(flux, Tu, Tb, h) +end + +""" + SlabSeaIceModel(grid; kw...) + +Pretty simple model for sea ice. +""" +function SlabSeaIceModel(grid; + clock = Clock{eltype(grid)}(0, 0, 1), + ice_thickness = Field{Center, Center, Nothing}(grid), + ice_salinity = 0, # psu + top_temperature = nothing, + top_thermal_flux = 0, + bottom_thermal_flux = 0, + top_thermal_boundary_condition = MeltingConstrainedFluxBalance(), + bottom_thermal_boundary_condition = IceWaterThermalEquilibrium(), + internal_thermal_flux = ConductiveFlux(eltype(grid), conductivity=2), + phase_transitions = PhaseTransitions(eltype(grid))) + + # Only one time-stepper is supported currently + timestepper = ForwardEulerTimestepper() + FT = eltype(grid) + + # TODO: pass `clock` into `field`, so functions can be time-dependent? + + # Wrap ice_salinity in a field + ice_salinity = field((Center, Center, Nothing), ice_salinity, grid) + + # Construct default top temperature if one is not provided + if isnothing(top_temperature) + # Check top boundary condition + if top_thermal_boundary_condition isa PrescribedTemperature + top_temperature = top_thermal_boundary_condition.temperature + else # build the default + top_temperature = Field{Center, Center, Nothing}(grid) + end + end + + # Convert to `field` (does nothing if it's already a Field) + top_temperature = field((Center, Center, Nothing), top_temperature, grid) + + # Construct an internal thermal flux function that captures the liquidus and + # bottom boundary condition. + parameters = (flux = internal_thermal_flux, + liquidus = phase_transitions.liquidus, + bottom_thermal_boundary_condition = bottom_thermal_boundary_condition) + + internal_thermal_flux_function = FluxFunction(slab_internal_thermal_flux; + parameters, + top_temperature_dependent=true) + + # Package the external fluxes and boundary conditions + external_thermal_fluxes = (top = top_thermal_flux, + bottom = bottom_thermal_flux) + + thermal_boundary_conditions = (top = top_thermal_boundary_condition, + bottom = bottom_thermal_boundary_condition) + + return SlabSeaIceModel(grid, + clock, + timestepper, + ice_thickness, + top_temperature, + ice_salinity, + external_thermal_fluxes, + thermal_boundary_conditions, + internal_thermal_flux_function, + phase_transitions) +end + +function set!(model::SSIM; h=nothing) + !isnothing(h) && set!(model.ice_thickness, h) + return nothing +end + +function time_step!(model::SSIM, Δt; callbacks=nothing) + grid = model.grid + Nx, Ny, Nz = size(grid) + + phase_transitions = model.phase_transitions + liquidus = phase_transitions.liquidus + + h = model.ice_thickness + Tu = model.top_temperature + model_fields = fields(model) + ice_salinity = model.ice_salinity + clock = model.clock + bottom_thermal_bc = model.thermal_boundary_conditions.bottom + top_thermal_bc = model.thermal_boundary_conditions.top + + Qi = model.internal_thermal_flux + Qb = model.external_thermal_fluxes.bottom + Qs = model.external_thermal_fluxes.top + + for i = 1:Nx, j=1:Ny + + @inbounds begin + Tuⁿ = Tu[i, j, 1] + S = ice_salinity[i, j, 1] + end + + # 1. Update thickness with ForwardEuler step + # 1a. Calculate residual fluxes across the top top and bottom + δQs = top_flux_imbalance(i, j, grid, top_thermal_bc, Tuⁿ, Qi, Qs, clock, model_fields) + δQb = bottom_flux_imbalance(i, j, grid, bottom_thermal_bc, Tuⁿ, Qi, Qb, clock, model_fields) + + # 1b. Impose an implicit flux balance if Tu ≤ Tm. + Tₘ = melting_temperature(liquidus, S) + δQs = ifelse(Tuⁿ <= Tₘ, zero(grid), δQs) + + # 1c. Calculate the latent heat of fusion at the top and bottom + Tbⁿ = bottom_temperature(i, j, grid, bottom_thermal_bc, liquidus) + ℒ_Tu = latent_heat(phase_transitions, Tuⁿ) + ℒ_Tb = latent_heat(phase_transitions, Tbⁿ) + + # 1d. Increment the thickness + @inbounds begin + h⁺ = h[i, j, 1] + Δt * (δQb / ℒ_Tb + δQs / ℒ_Tu) + h⁺ = max(zero(grid), h⁺) + h[i, j, 1] = h⁺ + end + + if !isa(top_thermal_bc, PrescribedTemperature) + # 2. Update top temperature + Tu⁺ = top_temperature(i, j, grid, top_thermal_bc, Tuⁿ, Qi, Qs, clock, model_fields) + + # 3. Set top temperature (could skip this for `PrescribedTemperature`) + @inbounds Tu[i, j, 1] = Tu⁺ + end + end + + tick!(model.clock, Δt) + + return nothing +end + +function update_state!(model::SSIM) + + top_thermal_bc = model.thermal_boundary_conditions.top + + if !isa(top_thermal_bc, PrescribedTemperature) + grid = model.grid + Nx, Ny, Nz = size(grid) + + Tu = model.top_temperature + model_fields = fields(model) + clock = model.clock + top_thermal_bc = model.thermal_boundary_conditions.top + Qi = model.internal_thermal_flux + Qs = model.external_thermal_fluxes.top + + # Update top temperature + for i = 1:Nx, j=1:Ny + Tu⁻ = @inbounds Tu[i, j, 1] + Tuⁿ = top_temperature(i, j, grid, top_thermal_bc, Tu⁻, Qi, Qs, clock, model_fields) + @inbounds Tu[i, j, 1] = Tuⁿ + end + + end + + return nothing +end + +end # module diff --git a/src/ThermalBoundaryConditions/ThermalBoundaryConditions.jl b/src/ThermalBoundaryConditions/ThermalBoundaryConditions.jl new file mode 100644 index 0000000..b64e095 --- /dev/null +++ b/src/ThermalBoundaryConditions/ThermalBoundaryConditions.jl @@ -0,0 +1,17 @@ +module ThermalBoundaryConditions + +""" + PrescribedTemperature() + +Thermal boundary condition indicating that temperature is prescribed on the boundary. +""" +struct PrescribedTemperature{T} + temperature :: T +end + +include("bottom_thermal_boundary_conditions.jl") +include("top_thermal_boundary_conditions.jl") +include("boundary_fluxes.jl") + +end + diff --git a/src/ThermalBoundaryConditions/bottom_thermal_boundary_conditions.jl b/src/ThermalBoundaryConditions/bottom_thermal_boundary_conditions.jl new file mode 100644 index 0000000..20a69e7 --- /dev/null +++ b/src/ThermalBoundaryConditions/bottom_thermal_boundary_conditions.jl @@ -0,0 +1,54 @@ +using ClimaSeaIce: melting_temperature + +##### +##### Bottom thermal boundary conditions +##### + +struct IceWaterThermalEquilibrium{S} + salinity :: S +end + +""" + IceWaterThermalEquilibrium(; external_fluxes::Tuple=tuple(), salinity=0) + +Represents an ice-water interface in thermal equilibrium, such that +the bottom temperature ``T_b`` is equal to the melting temperature, + +```math +T_b = Tₘ(S) +``` + +where ``S`` is the `salinity` at the ice-water boundary. + +Both freezing and melting may occur at an ice-water boundary. +The rate of change of the ice-water interface, ``d h_b / dt``, +is related to the sum of `fluxes` into the ice-water interface, + +""" +IceWaterThermalEquilibrium(; salinity=0) = IceWaterThermalEquilibrium(salinity) + +@inline bottom_temperature(i, j, grid, bc::PrescribedTemperature, args...) = @inbounds bc.temperature[i, j] +@inline bottom_temperature(i, j, grid, bc::PrescribedTemperature{<:Number}, args...) = bc.temperature + +@inline function bottom_temperature(i, j, grid, bc::IceWaterThermalEquilibrium, liquidus) + Sₒ = @inbounds bc.salinity[i, j, 1] + return melting_temperature(liquidus, Sₒ) +end + +@inline function bottom_flux_imbalance(i, j, grid, bottom_thermal_bc, top_temperature, + internal_fluxes, external_fluxes, clock, model_fields) + + # + # ice ↑ Qi ≡ internal_fluxes. Example: Qi = - k ∂z T + # |⎴⎴⎴| + # ----------------------- ↕ hᵇ → ℒ ∂t hᵇ = δQ _given_ T = Tₘ + # |⎵⎵⎵| + # water ↑ Qx ≡ external_fluxes + # + + Qi = getflux(internal_fluxes, i, j, grid, top_temperature, clock, model_fields) + Qx = getflux(external_fluxes, i, j, grid, top_temperature, clock, model_fields) + + return Qi - Qx +end + diff --git a/src/ThermalBoundaryConditions/boundary_fluxes.jl b/src/ThermalBoundaryConditions/boundary_fluxes.jl new file mode 100644 index 0000000..cb40150 --- /dev/null +++ b/src/ThermalBoundaryConditions/boundary_fluxes.jl @@ -0,0 +1,96 @@ +##### +##### Fluxes +##### + +# Flux extractor function +# getflux(flux, i, j, grid, T_top, clock, model_fields) + +@inline getflux(flux::Number, i, j, grid, args...) = flux +@inline getflux(flux::AbstractArray{<:Any, 2}, i, j, grid, args...) = @inbounds flux[i, j] + +# Make sure to check the size on flux construction +@inline getflux(flux::AbstractArray{<:Any, 3}, i, j, grid, args...) = @inbounds flux[i, j, 1] + +# Tuples +@inline getflux(fluxes::Tuple{}, i, j, grid, args...) = zero(grid) +@inline getflux(fluxes::Tuple{<:Any}, args...) = getflux(fluxes[1], args...) +@inline getflux(fluxes::Tuple{<:Any, <:Any}, args...) = getflux(fluxes[1], args...) + getflux(fluxes[2], args...) +@inline getflux(fluxes::Tuple, args...) = getflux(fluxes[1], args...) + _getflux(fluxes[2:end], args...) + +@inline _getflux(fluxes::Tuple{}, i, j, grid, args...) = zero(grid) +@inline _getflux(fluxes::Tuple{<:Any}, grid, args...) = getflux(fluxes[1], args...) +@inline _getflux(fluxes::Tuple, args...) = getflux(fluxes[1], args...) + getflux(fluxes[2:end], args...) + +struct SurfaceTemperatureDependent end + +struct FluxFunction{P, T, F} + func :: F + parameters :: P + function FluxFunction{SurfaceTemperatureDependence}(func, parameters=nothing) where SurfaceTemperatureDependence + T = SurfaceTemperatureDependence + P = typeof(parameters) + F = typeof(func) + new{P, T, F}(func, parameters) + end +end + +""" + FluxFunction(func; parameters=nothing, top_temperature_dependent=false) + +Return `FluxFunction` representing a flux across an air-ice, air-snow, or ice-water interface. +The flux is computed by `func` with the signature + +```julia +flux = func(i, j, grid, clock, top_temperature, model_fields) +``` + +if `isnothing(parameters)`, or + +```julia +flux = func(i, j, grid, clock, top_temperature, model_fields, parameters) +``` + +if `!isnothing(parameters)`. If `func` is `top_temperature_dependent`, then it will be recomputed +during a diagnostic solve for the top temperature. +""" +function FluxFunction(func; parameters=nothing, top_temperature_dependent=false) + T = top_temperature_dependent ? SurfaceTemperatureDependent() : Nothing + return FluxFunction{T}(func, parameters) +end + +@inline getflux(flux::FluxFunction{<:Nothing}, args...) = flux.func(args...) +@inline getflux(flux::FluxFunction, args...) = flux.func(args..., flux.parameters) + +##### +##### Implementations +##### + + +struct RadiativeEmission{FT} + emissivity :: FT + stefan_boltzmann_constant :: FT + reference_temperature :: FT +end + +""" + RadiativeEmission(FT=Float64; kw...) + +Returns a flux representing radiative emission from a surface. +""" +function RadiativeEmission(FT=Float64; + emissivity = 1, + stefan_boltzmann_constant = 5.67e-8, + reference_temperature = 273.15) + + return RadiativeEmission(convert(FT, emissivity), + convert(FT, stefan_boltzmann_constant), + convert(FT, reference_temperature)) +end + +@inline function getflux(emission::RadiativeEmission, i, j, grid, T, clock, fields) + ϵ = emission.emissivity + σ = emission.stefan_boltzmann_constant + Tᵣ = emission.reference_temperature + return ϵ * σ * (T + Tᵣ)^4 +end + diff --git a/src/ThermalBoundaryConditions/top_thermal_boundary_conditions.jl b/src/ThermalBoundaryConditions/top_thermal_boundary_conditions.jl new file mode 100644 index 0000000..73f12c8 --- /dev/null +++ b/src/ThermalBoundaryConditions/top_thermal_boundary_conditions.jl @@ -0,0 +1,103 @@ +##### +##### Surface thermal boundary conditions +##### + +struct MeltingConstrainedFluxBalance{STS} + top_temperature_solver :: STS +end + +struct LinearizedSurfaceTemperatureSolver end +struct NonlinearSurfaceTemperatureSolver end + +""" + MeltingConstrainedFluxBalance(top_temperature_solver=NonlinearSurfaceTemperatureSolver()) + +Return a boundary condition that determines the top (or "upper surface") temperature ``Tᵤ`` +to equilibrate the top heat fluxes, + +```math +Qₓ₁(Tᵤ) + Qₓ₂(Tᵤ) + ⋯ - Qᵢ = Σᴺ Qₓₙ(Tᵤ) - Qᵢ = δQ , +``` + +where ``Qᵢ`` is the intrinsic flux into the top from within the ice +(typically, a conductive flux), ``Qₓₙ`` represent external fluxes into the +air above the ice, ``δQ`` is the residual flux, and ``Tᵤ`` is the (upper) +top temperature. ``Tᵤ`` is evaluated under the constraint that + +```math +Tᵤ ≤ Tₘ(S), +``` + +where ``Tₘ(S)`` is the melting temperature, which is a function of the +ice salinity at the top, ``S``. When ``Tᵤ < Tₘ(S)``, the top is +frozen and ``δQ = 0``. When the constraint operates, such that ``Tᵤ = Tₘ(S)``, +the top is melting and the residual flux is non-zero. + +```math +δQ ≡ Σᴺ Qₙ(Tₘ) - Qᵢ(Tₘ). +``` + +The residual flux is consumed by the cost of transforming ice into liquid water, +and is related to the rate of change of ice thickness, ``h``, by + +```math +d/dt hₛ = δQ / ℒ(Tᵤ) +``` + +where ``ℒ(Tᵤ)`` is the latent heat, equal to the different between +the higher internal energy of liquid water and the lower internal energy of solid ice, +at the temperature ``Tᵤ``. + +""" +MeltingConstrainedFluxBalance() = MeltingConstrainedFluxBalance(NonlinearSurfaceTemperatureSolver()) + +##### +##### Flux imbalance and temperature +##### + +@inline function top_flux_imbalance(i, j, grid, top_thermal_bc, top_temperature, + internal_fluxes, external_fluxes, clock, model_fields) + + # Schematic of the Stefan condition at an upper top + # + # air ↑ Qx ≡ external_fluxes. Example: Qx = σ T⁴ + # |⎴⎴⎴| + # ----------------------- ↕ hₛ(t) → ℒ ∂t hₛ = δQ | T ≤ Tₘ + # |⎵⎵⎵| + # ice ↑ Qi ≡ internal_fluxes. Example Qi = - k ∂z T + # + + Qi = getflux(internal_fluxes, i, j, grid, top_temperature, clock, model_fields) + Qx = getflux(external_fluxes, i, j, grid, top_temperature, clock, model_fields) + + # The imbalance is defined such that + # negative imbalance => heat accumulates (out > in) ⟹ growth + return Qx - Qi +end + +@inline top_temperature(i, j, grid, ::PrescribedTemperature, Tu, args...) = Tu + +using RootSolvers: SecantMethod, find_zero, CompactSolution + +@inline function top_temperature(i, j, grid, top_thermal_bc, + current_top_temperature, + internal_fluxes, external_fluxes, + clock, model_fields) + + Tu = @inbounds current_top_temperature[i, j, 1] + T₁ = Tu + T₂ = Tu - 1 + FT = eltype(grid) + method = SecantMethod{FT}(T₁, T₂) + solution_type = CompactSolution() + + flux_balance(T) = getflux(external_fluxes, i, j, grid, T, clock, model_fields) - + getflux(internal_fluxes, i, j, grid, T, clock, model_fields) + + solution = find_zero(flux_balance, method, solution_type) + + return solution.root +end + + + diff --git a/test/runtests.jl b/test/runtests.jl index 01d305c..59657e8 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,15 +1,15 @@ using Test -using ClimaSeaIce using Oceananigans -using ClimaSeaIce.EulerianThermodynamicSeaIceModels: EulerianThermodynamicSeaIceModel, MolecularDiffusivity +using ClimaSeaIce +using ClimaSeaIce.EnthalpyMethodSeaIceModels: EnthalpyMethodSeaIceModel, MolecularDiffusivity κ = 1e-5 grid = RectilinearGrid(size=3, z=(-3, 0), topology=(Flat, Flat, Bounded)) closure = MolecularDiffusivity(grid, κ_ice=κ, κ_water=κ) -model = EulerianThermodynamicSeaIceModel(; grid, closure) +model = EnthalpyMethodSeaIceModel(; grid, closure) -@test model isa EulerianThermodynamicSeaIceModel +@test model isa EnthalpyMethodSeaIceModel # Test that it runs simulation = Simulation(model; Δt = 0.1 / κ, stop_iteration=3)