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  • cryogrid/cryogridjulia
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# This file is machine-generated - editing it directly is not advised
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......@@ -641,10 +756,10 @@ uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"
[[ReverseDiff]]
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......@@ -660,39 +775,44 @@ version = "0.3.0+0"
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[[SharedArrays]]
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......@@ -700,9 +820,9 @@ uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
[[SimpleTraits]]
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[[SimulationLogs]]
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......@@ -715,37 +835,43 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
[[SortingAlgorithms]]
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[[Statistics]]
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......@@ -757,44 +883,44 @@ uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"
[[StatsBase]]
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[[StatsFuns]]
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[[StrideArraysCore]]
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[[SymbolicUtils]]
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git-tree-sha1 = "713685972c3991b23a430fea59e32136140f2528"
deps = ["ConstructionBase", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "Metatheory", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TermInterface", "TreeViews"]
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version = "4.0.0"
[[TOML]]
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......@@ -808,40 +934,52 @@ version = "1.0.1"
[[Tables]]
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[[TimerOutputs]]
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[[Tokenize]]
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[[TreeViews]]
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......@@ -849,10 +987,11 @@ git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
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[[URIs]]
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[[TriangularSolve]]
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uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
version = "0.1.8"
[[UUIDs]]
deps = ["Random", "SHA"]
......@@ -868,20 +1007,15 @@ uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[Unitful]]
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[[UnsafeArrays]]
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[[VectorizationBase]]
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[[VertexSafeGraphs]]
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......@@ -891,25 +1025,19 @@ version = "0.1.2"
[[WoodburyMatrices]]
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[[Zlib_jll]]
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[[Zygote]]
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[[ZygoteRules]]
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[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
......
name = "CryoGrid"
uuid = "a535b82e-5f3d-4d97-8b0b-d6483f5bebd5"
authors = ["Brian Groenke <brian.groenke@awi.de>", "Moritz Langer <moritz.langer@awi.de>"]
version = "0.2.0"
version = "0.5.1"
[deps]
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BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
......@@ -14,19 +13,19 @@ DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
DimensionalData = "0703355e-b756-11e9-17c0-8b28908087d0"
Downloads = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
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Flatten = "4c728ea3-d9ee-5c9a-9642-b6f7d7dc04fa"
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IfElse = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
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Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
Lazy = "50d2b5c4-7a5e-59d5-8109-a42b560f39c0"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
ModelParameters = "4744a3fa-6c31-4707-899e-a3298e4618ad"
OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
PreallocationTools = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
......@@ -34,9 +33,17 @@ RuntimeGeneratedFunctions = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
SimulationLogs = "e3c6736c-93d9-479d-93f3-96ff5e8836d5"
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# CryoGrid.jl
[![][docs-dev-img]][docs-dev-url]
[docs-dev-img]: https://img.shields.io/badge/docs-latest-blue.svg
[docs-dev-url]: https://cryogrid.github.io/CryoGrid.jl/dev/
Julia implementation of the CryoGrid land surface model using `DifferentialEquations.jl` and the [SciML](https://github.com/SciML)
package ecosystem.
......@@ -32,47 +37,49 @@ using Plots
# load provided forcing data from Samoylov;
# The forcing file will be automatically downloaded to the input/ folder if not already present.
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature (converted to Kelvin) as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# get preset soil and initial temperature profile for Samoylov
soilprofile, tempprofile = CryoGrid.Presets.SamoylovDefault
# basic 1-layer heat conduction model (defaults to free water freezing scheme)
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), CryoGridModels.SamoylovDefault)
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile)
# define time span (1 year)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan)
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve discretized system, saving every 6 hours;
# Trapezoid on a discretized PDE is analogous to the well known Crank-Nicolson method.
out = @time solve(prob, Trapezoid(), abstol=1e-3, reltol=1e-4, saveat=6*3600.0, progress=true) |> CryoGridOutput;
out = @time solve(prob, Trapezoid(), saveat=6*3600.0, progress=true) |> CryoGridOutput;
zs = [1.0,5,10,20,30,50,100,500,1000]u"cm"
cg = Plots.cgrad(:copper,rev=true)
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
```
![Ts_output_freew](res/Ts_H_tair_freeW_2010-2011.png)
Alternatively, we can use a van Genuchten freeze curve:
Alternatively, we can use a Dall'Amico freeze curve:
```julia
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), SamoylovDefault, freezecurve=SFCC(VanGenuchten()))
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile, freezecurve=SFCC(DallAmico()))
# Set-up parameters
p = copy(model.pproto)
p.soil.α .= 4.0
p.soil.n .= 2.0
p.soil.Tₘ .= 273.15
p = parameters(model)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
prob = CryoGridProblem(model,tspan,p)
# stiff solvers don't work well with van Genuchten due to the ill-conditioned Jacobian;
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# stiff solvers don't work well with Dall'Amico due to the ill-conditioned Jacobian;
# We can just forward Euler instead.
out = @time solve(prob, Euler(), dt=120.0, saveat=6*3600.0, progress=true) |> CryoGridOutput;
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
```
![Ts_output_vgfc](res/Ts_H_tair_vg_2010-2011.png)
Note that `SoilHeat` uses energy as the state variable by default. To use temperature as the state variable instead:
```julia
# Note that this will work with any freeze curve, here we use Westermann (2011).
# :T is the variable name for temperature, :H represents enthalpy/energy.
# This is used in the specification of the Heat process type.
model = CryoGridModels.SoilHeat(:T, TemperatureGradient(tair), SamoylovDefault, freezecurve=SFCC(Westermann()))
# While this will work with any freeze curve, here we use Westermann (2011) as an example.
model = CryoGrid.Presets.SoilHeatColumn(:T, TemperatureGradient(tair), soilprofile, freezecurve=SFCC(Westermann()))
```
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......@@ -428,12 +509,6 @@ uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
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......@@ -552,22 +648,22 @@ uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
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......@@ -579,17 +675,23 @@ version = "1.1.0"
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......@@ -597,10 +699,20 @@ git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
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......@@ -609,9 +721,9 @@ version = "1.7.1"
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......@@ -621,38 +733,39 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
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......@@ -661,10 +774,10 @@ uuid = "ae029012-a4dd-5104-9daa-d747884805df"
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......@@ -680,39 +793,44 @@ version = "0.3.0+0"
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......@@ -720,9 +838,9 @@ uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
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......@@ -744,77 +862,83 @@ deps = ["LinearAlgebra", "Random"]
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......@@ -828,40 +952,52 @@ version = "1.0.1"
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uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.67"
[[TreeViews]]
deps = ["Test"]
......@@ -869,10 +1005,11 @@ git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
version = "0.3.0"
[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"
[[TriangularSolve]]
deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
git-tree-sha1 = "ec9a310324dd2c546c07f33a599ded9c1d00a420"
uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
version = "0.1.8"
[[UUIDs]]
deps = ["Random", "SHA"]
......@@ -888,48 +1025,37 @@ uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[Unitful]]
deps = ["ConstructionBase", "Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "b3682a0559219355f1e3c8024e9f97adce2d4623"
git-tree-sha1 = "0992ed0c3ef66b0390e5752fe60054e5ff93b908"
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[[UnsafeArrays]]
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uuid = "c4a57d5a-5b31-53a6-b365-19f8c011fbd6"
version = "1.0.2"
version = "1.9.2"
[[VectorizationBase]]
deps = ["ArrayInterface", "Hwloc", "IfElse", "Libdl", "LinearAlgebra", "Static"]
git-tree-sha1 = "0ba060e248edfacacafd764926cdd6de51af1343"
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "17e5847bb36730d90801170ecd0ce4041a3dde86"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
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version = "0.21.22"
[[VertexSafeGraphs]]
deps = ["LightGraphs"]
git-tree-sha1 = "b9b450c99a3ca1cc1c6836f560d8d887bcbe356e"
deps = ["Graphs"]
git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.1.2"
version = "0.2.0"
[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"
version = "0.5.5"
[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
[[Zygote]]
deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
git-tree-sha1 = "531474afbc343c3c7cb9b71c2771813c6defd550"
uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
version = "0.6.14"
[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.1"
version = "0.2.2"
[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
......
......@@ -7,13 +7,14 @@ const modules = [
CryoGrid,
CryoGrid.Utils,
CryoGrid.Numerics,
CryoGrid.Forcings,
CryoGrid.Layers,
CryoGrid.Processes,
CryoGrid.Physics,
CryoGrid.Boundaries,
CryoGrid.HeatConduction,
CryoGrid.SEB,
CryoGrid.Setup,
CryoGrid.Models,
CryoGrid.Land,
CryoGrid.Presets,
CryoGrid.Diagnostics,
CryoGrid.Callbacks,
]
......@@ -29,19 +30,17 @@ makedocs(modules=modules,
],
"Library" => [
"Index" => "api/index.md",
"Common" => [
"Interface" => "api/interface.md",
"Numerics" => "api/numerics.md",
"Forcings" => "api/forcings.md",
"Utilities" => "api/utils.md",
],
"Processes" => [
"Method interface" => "api/toplevel.md",
"Numerics" => "api/numerics.md",
"Utilities" => "api/utils.md",
"Physics" => [
"Heat Conduction" => "api/heat_conduction.md",
"Surface Energy Balance" => "api/seb.md",
],
"Setup" => "api/setup.md",
"Land" => "api/land.md",
"Diagnostics" => "api/diagnostics.md",
"Callbacks" => "api/callbacks.md",
"Models" => "api/models.md",
"Presets" => "api/presets.md",
],
"Contributing" => "contributing.md",
])
......
# Boundary conditions and forcings
```@autodocs
Modules = [Boundaries]
Private = false
Order = [:type, :function, :macro]
```
\ No newline at end of file
# Forcings
# Diagnostics
```@autodocs
Modules = [CryoGrid.Forcings]
Modules = [Diagnostics]
Private = false
Order = [:type, :function, :macro]
```
\ No newline at end of file
```
# Land
```@autodocs
Modules = [Land]
Private = false
Order = [:type, :function, :macro]
```
File moved
# Setup
# Interface
# [Top level methods and types](@id toplevel)
```@autodocs
Modules = [CryoGrid.Interface]
Modules = [CryoGrid]
Private = false
Order = [:type, :constant, :function, :macro]
```
# Overview
## Setting up a model
At the highest level, a model in `CryoGrid.jl` is defined by a [`Grid`](@ref) and a [`Stratigraphy`](@ref), constructed top-down from individual [`StratNode`](@ref)s, each of which consists of a [`Layer`](@ref) and one or more [`Process`](@ref)es. Each node in the `Stratigraphy` is assigned a depth, which then aligns it with the `Grid`. All models must consist of at least three layers/nodes: `Top` and `Bottom` layers with corresponding boundary conditions, as well as one or more [`SubSurface`](@ref) layers. Here we define a simple three-layer model (or one-layer, exlcuding the boundaries) with a single sub-surface process, i.e. [`Heat`](@ref) (heat conduction):
At the highest level, a model in `CryoGrid.jl` is defined by a [`Grid`](@ref) and a [`Stratigraphy`](@ref), constructed top-down from individual [`StratComponent`](@ref)s, each of which consists of a [`Layer`](@ref) and one or more [`Process`](@ref)es. Each node in the `Stratigraphy` is assigned a depth, which then aligns it with the `Grid`. All models must consist of at least three layers/nodes: `Top` and `Bottom` layers with corresponding boundary conditions, as well as one or more [`SubSurface`](@ref) layers. Here we define a simple three-layer model (or one-layer, exlcuding the boundaries) with a single sub-surface process, i.e. [`Heat`](@ref) (heat conduction):
```julia
# ... load forcings, set up profiles, etc.
# see examples/heat_vgfc_seb_saoylov_custom.jl for more details
strat = Stratigraphy(
-2.0u"m" => Top(SurfaceEnergyBalance(Tair,pr,q,wind,Lin,Sin,z)),
0.0u"m" => Ground(:soil, Soil(soilprofile), Heat{:H}(tempprofile, freezecurve=SFCC(VanGenuchten()))),
1000.0u"m" => Bottom(GeothermalHeatFlux(0.053u"J/s/m^2"))
-2.0u"m" => top(SurfaceEnergyBalance(Tair,pr,q,wind,Lin,Sin,z)),
0.0u"m" => subsurface(:soil, Soil(soilprofile), Heat(:H;freezecurve=SFCC(DallAmico()))),
1000.0u"m" => bottom(GeothermalHeatFlux(0.053u"J/s/m^2"))
);
grid = CryoGrid.Models.DefaultGrid_5cm
model = CryoGridSetup(strat,grid);
grid = CryoGrid.Presets.DefaultGrid_5cm
model = LandModel(strat,grid);
```
This model can then be used to construct an `ODEProblem` (from `DiffEqBase.jl`) via the `CryoGridProblem` constructor:
```julia
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
prob = CryoGridProblem(model,tspan) # produces an ODEProblem with problem type CryoGridODEProblem
p = parameters(model)
# define initial conditions for temperature using a given profile;
# The default initializer linearly interpolates between profile points.
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
prob = CryoGridProblem(model, u0, tspan, p, savevars=(:T,)) # produces an ODEProblem with problem type CryoGridODEProblem
```
It can then be solved simply using the `solve` function (also from `DiffEqBase` and `OrdinaryDiffEq`):
......@@ -29,10 +34,10 @@ It can then be solved simply using the `solve` function (also from `DiffEqBase`
out = @time solve(prob, Euler(), dt=5*60.0, saveat=24*3600.0, progress=true) |> CryoGridOutput;
```
The result is a `CryoGridOutput` type which provides access to `DimArrays` containing the model outputs over time and space:
The result is a `CryoGridOutput` type which provides `DimArray`s containing the model outputs over time and space:
```
julia> out.soil.T
julia> out.T
278×366 DimArray{Float64,2} with dimensions:
Z: Quantity{Float64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}[0.01 m, 0.03 m, …, 850.0 m, 950.0 m] Sampled: Ordered Irregular Points,
Ti (Time): DateTime[2010-10-30T00:00:00, …, 2011-10-30T00:00:00] Sampled: Ordered Irregular Points
......@@ -40,13 +45,13 @@ julia> out.soil.T
## Defining model behavior
Notice that, in the example above, it is types such as `Soil`, `Heat`, `SFCC`, etc. that specify which components the model should use. These components are defined by adding method dispatches to the functions defined in the [`Interface`](@ref) module. State variables are declared via the [`variables`](@ref) method, e.g:
Notice that, in the example above, it is types such as `Soil`, `Heat`, `SFCC`, etc. that specify which components the model should use. These components are defined by adding method dispatches to the [core model API](@ref toplevel) methods. State variables are declared via the [`variables`](@ref) method, e.g:
```julia
""" Variable definitions for heat conduction (enthalpy) on soil layer. """
variables(soil::Soil, heat::Heat{:H}) = (
Prognostic(:H, Float"J/m^3", OnGrid(Cells)),
Diagnostic(:T, Float"K", OnGrid(Cells)),
Diagnostic(:T, Float"°C", OnGrid(Cells)),
Diagnostic(:C, Float"J//K*/m^3", OnGrid(Cells)),
Diagnostic(:Ceff, Float"J/K/m^3", OnGrid(Cells)),
Diagnostic(:k, Float"W/m/K", OnGrid(Edges)),
......@@ -57,7 +62,7 @@ variables(soil::Soil, heat::Heat{:H}) = (
)
```
When the `Heat` process is assigned to a `Soil` layer, `CryoGridSetup` will invoke this method and create state variables corresponding to each [`Var`](@ref). [`Prognostic`](@ref) variables are assigned derivatives (in this case, `dH`, since `H` is the prognostic state variable) and integrated over time. `Diagnostic` variables provide in-place caches for intermediary variables/computations and are automatically tracked by the modeling engine (i.e. their saved values will appear in `CryoGridOutput`).
When the `Heat` process is assigned to a `Soil` layer, `LandModel` will invoke this method and create state variables corresponding to each [`Var`](@ref). [`Prognostic`](@ref) variables are assigned derivatives (in this case, `dH`, since `H` is the prognostic state variable) and integrated over time. `Diagnostic` variables provide in-place caches for intermediary variables/computations and can be automatically tracked by the modeling engine.
Each variable definition consists of a name (a Julia `Symbol`), a type, and a shape. For variables discretized on the grid, the shape is specified by `OnGrid`, which will generate an array of the appropriate size when the model is compiled. The arguments `Cells` and `Edges` specify whether the variable should be defined on the grid cells or edges respecitvely.
......@@ -77,6 +82,6 @@ end
!!! warning
Prognostic state variables like `H` in the example above **should not be directly modified** in user code. This is especially crucial when using higher order or implicit integrators as unexpected changes to the underlying state may destroy the accuracy of their internal interpolators. For modleing discontinuities, use [`Callbacks`](@ref) instead.
Prognostic state variables like `H` in the example above **should not be directly modified** in user code. This is especially important when using higher order or implicit integrators as unexpected changes to the underlying state may destroy the accuracy of their internal interpolators. For modleing discontinuities, use [`Callbacks`](@ref) instead.
Note that `state` is a `NamedTuple` with fields corresponding to the variables declared by the `variables` function for `Soil` and `Heat`. Additionally, output arrays for the time derivatives are provided (here `dH`), as well as the current timestep, layer upper boundary depth, parameters, and variable grids (accessible via `state.t`, `state.z`, `state.params`, and `state.grids` respectively). Note that `state` will also contain other variables declared on this `Soil` layer by other `SubSurfaceProcess`es, allowing for implicit coupling between processes where appropriate.
Note that `state` is of type [`LayerState`](@ref) with fields corresponding to the variables declared by the `variables` function for `Soil` and `Heat`. Additionally, output arrays for the time derivatives are provided (here `dH`), as well as the current timestep, layer boundary depths, and variable grids (accessible via `state.t`, `state.z`, and `state.grids` respectively). Note that `state` will also contain other variables declared on this `Soil` layer by other `SubSurfaceProcess`es, allowing for implicit coupling between processes where appropriate.
## Quick start
After [installing](installation.md) `CryoGrid.jl`, you can get started right away with a simple soil heat model. The [`Models`](@ref) module (aliased `CryoGridModels`) provides pre-specified models that can be obtained with a single function call. It is also possible to modify the soil and initial temperature profiles via `SoilLayerConfig`; here `SamoylovDefault` is used.
After [installing](installation.md) `CryoGrid.jl`, you can get started right away with a simple soil heat model. The [`Presets`](@ref) module (aliased `CryoGrid.Presets`) provides pre-specified model configurations that can be obtained with a single function call. It is also possible to modify the soil and initial temperature profiles via `SoilLayerConfig`; here `SamoylovDefault` is used.
Single layer heat conduction model with free water freeze curve and air temperature upper boundary condition:
```julia
using CryoGrid
......@@ -8,47 +10,49 @@ using Plots
# load provided forcing data from Samoylov;
# The forcing file will be automatically downloaded to the input/ folder if not already present.
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature (converted to Kelvin) as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# get preset soil and initial temperature profile for Samoylov
soilprofile, tempprofile = CryoGrid.Presets.SamoylovDefault
# basic 1-layer heat conduction model (defaults to free water freezing scheme)
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), CryoGridModels.SamoylovDefault)
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile)
# define time span (1 year)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan)
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve discretized system, saving every 6 hours;
# Trapezoid on a discretized PDE is analogous to the well known Crank-Nicolson method.
out = @time solve(prob, Trapezoid(), abstol=1e-3, reltol=1e-4, saveat=6*3600.0, progress=true) |> CryoGridOutput;
out = @time solve(prob, Trapezoid(), saveat=6*3600.0, progress=true) |> CryoGridOutput;
zs = [1.0,5,10,20,30,50,100,500,1000]u"cm"
cg = Plots.cgrad(:copper,rev=true)
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
```
![Ts_output_freew](../../res/Ts_H_tair_freeW_2010-2011.png)
![Ts_output_freew](res/Ts_H_tair_freeW_2010-2011.png)
Alternatively, we can use a van Genuchten freeze curve:
Alternatively, we can use a Dall'Amico freeze curve:
```julia
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), SamoylovDefault, freezecurve=SFCC(VanGenuchten()))
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile, freezecurve=SFCC(DallAmico()))
# Set-up parameters
p = copy(model.pproto)
p.soil.α .= 4.0
p.soil.n .= 2.0
p.soil.Tₘ .= 273.15
p = parameters(model)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
prob = CryoGridProblem(model,tspan,p)
# stiff solvers don't work well with van Genuchten due to the ill-conditioned Jacobian;
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# stiff solvers don't work well with Dall'Amico due to the ill-conditioned Jacobian;
# We can just forward Euler instead.
out = @time solve(prob, Euler(), dt=120.0, saveat=6*3600.0, progress=true) |> CryoGridOutput;
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
```
![Ts_output_vgfc](../../res/Ts_H_tair_vg_2010-2011.png)
Note that `SoilHeat` uses energy as the state variable by default. To use temperature as the state variable instead:
```julia
# Note that this will work with any freeze curve, here we use Westermann (2011).
# :T is the variable name for temperature, :H represents enthalpy/energy.
# This is used in the specification of the Heat process type.
model = CryoGridModels.SoilHeat(:T, TemperatureGradient(tair), SamoylovDefault, freezecurve=SFCC(Westermann()))
```
# While this will work with any freeze curve, here we use Westermann (2011) as an example.
model = CryoGrid.Presets.SoilHeatColumn(:T, TemperatureGradient(tair), soilprofile, freezecurve=SFCC(Westermann()))
```
\ No newline at end of file
using CryoGrid
using Plots
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature as upper boundary forcing;
# convert Tair to Kelvin
tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
# basic 1-layer heat conduction model (defaults to free water freezing scheme)
grid = CryoGridModels.DefaultGrid_5cm
model = CryoGridModels.SoilHeat(:H, TemperatureGradient(tair), CryoGridModels.SamoylovDefault; grid=grid)
tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# "simple" heat conduction model w/ 5 cm grid spacing (defaults to free water freezing scheme)
grid = CryoGrid.Presets.DefaultGrid_5cm
model = CryoGrid.Presets.SoilHeatColumn(:H, TemperatureGradient(tair), CryoGrid.Presets.SamoylovDefault; grid=grid)
# define time span
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan)
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve with Crank-Nicolson (Trapezoid) and construct CryoGridOutput from solution
out = @time solve(prob, Trapezoid(), abstol=1e-4, reltol=1e-4, saveat=24*3600.0, progress=true) |> CryoGridOutput;
# Plot it!
zs = [1:10...,20:10:100...]
cg = Plots.cgrad(:copper,rev=true);
plot(out.soil.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.soil.T[Z(zs)] .- 273.15, color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
plot(out.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.T[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
using CryoGrid
using Plots
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature as upper boundary forcing;
# convert Tair to Kelvin
tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
# basic 1-layer heat conduction model (defaults to free water freezing scheme)
grid = CryoGridModels.DefaultGrid_5cm
model = CryoGridModels.SoilHeat(:H, TemperatureGradient(tair), CryoGridModels.SamoylovDefault;
grid=grid, freezecurve=SFCC(VanGenuchten()))
tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# "simple" heat conduction model w/ 5 cm grid spacing
grid = CryoGrid.Presets.DefaultGrid_5cm
soilprofile, tempprofile = CryoGrid.Presets.SamoylovDefault
model = CryoGrid.Presets.SoilHeatColumn(:H, TemperatureGradient(tair), soilprofile; grid=grid, freezecurve=SFCC(DallAmico()))
# define time span
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = copy(model.pproto)
p.soil.α .= 4.0
p.soil.n .= 2.0
p.soil.Tₘ .= 273.15 # K
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan,p)
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve with forward Euler (fixed 10 minute timestep) and construct CryoGridOutput from solution
out = @time solve(prob, Euler(), dt=10*60.0, saveat=24*3600.0, progress=true) |> CryoGridOutput;
# Plot it!
zs = [1:10...,20:10:100...]
cg = Plots.cgrad(:copper,rev=true);
plot(out.soil.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.soil.T[Z(zs)] .- 273.15, color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
\ No newline at end of file
plot(out.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.T[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
\ No newline at end of file
using CryoGrid
using Plots
# Custom grid (though actually pretty much the same as CryoGridModels.DefaultGrid_2cm)
# Custom grid (though actually pretty much the same as CryoGrid.Presets.DefaultGrid_2cm)
const gridvals = vcat([0:0.02:2...,2.05:0.05:4.0...,
4.1:0.1:10...,10.2:0.2:20...,21:1:30...,
35:5:50...,60:10:100...,200:100:1000...]...)
35:5:50...,60:10:100...,200:100:1000...]...)u"m"
# soil profile: depth => (excess ice, natural porosity, saturation, organic fraction)
soilprofile = SoilProfile(
0.0u"m" => SoilProperties(χ=0.0,ϕ=0.80,θ=1.0,ω=0.75), #(θw=0.80,θm=0.05,θo=0.15,ϕ=0.80),
0.1u"m" => SoilProperties(χ=0.0,ϕ=0.80,θ=1.0,ω=0.25), #(θw=0.80,θm=0.15,θo=0.05,ϕ=0.80),
0.4u"m" => SoilProperties(χ=0.30,ϕ=0.55,θ=1.0,ω=0.25), #(θw=0.80,θm=0.15,θo=0.05,ϕ=0.55),
3.0u"m" => SoilProperties(χ=0.0,ϕ=0.50,θ=1.0,ω=0.0), #(θw=0.50,θm=0.50,θo=0.0,ϕ=0.50),
10.0u"m" => SoilProperties(χ=0.0,ϕ=0.30,θ=1.0,ω=0.0), #(θw=0.30,θm=0.70,θo=0.0,ϕ=0.30),
)
0.0u"m" => soilparameters(xic=0.0,por=0.80,sat=1.0,org=0.75), #(θw=0.80,θm=0.05,θo=0.15,ϕ=0.80),
0.1u"m" => soilparameters(xic=0.0,por=0.80,sat=1.0,org=0.25), #(θw=0.80,θm=0.15,θo=0.05,ϕ=0.80),
0.4u"m" => soilparameters(xic=0.30,por=0.55,sat=1.0,org=0.25), #(θw=0.80,θm=0.15,θo=0.05,ϕ=0.55),
3.0u"m" => soilparameters(xic=0.0,por=0.50,sat=1.0,org=0.0), #(θw=0.50,θm=0.50,θo=0.0,ϕ=0.50),
10.0u"m" => soilparameters(xic=0.0,por=0.30,sat=1.0,org=0.0), #(θw=0.30,θm=0.70,θo=0.0,ϕ=0.30),
),
# mid-winter temperature profile
tempprofile = TempProfile(
tempprofile = TemperatureProfile(
0.01u"m" => -15.9u"°C",
0.05u"m" => -15.49u"°C",
0.10u"m" => -15.32u"°C",
......@@ -23,9 +23,8 @@ tempprofile = TempProfile(
0.40u"m" => -13.50u"°C",
1000.0u"m" => 10.2u"°C",
)
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# convert Tair to Kelvin
Tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
Tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# assume other forcings don't (yet) have units
pr = TimeSeriesForcing(forcings.data.pressure, forcings.timestamps, :p);
q = TimeSeriesForcing(forcings.data.q, forcings.timestamps, :q);
......@@ -35,25 +34,24 @@ Sin = TimeSeriesForcing(forcings.data.Sin, forcings.timestamps, :Sin);
z = 2.; # height [m] for which the forcing variables (Temp, humidity, wind, pressure) are provided
tspan = (DateTime(2010,1,1), DateTime(2011,1,1))
strat = Stratigraphy(
-2.0u"m" => Top(SurfaceEnergyBalance(Tair,pr,q,wind,Lin,Sin,z)),
-2.0u"m" => top(SurfaceEnergyBalance(Tair,pr,q,wind,Lin,Sin,z)),
# Note: You can change Heat{:H} to Heat{:T} to use temperature as the prognostic state variable.
0.0u"m" => Ground(:soil, Soil(soilprofile), Heat{:H}(tempprofile, freezecurve=SFCC(VanGenuchten()))),
1000.0u"m" => Bottom(GeothermalHeatFlux(0.053u"J/s/m^2"))
0.0u"m" => subsurface(:soil, Soil(soilprofile), Heat{:H}(freezecurve=SFCC(DallAmico()))),
1000.0u"m" => bottom(GeothermalHeatFlux(0.053u"J/s/m^2"))
);
grid = Grid(gridvals);
model = CryoGridSetup(strat,grid);
model = LandModel(strat,grid);
# define time span
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = copy(model.pproto)
p.soil.α .= 4.0
p.soil.n .= 2.0
p.soil.Tₘ .= 273.15 # K
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan,p)
# solve with forward Euler (fixed 2 minute time steps) and construct CryoGridOutput from solution
out = @time solve(prob, Euler(), dt=2*60.0, saveat=24*3600.0, progress=true) |> CryoGridOutput;
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve with forward Euler (w/ CFL) and construct CryoGridOutput from solution
out = @time solve(prob, Euler(), dt=2*60.0, callback=CFLStepLimiter(model), saveat=24*3600.0, progress=true) |> CryoGridOutput;
# Plot it!
zs = [1:10...,20:10:100...]
cg = Plots.cgrad(:copper,rev=true);
plot(out.soil.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.soil.T[Z(zs)] .- 273.15, color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
plot(out.H[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Enthalpy", leg=false, dpi=150)
plot(out.T[Z(zs)], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, size=(800,500), dpi=150)
......@@ -3,33 +3,36 @@ using Plots
# load provided forcing data from Samoylov;
# The forcing file will be automatically downloaded to the input/ folder if not already present.
forcings = loadforcings(CryoGridModels.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature (converted to Kelvin) as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(u"K", forcings.data.Tair), forcings.timestamps, :Tair);
forcings = loadforcings(CryoGrid.Presets.Forcings.Samoylov_ERA_obs_fitted_1979_2014_spinup_extended_2044, :Tair => u"°C");
# use air temperature as upper boundary forcing
tair = TimeSeriesForcing(ustrip.(forcings.data.Tair), forcings.timestamps, :Tair);
# get preset soil and initial temperature profile for Samoylov
soilprofile, tempprofile = CryoGrid.Presets.SamoylovDefault
# basic 1-layer heat conduction model (defaults to free water freezing scheme)
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), CryoGridModels.SamoylovDefault)
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile)
# define time span (1 year)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
p = parameters(model)
initT = initializer(:T, tempprofile)
u0 = initialcondition!(model, tspan, p, initT)
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,tspan)
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# solve discretized system, saving every 6 hours;
# Trapezoid on a discretized PDE is analogous to the well known Crank-Nicolson method.
out = @time solve(prob, Trapezoid(), abstol=1e-3, reltol=1e-4, saveat=6*3600.0, progress=true) |> CryoGridOutput;
out = @time solve(prob, Trapezoid(), saveat=6*3600.0, progress=true) |> CryoGridOutput;
zs = [1.0,5,10,20,30,50,100,500,1000]u"cm"
cg = Plots.cgrad(:copper,rev=true)
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
savefig("res/Ts_H_tair_freeW_2010-2011.png")
model = CryoGridModels.SoilHeat(TemperatureGradient(tair), SamoylovDefault, freezecurve=SFCC(VanGenuchten()))
model = CryoGrid.Presets.SoilHeatColumn(TemperatureGradient(tair), soilprofile, freezecurve=SFCC(DallAmico()))
# Set-up parameters
p = copy(model.pproto)
p.soil.α .= 4.0
p.soil.n .= 2.0
p.soil.Tₘ .= 273.15
p = parameters(model)
tspan = (DateTime(2010,10,30),DateTime(2011,10,30))
prob = CryoGridProblem(model,tspan,p)
# stiff solvers don't work well with van Genuchten due to the ill-conditioned Jacobian;
# CryoGrid front-end for ODEProblem
prob = CryoGridProblem(model,u0,tspan,p,savevars=(:T,))
# stiff solvers don't work well with Dall'Amico due to the ill-conditioned Jacobian;
# We can just forward Euler instead.
out = @time solve(prob, Euler(), dt=120.0, saveat=6*3600.0, progress=true) |> CryoGridOutput;
plot(out.soil.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false, dpi=150)
plot(out.T[Z(Near(zs))], color=cg[LinRange(0.0,1.0,length(zs))]', ylabel="Temperature", leg=false)
savefig("res/Ts_H_tair_vg_2010-2011.png")
\ No newline at end of file
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......@@ -2,15 +2,18 @@ module Callbacks
import CryoGrid
using CryoGrid.Drivers: HeatOnlyLandModel
using CryoGrid.Numerics
using CryoGrid.Setup: CryoGridSetup, HeatOnlySetup
using CryoGrid.Land: LandModel, getvar
using CryoGrid.Utils
using DiffEqCallbacks
using IfElse
"""
CryoGridCallbackFunction{TState,TSetup}(setup, state)
Helper type for defining callbacks on CryoGrid models. Given a CryoGridSetup and some additional user-defined state type
Helper type for defining callbacks on CryoGrid models. Given a LandModel and some additional user-defined state type
`TState`, the user can provide dispatches for `CryoGridCallbackFunction{TState}` that satisfy the relevant `DifferentialEquations.jl`
callback function signature. For example:
......@@ -22,7 +25,7 @@ end
function (fn::CryoGridCallbackFunction{MyState})(u,p,t)
...
end
function MyCallback(setup::CryoGridSetup)
function MyCallback(setup::LandModel)
state = MyState(...)
fn = CryoGridCallbackFunction(setup, state)
# create and return SciML callback here
......@@ -32,7 +35,7 @@ end
struct CryoGridCallbackFunction{TState,TSetup}
setup::TSetup
state::TState
CryoGridCallbackFunction(setup::CryoGridSetup, state::TState) where TState = new{TState, typeof(setup)}(setup, state)
CryoGridCallbackFunction(setup::LandModel, state::TState) where TState = new{TState, typeof(setup)}(setup, state)
end
(fn::CryoGridCallbackFunction)(u,p,t) = error("no method dispatch provided for callback function $(typeof(fn))")
......