From df5dce829fd020e6aa1e0cc8de38b4cb1c0dad96 Mon Sep 17 00:00:00 2001
From: Marco Matthies <71844+marcom@users.noreply.github.com>
Date: Mon, 19 Aug 2024 08:09:59 +0200
Subject: [PATCH] Docs: add a Pluto notebook on the ALMaSS vegetation growth
model
---
docs/notebook-almass-vegetation.jl | 1425 ++++++++++++++++++++++++++++
1 file changed, 1425 insertions(+)
create mode 100644 docs/notebook-almass-vegetation.jl
diff --git a/docs/notebook-almass-vegetation.jl b/docs/notebook-almass-vegetation.jl
new file mode 100644
index 0000000..aa6bac4
--- /dev/null
+++ b/docs/notebook-almass-vegetation.jl
@@ -0,0 +1,1425 @@
+### A Pluto.jl notebook ###
+# v0.19.45
+
+using Markdown
+using InteractiveUtils
+
+# ╔═╡ 1ce4cf02-4d80-11ef-0759-99876c2c9002
+begin
+ using PlutoUI, Unitful, Plots
+ using Unitful: MJ, m, d
+ TableOfContents()
+end
+
+# ╔═╡ 26ad42b4-ec55-4c43-b45a-59fe99e8a067
+md"""
+# ALMaSS vegetation model
+
+Based on the information in ALMaSSVegetationModelling.pdf (https://git.idiv.de/persefone/persefone-model/-/blob/master/docs/ALMaSSVegetationModelling.pdf).
+"""
+
+# ╔═╡ eef634af-2157-4f6d-96de-d01ebb3a80a2
+md"""
+## TODO
+
+- calculation of LAI-green from temperature (using growth curves and GDD)
+ - at the moment daily avg temperature has no effect on LAI-green and hence no
+ effect on accumulated dry matter
+
+"""
+
+# ╔═╡ 6e2001c5-69cc-4830-8426-a35990c1a03d
+md"""
+## Open questions
+
+- meaning of: radiation vs normal radiation?
+- units of incoming daily radiation? maybe: MJ/m^2/day
+"""
+
+# ╔═╡ 01331c5a-00bd-4504-85ac-d7aec1a0c14d
+md"""
+
+## Variables used in the model
+
+- `ε`: radiation use efficiency (g/MJ)
+- `ϕ`: fraction of incoming light intercepted by crop canopy (0 to 1, no units)
+ - `ϕ(LAI_green(d))`, where `LAI_green(d)` is the green leaf area index (m^2/m^2)
+- `f(T)`: effect of temperature `T` (K or °C) on dry matter growth (no units)
+- `R(d)`: incoming global radiation (MJ/m^2)
+- `p(d)`: effect of fertiliser (no units)
+
+- `LAI_green(d)` is taken from empirical curves, taking into account `gdd`,
+ `LAI_total` also includes dead leaves
+- `gdd`: growing-degree-days (unit "K days"),
+ - `gdd(n)=sum(max(0, (max_or_avg_temp(d) - min_growth_temp) for d = 1:n)`
+
+"""
+
+# ╔═╡ f3e009e2-c565-41dc-b35d-096400e867c3
+md"""
+## Accumulated dry matter: W
+"""
+
+# ╔═╡ 6534f518-9465-4bd2-9f74-51a12bdc412f
+md"""
+## Growing-degree days: GDD
+"""
+
+# ╔═╡ 1488ab39-d9f7-48a6-a22c-8ad4a90e17f5
+"""
+ gdd(n): growing-degree days (d K, day Kelvin)
+"""
+function gdd(n::Integer;
+ avg_daily_temperature = d -> 14.0u"°C",
+ min_growth_temperature = 10.0u"°C")
+ # TODO: check if formula is correct
+ g = sum(max(0.0u"K", avg_daily_temperature(d) - min_growth_temperature)
+ for d = 1:n)
+ return g * 1.0u"d"
+end
+
+# ╔═╡ c489e5c3-24b1-48c8-b587-7e75154722ef
+let
+ x = range(1, 15)
+ # artificial avg daily temperature data
+ avgT = (0.5 * sin.(x).^2 .+ 9.8) * u"°C"
+ min_growth_temperature = 10.0u"°C"
+ y_gdd = ustrip.(gdd.(x; avg_daily_temperature = d -> avgT[d]))
+ y_avgT = ustrip.(avgT)
+ y_minT = [ustrip(min_growth_temperature) for _ in eachindex(x)]
+ p1 = plot(x, y_gdd;
+ title="Growing-degree days (GDD)",
+ label="GDD (day K)",
+ xlabel="Day number",
+ xticks=x,
+ ylabel="Growing-degree days (day K)",
+ color=:green,
+ legend=:topleft,
+ marker=:circle)
+ plot!(twinx(), x, [y_minT y_avgT];
+ label=["Min growth temperature" "Daily avg temperature"],
+ ylabel="Daily average temperature (°C)",
+ legend=:topright,
+ marker=[:none :circle])
+end
+
+# ╔═╡ 38158dbc-a702-4c86-8cda-6e08c631a22a
+md"""
+## Fraction of intercepted light: ϕ
+"""
+
+# ╔═╡ 5800ddc2-4fcb-452b-901f-7eb510aea4f5
+"""
+ ϕ(LAI_green): fraction of intercepted light (no units, 0 to 1)
+
+Arguments:
+ - `LAI_green`: leaf area index of green leaves (green leaf cover m^2 / ground area m^2)
+"""
+function ϕ(LAI_green)
+ """
+ k: extinction coefficient (no units), set to k = 0.4 in general
+ """
+ k = 0.4u"m^2/m^2"
+
+ 1 - exp(-k * LAI_green)
+end
+
+# ╔═╡ 41411efa-5ff7-4e79-b6ee-d932b506758c
+let
+ x = range(0, 10, length=100)
+ y = ϕ.(x)
+ plot(x, y;
+ title="Fraction of light intercepted by green leaves",
+ label="fraction of intercepted light ϕ",
+ xlabel="LAI-Green, green leaf area index (leaf cover m^2 / area m^2)",
+ ylabel="Fraction intercepted light (no units)")
+end
+
+# ╔═╡ 1bef060e-f0cc-4359-941b-9b1e06895fd7
+md"""
+## Incoming daily solar radiation: R
+"""
+
+# ╔═╡ 551ee825-d63c-420c-980c-2d1bbf12dec0
+"""
+ R_Odum(d): normal daily global radiation (MJ m^-2) in Ødum, Denmark
+
+Arguments:
+- `d`: day of the year (1 to 365, no units)
+"""
+function R_Odum(d::Real)
+ # Fourier series approx. for Ødum, Denmark
+ ω = 2π / 365
+ b₀ = 9.478
+ b₁ = -9.221
+ b₂ = 1.458
+ b₃ = 0.653
+ b₄ = -0.421
+
+ return (b₀
+ + b₁ * cos(ω * d)
+ + b₂ * sin(ω * d)
+ + b₃ * cos(2 * ω * d)
+ + b₄ * sin(2 * ω * d)) * u"MJ/m^2"
+end
+
+# ╔═╡ 5dbf2aac-0cf0-4a15-b1cb-d804eed52a4f
+"""
+ W(n): accumulated dry matter at day `n` (g/m^2)
+
+ W(n :: Integer;
+ biomass_per_light_energy :: Real, # (g/MJ)
+ daily_avg_temperature :: Function{d::Int -> T(d)::Real}, # (°C)
+ LAI_green :: Function{d::Int -> L(d)::Real}, # (no unit)
+ temperature_scaling :: Function{T -> f(T)}, # (no unit)
+ fertiliser_scaling :: Function{d -> p(d)}, # (no unit)
+ incoming_radiation :: Function{d -> R(d)}) # (MJ/m^2)
+
+Formula used:
+ `W(n) = sum(ε * ϕ(L(d)) * f(T(d)) * R(d) * p(d) for d = 1:n)`
+
+Arguments
+- `biomass_per_light_energy`, `ε`
+- `daily_avg_temperature`, `T(d)`
+- `LAI_green`, `L(d)`
+- `temperature_scaling`, `f(T)`
+- `fertiliser_scaling`, `p(d)`
+
+Formula from pdf:
+ `W(n) = sum(ε * ϕ * f(T) * R(d) for d = 1:n)`
+"""
+function W(n::Integer;
+ biomass_per_light_energy = 1.4u"g/MJ", # ε
+ daily_avg_temperature = d -> 15u"°C", # T(d)
+ LAI_green = d -> 5.0u"m^2/m^2", # L(d)
+ temperature_scaling = T -> 1.0, # f(T)
+ fertiliser_scaling = d -> 1.0, # p(d)
+ incoming_radiation = R_Odum) # R(d)
+ ε = biomass_per_light_energy
+ T = daily_avg_temperature
+ L = LAI_green
+ f = temperature_scaling
+ p = fertiliser_scaling
+ R = incoming_radiation
+ sum(ε * ϕ(L(d)) * f(T(d)) * R(d) * p(d) for d = 1:n)
+end
+
+# ╔═╡ 3d3fba49-beb0-4521-b787-b3a5455796e0
+# ╠═╡ disabled = true
+#=╠═╡
+let
+ x = range(1, 365, length=365)
+
+ # artificial data for daily avg temperature
+ T(d) = (cos(d * 2π/365 + 0.9π) .* 8 .+ 10) * u"°C"
+ yT = ustrip.(T.(x))
+
+ function L(d)
+ # TODO: assumes 1 <= d <= 365
+ L_start = 0.01
+ L_level = 8.0
+ L_end = 0.01
+ d_rampup = 75
+ d_level = 150
+ d_rampdown = 220
+ d_end = 250
+ return if 0 <= d < d_rampup
+ L_start
+ elseif d_rampup <= d < d_level
+ L_start + (d - d_rampup) * (L_level - L_start) / (d_level - d_rampup)
+ elseif d_level <= d < d_rampdown
+ L_start + L_level
+ elseif d_rampdown <= d < d_end
+ L_start + L_level - (d - d_rampdown) * (L_level - L_end) / (d_end - d_rampdown)
+ elseif d_end <= d <= 365
+ return L_end
+ else
+ error("Illegal day $d, has to be 0 <= d <= 365")
+ end * u"m^2/m^2"
+ end
+ yL = L.(x)
+
+ y = W.(Int.(x);
+ daily_avg_temperature = T,
+ incoming_radiation = R_Odum,
+ )
+ p1 = plot(x, y;
+ title="Accumulated dry matter: W",
+ label="Dry matter in g / m^2",
+ xlabel="Day of the year (1 to 365)",
+ ylabel="Accumulated dry matter"
+ )
+ p1 = plot!(twinx(), yT;
+ label="Daily avg temp (°C)",
+ color="red",
+ ylabel="Daily avg temperature (°C)",
+ )
+ p2 = plot(x, yL;
+ title = "Green leaf area index (LAI-green)",
+ label = "LAI-green",
+ xlabel="Day of the year (1 to 365)",
+ ylabel="LAI-green",
+ #marker = :circle,
+ )
+ plot(p1, p2; layout=(2,1), size=(600,600))
+end
+ ╠═╡ =#
+
+# ╔═╡ 08624eb0-465b-411d-9706-104382aef0ff
+let
+ x = range(1, 365, length=365)
+ y = R_Odum.(x)
+ plot(x, y;
+ title="Fourier series approximation to\n" *
+ "incoming daily radiation in Ødum, Denmark",
+ label="R: radiation in MJ m^-2",
+ xlabel="Day of the year (1 to 365)",
+ ylabel="Incoming daily radiation")
+end
+
+# ╔═╡ 2cf7ef76-1f47-48b0-9d85-0f967d15d537
+
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
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+
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+
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+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.6+0"
+
+[[deps.eudev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
+git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
+uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
+version = "3.2.9+0"
+
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.43.0+0"
+
+[[deps.gperf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
+uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
+version = "3.1.1+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.9.0+0"
+
+[[deps.libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.8.0+1"
+
+[[deps.libdecor_jll]]
+deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
+git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
+uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
+version = "0.2.2+0"
+
+[[deps.libevdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
+uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
+version = "1.11.0+0"
+
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[deps.libinput_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
+git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
+uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
+version = "1.18.0+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.43+1"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+2"
+
+[[deps.mtdev_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
+uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
+version = "1.1.6+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.52.0+1"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+version = "17.4.0+2"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+1"
+"""
+
+# ╔═╡ Cell order:
+# ╟─26ad42b4-ec55-4c43-b45a-59fe99e8a067
+# ╟─eef634af-2157-4f6d-96de-d01ebb3a80a2
+# ╟─6e2001c5-69cc-4830-8426-a35990c1a03d
+# ╟─01331c5a-00bd-4504-85ac-d7aec1a0c14d
+# ╠═1ce4cf02-4d80-11ef-0759-99876c2c9002
+# ╟─f3e009e2-c565-41dc-b35d-096400e867c3
+# ╠═5dbf2aac-0cf0-4a15-b1cb-d804eed52a4f
+# ╠═3d3fba49-beb0-4521-b787-b3a5455796e0
+# ╟─6534f518-9465-4bd2-9f74-51a12bdc412f
+# ╠═1488ab39-d9f7-48a6-a22c-8ad4a90e17f5
+# ╠═c489e5c3-24b1-48c8-b587-7e75154722ef
+# ╟─38158dbc-a702-4c86-8cda-6e08c631a22a
+# ╠═5800ddc2-4fcb-452b-901f-7eb510aea4f5
+# ╠═41411efa-5ff7-4e79-b6ee-d932b506758c
+# ╟─1bef060e-f0cc-4359-941b-9b1e06895fd7
+# ╠═551ee825-d63c-420c-980c-2d1bbf12dec0
+# ╠═08624eb0-465b-411d-9706-104382aef0ff
+# ╠═2cf7ef76-1f47-48b0-9d85-0f967d15d537
+# ╟─00000000-0000-0000-0000-000000000001
+# ╟─00000000-0000-0000-0000-000000000002
--
GitLab