diff --git a/docs/notebook-almass-vegetation.jl b/docs/notebook-almass-vegetation.jl new file mode 100644 index 0000000000000000000000000000000000000000..aa6bac47831f0449f1ce4c738023a4978fd9c33f --- /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 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" +Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d" + +[compat] +Plots = "~1.40.4" +PlutoUI = "~0.7.59" +Unitful = "~1.21.0" +""" + +# ╔═╡ 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+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