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notebook-almass-vegetation.jl 46.11 KiB 
### 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


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Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

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[[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"
"""

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