Microwave Dielectric Models

CanopyOptics ships a small but extensible family of complex permittivity models for the materials that appear in canopy radiative transfer at microwave frequencies: water, ice, soil, and fresh leaves. They all share one entry point — the dielectric(material, T_kelvin, f_GHz) function — and dispatch is on the material type.

using CanopyOptics
using CairoMakie

The shared contract

Every material type implements dielectric(model, T, f) and returns a Complex permittivity with the loss in the positive imaginary part (physics convention e^{-iωt}). Temperature is in kelvin, frequency in GHz.

materials = (
    "Pure water"   => LiquidPureWater(),
    "Salt water"   => LiquidSaltWater(S = 35.0),
    "Pure ice"     => PureIce(),
    "Moist soil"   => SoilMW(sand_frac = 0.4, clay_frac = 0.2, mᵥ = 0.30, ρ = 1.5),
    "Fresh leaf"   => LeafUlabyElRayes1987(M_g = 0.5),
)

T = 273.0       # K (0 °C — sits inside every model's validity range)
f = 1.4         # GHz (SMOS L-band)

for (name, mat) in materials
    println(rpad(name, 12), " ε(T=$T K, f=$f GHz) = ", dielectric(mat, T, f))
end

Pure water   ε(T=273.0 K, f=1.4 GHz) = 85.87525601604212 + 12.562773920294383im
Salt water   ε(T=273.0 K, f=1.4 GHz) = 75.49363163556556 + 47.62817767459573im
Pure ice     ε(T=273.0 K, f=1.4 GHz) = 3.1884 + 0.0005817032208281714im
Moist soil   ε(T=273.0 K, f=1.4 GHz) = 19.55213755404344 + 3.5064493675752355im
Fresh leaf   ε(T=273.0 K, f=1.4 GHz) = 17.207824939118865 + 5.681666388776218im

Each method enforces its own validity domain — calls outside the documented range throw ArgumentError rather than silently returning unsupported values:

try
    dielectric(LeafUlabyElRayes1987(M_g = 0.5), 295.0, 100.0)
catch err
    println("rejected: ", err)
end

rejected: ArgumentError("Frequency must be ∈ [0.2, 20] GHz for Ulaby & El-Rayes 1987 (got 100.0)")

Frequency sweep — fresh leaf vs liquid water

A fresh leaf at half gravimetric moisture sits well below the bulk water response because only the free-water and bound-water volume fractions couple to the EM field; the rest is non-dispersive plant matter.

freqs = range(0.2, 20.0, length = 80)
ε_water = [dielectric(LiquidPureWater(),                280.0, f) for f in freqs]
ε_leaf  = [dielectric(LeafUlabyElRayes1987(M_g = 0.5), 280.0, f) for f in freqs]

fig = Figure(size = (640, 360))
ax = Axis(fig[1, 1]; xlabel = "frequency (GHz)", ylabel = "ε",
          title = "Permittivity vs frequency at T = 280 K")
lines!(ax, freqs, real.(ε_water); label = "water  ε'")
lines!(ax, freqs, imag.(ε_water); label = "water  ε''", linestyle = :dash)
lines!(ax, freqs, real.(ε_leaf);  label = "leaf   ε'")
lines!(ax, freqs, imag.(ε_leaf);  label = "leaf   ε''", linestyle = :dash)
axislegend(ax; position = :rt)
fig

Moisture sweep — leaf

At fixed C-band frequency the real and imaginary parts of the leaf permittivity rise monotonically with gravimetric moisture, dominated by the free-water contribution at high M_g.

mgs   = range(0.0, 0.7, length = 41)
ε_mg  = [dielectric(LeafUlabyElRayes1987(M_g = m), 295.0, 5.0) for m in mgs]

fig2 = Figure(size = (640, 360))
ax2 = Axis(fig2[1, 1]; xlabel = "gravimetric moisture M_g",
           ylabel = "ε", title = "Leaf permittivity at f = 5 GHz")
lines!(ax2, mgs, real.(ε_mg); label = "ε'")
lines!(ax2, mgs, imag.(ε_mg); label = "ε''", linestyle = :dash)
axislegend(ax2; position = :lt)
fig2

Adding a new material

Any new material is one struct + one method. The dispatch pattern keeps the call site identical:

struct MyMaterial{FT} <: AbstractVegetation        # or AbstractWater / AbstractSoil
    # … parameters …
end

function CanopyOptics.dielectric(mod::MyMaterial, T::Real, f::Real)
    # … returns Complex{FT} …
end

Once defined, MyMaterial plugs into anything downstream that takes an <: AbstractMaterial — the planned microwave-canopy expansion will build on this same hierarchy.

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