Abstract Type for canopy scattering

Abstract Type for leaf distributions

Abstract Type for leaf composition

Abstract Material Type (can be all)

Abstract type for Prospect model versions

Abstract soil type

Abstract water type

Model for bi-lambertian canopy leaf scattering

All leaf-related parameters

struct LeafDistribution{FT<:AbstractFloat}

A struct that defines the leaf angular distribution in radians (from 0->π/2; here scaled to [0,1])

Fields

• LD: Julia Univariate Distribution from Distributions.js

• scaling: Scaling factor to normalize distribution (here mostly 2/π as Beta distribution is from [0,1])

struct PigmentOpticalProperties{FT}

A struct which stores important absorption cross sections of pigments, water, etc

Fields

• λ: Wavelength [length]

• nᵣ: Refractive index of leaf material

• Kcab: specific absorption coefficient of chlorophyll (a+b) [cm² μg⁻¹]

• Kcar: specific absorption coefficient of carotenoids [cm² μg⁻¹]

• Kant: specific absorption coefficient of Anthocyanins [cm² nmol⁻¹]

• Kb: specific absorption coefficient of brown pigments (arbitrary units)

• Kw: specific absorption coefficient of water [cm⁻¹]

• Km: specific absorption coefficient of dry matter [cm² g⁻¹]

• Kp: specific absorption coefficient of proteins [cm² g⁻¹]

• Kcbc: specific absorption coefficient of carbon based constituents [cm² g⁻¹]

struct LeafProperties{FT}

A struct which stores important variables of leaf chemistry and structure

Fields

• N: Leaf structure parameter [0-3]

• Ccab: Chlorophyll a+b content [µg cm⁻²]

• Ccar: Carotenoid content [µg cm⁻²]

• Canth: Anthocynanin content [nmol cm⁻²]

• Cbrown: Brown pigments content in arbitrary units

• Cw: Equivalent water thickness [cm], typical about 0.002-0.015

• Cm: Dry matter content (dry leaf mass per unit area) [g cm⁻²], typical about 0.003-0.016

• Cprot: protein content [g/cm]

• Ccbc: Carbone-based constituents content in [g/cm⁻²] (cellulose, lignin, sugars...)

Pure liquid water

Salty liquid water

Pure Ice

Soil MW properties

Model for specular canopy leaf scattering

All wood-related parameters (branch or trunk)

dirVector{FT}

Struct for spherical coordinate directions in θ (elevation angle) and ϕ (azimuth angle)

Fields

• θ

• ϕ

dirVector_μ{FT}

Struct for spherical coordinate directions in θ (elevation angle) and ϕ (azimuth angle)"

Fields

• μ

• ϕ

Integrated projection of leaf area for a single leaf inclination of θₗ, assumes azimuthally uniform distribution

Integrated projection of leaf area for a single leaf inclination of θₗ, assumes azimuthally uniform distribution

Fresnel reflection, needs pol_type soon too!

G(μ::Array{FT}, LD::AbstractLeafDistribution; nLeg=20)

Returns the integrated projection of leaf area in the direction of μ, assumes azimuthally uniform distribution and a LD distribution for leaf polar angle θ. This function is often referred to as the function O(B) (Goudriaan 1977) or G(Ζ) (Ross 1975,1981), see Bonan modeling book, eqs. 14.21-14.26.

Arguments

• μ an array of cos(θ) (directions [0,1])
• LD an AbstractLeafDistribution type struct, includes a leaf distribution function
• nLeg an optional parameter for the number of legendre polynomials to integrate over the leaf distribution (default=20)

Examples

julia> μ,w = CanopyOptics.gauleg(10,0.0,1.0);       # Create 10 quadrature points in μ      
julia> LD  = CanopyOptics.spherical_leaves()        # Create a default spherical leaf distribution
julia> G   = CanopyOptics.G(μ, LD)                  # Compute G(μ)
10-element Vector{Float64}:
 0.5002522783000879
 0.5002715115149204
 0.5003537989277846
 0.5004432798701134
 0.5005134448870893
 0.5003026448466977
 0.4999186257540982
 0.4994511190721635
 0.49907252201082375
 0.49936166823681594

Eq 46 in Shultis and Myneni

The reduction factor proposed by Nilson and Kuusk, κ ≈ 0.1-0.3, returns exp(-κ * tan(abs(α))

Given a complex number, return the complex number with absolute value of both parts

Given a complex number, return the complex number with same real part and absolute value of imaginary part

Calculate forward scattering amplitudes

Calculate scattering coefficients for a thin disk

Brute Force G calculation (for testing

calctav(α::FT, nr::FT) where {FT<:AbstractFloat}

Computes transmission of isotropic radiation across a dielectric surface (Stern F., 1964; Allen W.A.,Appl. Opt., 3(1):111-113 1973)). From calctav.m in PROSPECT-D

Arguments

• α angle of incidence [degrees]
• nr Index of refraction

compute_Z_matrices(mod::BiLambertianCanopyScattering, μ::Array{FT,1}, LD::AbstractLeafDistribution, m::Int)

Computes the single scattering Z matrices (𝐙⁺⁺ for same incoming and outgoing sign of μ, 𝐙⁻⁺ for a change in direction). Internally computes the azimuthally-averaged area scattering transfer function following Shultis and Myneni (https://doi.org/10.1016/0022-4073(88)90079-9), Eq 43::

$Γ(μ' -> μ) = \int_0^1 dμ_L g_L(μ_L)[t_L Ψ⁺(μ, μ', μ_L) + r_L Ψ⁻(μ, μ', μ_L)]$

assuming an azimuthally uniform leaf angle distribution. Normalized Γ as 𝐙 = 4Γ/(ϖ⋅G(μ)). Returns 𝐙⁺⁺, 𝐙⁻⁺

Arguments

• mod : A bilambertian canopy scattering model BiLambertianCanopyScattering, uses R,T,nQuad from that model.
• μ::Array{FT,1}: Quadrature points ∈ [0,1]
• LD a AbstractLeafDistribution struct that describes the leaf angular distribution function.
• m: Fourier moment (for azimuthally uniform leave distributions such as here, only m=0 returns non-zero matrices)

compute_lambertian_Γ(μ::Array{FT,1},μꜛ::Array{FT,1}, r,t, LD::AbstractLeafDistribution; nLeg = 20)

Computes the azimuthally-averaged area scattering transfer function following Shultis and Myneni (https://doi.org/10.1016/0022-4073(88)90079-9), Eq 43:

$Γ(μ' -> μ) = \int_0^1 dμ_L g_L(μ_L)[t_L Ψ⁺(μ, μ', μ_L) + r_L Ψ⁻(μ, μ', μ_L)]$

assuming an azimuthally uniform leaf angle distribution.

Arguments

• μ::Array{FT,1} : Quadrature points incoming direction (cos(θ))
• μꜛ::Array{FT,1}: Quadrature points outgoing direction (cos(θ))
• r : Leaf lambertian reflectance
• t : Leaf lambertian transmittance
• LD a AbstractLeafDistribution struct that describes the leaf angular distribution function.
• nLeg = 20: number of quadrature points used for integration over all leaf angles (default is 20).

Eq 45 in Shultis and Myneni, fixed grid in μ for both μ and μ'

Eq 45 in Shultis and Myneni, fixed grid in μ for both μ and μ'

createLeafOpticalStruct(λ_bnds)

Loads in the PROSPECT-PRO database of pigments (and other) absorption cross section in leaves, returns a [`LeafOpticalProperties`](@ref) type struct with spectral units attached.

Arguments

- `λ_bnds` an array (with or without a spectral grid unit) that defines the upper and lower limits over which to average the absorption cross sections

Examples

julia> using Unitful                                                               # Need to include Unitful package 
julia> opti = createLeafOpticalStruct((400.0:5:2400)*u"nm");                       # in nm
julia> opti = createLeafOpticalStruct((0.4:0.1:2.4)*u"μm");                        # in μm
julia> opti = CanopyOptics.createLeafOpticalStruct((10000.0:100:25000.0)u"1/cm");  # in wavenumber (cm⁻¹)

createLeafOpticalStruct()
As in createLeafOpticalStruct(λ_bnds) but reads in the in Prospect-PRO database at original resolution (400-2500nm in 1nm steps)

Compute the coefficients of the series expansion of cylinder scattering amplitude.

Equation 24 in Electromagnetic Wave Scattering from Some Vegetation Samples (KARAM, FUNG, AND ANTAR, 1988) http://www2.geog.ucl.ac.uk/~plewis/kuusk/karam.pdf

dielectric(mod::SoilMW, T::FT,f::FT)

Computes the complex dieletric of soil (Ulaby & Long book)

Arguments

• mod an SoilMW type struct (includes sandfrac, clayfrac, water_frac, ρ)
• T Temperature in [⁰K]
• f Frequency in [GHz]

Examples

julia> w = SoilMW(sand_frac=0.2,clay_frac=0.2, water_frac = 0.3, ρ=1.7 )     # Create struct for salty seawater
julia> dielectric(w,283.0,10.0)
53.45306674215052 + 38.068642430090044im

dielectric(mod::LiquidPureWater, T::FT,f::FT)

Computes the complex dieletric of liquid pure walter (Ulaby & Long book)

Arguments

• mod an LiquidSaltWater type struct
• T Temperature in [⁰K]
• f Frequency in [GHz]

Examples

julia> w = CanopyOptics.LiquidPureWater()     # Create struct for salty seawater
julia> CanopyOptics.dielectric(w,283.0,10.0)
53.45306674215052 + 38.068642430090044im

dielectric(mod::LiquidSaltWater, T::FT,f::FT)

Computes the complex dieletric of liquid salty walter (Ulaby & Long book)

Arguments

• mod an LiquidSaltWater type struct, provide Salinity in PSU
• T Temperature in [⁰K]
• f Frequency in [GHz]
• S Salinity in [PSU] comes from the mod LiquidSaltWater struct

Examples

julia> w = CanopyOptics.LiquidSaltWater(S=10.0)     # Create struct for salty seawater
julia> CanopyOptics.dielectric(w,283.0,10.0)
51.79254073931596 + 38.32304044382495im

dielectric(mod::PureIce, T::FT,f::FT)

Computes the complex dieletric of liquid pure walter (Ulaby & Long book)

Arguments

• mod an PureIce type struct
• T Temperature in [⁰K]
• f Frequency in [GHz]

Examples

julia> w = CanopyOptics.PureIce()     # Create struct for salty seawater
julia> CanopyOptics.dielectric(w,283.0,10.0)
53.45306674215052 + 38.068642430090044im

erectophile_leaves(FT=Float64)

Creates a LeafDistribution following a erectophile (mostly vertical) distribution using a Beta distribution

Standard values for θₗ (63.24) and s (18.5) from Bonan https://doi.org/10.1017/9781107339217.003, Table 2.1

3.1.2 in SAATCHI, MCDONALD

Oh et al, 1992 semi-emprical model for rough surface scattering

Equation 3.1.5 in Coherent Effects in Microwave Backscattering Models for Forest Canopies (SAATCHI, MCDONALD) https://www.researchgate.net/publication/3202927Semi-empiricalmodelofthe_ ensemble-averageddifferentialMuellermatrixformicrowavebackscatteringfrombaresoilsurfaces

plagiophile_leaves(FT=Float64)

Creates a LeafDistribution following a plagiophile (mostly 45degrees) distribution using a Beta distribution

Standard values for θₗ (45.0) and s (16.27) from Bonan https://doi.org/10.1017/9781107339217.003, Table 2.1

planophile_leaves(FT=Float64)

Creates a LeafDistribution following a planophile (mostly horizontal) distribution using a Beta distribution

Standard values for θₗ (26.76) and s (18.51) from Bonan https://doi.org/10.1017/9781107339217.003, Table 2.1

prospect(leaf::LeafProspectProProperties{FT},
                optis) where {FT<:AbstractFloat}

Computes leaf optical properties (reflectance and transittance) based on PROSPECT-PRO

Arguments

• leaf LeafProspectProProperties type struct which provides leaf composition
• optis LeafOpticalProperties type struct, which provides absorption cross sections and spectral grid

Examples

julia> opti = createLeafOpticalStruct((400.0:5:2400)*u"nm");
julia> leaf = LeafProspectProProperties{Float64}(Ccab=30.0);
julia> T,R = prospect(leaf,opti);

Calculate scattering cross-section of a finite length cylinder with specified orientation

Calculate bistatic scattering amplitude in the cylinder coordinate

Equations 26, 27 in Electromagnetic Wave Scattering from Some Vegetation Samples (KARAM, FUNG, AND ANTAR, 1988) http://www2.geog.ucl.ac.uk/~plewis/kuusk/karam.pdf

Eq 37 in Shultis and Myneni

spherical_leaves(FT=Float64)

Creates a LeafDistribution following a spherical (distributed as facets on a sphere) distribution using a Beta distribution

Standard values for θₗ (57.3) and s (21.55) from Bonan https://doi.org/10.1017/9781107339217.003, Table 2.1

uniform_leaves(FT=Float64)

Creates a LeafDistribution following a uniform distribution (all angles equally likely)

Convert an input array with Spectral units (or none) to a grid in nm

Calculation of average backscatter cross-section of a finite length cylinder, exact series solution (KARAM, FUNG, AND ANTAR, 1988)

Calculation of average forward scattering amplitudes of a finite length cylinder, exact series solution

Calculate zeta function using bessel functions

Equation 26 in Electromagnetic Wave Scattering from Some Vegetation Samples (KARAM, FUNG, AND ANTAR, 1988) http://www2.geog.ucl.ac.uk/~plewis/kuusk/karam.pdf

Get Beta Distribution parameters using standard tabulated values θₗ,s, Eq. 2.9 and 2.10 in Bonan