03. Leaf Radiative Transfer Models

What you will learn

  • What each of the four leaf models simulates, and the one structural difference that actually separates them.

  • Which inputs matter for each.

  • How to run, plot, and scientifically interpret all four side by side.

Concept

A leaf model turns a handful of biochemical/structural traits into a reflectance and transmittance spectrum. All four models here share the same core idea (light absorbed by pigments/water/dry matter, scattered by internal cell-wall/air-space interfaces) but differ in exactly what they add on top of that core:

Model

What it simulates

What makes it different

PROSPECT-D

Reflectance/transmittance from pigments (Cab/Car/Anth), water (EWT), and one lumped dry-matter term (LMA).

The reference broadleaf model.

PROSPECT-PRO

Same physics, but splits LMA into Prot (protein) + CBC (cellulose/lignin).

Only the dry-matter parameterization differs.

Fluspect-B / Fluspect-Cx

PROSPECT-D’s optics plus chlorophyll-fluorescence excitation- emission matrices; Fluspect-Cx additionally adds a photoprotection (Cx) term.

Adds fluorescence – needed wherever solar-induced fluorescence (SIF) matters, e.g. 06. SCOPE.

LIBERTY

Reflectance/transmittance for conifer needles, from explicit cell geometry instead of PROSPECT’s Fresnel-refraction layer.

Not a PROSPECT variant – a structurally different model, built for needle anatomy.

Python tools used

Function

Key arguments

prospect_d()

N, Cab, Car, Anth, Cbrown, EWT, LMA, alpha – see 02. Parameters & Traits.

prospect_pro()

Same as above but LMA replaced by Prot, CBC (pass LMA=0.0 explicitly).

fluspect_b()

Cab, Car, EWT, LMA, Cs, N, fqe, Cx (positional) – returns .MbI/.MbII (211x351 excitation-emission matrices, PSI/PSII).

fluspect_cx()

Adds Prot, CBC, Anth on top of fluspect_b’s arguments – returns a single combined .Mb (211x351) instead of separate PSI/PSII.

liberty()

cell_d, inter_c, baseline_abs, leaf_thick, albino_abs, Cab, EWT, lign_cell, Nitrogen – see 02. Parameters & Traits.

Run the example

from toolsrtm import prospect_d, prospect_pro, liberty, fluspect_b, fluspect_cx

pro_d = prospect_d(N=1.5, Cab=40, Car=8, Anth=1, Cbrown=0, EWT=0.01, LMA=0.009, alpha=40)
pro_pro = prospect_pro(N=1.5, Cab=40, Car=8, Anth=1, Cbrown=0, EWT=0.01, LMA=0.0,
                        alpha=40, Prot=0.002, CBC=0.007)
lib = liberty(cell_d=40, inter_c=0.045, baseline_abs=0.0006, leaf_thick=1.6,
              albino_abs=0, Cab=40, EWT=0.01, lign_cell=2, Nitrogen=1)
flu_b = fluspect_b(N=1.5, Cab=40, Car=8, Anth=1, EWT=0.01, LMA=0.009, Cs=0, fqe=0.01, Cx=0)
flu_cx = fluspect_cx(N=1.5, Cab=40, Car=8, Anth=1, EWT=0.01, LMA=0.009, Cs=0,
                      fqe=0.01, Cx=0.3, Prot=0.0, CBC=0.0)

print("PROSPECT-D  reflectance at 550nm:", pro_d.refl[150])
print("PROSPECT-PRO reflectance at 550nm:", pro_pro.refl[150])
print("LIBERTY     reflectance at 550nm:", lib.refl[150])
print("Fluspect-B  reflectance at 550nm:", flu_b.refl[150])
print("Fluspect-Cx reflectance at 550nm:", flu_cx.refl[150])
print("Fluspect-B fluorescence matrix (MbI) shape:", flu_b.MbI.shape)

import matplotlib.pyplot as plt
for name, r, c in [("PROSPECT-D", pro_d, "#0072B2"), ("PROSPECT-PRO", pro_pro, "#D55E00"),
                    ("LIBERTY", lib, "#009E73")]:
    plt.plot(r.lambda_, r.refl, color=c, label=name)
plt.legend(); plt.xlabel("Wavelength (nm)"); plt.ylabel("Reflectance")

Result

Printed output (exact, deterministic):

PROSPECT-D  reflectance at 550nm: 0.13359835005159199
PROSPECT-PRO reflectance at 550nm: 0.1340437450891865
LIBERTY     reflectance at 550nm: 0.062101770920629594
Fluspect-B  reflectance at 550nm: 0.15995957791874202
Fluspect-Cx reflectance at 550nm: 0.14156441320107857
Fluspect-B fluorescence matrix (MbI) shape: (211, 351)
PROSPECT-D vs PROSPECT-PRO vs LIBERTY leaf reflectance and transmittance, real output of the code above

Real output: PROSPECT-D and PROSPECT-PRO overlap almost everywhere (same underlying physics, same total dry matter – LMA=0.009 is equivalent to Prot=0.002 + CBC=0.007); LIBERTY (needle anatomy) is visibly different in the NIR plateau and SWIR.

Fluspect-B leaf optics and fluorescence excitation-emission matrix, real output

Real output: Fluspect-B’s reflectance/transmittance (left) and its backward chlorophyll-fluorescence excitation-emission matrix (right, MbI) – the two characteristic emission peaks near 685nm (PSII) and 740nm (PSI) are visible at both the blue (~440nm) and red (~660-680nm) chlorophyll excitation bands. No other leaf model on this page produces this second plot at all.

LIBERTY conifer-needle leaf reflectance and 1-transmittance, real output

Real output: LIBERTY’s conifer-needle optics – flatter NIR plateau and different SWIR absorption shape than broadleaf PROSPECT, reflecting the needle-specific anatomy the model targets.

Interpretation

PROSPECT-D and PROSPECT-PRO track each other closely everywhere (0.1336 vs. 0.1340 at 550nm) – expected, since LMA=0.009 and Prot=0.002 + CBC=0.007 represent the same total dry-matter mass through the same underlying absorption physics, just split two different ways. LIBERTY sits well below both at 550nm (0.062) and diverges further in the NIR/SWIR (see the figure) – a real anatomical difference, not a bug: conifer needles pack mesophyll cells more densely than broadleaf tissue, giving less internal air-space scattering and therefore a flatter, lower NIR plateau. Fluspect-B is close to but not identical to PROSPECT-D (0.160 vs. 0.134 at 550nm, within ~1% of each other by 800nm in the NIR plateau) – the two share the same absorption physics but not byte-identical coefficient tables, so expect small, mostly visible-region differences, not an exact match. Fluspect-Cx’s extra Cx=0.3 term (partial photoprotection) shifts its 550nm value between Fluspect-B’s and PROSPECT-D’s, consistent with a small absorption change rather than a structural one.

Try it yourself

  • Set Cx=1.0 (full photoprotection) on fluspect_cx and compare against Cx=0.

  • Swap lib’s inter_c (intercellular air-space fraction) from 0.045 to 0.06 and see how much closer the NIR plateau moves toward PROSPECT-D’s.

  • Compute flu_b.MbI.sum() at a few different fqe values and check it scales linearly (it should – fqe is a quantum efficiency, a direct multiplier on emitted fluorescence).

Common mistakes

  • fluspect_b/fluspect_cx’s arguments are largely positional – check the signature before assuming keyword order matches prospect_d’s.

  • fluspect_b returns separate .MbI/.MbII (PSI/PSII); fluspect_cx returns one combined .Mb instead – not the same attribute name.

  • LIBERTY’s inputs are real cell geometry (micrometers, fractions), not PROSPECT pigment concentrations – copying a PROSPECT trait value into LIBERTY’s similarly-named argument is not meaningful.

Next

04. Canopy Radiative Transfer Models – turning any of these leaf spectra into a canopy-level reflectance, and what changes between fourSAIL, fourSAIL2, and INFORM.

Using R? -> ToolsRTM Tutorial 02: From Leaf to Canopy Reflectance