Binning spectra#

Module crt1d.spectra provides some tools for working with spectra. By binning or smearing spectra, we can use spectra together that were originally on different grids. Also, we can decrease canopy RT computational time by reducing spectral resolution.

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

import crt1d as crt

Average optical properties#

Below, we can see that when we compute the average reflectance, over certain regions the above doesn’t matter much (PAR/visible). In the NIR, however, there is a strong preference for smaller wavelengths, which overall weights leaf reflectance towards higher values.

In the below, 'uniform' corresponds to standard smearing, with no solar weighting.

First, we calculate average values using the original spectrum, loaded above.

# On the original leaf reflectance spectrum
boundss = [(0.4, 0.7), (0.7, 1.0), (1.0, 2.5), (0.3, 2.5)]
lights = ["planck", "uniform"]

for bounds in boundss:
    print(bounds)
    for light in lights:
        ybar = crt.spectra.avg_optical_prop(
            ds0_l.rl, bounds, x=ds0_l.wl, light=light
        )
        print(f" {light}: {ybar:.4g}")

(0.4, 0.7)
 planck: 0.1316
 uniform: 0.1317
(0.7, 1.0)
 planck: 0.4641
 uniform: 0.4812
(1.0, 2.5)
 planck: 0.3956
 uniform: 0.3017
(0.3, 2.5)
 planck: 0.2744
 uniform: 0.2944

Now, we use the spectrum smeared above.

# On a smeared/binned leaf reflectance spectrum
ds2 = crt.spectra.smear(ds0, bins2)
data = (
    ds2.sel(wl=ds1_l.wl.values, method="nearest").I_dr +
    ds2.sel(wl=ds1_l.wl.values, method="nearest").I_df
)
lights = ["planck", "uniform", data]

for bounds in boundss:
    print(bounds)
    for light in lights:
        ybar = crt.spectra.avg_optical_prop(
            ds1_l.rl, bounds, xe=ds1_l.wle, light=light
        )
        if isinstance(light, str):
            print(f" {light}: {ybar:.4g}")
        else:
            print(f" data: {ybar:.4g}")

(0.4, 0.7)
 planck: 0.1463
 uniform: 0.1492
 data: 0.1581
(0.7, 1.0)
 planck: 0.4401
 uniform: 0.4641
 data: 0.4382
(1.0, 2.5)
 planck: 0.3953
 uniform: 0.3016
 data: 0.3849
(0.3, 2.5)
 planck: 0.2754
 uniform: 0.2943
 data: 0.3197

👆 Notice that the values for 'uniform' and 'planck' are similar (though not identical) to the calculations on the pre-smeared spectrum.

Planck function#

Planck radiance is one of the light options can be used to weight values when smearing the spectra with the method='avg_optical_prop' option. This is important for albedo, for example, because albedo in some waveband (such as visible or shortwave) depends on both the albedo spectrum and the spectrum of the illuminating light.

wl_um = np.linspace(0.3, 2.6, 200)
fig, ax = plt.subplots()
for T_K in [4000, 5000, 5800, 6000]:
    ax.plot(wl_um, crt.spectra.l_wl_planck(T_K, wl_um), label=T_K)
ax.set(
    xlabel=r"Wavelength $\lambda$ [μm]",
    ylabel=r"Spectral radiance $L(\lambda)$ [W sr$^{-1}$ m$^{-2}$ m$^{-1}$]",
)
ax.legend(title="Blackbody temperature (K)");

../_images/6988f8e3f9f02406b38462460eb7872a1bec1ef2885c0209eef1c3a283838ec3.png

Binning spectra#

Solar#

Leaf/soil optical properties#

Average optical properties#

Planck function#