Spectra

With the accurate geometry described in the previous section along with the assumption of identical brdf shapes with wavelength, a ray tree can be generated. To convert this to an intensity signal the elements need to be “coloured in” with accurate reflectance and transmittance spectra.

There have been many campaigns to collect element reflectance and transmittance spectra (for example BORREAS (Sellers et al. 1997) and OTTER (Peterson and Waring 1994)) and libraries

of different species are readily available (Hosgood et al. 1994). These tend to be hemispherically averaged values, ignoring any directional effects, leaving the user no choice but to assume Lamber- tian behaviour. Whilst there have been some studies of directional reflectance (Grant et al. 1993) there are no libraries readily available and so they are not widely used.

The measurement of reflectance and transmittance is typically carried out with an integrating sphere such as the Licor LI-1800 (LI-COR 1988). These have a sphere with a reflective coating to collect hemispherically reflected light, containing a source illuminating an area (of about 1cm2₎

with a detector placed either behind the target to measure transmittance or in the wall of the sphere to measure hemispherical reflectance. This calculation assumes that all light is incident

upon the target material, requiring a sample that fills the 1cm2 _{window; easy enough for broad}

leaves and bark but not for needle leaves. Some investigators cram enough needles into the window, ensuring there are no gaps by using multiple layers. This will increase measured reflectance through multiple scattering and drastically decrease apparent transmittance. Otherwise a single layer is carefully laid out, correcting for any gaps by repeating the transmission measurement with all needles painted matte black (Daughtry et al. 1989).

There have been few attempts to model element optical properties compared to the number of canopy models (Liang 2004), perhaps due to the relative ease of collecting real element reflectance data. However, models are required to invert element biophysical properties from remote sensing signals.

Leaves The earliest attempts to model leaf optical properties treated them as a semi-infinite

parallel plate of cells bounded by air above and below (Allen et al. 1969). Light undergoes multiple scattering between the plate’s bounds so that the reflectance and transmittance could take more into account than pigments alone. This was extended to multiple layers of leaf cells with air gaps between to better represent real leaf structure (Allen et al. 1970a); reflectance and transmittance depend upon pigment concentration, the number of cell layers and their refractive index.

The idea was extended by Jacquemoud and Baret (1990) to take illumination angle into account to produce the popular PROSPECT model. This has been modified over the years to allow

modelling of leaves in all states of health (Jacquemoud et al. 1995) and is seen as the state of the art, being by far the most widely used (Liang 2004). The modified version is driven by five parameters; the number of layers, chlorophyll concentration, water content, protein content and a “lignin and cellulose” parameter. These parameters can be adjusted to represent the reflectance and transmittance of many types of leaves and attempts have been made to invert leaf biochemistry from spectral canopy reflectance (Zarco-Tejada et al. 2004), although the accuracy has been low except for a limited set of conditions (Liang 2004).

Figure 6 shows an example of a spectrum created from PROSPECT compared to a measured spectrum of white fir collected in the Sierra Nevada mountains (July 2008). The model has captured the main features, although PROSPECT is optimised for broad leaves which have slightly different reflectance values from the needle leaves shown here.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 250 500 750 1000 1250 1500 1750 2000 2250 2500 Reflectance Wavelength (nm) Prospect Real data

Figure 6: Comparison of real white fir needle leaf spectra and a two layered PROSPECT leaf

The parallel plate model’s assumption of semi-infinite layers is fine for broad leaves (where the width is much greater than thickness) but does not hold for needle leaves. In addition the cellular structure of needles is slightly different than for broad leaves (spherical cells (Dawson et al. 1998) as opposed to rhomboids (Govaerts et al. 1996)). The LIBERTY model (Dawson et al. 1998) was created to try to address some of these issues. It used a modified parallel plate where the upper boundary is replaced by a set of Lambertian spheres (representing cells) with multiple scattering between these spheres and a plane below. The finite horizontal extent of a needle (compared to its thickness) was not taken into account. It has been suggested that this can be used to invert leaf biochemistry in the same way as PROSPECT (Dawson et al. 1999).

Other methods for modelling have been proposed, including Markov chain (Maier et al. 1999), turbid medium (Richter and Fukshansky 1996) and Monte Carlo ray tracing (Govaerts et al. 1996). As they are harder to parametrise or far more computationally expensive they have not achieved the same popularity as parallel plate models (Liang 2004). They do have the advantage of being able to take cell level heterogeneity into account, a feature the parallel plate model cannot. These models may then be better for examining the angular dependence of leaf spectra, particularly Monte Carlo ray tracing (if an explicit cell model can be generated) although the author is not aware of any angular comparisons with parallel plate models.

Bark There has been far less interest in understanding the reflectance of bark; leaves being the

main energy and chemical exchange organs of a plant. As far as the author is aware there have been no attempts to create predictive bark reflectance models, other than psycho-physical attempts for purely artistic use (Dana et al. 1999). The field data libraries mentioned in the previous section also contain spectra for wood and bark and these will have to suffice.

It is unclear how the reflectance will change with viewer and illumination angle, or whether coherent backscatter will be make a noticeable contribution.

Soil Soil reflectance is of interest for ecology, agriculture and hydrology where the type, grain size, moisture level and organic content are needed by models (Liang 2004). Models have been created in order to determine soil properties from remotely sensed data. A comprehensive review is available in (Liang 2004), chapter 4 and as such an inversion will not be attempted in this thesis, the review will be kept brief, covering only those issues relevant to forests (for which they form the lower bounding layer) and lidar.

One popular approach is the solution of Chandrasekhar’s (Chandrasekhar 1960) radiative trans- fer equations (Hapke 1981). This treats the soil as a turbid medium of small particles and, just like canopy models, various modifications are needed to take into account all effects, particularly self shadowing (Jacquemoud et al. 1992). For these models, soil grain size, refractive index, water con- tent and organic concentration are the driving parameters. Unlike vegetation canopies, coherent backscatter is not negligible (Hapke et al. 1996) and so the hotspot reflectance (such as measured

by a lidar) may be higher than predicted from the hemispherical average.

More geometrically explicit models have been developed to account for self shadowing in a physical way. These use much the same techniques as geometric canopy models (Ni et al. 1999) with the proportions of shadow and direct sunlit material controlling brdf (Ciernewski 1999). Unlike canopy models the geometric primitives (typically spheres or ellipsoids) are not filled with turbid media but are either opaque or characterised by a refractive index; in addition grains are generally evenly spaced on grids. These models are harder to invert but show promise for representing observed soil brdfs.

Like vegetation there are libraries of soil reflectance values (Stoner et al. 1980). It has been found that these spectra cluster into groups and can be explained as a mixture of five generic examples or “soil vectors” (Price 1990). Any deviations from these were assumed to be due to measurement error and detector noise (these vectors could account for 99.6% of observed variance). These vectors have been used to “colour in” soil in computer models (Disney et al. 2006).