2.2.1. Construction of a Dorsiventral Leaf Adjusted Ratio Index

A semi-empirical leaf reflectance model was proposed by Baret et al. [33], and can be expressed as:

$$R = R\_{\mathfrak{s}} + S \exp\left(-\Sigma k\_{\mathrm{i}} \mathbb{C}\_{\mathrm{i}}\right) \tag{1}$$

where *R*<sup>s</sup> is the reflectance of the leaf surface, *S* represents scattering effects of the leaf mesophyll structure, and *k*<sup>i</sup> and *C*<sup>i</sup> are the extinction coefficient and chlorophyll concentration, respectively. *R*<sup>s</sup> and *S* are thought to be the main factors introducing variability between adaxial and abaxial leaf reflectance, as they depend on the differences in the leaf surface and internal mesophyll structure Datt [12]. Based on this model and the principle that there is no absorption at 850 nm by any leaf pigment (i.e., Σ*k*i*C*<sup>i</sup> = 0), Datt [12] proposed an index of (R850 − R710)/(R850 − R680). The index removed *R*s and *S*. Lu et al. [21] extended the wavelengths in the Datt's index to 400–1000 nm, which can also remove *R*s and *S*. The formula of MDATT is:

$$\text{MDAT} = \frac{\left(\mathbf{R}\_{\lambda\_1} - \mathbf{R}\_{\lambda\_2}\right)}{\left(\mathbf{R}\_{\lambda\_1} - \mathbf{R}\_{\lambda\_3}\right)} = \frac{\exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_1)}\mathbf{C}\_{\text{chl}}\right) - \exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_2)}\mathbf{C}\_{\text{chl}}\right)}{\exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_1)}\mathbf{C}\_{\text{chl}}\right) - \exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_3)}\mathbf{C}\_{\text{chl}}\right)}\tag{2}$$

where Cchl is the chlorophyll content and kchl(λ1), kchl(λ2), and kchl(<sup>λ</sup>3) are the specific absorption coefficients for Chl at wavelengths λ1, λ2, and λ3, respectively.

Using the MDATT as a basis, we constructed a dorsiventral leaf adjusted ratio index (DLARI) by substituting the *R*λ<sup>1</sup> term with an additional wavelength (Rλ<sup>4</sup> ) in the denominator:

$$\text{DLARI} = \frac{\left(\mathbf{R}\_{\lambda\_1} - \mathbf{R}\_{\lambda\_2}\right)}{\left(\mathbf{R}\_{\lambda\_3} - \mathbf{R}\_{\lambda\_4}\right)} = \frac{\exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_1)}\mathbf{C}\_{\text{chl}}\right) - \exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_2)}\mathbf{C}\_{\text{chl}}\right)}{\exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_3)}\mathbf{C}\_{\text{chl}}\right) - \exp\left(-\mathbf{K}\_{\text{chl}(\lambda\_4)}\mathbf{C}\_{\text{chl}}\right)}\tag{3}$$

Like the MDATT, the DLARI is also expected to suppress the effects of *R*s and *S*. The efficiency of incorporating an additional band is evaluated in the following sections.
