#### 3.1. VI Data Quality

[15] The quality of VI (EVI/NDVI) data in each pixel can be assessed using the accompanying 16-bit quality flags, in both 1 × 1 km^{2} as well as the 0.05° × 0.05° products. Sets of bits, from these 16 bits, are assigned to flags pertaining to clouds and aerosols (details can be found in work by *Samanta et al.* [2010, 2011a, 2011b] and *Xu et al.* [2011]). Each 1 × 1 km^{2}16-day composite VI value is considered valid when (a) VI data is produced—“MODLAND_QA” equals 0 (good quality) or 1 (check other QA), (b) VI Usefulness is between 0 and 11, (c) Clouds are absent—“Adjacent cloud detected” (0), “Mixed Clouds” (0) and “Possible shadow” (0), and (d) Aerosol content is low or average—“Aerosol Quantity” (1 or 2). Note that “MODLAND_QA” checks whether VI is produced or not, and if produced, its quality is good or whether other quality flags should also be checked. Besides, VI Usefulness Indices between 0 to 11 essentially include all VI data. Thus, these two conditions serve as additional checks. Each 0.05° × 0.05° 16-day VI pixel is considered valid when (a) VI data is produced—“MODLAND_QA” equals 0 (good quality) or 1 (check other QA), (b) VI Usefulness is between 0 and 11, (c) Clouds are absent—“Adjacent cloud detected” (0) and “Mixed Clouds” (0), and (d) Aerosol content is low or average—“Aerosol Quantity” (1 or 2). Here, the utility of “MODLAND_QA” and VI Usefulness flags is the same as in the case of 1 × 1 km^{2} VI validity.

#### 3.2. LAI Data Quality

[16] The quality of LAI data in each 1 × 1 km^{2}8-day pixel can be assessed using two accompanying 8-bit quality flags, FparLai_QC and FparExtra_QC (details can be found in work by*Samanta et al.* [2011b]). The validity of LAI was determined through a two-stage process: (1) a 1 × 1 km^{2}8-day LAI pixel was considered valid when (a) data is of good quality—“SCF_QC” equals 0 (main algorithm without saturation) or 1 (main algorithm with saturation), (b) Clouds are absent—“CloudState” (0), “Cirrus” (0), “MODAGAGG_Internal_CloudMask” (0) and “MODAGAGG_Cloud_Shadow” (0). (2) As the 8-day LAI aerosol flag does not distinguish between average and high aerosol loadings nor reports climatology aerosols, valid 8-day values are averaged to 16-day LAI whose validity was further determined using MOD13A2 cloud and aerosol flags: (a) VI data is produced-“MODLAND_QA” equals 0 (good quality) or 1 (check other QA), (b) VI Usefulness is between 0 and 11, (c) Clouds are absent—“Adjacent cloud detected” (0), “Mixed Clouds” (0) and “Possible shadow” (0), and (d) Aerosol content is low or average-“Aerosol Quantity” (1 or 2). Valid 1 × 1 km^{2}16-day values were averaged to obtain monthly LAI. Finally, valid 1 × 1 km^{2} monthly LAI values are aggregated to 8 × 8 km^{2} spatial resolution. This 8 × 8 km^{2} monthly LAI data set spanning February 2000–December 2009 was used in this study.

[17] In order to test the effectiveness of the quality flags, we have analyzed the seasonal time series of surface reflectances and vegetation indices (VI) of both uncorrupted (clean) and corrupted (contaminated) data (Figure S1). Interaction of photons with dense Amazonian forests is characterized by strong scattering in near-infrared (NIR), and equally strong absorption in the shorter red and blue wavelengths. The NIR reflectance of these forests is an order of magnitude greater than the reflectance at red (blue) wavelengths. On the other hand, atmospheric influences scatter more strongly in the shorter red/blue wavelengths. Thus, NIR reflectance is much less affected by atmospheric effects in comparison to red (blue) reflectance, which is shown inFigure S1a. Contaminated red reflectances are artificially higher-almost double in magnitude in comparison to clean values (Figure S1a). The difference between clean and contaminated red reflectance remains steady during the course of the year, which indicates lack of bias due to seasonal changes in atmospheric effects, such as high aerosol loads in the dry season from biomass burning (e.g., as discussed by *Samanta et al.* [2010]). These changes in surface reflectances translate into lower estimates of surface greenness or VIs. NDVI reduces by about 24% and EVI by about 18%, especially during the dry season (Figure S1b). Moreover, *Myneni et al.* [2007]have reported that residual atmospheric effects reduce leaf area index (LAI) estimates by about 5% during the dry season. These results show that seasonal variations in atmosphere-corrupted data are inconsistent with those observed with clean data. Furthermore, any remaining residual atmospheric influences that would reduce seasonal changes in measured greenness are eliminated by ensuring that the observed increase in VIs is greater than the errors in VIs (as mentioned in the caption ofFigure 6). Thus, we conclude that the seasonal changes in vegetation greenness reported in the manuscript are not an artifact of residual atmospheric effects in surface reflectances.

#### 3.4. Sensitivity of BRF to Variation in LAI and Leaf Optics

[19] The theory of spectral invariants [*Knyazikhin et al.*, 2010] was used to examine the sensitivity of the canopy near-infrared (NIR)*BRF* to LAI and leaf optical properties under saturation conditions. If the impact of canopy background on canopy reflectance is negligible as in the case of dense Amazonian forests, the spectral *BRF* can be approximated as [*Knyazikhin et al.*, 2010; *Schull et al.*, 2010; *Huang et al.*, 2008]:

Here *ρ* is the directional escape probability, i.e., probability that a photon scattered by a leaf will escape the vegetation medium in a given direction Ω. It also can be interpreted as the probability of seeing a gap in the direction Ω from a leaf surface [*Stenberg*, 2007]. Spherical integration of *ρ* over all directions gives the total escape probability, (1−*p*), where *p* is the recollision probability, i.e., the probability that a photon scattered by a leaf will interact with another leaf in the canopy again. Further, *i*_{0}, the probability of initial collision, or canopy interceptance, is the portion of incoming photons that collide with leaves for the first time. It depends on the direction of radiation incident on the vegetation canopy. Finally, *ω*_{λ} is the leaf albedo, which is the portion of the radiation incident on the surface of an individual leaf that the leaf transmits or reflects. In the present approach, this is the only variable that is dependent on the wavelength. It allows the parameterization of *BRF* in terms of leaf albedo rather than wavelength. Therefore wavelength dependence will be suppressed in further notations.

[20] Two separate factors are shown in equation (5), each exhibiting a different sensitivity to canopy structure and leaf optics. The wavelength independent ratio *P* = *ρ*/(1 − *p*) gives the portion of gaps as seen from a leaf surface in a given direction Ω. This variable is sensitive to canopy geometrical properties such as spatial distribution of trees, ground cover, crown shape, size, and transparency [*Schull et al.*, 2010]. In the case of Amazon forests, changes in canopy structure over monthly time-scales are assumed negligible. At high LAI values, the canopy interceptance*i*_{0} varies insignificantly with LAI due to the saturation. Under such conditions, the observed variation in NIR *BRF* is much stronger than corresponding variation in *K* = *Pi*_{0}, typically 2–3%, and thus changes in canopy structure alone cannot explain the observations (cf. Section 3.4.1).

[21] The second factor is the canopy scattering coefficient, *W*_{λ} = *ω*_{λ} (1 − *p*) / (1 − *pω*_{λ}) [*Smolander and Stenberg*, 2005], which depends on both canopy structure and leaf optics. It increases with the leaf albedo; the more the leaves scatter, the brighter the canopy is. Variations in LAI, however, trigger an opposite tendency. As the recollision probability increases with LAI [*Knyazikhin et al.*, 1998; *Smolander and Stenberg*, 2005; *Rautiainen et al.*, 2009], an increase in LAI results in more photon-canopy interactions and consequently a higher chance for photon to be absorbed. This mechanism makes the canopy appear darker. The effect of multiple scattering is described by the denominator in the equation for*W*_{λ} [*Huang et al.*, 2008], which in turn is fully determined by the product *κ* = *pω*_{λ}. An increase in *κ* not only enhances the effect of multiple scattering but also changes the sensitivity of the *BRF*: the closer its value is to unity, the stronger the response of canopy *BRF* to variations in canopy structure and leaf optics. If variation in *K* is negligible, changes in *BRF* can be reduced to examining variations in the scattering coefficient.

[22] The vegetation canopy is parameterized in terms of the recollision probability, 0 ≤ *p* ≤ 1, leaf albedo, 0 ≤ *ω* ≤ 1, and the sensitivity parameter, *κ* = *pω* ≤ min(*ω*, *p*). Let the sensitivity of *BRF* to canopy structure and leaf optics at time *t* and *t*_{1} = *t* + Δ*t* be *κ* and *κ*_{1} = *κ* + *δκ*, *δκ* ≥ 0, respectively. Note that *κ* and *κ*_{1} do not uniquely specify the recollision probabilities and leaf albedos since various combinations can result in the same values of the sensitivity parameter, which impact canopy reflective properties differently. To characterize the contribution of LAI to a change in the sensitivity parameter from by *κ* to *κ*+*δκ*, the following impact function is introduced:

In general, *k* varies between −∞ and +∞. Values of *k* greater than 1 imply a decrease in leaf albedo, i.e., *δω*/*ω* < 0. Variations in LAI and leaf optics make the vegetation darker in this case. On the other hand, a decrease in canopy structure, *δp*/*p* < 0, involves a negative value of the parameter *k*. In this case, changes in *p* and *ω* lead to brightening of the vegetated surface. This study will focus on the case when both LAI and leaf albedo increase, i.e., *k* varies between 0 (no change in LAI) and 1 (no change in leaf albedo). Such variations trigger competing processes: changes in LAI tend to darken the vegetation while variations in the leaf albedo suppress it. It should be emphasized, however, that this mechanism refers to the scattering coefficient *W*_{λ} and is applicable to *BRF* = *KW*_{λ} (cf. equation (5)) if variations in *K* are negligible. In general, *K* increases with LAI and therefore compensates for a decrease in the canopy scattering coefficient. This lowers the darkening effect and even can result in an increase in the canopy *BRF* (cf. Sections 3.4.2 and 3.4.3).

[23] Under saturation conditions (i.e., *δBRF*/*BRF* ≫ *δK*/*K*), the impact function (*k*), sensitivity parameter (*κ*), leaf albedo at time *t* (*ω*), variations *δBRF*/*BRF*, *δK*/*K* and *δκ*/*κ* are related as (cf. Section 3.4.1):

where

Here *β* characterizes the amplitude of the variability in reflectance. Since the goal of this study is to examine contributions of LAI and leaf albedo to large positive changes in the canopy *BRF* under saturation conditions, i.e., *δBRF/BRF* ≫ *δK/K*, this analysis is restricted to the case when *β* > 0. It should be noted that in general, *δK/K* is proportional to the impact function *k* (cf. Section 3.4.1). Under saturation conditions, this term can be neglected, and thus, equation (7) quantifies the impact of canopy structure on the *BRF* when both LAI and *ω* vary.

[24] If *k*(*ω*) = 1 (*δκ*/*κ* = *δp*/*p*), then (*ω*−*κ*)*θ*/*ω* = 1. This relationship holds true if and only if *β* ≤ 0 (cf. Section 3.4.1). It means that LAI alone cannot explain positive changes in canopy *BRF* under the saturation condition.

[25] If *k*(*ω*) = 0 (*δκ*/*κ* = *δω*/*ω*), then either *ω* = *κ* or *θ* = 0. The former corresponds to an extreme and unrealistic case when *p* = 1. It means that photons cannot escape the vegetation canopy and therefore *BRF* = 0. The latter implies that variations in canopy *BRF* are proportional to *δω*/*ω*, i.e.,

One can see that the closer the value of the sensitivity parameter is to unity, the stronger the response of the *BRF* to leaf albedo. Changes in leaf optics alone can explain a rather large range of variation in canopy reflectance under the saturation conditions.

[26] If 0 < *k*(*ω*) < 1 (i.e., *δp*/*p* > 0 and *δω*/*ω* > 0), the contribution of LAI to the *BRF* is given by equation (7). It should be emphasized that this equation refers to the case when both LAI and the leaf albedo are changing. Figure 4 illustrates the LAI versus leaf albedo “competing process” under saturation conditions, which results in the observed *BRF* change by 23% (*δBRF*/*BRF* = 0.23 and *δBRF*/*BRF* ≫ *δK*/*K* = 0.01, cf. Sections 3.4.2 and 3.4.3).

[27] It follows from equation (5) that

We parameterize the relative variation in *BRF* in terms of the sensitivity parameter, *κ*, its variation, *δκ*/*κ*, and the impact function, *k*, by substituting *p* = *κ*/*ω*, *δp*/*p* = *kδκ*/*κ* and *δω*/*ω* = (1−*k*)*δκ*/*κ* into equation (9). Solving the resulting equation for *k* yields equation (7).

[28] Case *k*(*ω*) = 1: Letting *δω*/*ω* = 0 in equation (9) and taking into account that *p*(1 − *ω*)/(1 − *pω*)(1 − *p*) decreases with *ω*, one gets

Thus, a positive response of *BRF* to a positive variation in the recollision probability can be achieved if the parameter *β* defined by equation (7a) is negative.

##### 3.4.2. Assumptions

[29] Since our goal is the qualitative description of the sensitivity of *BRF* to LAI and leaf albedo under the saturation conditions, we use a simple canopy model to specify the relationship between *δp*/*p*, *δ*LAI/LAI and *δK*/*K*. We idealize the vegetation canopy as a spatially homogeneous layer filled with small planar elements of infinitesimally small sizes. All organs other than green leaves are ignored. For such a structurally simple uniform canopy, *Stenberg* [2007] found an analytical formula that relates the recollision probability, *p*, and canopy interceptance, *i*_{0,d}, under diffuse illumination condition, i.e.,

Analyses of LAI-2000 data suggest the following relationship between*i*_{0,d} and *LAI* [*Rautiainen et al.*, 2009]

where the coefficient *k*_{CAN} = 0.81 was found to be almost insensitive to stand age, tree species or growing conditions. Finally, the canopy interceptance, *i*_{0}, can be estimated as *i*_{0} = 1 − exp(−*G* ⋅ LAI/*μ*_{0}) where *G* and *μ*_{0} are the geometry factor [*Ross*, 1981] and cosine of the solar zenith angle (SZA), respectively. It follows from this equation and equation (11) that

where *α* = *G*/(*k*_{CAN}*μ*_{0}). For simplicity, the geometry factor *G* is set to *k*_{CAN}*μ*_{0} = 0.81*cos(30) = 0.81*0.87 = 0.70 (mean SZA = 30°, std. = 5°–6° (20%)). The mean SZA for the dry season is about 30° and varies by about 5°–6° during this time, as reported in the MODIS VI data. Therefore, the small changes in SZA are not likely to induce large changes in *μ*_{0}, and *G*. Under the above assumptions, LAI is the only variable that fully describes canopy structure. The recollision probability (*p*) is an increasing function of LAI.

[30] We neglect angular dependence of the directional escape probability by replacing this term by its hemispherically integrated counterpart, i.e., *ρ*(Ω) = *r*/*π* where *r* is the probability that a scattered photon will escape the vegetation canopy through its upper boundary. Neglecting radiation transmitted through a very dense canopy, we get *ρ*(Ω) = (1 − *p*)/*π*. The relative portion of gaps as seen from a leaf surface, *P* = *ρ*/(1 − *p*), is approximated by a constant and thus *δK*/*K* = *δP*/*P* + *δi*_{0}/*i*_{0} ≈ *δi*_{0}/*i*_{0}. Note that this approximation is accurate for the uniform canopies with horizontally oriented leaves since such canopies transmit and reflect radiation diffusely and approximate for other canopies.

##### 3.4.3. Properties of the Impact Function

[31] The impact function *k* requires specification of the parameter *θ*, which includes the term *δBRF*/*BRF*−*δK*/*K* that appears in *β*. Our structurally simple canopy suggests negligible contribution of *δK*/*K* ≈ *δi*_{0}/*i*_{0} under the saturation conditions. For example, a change in LAI from 5 to 6 results in *δi*_{0}/*i*_{0} ≈ 1% which is significantly below the observed variation, *δBRF*/*BRF* ≈ 23%, in NIR surface reflectance. Although a more realistic canopy model can result in a different value of the relative variation in *K*, its use would not change our qualitative results as long as *δBRF*/*BRF* ≫ *δK*/*K*. Figure 5 and the following properties of the impact function provide the necessary justification.

[32] If *θ* ≥ 0, the impact function *k* has the following properties (Figure 5).

[33] D. *If θ > *1, the equation *k*(*ω*) = 1 has a unique solution given by *ω** = *κψ* where

The function *ψ* increases with *β* and decreases with *κ*.

[34] If *θ* ≤ 0, its properties can be formulated in a similar manner (see Figure 5). Let *θ* > 0, i.e., *β* < 1/(1 − *κ*). As one can see from Figure 5, interpretation of variation in the *BRF* depends on the location of the asymptote and the root of the equation *k*(*ω*) = 1 relative to unity. The following cases are possible.

[35] Case 1: 0 < *θ* < 1, i.e., *β* > *κ*/(1 − *κ*). The asymptote is below unity. If *ω* ≤ *κ*, the impact of canopy structure is negative (i.e., LAI should decrease in order to achieve a given variation in *BRF*). If *ω* > *κ*, both the canopy structure and leaf optics have a positive impact. If *θ* tends to zero, the impact of canopy structure becomes negligible.

[36] Case 2: *θ* ≥ 1, i.e., *β* ≤ *κ*/(1 − *κ*). The asymptote is above unity. The equation *k*(*ω*) = 1 has a solution given by *ω** = *κψ*. Since *ψ* increases with *β*, the solution is above unity if *β* > 0; is equal to 1 if *β* = 0 and approaches to *κ* if *β* tends to −∞. If *κ* tends to unity, the solution tends to unity, resulting in a jump from *k* = 0 to 1 at *ω* = *κ*. Thus, if *ω* ≤ *κ*, the impact of canopy structure is negative. If *κ* < *ω* ≤ *ω**, both structure and leaf optics positively contribute to variation in *BRF*. If *ω* > *ω**, the impact of structure is positive and leaf optics is negative.

[37] To summarize, a small variation in the parameter *β* does not change qualitatively the behavior of the impact function. Under saturation conditions, i.e., *δBRF*/*BRF* ≫ *δK*/*K*, and the term *δK*/*K* can be neglected.