Global remote sensing of water-chlorophyll ratio in terrestrial plant leaves.

I evaluated the use of global remote sensing techniques for estimating plant leaf chlorophyll a + b (C(ab); μg cm(-2)) and water (C(w); mg cm(-2)) concentrations as well as the ratio of C(w)/C(ab) with the PROSAIL model under possible distributions for leaf and soil spectra, leaf area index (LAI), canopy geometric structure, and leaf size. First, I estimated LAI from the normalized difference vegetation index. I found that, at LAI values <2, C(ab), C(w), and C(w)/C(ab) could not be reliably estimated. At LAI values >2, C(ab) and C(w) could be estimated for only restricted ranges of the canopy structure; however, the ratio of C(w)/C(ab) could be reliably estimated for a variety of possible canopy structures with coefficients of determination (R(2)) ranging from 0.56 to 0.90. The remote estimation of the C(w)/C(ab) ratio from satellites offers information on plant condition at a global scale.

Introduction

Leaf chlorophyll a + b (Cab; μg cm−2), dry matter (Cm; mg cm−2), and water (Cw; mg cm−2) concentrations provide information on plant physiological status and ecosystem functioning (e.g., terrestrial heat, water, and CO2 balances) (Zarco-Tejada et al. 2003). Nevertheless, global remote estimates of vegetation status mainly focus on leaf area index (LAI; Garrigues et al. 2008), fraction of absorbed photosynthetically active radiation (FAPAR; Running et al. 2004), phenology (Zhang et al. 2006), leaf clumping (Chen et al. 2005), and vegetation height (Simard et al. 2011).

Site-specific studies have clarified the relationships between plant canopy spectral reflectance and Cab (Zarco-Tejada et al. 2004; Gitelson et al. 2005; Darvishzadeh et al. 2012; Si et al. 2012), Cm, (Fourty and Baret 1997) and Cw (Bowyer and Danson 2004; De Santis et al. 2006; Zarco-Tejada et al. 2003). However, global or regional relationships between these factors are not clearly understood because other characteristics of the plant canopy impact those relationships. In this note, I evaluated the use of global remote sensing techniques for estimating Cab, Cm, Cw, and the Cw/Cab ratio using the PROSAIL model (Jacquemoud et al. 2009) at varying possible distributions of leaf and soil spectra, LAI, canopy geometric structure, and leaf size.

Materials and Methods

I used the PROSAIL model, which is a combination of the SAIL (Verhoef 1984) and PROSPECT (Jacquemoud and Baret 1990) models, for calculating the relationships between the top-of-the-atmosphere (TOA) canopy spectral reflectance and Cab, Cm, Cw, and Cw/Cab. The input parameters of the PROSAIL model are listed in Table 1, and I noted TOA canopy spectral reflectance from the model outputs.

Table 1

Input parameters for the PROSAIL model

	Unit	Value/function
ln(Cab)	μg cm−2	N(3.79, 0.352)*
ln(Cm)	mg cm−2	N(1.57, 0.422)*
ln(Cw)	mg cm−2	N(2.32, 0.472)*
The coefficient of correlation between ln(Cab) and ln(Cm)	–	0.56
The coefficient of correlation between ln(Cw) and ln(Cab) or ln(Cm)	–	0
The parameter characterizing the leaf mesophyll structure, N	–	N(1.7, 0.22)*
Soil reflectance	–	JHU-SL based statistic model
Clumping index, Ω	–	Any (fixed at 0.7 for LAI calculation)
Leaf angle distribution, LAD	–	Erectophile, spherical, plagiophile, uniform, extremophile, and planophile
Canopy hotspot parameter, Sl	–	0.0001, 0.001, 0.01, and 0.1
Leaf area index, LAI = LAIr • Ω	–	0–10 (10−6 interval)
Solar incident zenith angle, θs	°	25 and 50
View zenith angle, θv	°	0
Solar illumination specular ratio, rsd	–	Constant (0.81, 0.91, 0.95, 0.98, and 1.0 in MODIS bands 3, 4, 1, 2, and 5–7)
Error function of the atmospheric correction	–	N(0, (0.005 + 0.05ρ)2)*

N(μ,σ2) denotes the normal distribution with mean μ and variance σ2.

I calculated the relationship between the normalized difference vegetation index (NDVI) and LAI (m2 m−2) following Kushida and Yoshino (2010). I used the TOA canopy spectral reflectance values at the Moderate Resolution Imaging Spectroradiometer (MODIS) red (620–670 nm; RR(%)) and near infrared (841–876 nm; RNIR(%)) bands to calculate NDVI as follows:

For the estimated LAI value ranges of 0.95–1.05, 1.95–2.05, 2.95–3.05, 3.95–4.05, 4.95–5.05, 5.95–6.05, and 6.95–7.05, I calculated the relationships between canopy spectral reflectance and Cab, Cm, Cw, and Cw/Cab.

I assumed that Cab, Cm, and Cw had lognormal distributions based on the leaf optical properties experiment (LOPEX93), which provides values for leaf pigment and water content of 70 leaf samples that represent approximately 50 species of woody and herbaceous plants (Hosgood et al. 1995). The means and standard deviations (SD) of the lognormal distributions and the correlations and ranges of the variables were also determined using the data values in LOPEX93. All calculations were carried out under variable soil spectrum conditions. The soil reflectance distribution for each of the bands was assumed to be lognormal or normal, based on the Johns Hopkins University Spectral Library (JHU-SL; Baldridge et al. 2009). The means and SD of the distributions and the correlations and ranges of the variables were determined using the data values in JHU-SL.

The clumping index (Ω; Chen et al. 2005) was incorporated in the model by setting the parameter at 0.7 to express the leaf clumping effect. Using this parameter, I adjusted the LAI value such that, in a plant canopy with an initial LAI value of LAIr and an Ω value of Ω, the adjusted LAI value became LAIr · Ω/0.7. The leaf angle distribution (LAD) was fixed as erectophile, spherical, plagiophile, uniform, extremophile, and planophile. The canopy hotspot parameter (Sl), which is equal to the ratio of the correlation length of leaf projections in the horizontal plane and the canopy height, was fixed at 0.0001, 0.001, 0.01, and 0.1. I used these ranges of LAD and Sl values to represent global distributions in these parameters. The solar incident zenith angle (θs) was fixed at 25° for all model evaluations except when model sensitivity to this parameter was evaluated, and, in this case, θs was increased to 50°. The specular ratio to the total solar illumination (rsd) was set at constant values representing typical atmospheric conditions on a clear day for each of the bands. I assumed that the error function of the atmospheric correction had an independent normal distribution with a mean of 0 and SD of 0.005 + 0.05ρ (no unit reflectance), where ρ is the reflectance value at a given spectral band (Vermote and Kotchenova 2008).

In the calculation of each of combinations of the LAD and Sl types, LAI values were provided from 0 to 10 at 10−6 intervals. I used pseudo-random numbers to express the lognormal and normal distributions of the leaf spectral parameters and soil reflectance. I calculated 107 cases to obtain the relationships between Cab, Cm, and Cw and their associated spectral reflectances.

I used the TOA canopy spectral reflectance values at the MODIS green (545–565 nm; RG(%)), near infrared (841–876 nm; RNIR(%)), and shortwave infrared (1628–1652 nm; R1640(%)) bands to estimate Cab, Cm, and Cw, respectively. The RG, RNIR, and R1640 bands correspond to absorption bands of chlorophyll a + b, dry matter, and water and dry matter combined, respectively. Absorptions of carotenoids and anthocyanins also concern with RG; however, in general, most of the leaf absorption at the green band corresponds to chlorophyll a + b. That was because the carotenoids concentration and Cab have a high positive correlation for a variety of plant species and the anthocyanins concentration appears when the leaves of deciduous trees turned red in autumn. For the estimation of Cw, the estimated Cm value from RNIR was multiplied by the ratio of the specific absorption coefficient of water (cm2 mg) to that of dry matter (cm2 mg), which is 0.787, and then removed this value (fi(RNIR)) from the estimated Cw because the PROSPECT model shows that both Cw and Cm contribute to R1640. For the estimation of Cw/Cab, the estimated Cw value was divided by the estimated Cab value.

I divided the ranges of the values of the TOA spectral reflectance or the abovementioned spectral indices into 8–12, and then calculated the average and SD of Cab, Cm, Cw, and Cw/Cab for each of the divided ranges. To express the relationships in mathematical formulas for each of the estimated LAI value ranges, I used regression equations in the form:

where a and b are constant values, x is the spectral reflectance (RG, RNIR, or R1640 + fi(RNIR)), and y is the leaf constituent (Cab, Cm, or Cw). For the ratio Cw/Cab for each of the estimated LAI value ranges, I used the regression equation in the form:

where a1, a2, b1, b2, c1, and c2 were constant values. The coefficient of determination (R2) was defined as:

where E is the root mean square error (RMSE) from the regression and SD is the standard deviation of the samples. Standard deviation for Cab, Cm, Cw, and Cw/Cab was 16.4 μg cm−2, 2.22 mg cm−2, 5.63 mg cm−2, and 0.174, respectively.

Results

The LAI was estimated from the NDVI with R2 of 0.39 for all combinations of the LAD and Sl types together when θs = 25° (Fig. 1). The SD of the estimated LAI values over the intervals 0.95–1.05, 1.95–2.05, 2.95–3.05, 3.95–4.05, 4.95–5.05, 5.95–6.05, and 6.95–7.05 were 0.4, 0.9, 1.6, 2.1, 2.2, 2.1, and 1.8, respectively. Similarly, the LAI was estimated form the NDVI with R2 of 0.30 when θs = 50°.

Figure 1

Relationship between normalized difference vegetation index and estimated leaf area index for all combinations of leaf angle distribution and Sl types (θs = 25°). The solid and dotted curves denote the average and the average ±SD, respectively, for each estimate.

I found a weak relationship between Cm and RNIR and a strong relationship between Cab, Cw, and Cw/Cab and their associated canopy spectral reflectances at the LAI values >2 when all the LAD and Sl types were equally probable in one pixel of a remotely sensed image (Fig. 2). At the LAI values of 1, the R2 of Cab, Cw, and Cw/Cab estimations were <0.22. The LAI estimates of 2, 4, and 6 in Figure 2 correspond to the estimated LAI ranges of 1.95–2.05, 3.95–4.05, and 5.95–6.05, respectively.

Figure 2

RG versus Cab, RNIR versus Cm, R1640 + f(RNIR) versus Cw, and estimated Cw/Cab versus observed Cw/Cab for all combinations of leaf angle distribution and Sl types and for estimated leaf area indices of 2, 4, and 6 (θs = 25°). The solid and dotted curves denote the average and the average ±SD, respectively, for each estimate.

However, for each of the estimated LAI ranges, as the LAD became more vertical or as Sl decreased, Cab, Cm, and Cw decreased for the same canopy spectral reflectance values (Fig. 3). As the relationships between leaf constituents and associated canopy reflectances were dependent on the LAD and Sl types, it was difficult to estimate Cab and Cw from the canopy spectral reflectances when different LAD and Sl types existed in the focal region of analysis. Rp2 and Re2 in Figure 3 were the coefficients of determination under erectophile and Sl = 0.0001 parameterization and under planophile and Sl = 0.1 parameterization, respectively. In contrast, for the estimation of the Cw/Cab ratio, estimation equations were independent of the LAD and Sl types (Fig. 3). The relationships between the estimated and observed Cw/Cab ratios for all combinations of the LAD and Sl types (Table 1) fell within the two regression curves for erectophile and Sl = 0.0001 parameterization and for planophile and Sl = 0.1 parameterization (Fig. 3).

Figure 3

RG versus Cab, RNIR versus Cm, R1640 + f(RNIR) versus Cw, and estimated Cw/Cab versus observed Cw/Cab for estimated leaf area indices of 2, 4, and 6 (θs = 25°). Lines denote the averages of all combinations of leaf angle distribution (LAD) and Sl types (solid lines), erectophile and Sl = 0.0001 (dotted lines), and planophile and Sl = 0.1 (dashed lines). R2e represents R2 when the LAD is erectophile and Sl = 0.0001, and R2p represents R2 when LAD is planophile and Sl = 0.1.

I found that the models were not sensitive to the value used for θs. For an LAI value of 1, the R2 of Cab, Cw, and Cw/Cab estimates were <0.30, and the relationship between Cm and the canopy spectral reflectance was weak. I could not estimate Cab and Cw when different LAD and Sl types existed in the focal region of analysis because the equations used to estimate Cab and Cw were dependent on the LAD and Sl types. However, the estimation equations for Cw/Cab were independent of the LAD and Sl types. Coefficients of the regression equations of Cw/Cab for all combinations of LAD and Sl types together in the form of equation (3) and the R2 are shown in Table 2.

Table 2

Coefficients of the equations for estimating Cw/Cab

θs	LAI	a1	b1	b2	a2	c1	c2	R2
25	2	12.231	1.003	1.659	0.177	0.859	0.691	0.58
	3	8.660	0.949	1.541	0.349	0.858	0.847	0.67
	4	6.632	0.903	1.446	0.443	0.781	0.845	0.72
	5	5.392	0.866	1.373	0.665	0.682	0.876	0.77
	6	4.604	0.841	1.326	1.300	0.587	0.981	0.83
	7	4.179	0.784	1.286	3.604	0.529	1.208	0.89
50	2	12.120	0.978	1.645	0.239	0.898	0.785	0.61
	3	8.776	0.914	1.525	0.400	0.881	0.888	0.67
	4	6.745	0.870	1.430	0.532	0.807	0.900	0.73
	5	5.727	0.831	1.369	0.937	0.706	0.971	0.78
	6	4.932	0.810	1.327	2.136	0.614	1.117	0.84
	7	4.549	0.726	1.281	7.318	0.535	1.391	0.90

Discussions and Conclusion

I evaluated global estimates of Cab, Cm, Cw, and Cw/Cab from TOA broadband spectral reflectance using the PROSAIL model for possible distributions of leaf and soil spectra, LAI, canopy geometric structure, and leaf size. For LAI values <2, Cab, Cw, and Cw/Cab had weak relationships with their associated spectral reflectances. For LAI values greater than 2, Cab and Cw could be reliably estimated only for certain ranges of LAD and Sl types while the ratio of Cw/Cab could be reliably estimated for all possible canopy structures with an R2 ranging from 0.56 to 0.90. The estimation equation of Cw/Cab from the spectral reflectance and the R2 value were dependent on the LAI values, but independent of the LAD and Sl types.

Levels of Cab, Cm, and Cw can be indicative of leaf physiology and plant condition, and attempts have been made to estimate these values with remote sensing applications (Ustin et al. 2009). In previous site-specific studies, Cab, Cm, and Cw were successfully estimated using this methodology (Fourty and Baret 1997; Bowyer and Danson 2004; Zarco-Tejada et al. 2004, 2003; Gitelson et al. 2005; De Santis et al. 2006; Darvishzadeh et al. 2012; Si et al. 2012); however, the use of remote sensing to estimate these values at regional and global scales has not been reported. My research suggests that estimates of Cab, Cm, and Cw are dependent on LAD and Sl types, and these types often vary across regional to global scales. As techniques for estimating LAD and Sl types through remote sensing have not been established, a generalized estimation of Cab, Cm, and Cw across broad spatial scales is difficult except in cases where specific LAD and Sl types can be inferred. In contrast, this study shows that the estimation of the Cw/Cab ratio through remote sensing techniques is generally possible across regional and global scales. The estimation of this ratio through remote sensing has not been previously considered as an indicator of plant canopy condition because the physiological meaning of the Cw/Cab ratio has been less well studied than those of Cab, Cm, and Cw. However, I found that the Cw/Cab ratio had a stronger relationship with its associated spectral band than Cab, Cm, and Cw had to their associated bands.

Previous studies described the meaning behind and variations in Cab, Cw, and Cw/Cab. The value of Cw/Cab is specific to plant species, although, in general, the ratio slightly decreases with spring sprout and increases with autumn defoliation (Gond et al. 1999; Ceccato et al. 2001). For example, Scots pine, lodgepole pine, sun flowers, and sugar beets have high Cw/Cab values (1.0–1.8); poplars, oaks, and rhododendrons have moderate ratio values (0.5–0.7); and maize and rice have low values (0.1–0.2; Ceccato et al. 2001; Gond et al. 1999; Hosgood et al. 1995). The value of Cw/Cab also generally increases when a plant responds to stressors related to water deprivation (Zhang and Kirkham 1996; Guerfel et al. 2009), heat (Jeon et al. 2006), chilling (Bacci et al. 1996; Jeon et al. 2006; Korkmaz et al. 2010), high light conditions (Jagtap et al. 1998), ultraviolet rays (Alexieva et al. 2001), high salinity (Jaleel et al. 2008; Dogan 2011), and heavy-metal contaminants (Anuradha and Rao 2009). The increase in the ratio as a result of plant stress is caused by a greater decrease in leaf chlorophyll compared with leaf water.

Therefore, a change in the Cw/Cab ratio through time is the result of either changes in species composition or changes in the response of plants to stress. The former generally occurs at a yearly to decadal scale, whereas the latter occurs at a daily to monthly scale. Although disturbances such as wildfires, insect attacks, and deforestation can cause an immediate change in species composition, an analysis of changes in LAI and NDVI can help to distinguish between the causes of changes in Cw/Cab. Thus, the remote estimation of the Cw/Cab ratio from satellites offers information on plant status at a global perspective.

Other than leaf chlorophyll a + b, leaf anthocyanins absorb the green light and generate the errors in the estimation of the Cw/Cab ratio. Leaf anthocyanins appear when the leaves of deciduous trees turned red in autumn or under chilling stress (Bacci et al. 1996). When a change in the estimated Cw/Cab ratio possibly appeared in such cases, an analysis of changes in the estimated LAI and NDVI can help to distinguish between the causes of changes in the estimated Cw/Cab, as the autumn coloration reduces NDVI (Zhang et al. 2012).

This study modeled the global vegetation as to obey PROSAIL model with parameters shown in Table 1. The R2 of the LAI estimation from NDVI with globally fixed equations were 0.30–0.39, whereas the R2 of the Cw/Cab ratio estimation in the way I presented in this note was 0.56–0.90, for the estimated LAI values >2. This indicates that the global remote estimation of the Cw/Cab ratio is more reliable than that of LAI.