Using an optimization procedure for the three-band model (Equation 18�7), for the 2008 data set, the optimal spectral region for λ1 was found to be around 670 nm, which is in accordance with previous studies (Dall’Olmo and Gitelson 2005: Gitelson, Schalles, and Hladik 2007; Gitelson et al� 2008)� The magnitude of the reciprocal reflectance at 670 nm was poorly correlated with chl-a concentration (Figure 18�11a)� Since (ρ670)−1 is directly related to chl-a absorption (Equation 18�13), an increase in chl-a concentration should lead to an increase in (ρ670)−1, but Figure 18�11a shows just the opposite for stations with chl-a concentrations < 20 mg ⋅ m−3; that is, (ρ670)−1 decreases as chl-a concentration increases� This is due to the role of suspended solids� The relationship between (ρ670)−1 and the concentra- tion of TSS (Figure 18�11b) shows a steep decrease in (ρ670)−1 as TSS concentration increases, confirming that scattering by suspended solids was a main factor controlling reflectance at 670 nm�
To reduce the effects of scattering by suspended particles and absorption by nonalgal particles and CDOM on the reflectance at 670 nm, ρ−1(λ2) at 710 nm was used� ρ−1710∝ (aCDOM(λ) + aNAP(λ) + awater(λ) + bb(λ))/bb(λ) was strongly related to the TSS concentration (not shown) as well as to absorption by all constituents except chl-a� The difference ρ−1670 − ρ−1710
∝ achl-a/bb(λ) was, therefore, more closely related to chl-a (Figure 18�12)� However, it was still dependent on backscattering, bb(λ), and thus was strongly affected (especially for chl-a < 10 mg ⋅ m−3) by the scattering of all suspended particles� The reflectance in the NIR region of the spectrum is clearly influenced by the concentration of TSS (Figure 18�10) and is closely related to bb(λ); so ρ750 ∝ bb(λ) was used to remove the effect of the differences between samples in scattering by suspended particles�
Taking into account all the aforementioned considerations and using them in the algo- rithm construction, we have found a very close relationship between chl-a concentration and the three-band NIR–red model (Equation 18�7) with simulated MERIS bands: determi- nation coefficient R2 ≈ 0�94 (Figure 18�13a and b)� We also established relationships between the chl-a concentration and the two-band models with simulated MODIS and MERIS bands� The two-band NIR–red model with simulated MERIS bands (Equation 18�9) had a close relationship (R2 ≈ 0�94) with chl-a concentration (Figure 18�13c) in the range typical for
2.5 5.0 7.5
TSS (mg ã L−1)
10.0 12.5 15.0
0.0000.0 0.001 0.002
0.003 y=0.0003e0.1.330x R2= 0.61
ρ750 (sr−1)
FIgure 18.10
Remote sensing reflectance at 750 nm versus the concentration of total suspended solids for the Fremont Lakes 2008 data set�
productive waters and slightly lower when chl-a concentrations were limited to 30 mg ⋅ m−3,
the range typical for coastal and estuarine waters (Figure 18�13d)� The two-band NIR–red model with simulated MODIS bands (Equation 18�8) also had a close linear relationship, with a chl-a concentrations ranging from 2 to 90 mg ⋅ m−3 and R2 = 0�75 (Figure 18�13e)� However, the model was almost not sensitive to chl-a concentrations below 30 mg ⋅ m−3 (Figure 18�13f)�
The R2 was below 0�18, which shows that the two-band MODIS NIR–red model is not reli- able for estimating low to moderate chl-a concentrations� Due to the low accuracy and unre- liability of the two-band MODIS NIR–red model at low to moderate chl-a concentrations, no attempt was made to calibrate this model for potential use with the satellite data�
Thus, we calibrated the NIR–red models with simulated MERIS bands and established the algorithms for estimating the chl-a concentration for the range of chl-a concentrations from 2 to 120 mg ⋅ m−3 measured in 2008:
chl-a=243 862� ×(3-Band MERIS NIR-red model) 27 219+ � (18�14)
chl-a=72 66� ×(2-Band MERIS NIR-red model)−46�535 (18�15)
00 300 600 900
5 10
(a) (b)
15 20 0 5 10 15
chl-a (mg ã m−3) TSS (mg ã L−1)
(ρ670)−1
(sr)
0 300 600 900
(ρ670)−1
(sr)
R2= 0.51 R2= 0.38
FIgure 18.11
Reciprocal remote sensing reflectance at 670 nm, (ρ670)−1, versus chl-a (a), and (ρ670)−1 versus total suspended sol- ids (b) concentrations for stations with chl-a concentrations, <20 mg ⋅ m−3�
30 60 90
−6000
−450
−300
−150 150 300
0
(ρ670)−1 −(ρ710)−1 (sr)
chl-a (mg ã m−3)
y=162.39ln(x)−510.19 R2= 0.83
FIgure 18.12
Relationship of chl-a concentration and the difference of the reciprocal reflectances at 670 and 710 nm�
The next step was to validate the algorithms (Equations 18�14 and 18�15) using the data set obtained in 2009� The relationships between the three-band and two-band MERIS NIR–red models and chl-a concentrations measured in 2009 were very close (R2 > 0�94), and the best fit functions of these relationships were very close to those obtained for the 2008 data� Using simulated MERIS band reflectances measured in 2009, we estimated chl-a concentrations, chl-aest (Equations 18�14 and 18�15), and compared them with the concen- trations measured analytically, chl-ameas� The relationships between the estimated and the measured chl-a concentrations were very close for both models, thereby allowing a highly accurate estimation of chl-a concentration (Figure 18�14)�
The three-band MERIS NIR–red model is
chl-aest=0 9475� ×chl-ameas+1 3693�
60
(a) (b)
(c) (d)
(e) (f)
90 30
3-band model-MERIS 2-band model-MERIS2-band model-MODIS 0 2-band model-MODIS2-band model-MERIS3-band model-MERIS
−0.2
−0.1
−0.06
−0.12
−0.18 0.0
0.1 0.2
1.2 1.0 0.8 0.6 0.4
0.4
0.3
0.2 1.6
2.0
1.2 0.8 0.4
0.6 0.5 0.4 0.3 0.2
0.06 0.00 R2= 0.94
R2= 0.94
R2= 0.75 R2= 0.17
R2= 0.82 chl-a (mg ã m−3)
0 10 20 30
R2= 0.84
chl-a (mg ã m−3)
0 10 20 30
chl-a (mg ã m−3)
0 10 20 30
chl-a (mg ã m−3)
60 90
30 0
chl-a (mg ã m−3)
60 90
30 0
chl-a (mg ã m−3)
FIgure 18.13
Performance of (a and b) three-band and (c and d) two-band models with simulated MERIS bands, and (e and f) two-band model with simulated MODIS bands for the estimation of chl-a in the Fremont Lakes 2008 in 2008�
a, c, and e show chl-a concentrations from 0 to 90 mg ⋅ m−3, while b, d, and f present chl-a concentrations below 30 mg ⋅ m−3 typical for coastal and estuarine waters�
The root mean square error (RMSE) of chl-a estimation was below 3�89 mg ⋅ m−3 for chl-a concentrations ranging from 4 to 104 mg ⋅ m−3�
The two-band MERIS NIR–red model is
chl-aest=0 9823� ×chl-ameas−0 6848� The RMSE of chl-a estimation was below 4�72 mg ⋅ m−3�