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A new method for estimating chlorophyll-a concentration in the Pearl River Estuary
Optik 126 (2015) 4510–4515
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Optik journal homepage: www.elsevier.de/ijleo
A new method for estimating chlorophyll-a concentration in the Pearl River Estuary Cong-Hua Xie a,∗ , Jin-Yi Chang a , Yuan-Zhi Zhang b a b
School of Computer Science and Engineering, Changshu Institute of Technology, Suzhou, Jiangsu Province, PR China Center Housing Innovations and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
a r t i c l e
i n f o
Article history: Received 8 August 2014 Accepted 22 August 2015 Keywords: Chlorophyll-a concentration Three-band model Pearl River Estuary
a b s t r a c t Accurate and reliable assessment of chlorophyll-a (Chl-a) concentration in turbid waters by remote sensing is challenging due to optical complexity of case II waters. Recently, an optimization procedure based on minimizing root mean square error (RMSE) with three-band model was suggested to retrieve the Chl-a concentration in the Pearl River Estuary (PRE) in China. However, it is sensitive to initial values of model parameters and it doesn’t consider other two bands information to determine each optimal band. To estimate the Chl-a concentration according to information of all bands without initial values, we proposed an optimization procedure based on maximizing correlation of the Chl-a concentration in situ and the Chl-a concentration estimated. Firstly, correlations are computed with the three-band model, in which each band varies from the minimal value to the maximal value. Secondly, the sum of correlations for all values of other two bands is computed to find the optimal value for the first band. Lastly, the sum of correlations for all values of other one band with the first optimal band is computed to find the second and third optimal bands. The calibrated three-band model is applied to retrieve the Chl-a concentration from the reflectance data in the PRE on May 16, 2008. RMSE and correlation indices of our method and two state-of-the-art methods in this dataset are shown the effectiveness of our method. These findings imply that the extensive database of remote sensing could be used to quantitatively monitor the Chl-a concentration in the PRE. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Water quality in many regions is polluted by high sediment load due to soil erosion and run-off from agricultural high populated areas, high agrochemical residuals and industrial pollution. Phytoplankton pigment concentration such as chlorophyll-a (Chla) is a well-known indicator of the ecological health of aquatic environment [1]. A practical, calibration-less, cost-effective and laborsaving method to estimate the Chl-a concentration accurately is important. Traditionally, the Chl-a concentration in waters is measured spectrophotometrically, after the samples have been collected, preserved and transported to the laboratory. This traditional approach is labor-intensive and time-consuming. Remote sensing provides us important information for the development of new strategies to estimate the Chl-a concentration [2]. There are increasing models and methods to estimate the Chl-a concentration in waters on the basis of the remote sensing data.
∗ Corresponding author. Tel.: +86 18913630635. E-mail address: [email protected] (C.-H. Xie). http://dx.doi.org/10.1016/j.ijleo.2015.08.100 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Records of satellite-derived the Chl-a concentration began in 1978 with the CZCS (Coastal Zone Color Scanner sensor) [3]. After that, a lot of algorithms were provided based on different satellites. Williams [4] estimated the sea surface temperature and the Chl-a concentration at San Matías Gulf, northern of the Argentine Patagonian Continental Shelf with the MODIS (Moderate Resolution Imaging Spectro-radiometer sensor). Krishna [5] examined the seasonal and inter-annual variability in SeaWiFS (Sea-viewing Wide Field-of-view Sensor)-derived estimates of near-surface Chla concentration off the central east coast of India from 1998 to 2003. However, accurate assessment of the Chl-a concentration in turbid waters with the remote sensing is still challenging due to the overlapping, uncorrelated absorptions by the colored dissolved organic matter (CDOM) and non-algal particles (NAP), which are much larger in turbid waters [6,7] than those in sea waters. Therefore, it is necessary to analyze the spectral properties of water constituents based on in situ spectral data and develop some reliable algorithms for estimating the Chl-a concentration in turbid waters. In many studies, close relationships have been found between the Chl-a concentration and NIR-to-red reflectance ratios. Stumpf [8] suggested using the following ratio of reflectance:
C.-H. Xie et al. / Optik 126 (2015) 4510–4515
Chl-a ∝
(NIR) (red)
(1)
For the Stumpf’s two-band method, most algorithms developed to quantify the Chl-a concentration are based on the properties of the red wavelength around 675 nm and the NIR wavelength varying between 700 and 725 nm [9]. A widely used two-band NIR–red model in the following [10]: Chl-a ∝
(705) (670)
(2)
Recently, a new conceptual model containing reflectance in three spectral bands in the red and near-infrared range of the spectrum was suggested for retrieving the Chl-a concentration in turbid productive waters. This three-band model was developed for the estimation of pigment contents in terrestrial vegetation firstly [11]. Dall’Olmo [12] provided evidence that this model could also be used to assess the Chl-a concentration in turbid productive waters. The model relates the Chl-a concentration to reflectance in three spectral bands: Chl-a ∝ (−1 (1 ) − −1 (2 ))(3 )
(3)
Yang [13] presented a modification of the three-band model to estimate the Chl-a concentration in productive waters with a very high concentration of inorganic suspended matter. Chl-a ∝
−1 (1 ) − −1 (2 ) −1 (3 ) − −1 (2 )
(4)
For the three-band model, it has been shown that 1 should be in the red range around 670 nm, 2 in the range 700–710 nm and 3 in the NIR range 730–750 nm [14]. However, for particular geographical and/or seasonal regions, the parameter values of the three-band model are empirically set according to the remotely sensed data and in situ measured data. Their validity is often confined to those regions. Therefore, we often entail re-parameterization of the algorithms for different water bodies. Morel [7] defined the ideal Case I water as pure culture of phytoplankton and the ideal Case II water as a suspension of non-living materials with zero concentration of pigments. Thus, Case I water contains a high concentration of phytoplankton compared to that of other particles, and the pigments play a major role in actual absorption. In contrast, the inorganic particles are dominant in Case II waters, and pigment absorption is of comparatively minor importance. The PRE in China is a large source of freshwater that carries suspended sediments, particulates, dissolved organic matter, and nutrients into the South China Sea [15]. In the PRE waters, freshwater and sea water are mixed over a distance of a few kilometers, and the level of the highly saline stratification from water surface to bottom layer varies from 0 to 3% [16]. The PRE waters are neither Case I nor Case II waters [15]. Therefore, it is difficult to retrieve the Chl-a concentration in the PRE waters. Zhang [15] and Chen [17] evaluated and calibrated the threeband model for estimating the Chl-a concentration in the PRE according to the Hyperion remote sensing imagery. They estimated the three-band model as follows: firstly, fixed two positions of 1 , 2 and 3 , where the initial positions of the three bands were 670 nm, 695 nm, and 750 nm, respectively; secondly, they used an iterative method to find the minimal RMSE to estimate the third position. This new idea gives us an effective method to select the optimal bands for the three-band model and to retrieve the Chla concentration with lineal time and space complexity. However, there are some problems for those methods: firstly, the three-band model is sensitive to the initial values for the three bands; and it is also difficult to determine the initial values for a given dataset; secondly, those methods only consider one band information to find the optimal value with fixed values for other two bands; that
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is, they don’t search all possible values of 1 , 2 and 3 . The motivation of this paper is to select the optimal bands according to all information of the three bands without the initial values. 2. Methods One cruise was conducted in the middle part of the PRE on 16 May 2008. The locations of 15 water sampling stations in the PRE were shown in Table 1. Water samples were collected by a surface water collector at the same time as the field spectral measurements were made. The sampling depth was 0.5 m beneath the water surface. Water samples at the 15 stations were collected and refrigerated in a cold and dark container and processed several hours later in the laboratory. During the water sampling process, data from two sample points S13 and S14 in Table 1 were not obtainable because these two points were very close to the mainland or an island. The original reflectance spectra dataset has 2046 wavelengths varying from 179.15 to 875.53 nm with the resolution of 0.38 nm and is labeled as 0 . A new dataset sampled from the original data has a wavelength varying from 179 to 874 nm with the resolution of 1 nm and is and labeled as 1 . Another new dataset sampled from 1 has 52 wavelengths varying from 355 to 874 nm with the resolution of 10 nm and is labeled as 2 . The Chl-a concentration was measured using the spectrophotometric determination method following the National Aeronautics and Space Administration (NASA) ocean optics protocols. Levels for spectra, Chl-a, TSS, sea surface temperature (SST) and salt from 15 locations sampled were measured and analyzed. Reflectance spectra were measured using the SD2000 spectroradiometer with a spectral resolution of 0.38 nm calibrated to yield absolute values of radiance. TSS concentration was determined gravimetrically from samples collected on the pre-combusted and pre-weighed GF/F filters with a diameter of 47 mm, dried at 95 ◦ C overnight. Subsequently, the suspended matter concentrations were quantified by weighing the dry filter again and subtracting the initial filter paper weight. In order to find the optimal spectral values of 1 , 2 and 3 for the three-band model in Eq. (3), we use the maximum correlation of the Chl-a concentration estimated and the groundtruth measured in situ for the optimization procedure. Assume the number of wavelength is m and the number of stations is n in data set . Model performance evaluation using correlation coefficient (r) reads r=
¯ ¯ (d − d)(y − y)) ¯ 2 (d − d)
¯ (y − y)
(5) 2
Table 1 The location of water sampling stations in the study. Locations
Longitude
Latitude
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15
113.7168 113.7337 113.7392 113.7346 113.7213 113.7171 113.6882 113.6844 113.6834 113.683 113.7329 113.7906 113.7853 113.7672 113.7662
22.68342 22.59973 22.54923 22.49848 22.44793 22.39888 22.34925 22.2825 22.23255 22.18162 22.2007 22.23172 22.27643 22.3172 22.36825
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where d¯ and y¯ are the mean of d and y, respectively. The correlation coefficient r ranges from −1 to 1. A value of 1 implies that a linear equation describes the relationship between d and y perfectly, with all data points lying on a line for which y increases as d increases. A value of −1 implies that all data points lie on a line for which y decreases as d increases. A value of 0 implies that there is no linear correlation between the variables. Algorithm 1. Optimization Procedure for the Three-band Model; Input: Re-sampled spectral data set m×n , Chl-a in situ Mn×1 for different stations, Wavelength m×1 ; Output: 1 , 2 and 3
We use the sum of the 2D correlations of 2 and 1 (the i* th wavelength) to determine the k* th wavelength as the optimal value of 3 . That is k∗ = arg min 1≤k≤m
B(l) =
1 (i,l)
−
1 (j,l)
(k, l);
Compute the correlation of the relative Chl-a Bn×1 and Chl-a in situ Mn×1 (7) C(i, j, k) = Correl(Bn×1 , Mn×1 );} (8) Output the ith, jth, kth wavelength of m×n that corresponding to the maximum correlation; (6)
Because the correlation C(i, j, k) in Algorithm 1 is a 3D(dimension) correlation about 1 , 2 and 3 , we need O(m3 ) time and space complexity to compute it. For example, for dataset 1 (m = 696, n = 13), we need 696×696×696×13 × 6 = 24.89 G bytes 1024×1024×1024 memory space which is too huge to complete. It is difficult to compute the correlations and determine the maximum correlation. Therefore, we compute the 2D correlations with two of 1 , 2 and 3 that vary from 356 to 874 nm and another fixes to a value. According to Eq. (3), for 1 = 2 , the correlation of Bn×1 and Mn×1 has no value. In order to compute conveniently, we assume the 2D correlations are zeros for 1 = 2 . According to Eq. (3), we exchange 1 and 2 in Eq. (3), and have (
−1
(1 ) −
−1
(2 ))(3 ) = −(
−1
(2 ) −
−1
(1 ))(3 )
(7)
}, where We label the 3D correlation C as a vector {C1 , C2 , · · ·, Cm Ci (1 ≤ i ≤ m) is a 2D correlation with the size of m × m. It is difficult to find the global maximum correlation of C(i, j, k) in Algorithm 1 because of the complexity of 3D space. In order to avoid the local maximum and find the maximum correlation fast and simply, we use the sum of the 2D correlations Ci of 2 and 3
to determine the i* th wavelength as the optimal value of 1 on the dataset 1 . That is
i∗ = arg max 1≤i≤m
m m j=1 k=1
Ci (j, k)
(9)
j=1
j∗ = arg max
m
Ci∗ (j, k)
(10)
k=1
On the basis of Algorithm 1 and Eqs. (8)–(10), we proposed the following improved algorithm. Algorithm 2. Three-band Model Based on the Sum of the 2D Correlations; Input: Re-sampled spectral dataset m×n , Chl-a for stations in situ Mn×1 , Wavelength m×1 ; Output: 1 , 2 and 3 (1) For(int i = 1; i < m + 1; i++)//the ith wavelength of m×n for 1 (2) { C = zeros(m, m);//initialize an m-by-m matrix For(int j = 1;j < m + 1; i++)//the jth wavelength of m×n (3) for 2 For(int k = 1;k < m + 1; i++)//the kth wavelength of m×n (4) for 3 (5) { B = zeros(n, 1);//initialize an n-by-1 matrix (6) For(int l = 1; l < n + 1; l++)//the lth station of Mn×1 (7) (8) (9) (10)
Compute B(l) =
(8)
1 (i,l)
−
1 (j,l)
(k, l);
Compute the correlation C(j, k) = Correl(Bn×1 , Mn×1 ); Ci (j, k) = |C(j, k)|; } Compute s1 (i) =
m m
Ci (j, k);}
j=1 k=1
(11)
According to Eq. (8) and s1 , compute the i* th wavelength for 1 = (i*);
(12)
Compute s2 (k) =
(13)
According to Eq. (9) and s2 , compute the k* th wavelength for 3 = (k*);
(14)
Compute s3 (j) =
(15)
According to Eq. (10) and s3 , compute the j* th wavelength for 2 = (j*).
m
(6)
Eq. (6) shows us that the absolute values of the 2D correlations with 2 fixed to a value and 1 and 3 varied from 356 to 874 are same to those of the 2D correlations with 1 fixed to a value and 2 and 3 varied from 356 to 874. Therefore, we compute the absolute value of the correlations to determine the optimal values: C (i, j, k) = |C(i, j, k)|(1 ≤ i, j, k ≤ m)
Ci∗ (j, k)
We use the sum of the 2D correlations of 3 and 1 (the i* th wavelength) to determine the j* th wavelength as the optimal value of 2 .
i∗ ≤j≤m
(1) For(int i = 1; i < m + 1; i++)//the ith wavelength of m×n for 1 (2) For(int j = 1;j < m + 1; i++)//the jth wavelength of m×n for 2 (3) For(int k = 1;k < m + 1; i++)//the kth wavelength of m×n for 3 {For(int l = 1; l < n + 1; l++)//the lth station of Mn×1 (4) (5) Estimate the relativeChl-a by
m
Ci∗ (j, k);
j=1
m
Ci∗ (j, k);
k=1
3. Results and discussion In the PRE waters sampled, the Chl-a concentration varied from 0.83 to 11.77 mg m−3 in those datasets. The TSS and Chl-a concentration were strongly correlated with the correlation coefficient R2 above 0.88 in Fig. 1. However, as the Chl-a concentration was below 2 mg m−3 , the correlation coefficient R2 was less than 0.5; high concentration of NAP governed the optical properties of these waters. The PRE waters with the Chl-a concentration below 2 mg m−3 were quite close to Case II. As the Chl-a concentration was above 2 mg m−3 , TSS and Chl-a correlate closely (R2 = 0.7). In these waters, both NAP and phytoplankton govern optical properties. The reflectance spectra of dataset 1 in Fig. 2 were quite similar in magnitude and shape to the reflectance spectra of productive waters with very well pronounced spectral features in the red
C.-H. Xie et al. / Optik 126 (2015) 4510–4515
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Fig. 1. Relationship between TSS and Chl-a concentration in PRE.
Fig. 2. Reflectance spectra for different wavelengths.
Fig. 5. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 436, (b) 1 = 456, (c) 1 = 476, (d) 1 = 496.
Fig. 3. Peak position versus Chl-a concentration.
Fig. 4. Correlations of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 356, (b) 1 = 376, (c) 1 = 396, (d) 1 = 416.
and NIR ranges of the spectrum, i.e. due to the Chl-a absorption near 670 nm and peaks around 690–700 nm [13]. The peak position shifted towards a longer wavelength from 686 to 696 nm as the Chl-a concentration increased from 1 to 11 mg m−3 in Fig. 3. The high correlation between Chl-a and TSS and the pronounced spectral features in the red and NIR range of the spectrum, typical
Fig. 6. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 516, (b) 1 = 536, (c) 1 = 556, (d) 1 = 576, (e) 1 = 596.
for productive turbid waters, are interesting features of the waters studied. According to Algorithm 2, we compute the 2D correlations with 1 fixed to a value and 2 and 3 varied from 356 to 874 nm. When 1 = 356, 376, 396 and 416 nm, the 2D correlations are shown in Fig. 4(a)–(d), respectively. From Fig. 4, we know that the 2D correlations of 2 and 3 become larger and larger with the increase of
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C.-H. Xie et al. / Optik 126 (2015) 4510–4515
Fig. 8. Correlation of the estimated Chl-a concentration and the ground truth measured in situ. (a) 1 = 756, (b) 1 = 776, (c) 1 = 796, (d) 1 = 816.
Fig. 9. The sum of the 2D correlations for all values of 2 and 3 .
Fig. 7. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 616, (b) 1 = 636, (c) 1 = 656, (d) 1 = 676, (e) 1 = 696, (f) 1 = 716, (g) 1 = 736.
1 from 356 to 416 nm. The changes of 2D correlations focus on the wavelength of 2 from 690 to 790 nm or 2 < 1 . When 1 = 436, 456, 476 and 496 nm, the 2D correlations are shown in Fig. 5(a)–(d), respectively. From Figs. 4 and 5, we know that the 2D correlations of 2 and 3 in Fig. 5 are larger than those in Fig. 4. Obviously, the sum of the 2D correlations in Fig. 5 is larger than that in Fig. 4. For 436 < 1 < 496 nm and 2 < 1 or 2 > 690 nm, the 2D correlations are near to 1 for all values of 3 . The 2D correlations also become larger and larger with the increase of the values of the 1 in Fig. 5. When 1 = 516, 536, 556, 576 and 596 nm, the 2D correlations are shown in Fig. 6(a)–(e), respectively. For 450 < 2 < 690 nm, the 2D correlations are smaller and smaller with the increase of 1 in Fig. 6. The 2D correlations for different values of 2 and 3 in Fig. 6 are smaller than those in Fig. 5. Obviously, the sum of the 2D correlations in Fig. 5 is smaller than those in Fig. 6. However, for 2 > 1 , the changes of 2D correlations are small. For 1 = 616, 636, 656, 676, 696, 716 and 736 nm, the 2D correlations are shown in Fig. 7(a)–(g), respectively. From Fig. 7, the 2D correlations for different values of 2 and 3 are increasing when 1 increases from 616 to 656 nm and decreasing when 1 increases from 656 to 736 nm. For 1 = 656 nm, the 2D correlations are near to the maximum for all values of 2 and 3 . For 2 < 1 , the 2D correlations are small. For 1 = 756, 776, 796 and 816 nm, the 2D correlations are shown in Fig. 8(a)–(d), respectively. From Fig. 8, we know that the 2D
Fig. 10. The sum of the 2D correlations for all values of 2 and 1 = 668 nm.
correlations for most of 2 and 3 are small. The 2D correlations are similar to each other in Figs. 4 and 8. From Figs. 4–8, we can know that the 2D correlations for 1 < 2 are larger and more stable than those for 1 > 2 . Therefore, we assume the following criterion for the three-band model: 1 < 2
(11)
According to Algorithm 2, the sum of the 2D correlations of 2 and 3 is shown in Fig. 9. We can find that the maximum correlation is located at 1 = 668 nm. The sum of the 2D correlations of 2 and 1 = 668 nm is shown in Fig. 10. We can find the optimal value of 3 is 743 nm. The sum of the 2D correlations of 3 and 1 = 668 nm is shown in Fig. 11. Although the optimal value of 2 is 661 nm in Fig. 11, we have 2 > 668 nm according to Eq. (11). Therefore, we have 2 = 700 nm according to Fig. 11. The three-band model is spectrally calibrated by iterative and least-square linear
C.-H. Xie et al. / Optik 126 (2015) 4510–4515
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4. Conclusions
Fig. 11. The sum of the 2D correlations for all values of 3 and 1 = 668 nm.
The three-band model was spectrally calibrated to select optimal bands for the most accurate estimation of Chl-a concentration in the PRE in the study. A strong linear relationship was established between measured Chl-a concentration and the results from the three-band model in Eq. (12). The correlations of the three bands show that the boundary of 1 = 2 is important. According to our experiment results, we need have 1 < 2 . Our method estimates three optimal bands for the three-band model without initial values and is applied to retrieve the Chl-a concentration with all information of the three bands. Experiment results show its robustness and reliability. However, the disadvantage of our method is that the computation time is too long. We will do some work to reduce it in the future with a fast speed algorithm. Acknowledgments This work is jointly supported by the National Science Foundation of China under Grant (41271434), the Natural Science Foundation of Jiangsu Province in China under Grant (BK2012209) and the Science and Technology Program of Suzhou in China under Grant (SYG201409). References
Fig. 12. Root mean square error of Chl-a concentration estimation plotted as a function of wavelength for 1 with different initial values for 2 and 3 : (a) 2 = 650, 3 = 730, (b) 2 = 670, 3 = 730, (c) 2 = 690, 3 = 730, (d) 2 = 700, 3 = 730. Table 2 RMSE and correlation comparison for different methods.
RMSE Correlation
Gitelson [10]
Zhang [15]
Our method
2.95 0.95
3.05 0.95
2.93 0.96
regression method. We have the following equation to estimate the Chl-a concentration: Chl-a = 36.98(−1 (1 ) − −1 (2 ))(3 ) + 2.9
(12)
Methods of Zhang [15] and Chen [17] are sensitive to the initial values of 1 , 2 and 3 . The optimization procedure was based on minimizing the RMSE of the Chl-a concentration estimates [15]. The RMSE of Chl-a estimation plotted as a function of wavelength for 1 with different initial values for 2 and 3 are shown in Fig. 12. The minimal values of the RMSE have been found at 1 = 656, 713, 684, 676 nm for different initial values of 2 and 3 are shown in Fig. 12(a)–(d), respectively. It is obviously that the results are sensitive to the initial values. To evaluate the effectiveness of our method, we compare it with methods of Zhang [15] and Giteson [10]. The initial values of 1 , 2 and 3 for method of Zhang [15] are 665, 700, 735 nm, respectively. Method of Gitelson [10] is computed with Eq. (2). The RMSE and correlation indices are computed according to the Chl-a concentration in sit and the Chl-a concentration estimated with those three methods and shown in Table 2. From Table 2, we can know that our method has better results than methods of Zhang [15] and Gitelson [10]. Results of method of Zhang [15] depends on the initial values for 1 , 2 and 3 . The time complexity for Giteson [12], Zhang [15] and our method are O(1), O(m) and O(m3 ), respectively.
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Optik journal homepage: www.elsevier.de/ijleo
A new method for estimating chlorophyll-a concentration in the Pearl River Estuary Cong-Hua Xie a,∗ , Jin-Yi Chang a , Yuan-Zhi Zhang b a b
School of Computer Science and Engineering, Changshu Institute of Technology, Suzhou, Jiangsu Province, PR China Center Housing Innovations and Shenzhen Research Institute, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
a r t i c l e
i n f o
Article history: Received 8 August 2014 Accepted 22 August 2015 Keywords: Chlorophyll-a concentration Three-band model Pearl River Estuary
a b s t r a c t Accurate and reliable assessment of chlorophyll-a (Chl-a) concentration in turbid waters by remote sensing is challenging due to optical complexity of case II waters. Recently, an optimization procedure based on minimizing root mean square error (RMSE) with three-band model was suggested to retrieve the Chl-a concentration in the Pearl River Estuary (PRE) in China. However, it is sensitive to initial values of model parameters and it doesn’t consider other two bands information to determine each optimal band. To estimate the Chl-a concentration according to information of all bands without initial values, we proposed an optimization procedure based on maximizing correlation of the Chl-a concentration in situ and the Chl-a concentration estimated. Firstly, correlations are computed with the three-band model, in which each band varies from the minimal value to the maximal value. Secondly, the sum of correlations for all values of other two bands is computed to find the optimal value for the first band. Lastly, the sum of correlations for all values of other one band with the first optimal band is computed to find the second and third optimal bands. The calibrated three-band model is applied to retrieve the Chl-a concentration from the reflectance data in the PRE on May 16, 2008. RMSE and correlation indices of our method and two state-of-the-art methods in this dataset are shown the effectiveness of our method. These findings imply that the extensive database of remote sensing could be used to quantitatively monitor the Chl-a concentration in the PRE. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction Water quality in many regions is polluted by high sediment load due to soil erosion and run-off from agricultural high populated areas, high agrochemical residuals and industrial pollution. Phytoplankton pigment concentration such as chlorophyll-a (Chla) is a well-known indicator of the ecological health of aquatic environment [1]. A practical, calibration-less, cost-effective and laborsaving method to estimate the Chl-a concentration accurately is important. Traditionally, the Chl-a concentration in waters is measured spectrophotometrically, after the samples have been collected, preserved and transported to the laboratory. This traditional approach is labor-intensive and time-consuming. Remote sensing provides us important information for the development of new strategies to estimate the Chl-a concentration [2]. There are increasing models and methods to estimate the Chl-a concentration in waters on the basis of the remote sensing data.
∗ Corresponding author. Tel.: +86 18913630635. E-mail address: [email protected] (C.-H. Xie). http://dx.doi.org/10.1016/j.ijleo.2015.08.100 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Records of satellite-derived the Chl-a concentration began in 1978 with the CZCS (Coastal Zone Color Scanner sensor) [3]. After that, a lot of algorithms were provided based on different satellites. Williams [4] estimated the sea surface temperature and the Chl-a concentration at San Matías Gulf, northern of the Argentine Patagonian Continental Shelf with the MODIS (Moderate Resolution Imaging Spectro-radiometer sensor). Krishna [5] examined the seasonal and inter-annual variability in SeaWiFS (Sea-viewing Wide Field-of-view Sensor)-derived estimates of near-surface Chla concentration off the central east coast of India from 1998 to 2003. However, accurate assessment of the Chl-a concentration in turbid waters with the remote sensing is still challenging due to the overlapping, uncorrelated absorptions by the colored dissolved organic matter (CDOM) and non-algal particles (NAP), which are much larger in turbid waters [6,7] than those in sea waters. Therefore, it is necessary to analyze the spectral properties of water constituents based on in situ spectral data and develop some reliable algorithms for estimating the Chl-a concentration in turbid waters. In many studies, close relationships have been found between the Chl-a concentration and NIR-to-red reflectance ratios. Stumpf [8] suggested using the following ratio of reflectance:
C.-H. Xie et al. / Optik 126 (2015) 4510–4515
Chl-a ∝
(NIR) (red)
(1)
For the Stumpf’s two-band method, most algorithms developed to quantify the Chl-a concentration are based on the properties of the red wavelength around 675 nm and the NIR wavelength varying between 700 and 725 nm [9]. A widely used two-band NIR–red model in the following [10]: Chl-a ∝
(705) (670)
(2)
Recently, a new conceptual model containing reflectance in three spectral bands in the red and near-infrared range of the spectrum was suggested for retrieving the Chl-a concentration in turbid productive waters. This three-band model was developed for the estimation of pigment contents in terrestrial vegetation firstly [11]. Dall’Olmo [12] provided evidence that this model could also be used to assess the Chl-a concentration in turbid productive waters. The model relates the Chl-a concentration to reflectance in three spectral bands: Chl-a ∝ (−1 (1 ) − −1 (2 ))(3 )
(3)
Yang [13] presented a modification of the three-band model to estimate the Chl-a concentration in productive waters with a very high concentration of inorganic suspended matter. Chl-a ∝
−1 (1 ) − −1 (2 ) −1 (3 ) − −1 (2 )
(4)
For the three-band model, it has been shown that 1 should be in the red range around 670 nm, 2 in the range 700–710 nm and 3 in the NIR range 730–750 nm [14]. However, for particular geographical and/or seasonal regions, the parameter values of the three-band model are empirically set according to the remotely sensed data and in situ measured data. Their validity is often confined to those regions. Therefore, we often entail re-parameterization of the algorithms for different water bodies. Morel [7] defined the ideal Case I water as pure culture of phytoplankton and the ideal Case II water as a suspension of non-living materials with zero concentration of pigments. Thus, Case I water contains a high concentration of phytoplankton compared to that of other particles, and the pigments play a major role in actual absorption. In contrast, the inorganic particles are dominant in Case II waters, and pigment absorption is of comparatively minor importance. The PRE in China is a large source of freshwater that carries suspended sediments, particulates, dissolved organic matter, and nutrients into the South China Sea [15]. In the PRE waters, freshwater and sea water are mixed over a distance of a few kilometers, and the level of the highly saline stratification from water surface to bottom layer varies from 0 to 3% [16]. The PRE waters are neither Case I nor Case II waters [15]. Therefore, it is difficult to retrieve the Chl-a concentration in the PRE waters. Zhang [15] and Chen [17] evaluated and calibrated the threeband model for estimating the Chl-a concentration in the PRE according to the Hyperion remote sensing imagery. They estimated the three-band model as follows: firstly, fixed two positions of 1 , 2 and 3 , where the initial positions of the three bands were 670 nm, 695 nm, and 750 nm, respectively; secondly, they used an iterative method to find the minimal RMSE to estimate the third position. This new idea gives us an effective method to select the optimal bands for the three-band model and to retrieve the Chla concentration with lineal time and space complexity. However, there are some problems for those methods: firstly, the three-band model is sensitive to the initial values for the three bands; and it is also difficult to determine the initial values for a given dataset; secondly, those methods only consider one band information to find the optimal value with fixed values for other two bands; that
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is, they don’t search all possible values of 1 , 2 and 3 . The motivation of this paper is to select the optimal bands according to all information of the three bands without the initial values. 2. Methods One cruise was conducted in the middle part of the PRE on 16 May 2008. The locations of 15 water sampling stations in the PRE were shown in Table 1. Water samples were collected by a surface water collector at the same time as the field spectral measurements were made. The sampling depth was 0.5 m beneath the water surface. Water samples at the 15 stations were collected and refrigerated in a cold and dark container and processed several hours later in the laboratory. During the water sampling process, data from two sample points S13 and S14 in Table 1 were not obtainable because these two points were very close to the mainland or an island. The original reflectance spectra dataset has 2046 wavelengths varying from 179.15 to 875.53 nm with the resolution of 0.38 nm and is labeled as 0 . A new dataset sampled from the original data has a wavelength varying from 179 to 874 nm with the resolution of 1 nm and is and labeled as 1 . Another new dataset sampled from 1 has 52 wavelengths varying from 355 to 874 nm with the resolution of 10 nm and is labeled as 2 . The Chl-a concentration was measured using the spectrophotometric determination method following the National Aeronautics and Space Administration (NASA) ocean optics protocols. Levels for spectra, Chl-a, TSS, sea surface temperature (SST) and salt from 15 locations sampled were measured and analyzed. Reflectance spectra were measured using the SD2000 spectroradiometer with a spectral resolution of 0.38 nm calibrated to yield absolute values of radiance. TSS concentration was determined gravimetrically from samples collected on the pre-combusted and pre-weighed GF/F filters with a diameter of 47 mm, dried at 95 ◦ C overnight. Subsequently, the suspended matter concentrations were quantified by weighing the dry filter again and subtracting the initial filter paper weight. In order to find the optimal spectral values of 1 , 2 and 3 for the three-band model in Eq. (3), we use the maximum correlation of the Chl-a concentration estimated and the groundtruth measured in situ for the optimization procedure. Assume the number of wavelength is m and the number of stations is n in data set . Model performance evaluation using correlation coefficient (r) reads r=
¯ ¯ (d − d)(y − y)) ¯ 2 (d − d)
¯ (y − y)
(5) 2
Table 1 The location of water sampling stations in the study. Locations
Longitude
Latitude
s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15
113.7168 113.7337 113.7392 113.7346 113.7213 113.7171 113.6882 113.6844 113.6834 113.683 113.7329 113.7906 113.7853 113.7672 113.7662
22.68342 22.59973 22.54923 22.49848 22.44793 22.39888 22.34925 22.2825 22.23255 22.18162 22.2007 22.23172 22.27643 22.3172 22.36825
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where d¯ and y¯ are the mean of d and y, respectively. The correlation coefficient r ranges from −1 to 1. A value of 1 implies that a linear equation describes the relationship between d and y perfectly, with all data points lying on a line for which y increases as d increases. A value of −1 implies that all data points lie on a line for which y decreases as d increases. A value of 0 implies that there is no linear correlation between the variables. Algorithm 1. Optimization Procedure for the Three-band Model; Input: Re-sampled spectral data set m×n , Chl-a in situ Mn×1 for different stations, Wavelength m×1 ; Output: 1 , 2 and 3
We use the sum of the 2D correlations of 2 and 1 (the i* th wavelength) to determine the k* th wavelength as the optimal value of 3 . That is k∗ = arg min 1≤k≤m
B(l) =
1 (i,l)
−
1 (j,l)
(k, l);
Compute the correlation of the relative Chl-a Bn×1 and Chl-a in situ Mn×1 (7) C(i, j, k) = Correl(Bn×1 , Mn×1 );} (8) Output the ith, jth, kth wavelength of m×n that corresponding to the maximum correlation; (6)
Because the correlation C(i, j, k) in Algorithm 1 is a 3D(dimension) correlation about 1 , 2 and 3 , we need O(m3 ) time and space complexity to compute it. For example, for dataset 1 (m = 696, n = 13), we need 696×696×696×13 × 6 = 24.89 G bytes 1024×1024×1024 memory space which is too huge to complete. It is difficult to compute the correlations and determine the maximum correlation. Therefore, we compute the 2D correlations with two of 1 , 2 and 3 that vary from 356 to 874 nm and another fixes to a value. According to Eq. (3), for 1 = 2 , the correlation of Bn×1 and Mn×1 has no value. In order to compute conveniently, we assume the 2D correlations are zeros for 1 = 2 . According to Eq. (3), we exchange 1 and 2 in Eq. (3), and have (
−1
(1 ) −
−1
(2 ))(3 ) = −(
−1
(2 ) −
−1
(1 ))(3 )
(7)
}, where We label the 3D correlation C as a vector {C1 , C2 , · · ·, Cm Ci (1 ≤ i ≤ m) is a 2D correlation with the size of m × m. It is difficult to find the global maximum correlation of C(i, j, k) in Algorithm 1 because of the complexity of 3D space. In order to avoid the local maximum and find the maximum correlation fast and simply, we use the sum of the 2D correlations Ci of 2 and 3
to determine the i* th wavelength as the optimal value of 1 on the dataset 1 . That is
i∗ = arg max 1≤i≤m
m m j=1 k=1
Ci (j, k)
(9)
j=1
j∗ = arg max
m
Ci∗ (j, k)
(10)
k=1
On the basis of Algorithm 1 and Eqs. (8)–(10), we proposed the following improved algorithm. Algorithm 2. Three-band Model Based on the Sum of the 2D Correlations; Input: Re-sampled spectral dataset m×n , Chl-a for stations in situ Mn×1 , Wavelength m×1 ; Output: 1 , 2 and 3 (1) For(int i = 1; i < m + 1; i++)//the ith wavelength of m×n for 1 (2) { C = zeros(m, m);//initialize an m-by-m matrix For(int j = 1;j < m + 1; i++)//the jth wavelength of m×n (3) for 2 For(int k = 1;k < m + 1; i++)//the kth wavelength of m×n (4) for 3 (5) { B = zeros(n, 1);//initialize an n-by-1 matrix (6) For(int l = 1; l < n + 1; l++)//the lth station of Mn×1 (7) (8) (9) (10)
Compute B(l) =
(8)
1 (i,l)
−
1 (j,l)
(k, l);
Compute the correlation C(j, k) = Correl(Bn×1 , Mn×1 ); Ci (j, k) = |C(j, k)|; } Compute s1 (i) =
m m
Ci (j, k);}
j=1 k=1
(11)
According to Eq. (8) and s1 , compute the i* th wavelength for 1 = (i*);
(12)
Compute s2 (k) =
(13)
According to Eq. (9) and s2 , compute the k* th wavelength for 3 = (k*);
(14)
Compute s3 (j) =
(15)
According to Eq. (10) and s3 , compute the j* th wavelength for 2 = (j*).
m
(6)
Eq. (6) shows us that the absolute values of the 2D correlations with 2 fixed to a value and 1 and 3 varied from 356 to 874 are same to those of the 2D correlations with 1 fixed to a value and 2 and 3 varied from 356 to 874. Therefore, we compute the absolute value of the correlations to determine the optimal values: C (i, j, k) = |C(i, j, k)|(1 ≤ i, j, k ≤ m)
Ci∗ (j, k)
We use the sum of the 2D correlations of 3 and 1 (the i* th wavelength) to determine the j* th wavelength as the optimal value of 2 .
i∗ ≤j≤m
(1) For(int i = 1; i < m + 1; i++)//the ith wavelength of m×n for 1 (2) For(int j = 1;j < m + 1; i++)//the jth wavelength of m×n for 2 (3) For(int k = 1;k < m + 1; i++)//the kth wavelength of m×n for 3 {For(int l = 1; l < n + 1; l++)//the lth station of Mn×1 (4) (5) Estimate the relativeChl-a by
m
Ci∗ (j, k);
j=1
m
Ci∗ (j, k);
k=1
3. Results and discussion In the PRE waters sampled, the Chl-a concentration varied from 0.83 to 11.77 mg m−3 in those datasets. The TSS and Chl-a concentration were strongly correlated with the correlation coefficient R2 above 0.88 in Fig. 1. However, as the Chl-a concentration was below 2 mg m−3 , the correlation coefficient R2 was less than 0.5; high concentration of NAP governed the optical properties of these waters. The PRE waters with the Chl-a concentration below 2 mg m−3 were quite close to Case II. As the Chl-a concentration was above 2 mg m−3 , TSS and Chl-a correlate closely (R2 = 0.7). In these waters, both NAP and phytoplankton govern optical properties. The reflectance spectra of dataset 1 in Fig. 2 were quite similar in magnitude and shape to the reflectance spectra of productive waters with very well pronounced spectral features in the red
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Fig. 1. Relationship between TSS and Chl-a concentration in PRE.
Fig. 2. Reflectance spectra for different wavelengths.
Fig. 5. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 436, (b) 1 = 456, (c) 1 = 476, (d) 1 = 496.
Fig. 3. Peak position versus Chl-a concentration.
Fig. 4. Correlations of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 356, (b) 1 = 376, (c) 1 = 396, (d) 1 = 416.
and NIR ranges of the spectrum, i.e. due to the Chl-a absorption near 670 nm and peaks around 690–700 nm [13]. The peak position shifted towards a longer wavelength from 686 to 696 nm as the Chl-a concentration increased from 1 to 11 mg m−3 in Fig. 3. The high correlation between Chl-a and TSS and the pronounced spectral features in the red and NIR range of the spectrum, typical
Fig. 6. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 516, (b) 1 = 536, (c) 1 = 556, (d) 1 = 576, (e) 1 = 596.
for productive turbid waters, are interesting features of the waters studied. According to Algorithm 2, we compute the 2D correlations with 1 fixed to a value and 2 and 3 varied from 356 to 874 nm. When 1 = 356, 376, 396 and 416 nm, the 2D correlations are shown in Fig. 4(a)–(d), respectively. From Fig. 4, we know that the 2D correlations of 2 and 3 become larger and larger with the increase of
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Fig. 8. Correlation of the estimated Chl-a concentration and the ground truth measured in situ. (a) 1 = 756, (b) 1 = 776, (c) 1 = 796, (d) 1 = 816.
Fig. 9. The sum of the 2D correlations for all values of 2 and 3 .
Fig. 7. Correlation of the estimated Chl-a concentration and the groundtruth measured in situ. (a) 1 = 616, (b) 1 = 636, (c) 1 = 656, (d) 1 = 676, (e) 1 = 696, (f) 1 = 716, (g) 1 = 736.
1 from 356 to 416 nm. The changes of 2D correlations focus on the wavelength of 2 from 690 to 790 nm or 2 < 1 . When 1 = 436, 456, 476 and 496 nm, the 2D correlations are shown in Fig. 5(a)–(d), respectively. From Figs. 4 and 5, we know that the 2D correlations of 2 and 3 in Fig. 5 are larger than those in Fig. 4. Obviously, the sum of the 2D correlations in Fig. 5 is larger than that in Fig. 4. For 436 < 1 < 496 nm and 2 < 1 or 2 > 690 nm, the 2D correlations are near to 1 for all values of 3 . The 2D correlations also become larger and larger with the increase of the values of the 1 in Fig. 5. When 1 = 516, 536, 556, 576 and 596 nm, the 2D correlations are shown in Fig. 6(a)–(e), respectively. For 450 < 2 < 690 nm, the 2D correlations are smaller and smaller with the increase of 1 in Fig. 6. The 2D correlations for different values of 2 and 3 in Fig. 6 are smaller than those in Fig. 5. Obviously, the sum of the 2D correlations in Fig. 5 is smaller than those in Fig. 6. However, for 2 > 1 , the changes of 2D correlations are small. For 1 = 616, 636, 656, 676, 696, 716 and 736 nm, the 2D correlations are shown in Fig. 7(a)–(g), respectively. From Fig. 7, the 2D correlations for different values of 2 and 3 are increasing when 1 increases from 616 to 656 nm and decreasing when 1 increases from 656 to 736 nm. For 1 = 656 nm, the 2D correlations are near to the maximum for all values of 2 and 3 . For 2 < 1 , the 2D correlations are small. For 1 = 756, 776, 796 and 816 nm, the 2D correlations are shown in Fig. 8(a)–(d), respectively. From Fig. 8, we know that the 2D
Fig. 10. The sum of the 2D correlations for all values of 2 and 1 = 668 nm.
correlations for most of 2 and 3 are small. The 2D correlations are similar to each other in Figs. 4 and 8. From Figs. 4–8, we can know that the 2D correlations for 1 < 2 are larger and more stable than those for 1 > 2 . Therefore, we assume the following criterion for the three-band model: 1 < 2
(11)
According to Algorithm 2, the sum of the 2D correlations of 2 and 3 is shown in Fig. 9. We can find that the maximum correlation is located at 1 = 668 nm. The sum of the 2D correlations of 2 and 1 = 668 nm is shown in Fig. 10. We can find the optimal value of 3 is 743 nm. The sum of the 2D correlations of 3 and 1 = 668 nm is shown in Fig. 11. Although the optimal value of 2 is 661 nm in Fig. 11, we have 2 > 668 nm according to Eq. (11). Therefore, we have 2 = 700 nm according to Fig. 11. The three-band model is spectrally calibrated by iterative and least-square linear
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4. Conclusions
Fig. 11. The sum of the 2D correlations for all values of 3 and 1 = 668 nm.
The three-band model was spectrally calibrated to select optimal bands for the most accurate estimation of Chl-a concentration in the PRE in the study. A strong linear relationship was established between measured Chl-a concentration and the results from the three-band model in Eq. (12). The correlations of the three bands show that the boundary of 1 = 2 is important. According to our experiment results, we need have 1 < 2 . Our method estimates three optimal bands for the three-band model without initial values and is applied to retrieve the Chl-a concentration with all information of the three bands. Experiment results show its robustness and reliability. However, the disadvantage of our method is that the computation time is too long. We will do some work to reduce it in the future with a fast speed algorithm. Acknowledgments This work is jointly supported by the National Science Foundation of China under Grant (41271434), the Natural Science Foundation of Jiangsu Province in China under Grant (BK2012209) and the Science and Technology Program of Suzhou in China under Grant (SYG201409). References
Fig. 12. Root mean square error of Chl-a concentration estimation plotted as a function of wavelength for 1 with different initial values for 2 and 3 : (a) 2 = 650, 3 = 730, (b) 2 = 670, 3 = 730, (c) 2 = 690, 3 = 730, (d) 2 = 700, 3 = 730. Table 2 RMSE and correlation comparison for different methods.
RMSE Correlation
Gitelson [10]
Zhang [15]
Our method
2.95 0.95
3.05 0.95
2.93 0.96
regression method. We have the following equation to estimate the Chl-a concentration: Chl-a = 36.98(−1 (1 ) − −1 (2 ))(3 ) + 2.9
(12)
Methods of Zhang [15] and Chen [17] are sensitive to the initial values of 1 , 2 and 3 . The optimization procedure was based on minimizing the RMSE of the Chl-a concentration estimates [15]. The RMSE of Chl-a estimation plotted as a function of wavelength for 1 with different initial values for 2 and 3 are shown in Fig. 12. The minimal values of the RMSE have been found at 1 = 656, 713, 684, 676 nm for different initial values of 2 and 3 are shown in Fig. 12(a)–(d), respectively. It is obviously that the results are sensitive to the initial values. To evaluate the effectiveness of our method, we compare it with methods of Zhang [15] and Giteson [10]. The initial values of 1 , 2 and 3 for method of Zhang [15] are 665, 700, 735 nm, respectively. Method of Gitelson [10] is computed with Eq. (2). The RMSE and correlation indices are computed according to the Chl-a concentration in sit and the Chl-a concentration estimated with those three methods and shown in Table 2. From Table 2, we can know that our method has better results than methods of Zhang [15] and Gitelson [10]. Results of method of Zhang [15] depends on the initial values for 1 , 2 and 3 . The time complexity for Giteson [12], Zhang [15] and our method are O(1), O(m) and O(m3 ), respectively.
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