Effects of Broad Bandwidth on the Remote Sensing of Inland Waters

ISPRS Journal of Photogrammetry and Remote Sensing 153 (2019) 110–122

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ISPRS Journal of Photogrammetry and Remote Sensing

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Effects of broad bandwidth on the remote sensing of inland waters: T Implications for high spatial resolution satellite data applications ⁎ Zhigang Caoa,b, Ronghua Maa, , Hongtao Duana, Kun Xuea a Key Laboratory of Watershed Geographic Sciences, Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, China b University of Chinese Academy of Sciences, Beijing 100049, China

ARTICLE INFO ABSTRACT

Keywords: High spatial resolution satellite sensors provide opportunities to observe spatial variations of biogeochemical High spatial resolution properties of small- and medium-sized inland water bodies. However, high spatial resolution sensors are usually Optical sensors equipped with wider spectral bandwidth (> 50 nm) that diminishes the features of the spectrum. Therefore, the Bandwidth effects of the border bandwidth issue need to be evaluated prior to application in aquatic environments. Basedon Inland waters the in situ optical data [remote sensing reflectance (Rrs) and absorption coefficients] and the radiative simu- Deep neural network lations of hyperspectral remote sensing reflectance and using band specifics of common sensors (e.g., OLCI, VIIRS, MSI, OLI, ETM+ and WFV) as examples, the effects of bandwidth on optical properties of inland waters were analyzed. The results showed the followings. (1) The difference between values at center-wavelength and

band-averaged values increased with increasing bandwidth for Rrs and the absorption coefficients. The differ-

ence was wavelength-dependent. The difference of Rrs at the visible band was within 0.25% but greater than 0.5% for the spectral bands near 710 nm and 665 nm. (2) The accuracy of the total absorption coefficient derived from QAA-750E, spectral match technique (SMT) and deep neural network (DNN) decreased with increasing bandwidth. The QAA-750E was more sensitive to bandwidth than SMT and DNN. Otherwise, the empirical algorithms for estimating chlorophyll-a (Chla) concentrations were significantly affected by bandwidth. The performance of algorithms for estimating cyanobacterial phycocyanin (PC) and suspended particulate matter (SPM) concentrations changed slightly with a wider bandwidth. Finally, the maximum bandwidth requirement for optical remote sensing in inland waters was proposed. For bandwidth options, it should be within 20 nm for 700–710 nm, ∼30 nm maximum for ∼560 nm and ∼665 nm, 60 nm for ∼620 nm, and ∼80 nm for ∼443 nm

and ∼490 nm, respectively. The difference between the Rrs of narrow bands (10–20 nm) and the Rrs of the bands with the recommended bandwidth was within 0.25%. The corresponding bandwidth from MSI and OLI sensors meet this criterion for Chla and SPM. However, the lack of spectral coverage near 700–710 nm may present a challenge to retrieve Chla concentration from OLI images. This study provided helpful theoretical and practical references for the retrieval of inland water parameters by high spatial resolution satellite sensors and its pro- spective development.

1. Introduction it is noticeable that medium- and small-sized lakes and reservoirs. For example, over 63.48% of the global lakes have areas less than 100 km2. The optical properties of inland water are complex and change ra- About 2557 of the 2693 lakes in China above 1 km2 are smaller than pidly. Therefore optical remote sensing of inland waters have been 100 km2 (Downing et al., 2006; Ma et al., 2010; Pekel et al., 2016). using the data of ocean color sensors due to freely available data with Medium- and small-sized lakes are a main subset of global inland wa- higher temporal coverage, signal-to-noise ratio (SNR) and spectral re- ters. Therefore, investigating and monitoring of those lakes require solution from MODIS Terra/Aqua (250 m and 500 m), MERIS Envisat higher spatial resolution satellite remote sensing data (Mouw et al., (300 m) and OLCI Sentinel 3A/B (300 m) sensors (Duan et al., 2017; 2015). In fact, the satellites with high spatial resolution like Landsat Palmer et al., 2015; Qi et al., 2014; Shen et al., 2017; Jiang et al., 2019). and SPOT have been used to monitor the parameters of water quality Because of the low spatial resolution, these data are only used to since the last century (Doxaran et al., 2002; Giardino et al., 2001; monitor the water environment in large lakes and reservoirs. However Olmanson et al., 2015; Olmanson et al., 2016; Zhou et al.,2014).

⁎ Corresponding author. E-mail address: [email protected] (R. Ma). https://doi.org/10.1016/j.isprsjprs.2019.05.001 Received 15 December 2018; Received in revised form 3 May 2019; Accepted 4 May 2019 0924-2716/ © 2019 Published by Elsevier B.V. on behalf of International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Z. Cao, et al. ISPRS Journal of Photogrammetry and Remote Sensing 153 (2019) 110–122

Table 1 Satellite instruments used in this study for the bandwidth evaluations. Note that only the visible and infrared bands are listed here.

Sensor OLCI VIIRS MSI OLI ETM+ TM WFV

Satellite Sentinel 3 Suomi NPP/NOAA-20 Sentinel 2 Landsat 8 Landsat 7 Landsat 4/5 GF 1/2 Duration 2015– 2011– 2015– 2013– 1999– 1983–2013 2013– Band number 21 11* 12 7 6 6 4 Resolution (m) 300 750 10/20/60 30 30 30 30 Revisit time (d) 1.5 0.5 5 16 16 16 16

* Only the 11 moderate-resolution (M) bands with a spatial resolution of 750 m for the VIIRS are listed.

Particularly, in recent years, with the launch of the Landsat-8, GF-1/2 inherent optical properties over inland water and interpret the band- and Sentinel 2A/B satellites (Table 1), more open source and high- width effects; (2) analyze the sensitivity of algorithms for estimating of quality imagery data are available, providing an opportunity to un- the total absorption coefficient (QAA-750E, SMT and DNN), the con- derstand environmental changes and processes of small- and medium- centration of Chla (red-NIR band ratio algorithm, three bands algo- sized water bodies with improved accuracy in observation (Ruddick rithm), the concentration of PC (PCI algorithm) and the concentration et al., 2016). However, these high spatial resolution (hereafter referred of SPM (red and NIR band algorithm) with increasing bandwidth; (3) to as high-resolution) sensors possesses low SNRs and might not com- recommend a bandwidth requirements for optical remote sensing in- pletely meet the requirements of water color research as suggested, e.g., land waters. ∼400:1 for visible bands and ∼600:1 for near-infrared (NIR) bands (Qi et al., 2017; Wang and Gordon 2018). Those sensors are usually 2. Materials and methods equipped with spectral bands that have a wide bandwidth (> 50 nm). Wide bandwidths diminish the features of spectrum and reduce the 2.1. Field-measured data ability to identify water substances (Dekker et al., 1992). Thus, the effect of wide bandwidth needs to be addressed and analyzed whenthe 2.1.1. Study area data are used to map optically active objects in the water. We selected three large, shallow freshwater lakes in China as the Currently, research focuses in the optical remote sensing of inland study areas (Fig. 1). Lake Taihu, Lake Hongze, Lake Chaohu are the waters include algal blooms, suspended particulate matter (SPM) or third (2338 km2), fourth (1597 km2), and fifth (770 km2) largest turbidity, chlorophyll-a (Chla), cyanobacterial phycocyanin (PC) and freshwater lakes in China, respectively. Water in Lake Taihu and Lake chromophoric dissolved organic matter (CDOM) (Mouw et al., 2015; Xu Chaohu are eutrophic with a high nutrient content and usually have et al., 2018; Jiang et al., 2019; Zhou et al., 2014). Satellite sensors must algal blooms. The phytoplankton biomass is high in those lakes (Duan be equipped with spectral bands that are sensitive enough to detect the et al., 2017, 2009). Water in Lake Hongze contains high level of tur- targeted materials. The green, red and NIR bands are sufficient for the bidity with high concentration of SPM due to runoff from the tributary detection of the spatial coverage of algal blooms and the estimation of of the Huai River, and dredging activities in this lake from 2012 to SPM, turbidity and water clarity (Neil et al., 2011; Song et al., 2017; March 2017, led to a dramatic increase in SPM (Cao et al., 2017). The Jiang et al., 2019; Xing and Hu 2016), and the specification of the Chla and SPM concentrations ranged from 5.60 to 99.01 µg/L (mean: wavelengths is not necessary. However, the estimation of the Chla 25.05 ± 23.24 μg/L) and 6.00–180 mg/L (mean: 52.32 ± 26.79 mg/ −1 −1 content in turbid inland lakes requires spectral coverage near 665 nm L), respectively, and the ag(443) ranged from 0.23 m to 5.02 m and 700–710 nm (Gitelson 1992; Simis et al., 2007), and the estimation (mean: 1.05 ± 0.50 mg/L) (Table 2). Hence, these three lakes have of the PC content requires spectral band near 620 nm (Simis et al., complex optical properties to represent a wide variety of inland lakes. 2005a). High-resolution sensors are not usually equipped with bands at Eight field surveys were conducted and a total of 156 valid datasets those wavelengths. Therefore, reported studies have developed effec- were collected. Fifty-two datasets were collected from Lake Taihu be- tive algorithms to monitor the HABs, SPM and water clarity in inland tween November 2016 and May 2017 (N = 52), 78 datasets were col- waters using the Landsat-8, Sentinel 2A/B and GF-1/2 satellites due to lected from Lake Hongze between April 2014 to February 2016, 26 their visible or significant signals on satellite images (Ho et al., 2017; datasets were collected from Lake Chaohu between October 2015 and Lee et al., 2016; Li et al., 2015; Liu et al., 2017); however, the higher January 2016 (Fig. 1, Table 2). Because the optical property of water performance algorithms for the Chla and PC concentration estimations covered by algal blooms is significantly different from that in natural still need to be studied further (Ha et al., 2017; Olmanson et al., 2016). water (Hu, 2009; Hu et al., 2010), the samples covered by algal blooms Even if bands cover these wavelengths, for example, the Landsat-8 OLI were excluded in this study. Surface water (depth: ∼50 cm) was col- includes the 665 nm and the MSI of Sentinel 2A/B covers the 665 nm lected using a standard 2-liter polyethylene water-sampling instrument and 705 nm, the bandwidth of sensors are wide to receive more ra- and then stored in the dark and kept cool with ice bags before the diance in exchange for higher spatial resolution. Broader bandwidths concentrations of Chla and SPM and the absorption coefficients were for satellite sensor bands will diminish the sensitivity of the spectral measured in a laboratory. features on which remote sensing of water constitutes (Dekker et al., 1992) and will affect the difference between the signal at the sensor and 2.1.2. Remote sensing reflectance the hyperspectrum and the retrieval of inherent optical properties (Lee, The Rrs at the discrete stations was measured with an ASD field 2009). Thus, understanding the effects of bandwidth on the optical spectrometer (FieldSpec Pro Dual VNIR, Analytical Spectra Devices, properties of the water and finding a balance between spatial resolution Inc.) with a 6-degree lens in front of the optical fiber, using the NASA and bandwidth to determine the sensor’s bandwidth requirement for protocols recommend by Mueller et al. (2003). At each station, the the high-resolution optical remote sensing of inland waters can not only measured spectrum was sampled at the 135° azimuth with respect to facilitate the evaluation of potential of traditional high resolution sen- the sun and with a nadir viewing angle of 45°, ranging from 350 nm to sors but also be used as a reference for future sensor designs. 1050 nm with an interval of 1 nm (Fig. 2a). The total water leaving In this study, we used field measurements and radiative numerical radiance (Lsw), the radiance of reference gray panel reflectance (Lp), simulations to study the effects of bandwidth on remote sensing ofin- and the sky radiance (Lsky) were measured to derive the Rrs as follows: land waters. The main objectives are to: (1) evaluate the impact of R ()(()())/L()= L L increasing bandwidth on optical remote sensing of apparent and rs sw sky p p (1)

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Fig. 1. Sample stations (N = 156) in Lake Taihu, Lake Hongze and Lake Chaohu in China. where ρ is the water surface reflectance factor dependent on sky con- Table 3 ditions, wind speeds, and solar zenith angle. It was assumed to be 0.028 Statistics for a(443) derived from the QAA-750E, the SMT and the DNN with based on the wind speed (< 5 m/s) and sky conditions (clear sky or low 20 nm, 50 nm, 100 nm and 150 nm bandwidths. cloud conditions) from field measurements according to the results of Bandwidth 20 nm 50 nm (Mobley, 1999). Additionally, ρp is the reflectance of the gray panel, which is 30% for our field measurements. Approach QAA-750E SMT DNN QAA-750E SMT DNN

R2 0.99 0.96 0.94 0.99 0.92 0.87 2.1.3. Chla, SPM and the absorption coefficient Slope 1.02 0.99 1.14 1.03 0.95 1.07 A glass fiber filter (70 mm Whatman GF/C) was used to filter the bias 0.09 0.04 0.55 0.07 0.07 0.99 water and was subsequently soaked in 90% acetone to extract the APD 0.19 0.62 0.82 0.43 0.95 1.11 pigments. Subsequently, the concentration of Chla was measured using Bandwidth 100 nm 150 nm a Shimadzu UV-2600 spectrophotometer (Gitelson et al., 2008; Werdell R2 0.97 0.88 0.88 0.90 0.87 0.84 et al., 2013). The SPM concentrations were gravimetrically determined Slope 0.96 0.80 0.96 0.83 0.69 1.05 bias 1.34 0.23 0.55 2.90 0.57 0.37 from samples collected from precombusted and preweighed Whatman APD 2.36 1.70 1.40 4.45 2.12 1.19 GF/F filters (47 mm) that were dried at 105 °C for 4 h. The SPMwas further differentiated into suspended inorganic matter (SPIM) and suspended organic matter (SPOM) by burning the organic matter from (1993) for wavelengths between 720 and 900 nm. the filters at 450 °C for 4 h and weighing the filters again(Cao et al., a()()()()()=a +a +a + a 2017). ph d g w (2)

The absorption coefficient of phytoplankton [aph(λ)], the absorption coefficient of detritus [ad(λ)], and the absorption coefficient of CDOM (ag(λ)) were measured in the laboratory using the quantitative filter 2.2. Simulated datasets technique. The total absorption coefficient, a(λ), was calculated as the sum of aph(λ), ad(λ), ag(λ), and the absorption coefficient of pure water The simulated datasets were generated using the widely used and [aw(λ)] (Fig. 2b). In this study, the aw(λ) was obtained from Pope and efficient HydroLight 5.0 package (Mobley, 1994). First, HydroLight’s Fry (1997) for wavelengths between 400 and 700 nm and by Kou et al. Case-II model with options for inland waters was selected. A four-

Table 2 Sampling dates, number of samples, ranges (min–max) and mean values (means ± standard deviations) of in situ measured concentrations of Chla, SPM, SPIM and the total absorption coefficients (a) and absorption coefficients of phytoplankton (aph), detritus (ad) and CDOM at 443 nm (ag). The details of the sampling stations are shown in Fig. 1.

Lake Lake Taihu Lake Hongze Lake Chaohu Dates Nov 2016, Mar 2017, May 2017 Apr 2014, Oct 2014, Feb 2016 Oct 2015 and Jan 2016 N 52 78 26 Statistics Range Mean Range Mean Range Mean

Chla (μg/L) 5.60–99.01 28.96 ± 22.31 2.70–85.64 14.19 ± 12.94 9.86–98.27 51.08 ± 25.14 SPM (mg/L) 16.00–180.00 67.75 ± 40.96 6.00–78.67 41.09 ± 13.81 18.00–118.00 44.83 ± 18.44 SPIM (mg/L) 4.00–157.33 44.81 ± 41.25 4.00–64.67 30.91 ± 13.25 18.00–93.00 31.65 ± 15.60 a(443) (m−1) 2.63–9.52 4.90 ± 1.75 2.20–8.25 3.79 ± 1.05 2.65–14.59 4.08 ± 1.13 −1 ad(443) (m ) 0.63–7.60 2.53 ± 1.50 0.56–6.11 2.14 ± 0.87 0.92–11.76 2.42 ± 1.01 −1 aph(443) (m ) 0.34–3.92 1.20 ± 0.70 0.22–2.04 0.71 ± 0.44 0.54–4.67 0.70 ± 0.39 −1 ag(443) (m ) 0.23–5.02 1.17 ± 0.73 0.27–1.77 0.94 ± 0.31 0.69–1.75 0.96 ± 0.33

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Table 4 3.0 m/s, as these are typical values for our study area. The Fresnel re- Requirements for the design for sensors for the remote sensing of inland waters. flectance and transmission coefficients of an air–water interface was Δλ was the requirement of bandwidth for the remote sensing of inland lakes determined by the default refractive index in HydroLight (n = 1.34). To recommended by this study, and the values in parentheses were from the ensure that the simulated datasets are representative of more water IOCCG (2012). The center wavelengths and corresponding bandwidths of OLI, bodies, the Chla ranged from 0.1 to 100 μg/L, the SPIM ranged from 0.1 MSI, ETM+, and WFV are listed below. −1 to 100 mg/L, and the ag(443) ranged from 0.001 to 6 m , as demon- λ (nm) Application Δλ (nm) OLI MSI ETM+ WFV strated in our measured data and other lake data in the world (Spyrakos et al., 2017). Furthermore, we used the specific absorption coefficient of 443 Chla absorption 80(15) 443(20) 443(27) \ \ peak phytoplankton and the specific absorption and backscattering coeffi- 490 Chla in clear water 80(15) 482(65) 490(98) 483(70) 485(70) cients of detritus from the field data instead of the corresponding 560 Chla in clear water 30(15) 561(75) 560(65) 565(80) 555(70) anonymous coefficients in the simulation (Xue et al., 2017). With var- 620 Cyanobacterial 60(15) \ \ \ \ ious combinations of concentrations and optical properties, a database phycocyanin of 12,000 R spectra ranging from 402.5 to 897.5 nm with 5 nm in- 665 Chla in turbid 30(10) 655(50) 665(38) 660(70) 660(60) rs water; SPM tervals was established. The dataset will be the database for the SMT 710 Chla in turbid 20(15) \ 705(19) and will be used to train the DNN model below. water

2.3. Average spectrum calculation component model of the IOPs of the water components (pure water, phytoplankton, mineral particles, and CDOM) was used in our com- The hyperspectral Rrs values were resampled to the band-averaged putations. Chla, SPIM and CDOM were assumed to be vertically in- Rrs for each satellite sensor using the relative spectral response function dependent, and the optical deep-water option was selected. In addition, (RSR) (Eq. (3)). Due to the absorption coefficient is inversely propor- the solar zenith angle was assumed to be 30° with a wind speed of tional to the Rrs, the band-averaged aph, ad, ag and aw values were obtained from a two-step process (Lee et al., 2016) and then used to

Fig. 2. (a) In situ Rrs at Lakes Taihu, Hongze and Chaohu. (b) The averaged total absorption coefficient [a(λ)]; the gray-filled area is the standard deviation. (c) The band distribution with bandwidths for the OLCI full-resolution (FR) bands (300 m), the VIIRS M-bands (750 m), the MSI (10 m, 20 m, 60 m), OLI (30 m), the ETM+

(30 m) and the WFV (16 m). The black dashed line is the averaged in situ Rrs. (d) Spectral values of the SNR under the radiance input of Ltypical (Hu et al., 2012) for the 6 sensors.

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calculate total absorption coefficient (a) (Eqs. (4), (5)) et al., 2005). The simulated Rrs database generated by HydroLight 5.0 900 above was taken as a lookup table. Then, we resampled the measured 400 Rrs ()()RSRi d and simulated Rrs database to the same satellite sensor using the RSR. Rrs() Bi = 900 RSRi ()d 400 (3) The matchup was conducted by examining the APD between the measured band-averaged Rrs and each spectrum in our database (Eq. (7)). 900 RSRi ( )(1/a ( ))d 400 N mea mod 2 a() Bi = 900 i=1 (()())Rrs i Rrs i RSRi ()d APD = 400 (4) N Rrsmea () i i=1 (7)

1 mea mod a(B i ) = where N is the number of spectral bands, and Rrs and Rrs re- a() Bi (5) rs present the measured and modeled R values, respectively. The band-averaged spectrum of six sensors, OLCI, VIIRS, MSI, OLI, ETM+ and WFV, were calculated in this research. The data of these 2.4.3. Deep neural network missions are freely available, and their band settings and corresponding The deep neural network (DNN) is a common, efficient method of bandwidths were shown in Fig. 2c and their SNRs were shown in deep learning. It has been used in complex image classification and Fig. 2d. Further, to quantify the impact of bandwidth, 16 visible and regression models. A DNN implements complex function approximation

NIR bands of the OLCI were selected to calculate the band-averaged Rrs through deep nonlinear network structures and demonstrates the and the band-averaged a with different bandwidths (the RSR is an ideal powerful ability to learn the essential and generic features of datasets rectangle and full response function). In final, the differences between from a finite dataset (Haykin, 1994; Krizhevsky et al., 2012;

Rrs and a at sensor wavelengths and at center wavelengths (hereafter Schmidhuber, 2015). To date, DNNs have been proven to be useful for a refer to as δRrs, δa, respectively) were compared. large number of applications in Earth system observations (Reichstein et al., 2019), for instance, for analyzing ocean, coastal and inland wa- 2.4. Algorithms for estimating the total absorption coefficient ters in terms of atmospheric correction, algal bloom detection, inversion algorithms, and bias correction (Fan et al., 2017; Lary et al., 2016; 2.4.1. QAA-750E Nazeer et al., 2017; Pahlevan et al., 2017; Qiu et al., 2018). Wide-band The semi-analytical approach proposed by Xue et al. (2019) was sensors usually equip a small number of bands with wider bandwidths used to derive a(λ) from Rrs of sensors (Eqs. (6a–e)). The QAA-750E was and lower SNRs, and the optical properties of inland water bodies are developed from the QAA-v6 (Lee, 2014) because the latter yielded complex. Therefore, the DNN method was employed in this study to unsatisfactory results in turbid inland waters due to the dynamic and retrieve the total absorption coefficient from the finite datasets. complex optical properties. In fact, the absorption of dissolved and A DNN model was built to retrieve a(λ) using Rrs. To achieve the suspended constituents at 750 nm [Δa(750)] can be negligible because best training performance, the DNN model focused on five aspects of of the very small total non-water absorption coefficients [anw(750)]. the design of the model structure and was implemented in the Google Thus, the reference wavelength in calculating a(λ) was changed to deep learning framework (TensorFlow 1.1) using Python (Pahlevan 750 nm, and a(λ0) [=aw(750) + Δa(750)] was assumed to be aw(750) et al., 2017). (1) The ReLU function was employed as the activating in QAA-750E. Also, bbp(750) was derived. Finally, bbp(λ) and a(λ) were function for every hidden layer of networks. (2) The function from estimated using the same semi-analytical equations as in the QAA-v6. Microsoft Research Asia (MSRA) was used to initialize the weight ma-

Note that the empirical formula of Y for deriving bb(λ) was tuned using trix for each layer. (3) The Adam optimizer was used to deal with the HydroLight data simulated using the local input parameters from gradient descent. (4) The weight decay (L2 regularization) and dropout Xue et al. (2017). was assigned in the model to prevent overfitting. (5) The grid search technique was implemented to obtain the optimal parameters of the rrs ()= Rrs ()/(0.52+ 1.7Rrs ()) (6a) model: the network layer number, the number of neurons in each layer, 2 1/2 the iteration count, the learning rate and the dropout value. Changing g0+[( g 0 ) + 4 g1 rrs ( )] u () = , whereg0 = 0.089 and g1 input parameters was used to train the DNN model individually, and 2g1 then the parameters corresponding to the optimal training effect were = 0.1245 (6b) adopted. a(750)= aw (750) + a(750) aw (750), 3. Results u(750)× a (750) bbp (750) = bbw (750) 1u (750) (6c) 3.1. Effects of increasing bandwidth

rrs (443) Y= 3.99 3.59 exp 0.9 Fig. 3 presents an example of the in situ hyperspectral Rrs (solid line) rrs (560) (6d) and corresponding band-averaged Rrs for six sensors calculated by Eq. (4). For the ocean color sensors, OLCI and VIIRS, the band-averaged Rrs 750 Y (1u ( ))bb ( ) bb( )= b bp (750)( )(),()+ bbw a = u () (6e) overlapped with the hyperspectral Rrs; however, some band-averaged Rrs values of those sensors designed for land application deviated from the in situ hyperspectral Rrs. It was easy to find that the band-averaged 2.4.2. Spectral matching technique Rrs from those bands equipped with the broad bandwidth (> 50 nm) on Briefly, the SMT can be divided into 3 steps. First, a simulated da- the OLI, MSI, ETM+ and WFV sensors was lower than that at center tabase of Rrs spectra corresponding to various inherent optical proper- wavelength, except for B3 of the ETM+ sensor. This result may be ties (IOPs) was built using a radiative transfer model. Second, the because the RSR for B3 of the ETM+ sensor covered a higher peak near measured Rrs was compared with each Rrs in the database, and the the center wavelength (660 nm) (Fig. 2c). closest match to the measured Rrs was found using a statistical metric, In general, δRrs increased with increasing bandwidth and δRrs was for example, the absolute percent difference (APD) in this study. The wavelength-dependent. δRrs at 665 nm and 709 nm was high than that environmental conditions are then assumed to be the same as the input at other wavelengths (Fig. 4a); for example, δRrs(665) and δRrs(709) conditions, and the IOP of the closest matching simulated database increased dramatically when the bandwidth was wider than 10 nm, spectrum was the result corresponding to the measured Rrs (Mobley δRrs(665) was ∼0.5% when the bandwidth was 80 nm, and δRrs(709)

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blue and green bands were not very sensitive to increasing bandwidth. For the absorption coefficients, aph was significantly influenced by increasing bandwidth, and δaph even exceeded 6% (Fig. 4b). δaph increased dramatically with increasing bandwidth and reached 1% when

the bandwidth was greater than 50 nm, and δaph(665) easily increased compared with δaph at other wavelengths. Compared to aph, ad and ag were not very sensitive to increasing bandwidth. Generally, δad(λ) decreased with increasing exponentially bandwidth, yet δad(443) increased logarithmically with increasing bandwidth (Fig. 4c). Contrary

to the trend of δad(λ), δag(λ) increased logarithmically with increasing bandwidth, and the value of δag(443) was ∼0.5% when the bandwidth was 50 nm and only reached ∼1% at the 120 nm bandwidth (Fig. 4d). The results demonstrated that δaph(665) was significantly affected by bandwidth, yet the δad(443) and δag(443) were relatively stable with increasing bandwidth. Consequently, the increasing bandwidth mainly influenced the optical properties at characteristic wavelengths fromthe phytoplankton pigments, including Chla.

3.2. Sensitivity of different IOP-retrieving algorithms for bandwidth Fig. 3. The average hyperspectral curve of Rrs and the band-averaged Rrs for the OLCI, the VIIRS, the OLI, the MSI, the ETM+ and the WFV. We can easily see that the band-averaged Rrs of the OLI, the MSI, the ETM+ and the WFV de- The sensitivities of the QAA-750E, SMT and DNN methods for es- viated from the in situ Rrs at those bands with wide bandwidths. timating a(λ) according to the bandwidth were compared to provide references to the remote sensing of optical properties over inland water using broad satellite sensors. Obviously, the QAA-750E was more sen- surpassed 1% at the bandwidth of 80 nm. δRrs at 443 nm, 560 nm and sitive than the SMT and the DNN (Fig. 5a); the a(443) values derived 620 nm was low (Fig. 4a), and the values for δRrs(443;560;620) were within 0.25% even if the bandwidth reached 150 nm. In other words, from the QAA-750E at the wide bandwidth were overestimated and deviated from the 1:1 line when the bandwidth surpassed 50 nm. And the Rrs in the red and in the red-edge bands (∼665 nm and ∼709 nm, respectively) were easily affected by increasing bandwidth, and the the APDs between the measured and estimated a(443) values were 2.36% and 4.45% for the 100 nm and 150 nm bandwidths, respectively.

Fig. 4. (a) APD variations between the band-averaged in situ Rrs at 443, 560, 620, 665 and 709 nm with different bandwidths and Rrs in the center wavelength.

(b)–(d) The APD variations between the band-averaged in situ aph, ad and ag, respectively, at 443, 560, 620 and 665 nm with different bandwidths and in the center wavelength.

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Fig. 5. (a)–(c) The difference between a(443) with 0 nm bandwidth and the band-averaged a(443) with various bandwidths derived from the QAA-750E, the SMT and the DNN, respectively. The statistical measures are summarized in Table 3. (d)–(f) The APD between the in situ total absorption coefficient and the band- averaged total absorption with wider bandwidths at 443, 490, 560, 620 and 665 nm derived from the QAA-750E, the SMT and the DNN, respectively.

For the SMT, the deviation also presented but was less than that from 4. Discussion the QAA-750E (Fig. 5b), and a(443) derived from the SMT were un- derestimated in the broader bandwidth, and the APDs were within 2% 4.1. Interpretation of the bandwidth effects for the 150 nm bandwidth. Relative to the previous two algorithms, a (443) derived from the DNN was not sensitive to the bandwidth and The signal received by satellite sensors is an integral value ac- was evenly distributed around the 1:1 line (Fig. 5c). Even if the band- cording to the RSR in a certain wavelength range (Sabins and Lulla, width was 150 nm, the value for δa(443) was approximately 1%. It 1987). Moreover, the signal of water is very low, therefore it is very should be noted that the values of a(443) derived from the DNN were important for a sensor to detect weak changes in the water. The dif- lower than the in situ a(443) values by 20%, which may be due to the ference does exist when the signal at the center wavelength is directly lack of high absorption samples in the training datasets. used to replace the band-averaged signal in applications. From a Subsequently, the performance of the three algorithms at different mathematical view, the difference is caused by the difference between wavelengths was compared (Fig. 5d–f). δa derived from the three al- the area under the curve and the rectangular area for the signal of a gorithms increased with increasing bandwidth at the several waveband calculation. The spectra of natural materials can be divided into lengths, as in the results above. The QAA-750E showed a larger de- three categories according to shape (Bowker et al., 1985): a straight line viation with increasing bandwidth, yet the DNN presented a relatively with a fixed reflectance, a monotonous smooth curve and a parabola stable trend. Specifically, when the bandwidth was 20nm, δa derived with a peak or valley (Fig. 6). First, we assumed that there was a band from the QAA-750E at all wavelengths were less than 0.5%, but it in- (Bx) with a wavelength range of λmin-λmax before the analysis. (1) For creased dramatically when the bandwidth was greater than 50 nm. In the straight line with a fixed reflectance (ρp)(Fig. 6a), it was easily to particular, the increasing rates of δa(560) and δa(665) were higher than conclude that the integral average value of Bx was equal to the re- other wavelengths (Fig. 5d). δa(λ) derived from the SMT also increased flectance value at any wavelength within λmin-λmax, and λc was the with increasing bandwidth. The differences at all wavelengths were less center wavelength of Bx. Thus, the bandwidth variation had no influ- than 1% when the bandwidth was less than 50 nm, and it only reached ence on these curves. Although the entire spectrum is basically non- 2% when the bandwidth was 100 nm (Fig. 5e). Compared with the existent in nature, the part of the spectrum curve with a very narrow QAA-750E and the SMT, the DNN did not present a significant increase, width can be as a straight line, and the effect of bandwidth can be and the differences of all wavelengths were less than 2%, even ifthe overlooked. (2) For a monotonous smooth curve without the inflection bandwidth exceeded 150 nm (Fig. 5f). The results demonstrated that point, the integral (A) is equal to the sum of A0 and A1 (see Fig. 6b), the SMT and especially the DNN were less sensitive to increasing and the curve within Bx can be taken as a straight line when the bandwidth than the QAA-750E, showing the potential of remote sensing bandwidth is very narrow, so that A1 approximately equals A2, then A of inland waters using broad satellite sensors (for example, the Landsat is equal to the sum of A0 and A2, i.e., δλ*ρ(λc); therefore, ρ(λc) can be 7 ETM+ and the Landsat 4/5 TM sensors). approximately equal to the band-averaged reflectance. However, the hypothesis that replacing a curve with a straight line for broad band-

width did not work correctly, and the difference between ρ(λc) and the band-averaged reflectance for a broad bandwidth will increase.

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Fig. 6. Schematic diagrams for the band-averaged spectrum calculated from the RSR for three types of curves: (a) a line with fixed value, (b) a monotonous curve, and (c) a curve with one peak. Here, λmin, λc, and λmax are the minimal, central and maximal wavelengths, respectively, for one band. ρ = 0 represents the x axis of the spectrum, and ρp is a part of one spectrum. Note that the RSR is the rectangle with 100% spectral response, and A0, A1 and A2 are the areas of polygons.

Furthermore, the curvature of the curve also determined the difference between ρ(λc) and band-averaged reflectance, and the large curvature increased the difference for the same bandwidth. (3) For a parabola with a peak or valley, as shown in Fig. 6c, the integral value was A0 between λmin and λmax, and the rectangular area was A0 + A1 + A2, i.e., δλ*ρ(λc). Note that A1 and A2 are the graphical areas enclosed by the sides of the curve and ρ(λc). For the narrow bandwidth in Bx, the area of A1 and A2 was very small, and the difference between ρ(λc) and A0/δλ was small; thus, the difference between ρ(λc) and the band- averaged reflectance was small. However, this difference will be larger for a broad bandwidth. Moreover, the parabola with a smaller full width at half maximum (FWHM) was more sensitive to the broader bandwidth. These results demonstrated that the shape and curvature of the curve determined the effects of the bandwidth, as interpreted froma mathematical view to clarify the effect of spectral bandwidth using a different perspective from Dekker et al. (1992).

δRrs(560), δRrs(665) and δRrs(709) increased substantially with increasing bandwidth because they were located in the part of parabola with a peak or a valley (Fig. 2a, b). In fact, they are sensitive wavelengths for Chla in turbid inland waters (Gitelson et al., 2008; Gons, 1999). In particular, the coverage of the band near 709 nm is very Fig. 7. Variations in the Pearson correlation coefficients between the spectral narrow and easily changes different types of water (Gitelson, 1992); index and the concentrations of Chla, PC and SPM. therefore, the broad bandwidth significantly affected δRrs(709). The same was true for δaph(665), which is closely related to Chla and varies (Fig. 7). The Pearson correlation coefficient (r) between SPM and greatly with increasing bandwidth (Gons et al., 2002, 2005). Further- Rrs(674) and Rrs(754) was greater than 0.85 and was essentially in- more, the increase in δRrs(620), the absorption peak of PC, was not very variant with increasing bandwidth, which clarified the high perfor- fast with increasing bandwidth. Actually, the FWHM of the absorption mance of the broad sensor in retrieving the SPM concentration in inland peak of PC at ∼620 nm is ∼75 nm (Simis et al., 2007, 2005b); there- waters. The r between PCI and PC was always approximately 0.87 when fore, Rrs(620) was not very sensitive to the bandwidth. ad and ag are the bandwidth was within 50 nm, and then it showed a gradually de- monotonous smooth curves, so that they were not sensitive to the increasing trend and was less than 0.80 with increasing bandwidth, de- creasing bandwidth. The slope of ad(443) was larger than at other monstrating that the broad bandwidth sensor had a weak effect on the wavelengths, and the spectral change was fast; thus, δad(443) was more PC concentration estimation. Compared with the SPM and the PCI re- sensitive to increasing bandwidth than other wavelengths. As the wa- trieval using a broad bandwidth, the performances of algorithms for velength increases, the changes in ad were more gradual, and thus, the estimating the PC concentration are significantly affected by the effect of bandwidth was smaller and smaller. Forδag, the larger un- bandwidth increasing. The r between Chla and Rrs(709)/Rrs(665) with certainty at longer wavelengths may be due to the lower value of ag at the TBA reached 0.90 when the bandwidth was within 20 nm, the r long wavelengths. gradually decreased and was less than 0.80 for a bandwidth of 50 nm, and it dramatically decreased afterwards until r was just 0.50 for a 4.2. Algorithm performance of remote sensing in broad bandwidth data bandwidth of 80 nm. Increasing bandwidth not only affected the performance of bio-optical models (Lee, 2009), but also decreased the Chla, PC and SPM concentrations are common parameters used to precision of empirical algorithms, particularly the algorithms used to evaluate the water quality of aquatic environments. Based on previous estimate the Chla concentration of inland waters. Therefore, the effect studies, typical empirical algorithms are selected to test their sensitiv- of broad bandwidth must be taken into consideration and calibrated ities to increasing bandwidth. Due to the special requirements of bands when broad bandwidth satellite data was used to retrieve the Chla for estimating the concentrations of Chla and PC in turbid waters, the concentration. band specifics of OLCI were used to obtain the band-averaged Rrs from Additionally, the OLCI and MSI data were also used to test the the in situ hyperspectral Rrs. The Rrs(709)/Rrs(665) and the three-band performances of the SPM and Chla algorithms in Lake IJsselmeer, algorithm (TBA) proposed by were used to retrieve the Chla con- Netherland, where the algorithms have been calibrated well and can be centration (Gitelson et al., 2008; Simis et al., 2007), the PCI algorithm directly used (Gons et al., 2002; Nechad et al., 2010). The Rrs of the was used to estimate the PC concentration (Qi et al., 2014), and the OLCI and MSI data were generated by the C2RCC processor in SNAP

Rrs(674) and Rrs(754) were used to obtain the SPM concentration 6.0, and the Chla and SPM concentrations were retrieved subsequently.

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Fig. 8. (a)–(c) The RGB image, the SPM concentrations and the Chla concentrations derived from the MSI, respectively, on 21 April 2018 in Lake IJsselmeer, The Netherlands. (e)–(g) The RGB image, the SPM concentrations and the Chla concentrations derived from the OLCI, respectively, on 21 April 2018. (d) and (h) The APD between the MSI-derived and the OLCI-derived concentrations of SPM and Chla, respectively. Note that the Chla concentrations were only measured in waters where

Rrs(∼665) > 0.005 and Rrs(∼704)/Rrs(∼665) > 0.63 (Vanhellemont and Ruddick, 2016).

The MSI- and OLCI-derived SPM concentrations on 21 April 2018 in SMT and the DNN can use the Rrs at all bands and are not sensitive to Lake IJsselmeer showed a consistent spatial pattern and range (Fig. 8a the broad bandwidth, therefore they may be a potential method to es- and b), and the APD between them was less than 20% in the whole lake timate the Chla and PC for high-resolution instruments in the future and even less than 10% in the clear water area (Fig. 8c). As demon- (Concha and Schott, 2016; IOCCG, 1998). strated above, the SPM estimation was not significantly affected by the increasing bandwidth of the sensor. However, the consistency of the 4.3. Requirements of bandwidth for remote sensing of inland waters Chla derived from the MSI and OLCI data was not very satisfied, and the APD of Chla derived from the OLCI data was more than 20% and even 4.3.1. Bandwidth requirement surpassed 50%. Although the spatial distribution shown by the two IOCCG (1998) and IOCCG (2012) recommended the requirements of sensors were similar, the MSI-derived Chla concentration was less than the bandwidth of ocean color sensors for 350–750 nm, 750–865 nm and the OLCI-derived concentration. In addition, the APDs in the northern 865–2130 nm were 10–15 nm, 20–40 nm and 20–50 nm, respectively. area and in the region near the island in the southern area were higher And, Ritchie et al. (1994) indicated that the bandwidth of 10–15 nm than in other regions, which may be caused by the adjacent effects due was required for 675–705 nm to support the retrieval of Chla in sus- to the coarse spatial resolution of the OLCI. Although other factors may pended dominated systems. In this study, two methods were used to also lead to differences in Chla concentration estimations, such as SNRs, determine the bandwidth requirement: (1) δRrs(λ) is within 0.25%, differences in Chla concentrations derived from broad and narrow which is a more rigorous requirement than the calibration accuracy bandwidth satellite sensors did exist and must be considered in prac- within 0.5% in ocean color; (2) when δRrs(λ) increases dramatically for tice. one bandwidth, the corresponding bandwidth is taken as another re- Due to the high spatial resolution sensors were usually designed for quirement. In final, the minimum was as the requirement forthe land applications, the band setting was not suitable for aquatic remote bandwidth. Note that the bandwidth requirement does not incorporate sensing, except for the MSI aboard Sentinel 2A/B, other instruments do other specifics of sensors, such as the spatial resolution, the SNRs,and not equip with the band near 700–710 nm for Chla concentration es- the spectral resolution. timation in turbid inland waters (Gitelson, 1992). Otherwise, for the Specifically, the bandwidth was 30 nm whenδRrs(709) was more MSI data, the broad bandwidth of these bands is wide in B4 (∼665 nm) than 0.25% (Fig. 4a); however, δRrs(709) increased dramatically when and B5 (∼705 nm), which decreases the performance of the Chla re- the bandwidth was greater than 20 nm. Therefore, the bandwidth retrieval algorithm. Thus, it is still a challenge to retrieve the Chla con- quirement for ∼709 nm was 20 nm, which was the same as in previous centration over inland waters using broad bandwidth sensors such as studies (Dekker et al., 1992; Ritchie et al., 1994). Similarly, δRrs(560) Landsat 7 EMT+, Landsat 8 OLI and GF-WFV. Moreover, many studies and δRrs(655) exceeded 0.25% when the bandwidth was 50 nm, yet demonstrate that PC is the unique pigment of cyanobacteria blooms in they increased rapidly when the bandwidth was 30 nm; therefore, the freshwater lakes with a diagnostic absorption peak at ∼620 nm, and bandwidth requirement was 30 nm. δRrs(443) and δRrs(620) surpassed cyanobacterial blooms can be detected using remote sensing (Duan 0.25% when the bandwidth was greater than 100 nm and increased et al., 2012; Qi et al., 2014; Simis et al., 2007; Sun et al., 2015). Cur- rapidly at shorter bandwidth, therefore the required bandwidth was rently, only OLCI has the band of ∼620 nm, empirical algorithms for within 80 nm and 60 nm, respectively (Fig. 4a). The detailed require- the PC estimation still need to be developed using the instruments ments of bandwidth for the remote sensing of inland waters in re- without the band of ∼620 nm (Sun et al., 2015; Tao et al., 2017). The presentative wavelengths are tabulated in Table 4. For the narrow

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Fig. 9. (a) APD variations between the band-averaged simulated Rrs at 443, 560, 620, 665 and 709 nm at different bandwidths. (b) Scatter plot for the simulated Rrs at center wavelengths and the corresponding band-averaged Rrs with the recommended bandwidth from Table 4. (c) The spectral similarity between the simulated

Rrs, Rrs of 13-class inland waters and the Rrs collected in the study area. Note that T1-T13 are the water types shown in Fig. 10, and HL is the simulated dataset from

HydroLight. (d) The scatter plot for the Rrs of 13-class inland waters at center wavelengths and the corresponding band-averaged Rrs with the recommended bandwidth from Table 4. bandwidth of ocean color sensors within 20 nm in the visible to NIR remote sensing inland waters. bands (Fig. 2), δRrs(560) and δRrs(665) were ∼0.03% and ∼0.06%, respectively. And they were ∼0.17% and ∼0.22% for the 30 nm 4.3.2. Credibility of the results bandwidth, generally, δRrs increased by ∼0.15%. In addition, δRrs(443) First, the simulated datasets were used to validate the requirements and δRrs(620) only increased by ∼0.09% between the 20 nm and 70 nm bandwidth. Consequently, it is not necessary to set narrow bands for all of bandwidth because the dataset covered more water situations and were not affected by errors from field measurements. δR increased wavelengths for the optical remote sensing of inland waters. Narrow rs bandwidth at 700–710 nm was required due to the band is very sensi- with increasing bandwidth (Fig. 9a), which was similar to the in situ Rrs (Fig. 4a). The δR values were > 0.05% for the 30 nm bandwidth at the tive to the water quality and is the key band to retrieve Chla in turbid rs waters (Gitelson, 1992; Simis et al., 2007). However, the 560 nm and 709 nm, 60 nm at the 665 nm and > 100 nm for other wavelengths. Moreover, δR (7 0 9) and δR (6 6 5) were significantly larger than for 665 nm have relatively wide FWHMs, and the bandwidth requirement rs rs can be as wide as ∼30 nm. As for ∼620 nm, the bandwidth should be other wavelengths and increased dramatically when the bandwidth was wider than 10 nm for the 709 nm and 30 nm for the 665 nm. Ad- less than 60 nm to ensure the accuracy of PC estimation. Otherwise, the bandwidth requirement for 443 nm and 490 nm was 80 nm in inland ditionally, the band-averaged Rrs with the recommended bandwidth was compared at corresponding wavelengths (Fig. 9b). All data were waters. This bandwidth requirement was consistent with the results of 2 empirical algorithms, as shown in Fig. 7. Currently, the bandwidths of distributed evenly along the 1:1 line with R > 0.99. Notably, there was a very high correlation coefficient between the averaged simulated B4 (19 nm) and B5 (38 nm) of MSI and B4 (50 nm) of OLI are a little less 2 than this requirement. The bandwidths at 443 nm and 490 nm of the and in situ Rrs (r = 0.81, APD = 8.34%). This result demonstrated that four instruments meet the requirements but do not meet the require- the bandwidth requirement was suitable for the simulated hyperspec- ments at ∼560 nm. Therefore, the bandwidth effect needs to be con- tral reflectance. sidered and calibrated when the broad bandwidth instrument is used to Due to the requirement of bandwidth generated from our local data, 4035 groups of Rrs, aph, ad and ag values collected in approximately 250

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Fig. 10. (a) The locations of sampled lakes, reservoirs, lagoons and rivers worldwide, which were from the LIMNADES (Lake Bio-optical Measurements and Matchup

Data for Remote Sensing: http://www.limnades.org) in situ bio-optical data repository. (b) Rrs values ranging from 400 nm to 800 nm for the 13 types of optical inland water. (c)–(e) aph, ad and ag, respectively, ranging from 400 nm to 700 nm for the 13 types of optical inland water. The solid red line represents the averaged curve using this study, and the dashed lines are curves of each type of inland water. Note that the gray rectangle in Fig. b is the bandwidth recommended by this research. lakes, reservoirs and lagoons were used to validate the credibility have a certain universality. (Fig. 10a). These spectra are divided into 13 types (Spyrakos et al., 2017), and the global mean ± SD (range) of Chla concentration, SPM 5. Conclusion concentration and ag(443) corresponding to these 13 types of water are 57.90 ± 97.61 μg/L (0.05–337.03 μg/L), 22.74 ± 23.72 mg/L (0.62–84.16 mg/L) and 1.82 ± 2.32 m−1 (0.15–8.64 m−1), respec- The field optical data, i.e., the Rrs and the total absorption coeffi- tively. Although our data did not cover so wide ranges, the 10 types of cient, in three subtropical, turbid, eutrophic shallow lakes were used to spectra within 3956 spectra were similar to our data. There were three analyze the effects of bandwidth on the optical remote sensing of inland reflectance peaks at 550–560 nm, ∼650 nm and 700–710 nm, andan waters. The results showed that the differences between spectral values absorption peak at ∼665 nm. Moreover, the widths of the peaks were at the center-wavelength and band-averaged results increased with in- essentially the same (Fig. 10b). Furthermore, the spectra of the global creasing bandwidth for both the Rrs and the absorption coefficients. inland water and our study areas were similar (Fig. 9c), except for Type Then, the bandwidth effect was interpreted using a mathematical method. It demonstrated that the spectral shape determined the incre- 1, Type 8, Type 10 and Type 11. The Rrs for the other 9 types of inland waters were significantly correlated (r2 > 0.50, APD < 30%) with the ment of difference of the bandwidth. Afterwards, the performance of the QAA-750E, the SMT and the DNN for total absorption coefficient Rrs collected from the study area (Fig. 9c). Otherwise, all aph have an absorption peak at ∼665 nm and are the same as our data. However, 7 estimation was analyzed. The QAA-750E was more sensitive to in- types of waters also have an absorption peak at 443 nm (Fig. 10c), so creasing bandwidth than the SMT and the DNN. Moreover, the band- that the bandwidth of 80 nm at 443 nm may lead to an increase of width increase did not have a significant impact on the empirical algorithms of SPM yet will cause large uncertainty for the Chla retrieval. uncertainty. Regarding ad and ag, all spectra are similar along a loga- rithmic function (Fig. 10d, e). Based on the recommended bandwidth Finally, the bandwidth requirements for the optical remote sensing of inland waters were recommended and validated using field data. from Table 4, the band-averaged Rrs and corresponding Rrs at center wavelengths were compared (Fig. 9d). Except several point pairs at 443 Narrow bands are not necessary for all wavelengths and this study was and 490 nm, all points were along the 1:1 line with (R2 > 0.99) for all only focused on the typical wavelengths regarding phytoplankton pig- 13 types of inland water. Although, the in situ data used in this research ments such as Chla and PC. It should be within 20 nm for 700–710 nm, is not representative of all water in the world, these data showed similar ∼30 nm maximum for ∼560 nm and ∼665 nm, 60 nm for ∼620 nm, features to most water bodies. Therefore, the bandwidth requirements and ∼80 nm for near ∼443 nm and ∼490 nm, respectively. The bandwidth requirement should be within 20 nm for

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700–710 nm, ∼30 nm maximum for ∼560 nm and ∼665 nm, 60 nm imaging spectroradiometer (MODIS) observations of cyanobacteria blooms in Taihu for ∼620 nm, and ∼80 nm for ∼443 nm and ∼490 nm, respectively. Lake. China. J. Geophys. Res.: Oceans 115, C04002. Hu, C.M., Feng, L., Lee, Z., Davis, C.O., Mannino, A., McClain, C.R., Franz, B.A., 2012. The results provided helpful theoretical and practical references for Dynamic range and sensitivity requirements of satellite ocean color sensors: learning high spatial resolution remote sensing over aquatic environments and from the past. Appl. Opt. 51, 6045–6062. the design of future research. IOCCG, 1998. Minimum requirements for an operational, ocean-colour sensor for the open ocean. In: Morel, A. (Ed.), Reports of the International Ocean-Colour Coordinating Group. IOCCG, Dartmouth, Canada. Acknowledgements IOCCG, 2012. Mission requirements for future ocean-colour sensor. In: McClain, C.R., Meister, G. 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