Spatio-Temporal Dynamics of Inherent Optical Properties in Oligotrophic Northern Gulf of Mexico Estuaries

Abstract

Coastal and estuarine ecosystems provide numerous economic and environmental benefits to society. However, increasing anthropogenic activities and developmental pressure may stress these areas and hamper their ecosystem services. Satellite remote sensing could be used as a tool for monitoring water quality parameters, including inherent optical properties (IOP) in coastal regions. Spatio-temporal information on IOP variability will help in understanding the dynamics of the water quality of estuaries. The objective of this research was to develop a novel hybrid model by combining and parameterizing existing quasi analytical and semi-analytical algorithms to estimate IOPs in four oligotrophic northern Gulf of Mexico Florida estuaries. The hybrid model was applied to above surface remote sensing reflectance data representing the Medium Resolution Imaging Spectrometer (MERIS) and Sentinel-3’s Ocean and Land Colour Instrument (OCLI) bands. The hybrid model produced a root means squared error (RMSE) of 0.32 m⁻¹ (13.95% NRMSE) for total absorption (a_t), 0.21 m⁻¹ (7.61% NRMSE) for detritus-gelbstoff absorption (a_dg), and 0.09 m⁻¹ (22.77% NRMSE) for phytoplankton pigment absorption (a_phi). Results showed that absorption by detritus and gelbstoff (a_dg) dominates the water in these estuaries. Monthly IOP variability in 2010 revealed that compared to other estuaries, magnitudes of IOPs was the highest in Pensacola Bay and therefore the highest attenuation. Findings also indicated that river discharge and precipitation predominantly govern the IOP variations in all four estuaries, showing an increase in IOP values following the high flow period. The hybrid model improved IOP retrieval in these low chlorophyll-a (Chl-a) estuaries where the existing spectral decomposition models did not perform satisfactorily.

INTRODUCTION

Estuaries are complex coastal systems where freshwater meets seawater making this environment a productive, suitable habitat, and source of food for numerous aquatic organisms (Levinton, 1982; Carlton, 1989; and Ma, 2005). Estuaries also provide social and economic services including tourism, recreational activities, and port facilities (Pendleton, 2010). The connection with terrestrial environments makes estuaries prone to anthropogenic disturbances. Frequent eutrophication from nutrient over-enrichment is a widespread threat to coastal estuaries because it reduces the benefits of the water body. Eutrophication impacts include changes in algal populations and species composition, decreased light availability, reduced dissolved oxygen supply in the water column, and increased organic matter production (Murrell et al., 2007). Increased anthropogenic activities near coastal and estuarine environments lower the ability to provide fisheries stock, and nursery habitats (Barbier et al., 2011). Coastal areas in Florida have undergone rapid development and are in need of continuous and real-time monitoring of water quality for improving coastal management practices. Traditional in situ monitoring is time consuming, resource intensive, and still only provides limited spatial and temporal coverage. Remote sensing offers a powerful complement to provide information about the water quality of these estuaries in a synoptic, rapid, near real-time, and inexpensive way. With these advantages, coastal managers may benefit by integrating satellite remote sensing into existing monitoring protocols for studying the water quality in these estuarine environments (Schaeffer et al., 2012; Jolliff et al.; and Keith et al., 2014). The northern Gulf of Mexico estuaries are one of these areas experiencing rapid developmental pressure, which will likely further impact the estuarine water quality. Integration of satellite remote sensing with traditional assessments can lead to a more holistic monitoring and assessment tool to quantify changes.

Satellite remote sensing techniques can help in the estimation of inherent optical properties (IOP) of estuarine waters. IOPs are defined as absorption (a) and backscattering (b_b) coefficients not dependent on the ambient light (Mobley, 2010). IOPs are important because of their strong linkage to the optically active constituents (OACs) in the water column, often used as indicators for water quality in coastal estuaries (Boss et al., 2009; Pavlov et al., 2015; and Zhu et al., 2013). OACs include suspended sediments, pigments, and organic matter (Lee et al., 2002). The IOPs translate to light absorption of color dissolved organic matter (CDOM [a_g]), phytoplankton (a_phi), and non-algal particulates (a_d), which play key roles in bio-geochemical processes and total light attenuation in the water column (Le et al., 2013). For example, CDOM relates to water pH and salinity, serves as a transporter for metals and non-polar organic contaminants, reduces light penetration particularly in the blue and UV spectrum, and changes the thermal properties of the water body (Brezonik et al., 2015). As a nutrient source and heavy metal tracer in water, CDOM is a promising indicator of coastal and estuarine water quality (Keith et al., 2014, Schaeffer et al., 2015). Phytoplankton, the primary producers, contributes to productivity of the water column. The magnitude, extent and duration of phytoplankton biomass influence the overall trophic status of an estuary (Racault et al., 2015). Non-algal particulates, such as inorganic suspended sediment, contribute to the overall turbidity or water clarity, which affects primary productivity of phytoplankton and benthic flora in estuaries (Phillips et al., 1995). Therefore, knowledge about the spatio-temporal variation of the IOPs are critical for improving management decisions to maintain the overall health and benefits of estuarine environments.

Over the last two decades, various types of models have been developed to derive IOPs in inland and coastal waters. These models are categorized into three broad approaches: empirical, semi-analytical, and quasi-analytical algorithm (QAA) (Ogashawara et al., 2017). The empirical models (Dall’Olmo et al., 2003; Gitelson et al., 2008; and Mishra and Mishra, 2012) are simpler to use and do not require physical understanding of the interaction between remote sensing reflectance (R_rs) and the IOPs, yet are limited in transferability to other water bodies and are prone to errors (Sathyendranath et al., 2001 and Lee et al., 2002). Semi-analytical models are more robust yet challenging and time consuming to implement, as they need accurate spectral models for each IOP (IOCCG, 2000). The QAA, originally developed by Lee et al. (2002) for clear waters and modified by Lee (2014) for coastal waters, is an inversion method for retrieving total absorption, $a_t\mathit{\left(}\lambda \mathit{\right)}$, and backscattering coefficients, $b_b\mathit{\left(}\lambda \mathit{\right)}$ based on physical relationship between R_rs and IOPs following radiative transfer principles. In general, the QAA first estimates the $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $b_b\mathit{\left(}\lambda \mathit{\right)}$ of water from R_rs. Then, it decomposes the $a_t\mathit{\left(}\lambda \mathit{\right)}$ into three components: phytoplankton pigment absorption, absorption by water, and combined colored organic matter and detritus absorption. Originally, the QAA was developed for oceanic oligotrophic waters where phytoplankton pigments dominate the absorption spectra in the water column. Recent studies have re-parametrized the QAA for different water types such as highly turbid coastal waters (Yang et al., 2013; and Le et al., 2009), inland reservoirs (Li et al., 2013., Ogashawara et al., 2016 and Watanabe et al., 2016), and turbid hyper-eutrophic inland waters (Mishra et al., 2013 and 2014). These studies show that the original QAA requires extensive adjustment or parameterization to improve its prediction accuracy, such as shifting the reference wavelength (λ₀) to a longer wavelength and modifying the model parameters based on adjusted empirical relationships. The success of QAAs depends on selecting the appropriate λ₀ and estimating parameters related to targeted water environment. Overall, the aforementioned studies suggest that the applicability of QAA is subjected to IOP composition, selection of appropriate λ₀, and accuracy of the intermediate empirical steps.

There have been previous studies on the variations in IOPs in Gulf of Mexico (GoM) waters such as Big Bend Proper Region, FL (Cannizzaro et al., 2013), Tampa Bay (Le et al., 2013) and West Florida Shelf (Bissett et al., 2005). Yet, none of these studies present specific insight about the spatio-temporal variability of IOPs in the four northern Gulf of Mexico estuaries in Florida, which have relatively lower chlorophyll-a (Chl-a) concentrations. Among few studies focusing on these estuaries, a recent study by Keith et al (2014) and Schaeffer et al (2015) demonstrated an effort to model water quality (Chl-a concentrations, CDOM absorption and turbidity) using remote sensing based empirical approaches. However, a hybrid approach leveraging both the QAA and semi-analytical modeling may provide significant improvement in IOP estimation and mapping (Fuli et al., 2006). The newly developed hybrid model presents opportunities for automatic retrieval and mapping of IOPs and hence concentrations of OACs in these estuaries reducing the need to acquire continued field validation data sets.

The goal of this study is to parametrize a hybrid model based on the framework of QAA for estimating spatio-temporal variations of IOPs in low Chl-a oligotrophic estuaries found in the northern Gulf of Mexico. The hybrid model is a fusion between an extensively used QAA and a semi-analytical model using measured absorption values at wavelengths representing the band centers of European Space Agency’s (ESA) retired Medium Resolution Imaging Spectrometer (MERIS) sensor and recently launched Sentinel-3 Ocean and Land Colour Instrument (OLCI). Application of this approach toward operational satellites would provide relevant information to quantify impacts of natural and anthropogenic events on the water quality in these northern Gulf of Mexico estuaries.

ESTUARIES LANDSCAPE AND ECOLOGICAL SETTINGS

The northern Gulf of Mexico Florida estuaries were the broad study sites for this research. Four major estuaries were sampled including Choctawhatchee River and Bay (CH), St. Andrew Bay (SA), Pensacola Bay (PB), and St. Joseph Bay (SJ). All sites are economically and ecologically important due to extensive seagrass meadows, vibrant aquatic life, and fisheries (Keppner and Keppner, 2001 and Thorpe et al., 2000). These estuaries have experienced pressure from rapid anthropogenic change such as housing development and agricultural expansion in the watershed (Forida DEP, 2004). Degradation and high erosion from the upland watershed may relate to elevated sedimentation in the estuaries (Florida DEP, 2004). Fragmented seagrass ecosystem loss was also observed, and there are numerous ongoing restoration projects in the region (Keppner and Keppner 2001; Florida DEP 2007; and Thorpe and Ryan, 2002).

These four Florida estuaries exhibit relatively similar climatic and marine characteristics. Climatologically, these four estuaries are subtropical and experience elevated rainfall during summer months from June to September (Hoyer et al., 2013 and Florida DEP, 2007). Despite this pattern, precipitation in this region can vary from season to season peaking in two periods; during late winter through early spring (February – April), and during summer (June – August) (SAIC, 1997). The watersheds tied to the estuaries also show varying land use and land cover (LULC) mosaics. A study by Le et al (2015) summarized the variation of IOPs corresponding to the LULC compositions for three of these estuaries. They showed that the SA watershed is dominated with natural landscape (evergreen forest + wetland), accounting for 60% of the watershed land cover. The same LULC class covered 52% and 47% of the watershed for PB and CH respectively (Le et al., 2015). Wind, which plays a determinant role in spatial distribution of IOPs magnitude, generally prevails during winter months (Wolfe et al., 1988; and SAIC, 1997) and higher energy is received by coastal regions in western Florida due to their proximity to the continental shelf and longer fetches, strengthening the wind effects for greater energy from waves (Wolfe et al., 1988).

The CH system receives its major freshwater inflow from Choctawhatchee River (Handley et al., 2007). CH is a stratified bay system with low tidal energy, limited flushing and a halocline with fluctuated salinity (Handley et al., 2007), and influenced by rainfall and resultant freshwater discharge (Hoyer et al., 2013). The SA bay system is the only main estuarine drainage basin completely within Florida, which is usually clear and receives freshwater inflow from Econfina Creek (average discharge of only 15.3 m³/s) (Handley et al., 2007). The PB drainage basin covers an area with a coastline of 885 km and the watershed size reaching up to 18,130 km². The PB watershed harbors Escambia River as the major river along with Blackwater and Shoal River (Florida DEP, 2007). SJ is shaped by a narrow line of land extending out from Cape San Blas, the southernmost part of the St. Joseph Peninsula. SJ is unique in being the only water system in Gulf of Mexico that does not have a freshwater source (Florida DEP, 2008).

METHODS

A. Field sampling, water quality measurements and ancillary data

The field dataset is comprised of measurements taken during the extensive 2-year long field campaigns conducted every month between January - December 2010, 2011 and in April 2012. Figure 1 shows the discrete sampling locations for calibration in the four estuaries (N = 120; CH = 23, PB = 46, SA = 26, and SJ = 25 samples). Water samples were collected from 0.5 m below surface using a 2L brown Nalgene bottle for IOP, Chl-a, total suspended solids (TSS) and CDOM analysis. All sample bottles were triple rinsed with surface water prior to the collection. Samples were typically processed within 24 hours of collection.

Figure 1.

Geographic locations of Choctawhatchee (CH), St. Andrew (SA), Pensacola (PB) and St. Joseph (SJ)estuaries. Points represent discrete water sampling locations and nearest weather station (yellow). Inset: red box is the study area within northern Gulf of Mexico.

Water samples were analyzed for absorption by total particulates on Whatman 25 mm GF/F filters with a Shimadzu UV1700 dual beam spectrophotometer (Shimadzu Corp, Kyoto, Japan) at 1 nm interval between 400 and 800 nm with 0.2 μm filtered sea water as the reference using the quantitative filter pad technique (Pegau, 2003). Spectra were normalized by subtracting each wavelength from the mean measured value between 790 and 800 nm (Mueller, 2003). Pigments were extracted from filters with warm methanol and rescanned to measure the detritus absorption (Kishino et al., 1985). The phytoplankton absorption coefficient, $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$, was calculated as the difference between total particulate absorption and detritus absorption $a_d\mathit{\left(}\lambda \mathit{\right)}$. Water samples for CDOM analysis were collected using a 200 ml Qusark bottle for the post-cruise analysis of $a_g\mathit{\left(}\lambda \mathit{\right)}$, and typically processed within 24 hours of collection. The $a_g\mathit{\left(}\lambda \mathit{\right)}$ was determined using water filtered through Whatman 47 mm GF/F filters (nominal pore size = 0.7 μm) into combusted glass flasks. Absorption was measured using a 10 cm cuvette with a Shimadzu UV1700 dual-beam spectrophotometer. Data were collected at 1 nm intervals between 200 and 750 nm. Milli-Q deionized water was used in the reference cell. Spectra were normalized by subtracting the measured value at 700 nm from all other wavelengths (Pegau et al., 2003). $a_t\mathit{\left(}\lambda \mathit{\right)}$ was calculated by adding all the absorption coefficient components, where:

$$a_t\mathit{\left(}\lambda \mathit{\right)}=a_w\mathit{\left(}\lambda \mathit{\right)}+a_d\mathit{\left(}\lambda \mathit{\right)}+a_g\mathit{\left(}\lambda \mathit{\right)}+a_{phi}\mathit{\left(}\lambda \mathit{\right)}$$ (1)

For analysis of Chl-a and suspended sediments, water samples were filtered through Whatman 47 mm GF/F filters (nominal pore size = 0.7 μm). In case of Chl-a, the filtrates were extracted in methanol and fluorescence was measured with a Turner Designs (TD700) fluorometer (Turner Designs, CA, USA). The associated pigment interference from Chl-b and phaeopigments were minimized using a 436 nm excitation filter, 680 nm emission filter, and two neutral density reference filters with a blue lamp (Welschmeyer, 1994). Concentrations of total suspended solids (TSSs), organic suspended solids (OSSs), and inorganic suspended solids (ISSs) were measured gravimetrically using EPA method 1684.

To obtain more information, river discharge, precipitation and surface run-off were collected from online databases. Mean monthly river discharge was collected from USGS database (http://waterdata.usgs.gov/nwis/) for four rivers for the period 2010 – 2012 (station codes are attached in appendix 1A. Mean monthly precipitation was also obtained from NOAA Climatic Data Center (https://www.ncdc.noaa.gov/cdo-web/datatools/) for nearest four stations (station names are in appendix 1B). Area-averaged surface run-off data were collected from NASA-Giovanni (http://giovanni.gsfc.nasa.gov/giovanni/ ) for the year 2010. Hourly data were averaged into daily data. Total Maximum Daily Load Planning Unit shapefiles from Florida Department of Environmental Protection Geospatial Open Data (http://geodata.dep.state.fl.us/datasets/) were used to provide an estimate for boundary delineation when extracting Giovanni data.

B. Remote sensing reflectance measurements

Spectral measurements using a HyperSAS spectroradiometer (Sea-Bird Scientific, Halifax, Canada) were carried out in the four estuaries. 767 water spectra were collected in different months from CH, PB, SA and SJ (CH = 187, PB = 317, SA = 137 and SJ = 126 samples). Spectral data with associated water quality measurements were selected for modeling. 120 spectra were selected for model calibration and 50 for validation with proportional numbers from each estuary. The descriptive statistics for calibration and validation datasets are presented in Table 2. HyperSAS (Sea-Bird Scientific, Halifax, Canada) is an instrument with sensors measuring radiometric quantities including water leaving radiance (L_t), sky radiance (L_i), and downwelling irradiance (E_s). L_t (uW/cm²/nm/sr) is measured using a water-viewing sensor, which accounts for the total radiance from water and sky radiance reflected by water surface. L_i is the sky radiance (uW/cm²/nm/sr) obtained from a sky directed sensor, while E_s is the downwelling irradiance (uW/cm²/nm) equating the downwelling irradiance just above surface obtained from an upward looking sensor with a hemispherical field of view (FOV). R_rs was calculated following the radiative transfer relationship (Mobley, 1999) and HyperSAS (Sea-Bird Scientific, Halifax, Canada) procedures (Zhu et al., 2014), defining the above-surface R_rs as:

$$R_{rs}=\frac{L_w}{E_d}$$ (2)

Table 2.

Descriptive statistics of the data used in model calibration and validation. SD and CV stand for standard deviation and coefficient of variation.

	Chl-a (mg/m3)	TSS (mg/L)	ag (/m) at wavelength (nm)						ad(/m) at wavelength (nm)						adg(/m) at wavelength (nm)						aphi (/m) at wavelength (nm)
			412	443	488	555	667	678	412	443	488	555	667	678	412	443	488	555	667	678	412	443	488	555	667	678
min	0.29	0.10	0.44	0.27	0.16	0.08	0.02	0.01	0.07	0.05	0.03	0.01	0.00	0.00	0.59	0.36	0.19	0.10	0.03	0.02	0.04	0.04	0.03	0.00	0.01	0.01
max	15.95	11.30	7.34	4.53	2.54	1.04	0.14	0.09	2.91	1.92	1.25	0.60	0.19	0.17	9.77	6.21	3.61	1.62	0.32	0.25	0.59	0.47	0.25	0.08	0.19	0.23
range	15.66	11.20	6.91	4.25	2.38	0.96	0.12	0.08	2.84	1.87	1.22	0.58	0.19	0.17	9.18	5.85	3.42	1.53	0.29	0.23	0.55	0.43	0.23	0.08	0.18	0.22
mean	4.96	3.17	2.54	1.52	0.80	0.34	0.05	0.03	0.76	0.50	0.31	0.14	0.05	0.04	3.30	2.02	1.11	0.49	0.09	0.07	0.19	0.18	0.10	0.03	0.06	0.08
median	3.94	2.60	2.01	1.19	0.62	0.26	0.04	0.02	0.56	0.36	0.23	0.11	0.03	0.03	2.66	1.66	0.90	0.38	0.08	0.06	0.16	0.16	0.10	0.03	0.06	0.07
SD	3.12	2.13	1.71	1.05	0.57	0.24	0.03	0.02	0.63	0.40	0.25	0.12	0.04	0.03	2.18	1.35	0.77	0.33	0.06	0.05	0.11	0.09	0.05	0.02	0.03	0.04
CV	0.63	0.67	0.67	0.69	0.71	0.70	0.60	0.59	0.83	0.79	0.81	0.81	0.82	0.83	0.66	0.67	0.69	0.68	0.64	0.66	0.58	0.50	0.46	0.51	0.52	0.52
min	0.87	0.56	0.23	0.11	0.03	0.02	0.01	0.00	0.02	0.01	0.01	0.01	0.00	0.00	0.35	0.19	0.07	0.04	0.02	0.01	0.04	0.05	0.03	0.00	0.00	0.02
max	9.21	8.25	8.63	5.22	2.80	1.28	0.20	0.13	2.55	1.61	0.97	0.42	0.14	0.12	10.82	6.62	3.69	1.69	0.34	0.24	1.13	0.75	0.50	0.26	0.25	0.29
range	8.34	7.69	8.40	5.11	2.77	1.25	0.19	0.12	2.53	1.60	0.96	0.41	0.13	0.12	10.48	6.43	3.62	1.65	0.32	0.23	1.09	0.71	0.47	0.26	0.25	0.27
mean	4.19	3.40	1.30	0.77	0.41	0.19	0.03	0.02	0.47	0.32	0.19	0.09	0.03	0.03	1.77	1.09	0.60	0.27	0.07	0.05	0.22	0.23	0.14	0.04	0.07	0.09
median	4.14	2.92	0.81	0.50	0.28	0.13	0.02	0.02	0.30	0.21	0.13	0.06	0.02	0.02	1.09	0.69	0.40	0.19	0.05	0.04	0.16	0.17	0.11	0.03	0.06	0.08
SD	2.20	1.88	1.47	0.89	0.47	0.21	0.03	0.02	0.50	0.32	0.20	0.09	0.03	0.03	1.88	1.14	0.63	0.28	0.05	0.04	0.19	0.15	0.09	0.04	0.05	0.05
CV	0.52	0.55	1.14	1.15	1.16	1.11	0.88	0.81	1.07	1.01	1.03	1.00	0.93	0.98	1.06	1.05	1.05	1.01	0.80	0.80	0.84	0.68	0.68	0.98	0.67	0.58

In order to estimate the L_w used in Equation (2), a proportionality factor was used as suggested in Mobley (1999):

$$R_{rs}=\frac{L_t-\rho \ast L_i}{E_S}$$ (3)

where, ρ is the proportionality factor, ρ=0.028 was set according to the operation manual of HyperSAS (Sea-Bird Scientific, Halifax, Canada) as specified in Zhu et al (2014). The hyperspectral data were measured between 350–800 nm and was resampled to six Medium-Resolution Imaging Spectrometer / Ocean Land Color Instrument (MERIS/OLCI) band centers: 412, 488, 560, 665 and 681 nm by convoluting the spectral response functions (SRF) of MERIS sensor as (Chen et al., 2015 and Mishra and Mishra, 2012):

$$R_{rs}\left({\lambda }_i\right)=\frac{{\sum }_{{\lambda }_i}^{{\lambda }_n}{S}_{\lambda }{R}_{rs}(\lambda )}{{\sum }_{{\lambda }_i}^{{\lambda }_n}{S}_{\lambda }}$$ (4)

C. QAA Model Implementation and Accuracy Assessment

Datasets were divided for calibration and validation. Calibration data were ranged from January 2010 to December 2010 with a total of 120 samples from four sites, and the validation data were from January 2011 to April 2012 with 50 samples from four sites. Two existing QAA models: QAA_v6 (Lee ZP, 2014), and QAA_709M (Mishra et al. 2014) were applied to the calibration dataset. QAA_v6 was developed for ocean and coastal waters, while QAA_709M was re-parametrized for hyper-eutrophic waters. The target IOPs for QAAs in general are $a_t\mathit{\left(}\lambda \mathit{\right)}$, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ which involves a series of sequential estimations where the accuracy of the final output $\mathit{\left(}{a}_{phi}\mathit{\right(}\lambda \mathit{\left)}\mathit{\right)}$ is influenced by the accuracy of the previous estimates, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_t\mathit{\left(}\lambda \mathit{\right)}$. For evaluating the accuracy, derived values of $a_t\mathit{\left(}\lambda \mathit{\right)}$, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ were compared with measured values using RMSE and NRMSE (Darvishzadeh et al., 2008).

$$RMSE={\left\{\frac{\mathit{1}}{n}\sum _{i=\mathit{1}}^n{\left[\left(q_{i}estimated\right)-\left(q_{i}measured\right)\right]}^{\mathit{2}}\right\}}^{\mathit{1}/\mathit{2}}$$ (5)

where, q is parameter of interest, and n is number of samples, and NRMSE, which facilitates comparison of RMSE in different scale

$$NRMSE=\frac{RMSE}{max-min\mathit{\left(}measured\mathit{\right)}}\ast \mathit{100}\%$$ (6)

RESULT AND DISCUSSION

A. R_rs and Water Quality

The above-surface R_rs spectra (n=120) from the study sites used in model calibration are presented in Figure 2.

Figure 2.

HyperSAS acquired R_rs dataset used for model calibration. The spectra were resampled to six MERIS/OLCI bands. Red dashed line represents the median value for each band.

Low reflectance in the blue region is usually associated with the dominance of CDOM and phytoplankton absorption. However, the blue absorption in this dataset is dominated by CDOM and not phytoplankton due to the oligotrophic nature of these estuaries. At 412 and 488 nm, the absorption is dominated by detritus-gelbstoff, ranging from 86.91% to 93.69% of $a_t\mathit{\left(}\lambda \mathit{\right)}$. In green and red region, the influence of particulate scattering is evident, where, the reflectance continued to increase and peaked between 560 and 665 nm. Very low concentration of Chl-a, ranging from 0.29 to 15.95 mg/m³ with an average of 4.95 mg/m³, is represented by the lack of a prominent absorption feature near 665nm. All four estuaries represented the typical characteristic of optically complex waters, where Chl-a, TSS and CDOM do not co-vary.

Existing QAAs and parameterization of the hybrid model

B.1. Performance of QAAs

QAA_v6 and QAA_709M were applied to the calibration dataset from the four estuaries without any modifications. QAA_v6 is the latest version of the native QAA originally developed by Lee et al (2002). The first QAA was developed for oceanic and clear coastal waters with 555 nm as λ₀ (Lee et al., 2002). QAA_v6 was developed for near-shore coastal waters with λ₀ at 670 nm. λ₀ was shifted to 665 nm before applying the QAA to the calibration data to match with MERIS band 7. Similarly, QAA_709M was developed by Mishra et al (2014) to resolve the IOPs for hyper-eutrophic cyanobacteria dominated waters with λ₀ at 709 nm. Among all IOPs obtained from QAA, the accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ is critical as it is further decomposed to derive $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$. Any uncertainty in estimating $a_t\mathit{\left(}\lambda \mathit{\right)}$ is assumed to be propagated to $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ as estimation error. Existing QAA models (QAA_v6 and QAA_709M) produced considerable errors in $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimates, which eventually resulted in negative $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimates. The $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ values in these estuaries are considerably low, with an average of 0.07 m⁻¹ at 667 nm. Errors resulted from $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimations because, in total these values were much larger than the $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$. Traditional $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimation using only existing QAAs would not work in these waters where $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ signals are very low (0.06 ± 0.03 m⁻¹) or approximately 10% of total absorption. IOP retrieval results from existing QAA_v6 and QAA_709M average RMSE within 412–678 nm was 0.72 m⁻¹ and 0.76 m⁻¹ which corresponded to NRMSE of 21.78% and 20.70% respectively (Table 4) for $a_t\mathit{\left(}\lambda \mathit{\right)}$. Model calibration results (Figure 3) showed larger errors at shorter wavelengths for $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$. Both existing QAAs produced NRMSE more than 25% for $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ retrieval thus resulted in consistently negative $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ prediction. Overall poor performance of existing QAA models resulting in negative absorption values justified the re-parameterization of a new QAA for these low Chl-a oligotrophic estuaries to improve retrievals of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$. To overcome this issue, a semi-analytical model was fused with the newly parameterized QAA output giving rise to a hybrid model for estimating $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$. Detailed information about QAA parameterization and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimation are provided below.

Table 4.

Comparison of performance between existing QAA_v6 and QAA_709M

	QAA_v6				QAA_709M
	${\text{a}}_{\text{t}}\mathit{\left(}\lambda \mathit{\right)}$		${\text{a}}_{\text{dg}}\mathit{\left(}\lambda \mathit{\right)}$		${\text{a}}_{\text{t}}\mathit{\left(}\lambda \mathit{\right)}$		${\text{a}}_{\text{dg}}\mathit{\left(}\lambda \mathit{\right)}$
Wavelength (nm)	RMSE (m−1)	NRMSE (%)	RMSE (m−1)	NRMSE (%)	RMSE (m−1)	NRMSE (%)	RMSE (m−1)	NRMSE (%)
412	2.21	23.59	2.56	27.87	2.34	25.02	2.66	28.96
443	1.19	20.02	1.60	27.34	1.28	21.62	1.66	28.38
488	0.53	15.56	0.97	28.43	0.60	17.47	1.00	29.30
555	0.15	9.85	0.47	30.85	0.19	12.37	0.48	31.48
667	0.10	28.84	0.09	31.47	0.09	23.86	0.09	32.01
678	0.11	32.79	0.07	29.84	0.08	23.83	0.07	30.35
Average	0.72	21.78	0.96	29.30	0.76	20.70	0.99	30.08

Figure 3.

Comparison of $a_t\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹) predicted using existing (A) QAA_v6 (λ₀: 665 nm) (Lee, 2014) and (B) QAA_709M (λ₀:709 nm) (Mishra et al., 2014). Red dotted line is the 1:1 line.

QAA parameters including χ, ζ, and ξ required adjustments specific to these optically complex and low Chl-a waters. χ is a log ratio of r_rs in several bands differentially sensitive to $a_t\mathit{\left(}\lambda \mathit{\right)}$. ζ or $a_{phi}\mathit{\left(}\mathit{410}\mathit{\right)}/a_{phi}\mathit{\left(}\mathit{440}\mathit{\right)}$ has been linked to chlorophyll concentration, while ξ or $a_{dg}\mathit{\left(}\mathit{410}\mathit{\right)}/a_{dg}\mathit{\left(}\mathit{440}\mathit{\right)}$ represents the slope for a_dg. Values of ζ and ξ can vary depending on water characteristics such as pigment composition, humic versus fluvic acids or detritus abundance (Lee et al., 2002). Errors in constituent retrieval such as with $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ are mainly driven by accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimation, as ξ and ζ tend not to change much over a large range (Aurin et al., 2012 and Lee et al., 2010). Coastal and inland waters exhibit complex optical characteristics because of variability in the composition of IOPs (IOCCG, 2000). As a result, developing a universally robust QAA is difficult and local information on water quality is often needed to improve the estimation accuracy of IOPs particularly $a_t\mathit{\left(}\lambda \mathit{\right)}$ (Lee et al., 2002). QAA_v6 and QAA_709 did estimate the $a_t\mathit{\left(}\lambda \mathit{\right)}$ with approximately 20% NRMSE. Yet, these QAAs underestimated $a_t\mathit{\left(}\lambda \mathit{\right)}$ higher than 1 m⁻¹ in the blue region (Figure 3). Thus, new parameterization was needed to improve the estimation accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and other IOPs for these low Chl-a estuaries.

B.2. Parameterization of a_t(λ_o)

The QAA models require the λ₀ to be a wavelength where absorption by pure water $\mathit{\left(}{a}_w\mathit{\right(}\lambda \mathit{\left)}\mathit{\right)}$ dominates and controls the magnitude of $a_t\mathit{\left(}\lambda \mathit{\right)}$. Studies have shown that the contribution of $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ toward $a_t\mathit{\left(}\lambda \mathit{\right)}$ can vary depending upon site characteristics (Mishra et al., 2014; Lee, 2014; and Le et al., 2009). The absorption budget from this dataset shows that at 665 and 678 nm, $\mathit{\left(}{a}_w\mathit{\right(}\lambda \mathit{\left)}\mathit{\right)}$ dominates the $a_t\mathit{\left(}\lambda \mathit{\right)}$ (Table 5), indicating that either 665 nm or 678 nm can be chosen as λ₀. a_dg significantly dominates the absorption in blue and green region with median values of portion ranging from 80% to 94%. In a_dg detritus-CDOM composition dataset, a_g is the dominating component with median values at blue-green region between 73% and 79% of a_dg. This suggests the CDOM-dominated nature of the water in the study site.

Table 5.

Absorption budget of the calibration dataset: Median values of $a_t\mathit{\left(}\lambda \mathit{\right)}$, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ and their associated proportion to ${\text{a}}_{\text{t}}\mathit{\left(}\lambda \mathit{\right)}$.

	Wavelength (nm)
	412	443	488	555	667	678
$a_{phi}\mathit{\left(}\lambda \mathit{\right)}$	0.16	0.16	0.10	0.03	0.06	0.07
$a_{dg}\mathit{\left(}\lambda \mathit{\right)}$	2.66	1.66	0.90	0.38	0.08	0.06
$a_w\mathit{\left(}\lambda \mathit{\right)}$	0.01	0.01	0.02	0.06	0.44	0.46
$a_t\mathit{\left(}\lambda \mathit{\right)}$	2.817	1.826	1.013	0.469	0.568	0.588
% of $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ to $a_t\mathit{\left(}\lambda \mathit{\right)}$	5.54	8.65	9.38	5.44	9.69	11.65
% of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ to $a_t\mathit{\left(}\lambda \mathit{\right)}$	94.30	90.96	89.18	81.86	13.74	9.78
% of $a_w\mathit{\left(}\lambda \mathit{\right)}$ to $a_t\mathit{\left(}\lambda \mathit{\right)}$	0.16	0.39	1.43	12.71	76.57	78.56

Studies have shown that accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ can be improved by empirical estimation based on the statistical relationship between χ and subsurface remote sensing reflectance $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$ (Le et al., 2009 and Mishra et al., 2014). QAA_v6, and QAA_709M relate $a_t\mathit{\left(}{\lambda }_{\mathit{0}}\mathit{\right)}$, $a_w\mathit{\left(}{\lambda }_{\mathit{0}}\mathit{\right)}$ and combinations of reflectance band ratios to empirically estimate $a_t\mathit{\left(}{\lambda }_{\mathit{0}}\mathit{\right)}$. The same approach was adopted by relating these components as:

$$a_t\left({\lambda }_{\mathit{0}}\right)=a_w\left({\lambda }_{\mathit{0}}\right)+a_{t-w}\left({\lambda }_{\mathit{0}}\right)$$ (7)

$a_{t-w}\mathit{\left(}{\lambda }_{\mathit{0}}\mathit{\right)}$ is empirically estimated from χ; where $\chi =lo{g}_{\mathit{10}}\mathit{\left[}\left({\lambda }_{\mathit{1}}+{\lambda }_{\mathit{2}}\right)/\left({\lambda }_{\mathit{3}}+\left(\left({\lambda }_{\mathit{4}}^{\mathit{2}}\right)/{\lambda }_{\mathit{5}}\right)\right)\mathit{\right]}$

Different band combinations using six MERIS bands, 443, 490, 560, 665, 681 and 709 nm, were tested for λ₁ λ₂, λ₃, λ₄, and λ₅. The best band combinations were selected based on R² and RMSE of the regression model (Figure 4A). The empirical model produced the smallest RMSE at 412 and 443 nm, which are critical for estimating CDOM and phytoplankton absorption.

Figure 4.

(A)Empirical relationship between $a_{t-w}\left({\lambda }_{\mathit{0}}\right)$ and $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$,. (B) a_dg at 443 nm vs. log-10 ratio of r_rs at 490 and 681 nm. The plots were established using calibration dataset (N = 120), 4(B). Relationship between $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$ and Log-₁₀(rrs490/681) (N = 120).

Accurate retrievals of $a_t\mathit{\left(}\lambda \mathit{\right)}$ is also influenced by parameters other than the χ factor. Considering the steps in QAAs, where, $a_t\mathit{\left(}\lambda \mathit{\right)}=\mathit{(}\mathit{1}-u\mathit{(}\lambda \mathit{\left)}\mathit{\right)}\left(b_{bw}\mathit{\left(}\lambda \mathit{\right)}+b_{bp}\mathit{\left(}\lambda \mathit{\right)}\right)/u\mathit{\left(}\lambda \mathit{\right)}$, the estimation accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ is also influenced by the accuracy of $b_{bp}\mathit{\left(}\lambda \mathit{\right)}$ retrieval. The steps 5 and 6 in QAA (Table 3) where $b_{bp}\mathit{\left(}\lambda \mathit{\right)}$ is related to the spectral power of the scattering coefficient was further investigated. An attempt was made to preserve the original band combinations of QAA while analyzing the impact of each constant used in the $a_t\mathit{\left(}\lambda \mathit{\right)}$ retrieval by optimization. An increment of 0.1 was applied to each constant and the $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimate results were reviewed. It was found that the modification made only to the first constant (set at 2.5 in Equation 8) provided noticeable change in $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimates. Thus, the Step 5 in the hybrid model was slightly modified to:

$$\eta =\mathit{2}.\mathit{5}\mathit{\left(}\mathit{1}-\mathit{0.5}exp\left(-\mathit{0.9}\frac{rrs\mathit{\left(}\mathit{443}\right)}{rrs\mathit{\left(}\mathit{560}\right)}\right)\mathit{\right)}\mathit{)}$$ (8)

Table 3.

Parameterization steps of the hybrid model for four estuaries.

Step	Property	Derivation
1	$r_{rs}\left(\lambda \right)$	$r_{rs}\left(\lambda \right)=R_{rs}\left(\lambda \right)/\left(0.52+1.7R_{rs}\left(\lambda \right)\right)$
2	$u(\lambda )=\frac{b_b(\lambda )}{a_t(\lambda )+b_{b(\lambda )}}$	$u(\lambda )=\frac{-0.0895+\sqrt{{(g_0)}^2+4g_1\ast r_{rs}(\lambda )}}{2\ast g_1};g_0=0.089,g_1=0.125$
3	${\lambda }_0$	$\chi =\log \left(\frac{r_{rs}\left(490\right)+r_{rs}\left(665\right)}{r_{rs}\left({\lambda }_0\right)+5\frac{{\left(r_{rs}\left(681\right)\right)}^2}{r_{rs}\left(490\right)}}\right)$ $\text{a}\left({\lambda }_0\right)=\text{a}\left(665\right)\approx {\text{a}}_{\text{w}}\left(665\right)+\left(0.3336·{\chi }^2-0.3562\chi \right)+0.1721)$
4	${\text{b}}_{\text{bp}}\left({\lambda }_0\right)={\text{b}}_{\text{bp}}\left(665\right)$	$\frac{\text{u}\left({\lambda }_0\right)\ast \text{a}\left({\lambda }_0\right)}{1-\text{u}\left({\lambda }_0\right)}-\text{bbw}\left(665\right)$
5	$\eta$	$\eta =2.5\times \left(1-0.5\times \exp \left(-0.9\times \frac{r_{rs}443}{r_{rs}560}\right)\right)$
6	${\text{b}}_{\text{bp}}\left(\lambda \right)$	${\text{b}}_{\text{bp}}\left({\lambda }_0\right){\left(\frac{{\lambda }_0}{\lambda }\right)}^{\text{n}}$
7	$\text{a}\left(\lambda \right)$	$(1-\text{u}(\lambda \left)\right)\left({\text{b}}_{\text{bw}}\left(\lambda \right)+{\text{b}}_{\text{bp}}\left(\lambda \right)\right)/\text{u}\left(\lambda \right)$
8	${\text{a}}_{\text{dg}}\left(443\right)$	$1.6634\exp \left(-3.639\times \log 10\frac{r_{rs}490}{r_{rs}681}\right)$
9	${\text{a}}_{\text{dg}}\left(\lambda \right)$	$a_{dg}\left(\lambda \right)=a_{dg}\left(443\right)e^{-S_{CDM}(\lambda -443)}$ $S_{dg}=0.012+\left(\frac{0.002}{0.6+\left(r_{rs}490/r_{rs}560\right)}\right)$
10	$\zeta$	$\zeta =0.74+\left(\frac{0.2}{0.8+r_{rs}443/r_{rs}560}\right)$
11	$\xi$	$\xi =\exp [S\times (665-412)]$ $S_{dg}=0.012+\left(\frac{0.002}{0.6+\left(r_{rs}490/r_{rs}560\right)}\right)$
12	$a_{phi}\left(665\right)$	$a_{\varphi }\left(443\right)=\frac{\left[\xi a_t\left(665\right)-a_t\left(412\right)\right]-\left[\xi a_w\left(665\right)-a_w\left(412\right)\right]}{\xi -\zeta }$
13	$a_{phi}\left(\lambda \right)$	$a_{\varphi }\left(\lambda \right)=a_{ph}\left(665\right)\times a_{\varphi }^{+}\left(\lambda \right)$ $\text{where}{a}_{\varphi }^{+}\left(\lambda \right)=\mathit{\text{median spectrum of measured normalized}}{a}_{phi}\left(\lambda \right)\mathit{\text{by}}{a}_{phi}\left(665\right)$

Incorporating the empirical model provided in Figure 4B to the new hybrid model (step 3 and step 8 in table 3) improved the calibration accuracy. The average RMSE of $a_t\mathit{\left(}\lambda \mathit{\right)}$ for the six MERIS bands using the hybrid model compared to QAA_v6 decreased from 0.72 m⁻¹ to 0.48 m⁻¹ followed by a decrease in the average NRMSE from 21.78 % to 13.04%.

B.3. Parameterization of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$

High uncertainty associated with estimation of $a_t\mathit{\left(}\lambda \mathit{\right)}$ at 412 nm and 443 nm can be detrimental to the overall IOP retrieval because the lower wavelengths are the most important variables to estimate $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ in QAA. $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ derivation in QAA_v6 using the steps proposed in the existing QAA yielded estimates with an average RMSE of 0.96 m⁻¹ and 29.30% NRMSE. Larger errors were found at 412 and 443 nm with RMSE of 2.56 m⁻¹ and 1.60 m⁻¹ respectively. Interferences from phytoplankton absorption in this blue region were relatively low with a contribution of 5.50% and 8.31% to $a_t\mathit{\left(}\lambda \mathit{\right)}$ at 412 and 443 nm.

To improve estimation, we applied the same empirical approach by relating combinations of $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$ band ratios at six MERIS bands as predictors for $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$. Previous studies applied this approach by exploiting the $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$ or $R_{rs}\mathit{\left(}\lambda \mathit{\right)}$ as single or band ratios in blue region (Mishra et al., 2014; Shanmugam, 2011 and Kowalczuk et al., 2006). In the blue region, interference of pigment absorption may be high, however, in these Northern Gulf of Mexico estuaries contributions of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ to $a_t\mathit{\left(}\lambda \mathit{\right)}$ were relatively high, with median values of 93.69% and 87.33% at 412 and 443 nm respectively. Two new steps were incorporated to improve the accuracy of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, first, estimating $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ at a specific wavelength using combinations of $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$ band ratios at six simulated MERIS bands, and second, modeling $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ using the CDOM exponential model. Selection of band ratios as the predictors was purely empirical, determined from their statistical significance. Following similar approach in previous studies, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ at 412 or 443 nm were regressed against log-10 ratio of $r_{rs}\mathit{\left(}\lambda \mathit{\right)}$. The best calibration performance was obtained from the relationship between a_dg at 443 nm and log-10 ratio of r_rs 490 and 681 nm (Figure 4B). That relationship was applied to the hybrid model and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ was further extrapolated by using the traditional model developed by (Bricaud, 1981):

$$a_{dg}\mathit{\left(}\lambda \mathit{\right)}=a_{d{g}_{-}}\mathit{443}{e}^{-S\mathit{(}\lambda -\mathit{443}\mathit{)}}$$ (9)

Incorporating the above model in the hybrid model improved the accuracy of the $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimation. Further effort was made to reduce the $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimation RMSE and NRMSE by simulating the S values using the calibration dataset. S is the slope factor characterizing the CDOM absorption curve, which varies by site. Obtaining accurate S values is difficult due to the influence of wavelength range selected and the differences in methods used for its computation (Helms, 2008). The spectral slope S values in natural waters range from 0.11 to 0.025 nm⁻¹ (Carder et al., 1999 and Yentsch, 1962). A simple optimization was performed to obtain the S value by changing the constants in the equation in Step 9 (Table 3) at regular increments and observing the impact of such change to both RMSE and NRMSE of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$. The modified S equation that gave the best result was found to be:

$$S=0.012+(0.002/0.6+\left(r_{rs}\mathit{443}/r_{rs}\mathit{560}\right)$$ (10)

The S modification improved the accuracy of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ retrievals by dropping the average NRMSE to 10.11%. Significant improvement in accuracy occurred at 667 and 678 nm where RMSE dropped around 50% from 0.06 and 0.05 to 0.03 and 0.02 m⁻¹ respectively.

B.4. Estimation of $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$

The $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ derivation is the final step in QAA where $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ is calculated by subtracting $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ from $a_t\mathit{\left(}\lambda \mathit{\right)}$. An accurate $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimation can be expected if a re-parametrized QAA produces high accuracy in $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimation. However, in waters where Chl-a concentration and hence $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ is very low, disproportionately high errors can be observed in $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$. In these estuaries, the average Chl-a concentration from calibration dataset was 4.19 mg/m³ and average $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ was only 0.06 m⁻¹ at 667 nm, accounting approximately 10% of $a_t\mathit{\left(}\mathit{667}\mathit{\right)}$. In addition, the total RMSE at $a_t\mathit{\left(}\mathit{667}\mathit{\right)}$ and $a_{dg}\mathit{\left(}\mathit{667}\mathit{\right)}$ was 0.08 m⁻¹, higher than the average $a_{phi}\mathit{\left(}\mathit{667}\mathit{\right)}$. As $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ is within the error limits of QAA retrieved $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, QAA produced erroneous often negative $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimates (Table 6).

Table 6.

RMSE of $a_t\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹) and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹) estimates at different wavelengths, calculated from calibration dataset (n = 120). Average a_phi represents the average values from 120 samples at each wavelength

Wavelength (nm)	RMSE_$a_t\mathit{\left(}\lambda \mathit{\right)}$	RMSE_$a_{dg}\mathit{\left(}\lambda \mathit{\right)}$	Total RMSE from $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$	Average $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ (m−1)
412	1.48	0.89	2.37	0.19
443	0.78	0.51	1.28	0.18
488	0.38	0.32	0.70	0.10
555	0.14	0.17	0.32	0.03
667	0.04	0.03	0.08	0.06
678	0.06	0.03	0.08	0.08
Average	0.48	0.32	0.80	0.11

Since the QAA models could not produce reliable $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimates, the approach to estimate $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ was modified in the hybrid model by applying a normalized $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ developed by Lee et al. (2010) as:

$$a_{phi}\mathit{\left(}\lambda \mathit{\right)}=a_{phi}\mathit{\left(}\mathit{665}\mathit{\right)}\ast {a^{+}}_{phi}\mathit{\left(}\lambda \mathit{\right)}$$ (13)

where, ${a^{+}}_{phi}\mathit{\left(}\lambda \mathit{\right)}$ is the median of normalized $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ spectra (normalized by $a_{phi}\mathit{\left(}\mathit{665}\mathit{\right)}$). The $a_{phi}\mathit{\left(}\mathit{665}\mathit{\right)}$ was estimated following Lee et al (2010) as:

$$a_{phi}\mathit{\left(}\mathit{665}\mathit{\right)}=\mathit{\left(}\mathit{\left(}\mathit{\left(}\xi *a_t\mathit{665}\mathit{\right)}-a_t\mathit{412}\mathit{\right)}-\mathit{\left(}\mathit{\left(}\xi *a_w\mathit{665}\mathit{\right)}-a_w\mathit{412}\mathit{\right)}\mathit{\right)}/\mathit{(}\xi -\zeta \mathit{)}$$ (14)

The ${a^{+}}_{phi}\mathit{\left(}\lambda \mathit{\right)}$ was derived by taking the median curve of the normalized a_phi spectra from calibration dataset by their absorption at 665 nm. The model is referred to as a hybrid model because of the significant alteration to the last steps of a standard QAA and inclusion of the semi-analytical step.

In a QAA approach, $R_{rs}\mathit{\left(}\lambda \mathit{\right)}$ is the only input to the algorithm. The IOPs such as b_bp, a_dg, and a_phi are the outputs often validated with measured IOPs. Since no measured $b_{bp}\mathit{\left(}\lambda \mathit{\right)}$ data was available, the empirical estimation could not be performed. b_bp is a critical IOP to quantify in environments influenced by sediment fluxes such as estuaries because it helps in understanding the sediment dynamics within the domain. Thus, one limitation of this study was the unavailability of in situ b_bp. However, despite the absence of b_bp estimates, the presence of IOPs such as a_t, a_dg and a_phi helped in outlining parts of factors controlling light availability in the water column. In this study, separation of a_g from a_dg was not carried out in the hybrid QAA modeling process. However, given the dominance of a_g in a_dg component (average % of a_g in a_dg from calibration and validation data was 72% and 77% respectively at 412 nm), we have confidence that the estimated a_dg is closely associated with a_g.

C. Validation of the hybrid model

Figure 5 and Table 7 show that the hybrid model produced reliable estimates. The re-parameterized QAA component of the hybrid model was able to retrieve $a_t\mathit{\left(}\lambda \mathit{\right)}$ with an average RMSE of 0.32 m⁻¹ and NRMSE of 13.95 %. Improvement obtained from the re-parameterized QAA implied that the band combinations used to estimate $a_t\mathit{\left(}\lambda \mathit{\right)}$ from existing QAA are not sufficiently robust to estimate $a_t\mathit{\left(}\lambda \mathit{\right)}$ accurately from oligotrophic estuaries. Multiple factors could be influencing the poor $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimation including decreased sensitivity of band combinations used in existing QAA to $a_t\mathit{\left(}\lambda \mathit{\right)}$ variations, and a significant contribution of $a_{t-w}\mathit{\left(}\lambda \mathit{\right)}$ at longer wavelengths. At 667 and 678 nm, the portion of OACs (CDOM and phytoplankton pigments) remained high, around 25%. The estimation became complicated because of interference from both CDOM and a_phi contribution at these wavelengths.

Figure 5.

Modeled versus measured $a_t\mathit{\left(}\lambda \mathit{\right)}$, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ derived from the hybrid model

Table 7.

RMSE and NRMSE of $a_t\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹), $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹) and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ (m⁻¹) estimates at different wavelengths, calculated from validation dataset (n = 50).

Wavelength (nm)	$a_t\mathit{\left(}\lambda \mathit{\right)}$		$a_{dg}\mathit{\left(}\lambda \mathit{\right)}$		$a_{phi}\mathit{\left(}\lambda \mathit{\right)}$
	RMSE (1/m)	NRMSE (%)	RMSE (1/m)	NRMSE (%)	RMSE (1/m)	NRMSE (%)
412	0.89	8.53	0.58	5.55	0.17	15.54
443	0.50	7.70	0.35	5.49	0.15	21.21
488	0.26	15.43	0.19	11.52	0.09	35.94
555	0.12	7.08	0.10	6.04	0.04	15.31
667	0.06	15.82	0.02	7.48	0.05	18.99
678	0.10	29.11	0.02	9.59	0.05	20.38
average	0.32	13.95	0.21	7.61	0.09	21.23

For $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, the hybrid model for validation dataset produced an average RMSE from six wavelengths of 0.21 m⁻¹ and NRMSE of 7.61% (Table 7). The $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimation accuracy average was similar to results previously reported for the same locations, which estimated a_CDOM at 412 nm with an RMSE of 0.2 m⁻¹ (Keith et al., 2014). However, the advantage of the re-parameterized hybrid model is that it estimates $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ not only at 412 nm but also at all MERIS and OLCI bands, providing an understanding of the a_dg spectra and other IOPs. Estimated $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ values were in the range of 0.015 – 0.28 m⁻¹ with an average RMSE of 0.09 m⁻¹ and average NRMSE of 21.23%. At 667 nm, the accuracy was even better (0.05 m⁻¹ RMSE or 18.99% NRMSE). The reduction of errors observed in $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimation was a significant improvement over QAA_v6 or QAA_M709 where many negative estimates were resulted and the average NRMSE for positive estimates was more than 100% (data not shown).

There were no significant differences observed in $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimates from the three empirical models. Overall RMSE for all models ranged from 0.21 to 0.26 m⁻¹. For $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, larger errors were observed at longer wavelength at 667 and 681 nm, while for $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$, larger errors were at 488 nm. Lower accuracies at higher wavelength for $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ could be primarily attributed to the very low absorption at those bands and minor mismatch between reflectance bands and the absorption bands. The reflectance bands at red and green regions used in this study are the emulated MERIS bands at 560, 665, and 681 nm, while the absorption measurements were made at 555, 667, and 678 nm. The 2–5 nm difference between reflectance and absorption bands can be important when the parameters under investigation have extremely low magnitude at higher wavelengths. It appears that the estimates using 2011 and 2012 datasets showed similar characteristics where IOPs were dominated by $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ varying from 75% to 86% of $a_t\mathit{\left(}\lambda \mathit{\right)}$ at shorter wavelengths (412 – 488 nm). Despite the small mismatch between MERIS band centers wavelengths and absorption measurement wavelengths, the hybrid model was able to produce reliable estimates.

B. Absorption variability among estuaries

a_t variability indicates the dynamics of total light-absorbing substances in the water. Knowing how the a_t changes both spatially and temporally will provide insight about how a_t responds to changing environmental factors such as precipitation and river discharge. To better understand this, NOAA rainfall and river discharge data acquired from the nearest weather stations for each estuary were used. To obtain temporal a_t data, the hybrid model was applied to the remaining $R_{rs}\mathit{\left(}\lambda \mathit{\right)}$ data from all four estuaries, collected between January 2010 and April 2012 with some gaps in measurements. The spatio-temporal variability in a_t for the four estuaries were analyzed and specific bands are presented for brevity. Temporal variation of $a_t\mathit{\left(}\lambda \mathit{\right)}$ is presented in Figure 6A. Overall, similar trends were observed for all sites with relatively higher $a_t\mathit{\left(}\lambda \mathit{\right)}$ in 2010 than in 2011. Variations of $a_t\mathit{\left(}\lambda \mathit{\right)}$ are associated with its composing agents: $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$, $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ and $a_w\mathit{\left(}\lambda \mathit{\right)}$, which are affected by the concentration of OACs in the water such as CDOM, sediments and phytoplankton. These constituents in water column can vary because of differing aquatic and surrounding terrestrial conditions such as hydrologic regime, climate, and landscape setting in the watersheds (Brezonik et al., 2015; Shanmugam et al., 2016).

Figure 6.

(A). Temporal variations of a_t(443) for four estuaries. Values represent average monthly estimates for each site, and (B)Ternary plots showing absorption compositions at different wavelengths for the four estuaries using 2010 estimates. Black circles - CH, red circle - PB, green triangles - SA, and yellow triangles – SJ at three wavelengths: 443 nm (6B), 555 nm (C), and 667 nm (6D)

$a_t\mathit{\left(}\lambda \mathit{\right)}$ in four estuaries also showed similar annual responses where values in first half of the year (2010) decreased from January to May and increased from June to August. From September 2010 to June 2011, despite the gaps of several months, $a_t\mathit{\left(}\lambda \mathit{\right)}$ in these estuaries were lower than from January 2010 to May 2010. This was a result of higher flow to these estuaries because of higher precipitation in 2010. In general, the mean precipitation in 2010 for these estuaries was relatively higher than 2011, which resulted in higher amount of river discharge.

Ternary plots comprising of all data from 2010 highlighted the composition characteristics of absorbing constituents in the four estuaries (Figure 6B, 6C, 6D). As evident in the plot, at 443 nm, compared to other absorptions (water and pigment), a_dg was clearly the most dominating absorbing constituent. $a_t\mathit{\left(}\lambda \mathit{\right)}$ estimates at 443 nm ranged from 0.24 m⁻¹ to 5.83 m⁻¹ and $a_{dg}\mathit{\left(}443\mathit{\right)}$ on average contributed 86.15 % to total absorption. It appears that the light absorbing agents for these estuaries are highly controlled by detritus and gelbstoff (a_dg) than by phytoplankton pigments (a_phi). At longer wavelengths such as 555 and 667 nm, despite its decreasing proportion, a_dg continued to dominate the absorption in the water column. In the green region, a_dg absorption on average accounted for 50% of the total absorption. At 667 nm, where pigment absorption usually dominates, the four estuaries showed very low contribution of pigments towards a_t. On average, $a_{phi}\mathit{\left(}\mathit{667}\mathit{\right)}$ only contributed 13.67% towards a_t, almost similar to $a_{dg}\mathit{\left(}\mathit{667}\mathit{\right)}$ which contributed 14%.

Distribution of IOPs from four estuaries did not show any clustering effect in the ternary plots implying that these estuaries exhibit similar OAC composition. Several scattered estimates in the ternary plots, where all values can be attributed to two stations: CH01 and SA07. These two stations are the closest locations to the open ocean. The salinity values at these stations are much higher than the average salinity in the estuary. These stations are least influenced by the riverine or terrestrial inputs, making the a_dg contribution to $a_t\mathit{\left(}\lambda \mathit{\right)}$ budget much smaller than other stations.

While a_t plays an important role in controlling the light availability, water quality and clarity, an understanding of the physical forces controlling the a_t would help to provide more insight on outlining best management practices for the estuaries. Although b_bp and a_d estimates commonly used for monitoring of the inorganic particulates are not available in this study, absorption parameters such as a_dg for CDOM/detritus, a_phi as an indicator of eutrophication, and a_t as an indicator of turbidity. In estuarine systems, such direct physical forcing or drivers to IOPs and CDOM particularly, can be accredited to river discharges, land use, tidal and wind mixing, and water circulation (Le et al., 2013 and Chen et al., 2007).

Our results showed that $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$ estimates were in good agreement with CDOM fluorescence (r = 0.88 for 2010 dataset). CDOM fluorescence has been used to characterize the CDOM sink and sources (Singh et al., 2010). In open sea water, CDOM concentration is mainly regulated by the formation of exudates and phytoplankton decomposition (Nelson and Siegel, 2002), whereas, CDOM in coastal waters is mainly determined by rainfall and river discharge transporting materials such as anthropogenic waste and plant decomposition substances (Bowers and Brett, 2008; Wang et al., 2014; and Pavlov et al., 2015). Precipitation data obtained from the nearest weather stations for 2010 showed fluctuations from January to December 2010 (NOAA, 2015) with a peak mainly in summer (Figure 7A-7D). River discharge data obtained from USGS for rivers draining to each estuary (USGS, 2010) showed that the trend in river discharges do not exhibit similar responses as local precipitation, especially from April to October. In general, a_t temporal patterns from four estuaries in Figures 7A-7D followed more closely to river discharges indicating high absorbing condition might be expected during high flow. Despite having no major tributaries, SA showed considerably high absorption. It is likely that the presence of multiple smaller tributaries in SA giving rise to similar effect as a major tributary.

Figure 7.

Monthly variations in total precipitation in each estuary in 2010 (blue line): CH (A), PB (B), SA (C) and SJ estuary (D). Variations in monthly mean discharges from major rivers flowing to each estuary in 2010 (black line). Red line with red dots indicates the average a_t(412) for the corresponding month. Relationship between mean monthly a_t(412)m⁻¹ and flow in 2010 in CH estuary (E), PB estuary (F) and SA estuary (G). No flow data is presented for SJ because there is no direct freshwater source.

Figures 7(E-G) supports the relationship between discharge and a_t. a_t – discharge relationship is most evident in CH estuary. The CH watershed is dominated by soft and sandy soil on steeper terrain, making it susceptible to erosion (Thorpe and Ryan, 2002). Considering this, it is likely that organic materials from soils and terrestrial plants brought through by erosion due to river flow contributed to the high $a_t\mathit{\left(}\lambda \mathit{\right)}$. Differing conditions can be observed from $a_t\mathit{\left(}\mathit{412}\mathit{\right)}$ – discharge relationship in Figures 7(E-G). In these figures, while PB and CH plots showed a stronger relationship between $a_{dg}\mathit{\left(}\mathit{412}\mathit{\right)}$ and the flow, the relationship for SA is weaker (R² = 0.17). Close relationship between $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$ and river discharge at CH and PB is similar to conditions in other coastal regions such as Tampa Bay, Florida and Barataria Basin, Louisiana, and other areas (Singh et al., 2010; Le et al., 2013; and Kowalczuk et al., 2010).

The variations observed in IOPs may also be linked to the surface runoff in the basin area bringing materials to the estuaries. Figures 8A-8C show how $a_t\mathit{\left(}\lambda \mathit{\right)}$ on the sampling dates associate with fluctuations in surface runoff. Despite gaps in available data, patterns in three estuaries show that materials brought to the estuaries by rainfall induced surface runoff might be the source of variability observed in IOPs. Different IOP values range between high and low flow months can be observed by analyzing discharge patterns more closely. During 2010, January to May can be considered as high flow (>5,000 ft³/s), and June to December as low flow (< 5,000 ft³/s) based on discharge data for CH and PB. IOPs for each estuary showed different patterns between high and low flow (Figure 9A-9F).

Figure 8.

Variations of IOPs plotted against daily average of surface runoff (blue line) for CH (A), PB (B) and SA estuary (C).

Figure 9.

Box plots showing variations in estimated $a_t\mathit{\left(}\lambda \mathit{\right)}$ for the four estutaries during high flow (left) and low flow (right) periods for Choctawhatchee (CH), Pensacola Bay (PB), St. Andrew (SA), and St. Joseph (SJ). Red lines indicate median $a_t\mathit{\left(}\lambda \mathit{\right)}$ values in the respective estuaries. (A-B) $a_t\mathit{\left(}\mathit{412}\mathit{\right)}$, (C-D) $a_t\mathit{\left(}\mathit{443}\mathit{\right)}\mathit{)}$, and (E-F) $a_t\mathit{\left(}\mathit{667}\mathit{\right)}$ observed during high flow and low flow conditions respectively.

The median of a_t during high flow period is generally higher compared to the low flow period. Among the four sites, SJ estuary can be considered as the most homogenous due to its relatively smaller variability in IOPs (coefficient of variations, CV, at $a_t\mathit{\left(}\mathit{412}\mathit{\right)}$ is 39%, compared to CH : 52% and SA : 54%). No natural river drains to St. Joseph Bay and the only water input is from Port. St. Joe navigation channel. The absence of riverine tides in SJ estuary leads to increased influence of seawater and thus CDOM concentration in this site can be linked to decay of vegetation from aquatic environment (Schaeffer et al., 2015). At all sites, $a_t\mathit{\left(}\mathit{443}\mathit{\right)}$ and $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$ values during high flow periods are higher than low flow periods. PB exhibited higher CDOM absorption than other estuaries because PB watershed accommodates larger river systems than the rest (Florida DEP, 2007). In addition, black water rivers in PB watershed are rich in refractory organic compounds such as fluvic and humic acid (Science Applications International Corporation, 1997). High precipitation induced river flow explains the high IOPs or CDOM in PB. During the two high flow periods, PB consistently showed highest values of a_t and $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$, whereas, SJ continued to be the least light absorbing estuary among all estuaries in this study.

Accumulative river discharges to PB can be the source of high absorbing water constituents. The majority of aquifer systems in the basin are sand and gravel composed of permeable sediments with ability to transmit large amounts of water. Blackwater and Yellow Rivers in PB watershed drain through acidic flat woods and wetland (Florida DEP, 2007). CDOM sources can be allochthonous from terrestrial decomposition and autochthonous from decay of aquatic vegetation within a water body (Brezonik et al., 2015). Given the ecological processes in PB, it appears that the absorbing agent can mostly be attributed to the CDOM resulted from acidic materials brought from wetland in the form of sediments flows.

SA and PB watersheds are dominated by natural landscape (evergreen and wetland), accounting for 60% and 52% of total watershed respectively (Le et al., 2015). This high portion of vegetated areas can potentially contribute to high amounts of CDOM and hence higher $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ in the water. SA estuary, despite its much lower discharge magnitudes, showed considerably high absorptions. This is probably due in part that a major portion of SA and PB watersheds is urban built-up and most of them are in close proximity to the estuary. Studies showed that CDOM variations in a water body can also be driven by anthropogenic sources. Waste from urban regions can be another source of elevated CDOM, which may result in urban nutrient-generated algae blooms (Zhu et al., 2013). Conversely, a_t (667) absorption variations do not show clear differences among sites and between high and low flow periods. At this wavelength, the dominance of a_dg and a_phi are relatively similar, ranging from 0 to 30%.

CDOM in near shore aquatic systems represents a mixture of humic and fulvic acid materials from terrestrial sources transported by rivers and marine production (Carder et al., 1989 and Nelson et al., 1998). Identifying the source of detritus and CDOM usually involves tracer studies. Relationships between CDOM and water quality properties such as Chl-a, TSS, salinity and temperature provide insight into the origins of CDOM (Astoreca et al., 2009). Table 8 summarizes the correlation of estimated $a_{dg}\mathit{\left(}443\mathit{\right)}$ with several water quality parameters. Strong positive correlation between $a_{dg}\mathit{\left(}443\mathit{\right)}$ and CDOM-Fluorescence indicates that a_g dominates in a_dg composition in all estuaries. This is also supported by the in situ IOP data showing a_g dominance in a_dg (median = 73 – 79%). Likewise, inverse close association between $a_{dg}\mathit{\left(}443\mathit{\right)}$ and salinity, and positive relationship with TSS suggests that surface hydrological forcing influence the a_dg variations in the estuaries (Table 8). With no tributaries draining to SJ, the estuary receives the least influence of terrestrial inputs compared to other estuaries as indicated by the smallest correlation of $a_{dg}\mathit{\left(}443\mathit{\right)}$ with TSS and salinity (data not shown). TSS in the estuaries includes considerable amount of organic materials (median values of % VSS to TSS range from 37 to 40% in four estuaries). However, a weak relationship between TSS-Chl-a (r = 0.037) and VSS-Chl-a (r = 0.23) suggests that algae might not be the only potential source of organic sediment.

Table 8.

Correlation values between a_dg(443) and Selected Water Quality Parameters

Estuary	CDOM-Fluorescence	Salinity	TSS	VSS	Chl-a
CH	0.85	−0.86	0.60	0.49	0.00
PB	0.80	−0.85	0.76	0.37	−0.35
SA	0.91	−0.80	0.59	0.30	0.36
SJ	0.73	−0.60	0.51	0.27	0.25
Combined	0.88	−0.80	0.69	0.47	0.12

Bowers and Brett (2008) showed that CDOM – salinity relationship might be complex and vary by sites depending on aquatic conditions. In estuaries where rivers serve as a steady source of discharge, CDOM is expected to vary proportionally and inversely with salinity (Bowers and Brett, 2008). Given significant portions of a_g in a_dg (median value of calibration-validation dataset: 73 – 79%), we can assume that the a_dg can represent CDOM concentration in the estuaries. This is further corroborated by the fact that the low $a_{dg}\mathit{\left(}\mathit{443}\mathit{\right)}$ values in SJ are consistently associated with high salinity levels. CDOM-salinity patterns in these regions are similar to other parts of Gulf of Mexico (Schaeffer et al., 2011 and Singh et al., 2010). Occurrence of terrestrial flooding to the bay systems may change the CDOM-salinity relationship in these estuaries (D’Sa, 2008). Weak relationship between $a_{dg}\mathit{\left(}443\mathit{\right)}$ and Chl-a (r=0.12 in the combined dataset) shows that phytoplankton decay might not be a dominant source of CDOM in these estuaries. In coastal areas, apart from phytoplankton decomposition, CDOM can also originate from various terrestrial sources such as humic materials resulting from soils and the decomposition of terrestrial plant litters.

It is clear that light absorption in these estuarine systems is highly dominated by detritus and CDOM, especially in blue and green regions, with river discharge serving as the major governing factor. For CH, PB and SA, absorptions during high flow were consistently higher than during low flow periods. CH and PB exhibit similar features of discharge driven CDOM, while for SA, algae may contribute to highly absorbing water systems, as opposed to SJ estuary with less riverine inputs and considerable vegetated areas. Relatively higher IOPs during high flow in 2010 is associated with increased discharge, precipitation, winter wind, and sediment re-suspension. Results presented here provide examples of potential data and information made available for water quality management by using a hybrid QAA and semi-analytical model to derive spatio-temporal variations of IOPs in low Chl-a, oligotrophic estuaries found in the northern Gulf of Mexico.

Conclusion

Existing QAA (QAA_v6) developed for sea and coastal waters (Lee, 2014) and hyper-eutrophic pond waters (Mishra et al., 2014), did not work well in retrieving $a_t\mathit{\left(}\lambda \mathit{\right)}$ at shorter wavelengths in northern Gulf of Mexico Florida estuaries due to their distinct inherent optical properties. QAA_6 using a λ₀ at 670 nm produced slightly lower average RMSEs than that of the re-parametrized QAA developed for hyper-eutrophic ponds with (λ₀) at 709 nm. Parameterization made to the QAA_v6 by incorporating novel empirical relationship, showed improvement in the accuracy of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimates. QAA_v6 and QAA_709M, derive $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ from the subtraction of $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ from $a_t\mathit{\left(}\lambda \mathit{\right)}$. This approach led to negative $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ estimates when $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ signal was so low that its magnitude is within the error range of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ estimates. The hybrid model developed in this study by utilizing 665 nm as the (λ₀) is able to produce reliable estimates of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$. Given reliable estimates of $a_t\mathit{\left(}\lambda \mathit{\right)}$ and $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ and $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ in this study, the parameterized model can be extended for further work investigating a_d – a_g separation as well as b_bp estimation once the measured data is available. This study shows that empirical parameterization of some steps in the QAA models can improve the estimation accuracies of some IOPs. Larger errors found in longer wavelengths can be related to low signal and interfering absorption by phytoplankton in these regions making estimation less reliable. One disadvantage of using the hybrid model is the need of measured $a_{phi}\mathit{\left(}\lambda \mathit{\right)}$ to calculate the normalized $a_{phi}\mathit{\left(}{\lambda }_{\mathit{0}}\mathit{\right)}$. The use of MERIS/Sentinel-3A OLCI simulated bands from hyperspectral measurements in this study demonstrated the applicability of the hybrid model to operational satellite sensors and its potential to be scaled-up in future studies. Despite being operationally inactive, MERIS can be a potential source for valuable historical data permitting long-term studies. MERIS band configuration was proven suitable to retrieve IOPs using the hybrid model, and it can also be used with the recently launched Sentinel-3A with identical wavebands. This hybrid model approach is transferable to the current Sentine-3A OCLI sensor for future assessments and additional validation of the hybrid model’s performance in low Chl-a oligotrophic estuaries and CDOM dominated water.

Considering the IOP variability, the four estuaries demonstrate responses to precipitation, terrestrial discharge and ocean water tides. Among the absorbing constituents, $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ was the dominant absorption component in all four estuaries. Higher $a_{dg}\mathit{\left(}\lambda \mathit{\right)}$ during high flow periods signifies the roles of terrestrial discharge as one of major sources of light absorbing materials. The parameterized model was able to produce reliable absorbing properties and can be helpful in providing a remote assessment tool for monitoring sediment dynamics and eutrophication status in the estuaries.

Tabel 1.

Symbols and abbreviations

Symbol	Description	Unit
$a_t\mathit{\left(}\lambda \mathit{\right)}$	Total absorption coefficient = $a_w\mathit{\left(}\lambda \mathit{\right)}+a_{dg}\mathit{\left(}\lambda \mathit{\right)}+a_{phi}\mathit{\left(}\lambda \mathit{\right)}$	m−1
$a_w\mathit{\left(}\lambda \mathit{\right)}$	Absorption coefficient of pure water	m−1
$a_{t-w}\mathit{\left(}\lambda \mathit{\right)}$	$a_t\mathit{\left(}\lambda \mathit{\right)}-a_w\mathit{\left(}\lambda \mathit{\right)}$	m−1
$a_d\mathit{\left(}\lambda \mathit{\right)}$	Absorption coefficient of detrital matter	m−1
$a_g\mathit{\left(}\lambda \mathit{\right)}$	Absorption coefficient of gelbstoff or colored dissolved organic matter (CDOM)	m−1
$a_{dg}\mathit{\left(}\lambda \mathit{\right)}$	$a_d\mathit{\left(}\lambda \mathit{\right)}+a_g\mathit{\left(}\lambda \mathit{\right)}$	m−1
$a_p\mathit{\left(}\lambda \mathit{\right)}$	Absorption coefficient of particulate matter	m−1
$a_{phi}\mathit{\left(}\lambda \mathit{\right)}$	Absorption coefficient of phytoplankton pigments	m−1
$b_{bw}\mathit{\left(}\lambda \mathit{\right)}$	Backscattering coefficients of pure water	m−1
$b_{bp}\mathit{\left(}\lambda \mathit{\right)}$	Backscattering coefficients of particulate matter	m−1
$b_b\mathit{\left(}\lambda \mathit{\right)}$	Total backscattering coefficients = $b_{bw}\mathit{\left(}\lambda \mathit{\right)}+b_{bp}\mathit{\left(}\lambda \mathit{\right)}$	m−1
$\eta$	Spectral power for backscattering coefficient
$R_{rs}\mathit{\left(}\lambda \mathit{\right)}$	Above-surface remote sensing reflectance	sr−1
$r_{rs}\mathit{\left(}\lambda \mathit{\right)}$	Subsurface remote sensing reflectance	sr−1
u	Ratio of backscattering coefficient to the sum of backscattering and absorption coefficients
S	Spectral slope of CDOM	nm−1
$\xi$	Ratio of adg(412) to adg(443)
$\zeta$	Ratio of aphi(412) to aphi(443)
$\chi$	Chi factor

Appendix 1A.

Names of USGS stations for river discharge

Estuary	River name	Longitude	Latitude	USGS code
CH	CHOCTAWHATCHEE RIVER AT CARYVILLE, FL	85°49′40″	30°46′32″	2365500
PB	ESCAMBIA RIVER NEAR CENTURY, FL	87°14′03	30°57′54″	2375500
SA	ECONFINA CREEK NEAR BENNETT, FL	85°33′24″	30°23′04″	2359500

Appendix 1B.

Names of NOAA stations for precipitation

Estuary	Station Name	LATITUDE	LONGITUDE
CH	EGLIN AFB 5.6 NE FL US	30.524	−86.492
PB	GONZALEZ 2.1 E FL US	30.569	−87.255
SA	PANAMA CITY FL US	30.249	−85.661
SJ	PORT ST. JOE 0.6 SE FL US	29.803	−85.289