EPA/600/R-15/211 | August 2015 

www.epa.gov/ord 

DATA REPORT FOR CALIBRATION 

OF A BIO-OPTICAL MODEL 

FOR NARRAGANSETT BAY
 

Glen Thursby, Steven Rego, Darryl Keith
	

Atlantic Ecology Division
	

National Health and Environmental Effects Research Laboratory
	

Office of Research and Development
	

US Environmental Protection Agency
	

Narragansett, RI 02882
 

August 5, 2015
 

Office of Research and Development 

National Health and Environmental Effects Research Laboratory 

EPA/600/R-15/211 

Data Report for Calibration 

of a Bio-Optical Model 

for Narragansett Bay

by

Glen Thursby, Steven Rego and Darryl Keith

Atlantic Ecology Division

National Health and Environmental Effects Research Laboratory

Office of Research and Development

US Environmental Protection Agency

Narragansett, RI 02882

August 5, 2015
- ii - 

NOTICE

The research described in this report has been funded wholly by the U.S Environmental 

Protection Agency. This report is contribution number ORD-013449 of the Atlantic Ecology 

Division, National Health and Environmental Effects Research Laboratory, Office of Research 

and Development. This document has been subjected to USEPA’s peer review process and has 

been approved for publication. The mention of trade names of commercial products does not 

constitute endorsement for use. 

ABSTRACT

Bio-optical models describe the quality and quantity of the light field at various depths in the 

water column. The absorption and scattering of light within the water column are wavelength 

dependent. The behavior of light also varies depending on the specific dissolved and particulate 

constituents in the water column, making local (or at least regional) calibration of such models 

necessary. This report provides the calibration data specific for Narragansett Bay, Rhode Island, 

relative to absorption by colored dissolved organic matter (CDOM), non-algal particles (NAP) 

and phytoplankton, and total backscattering. With the calibration in place, information on the 

concentration of CDOM, total suspended solids and chlorophyll a is all that is needed in order 

to calculate the light for any depth for sites those parameters represent.

Keywords: bio-optical model, Narragansett Bay, diffuse attenuation coefficient, light absorption, 

light scattering

ACKNOWLEDGEMENTS

Dr. Brenda Rashleigh, Dr. Peg Pelletier and Mr. Joseph LiVolsi reviewed the final draft of the 

data report. Joseph Bishop assisted with the analyses. Dr. Charles Gallegos from the Smithonian 

Environmental Research Center provided valuable insights during our early attempts to 

understand bio-optical modeling. 
- 1 - 

INTRODUCTION

The data contained in this report supports the development of calibration curves for the use of 

a bio-optical model for Narragansett Bay, RI. The calibration will support research evaluating 

the applicability of a bio-optical model for light quantity in establishing depth limits for seagrass

(Zostera marina) in Narragansett Bay, RI. To accomplish this, a site specific calibration of the 

model was necessary. The model provides estimates of changes in light quantity and quality with 

depth which can be used, to predict the maximum depth likely for seagrass. In the case of 

Narragansett Bay, the seagrass is Zostera marina. As light travels through the water column 

it interacts with water molecules, dissolved materials, suspended inorganic and organic 

particulates and phytoplankton, resulting in a variety of absorption and scattering phenomena. 

Because these phenomena (especially absorption) are wavelength dependent and vary with the 

particular constituents of a given waterbody, it is necessary to calibrate the bio-optical model’s 

parameters for each region of the country—and maybe for each body of water of interest within 

those regions. With calibrations completed, measures of colored dissolved organic matter 

(CDOM), total suspended solids (TSS) and chlorophyll a (Chl a) for any given location allows 

estimates of light penetration to be calculated. 

The model used is based on Lee et al. (2005), as described by Kenworthy et al. (2014). 

KKdd(λλ) = (1 + 0.005θθ0)aatt(λλ) + 4.18[1 − 0.52eeeeee(−10.8aatt)]bbbb(λλ) EQ 1

Where:

λ = wavelength of light (nm)—Equation 1 is wavelength dependent,

Kd (λ) = spectral diffuse attenuation coefficient (m-1),

θ0 = above-water solar angle of incidence (degrees)—zenith angle, 

at (λ) = total absorption coefficient (m-1)—note, λ omitted when this is in the exponent 

 for simplicity,

bb (λ) = backscattering coefficient (m-1).

By integrating over the visible wavelengths, the diffuse attenuation coefficient for 

photosynthetically active radiation (PAR) can be calculated,

 KKdd(PPPPPP) = 1

zz ln (

PPPPPPzz

PPPPPP0

). EQ 2

Where:

Kd (PAR) = diffuse attenuation coefficient, integrated over 400 to 700 nm, 

z = depth in meters,

PARz = light spectrum at depth z, and 

PAR0 = light spectrum at surface.

The Equation 1 requires two site specific pieces of information, the absorption and back 

scattering coefficients. The absorption coefficient (m-1) is an additive equation: 

aatttttttttt(λλ) = aaww wwww(λλ) + aaCCCCCCCC(λλ) + aapp pppp pp(λλ) + aapppppppp pp pp(λλ) EQ 3
 - 2 - 

Where total absorption is a function of four primary components, absorption by water itself, 

by colored dissolved organic matter (CDOM), by particles (total suspended solids—TSS) and 

by pigments (i.e., phytoplankton—usually related to chlorophyll a). Absorption by pure water 

is a fixed function (wavelength dependent), and the relationship between wavelength and 

absorption from Pope and Fry (1997) is usually used. The difference in the absorption of light 

between pure water and seawater is minimal and often ignored. The other three components 

have predictable relationships between absorption and wavelength of light; however, these 

relationships need to be calibrated for each body of water. 

Since we are interested ultimately in how much light makes it down to a given depth for 

seagrass, absorption only gives a portion of the story. Light also is scattered within the water 

column. While most of this light is scattered in the forward direction (e.g., continues downward), 

a significant portion of the light entering the water column is scattered back out of the system. 

The percentage of light backscattered is empirically derived for each area of interest. Total 

scattering (m-1) is calculated as:

bb(λλ) = bbpp(λλ) + bbww(λλ) EQ 4 

Where bbww(λλ) is the total scattering associated with pure water (also referred to as molecular 

scattering), and, light absorption, is considered a constant, wavelength dependent factor. 

The other parameter, bbpp(λλ), is total particulate scattering (in all directions). Unlike absorption, 

there is no easy method to distinguish between pigmented and non-pigmented particle scattering.

The methods to calibrate each of the parameters associated with the bio-optical model are 

presented below. All of the data represented by the calibration figures are presented in 

Appendices. 

METHODS

This calibration establishes the relationship between several easily measured water column 

properties (Chl a, TSS and CDOM) and the components of absorption and scattering that 

contribute to Equation 1. Samples from Narragansett Bay were collected from the upper, 

middle and lower Bay (see Figure 1) from different times of the year, representing Zostera’s 

predominant growing season. The purpose of the sampling scheme was to establish how variable 

the calibration parameters are with respect to time and space. One calibration has been 

established for the entire Bay for all months within which the seagrass Zostera marina grows. 
- 3 - 

Figure 1. Map of Narragansett Bay showing location of sampling stations
 - 4 - 

Absorption by water

There is no calibration associated with the absorption by pure water. It is considered a standard

relationship, and is plotted in Figure 2. In general, the additional absorption at seawater salinities 

due to the salts is minimal in the 400 to 680 nm range (Kirk 2011), and is usually ignored in 

coastal applications. 

Figure 2. The relationship between wavelength and absorption coefficient in pure 

water. Data from Pope and Fry, 1997

Absorption by CDOM—The relationship between absorption coefficient due to Colored 

Dissolved Organic Matter (CDOM) and wavelength of light follows an exponential decay 

function (Bricaud et al. 1981, Kirk 2011). The slope for the decay function (designated as 

SCDOM) is generally consistent for a given body of water. Because the relationship between 

absorbance and wavelength is assumed consistent, the curve can be normalized to a single 

reference wavelength—usually 440 nm. 

aaCCCCCCCC(λλ) = ee−SSCCCCCCCC(λλ−440) EQ 5

The actual absorbance of light at a given wavelength will be governed entirely by the 

concentration of CDOM at the reference wavelength. Therefore, all that is needed is the 

absorbance at 440 on a filtered sample in order to “reconstitute” the entire absorbance vs 

wavelength curve. That is:

aaCCCCCCCC(λλ) = aaCCCCCCCC(440) ∗ aaCCCCCCCC(λλ) EQ 6

Note : a(440) vs CDOM concentration is generally considered to be a linear relationship. 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

400 500 600 700 800

Absorption Coefficient (m-1)

Wavelength (nm)

awater (λ)
- 5 - 

Calibration method: water samples were processed as described in Keith et al. (2002). CDOM 

measurements were made using a Perkin-Elmer Lambda 35 spectrophotometer using a 10 cm 

path length cell with deionized water as the reference. Measured absorbance was recorded at

1 nm intervals from 400 to 750 nm. Final data scans were averaged1 every 5 nm.

Generally, when using a spectrometer to measure the concentration of a dissolved compound or 

compounds the only interaction of the beam of light with the substance in the cuvette is either 

absorption or transmission. However, even under the best of conditions some light will be 

scattered out of the pathway (scattering due to water is accounted for with the blank, but not 

scattering due to CDOM). Since this is neither absorbed nor transmitted, it is a source of error—

it did not get measured as part of the transmitted light. To correct for this, measured absorbance 

recorded at 750 nm was subtracted from values measured at all of the other wavelengths. 

Absorbance at 750 nm is usually assumed to be zero, therefore any recorded non-transmittance 

at 750 nm was assumed to be a loss of light due to scattering rather that true absorbance. These 

corrected measurements are in absorbance, which is the log10 of the ratio of transmitted to 

incident light. Because we are interested in the absorption coefficient (which is related 

to exponential decay), we actually need the natural log of that ratio—which is the same as 

multiplying the original Perkin-Elmer absorbance by 2.303 (the natural log of 10). Finally, 

the absorption coefficient was divided by the path length in meters (0.1 m) to convert the 

units to m-1. 

Absorption by non-pigmented particles (or non-algal particles (NAP)—As with CDOM, the 

relationship between absorbance due to non-pigmented particulates and wavelength of light 

follows an exponential decay function (Gallegos 2001, Roesler et al. 1989). This decay 

coefficient (SNAP) is fairly consistent for a given body of water. As with CDOM, the NAP curves 

also were normalized to a reference wavelength—440 nm. 

aaNN (λλ) = ee−SSNNNNNN(λλ−440) EQ 7 

The actual absorbance of light at a given wavelength will be governed largely by the 

concentration of TSS at the reference wavelength. Once that relationship is established the entire 

absorption curve can be recreated. That is:

aaNN (λλ) = aaNN (440) ∗ aaNN (λλ) EQ 8 

Note: unlike CDOM, aNAP (440) vs TSS concentration is not necessarily a linear relationship. 

Therefore, the calibration step needs to include establishing the site-specific relationship between 

the absorbance at a reference wavelength (usually 440 nm) and TSS. Our data for aNAP vs TSS 

was very scattered. However, the range of TSS values in Narragansett Bay was narrow compared 

to other locations (e.g, Chesapeake Bay—Gallegos et al. 2006). Our data appeared to be 

consistent with that presented by Babin et al. (2003), therefore in our final model we used their 

relationship between aNAP and TSS. 

 

1 For example, data for 400 nm is the average of 400 through 404 nm, for 405 the average of 405 through 409, 

and so forth. 
 - 6 - 

Calibration method: Calibration was performed in two parts. We followed the procedure 

outlined in Gallegos and Neale (2002) and Mitchell et al. (2003), except we used a 50 mm 

integrating sphere coupled to the Perkin-Elmer Lambda 35. Sample water (200 mL) was filtered 

using a glass fiber filter (GF/F, nominal pore size of 0.7 μm), and absorption on the filter 

(from 350 to 750 nm) was measured before and after extraction with methanol (to remove algal 

pigments—see below)2

. The second measurement is the one needed for non-pigmented particles. 

The difference between the two spectra is the absorption by phytoplankton pigments (see next 

section). Just as with CDOM, the decay slope for absorption coefficient plotted against 

wavelength was calculated by fitting the exponential equation to the data. The second calibration 

step was to establish the relationship between TSS and absorption at 440 nm. TSS was

determined by filtering a volume of water (e.g., 500 mL) onto a pre-weighed glass fiber filter. 

Just as with CDOM, we multiplied the absorbance data from the spectrophotometer by 2.303 

to convert to absorption coefficients (see Kishino et al. 1985, Tassan and Ferrari 1995). In 

addition, correction for volume filtered and area of the filter was included (see below). The 

750 nm correction listed above for CDOM is even more important with the quantitative filter 

technique. Scattering of the light away from the entrance of the integrating sphere may be 

appreciable, and will be recorded as absorption. Generally, absorption at 750 nm is considered 

to be negligible, so any values recorded at this wavelength were likely due to scattering.

In addition to the above scattering error, photons have a high probability of experiencing 

multiple scattering events on their way through the filter. This increases the effective path length 

of the light for which correction is also needed. Fortunately, Cleveland and Weidemann (1993) 

have done this correction empirically:

OODD ss (λλ) = 0.378 OO ff (λλ) + 0.523 OO ff (λλ)2 EQ 9 

Where ODsusp is the optical density of the suspended particles for a given wavelength, and ODfilt

is the optical density of the particles on the filters. Remember, optical density is the ratio of the 

log10 of the absorbance of the sample to the log10 of a reference. To adjust this to an absorption 

coefficient—which accounts for the exponential decrease in light with depth—we have to 

convert to natural logarithms (multiply by 2.303). Finally, we have to account for the volume 

filtered (V) and the clearance area (A) of the filter. If we express the former in m3 and the latter 

in m2, then the unit for the absorption coefficient will be in m-1: 

aaNN (λλ) = 2.303 ssssssss(λλ)

VV� EQ 10 

Methanol treatment—After each filter was measured for total particle absorption, each was 

placed into a separate polystyrene petri dish (60 x 15 mm) and 10 mL of room temperature 

methanol was gently added. Extraction in the methanol lasted a minimum of 1 hr. Filters were 

then removed from the petri dish, replaced into the filter apparatus, and the methanol within the 

petri dish run through the filter to remove any particulates that might have been dislodged during 

 

2 Because the degree of wetness of the filter can affect the scan results, after filtering each sample, 100uL of 0.22 um 

filtered seawater was added back to each filter just prior to measurements.
- 7 - 

the extraction process. Afterwards, 10 mL of 0.22 um filtered seawater was used to rinse the 

methanol from the filter. 

Absorption by phytoplankton—The relationship between absorbance due to phytoplankton and 

wavelength does not follow a set function (e.g., exponential) as did CDOM and non-algal 

particulates. Therefore, an empirically derived absorption spectrum is used in the modeling 

effort. We used two procedures to establish this average spectrum. The first is derived from the 

most recent research on seagrass bio-optical models. (Biber et al. 2008, Gallegos 2005, Gallegos 

and Neale 2003, Gallegos et al. 2006). Here the empirically derived spectra were normalized to 

absorption at 675 nm and then averaged by wavelength. 

aaφφ(λλ) = φφ(λλ)

φφ(675) EQ 11 

Where:

aaφφ(λλ) = the normalized absorption of pigmented particles for a given wavelength, 

aaφφ(λλ) = the absorption of pigmented particles for a given wavelength, and 

aaφφ(675) = the absorption of pigmented particles at 675 nm. 

A relationship between chlorophyll a (Chl a) concentration and aaφφ(675) was used to establish 

a specific pigment absorption spectra for a given location. As with aNAP(440) vs TSS 

concentration, the relationship between absorption at 675 nm and chl a concentration is not 

necessarily linear. Therefore, the calibration step included establishing the site specific 

relationship between the absorbance at 675 nm and chl a concentration.

aaφφ(675) = [CChll aa]

BB EQ 12 

The coefficients A and B are empirically derived. The actual absorbance of light at a given 

wavelength now can be estimated entirely by the concentration of chlorophyll a using the 

reference wavelength. That is:

aaφφ(λλ) = aaφφ(675) ∗ aaφφ(λλ) EQ 13 

In a second approach, we established relationships between Chl a and every wavelength between 

400 and 700 nm in 5 nm steps. This is the approach used by Bricaud et al. (1995) and Matsuoka, 

et al. (2007). This latter approach accounts for the fact that phytoplankton light absorption in the 

blue region of light is much more variable than that in the red region. This is largely due to 

packaging effect (the amount of pigment per unit cell and its arrangement within the cell), photoacclimation, or both. Photo-acclimation can result in a significant change in the concentration of 

accessory photosynthetic pigments, as well as non-photosynthetic, photo-protective pigments. 

Both of these types of pigments have their greatest absorption in the blue region. 

Calibration method: As with absorption by non-pigmented particles, absorption by 

phytoplankton pigments requires two steps. However, the first step—establishing the absorption 

spectrum—was accomplished during the calibration of the non-pigmented particles by 

subtracting from the total absorption spectrum of the filter the absorption spectrum of the 
 - 8 - 

particulates alone. The second calibration step needed was to establish the relationship between 

the concentration of Chl a and absorption (from the particle filter method) at wavelengths of 

interest. In general, the procedure for collecting and processing water samples followed those 

used by NASA (Mitchell, et al. 2003)—which were consistent with the procedure used by 

Gallegos and Neale (2002) for their work in Case 2 waters. Chlorophyll a analyses were similar 

to those described in Keith et al. (2002). Samples (100 mL) were filtered onto 47 mm Whatman 

GF/F filters using a hand vacuum pump. Filters were placed into 15 mL screw-capped 

polystyrene tubes containing 10 mL of 90% acetone, and extracted in a freezer overnight 

(approximately 18 hr) in the dark. Fluorescence was measured using a Turner Designs Model 

AU-10 fluorometer equipped with the Non-Acidification Optical Kit (P/N 10-040R). 

Scattering

Unlike absorption, whose parameters can be measured with typical instrumentation available 

in most laboratories, scattering requires specialized equipment. We used an ac-s in situ 

spectrophotometer from WET Labs to measure total scattering. This instrument simultaneously 

measures total light attenuation and total absorbance in approximately 4nm increments between 

the wavelengths of 400 and 730 nm. Scattering is calculated by the difference between total 

attenuation and total absorption. Absorption was corrected for scattering using 739 nm as the 

reference wavelength according to the procedure described by Slade et al. (2010). The ac-s 

measurements were made in the laboratory using a gravity fed system (Slade et al. 2010). 

The actual scattering of light at a given wavelength is governed largely by the concentration 

of TSS. Scattering is assumed to be minimally influenced by CDOM (if at all) and Chl a has no 

direct influence. Its influence on scattering is through the “particles” (phytoplankton) with which 

it is associated. The relationship between scattering at a reference wavelength (555 nm) and total 

suspended solids (TSS) is described by the equation (Kenworthy et al. 2014): 

bbpp(555) = ααTTTTTTββ EQ 14

Where:

bbpp(555) = total particle scattering at 555 nm, 

TSS = total suspended solides (mg/L), and 

α and β are empirically derived coefficients. 

In 2014 backscattering was measured directly in situ Narragansett Bay using a Satlantic 

Profiler II Ocean Profiler (Satlantic LP Canada), equipped with a backscattering sensor 

(a 470 and 700 nm). We also made some direct backscattering measurements in 2013 using 

a HydroScat (Hydro-Optics, Biology and Instrumentation Laboratories) (at 420 nm). The data 

from both were combined3 to establish the relationship between TSS (mg/L) and backscattering 

 

3 Backscattering data from the HydroScat at 420nm was adjusted downward using the relationship between 

wavelength and particle backscattering established using the Satlantic profiler. 
- 9 - 

coefficient (m-1). Wavelength specific backscattering was calculated assuming a linear 

relationship between backscattering at 470 and 700 nm. 

As with absorption, there is no calibration associated for scattering by pure water, it is 

considered a standard relationship with wavelength of light (Buiteveld et al. 1994). 

Backscattering is assumed to be half of the total scattering The backscattering absorption 

coeffients are plotted in Figure 3. 

Figure 3. Plot of standard backscattering coefficient for pure water (Buiteveld et al. 1994)

RESULTS

CDOM Calibration

Figure 4 shows the CDOM scans for samples collected during the summer 2013 and spring 2014. 

Figure 5 is a summary of all of the data in Figure 4 normalized at 440 nm. The overall average 

spectral slope (SCDOM) was 0.0159 nm-1 with a standard deviation of 0.0011 nm-1 (n = 51). This 

is similar to the spring/summer average for data reported by Keith et al. (2002) from the years 

1999 and 2000 (0.0166 nm-1). It is also similar to the overall average (0.0176 nm-1) presented in 

Babin et al. (2003) for 346 CDOM samples for coastal waters around Europe. It appears that, at 

least for coastal waters, the calibration curve for CDOM is fairly consistent. 

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

400 450 500 550 600 650 700

scattering coefficient (m-1)

Wavelength (nm)

Backscattering = 1/2 bw
 - 10 - 

Figure 4. CDOM absorption scans for samples from Narragansett Bay—summer 2013 and spring 2014. 

Data for these curves are presented in Appendix A

Figure 5. Summary of CDOM calibration data for Narragansett Bay—normalized at 440 nm. Solid black 

line is the mean of all 51 curves. Red dashed lines are plus and minus one standard deviation. Solid yellow 

line is the best fit trend line (Equation 5). The open and closed markers are data from Gallegos and Neale 

(2002) for the Rhode River, Maryland and the St. Johns River, Florida, respectively

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

400 450 500 550 600 650 700

CDOM Abs Coefficient (m-1)

Wavelength (nm)

CDOM--Narragansett Bay

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

400 450 500 550 600 650 700

Abs/Abs(440)

Wavelength (nm)

CDOM--Normalized & SD
- 11 - 

NAP Calibration 

Figure 6 shows the Non-algal particle (NAP) absorption scans for samples collected during the 

summer of 2013. Figure 7 is a summary the data presented in Figure 6 normalized to 440 nm. 

The overall average spectral slope (SNAP) was 0.0136 nm-1 (n = 37). As with CDOM, this also is 

similar to the overall average (0.0123 nm-1) presented in Babin et al. (2003) for 348 NAP 

samples for coastal waters around Europe. Although, it is greater than the average reported 

(0.0088 nm-1) for recent work in the Chesapeake Bay (Gallegos et al. 2006). Figure 7 also shows 

a slight depression in the absorption coefficient for wavelengths less than 425 nm. It is not clear 

why this happened; however, a similar effect is shown in samples from the Baltic Sea in Babin et 

al. (2003). For the purposes of the bio-optical model for Narragansett Bay, this slight shift in 

absorption coefficient was ignored. 

The absorption curves for NAP occasionally were not smooth, especially in the 400 to 450 and 

650 to 700 nm ranges. This is not uncommon. We followed the procedure as presented by Babin 

et al. (2003) and Matsuoka et al. (2011), whereby the non-linear regression was conducted on 

each curve without the data in these ranges. This was done to “avoid any residual pigment 

absorption that might still have been present.” 

Figure 6. Non-algal particle (NAP) absorption scans from Narragansett Bay—summer 2013 (July, August 

and September). Data for these curves are presented in Appendix B

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

400 450 500 550 600 650 700

NAP Abs Coefficient (m-1)

Wavelength (nm)

NAP Absorption
 - 12 - 

Figure 7. Summary of NAP calibration data for Narragansett Bay—normalized at 440 nm. Blue markers 

represent the mean of all 37 curves. Red dashed lines are plus and minus one standard deviation. Solid black 

line is the best fit trend line (Equation 7)

Typically, a correlation between absorption by non-pigmented particles and TSS is used to adjust 

the normalized calibration curve to in situ absorption coefficients (Gallegos et al. 2006, and 

others—including Kenworthy et al. 2014). Figure 8 (top left) shows the relationship between 

aNAP (440) and TSS for samples collected in Narragansett Bay. There does not appear to be a 

relationship. However, the range of TSS values in our data set is narrow compared to those in 

other data sets. Gallegos et al. (2006) show what appears to be a similar amount of scatter within 

their Figure 9a. Our Figure 8 (top right) shows the Narragansett Bay data re-plotted with the 

range on the axes the same as the range used in Gallegos et al. (2006). The degree of vertical 

scatter is similar to that displayed in Gallegos et al. (2006) Figure 9c—although the absorption 

coefficient in Narragansett Bay for a give TSS value is slightly less than that in their Figure 9c. 

Similarly, we re-plotted the data along with the regression for aNAP vs TSS (SPM4

 in their paper) 

published in Babin et al. (2003), see Figure 8 (bottom). The degree of scatter within the range of 

TSS for Narragansett Bay is similar to that depicted in Figure 15 of Babin et al. (2003). The 

central tendency of our absorption coefficient data appears to line up fairly well with the 

regression from Babin et al. (2003), so for the purpose of using TSS to establish NAP absorption 

(m-1) within Narragansett Bay, we used their equation (0.31 * TSS in mg/L). 

 

4 Suspended Particle Matter

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

400 450 500 550 600 650 700

Abs/Abs(440)

Wavelength (nm)

Normalized Absorbance: NAP
- 13 - 

 

Phytoplankton Calibration 

Figure 9 shows the phytoplankton (pigmented particles) absorption scans for samples collected 

during the summer of 2013 (July, August and September). Each curve is normalized to the 

absorption at 675 nm. Figure 10 shows the average of all 31 normalized curves. This is the 

empirical calibration curve for the bio-optical model. The final absorption curve is created based 

on the chlorophyll a concentration for a given site (see Equation 3). Figure 11 shows the 

relationship between chl a and phytoplankton particle absorption at 675 nm. A similar plot is 

shown in Figure 12 for chl a and absorption at 440 nm. Table 1 contains all of the coefficients 

for absorption at wavelengths ranging from 400 to 700 nm in 5 nm increments relative to chl a

concentration. These data can be used to establish a calibration curve whose shape will vary 

depending on the concentration of chl a. This is the process used by Matsuoka et al. (2007) and 

others to create their absorption curves. Figure 13 compares calculated absorption curves using 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25

NAP Abs(440)

TSS (mg/L)

aNAP(440),(m-1)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0 50 100 150 200 250

NAP Abs(440)

TSS (mg/L)

aNAP(440),(m-1)

0.0001

0.001

0.01

0.1

1

0.01 0.1 1 10 100

NAP Abs(440)

TSS (mg/L)

aNAP(440),(m-1)

Figure 8. The relationship between non-algal 

particle absorption and total suspended solids for 

Narragansett Bay. The data in the plot at the top 

left are re-plotted in the top right plot using the 

axes ranges from Gallegos et al. (2006). The data 

are re-plotted again in final panel using the axes 

from Babin et al. (2003). Data are in Appendix C.
 - 14 - 

both procedures. The “normalize” curves use Figure 10 and the relationship in Figure 11 

to create the five phytoplankton absorption curves for chl a ranging from 0.5 to 20 ug/L. 

The “A-B” curves used the data presented in Table 1 to create an additional five absorption 

curves. The difference between the two calibration techniques is chl a concentration dependent 

and confined largely to the blue end of the spectrum. This region of the curves are influenced 

by photo-acclimation. During photo-acclimation cells growing in higher light (e.g, low 

concentrations of Chl a in the water) create additional pigments (mostly non-photosynthetic 

pigments) for protection against the higher energy wavelengths (the blue region). The clearer 

the water (i.e., the lower the concentration of Chl a), the greater the expected concentration of 

photo-protective pigments—which have their primary absorption in the higher energy (short 

wavelengths) end of the spectrum. 

Figure 9. Phytoplankton particle absorption scans from Narragansett Bay—summer 2013 (July, August and 

September). Each curve is normalized to its absorption at 675 nm. Original, non-normalized data are in 

Appendix D

0.0

0.5

1.0

1.5

2.0

2.5

3.0

400 450 500 550 600 650 700

Phytoplankton Abs (m-1)

Wavelength (nm)

Summer--2013 
- 15 - 

Figure 10. Average of the normalized pigmented particle (phytoplankton) absorption scans from Figure 9

Figure 11. The relationship between chl a concentration and particle absorption at 675 nm. Data are in 

Appendix E

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

400 450 500 550 600 650 700

Phytoplankton Abs (m-1)

Wavelength (nm)

2013 AVG--normalized to 675

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25 30 35 40

Abs (675) m-1

Chl a (ug/L)

Abs (675)
 - 16 - 

Figure 12. The relationship between chl a concentration and particle absorption at 440 nm. Data are in 

Appendix E

Figure 13. A comparison of phytoplankton particle absorption spectra using two different methods of 

calibration. See text for explanation. Top 2 plots are for 20 ug/L, next 2 are for 10 ug/L, and so on

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30 35 40

Abs (440) m-1

Chl a (ug/L)

Abs (440)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

400 450 500 550 600 650 700

Phytoplankton Abs (m-1)

Wavelength (nm)

Phytoplankton Normalized 20 ug/L

Normalized 10 ug/L

Normalized 5 ug/L

Normalized 2.5 ug/L

Normalized 0.5 ug/L

A-B 20 ug/L

A-B 10 ug/L

A-B 5 ug/L

A-B 2.5 ug/L

A-B 0.5 ug/L
- 17 - 

Table 1. Parameters for power regression expressed as Abs(λ) = A*Chl aB. Units of absorption are m-1, units for 

chl a are ug/L. These data are used to create absorption curves for phytoplankton particles—the shape of which is 

chl a concentration dependent. 

Wavelength 

(nm) A B r2

Wavelength 

(nm) A B r2

400 0.0576 0.636 0.647 555 0.0111 0.819 0.772

405 0.0617 0.642 0.678 560 0.0097 0.831 0.735

410 0.0663 0.644 0.700 565 0.0094 0.814 0.756

415 0.0703 0.643 0.715 570 0.0089 0.815 0.757

420 0.0634 0.669 0.713 575 0.0081 0.840 0.761

425 0.0641 0.662 0.674 580 0.0075 0.862 0.769

430 0.0675 0.669 0.723 585 0.0074 0.867 0.766

435 0.0702 0.672 0.751 590 0.0071 0.870 0.753

440 0.0695 0.673 0.764 595 0.0068 0.867 0.726

445 0.0675 0.667 0.770 600 0.0067 0.869 0.716

450 0.0642 0.670 0.779 605 0.0071 0.872 0.728

455 0.0632 0.669 0.787 610 0.0077 0.881 0.760

460 0.0627 0.666 0.792 615 0.0085 0.886 0.788

465 0.0611 0.664 0.795 620 0.0089 0.885 0.806

470 0.0588 0.659 0.786 625 0.0093 0.881 0.815

475 0.0557 0.658 0.782 630 0.0098 0.877 0.830

480 0.0533 0.661 0.780 635 0.0102 0.861 0.839

485 0.0506 0.673 0.786 640 0.0104 0.844 0.839

490 0.0476 0.686 0.796 645 0.0104 0.835 0.847

495 0.0436 0.701 0.805 650 0.0103 0.858 0.865

500 0.0389 0.717 0.810 655 0.0116 0.891 0.898

505 0.0344 0.731 0.809 660 0.0158 0.895 0.921

510 0.0302 0.748 0.810 665 0.0220 0.882 0.929

515 0.0266 0.763 0.806 670 0.0272 0.867 0.933

520 0.0238 0.774 0.802 675 0.0282 0.855 0.931

525 0.0213 0.787 0.805 680 0.0237 0.864 0.928

530 0.0190 0.802 0.809 685 0.0162 0.888 0.916

535 0.0172 0.810 0.808 690 0.0089 0.913 0.871

540 0.0156 0.816 0.808 695 0.0050 0.904 0.776

545 0.0140 0.819 0.800 700 0.0032 0.879 0.626

550 0.0126 0.818 0.792

Backscattering Calibration

Scattering is the most variable of the parameters measured for water clarity estimates using a 

bio-optical model. Scattering data also are not as prevalent in the literature as are absorption 

data, since scattering measurements require specialized instrumentation that has only recently 

become more available. Calibration for scattering coefficients typically involves establishing 

a correlation between TSS and total scattering for a reference wavelength (usually 555 nm). 

Although relationships between a combination of parameters (e.g., TSS, Chl a and CDOM) have 
 - 18 - 

been used occasionally (Gallegos 2005). No matter what parameter or combination of 

parameters, the variability of scattering coefficients is usually fairly high, especially when 

compared with that for absorption coefficients. One plausible explanation is that scattering is 

highly dependent on not only the concentration of suspended matter, but also the specific make 

up of that material with respect to size, shape and composition (especially inorganic versus 

organic). And, unlike absorption measurements, there is not an easy method to segregate 

measurements on the different components. 

Figure 14 shows the relationship between total scattering at 555 nm and the concentration of TSS 

for samples collected in Narragansett Bay. Clearly there is not a good relationship. There also 

was no relationship between location or time of year, with respect to the relationship. Gallegos 

(2005) explains some of the variation observed in scattering coefficient for water samples 

collected in the lower St. Johns River, Florida by segregating his samples by salinity. He was 

able to show better relationships among TSS and total scattering than we were; however, the 

ranges of values for both TSS and measured scattering were greater for his measurements. When 

our data are plotted with these expanded ranges (Figure 15), the degree of variability is very 

similar to that presented in Figure 9c of Gallegos (2005). This is also true when we compare our 

data using observation from Figure 11a in Gallegos et al. (2006) for Chesapeake Bay. Figure 16 

is our data re-plotted again, this time using the axes ranges from Gallegos et al. (2006). 

Figure 14. Relationship between total scattering at 555 nm and total suspended solids for Narragansett 

Bay. Data are in Appendix F

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30 35

Scattering Coefficient (m-1)

TSS (mg/L)

b(555)
- 19 - 

Figure 15. The same data as presented in Figure 14 except the axes are expanded to coincide with those 

from Gallegos (2005) 

Figure 16. The same data as presented in Figure 14 except the axes are expanded to coincide with those 

from Gallegos et al. (2006)

0

2

4

6

8

10

12

14

16

18

20

22

0 10 20 30 40 50 60 70 80

Scattering Coefficient (m-1)

TSS (mg/L)

b(555)

0

10

20

30

40

50

60

70

80

90

100

110

120

0 25 50 75 100 125 150 175 200 225 250

Scattering Coefficient (m-1)

TSS (mg/L)

b(555)
 - 20 - 

Our highly variable relationship between total scattering and TSS is consistent with what others 

have experienced. We were able, however, to establish a better relationship between TSS and 

particle backscattering. Data showing this are presented in Figure 17. Gallegos et al. (2006) also 

had a relationship between backscattering and TSS. The range of their data was estimated from 

their Figure 12c. The backscattering data from Gallegos et al. (2006) was measured at 532 nm. 

We adjusted these data upward by about 10% to account for the slight influence of wavelength 

on backscattering (see below). Even though backscattering is a better relationship to TSS, it still 

is not great, but it is likely the best that can be done for now. The regression line is a non-linear 

fit to a power function. The equation for the line is: 

bbbb (470) = 0.0095 ∗ TTTTTT0.379 EQ 15

Where:

bbbb (470)= particle backscattering at 470 nm (m-1), and

TSS = total suspended solids (mg/L). 

A calibration curve for backscattering versus wavelength was established using the data we have 

for backscattering at 470 nm and 700 nm from the Satlantic profiles. By necessity we assumed 

that the relationship between wavelength and backscattering was linear. This line is:

bbbb (λλ) = −0.041 � λλ

1000� + 0.0477 EQ 16

We then took these data and normalized them to bbp (470). This relationship is multiplied by the 

bbp (470) calculated from the relationship in Figure 17 to achieve the final backscattering 

coefficients for a given site.

Figure 17. Relationship between backscattering at 470 nm and total suspended solids for Narragansett Bay. The red 

markers are data collected using a HydroScat in 2013. The blue markers are data from the Satlantic Profiler in 2014. 

The blue solid line is the regression (Equation 15) fit to the red and blue markers. The vertical dashed lines are 

ranges estimated from Gallegos et al. (2006) for comparison. Data are in Appendix F.

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0 5 10 15 20 25 30 35

bbp(470)

TSS (mg/L)

backscattering (m-1)
- 21 - 

PUTTING IT ALL TOGETHER

Referring back to Equation 1, we need three pieces of information in order to calculate the 

diffuse extinction coefficient (Kd): the solar zenith angle of incidence in degrees, total absorption 

by wavelength, and total backscattering, also by wavelength. The zenith angle is easily 

calculated using NOAA’s solar calculator, which can be used directly on their webpage, or 

spreadsheets can be downloaded (http://www.esrl.noaa.gov/gmd/grad/solcalc/calcdetails.html).

All that is needed is the latitude and longitude for a site, date, time zone and time of day. For 

total absorption and backscattering all that is needed are measurements or modeled values for 

CDOM, TSS and Chl a. 

Total absorption (Equation 3) is wavelength dependent. We have chosen to make the calculation 

in 5 nm increments from 400 to 700 nm. Absorption by water (awater) has a fixed relationship 

with wavelength (see Figure 2). Absorption by CDOM for Narragansett Bay is calculated from: 

aaCCCCCCCC(λλ) = aaCCCCCCCC(440) ∗ ee−0.0159∗(λλ−440)

Where: aaCCCCCCCC(440) is the directly measured (or modeled) value of CDOM absorption at 440 nm. 

Absorption by non-algal particles is calculated by first deriving the absorption at 440 nm: 

aaNN (440) = 0.31 ∗ TTTTTT

Where: TSS is total suspended solids in mg/L. Absorption for each wavelength of interest is 

then calculated using:

aaNN (λλ) = aaNN (440) ∗ ee−0.0136∗(λλ−440)

Finally, absorption by phytoplankton, aaφφ(λλ), is estimated by first deriving the absorption at 

675 nm, using: 

aaφφ(675) = 0.0282[CChll aa]

0.855

Where: [Chl a] is the concentration of chlorophyll a in μg/L. This value is then used to establish 

the absorption at all of the wavelengths of interest, using: 

aaφφ(λλ) = aaφφ(675) ∗ aaφφ(λλ)

Where: aaφφ(λλ) is the wavelength dependent absorption curve, normalized to 675 nm 

(see Figure 10). Alternately, we could derive the phytoplankton absorption curve by calculating 

absorption for each wavelength as an independent relationship with the concentration of Chl a 

(see Table 1). 

Total backscattering is calculated as the sum of backscattering from pure water and 

backscattering due to everything else. Backscattering from water is considered a fixed 

relationship with wavelength (see Figure 3). Backscattering by the constituents within 
 - 22 - 

Narragansett Bay water is calculated based on spectral backscattering coefficients normalized 

to 470 nm. Backscattering at 470 nm is calculated using:

bbbb (470) = 0.0095 ∗ TTTTTT0.379

Where: TSS is total suspended solids in mg/L. Final spectral backscattering coefficients 

are calculated using:

bbbb (λλ) = bbbb (470) ∗ (1.678 − 0.00144 ∗ λλ)

The latter portion of the right side of the above equation is the Equation 16 normalized at 470 nm 

(dividing Equation 16 by Equation 16 solved using λ = 470).

The total spectral absorption and spectral backscattering coefficients are then plugged into 

Equation 1 to calculate the spectral diffuse attenuation coefficients. These are used, in turn, in 

Equation 2 to calculate the total diffuse attenuation coefficient for photosynthetically active 

radiation (PAR). To do this you need the spectrum of light at the surface of the water. This 

information can be calculated using readily available free software from the National Renewable 

Energy Laboratory (http://www.nrel.gov/rredc/smarts/). What is needed is the global horizontal 

irradiance (the irradiance hitting a horizontal surface). This is a combination of direct, beam and 

diffuse irradiance. The units used are not important (Wm-2 or photon flux are often used), the 

attenuation coefficent is a ratio—the units cancel out. 
- 23 - 

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- 25 - 

Appendices

Appendices A through F are in the attached Microsoft Excel file, Bio-optical model appendices—

data for Narragansett Bay.xlsx. To access the file, select the attachments icon within Adobe 

Acrobat. It contains the data used to create the figures associated with the calibration for absorption 

and scattering.