Optical closure in a complex coastal environment: particle effects

Optical closure in a complex coastal environment: particle effects Grace Chang,1,* Andrew Barnard,2 and J. Ronald V. Zaneveld2 1

Ocean Physics Laboratory, University of California Santa Barbara, 6487 Calle Real, Suite A, Goleta, California 93117, USA 2WET Labs, Inc., 620 Applegate Street, Philomath, Oregon 97370, USA *Corresponding author: [email protected] Received 23 April 2007; revised 5 September 2007; accepted 6 September 2007; posted 7 September 2007 (Doc. ID 82300); published 25 October 2007

An optical dataset was collected on a mooring in the Santa Barbara Channel. Radiative transfer modeling and statistical analyses were employed to investigate sources of variability of in situ remote sensing reflectance 关rrs共␭, 4 m兲兴 and the f兾Q ratio. It was found that the variability of inherent optical properties and the slope of the particle size distribution (␰) were strongly related to the variability of rrs共␭, 4 m兲. The variability of f兾Q was strongly affected by particle type characteristics. A semianalytical radiative transfer model was applied and effects of variable particle characteristics on optical closure were evaluated. Closure was best achieved in waters composed of a mixture of biogenic and minerogenic particles. © 2007 Optical Society of America OCIS codes: 010.4450, 280.0280.

1. Introduction

Significant advances in measurement techniques for the inherent optical properties (IOPs, properties that do not depend on the radiance distribution) and apparent optical properties (AOPs, properties that depend on the IOPs and the radiance distribution) of seawater [1] have been made recently. Specifically, the spectral backscattering coefficient can now be measured in situ at a wide range of temporal and spatial scales and radiometric quantities and measurements of absorption, scattering, and attenuation coefficients can now be made at hyperspectral resolution (⬃100 wavelengths in the visible). Despite these technological developments, the forward and inverse problems in ocean optics, i.e., optical closure, have yet to be resolved. The forward problem involves two components: (1) the determination of IOPs from characteristics of the particulate and dissolved material and (2) the prediction of AOPs from IOPs using radiative transfer. This second component has been achieved successfully, e.g., Monte Carlo simulations and computational models (Hydrolight [2]); closure 0003-6935/07/317679-14$15.00/0 © 2007 Optical Society of America

issues lie mainly within the first component. The inverse problem can also be separated into two components: (1) the inversion of AOPs for the derivation of IOPs and (2) the determination of particulate and dissolved properties from the IOPs; both components are important for evaluation of remote sensing data for key environmental parameters (e.g., [3]). Ocean color remote sensing data yield synopticscale observations of quantities such as spectral water-leaving radiance or remote sensing reflectance, which can be inverted to obtain spectral absorption and backscattering through the equations of radiative transfer (e.g., [4]): Rrs共␭兲 ⫽ Lw共␭, 0⫹兲兾Ed共␭, 0⫹兲,

(1a)

⬇ 关f共␭兲兾Q共␭兲兴兵bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴其, (1b) where Rrs共␭兲 is spectral remote sensing reflectance just above the sea surface, Lw共␭, 0⫹兲 is spectral waterleaving radiance, Ed共␭, 0⫹兲 is spectral downwelling irradiance just above the sea surface, bbt共␭兲 is total spectral backscattering, at共␭兲 is total spectral absorption, and the f兾Q ratio (wavelength notation hereafter suppressed) is a parameter that depends on the shape of the upwelling light field and the volume 1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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Table 1. Notation

Symbol

Units ⫺1

ad(␭) adg(␭) ag(␭) ap(␭) aph(␭) apg(␭) at(␭) bbp(␭)兾bp(␭) bbp(␭) bbt(␭) bp(␭) bt(␭) or b cg(␭) cp(␭) cpg(␭) ct(␭) or c(␭) Chl Ed(␭, 0⫹) Ed(␭, z) f兾Q or f(␭)兾Q(␭)

m m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 m⫺1 ␮g l⫺1 W m⫺2 nm⫺1 W m⫺2 nm⫺1 sr⫺1

g0 and g1

sr⫺1

KL(␭, z) or KL Lu(␭, z) Lw(␭) n np rrs(␭, 4 m) or rrs(␭) Rrs(␭) z ␥ ␭ ␻0(␭) or ␻0 ␰

m⫺1 W m⫺2 nm⫺1 sr⫺1 W m⫺2 nm⫺1 sr⫺1

sr⫺1 sr⫺1 m nm

Definition Spectral detrital absorption coefficient Spectral detrital plus gelbstoff absorption coefficient Spectral gelbstoff absorption coefficient Spectral particulate absorption coefficient Spectral phytoplankton absorption coefficient Spectral particulate plus gelbstoff absorption coefficient Spectral total absorption coefficient Spectral backscattering ratio Spectral particulate backscattering coefficient Spectral total backscattering coefficient Spectral particulate scattering coefficient Spectral total scattering coefficient Spectral gelbstoff attenuation coefficient Spectral particulate attenuation coefficient Spectral particulate plus gelbstoff attenuation coefficient Spectral total attenuation coefficient Chlorophyll concentration Spectral downwelling irradiance just above the sea surface Spectral downwelling irradiance at a depth z A parameter that depends on the shape of the upwelling light field and the volume scattering function where Q or Q(␭) is the ratio of irradiance to radiance at the same depth g-constants representing the angular dependency of the underwater light field empirically derived by Lee et al. [34] Spectral diffuse attenuation coefficient for upwelling radiance at a depth z Spectral upwelling radiance at a depth z Spectral water-leaving radiance Number of data points Real part of the index of refraction of particles Spectral remote sensing reflectance at a depth z, where z ⫽ 4 m Spectral remote sensing reflectance just above the sea surface Depth below the sea surface Slope of the particulate attenuation spectrum Wavelength of light Ratio of particulate scattering to particulate plus gelbstoff attenuation Slope of the particle size distribution

scattering function (VSF) [5] (see Table 1 for notation guide). In turn, the IOPs can be used as proxies to ascertain biogeochemical parameters for application to broad environmental issues [6]. Spectral absorption can be decomposed into absorption by its constituents: the phytoplankton, detrital, and dissolved components of absorption [aph共␭兲, ad共␭兲, and ag共␭兲; Table 1] (e.g., [7–9]). Phytoplankton absorption spectra can be used to determine species by group including harmful algal species [10,11] and to estimate primary productivity [12,13]. Estimates of colored dissolved organic matter (CDOM) concentration can be determined by the dissolved component of absorption [14]. Recent efforts have focused on the utility of spectral backscattering for estimates of particle size distribution, particle composition, and index of refraction of particles [15–19]. These quantities are important for evaluation of sediment resuspension and transport and thus, beach erosion and the movement of buried contaminants. In addition to absorption and backscattering, Roesler and Boss [20] presented a method of estimating the spectral attenuation coefficient, 7680

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c(␭), from ocean color remote sensing data. Spectral attenuation can give an indication of particle concentration and size distribution [21]. Because quantities such as the f兾Q ratio are poorly understood for coastal waters, and cannot be measured directly in situ or remotely, most algorithms used to derive the IOPs from ocean color remote sensing data incorporate assumptions about the angular dependency of the underwater light field and the backscattering spectra. These assumptions and relationships often work sufficiently for open ocean waters, however the presence of high concentrations of CDOM, inorganic particulates, or both components can confound optical closure for the coastal ocean. Mobley et al. [22] and, more recently, Tzortziou et al. [23] investigated the effects of the VSF on radiative transfer and optical closure. Both authors found that a measured VSF (or backscattering spectra), rather than an assumed VSF (e.g., [24]) is critical for obtaining optical closure when using radiative transfer models or satellite algorithms. Barnard et al. [25] presented a backscattering-independent, triple-ratio

remote sensing reflectance algorithm to derive the IOPs from the AOPs. This method significantly reduces the contribution of the quantity, f兾Q, to the radiative transfer equation. Although the Barnard et al. [25] approach obtains closure with a high degree of accuracy, it makes assumptions about the shape of the backscattering spectrum. The shape and spectral quality of the underwater light field are critically important for inversions of remote sensing reflectance for accurate estimates of the IOPs and biogeochemical parameters, particularly in coastal (or case II) waters. The purpose of this work is to investigate effects of particles and their characteristics on optical closure in a biogeochemically complex coastal environment. Relationships between optical and particle properties are also examined. 2. Methods A.

Field Experiment

We collected time series datasets of physical and biooptical data on a shallow-water mooring, the Santa Barbara Channel Relocatable Mooring (CHARM), as part of the National Oceanographic Partnership Program Multidisciplinary Ocean Sensors for Environmental Analyses and Networks (NOPP MOSEAN) project. The CHARM was located ⬃1.5 km off the coast of La Conchita, California in 25 m water depth (Fig. 1). Instruments on the CHARM relevant to this study were colocated at 4 m water depth. These included: Satlantic Inc. hyperspectral radiometers for upwelling radiance and downwelling irradiance (also deployed at surface and 10 m water depth; ⬃3.3 nm resolution between 400 and 800 nm), absorption and attenuation meters [hyperspectral (ac-s; ⬃4 nm resolution between 400 and 730 nm) and spectral (ac-9; ␭ ⫽ 412, 440, 488, 510, 532, 555, 650, 676, and 715 nm)], spectral backscattering meter (␭ ⫽ 470, 532, and 660 nm), and a fluorometer for chlorophyll concentration. Complementary measurements included temperature, salinity, and current velocity profiles. The CHARM was first deployed in May 2003 and has since been deployed between the months of February and October (with a mooring turnaround in spring) from 2004 until the present. Data used in this study are from 12 February–25 March 2004 (year days 43– 85, 2004; deployment 2), 14 May–30 May 2004 (year days 135–151, 2004; deployment 3), 4 February–10 March 2005 (year days 35– 69, 2005; deployment 4), and 2–31 May 2005 (year days 122– 151, 2005; deployment 5). A total of 125 days of optical data is presented. B.

Data Processing

Radiometer data were collected every hour for approximately 1 min between 0600 and 1800, local time [Pacific Standard Time (PST)]. Measurements of upwelling radiance, Lu共␭, z兲, and downwelling irradiance, Ed共␭, z兲, were self-corrected using shuttered dark counts collected hourly. Radiometers were factory

Fig. 1. (Color online) Left: Map of the Santa Barbara Channel showing the location of the CHARM (upper inset shows coastal California, USA; star indicates the location of the Santa Barbara Channel). Right: Schematic of the CHARM with 4 m instrumentation package. Lu共␭兲 and Ed共␭兲 ⫽ hyperspectral upwelling radiance and downwelling irradiance sensors, ac-s or ac-9 ⫽ hyperspectral or spectral absorption and attenuation meter, ECObb3 ⫽ spectral backscattering meter, ECOfl ⫽ fluorometer, Temp ⫽ temperature, and Sal ⫽ salinity. Depths of other sensor packages are indicated.

calibrated yearly and data were processed following each four-month CHARM deployment. Differences between precalibrations and postcalibrations were subtracted from processed data. The error associated with radiometer self-shading, ␧, can be represented as (wavelength notation suppressed [26]) ␧ ⫽ 共LuT ⫺ LuM兲兾LuT, ⫽ 关1 ⫺ exp共⫺katr兲兴,

(2a) (2b)

where LuT is radiance corrected for self-shading and LuM is uncorrected radiance, at is the total absorption coefficient, r is the radius of the instrument housing, and k ⫽ 2兾tan ␪0w (␪0w is the refracted solar zenith angle). This method was developed assuming that bt ⬍⬍ at [26]. However, scattering dominates in this coastal environment 关0.61 ⬍ ␻0共530 nm兲 ⬍ 0.99; mean共␻0兲 ⫽ 0.90; Table 1], therefore the diffuse attenuation coefficient for upwelling radiance, KL, was substituted for the absorption coefficient, at, in Eq. (2b): d (3a) KL共␭, z兲 ⫽ ⫺ 关ln Lu共␭, z兲兴, dz 1 Lu共␭, z2兲 , (3b) ⬇⫺ ln ⌬z Lu共␭, z1兲 1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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where z2 and z1 are different depths of radiometric measurements and z2 ⬎ z1 [z2 ⫽ 10 m and z1 ⫽ 4 m]. For this study, Lu共␭, z兲 and Ed共␭, z兲 data collected before 1000 and after 1600 PST were removed due to spikes in the data caused by lower sun angles. We computed remote sensing reflectance, rrs共␭, 4 m兲, from Lu共␭, 4 m兲 and Ed共␭, 4 m兲 spectra at z ⫽ 4 m water depth using the following relationship: rrs共␭, 4 m兲 ⫽ Lu共␭, 4 m兲兾Ed共␭, 4 m兲.

(4)

By using 4 m data, we avoided potential errors associated with extrapolation of radiometric data through the sea surface. The ac-s and ac-9 sampled once per hour for 12 s (because of calibration issues, the ac-s was replaced by an ac-9 for deployment 5) and the spectral backscattering meter (ECObb3, WET Labs, Inc.) burst sampled for ⬃12 s every 15 min. All three sensors were factory calibrated yearly to quantify instrument drift. The difference between precalibrations and postcalibrations were accounted for while processing absorption, attenuation, and backscattering data. Temperature and salinity corrections were applied to ac-s data following the methods presented by Sullivan et al. [27] and to ac-9 data according to Pegau et al. [28]. We used the proportional method scattering correction presented by Zaneveld et al. [29]. The ac meters produce in situ measurements of the total absorption and attenuation coefficients minus the contribution by water [apg共␭兲 and cpg共␭兲, where p ⫽ particulate and g ⫽ gelbstoff or dissolved portion]. The ECObb3 measures the total backscattering coefficient 关bbt共␭兲兴. Note that the red channel of the spectral backscattering meter for deployments 4 and 5 was damaged and therefore its data are not presented here. C. Data Analyses

To demonstrate self-consistency between measured IOPs and AOPs, the numerical radiative transfer model, Hydrolight [2], was employed. IOPs [at共␭兲, ct共␭兲, and bbt共␭兲] measured daily at noon throughout the time series were inputted into Hydrolight. Pure water absorption coefficients were taken from Pope and Fry [30]. Solar angles were computed for each date and time and wind speeds were assumed to be 4 m s⫺1 during winter and summer and 10 m s⫺1 during spring, which were average values collected at the CHARM site in 2003 (wind speeds at the CHARM mooring were not measured in 2004 and 2005). Cloud cover was assumed to be 0% (also not measured), the solar and sky components of irradiance were computed from the RADTRAN model, and waters were assumed to be optically deep. Hydrolight-computed radiometric quantities for Lu共␭, z兲 and Ed共␭, z兲 at seven wavelengths between 400 and 700 nm, 50 nm wavelength resolution, were then compared to those measured by radiometers on the CHARM mooring. Hydrolight-derived Lu共␭, z兲 and Ed共␭, z兲 compared quite well to measured radiometric quantities (Fig. 2), 7682

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Fig. 2. (Color online) An example of Hydrolight-simulated (squares) and radiometer-measured (circles). (a) Lu共␭, 4 m兲 and (b) Ed共␭, 4 m兲 indicating that measured IOPs and AOPs are selfconsistent and of high quality. Data shown are from deployment 2.

indicating that in situ IOPs and AOPs were of high quality. Average r2 values for measured versus derived Lu共␭, z兲 was 0.94, with average percent differences within 20% for blue to green wavelengths, where measured radiometric quantities generally have higher signal to noise ratios and thus, less error. Linear regressions between simulated and measured Ed共␭, z兲 values resulted in average r2 ⫽ 0.92 and average percent differences within 25% for blue to green wavelengths. The high r2 values show that spectral shapes of measured IOPs and AOPs are accurate, however the magnitudes of simulated Lu共␭, z兲 and Ed共␭, z兲 may not have been true due to assumptions made about environmental conditions. We measured a comprehensive set of IOPs and AOPs and therefore directly calculated the f兾Q ratio using a modified version of Eqs. (1) and (4):

关f共␭兲兾Q共␭兲兴 ⫽ 兵关at共␭兲 ⫹ bbt共␭兲兴兾bbt共␭兲其关rrs共␭, 4 m兲兴. (5) To investigate effects of particle characteristics on the variability of rrs共␭, 4 m兲 and the f兾Q ratio, we estimated the particle size distribution (PSD) slope, ␰, according to the relationship: ␰ ⫽ ␥ ⫹ 3 ⫺ 0.5 exp 共⫺6 ␥兲, where ␥ is the slope of the particulate attenuation spectrum 关cp共␭兲兴 [15,16,21]. The nonlinear relationship is used here because ␥ values are close to zero and ␰ values are close to 2.5 (see Fig. 3 in [15,16]). Higher values of ␰ qualitatively indicate a smaller mean size of the particles and vice versa. To derive cp共␭兲, we assumed that the dissolved component of the attenuation coefficient was equal to the dissolved component of the absorption coefficient, cg共␭兲 ⫽ ag共␭兲, and estimated ag共␭兲 by deconvolving ac-s or ac-9 measured total minus water absorption into components of phytoplankton, detritus, and gelbstoff absorption following the methods presented by Roesler et al. [7]. Modeled partitioned absorption was compared with ag共␭兲, ad共␭兲, and aph共␭兲 obtained from discrete water samples and spectrophotometric analyses performed during Plumes and Blooms (PnB) ship cruises [31]. Normalized partitioned absorption components compared well with discrete water samples despite the 10 km distance between measurement locations; results are not shown. The parameter, ␥, was obtained by linear regression fit of cp共␭兲. We

also computed the real part of the bulk refractive index of particles, np, according to Twardowski et al. [15] (wavelength notation suppressed): np ⫽ 1 ⫹ 共bbp兾bp兲0.5377⫹0.4867共␥兲2关1.4676 ⫹ 2.2950共␥兲2 ⫹ 2.3113共␥兲4兴, (6) where bp is the particulate scattering coefficient obtained by the difference bp共␭兲 ⫽ cp共␭兲 ⫺ ap共␭兲 and bbp is the particulate backscattering coefficient. Oceanic particle values of np range between 1.0 and 1.26 (relative to seawater) and give an indication of the composition of particles. Lower values of np typically represent biogenic particles and higher values generally indicate minerogenic particles. The contribution of scattering to attenuation was computed according to ␻0共␭兲 ⫽ bp共␭兲兾cpg共␭兲

and the six different at共␭兲 and bbt共␭兲 at 4 m were then used in Eq. (5) to compute the f兾Q ratio. (3) Hydrolight was also used to investigate environmental effects on the f兾Q ratio. The mean value of cpg共␭兲 for the CHARM time series was identified and associated IOPs at this time period were used as inputs into the Hydrolight model. The following analyses were conducted: (1) cloud cover was varied from 0% to 100% by steps of 20% while wind speed and solar angle were held constant at 5 m s⫺1 and 30°, respectively; (2) input wind speeds ranged from 0 to 15 m s⫺1 by steps of 3 m s⫺1 with cloud index and solar angle set at 0% and 30°, respectively; and (3) solar angle was changed from 0° to 80°, every 20°, holding cloud index at 0% and wind speed at 5 m s⫺1. For these simulations, the solar and sky components of irradiance were computed from the RADTRAN model. All other assumptions were similar to the above-described model runs.

(7)

(see Table 1 for notation). Several different types of analyses were employed to investigate the relationship between particle characteristics and rrs共␭兲 (depth notation hereafter suppressed) and the computed f兾Q ratio. (1) Linear correlations between rrs共␭兲 and f兾Q with the partitioned absorption, particle scattering, backscattering, and attenuation coefficients; backscattering ratio; ratio of backscattering to absorption, single-scattering albedo; index of refraction of particles; slope of the particle size distribution; and chlorophyll concentration (at共␭兲, adg共␭兲, aph共␭兲, bp共␭兲, bbt共␭兲, ct共␭兲, bbp共␭兲兾bp共␭兲, bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴, ␻0共␭兲, np, ␰, and Chl, respectively; Table 1) were examined using scatterplots and slope diagrams. Briefly, a slope diagram is a linear regression between a pair of properties where the abscissa is the wavelength and the ordinate is the value of the slope of the regression between the pair of variables at corresponding wavelengths. The 95% confidence interval of the linear slope that crosses the zero line in a slope diagram indicates that there is no significant linear relationship between the properties [32]. (2) The effects of IOP spectral and magnitudinal variability on the f兾Q ratio were investigated using Hydrolight [2]. Mean values of IOPs [at共␭兲, ct共␭兲, and bbt共␭兲], Ed共␭, 0⫹兲, and Chl during turbid inorganic and turbid organic periods (see Section 3) were obtained and four intermediate gradations were computed for values lying between these mean values. These six conditions (turbid inorganic, turbid organic, and the four intermediate levels) were inputted into Hydrolight, assuming 5 m s⫺1 wind speed, 30° solar angle, and optically deep waters. Pure water absorption coefficients were taken from Pope and Fry [30], and the Prieur and Sathyendranath [33] phytoplankton specific absorption spectrum was used to determine how much light was absorbed by chlorophyll so that measured chlorophyll fluorescence could be included in the Hydrolight simulations. Hydrolight-derived rrs共␭兲

To test for optical closure, we applied a simple semianalytical optical closure formulation to the measured IOPs and AOPs. The model presented by Lee et al. [34], based on the algorithm presented by Gordon et al. [4], was used to derive at共␭兲 and bbt共␭兲 from measured rrs共␭兲:

Ⲑ

1兾2 2 关bbt兾共at ⫹ bbt兲兴 ⫽ 兵⫺g0 ⫹ 关g0 ⫹ 4g1rrs兴 其 共2g1兲

(8)

(wavelength and depth notations suppressed), where the g-constants represent the angular dependency of the underwater light field. This quasi-analytical algorithm first computes at共␭兲 at a reference wavelength (typically 555 nm), which is related to remote sensing reflectance (see [34] for algorithm details). Then, since at共555兲 and rrs共555兲 are known, bbt共555兲 can be derived. Spectral bbt共␭兲 was modeled assuming that its shape decreases monotonically with increasing wavelength [35,36] (see Section 4) and then applied to Eq. (8) to compute spectral at共␭兲. We chose to evaluate the semianalytical closure formulation presented by Lee et al. [34] because it was derived for a variety of optical water types and it can easily be applied to all measurements of remote sensing, e.g., satellite ocean color and in situ radiometric measurements. Comparatively, Hydrolight is more computationally intensive and is not as easily automated for routine remote sensing monitoring purposes. The Lee et al. [34] algorithm can be effortlessly implemented in any automatic data processing routine. As such, evaluation of particle effects on each of the optical components can be performed separately and relatively quickly. 3. Observations

Optical variability in the Santa Barbara Channel coastal region has been shown to be heavily influenced by physical processes. Otero and Siegel [37] employed statistical analyses of optical and physical properties to reveal that seasonal phytoplankton blooms are controlled primarily by wind-driven up1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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Table 2. Mean, Median, Minimum, Maximum, Standard Deviation, and Variance of Various Optical Properties Measured during CHARM Deployments 2–5

Statistic

np

Chl

0.0102 0.0191 0.0168 0.0166

2.4924 2.4954 2.4986 2.4965

1.1157 1.1742 1.1601 1.1607

1.4963 2.8725 1.4307 4.1408

0.0093 0.0149 0.0172 0.0192

0.0069 0.0184 0.0177 0.0166

2.4924 2.4954 2.4986 2.4966

1.1013 1.1713 1.1676 1.1621

1.3885 2.7237 1.1773 3.2670

0.4127 0.5101 0.2314 0.3075

0.0027 0.0079 0.0022 0.0039

0.0016 0.0121 0.0027 0.0076

2.4732 2.4928 2.4690 2.4884

1.0464 1.1366 1.0611 1.1064

0.2334 0.7055 0.2093 0.5113

4.4790 1.5559 16.4447 2.8819

4.6614 1.7449 17.1821 3.1019

0.0972 0.0437 0.2052 0.0653

0.0624 0.0295 0.0381 0.0476

2.4993 2.4970 2.5171 2.5011

1.3301 1.2208 1.2533 1.2855

4.8419 8.7254 7.4860 27.451

0.6393 0.1526 2.0650 0.3938

0.6407 0.1683 2.1842 0.4278

0.0135 0.0048 0.0423 0.0098

0.0090 0.0032 0.0059 0.0040

0.0033 0.0007 0.0043 0.0018

0.0505 0.0154 0.0332 0.0205

0.6491 1.3058 1.0832 2.9201

apg(530)

bp(530)

cpg(530)

bbp(532)

Mean

2 3 4 5

0.0732 0.1129 0.1914 0.1247

1.5147 0.8313 1.7909 1.2261

1.5879 0.9443 1.9824 1.3508

0.0141 0.0160 0.0334 0.0209

Median

2 3 4 5

0.0695 0.1110 0.1705 0.1243

1.4811 0.8150 1.0784 1.1936

1.5483 0.9304 1.2463 1.3158

Minimum

2 3 4 5

0.0412 0.0653 0.0116 0.0257

0.3617 0.4306 0.2140 0.2623

Maximum

2 3 4 5

0.2114 0.2397 0.8708 0.3938

Standard Deviation

2 3 4 5

0.0195 0.0243 0.1460 0.0425

welling processes in spring and summer and sediment plumes by runoff and resuspension events in winter. Toole and Siegel [38] analyzed Santa Barbara Channel PnB data to show that Rrs共␭兲 variability is primarily driven by backscattering processes. Here, as performed by Chang et al. [39], we utilize optical proxies to characterize different optical water types throughout CHARM deployment periods. Relationships between absorption and attenuation or scattering are used to qualitatively differentiate between particulate and dissolved matter, and backscattering ratio and Chl are used to distinguish between biogenic and minerogenic particles. We also use modeled partitioned absorption to describe the waters’ constituents. Below is a brief description of various optical water types observed during the relevant deployment periods of the CHARM. Statistical information (mean, minimum, maximum, and standard deviation) for various optical properties during each deployment period is presented in Table 2. Time series and spectral plots of optical properties are shown in Figs 3– 6. Deployment 2 (winter 2004) was dominated by advective processes and marked by the presence of the Ventura River plume (2P) with high concentrations of inorganic particles and to a lesser extent, CDOM (not shown). Increases in optical properties seen during the plume were mainly caused by sediment resuspension and transport. Three other optical water types (WTs) existed during this deployment: 2WT1— relatively clear waters with higher Chl and higher index of refraction (or smaller) particles, 2WT2— relatively turbid waters with a mixture of biogenic and minerogenic particles, and 2WT3—settling or ad7684

bbp共532兲

␰

Deployment

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bp共530兲

vection of inorganic particles from the plume and then a bloom caused by nutrient input to the CHARM site, with higher Chl waters with CDOM (not shown) and lower index of refraction (or larger) particles (Fig. 3). Temperature–salinity plots indicate a mixture of three different water masses (not shown; see [39] for details). Optical water types were difficult to distinguish during deployment 3 (spring–summer 2004; 3WT), meaning that relationships between optical properties were similar throughout the duration of the time series. The waters at the CHARM site were stratified (temperature difference between 0.5 and 24 m was ⬃7 °C; not shown), relatively clear (mean 关c共530 nm兲 ⫽ 0.94 m⫺1兴; Fig. 4), and low in CDOM (not shown). Likely due to springtime upwelling, Chl was higher compared to winter conditions and subsequently, the contribution of absorption to attenuation was greater relative to the other deployments and backscattering was relatively low. However, the backscattering ratio was relatively high compared to the other three deployments, suggesting smaller or higher index of refraction particles (Fig. 4). Hence, the f兾Q ratio was higher than the average value of 0.08 sr⫺1, yet mostly within the ranges previously reported [40 – 42]. Deployment 4 (winter 2005) was a stormy period and marked by an advective event (4Adv), several plumes (4P1 and 4P2; note that record rainfall was recorded in 2005), and a bloom (4B) (Fig. 5). The advective event was characterized as relatively turbid and highly backscattering with moderate Chl and phytoplankton absorption (not shown), i.e., minero-

Fig. 3. Deployment 2 time series of measured (a) particulate scattering coefficient at 530 nm [bp共530兲; blue] and single scattering albedo at 530 nm [␻0共530兲; purple], (b) chlorophyll concentration (Chl), (c) particulate backscattering coefficient at 532 nm 关bbp共532兲兴, (d) particulate backscattering ratio 关bbp共532兲兾bp共530兲兴, (e) real refractive index of particles (np; black) and particulate size distribution slope (␰; orange) derived following Boss et al. [16], and (f) computed f兾Q ratio. The case II mean f兾Q value of 0.08 [41] is indicated. Vertical lines separate different optical water types, which are labeled (WT ⫽ water type) and described in Section 3. Spectral stackplots of hourly measured (g) total minus water absorption 关apg共␭兲兴 (mean spectra of apg共␭兲 and partitioned detrital plus gelbstoff and phytoplankton absorption [adg共␭兲 and aph共␭兲, respectively] are shown as thicker curves), (h) total minus water attenuation 关cpg共␭兲兴, (i) bbp共␭兲, and (j) remote sensing reflectance at 4 m 关rrs共␭兲兴. Solid and dashed curves denote mean and standard deviation of spectra, respectively.

genic and some biogenic particles. The presence of the first plume can be described by an ⬃3 psu drop in salinity (not shown) and waters that were optically similar to the advective event. An ⬃4 psu drop in salinity (not shown) accompanied the second plume. These plume waters were highly turbid; absorption and scattering coefficients were very high yet Chl and backscattering ratios were relatively low (Fig. 5). Plume 2 waters were higher in CDOM and detrital concentrations (not shown). A bloom occurred after dissipation of plume 2. Bloom waters were high in Chl and low in backscattering ratio. Two other optical water types were observed (4WT1 and 4WT2), both relatively clear and consisting of a mixture of particle types. Deployment 4 was overall, by far the most turbid of all deployments observed. The spectral

Fig. 4. Same as Fig. 3 but for deployment 3.

shape of the absorption coefficient throughout the deployment was indicative of detritus and CDOM [exponential decrease with increasing wavelength; Fig. 5(g)]. Two different water masses are delineated in temperature–salinity plots (not shown). The f兾Q ratio for deployments 2 and 4 was generally much higher than values reported for case I waters [f兾Q between 0.08 and 0.12 sr⫺1; [40,41]; Figs. 3(f) and 5(f)]. These very high f兾Q ratios were likely the result of multiple scattering processes [42] and although data processing methods ensure high quality data (see below), these high f兾Q ratios are not explainable by theory and values greater than 0.2 sr⫺1 are not shown or used in further analyses. Deployment 5 (spring–summer 2005) waters were relatively clear throughout the deployment (Fig. 6). Optical water types were difficult to distinguish during this time period, with at least three different types characterized as: (5WT1) mixture of biogenic and minerogenic particles, (bloom, 5B) highly scattering but relatively low in backscattering ratio with high Chl and high phytoplankton absorption (not shown), and (5WT2) higher in backscattering, backscattering ratio, lower in Chl, and higher in detrital absorption (not shown). Phytoplankton absorption accounted for a higher proportion of total absorption as compared to the other deployments [Fig. 6(g)]. Temperature–salinity plots indicate two different water masses (not shown). The f兾Q ratio during 5WT1 and 5B conditions of deployment 5 was comparable to previously reported case I and II values 1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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2

0.9 1 Bloom

0.06

WT2

0.8

(c)

0.04 0.02 0

f/Q(532) (sr−1)

4

(e)

3.75 3.5

3.25

ξ

1.1 1.05

1 0.75 (g) 0.5 0.25 0 0.06 0.04

3

apg adg aph

(i)

0.02 0 400 500 600 700 Wavelength (nm)

cpg(λ) (m−1)

130 140 150 Year Day (2005)

−1

bbp(λ) (m )

a(λ) (m−1)

1 120

rrs(λ,4m) (sr−1)

np(532)

1.2 1.15

(b)

Bloom

20 WT1 WT2

10 0

bbp(532)/bp(530)

0 bbp(532) (m−1)

30

WT1

Chl (µg l−1)

1

(a)

ω0(530)

bp(532) (m−1)

3

0.06

(d)

0.04 0.02 0 0.25 0.2 (f) 0.15 0.1 0.05 0 120

130 140 150 Year Day (2005)

4 3 (h) 2 1 0

0.04 0.03 (j) 0.02 0.01 0 400 500 600 700 Wavelength (nm)

Fig. 5. Same as Fig. 3 but for deployment 4. Adv ⫽ advective event. Note that the red channel of the backscattering meter was damaged.

Fig. 6. Same as Fig. 3 but for deployment 5. Note that the red channel of the backscattering meter was damaged.

[40 – 42] and slightly elevated during higher scattering conditions of 5WT2. Optical water types during the four deployments were broadly characterized as turbid inorganic (number of data points, n ⫽ 84), turbid organic 共n ⫽ 163兲, turbid mixture of particle types 共n ⫽ 22兲, or relatively clear 共n ⫽ 236兲 for data analyses purposes. Turbid inorganic periods included deployment 2 plume (2P), deployment 4 plumes (4P1 and 4P2), and deployment 5 WT2 (5WT2). Deployment 2 WT3 (2WT3), and blooms during deployments 4 and 5 (4B and 5B) are characterized as turbid organic and deployment 2 WT2 and deployment 4 advective event (2WT2 and 4Adv) as turbid mixture of particle types. Relatively clear waters occurred during deployment 2 WT1 (2WT1), deployment 3 (3WT), deployment 4 WT1 and WT2 (4WT1 and 4WT2), and deployment 5 WT1 (5WT1).

relationship between the slopes of rrs共␭兲 and at共␭兲 and positive relationship between rrs共␭兲 and bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴. Additionally, based on theory and simulations, f兾Q should be positively related to bbt共␭兲兾 关at共␭兲 ⫹ bbt共␭兲兴 [43]. The following generalizations can be made for all optical water types investigated.

4. Results and Discussion A.

Linear Regressions and Slope Diagrams

Linear relationships between various optical properties and rrs共␭兲, and optical properties and the f兾Q ratio were further examined with scatterplots and slope diagrams (see Subsection 2.C; Fig. 7) for each of the four different optical water types (turbid inorganic, turbid organic, turbid mixture, and relatively clear). Based solely on Eq. (5), we expect to see a negative 7686

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Y Remote sensing reflectance was significantly positively correlated with adg共␭兲, bbt共␭兲, and bbt共␭兲兾 关at共␭兲 ⫹ bbt共␭兲兴 [Fig. 7(a)], implying that bbt共␭兲 exhibited high rates of variability and covariance between bbt共␭兲 and at共␭兲 existed. Y The f兾Q ratio was always strongly negatively correlated with bbp共␭兲兾bp共␭兲 and np, and weakly [negatively correlated with bbt共␭兲 and bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴 during turbid inorganic periods [Fig. 7(c)], suggesting a tight coupling between particle type and f兾Q, with lower f兾Q values during sediment plumes and higher values during blooms, also reported by Kostadinov et al. [31]. The negative relationship between f兾Q and backscattering is unexpected and suggests that the AOPs and IOPs can vary independently of each other with rrs共␭兲 varying much slower than the IOPs at times. Thus, f兾Q exhibits a weak negative relationship with bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴 [see Eq. (5)]. Scatterplots of f兾Q versus bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴 show a shotgun relationship between the two quantities (not shown).

turbid organic; Fig. 7(f), turbid inorganic shown], meaning that high concentrations of phytoplankton resulted in less scattering and lower magnitudes of rrs共␭兲 and high concentrations of inorganic particles led to higher scattering and higher rrs共␭兲. Y During turbid conditions when organic particles were present, ␻0共␭兲 was positively correlated with f兾Q. Y The f兾Q ratio was negatively related to aph共␭兲, bbt共␭兲, and ␰ [Fig. 7(d)] during conditions not dominated by inorganic particles, i.e., larger particles were likely organic in nature. Interestingly, these larger organic particles resulted in higher values of f兾Q, which is consistent with other findings in the Santa Barbara Channel (see above and Kostadinov et al. [31]). Note that these results are from simple linear relationships and do not describe the complex optical nature of particles in seawater. Unfortunately, more specific relationships between f兾Q and the IOPs and particle characteristics cannot be made across these four optical water types. This is disheartening as it suggests that f兾Q cannot be predicted based on broad optical water types. B.

Fig. 7. (Color online) Example slope diagrams showing significant linear relationships, i.e., when the 95% confidence intervals of slopes (horizontal error bars) do not cross the zero line, between remote sensing reflectance 关rrs共␭兲兴 and in situ spectral (a) detrital plus gelbstoff absorption coefficient 关adg共␭兲兴, total backscattering coefficient 关bbt共␭兲兴, and bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴 (inset shows a scatter plot of rrs共␭兲 versus bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴 at ␭ ⫽ 530 nm); and (b) the slope of the particle size distribution (␰) [inset shows a scatter plot of rrs共␭兲 versus ␰ at ␭ ⫽ 530 nm]; and between the f兾Q ratio and (c) backscattering ratio 关bbp共␭兲兾bp共␭兲兴, real part of the index of refraction of particles 共np兲 [inset shows a scatter plot of 共f兾Q兲共␭兲 versus np at ␭ ⫽ 530 nm], and bbt共␭兲兾关at共␭兲 ⫹ bbt共␭兲兴, all during turbid inorganic periods. Correlations between the f兾Q ratio and (d) phytoplankton absorption coefficient 关aph共␭兲兴, bbt共␭兲, and ␰ during turbid organic periods. Slope diagrams between rrs共␭兲 and (e) bbp共␭兲兾bp共␭兲 and np are shown for turbid mixed conditions and (f) singlescattering albedo 关␻0共␭兲兴 and aph共␭兲 during turbid organic waters. Different optical and particle properties are labeled.

Hydrolight

Hydrolight model results indicate that the variability in spectral shape and magnitude of the f兾Q ratio was driven primarily by changes in the IOPs (Fig. 8) as opposed to environmental effects (wind speed, cloud index, and solar angle; not shown), as expected. Wind speed and cloud index had only a slight influence on the red wavelength of rrs共␭兲 and the f兾Q ratio (not shown). Variable solar angle greatly affected rrs共␭兲

Y Linear correlations between rrs共␭兲 and f兾Q with Chl were insignificant (not shown). Differences between linear relationships for the four optical water types are presented below. Y Particle type characteristics [bbp共␭兲兾bp共␭兲 and np] were positively associated with rrs共␭兲 during turbulent periods when inorganics were present [turbid inorganic and turbid mixture; Fig. 7(e), turbid inorganic shown], i.e., smaller, harder particles resulted in higher values of rrs共␭兲, which was to be expected. Y Remote sensing reflectance was positively correlated with ␻0 and negatively correlated with aph共␭兲 when conditions were turbid and dominated by one particular type of particle [turbid inorganic and

Fig. 8. (Color online) Spectral (a) total absorption 关at共␭兲兴, (b) total attenuation 关ct共␭兲兴, and (c) total backscattering 关bbt共␭兲兴 coefficients used as inputs into the radiative transfer model, Hydrolight. IOPs were varied from minerogenic-dominated waters (turbid inorganic; circles; measured) to Chl-dominated waters (turbid organic; diamonds; measured) by equal steps (simulated data). Hydrolightderived (d) rrsHL共␭兲 and (e) f兾Q ratio computed using Eq. (5), Hydrolight-derived rrsHL共␭兲, and measured IOPs at 4 m water depth. A dashed line indicates where f兾Q ⫽ 0.08 sr⫺1. Symbols for (d) and (e) are the same as those used for (a)–(c). 1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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and the computed f兾Q ratio at the red wavelengths (not shown). Lower solar angles (approaching sunset) resulted in higher values of rrs共␭兲 and f兾Q at ␭ ⬎ 660 nm. Interestingly, input values of bbt共␭兲 were greater during turbid inorganic conditions while at共␭兲 and ct共␭兲 were greater during turbid organic conditions [Figs. 8(a)– 8(c)]. The computed f兾Q ratio was higher

during minerogenic-dominated waters at 470 and 532 nm [Fig. 8(e)], which is to be expected based on simulations (e.g., [42]). Spectrally, the increase in bbt共470兲 was more rapid compared with the other two wavelengths as waters shifted from biogenically to minerogenically dominated. Thus, f兾Q spectral variability shifted accordingly, with flatter spectra between 470 and 532 nm during turbid or-

Table 3. Comparisons between Measured and Derived at(␭) and bbt(␭)a

IOP

Water Type

412 nm

440 nm

488 nmb

510 nm

532 nm

555 nm

al(␭)

Deployment 2

0.12 ⫺5%

0.14 ⫺5%

0.23 6%

0.25 7%

0.26 11%

0.22 5%

Deployment 3

0.32 ⫹18%

0.48 ⫹13%

0.63 ⫹20%

0.61 ⫹19%

0.56 ⫹16%

0.41 ⫹8%

Deployment 4

0.69 ⫹3%

0.72 ⫹4%

0.73 ⫹1%

0.74 ⫺9%

0.75 ⫺9%

0.77 ⫺11%

Deployment 5

0.05 ⫺0.1%

0.01 ⫺10%

0.00 ⫺7%

0.00 ⫺6%

0.00 ⫺4%

0.00 ⫺0.1%

Turbid inorganic

0.10 ⫺39% 40%

0.26 ⫺33% 35%

0.20 ⫺31% 34%

0.23 ⫺29% 32%

0.30 ⫺25% 28%

0.36 ⫺19% 23%

Turbid organic

0.41 ⫹14% 28%

0.31 ⫹21% 33%

0.29 ⫹26% 36%

0.31 ⫹20% 30%

0.35 ⫹18% 26%

0.31 ⫹12% 19%

Turbid mixture

0.78 ⫹0.5% 17%

0.75 ⫺1% 20%

0.80 ⫹1% 22%

0.75 ⫺0.1% 21%

0.73 ⫺0.1% 21%

0.77 ⫺6% 14%

Clear mixture

0.54 ⫹30% 35%

0.64 ⫹29% 33%

0.70 ⫹28% 31%

0.69 ⫹20% 24%

0.72 ⫹16% 19%

0.73 ⫹7% 12%

bbt(␭)

Deployment 2

0.20 17%

0.19 ⫺3%

Deployment 3

0.28 18%

0.28 ⫺13%

Deployment 4

0.84 ⫺31%

0.84 ⫺52%

Deployment 5

0.37 ⫺41%

0.12 ⫺61%

Turbid inorganic

0.58 ⫹13% 29%

0.50 ⫺18% 32%

Turbid organic

0.45 ⫹40% 50%

0.43 ⫹19% 40%

Turbid mixture

0.85 ⫹37% 46%

0.88 ⫹19% 33%

Clear mixture

0.61 ⫹57% 61%

0.65 ⫹31% 40%

a Comparisons use the methods presented by Lee et al. [34]. Linear regression r2 values and average percent differences for select wavelengths are shown. r2 values equal to or greater than 0.50 are in boldface. Percent differences were computed as follows: %diff ⫽ [(modeled ⫺ measured)兾measured] ⫻ 100. Average absolute values of percent differences were also computed for different optical water types and reported. b 470 nm for bbt(␭).

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ganic conditions [Fig. 8(e)]. The f兾Q ratio at 532 nm appeared to remain constant as IOPs were shifted toward a more plumelike environment. Remote sensing reflectance and f兾Q at 660 nm behaved as expected—a negatively correlated trend between rrs共␭兲 and at共␭兲 and vice versa for bbt共␭兲, and a positive relationship between f兾Q and bbt共␭兲 and vice versa for at(␭) [Eqs. (1b) and (5); Fig. 8]. These results emphasize that nonphytoplankton particles can greatly influence closure algorithms and bbt共␭兲 should not be ignored in the denominator of Eq. (1b) when bt共␭兲 ⬎⬎ at共␭兲 [44]. C. Optical Closure

Optical closure was performed for full-deployment time series as well as the four different optical water types using the algorithm presented by Lee et al. [34] (see Subsection 2.C; Figs. 9 and 10; Table 3). Due to the biogeochemically complex nature of the CHARM site, derivations of at共␭兲 and bbt共␭兲 did not compare well to measured optical properties overall except for during the relatively clear deployment 3 and the very turbid deployment 4. Some of the discrepancies between measured and modeled properties can be attributed to the semiempirical nature of this algorithm, which make assumptions about the shape of the backscattering spectrum and the angular dependency of the underwater light field (through the g-constants). The derivations of at共␭兲 and bbt共␭兲 were highly sensitive to optical water type and wavelength (Table 3). In general, modeled at共␭兲 and bbt共␭兲 compared best to measured values at the green wavelength 共555 nm兲, where measured rrs共␭兲 generally has fewer errors. Very low signal to noise ratios for measured rrs共␭兲 at the red wavelengths likely led to insignificant r2 values and percent differences that were consistently greater than 100% (red wavelength results are not shown). Optical water types that were a clear or turbid mixture of biogenic and minerogenic particles resulted in improved closure results for at共␭兲 [Figs. 9(e)–9(h); Table 3], with significant r2 values (usually greater than 0.7) and slight overestimation of at共␭兲 (generally ⬍25%). These results were expected given that the model was generated for a wide variety of optical water types consisting of a mixture of particle types, sizes, and concentrations. Total absorption was for the most part underestimated during highly turbid periods when inorganic particles dominated, particularly when at共␭兲 and ct共␭兲 exceeded 0.5 and 3 m⫺1, respectively [ct共␭兲 not shown; Figs. 9(a) and 9(b)]. On the contrary, the presence of organic particles led to overestimation of at共␭兲 [Figs. 9(c) and 9(d); Table 3]. Derivations of bbt共␭兲 generally resulted in significant r2 values, although modeled versus measured magnitudes of bbt共␭兲 were quite deviated and generally overestimated (Fig. 10; Table 3). The only optical water type that did not exhibit significant r2 values was turbulent organic (Table 3). Percent differences

Fig. 9. (Color online) (a), (c), (e), (g) Total absorption coefficient derived using the model presented by Lee et al. [34] 关atder共␭兲兴 compared with at共␭兲 measured at the CHARM site by an in situ ac-s 关atmeas共␭兲兴. (b), (d), (f), (h) atder共␭兲兾atmeas共␭兲 versus atmeas共␭兲 [plotted on a log scale; a solid line denotes atder共␭兲兾atmeas共␭兲 ⫽ 1.0 and dashed lines indicate atder共␭兲兾atmeas共␭兲 ⫽ 1.25 and 0.75] for (a), (b) turbid inorganic, (c), (d) turbid organic, (e), (f) turbid mixed, and (g), (h) relatively clear conditions. atmeas共␭兲 was interpolated to nine wavelengths. ␭ ⫽ 412 (crosses), 440 (squares), 488 (circles), 510 (pluses), 532 (triangles), and 555 nm (asterisks) (red wavelengths not shown).

for all conditions were greater than 25%, with the closest values (29% and 32% for 470 and 532 nm, respectively) found during turbid conditions dominated by inorganic particles [Figs. 10(a) and 10(b); Table 3]. The large percent differences between modeled and measured bbt共␭兲 shown in Table 3 can in part be explained by the assumptions about the angular dependency of the underwater light field through the g-constants. These g-constants were derived using a combination of Monte Carlo and Hydrolight simulations for surface measurements of the IOPs and AOPs whereas our analyses make use of optical data collected at 4 m (recall that this was to avoid potential errors associated with extrapolation of radiometric data through the sea surface). Discrepancies between modeled and measured bbt共␭兲 can also be attributed to assumptions made about the shape of the backscat1 November 2007 兾 Vol. 46, No. 31 兾 APPLIED OPTICS

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5. Summary and Conclusions

We present a rich set of optical data collected on a mooring in the biogeochemically complex coastal waters of the Santa Barbara Channel. Results from statistical analyses, numerical radiative transfer modeling, and application of a semianalytical optical closure algorithm of 125 days’ of optical data measured in situ over a period of more than 1 yr suggest that

Fig. 10. (Color online) Same as Fig. 9 but for total backscattering coefficient at 470 (circles) and 532 nm (triangles) measured by an ECObb3.

tering spectrum. The algorithm presented by Lee et al. [34] assumes that the backscattering coefficient decreases monotonically with increasing wavelength following the widely used expression [35,36] bbt共␭兲 ⫽ bbw共␭兲 ⫹ bbp共555兲共555兾␭兲␩,

(9)

where bbw共␭兲 is the backscattering coefficient of pure seawater [45] and the power parameter, ␩, written as ␩ ⫽ 2.2(1 ⫺ 1.2 exp兵⫺0.9关rrs共440兲兾rrs共555兲兴其).

(10)

The shape of measured backscattering spectra for deployment 2 does not follow that expressed in Eq. (9) (Fig. 3). Complementary profiled spectral backscattering data collected on CHARM cruises (data not shown) are similar in shape to those shown in Fig. 3. Due to the damage to the red wavelength on the backscattering meter during deployments 4 and 5, we were unable to determine the actual shape of bbt共␭兲 during those time periods. However, the results of closure analyses for derived versus measured bbt共␭兲 indicate that backscattering spectral shape resembled that described by Eq. (9) during deployment 4 but not for deployment 5 (Table 3). 7690

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Y The variability of IOPs and AOPs was strong; changes in optical properties were likely driven by advective events, e.g., plumes, upwelling, blooms [30,37–39]. Y In general, variability of the IOPs were strongly related to the variability of rrs共␭兲. Since the IOPs are related to the concentration of particles, this implies that; to first order, rrs共␭兲 highly depends on the concentration of particles. Hence, the absolute value of bbt共␭兲 is more important to rrs共␭兲 than the shape of the VSF. Y Remote sensing reflectance was influenced by the nature of particles only during periods when high concentrations of inorganic particles were present. In these conditions, the shape of the VSF is important to rrs共␭兲. Y The variability and spectral shape of f兾Q was always strongly affected by particle type characteristics, e.g., the contribution to total backscattering of Chl-bearing versus minerogenic particles, real part of the index of refraction of particles. This result is expected; theory states that f兾Q depends on the shape of the VSF. Y The slope of the particle size distribution was important to f兾Q variability during times when optical water types were not dominated by inorganic particles. Y High concentrations of larger-sized organic particles resulted in increased f兾Q values. Y Unfortunately, more specific relationships between particle characteristics and the magnitude and spectral shape of the f兾Q ratio cannot be identified. Y Successful derivation of IOPs from AOPs is strongly affected by wavelength and optical water type, with better algorithm performance at the green wavelengths and during turbid and relatively clear mixed particle assemblages, likely due to the algorithm being based on average conditions. Waters with a single type of particle would thus have a bias. These insights into optical influences on closure between the IOPs and AOPs are important for proper understanding of the angular dependency of the underwater light field and the effects of backscattering processes on remote sensing reflectance. This is particularly important for biogeochemically complex waters where optical closure is often confounded by the presence of inorganic particulates, CDOM, or both components. Further analytical studies are necessary to examine in detail the capability to predict f兾Q or the g-constants based on water mass characteristics and elementary light conditions. Quantification

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