Effects of physical forcing and particle characteristics on underwater imaging performance

Abstract

[1] We computed the modulation transfer function (MTF), which is the magnitude of the Fourier transform of the point spread function, for two different water bodies using measurements of optical properties and analytical formulations. Knowledge of the MTF is important for the interpretation of images from underwater electro-optical systems. The data were collected from two field sites as part of the Office of Naval Research sponsored Radiance in a Dynamic Ocean program: (1) Scripps Institution of Oceanography (SIO) Pier, a shallow-water, eutrophic environment, and (2) the Santa Barbara Channel (SBC), a deeper, mesotrophic environment. Wavelet analysis was employed to investigate the sources of variability of the MTF and the periodicities at which they occur. Results suggest that the MTF was strongly related to wind conditions and advection events and the optical properties serving as proxies for particle concentration and composition in the SBC. Increased wind speeds and stresses resulted in upper water column mixing, decreased water clarity, and reductions in image transmission. Rip currents accompanied by high concentrations of reflective particles observed at SIO Pier resulted in increases in the MTF. Optically derived particle composition characteristics such as the bulk particle real index of refraction and particle size distribution are shown to be related to the variability of imaging performance at both field sites.

Key Points

• Imaging parameters were related to particle composition characteristics
• Optical properties were strongly influenced by meteorological processes
• Image transmission was similar between eutropic and mesotropic sites

1. Introduction

[2] The Office of Naval Research (ONR) sponsored Radiance in a Dynamic Ocean (RaDyO) program was motivated by the confounding effects of dynamic surface boundary layer (SBL) processes on underwater image reconstruction. The blurring of underwater images taken in natural waters is not only attributed to surface wave effects, but is due also to scattering by particulates. Quantification of the blurring effect by both scattering and SBL processes can aid in the enhancement or restoration of images taken underwater. The optical property, scattering coefficient, is not directly useful for image restoration because it describes only single scattering. (The scattering coefficient, b, and the volume scattering function (VSF), β, are inherent optical properties (IOPs), which depend only on the substances comprising the aquatic medium.) Multiple scattering effects can be better quantified by use of the point spread function (PSF) [e.g., Duntley, 1971; Wells, 1973; Voss, 1991; Fournier and Jonasz, 1999; Dolin et al., 2006; Hou et al., 2008], which describes the system response to a point source:

where g(x, y) is the convoluted signal, f(x, y) is the original signal, h(x, y) is the entire system PSF, and n(x, y) is the noise term. Equation (1) indicates that knowledge of the PSF facilitates the enhancement or restoration of the original signal [Gonzalez and Woods, 2002].

[3] The PSF can be used to quantify contrast modulation by taking its Fourier transform to arrive at the optical transfer function (OTF). The magnitude of the OTF is the modulation transfer function (MTF), which describes the contrast response of a system at different spatial frequencies [Wells, 1973; Hou et al., 2007]. The MTF of an aquatic medium, H(ψ, z), can be represented by

where Z is the range, D(ψ) is the decay transfer function (DTF), and ψ is spatial frequency (Table 1 provides notation definitions). By application of small-angle scattering approximations [Wells, 1973], the collimated DTF can be approximated as

where S(ψ) is the light scattered back into the acceptance cone and c is the beam attenuation coefficient:

where β(θ) is the VSF, θ is the scattering angle, and J_o is the zero-order Bessel function. The desired focused DTF can then be obtained by transformation in terms of spatial frequency (2πθψ) (see Wells [1973] for more details):

Table 1. List of Abbreviations and Notations

Abbreviation/Notation	Definition
ac-9, ac-s	Absorption-attenuation meter at 9 (ac-9) or 87 (ac-s) wavelengths (WET Labs)
ADCP	Acoustic Doppler current profiler (Teledyne RD Instruments)
AOP	Apparent optical property
BI	Bubble index = β(70°)/β(120°)
COI	Cone of influence
CTD	Conductivity-temperature-depth
CWT	Continuous wavelet transform
DTF	Decay transfer function
ECO-bb	Backscattering meter at three (ECO-bb3) or nine (ECO-bb9) wavelengths (WET Labs)
ECO-FLNTU	Chlorophyll fluorescence and turbidity meter (WET Labs)
FLIP	Research platform Floating Instrument Platform
FFT	Fast Fourier transform
IOP	Inherent optical property
KM	Research vessel Kilo Moana
LISST	Laser in situ scattering and transmissometery sensor (Sequoia Scientific)
MASCOT	Multi Angle SCattering Optical Tool (WET Labs)
MET	Meteorological package
MTF	Modulation transfer function
ONR	Office of Naval Research
OTF	Optical transfer function
PSF	Point spread function
RaDyO	Radiance in a Dynamic Ocean
SBC	Santa Barbara Channel
SBL	Surface boundary layer
SIO	Scripps Institution of Oceanography
STFT	Short-time Fourier transform
VSF	Volume scattering function
WTC	Wavelet coherence
XWT	Cross-wavelet transform
Chl	Chlorophyll concentration (μg/L)
D(ψ)	Decay transfer function, DTF (equations (3), (5), and (7))
H(ψ, z)	Modulation transfer function, MTF (equation (2))
S(ψ)	Light scattered back into the acceptance cone (equation (4))
Jo	Zero-order Bessel function
N	Number of samples
Z	Range (m)
ag	Dissolved material absorption coefficient (m^−1)
apg	Particulate plus dissolved material absorption coefficient (m^−1)
b	Scattering coefficient (total) (m^−1)
bbp	Particulate backscattering coefficient (m^−1)
bp	Particulate backscattering ratio = bbp/bp
bp	Particulate scattering coefficient (m^−1)
c	Attenuation coefficient (total) (m^−1)
cp	Particulate attenuation coefficient (m^−1)
cpg	Particulate plus dissolved material attenuation coefficient (m^−1)
np	Real part of the index of refraction of particles
Ψ	Spatial frequency (rad^−1)
β, β(θ)	Volume scattering function (m^−1)
γ	Slope of the particulate attenuation spectrum
λ	Wavelength of light (nm)
θ	Scattering angle
θo	Mean square angle
σt	Density of seawater
ωo	Single-scattering albedo

[4] In situations where the VSF may not be quantified, the following assumptions about the VSF have been made [e.g., Wells, 1973]:

where θ_o is mean square angle and b is the scattering coefficient:

therefore a closed-form solution for the MTF is possible without direct measurements of the VSF:

[5] Our primary objective is to determine the relationships between the physical processes and optical properties that affect the variability of the MTF. The MTF of two different optical water types are investigated: (1) a dynamic, shallow-water, eutrophic environment and (2) a relatively clear, deep water, mesotrophic environment.

2. Approach

[6] We present data collected during two different RaDyO field experiments: Scripps Institution of Oceanography (SIO) Pier, California, in January 2008 and Santa Barbara Channel (SBC), California, in September 2008 (Figure 1). Both experiments involved measurements of atmospheric and oceanic physical parameters and IOPs and apparent optical properties (AOPs), which depend on the IOPs and the light field. The SIO Pier experiment naturally exploited the pier as a stable research platform. In the SBC, upper ocean physical measurements were made from research platform Floating Instrument Platform (R/P FLIP or FLIP), which was moored at 34° 12′ 18″N, 119° 37′ 44″W in about 175 m water depth. Measurements of optical properties were conducted from R/P FLIP and the research vessel Kilo Moana (R/V KM or KM), which was located nearby (at approximately 34° 13′ 12″N, 119° 37′ 58″W; Figure 1) [Chang et al., 2010].

Figure 1

Map of California indicating the sites of the Radiance in a Dynamic Ocean (RaDyO) field experiments. The Santa Barbara Channel (SBC) experiment is shown in yellow with R/P FLIP and R/V KM locations denoted on the inset map of the SBC. The SIO Pier experiment is drawn in red; a photograph of SIO Pier with the location of profiler measurements (red star) is shown. The lower left inset is a photograph of one of the optical profilers used for both experiments.

[7] Relevant instrumentation and properties measured during the two experiments were (1) meteorological parameters, for example, wind speed and wind stress; (2) an acoustic Doppler current profiler (ADCP; RDI 600 kHz) for current velocity and direction; (3) Sea-Bird Electronics, Inc., SBE49 FastCAT for conductivity-temperature-depth (CTD; density, σ_t, was computed on the basis of the paper by United Nations Educational, Scientific and Cultural Organization [1981]); (4) WET Labs, Inc., absorption-attenuation meter (ac meter) for absorption, attenuation, and scattering (by difference) coefficients at nine (ac-9) or 87 (ac-s) wavelengths; (5) WET Labs, Inc., ECO-bb for backscattering coefficient at three (ECO-bb3) or nine (ECO-bb9) wavelengths; (6) Sequoia Scientific, Inc., Laser In Situ Scattering and Transmissometry (LISST-100X) for near-forward VSF at 32 log-spaced bins; (7) WET Labs, Inc., ECO-FLNTU for chlorophyll fluorescence and turbidity; and (8) WET Labs, Inc., newly developed Multi Angle SCattering Optical Tool (MASCOT) sensor for VSF measurements between 10° and 170° at 10° intervals.

[8] The hydrographic and optical instrumentation (items 3–7 above; Figure 1) was profiled several times per day from SIO Pier (15–24 January 2008) and from the FLIP and KM between 11 and 20 September 2008. MASCOT measurements were made from the KM only. Measurements were collected between surface to approximately 4 to 6 m water depth at SIO Pier and to between 2 and 120 m in the SBC. Hydrographic and optical time series were constructed from data collected at 2 m water depth for each experiment (N = 43 and 70 for the SIO Pier and SBC experiments, respectively). Meteorological (MET) packages were located on the portside boom of FLIP and on board the KM in the SBC. The FLIP MET package collected data every 20 min from 12–23 September 2008 and the KM measured meteorological data every 5 min over the duration of the experiment. ADCPs were mounted on the hulls of the FLIP at ∼30 m depth (uplooking) and the KM at ∼15 m depth (downlooking) during the SBC experiment. Current velocity and direction data were collected hourly at 0.75 m bin spacing from FLIP and every 15 min at 0.4 m bin spacing from the KM. Because the SIO Pier experiment was primarily intended as a test for newly developed instrumentation, physical and optical measurements were not necessarily conducted concurrently; therefore physical data from SIO Pier are not presented here.

[9] Many of the optical sensors required calibration and corrections to ensure accurate measurements. The ac-9 and ac-s are referenced to pure water and additional measurements were made with an ac-9 absorption tube that was equipped with a 0.2 μm filter. Therefore ac meter outputs included particulate plus dissolved absorption and attenuation coefficients, a_pg(λ) and c_pg(λ), respectively, and dissolved absorption coefficient, a_g(λ). Wavelength dependence is denoted by λ (Table 1). Particulate absorption, attenuation, and scattering coefficients, a_p(λ) = a_pg(λ) − a_g(λ), c_p(λ) = c_pg(λ) − a_g(λ), and b_p(λ), were derived by difference [Twardowski et al., 1999]. Total absorption, attenuation, and scattering coefficients were derived by adding the pure water contributions determined by Pope and Fry [1997]. The ac-9 used onboard the KM was calibrated daily with pure water whereas the ac-s deployed from the FLIP was calibrated just prior to and just following the field experiment. No instrument drift was found for the ac-s and the minimal drift (<0.01 m⁻¹ d⁻¹) in the filtered ac-9 was assumed to be linear. All sensors were calibrated daily with pure water for the SIO Pier experiment. Temperature and salinity corrections were applied to ac meter data according to methods described by Pegau et al. [1997] and Sullivan et al. [2006], and Zaneveld et al. [1994] scattering corrections were employed for the nonfiltered ac meters. The time lag associated with the use of the 0.2 μm filter was quantified and corrected [Twardowski et al., 1999]. Backscattering coefficients, b_bp(λ), were computed from the measured VSF at 124° using methods presented by Sullivan and Twardowski [2009] and pure water backscattering values provided by Zhang et al. [2009].

[10] Profiler measurements were used to compute optical products: backscattering ratio, _bp(λ) = b_bp(λ)/b_p(λ); the slope of the c_p(λ) spectrum, γ, an indicator of particle size distribution [Boss et al., 2001]; the real part of the index of refraction of particles, n_p, from γ and _bp(λ) [Twardowski et al., 2001], useful for obtaining information about the relative density of particles; the single-scattering albedo, ω_o = b/c; and chlorophyll concentration (Chl) from chlorophyll fluorescence and spectral absorption using the methods of Sullivan et al. [2005]. The MASCOT data were used to compute a “bubble index” (BI), where BI = β(70°)/β(120°). This BI is based on theoretically computed VSFs of relatively large bubbles (>10 μm), which show pronounced enhancement of the VSF between 60° and 80°. Hence, increases in the BI can be indicative of a relative increase in the concentration of larger bubbles. Czerski et al. [2011] and M. S. Twardowski et al. (The optical volume scattering function in the surf zone inverted to derive particulate sediments and bubble populations, submitted to Journal of Geophysical Research, 2011) provide more details about the optical (and acoustical) properties of bubbles.

[11] Measured optical properties at 532 nm from each experiment were used to compute the imaging performance parameter, MTF, at ranges set equal to the water depth. The MTF formulation presented by Wells [1973] (equations (2)–(5)) was utilized here, with near-forward angle scattering provided by the LISST-100X. The β approximation (equation (6)) was evaluated using SIO Pier data by comparing the MTF computed using the LISST-measured near-forward angle scattering (θ between 0.05 and 8.25°) and the zero-order Bessel function, J_o (equation (4)) versus that computed using an approximated VSF (equation (6)) and a mean square angle determined from LISST measurements.

[12] Relationships between physical, hydrographic, and optical properties and the imaging performance parameter, MTF, were determined for the SBC experiment by use of wavelet analysis. Continuous wavelet transforms (CWTs), cross-wavelet transforms (XWTs), and wavelet coherence (WTC) are useful tools for analyzing localized, intermittent oscillations in data series, as well as the relationship and linkages between two data series and the strength of the relationship(s) [see Grinsted et al., 2004]. Fourier expansion (e.g., fast Fourier transform; FFT) has traditionally been the technique employed for determining the frequencies present in a signal. However, FFTs have only frequency resolution and no time resolution. In other words, although FFTs can reveal all frequencies present in a signal, they cannot determine when these frequencies are present in time. Similar to this, coherence analysis can be used to find common periodicities between two different time series; however, determined commonality is not localized in time or space. Short-time Fourier transforms (STFTs) were developed to determine frequency and phase of a signal as it changes over time. However, STFTs have a fixed resolution; for example, temporal and frequency resolution are dependent solely on the windowing function, where a wider window provides better frequency resolution and poor time resolution and vice versa for a narrower window. To alleviate these problems, wavelet analysis can be utilized to expand data series into time-frequency space and thus identify localized intermittent periodicities at multiple frequency and temporal resolutions.

[13] Here, a series of Morlet wavelets were applied to 2 m time series data as band-pass filters. The wavelets were stretched in time by varying their scale and normalizing them to have unit energy. The statistical significance of wavelet power was assessed for various properties to determine dominant scales of variability and the periods at which they occur [Grinsted et al., 2004]. Periods and frequencies of high and significant wavelet power can be interpreted as dominant modes of variability at specific times. XWTs and WTCs were then applied to time series data to expose high common power and relative phase between two variables in time-frequency space. A Monte Carlo test was performed to determine the statistical significance of the computed coherence. In addition to CWT, XWT, and WTC analysis for 2 m time series data, WTC methods were applied to depth-resolved profiles of physical and optical properties and the MTF. Using this method, common periodicities between two different parameters in vertical space were resolved as a function of depth.

3. Results

3.1. Santa Barbara Channel

[14] The SBC field experiment was highly influenced by a diurnal wind pattern that was observed during the 2 week field campaign [Chang et al., 2010]. Winds were generally calm (<4 m/s) in the mornings and increased by at least a factor of two by afternoon. Starting in the afternoon of 15 September 2008, persistent strong winds (>5 m/s) were sustained over the course of 2 days (Figure 2a). Hydrographic properties suggest upper water column mixing during the period of sustained high wind speeds (15–17 September). The diurnal signal became less prominent following the period of persistent winds. Near-surface current velocity variability was often coupled with wind speed (Figure 2b).

Figure 2

Time series of (a) wind stress (black) and wind speed (gray), (b) 2 m current velocity, (c) 2 m temperature (black dots) and density (σ_t; gray triangles), and (d) 2 m c_pg(532) (black dots) and b_p(532) (gray triangles) measured during the SBC RaDyO field experiment.

[15] A distinct change in the hydrographic properties occurred toward the end of the experiment (19 September). This event was associated with lower surface temperatures and higher Chl and IOP values (Figure 2 and orange to red lines in Figure 3) and was likely related to advection associated with a shift in the state of SBC surface circulation [Hendershott and Winant, 1996]. A broad Chl maximum was observed at about 12 m water depth and IOPs exhibited a distinct maximum in values at about 10 m during this advection event (orange to red lines in Figure 3). McPhee-Shaw et al. [2006] describe a mid-September 2005 phytoplankton bloom that was observed within a few kilometers of the SBC RaDyO experiment site. The 2005 bloom was accompanied by a greater than 1°C cooling of surface waters, similar to observations presented here. These September blooms could be linked to the frequent reversals in currents, eddy circulation, and a disconnect between outer and inner shelf dynamics that results in upwelling effects [Harms and Winant, 1998; McPhee-Shaw et al., 2006].

Figure 3

Profiles of (a) temperature, (b) salinity, (c) σ_t, (d) c_pg(532), (e) n_p, (f) Chl, and (g) MTF at Ψ = 3 rad⁻¹, collected from FLIP during the SBC RaDyO experiment. Different colors indicate increasing time periods of sampling from deep blue (11 September) to yellow-green (17 September) to red (20 September).

[16] The strong diurnal wind pattern was quite apparent in CWT results (data not shown). Results indicate that the diurnal signal was observed in wind speed and stress, current velocity, and most IOPs and optical products prior to 15 or 17 September 2008. Consequently, the MTF at 2 m range followed a similar temporal pattern (180° phase) as the IOPs and wind speed. The MTF decreased during high wind speeds and mixed periods (Figures 2 and 4). The diurnal signal was significant for salinity and Chl on 13 and 14 September only and not as strong for ω_o. Semidiurnal periodicity (0.25 to 0.5 day) was observed in current velocity CWT results on all days except 16 September, likely related to tidal oscillations and stratification that was disrupted during the mixed conditions of the sustained strong wind event. The MTF and salinity at 2 m also exhibited this semidiurnal tidal periodicity during stratified conditions on 13 and 14 September. A low-frequency signal (2 days) was apparent in _bp data between 15 and 19 September.

Figure 4

(a) MTF as a function of spatial frequency for select time periods and (b) time series of MTF for Ψ = 3 rad⁻¹ (black dots) and Ψ = 50 rad⁻¹ (gray triangles) calculated from 2 m optical data collected in the SBC (equations (2)–(5)).

[17] Figure 5 shows results from time series XWT and WTC analysis between the MTF and physical and optical parameters collected at 2 m during the SBC RaDyO field experiment. Frequencies in units of days are shown along the y axis and the time period of measurements is along the x axis. The “cone of influence” (COI) is outlined. Regions outside of the COI are affected by edge effects; we take caution when interpreting results in this region. Periods of high wavelet power are shown in red, and statistically significant periods are outlined with thick, black lines. In order to determine statistically significant coherence, both the XWT and WTC time series must be interpreted together. In other words, time frequencies of high common power and high coherence, meaning periods when both parameters (e.g., XWT and WTC) show strong, common frequency peaks, must be located.

Figure 5

Results from cross-wavelet transform (XWT) and wavelet coherence (WTC) analysis for the SBC MTF at Ψ = 3 rad⁻¹ with (a) wind speed, (b) b_bp, and (c) γ. Arrows indicate the phase direction between the two properties. An arrow pointing to the right indicates positive phase, and an arrow pointing to the left indicates negative phase.

[18] The MTF at 2 m water depth was significantly coherent with all featured properties (as shown in Figure 3 in addition to wind speed and stress, current velocity, b_p(532), b_bp(532), _bp(λ), and γ) at the diurnal frequency prior to the wind event on 15 September 2008 except current velocity and salinity (not shown); b_bp(532) and MTF are coherent prior to about 14 September 2008 (Figure 5). The parameter, b_bp(532) is a good proxy for overall particle concentration (particularly minerals) and turbidity, which classically are the parameters thought to most directly control imaging performance. Interestingly, stronger coherence was observed in those parameters that are proxies for particle composition such as γ (describing size distribution; Figure 5) and n_p (describing particle index of refraction and hence, relative particle density; not shown). This coherence continued through 18 September for these composition-related optical products. Significant coherence was also observed at higher frequencies (0.25 to 0.5 day) for wind speed and σ_t (not shown) between 13 and 15 September. Coherence phase arrows indicate that wind speed and stress were negatively related to the near-surface MTF; that is, higher wind speeds resulted in more turbid waters near the surface. Density was positively related to the MTF, with density periodicity slightly leading MTF (not shown). The MTF was positively related to γ (Figure 5) and negatively related to n_p (not shown) at time periods prior to 17 September. Chl at 2 m was negatively related to and slightly lagged MTF (not shown).

[19] Coherence between the MTF with various physical, hydrographic, and optical properties and products were quantified as a function of depth/range to investigate possible linkages between imaging performance and environmental conditions. We are concerned only with relationships between parameters and not necessarily the strength of periodicity; therefore only WTC results are discussed here (Figure 6). A comparison between stratified (11 September), mixed (17 September), and advection/bloom (20 September) results show distinct differences in the spatial pattern of coherence between the MTF and hydrography and optical properties (MTF with σ_t and attenuation, c_pg(532), shown in Figure 6). During stratified conditions, strong coherence was found between the MTF and σ_t and the IOPs just above the pycnocline at about 15 to 20 m water depth, with periodicity of about 1 to 2 m (Figures 6a and 6b). This mid-upper water column coherence was also observed during the advection/bloom event after 19 September; however the MTF and hydrographic properties and IOPs were coherent over a larger vertical distance, from 12 m to the edge of the COI at periodicities of up to 2 m and longer (Figures 6e and 6f). A different vertical pattern in coherence was observed during mixed conditions. Strong coherence between MTF and σ_t was determined at a longer periodicity (>3 m) for all depths and MTF and the IOPs were coherent at very small scales (<1 m) centered around about 10 m water depth during periods of persistent strong winds (Figures 6c and 6d). MTF and the IOP products related to particle composition characteristics were again coherent during all conditions, at about 20 m water depth at periodicity of 1 m during stratified and advection/bloom periods and at about 12 m water depth during mixed conditions (not shown).

Figure 6

SBC depth-resolved wavelet coherence results between the MTF at Ψ = 3 rad⁻¹ and σ_t and between the MTF at Ψ = 3 rad⁻¹ and c_pg(532) collected during (a and b) stratified conditions on 11 September, (c and d) mixed conditions on 17 September, and (e and f) the advection/bloom event on 20 September 2008. Profiles of (g) σ_t and (h) c_pg(532) for stratified (blue), mixed (green), and advection/bloom (red) conditions.

3.2. SIO Pier

[20] The environmental conditions were highly variable over the time period of the RaDyO SIO Pier experiment. Clear skies, high clouds, patchy clouds, morning marine layer, fog, fully overcast, rain, light winds, and strong winds (>20 knots) were all observed over the 2 week time period of the field experiment. Surface observations of the waters around SIO Pier revealed a range of conditions, from high clarity (visible bottom) and calm to foamy with white caps, bubble injection, and swell. Strong riptides accompanied by turbid plumes of highly reflective inorganic particles were observed several times, as were surface patches of bioscum and biofilm. The water column was generally well mixed with relatively high concentrations of chlorophyll (average Chl = 2.2 μg/L; Figure 7).

Figure 7

SIO Pier time series of 2 m (a) c_pg(532) (black dots) and Chl (gray triangles) and (b) b_bp(532) (black dots) and n_p (gray triangles). (c) MTF (Ψ = 3 rad⁻¹ in black dots and Ψ = 50 rad⁻¹ in gray squares).

[21] Although concurrent physical and optical data are not readily available for the SIO Pier experiment, it was observed that optical properties were highly influenced by advective forcing (e.g., tides, waves, rip currents) and phytoplankton pigment concentration (seen in Chl data) at the site. Beam attenuation (532 nm) at 2 m depth varied between about 0.4 and 1.3 m⁻¹, and backscattering (532 nm) was quite high (0.003 to 0.03 m⁻¹), likely owing to the presence of highly reflective minerogenic particles observed at the field site (Figures 7a and 7b). These particles were particularly noticeable during the occurrence of rip currents on 16 January 2008. The highly reflective particles with relatively high bulk refractive index resulted in a greater than threefold increase in b_bp(532) and MTF at spatial frequencies less than 5 rad⁻¹. Interestingly, c_pg(532) was not substantially elevated during the rip current event; it was not the highest value observed during the SIO Pier experiment. Chlorophyll concentrations were near minimum values during the rip current time period (0.79 mg/L).

4. Discussion

[22] The results presented here imply that for the RaDyO field experiments, variability of near-surface MTF was strongly influenced by physical forcing–meteorological processes in the SBC and rip currents at SIO Pier. Highly reflective minerogenic particles with relatively high bulk particle index of refraction were associated with SIO Pier rip currents, which resulted in a large increase in the MTF. These particles, although not explicitly sampled or analyzed, appeared like mica flakes, which although rare in beach sand, have been observed along beaches in San Diego, CA (see http://www.youtube.com/watch?v=STEZV–7WOo). This increase in the MTF was likely due to enhanced reflectivity coupled with relatively high visibility; beam attenuation was not greatly elevated during the rip current event and Chl was at a minimum. During diurnal winds and the sustained strong wind event in the SBC, higher wind speeds were associated with particle characteristics indicative of larger, nonpigmented particles with higher relative indices of refraction and decreases in the MTF. These observations are particularly interesting as one would expect the imaging performance parameter to be influenced primarily by particle concentration as revealed by the magnitude of IOPs; however here we find that particle size and type (relative density information gained from the real index of refraction of particles) were important sources of variability in the MTF.

[23] The presence of larger particles with higher index of refraction observed during the high winds of the SBC RaDyO experiment could have been the result of wind-induced mixing of the upper water column waters and surface bubble injection or an increase in non–chlorophyll containing particles (perhaps minerogenic particles or senescent diatoms) or a combination of both of these factors. Anderson et al. [2008, and references therein] have reported on phytoplankton succession in the SBC, with diatom dominance during upwelling periods (spring and summer), followed by continued surface depletion of nutrients and stratification, and likely diatom sinking in the autumn. It is possible that these senescent diatoms were retained in near-surface waters during strong mixing associated with high winds.

[24] Surface bubble injection is often associated with strong sustained winds, which in itself would result in substantive changes in particle composition characteristics in surface waters [Zhang et al., 2011]. Information about bubble concentration was obtained from the bubble index (BI), which was derived from the ratio of MASCOT-measured VSFs at 70° and 120°. The BI can be used as a proxy for the concentration of the large bubble subpopulation, following Twardowski et al. (submitted manuscript, 2011). The derived concentration of relatively large bubbles (>10 μm in diameter) increased by nearly an order of magnitude on 15 September 2008 and by a factor of three on 18 September, coinciding with periods of sustained elevated wind speeds (Figure 8). The increase in the concentration of the large bubble subpopulation was accompanied by a decrease in the slope of the particulate attenuation spectra, indicative of an increase in particle size (Figure 8).

Figure 8

Time series of (a) wind speed, (b) volumetric bubble concentration (number per cubic meter) derived from bubble index, and (c) n_p (black dots) and γ (gray triangles) measured from KM during the SBC RaDyO experiment.

[25] Although not statistically significant in 2 m time series data, the advection/bloom event starting on 19 September 2008 resulted in significant coherence between the MTF and the IOPs and IOP products indicative of particle concentration and composition at about 20 m water depth (Figure 6). This event was marked by a decrease in the MTF, increases in the magnitude of all IOPs, Chl, and n_p and a decrease in γ, indicative of an increase in the concentration of larger biogenic particles with relatively higher refractive index (Figures 2–4 and 8; orange to red lines in Figure 3). The concentration of the large bubble subpopulation during this time period was relatively low, suggesting lesser effects due to surface bubble injection and more to a phytoplankton bloom that was associated with a shift in the SBC circulation (Figure 8).

[26] The results presented here show that the effects of particle composition on the shape of the VSF in the near-forward direction are important to imaging performance, which is a unique observation facilitated by advancements in in situ optical instrumentation. In order to elucidate the relative importance of particle effects on the MTF, we performed a sensitivity analysis of particle concentration versus composition effects on the variability of the MTF. This was accomplished by using the β approximation formulation for the MTF (Figure 9) [see also, Hou et al., 2007, Figure 2]. In the context of equations (6) and (7), the particle composition effect is embodied in the mean square angle, θ_o. Particle concentration effects were explored by varying the beam attenuation coefficient, c_pg(532), between 0.5 and 1.0 m⁻¹ by steps of 0.1 m⁻¹ while keeping the mean square angle, θ_o, constant at 0.07 rad, which is θ_o computed for the LISST measurements. The mean square angle was then varied between 0.03 and 0.19 rad by steps of 0.04 rad while keeping c_pg(532) constant at 0.6 m⁻¹ to investigate relative particle composition effects. Note that we are using variability in θ_o as a proxy for relative changes in particle composition. The range was set at 2 m and ω_o was 0.9 in both situations. Results suggest that at θ_o between 0.07 and 0.11 rad, particle concentration and composition affected MTF variability similarly. At θ_o greater than 0.11 rad, MTF variability was stronger with variable IOPs; that is, particle concentration effects dominated. Strikingly, when θ_o is between 0.03 and 0.07 rad (i.e., particle size distributions trending toward larger sizes), the MTF is much higher for frequencies less than 30 rad⁻¹. Here, particle composition effects dominated MTF variability, in a relative sense. For the specific ranges of variability in optical properties we observed during the study, these modeling results are consistent with the strong coherence observed between particle composition parameters and imaging performance.

Figure 9

Particle concentration versus composition effects on MTF variability. (a) MTF computed by varying the beam attenuation coefficient c (as indicated), while keeping the mean square angle θ_o constant at 0.07 rad (equations (2), (6), and (7)). (b) MTF computed by varying θ_o (as indicated) while keeping c constant at 0.6 m⁻¹. The range was set at 2 m, and ω_o was 0.9 in both situations.

[27] It is worth noting that the small-angle approximation (equation (6)) [e.g., Wells, 1973] assumes strong forward scattering, which was not the case during the SIO Pier rip currents. To explore this further, we evaluated MTFs computed from the DTF using measured β (equation (4)) versus those calculated using approximated β (equation (6); θ_o = 0.07 rad) for the SIO Pier data set. Results from this analysis are shown in Figure 10. The β approximation method produced very similar MTFs to those computed using measured β, particularly at high spatial frequencies (>10 rad⁻¹). MTFs at spatial frequencies less than 10 rad⁻¹ were not comparable during periods when the backscattering coefficient exceeded 0.012 m⁻¹ (Figures 7 and 10) Results from the two methods deviated greatly from each other at all spatial frequencies during the rip current event (Figure 10). Here, we show that in highly backscattering environments such as those with substantial minerogenic particles, the shape of the VSF cannot be assumed when computing imaging performance parameters such as the MTF.

Figure 10

SIO Pier time series of 2 m MTF at (a) Ψ = 3 rad⁻¹ and (b) Ψ = 50 rad⁻¹, with MTFs computed using the β approximation [e.g., Wells, 1973] shown as gray triangles.

5. Summary and Conclusions

[28] The comprehensive optical data set presented here afforded the opportunity to make direct computations of an imaging modulation parameter, the MTF, using field-measured data including small-angle VSFs. It also allowed the investigation of physical and particle effects on image modulation in two different environments: (1) a mesotrophic, relatively deep water environment (SBC) and (2) a dynamic, eutrophic, shallow-water environment (SIO Pier). Wavelet analysis was employed for SBC data to investigate the sources of variability of the MTF and the periodicities at which they occur.

[29] MTF variability in both environments was highly influenced by physical forcing. The 2 week SBC field experiment can be partitioned into three distinct periods: (1) diurnal winds (11–15 September), (2) persistent strong winds and upper water column mixing (15–18 September), and (3) an advection event characterized by relatively high Chl and elevated optical quantities (19–21 September). The near-surface MTF and optical properties were strongly related to wind conditions. Increased wind speeds and stresses resulted in upper water column mixing, decreased water clarity, and reductions in image transmission. During the advection/bloom event, the MTF was significantly correlated with all optical parameters indicative of particle characteristics at about 20 m water depth. The optical properties measured at SIO Pier also appeared to have been influenced primarily by advective and biological processes. The presence of large concentrations of highly reflective minerogenic particles during rip currents at SIO Pier resulted in large changes in the MTF.

[30] Optically derived particle characteristics such as bulk particle index of refraction and particle size distribution were shown to be significantly related to the variability of the MTF. This, in addition to the great temporal variability in environmental conditions observed at two different field sites stresses the importance of obtaining or predicting optical properties and derived particle composition characteristics (describing relative particle size and type) at temporal and spatial scales necessary to quantify rapid changes in image processing parameters. Importantly, estimates of water clarity or turbidity are not the only factors influencing the variability of the image performance parameters, particularly at steep near-forward scattering angles, where variability in the MTF was found to be dominated by particle composition effects. We also show that the standard approximation for the VSF cannot be used to compute imaging performance in environments with highly backscattering/reflective particles.

Acknowledgments

[31] This research is supported by the Office of Naval Research Environmental Optics program as part of the Radiance in a Dynamic Ocean (RaDyO) project. The authors are grateful to Jules Jaffe and an anonymous reviewer for greatly improving an earlier version of this paper. Thanks also to the captains and crews of the R/P FLIP and the R/V Kilo Moana; Frank Spada, Francesco Nencioli, Scott Freeman, and Matt Slivkoff for their assistance with data collection; Chris Zappa for wind stress data; and Luc Lenain and Ken Melville for ADCP current data.