Analytic remote-sensing optical algorithms requiring simple and practical field parameter inputs

Spectral in-water measurements of downward irradiance (E(d)), upward irradiance (E(u)), and nadir radiance (L(u)) are sufficient to calculate the scalar irradiances E(0), E(0d), and E(0u), the average cosines mu, mu(d), and mu(u), the light absorption coefficient a, the backscattering coefficient b(b), and the so-called f factor that relates to R, a, and b(b). The solar elevation of 42 degrees is a special case in which mu(d) is independent of all variables except solar elevation. The algorithms are valid for solar elevations between 12 degrees and 81 degrees for horizontally stratified clear and turbid deep waters.     

Ocean inherent optical property estimation from irradiances

A method is evaluated for estimating the absorption coefficient a and the backscattering coefficient b(b) from measurements of the upward and downward irradiances E(u)(z) and E(d)(z). With this method, the reflectance ratio R(z) and the downward diffuse attenuation coefficient K(d)(z) obtained from E(u)(z) and E(d)(z) are used to estimate the inherent optical properties R(infinity) and K(infinity) that are the asymptotic values of R(z) and K(d)(z), respectively. For an assumed scattering phase function beta , there are unique correlations between the values of R(infinity) and K(infinity) and those of a and b(b) that can be derived from the radiative transfer equation. Good estimates of a and the Gordon parameter G = b(b)/(a + b(b)) can be obtained from R(infinity) and K(infinity) if the true scattering phase function is not greatly different from the assumed function. The method works best in deep, homogeneous waters, but can be applied to some cases of stratified waters. To improve performance in shallow waters where bottom effects are important, the deep- and shallow-measurement reflectance models also are developed.     

Estimation of absorption and backscattering coefficients from in situ radiometric measurements: theory and validation in case II waters

A model that relates the coefficients of absorption (a) and backscattering (b(b)) to diffuse attenuation (K(d)), radiance reflectance (R(L)), and the mean cosine for downward irradiance (mu(d)) is presented. Radiance transfer simulations are used to verify the physical validity of the model for a wide range of water column conditions. Analysis of thee radiance transfer simulations suggest that absorption and backscattering can be estimated with average errors of 1% and 3%, respectively, if the value of mu(d) is known with depth. If the input data set is restricted to variables that can be derived from measurements of upward radiance (L(u)) and downward irradiance (E(d)), it is necessary to use approximate values of mu(d). Examination of three different approximation schemes for mu(d) shows that the average error for estimating a and b(b) increases to approximately 13%. We tested the model by using measurements of L(u) and E(d) collected from case II waters off the west coast of Scotland. The resulting estimates of a and b(b) were compared with independent in situ measurements of these parameters. Average errors for the data set were of the order of 10% for both absorption and backscattering.     

Semi-empirical correction algorithm for AC-9 measurements in a coccolithophore bloom

Values for the coefficients of absorption (a) and attenuation (c) obtained from AC-9 measurements in coccolithophore blooms do not provide satisfactory inputs for radiance transfer models. We have therefore modified the standard AC-9 scattering correction algorithm by including an extra term, F(lambda, lambda(r)), which allows for possible wavelength dependence in the scattering phase function. We estimated the magnitude of F(lambda, lambda(r)), which is unity in the standard algorithm, by adjusting the absorption and scattering values in Hydrolight radiance transfer calculations until the depth profiles of downward irradiance (E(d)) and upward radiance (L(u)) matched those measured in situ. The modified algorithm was tested with data from a phytoplankton bloom dominated by the coccolithophore Emiliania huxleyi, which occurred in the western English Channel in May 2001. In this paper, we only have sufficient data to adequately constrain the radiance transfer model in one wave band centered on 488 ma. A single value of F(lambda, lambda(r)) = 1.4 was found to produce satisfactory agreement between modeled and observed profiles at four widely spaced stations within the bloom. Measurements of the ratio of backscattering (b(b)) to total scattering (b) showed significant wavelength dependence at these stations.     

Comparison of the ocean inherent optical properties obtained from measurements and inverse modeling

A model developed recently by Loisel and Stramski [Appl. Opt. 39, 3001-3011 (2000)] for estimating the spectral absorption a(lambda), scattering b(lambda), and backscattering b(b)(lambda) coefficients in the upper ocean from the irradiance reflectance just beneath the sea surface R(lambda, z = 0(-)) and the diffuse attenuation of downwelling irradiance within the surface layer ?K(d)(lambda)?(1) is compared with measurements. Field data for this comparison were collected in different areas including off-shore and near-shore waters off southern California and around Europe. The a(lambda) and b(b)(lambda) values predicted by the model in the blue-green spectral region show generally good agreement with measurements that covered a broad range of conditions from clear oligotrophic waters to turbid coastal waters affected by river discharge. The agreement is still good if the model estimates of a(lambda) and b(b)(lambda) are based on R(lambda, z = 0(-)) used as the only input to the model available from measurements [as opposed to both R(lambda, z = 0(-)) and ?K(d)(lambda)?(1) being measured]. This particular mode of operation of the model is relevant to ocean-color remote-sensing applications. In contrast to a(lambda) and b(b)(lambda) the comparison between the modeled and the measured b(lambda) shows large discrepancies. These discrepancies are most likely attributable to significant variations in the scattering phase function of suspended particulate matter, which were not included in the development of the model.     

Toward closure of upwelling radiance in coastal waters

We present three methods for deriving water-leaving radiance L(w)(lambda) and remote-sensing reflectance using a hyperspectral tethered spectral radiometer buoy (HyperTSRB), profiled spectroradiometers, and Hydrolight simulations. Average agreement for 53 comparisons between HyperTSRB and spectroradiometric determinations of L(w)(lambda) was 26%, 13%, and 17% at blue, green, and red wavelengths, respectively. Comparisons of HyperTSRB (and spectroradiometric) L(w)(lambda) with Hydrolight simulations yielded percent differences of 17% (18%), 17% (18%), and 13% (20%) for blue, green, and red wavelengths, respectively. The differences can be accounted for by uncertainties in model assumptions and model input data (chlorophyll fluorescence quantum efficiency and the spectral chlorophyll-specific absorption coefficient for the red wavelengths, and scattering corrections for input ac-9 absorption data and volume scattering function measurements for blue wavelengths) as well as radiance measurement inaccuracies [largely differences in the depth of the L(u)(lambda, z) sensor on the HyperTSRB].     

Algorithms for ocean-bottom albedo determination from in-water natural-light measurements

A method for determining the ocean-bottom optical albedo R(b) from in-water upward and downward irradiance measurements at a shallow site is presented, tested, and compared with a more familiar approach that requires additional measurements at a nearby deep-water site. Also presented are two new algorithms for estimating R(b) from measurements of the downward irradiance and vertically upward radiance. All methods performed well in numerical situations at depths at which the influence of the bottom on the light field was significant.     

Removal of surface reflection from above-water visible-near infrared spectroscopic measurements

Water quality estimation in fresh and marine water systems with in situ above-water spectroscopy requires measurement of the volume reflectance (rho(v)) of water bodies. However, the above-water radiometric measurements include surface reflection (L(r)) as a significant component along with volume reflection. The L(r) carries no information on water quality, and hence it is considered as a major source of error in in situ above-water spectroscopy. Currently, there are no methods to directly measure L(r). The common method to estimate L(r) assumes a constant water surface reflectance (rho(s)) of 2%, and then subtracts the L(r) thus calculated from the above-water radiance measurements to obtain the volume reflection (L(v)). The problem with this method is that the amount of rho(s) varies with environmental conditions. Therefore, a methodology was developed in this study for direct measurement of water volume reflectance above water at nadir view geometry. Other objectives of this study were to analyze the contribution of L(r) to the total water reflectance under various environmental conditions in a controlled setup and to develop an artificial neural network (ANN) model to estimate rho(s) from environmental conditions. The results showed that L(r) contributed 20-54% of total upwelling radiance from water at nadir. The rho(s) was highly variable with environmental conditions. Using sun altitude, wind speed, diffuse lighting, and wavelength as inputs, the ANN model was able to accurately simulate rho(s), with a low root mean square error of 0.003. A sensitivity analysis with the ANN model indicated that sun altitude and diffuse light had the highest influence on rho(s), contributing to over 82% of predictability of the ANN model. Therefore, the ANN modeling framework can be an accurate tool for estimating surface reflectance in applications that require volume reflectance of water.     

Ocean inherent optical property determination from in-water light field measurements

An algorithm is described and evaluated for determining the absorption and backscattering coefficients a(z) and bb(z) from measurements of the nadir-viewing radiance Lu(z) and downward irradiance Ed(z). The method, derived from radiative transfer theory, is similar to a previously proposed one for Eu(z) and Ed(z)and both methods are demonstrated with numerical simulations and field data. Numerical simulations and a sensitivity analysis show that good estimates of a(z) and bb(z) can be obtained if the assumed scattering phase function is approximately correct. In an experiment in Long Island Sound, estimates of a(z) derived with these methods agreed well with those obtained from an in situ reflecting tube instrument.     

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: homogeneous waters

A full multiple-scattering algorithm for inverting upwelling radiance (L(u)) or irradiance (E(u)) and downwelling irradiance (E(d)) profiles in homogeneous natural waters to obtain the absorption (a) and backscattering (b(b)) coefficients is described and tested with simulated data. An attractive feature of the algorithm is that it does not require precise knowledge of the scattering phase function of the medium. For the E(u)-E(d) algorithm, tests suggest that the error in the retrieved a should usually be ?1%, and the error in b(b)?10-20%. The performance of the L(u)-E(d) algorithm is not as good because it is more sensitive to the scattering phase function employed in the inversions; however, the error in a is usually still small, i.e., ?3%. When the algorithm is extended to accommodate the presence of a Lambertian-reflecting bottom, the retrievals of a are still excellent, even when the presence of the bottom significantly influences the upwelling light field; however, the error in b(b) can be large.     

Enhanced solar irradiance across the atmosphere-sea ice interface: a quantitative numerical study

A radiative transfer model for the coupled atmosphere-sea ice system is used to study the change in downward irradiance across the air-ice interface. Computations demonstrate that the downward solar irradiance can be significantly enhanced across the air-ice interface. The enhancement is mainly due to light in the ice that is scattered upward and then totally reflected by the air-ice interface. It depends primarily on the change in the index of refraction across this interface and the optical properties of the sea ice, but also on the direct solar and sky illumination of the interface.     

Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability

Three independent ocean color sampling methodologies are compared to assess the potential impact of instrumental characteristics and environmental variability on shipboard remote-sensing reflectance observations from the Santa Barbara Channel, California. Results indicate that under typical field conditions, simultaneous determinations of incident irradiance can vary by 9-18%, upwelling radiance just above the sea surface by 8-18%, and remote-sensing reflectance by 12-24%. Variations in radiometric determinations can be attributed to a variety of environmental factors such as Sun angle, cloud cover, wind speed, and viewing geometry; however, wind speed is isolated as the major source of uncertainty. The above-water approach to estimating water-leaving radiance and remote-sensing reflectance is highly influenced by environmental factors. A model of the role of wind on the reflected sky radiance measured by an above-water sensor illustrates that, for clear-sky conditions and wind speeds greater than 5 m/s, determinations of water-leaving radiance at 490 nm are undercorrected by as much as 60%. A data merging procedure is presented to provide sky radiance correction parameters for above-water remote-sensing reflectance estimates. The merging results are consistent with statistical and model findings and highlight the importance of multiple field measurements in developing quality coastal oceanographic data sets for satellite ocean color algorithm development and validation.     

Determination of the fluorescence quantum yield by oceanic phytoplankton in their natural habitat

Sun-stimulated chlorophyll a fluorescence has been measured in situ, within the upward and downward light fields, in oceanic waters with chlorophyll concentrations of 0.04-3 mg m(-3). We combined these signals with phytoplankton absorption spectra to derive the fluorescence quantum yield, phi (number of photons emitted by fluorescence/number of absorbed photons). phi was derived separately from hyperspectral (upward and downward) irradiance measurements (with a LI-COR Instruments spectroradiometer) and from nadir radiance near 683 nm (with a Biospherical Instruments profiler). The contribution of inelastic Raman scattering to the signal in the red band was assessed and subtracted. Raman-corrected phi values derived from the two instruments compared well. Vertical phi profiles were strongly structured, with maximal (5-6%) values at depth, whereas phi was approximately =1% in near-surface waters (measurements made approximately at solar noon). These near-surface values are needed for interpretation of remotely sensed fluorescence signals. This optical study shows that the fluorescence yield of algae in their natural environment can be accurately derived in a nonintrusive way with available instrumentation and adequate protocols.     

Hyperspectral remote sensing for shallow waters. I. A semianalytical model

For analytical or semianalytical retrieval of shallow-water bathymetry and/or optical properties of the water column from remote sensing, the contribution to the remotely sensed signal from the water column has to be separated from that of the bottom. The mathematical separation involves three diffuse attenuation coefficients: one for the downwelling irradiance (K(d)), one for the upwelling radiance of the water column (K(u)(C)), and one for the upwelling radiance from bottom reflection (K(u)(B)). Because of the differences in photon origination and path lengths, these three coefficients in general are not equal, although their equality has been assumed in many previous studies. By use of the Hydrolight radiative-transfer numerical model with a particle phase function typical of coastal waters, the remote-sensing reflectance above (R(rs)) and below (r(rs)) the surface is calculated for various combinations of optical properties, bottom albedos, bottom depths, and solar zenith angles. A semianalytical (SA) model for r(rs) of shallow waters is then developed, in which the diffuse attenuation coefficients are explicitly expressed as functions of in-water absorption (a) and backscattering (b(b)). For remote-sensing inversion, parameters connecting R(rs) and r(rs) are also derived. It is found that r(rs) values determined by the SA model agree well with the exact values computed by Hydrolight (~3% error), even for Hydrolight r(rs) values calculated with different particle phase functions. The Hydrolight calculations included b(b)/a values as high as 1.5 to simulate high-turbidity situations that are occasionally found in coastal regions.     

Above-water radiometry in shallow coastal waters

Above- and in-water radiometric data were collected from two coastal platforms: a small boat and an oceanographic tower. The above-water data were processed with and without a correction for bidirectional effects (Q02 and S95, respectively). An intercomparison of water-leaving radiances over a wide range of environmental conditions showed (a) total uncertainties across the blue-green domain were to within 4%, (b) a convergence of the Q02 method with the in-water method (average Q02 intercomparisons were to within 4%), and (c) chlorophyll a concentrations derived from Q02 reflectances and the OC4V4 (Ocean Color 4 Version 4) algorithm agreed with independent high-performance liquid-chromatography determinations to within approximately 32%.     

Uniqueness in remote sensing of the inherent optical properties of ocean water

We examine the problem of uniqueness in the relationship between the remote-sensing reflectance (Rrs) and the inherent optical properties (IOPs) of ocean water. The results point to the fact that diffuse reflectance of plane irradiance from ocean water is inherently ambiguous. Furthermore, in the 400 < lambda < 750 nm region of the spectrum, Rrs(lambda) also suffers from ambiguity caused by the similarity in wavelength dependence of the coefficients of absorption by particulate matter and of absorption by colored dissolved organic matter. The absorption coefficients have overlapping exponential responses, which lead to the fact that more than one combination of IOPs can produce nearly the same Rrs spectrum. This ambiguity in absorption parameters demands that we identify the regions of the Rrs spectrum where we can isolate the effects that are due only to scattering by particulates and to absorption by pure water. The results indicate that the spectral shape of the absorption coefficient of phytoplankton, a(ph)(lambda), cannot be derived from a multiparameter fit to Rrs(lambda). However, the magnitude and the spectral dependence of the absorption coefficient can be estimated from the difference between the measured Rrs(lambda) and the best fit to Rrs(lambda) in terms of IOPs that exclude a(ph)(lambda).     

Atmospheric correction of satellite ocean color imagery: the black pixel assumption

The assumption that values of water-leaving radiance in the near-infrared (NIR) are negligible enable aerosol radiative properties to be easily determined in the correction of satellite ocean color imagery. This is referred to as the black pixel assumption. We examine the implications of the black pixel assumption using a simple bio-optical model for the NIR water-leaving reflectance [rho(w)(lambda(NIR))](N). In productive waters [chlorophyll (Chl) concentration >2 mg m(-3)], estimates of [rho(w)(lambda(NIR))](N) are several orders of magnitude larger than those expected for pure seawater. These large values of [rho(w)(lambda(NIR))](N) result in an overcorrection of atmospheric effects for retrievals of water-leaving reflectance that are most pronounced in the violet and blue spectral region. The overcorrection increases dramatically with Chl, reducing the true water-leaving radiance by roughly 75% when Chl is equal to 5 mg m(-3). Relaxing the black pixel assumption in the correction of Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) satellite ocean color imagery provides significant improvements in Chl and water-leaving reflectance retrievals when Chl values are greater than 2 mg m(-3). Improvements in the present modeling of [rho(w)(lambda(NIR))](N) are considered, particularly for turbid coastal waters. However, this research shows that the effects of nonzero NIR reflectance must be included in the correction of satellite ocean color imagery.     

Irradiance inversion algorithm for absorption and backscattering profiles in natural waters: improvement for clear waters

Our iterative inversion algorithm for retrieving absorption a(z) and backscattering b(b)(z) from profiles of upwelling and downwelling irradiance, on the basis of assuming a depth-independent phase function for the medium, was found to have unsatisfactory accuracy for b(b)(z) in clear waters. We modified the algorithm here by assuming a depth-independent phase function for the particles and then performing an additional iteration over the fraction of total scattering that is due to the water itself. The modified algorithm's accuracy is considerably improved over the original in clear waters and reduces to the original in waters for which the particle contribution to b(b)(z) is dominant.     

Use of a Spectralon panel to measure the downwelling irradiance signal: case studies and recommendations

Field determinations of the remote sensing reflectance signal are necessary to validate ocean color satellite sensors. The measurement of the above-water downwelling irradiance signal Ed(0+) is commonly made with a reference plaque of a known reflectance. The radiance reflected by the plaque (L(dspec)) can be used to determine Ed(0+) if the plaque is assumed to be near Lambertian. To test this assumption, basic experiments were conducted on a boat under changing sky conditions (clear, cloudy, covered) and with different configurations for simultaneous measurements of L(dspec) and Ed(0+). For all measurement configurations, results were satisfactory under a clear sky. Under cloudy or covered skies, shadow effects on the plaque induced errors up to 100% in the determination of Ed(0+). An appropriate measurement configuration was defined, which enabled Ed(0+) to be determined with an accuracy of better than +/- 15% regardless of the sky conditions.     

An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance

Remote-sensing reflectance (R(rs)), which is defined as the ratio of water-leaving radiance (L(w)) to downwelling irradiance just above the surface (E(d)(0?)), varies with both water constituents (including bottom properties of optically-shallow waters) and angular geometry. L(w) is commonly measured in the field or by satellite sensors at convenient angles, while E(d)(0?) can be measured in the field or estimated based on atmospheric properties. To isolate the variations of R(rs) (or L(w)) resulting from a change of water constituents, the angular effects of R(rs) (or L(w)) need to be removed. This is also a necessity for the calibration and validation of satellite ocean color measurements. To reach this objective, for optically-deep waters where bottom contribution is negligible, we present a system centered on water's inherent optical properties (IOPs). It can be used to derive IOPs from angular R_rs and offers an alternative to the system centered on the concentration of chlorophyll. This system is applicable to oceanic and coastal waters as well as to multiband and hyperspectral sensors. This IOP-centered system is applied to both numerically simulated data and in situ measurements to test and evaluate its performance. The good results obtained suggest that the system can be applied to angular R(rs) to retrieve IOPs and to remove the angular variation of R(rs).