Normalized water-leaving radiance: revisiting the influence of surface roughness

Many spaceborne sensors have been deployed to image the ocean in the visible portion of the spectrum. Information regarding the concentration of water constituents is contained in the water-leaving radiance-the radiance that is backscattered out of the water and subsequently propagates to the top of the atmosphere. Recognizing that it depends on the viewing and Sun geometry, ways have been sought to normalize this radiance to a single Sun-viewing geometry--forming the normalized water-leaving radiance. This requires understanding both the bidirectional nature of the upwelling radiance just beneath the surface and the interaction of this radiance with the air-water interface. I believe that the latter has been incorrectly computed in the past when a water surface roughened by the wind is considered. The presented computation suggests that, for wind speeds as high as 20 m/s, the influence of surface roughness is small for a wide range of Sun-viewing geometries, i.e., the transmittance of the (whitecap-free) air-water interface is nearly identical (within 0.01) to that for a flat interface.     

Satellite-sensor calibration verification with the cloud-shadow method

An atmospheric-correction method appropriate for high-spatial-resolution sensors that uses cloud-shaded pixels together with pixels in a neighboring region of similar optical properties is described. This cloud-shadow method uses the difference between the total radiance values observed at the sensor for these two regions, thus removing the nearly identical atmospheric radiance contributions to the two signals (e.g., path radiance and Fresnel-reflected skylight). What remains is largely due to solar photons backscattered from beneath the sea to dominate the residual signal. Normalization by the direct solar irradiance reaching the sea surface and correction for some second-order effects provides the remote-sensing reflectance of the ocean at the location of the neighbor region, providing a known ground target spectrum for use in testing the calibration of the sensor. A similar approach may be useful for land targets if horizontal homogeneity of scene reflectance exists about the shadow. Monte Carlo calculations have been used to correct for adjacency effects and to estimate the differences in the skylight reaching the shadowed and neighbor pixels.     

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.     

Oceanic radiance model development and validation: application of airborne active-passive ocean color spectral measurements

It is shown that airborne active-passive (laser-solar) ocean color data can be used to develop and validate oceanic radiance models. The two principal inputs to the oceanic radiance model, chlorophyll pigment and incident solar irradiance, are obtained from a nadir-viewing laser-induced fluorescence spectrometer and a zenith-viewing radiometer, respectively. The computed water-leaving radiances are validated by comparison with the calibrated output of a separate nadir-viewing radiometer subsystem. In the North Atlantic Ocean, the calculated and the observed airborne radiances are found to compare very favorably for the 443-, 520-, and 550-nm wavelengths over an ～ 170-km flight track east of St. John's, Newfoundland. The results further suggest that the semianalytical radiance model of ocean color, the airborne active (laser) fluorescence spectrometer, and the passive (solar) radiometric instrumentation are all remarkably precise.     

Diffuse reflectance of oceanic waters. III. Implication of bidirectionality for the remote-sensing problem

The upwelling radiance field beneath the ocean surface and the emerging radiance field are not generally isotropic. Their bidirectional structure depends on the illumination conditions (the Sun's position in particular) and on the optical properties of the water body. In oceanic case 1 waters, these properties can be related, for each wavelength λ, to the chlorophyll (Chl) concentration. We aim to quantify systematically the variations of spectral radiances that emerge from an ocean with varying Chl when we change the geometric conditions, namely, the zenith-Sun angle, the viewing angle, and the azimuth difference between the solar and observational vertical planes. The consequences of these important variations on the interpretation of marine signals, as detected by a satelliteborne ocean color sensor, are analyzed. In particular, the derivation of radiometric quantities, such as R (λ), the spectral reflectance, or [ L(w)(λ)](N), the normalized water-leaving radiance that is free from directional effects, is examined, as well as the retrieval of Chl. We propose a practical method that is based on the use of precomputed lookup tables to provide values of the f/Q ratio in all the necessary conditions[ f relates (R(λ) to the backscattering and absorption coefficients, whereas Q is the ratio of upwelling irradiance to any upwelling radiance]. The f/Q ratio, besides being dependent on the geometric configuration (the three angles mentioned above), also varies with λ and with the bio-optical state, conveniently depicted by Chl. Because Chl is one of the entries for the lookup table, it has to be derived at the beginning of the process, before the radiometric quantities R(λ) or [L(W)(λ)](N) can be produced. The determination of Chl can be made through an iterative process, computationally fast, using the information at two wavelengths. In this attempt to remove the bidirectional effect, the commonly accepted view relative to the data-processing strategy is somewhat modified, i.e., reversed, as the Chl index becomes a prerequisite parameter that must be identified prior to the derivation of the fundamental radiometric quantities at all wavelengths.     

Contribution of Raman scattering to water-leaving radiance: a reexamination

We have reexamined the contribution of Raman scattering to the water-leaving radiance in case 1 waters by carrying out radiative transfer simulations that combine the latest reported measurements of the absorption coefficient of pure water with direct measurements of the spectral variation of the Raman-scattering coefficient. The resulting contribution of Raman scattering is then compared with experimental measurements of the water-leaving radiance, and the fractional contribution of radiance produced by Raman scattering to the total radiance measured at a given wavelength is determined. The results show that (1) the contribution of Raman scattering to the water-leaving radiance in an ocean of pure seawater is as much as 50-100% larger than earlier predictions, and (2) the Raman contribution does not decay as rapidly with increasing concentrations of chlorophyllouslike pigments C as predicted earlier. In fact, the Raman fraction for C 8% at wavelengths of interest in ocean color remote sensing and therefore cannot be ignored in ocean color modeling.     

Asymptotic optical depths in source-free ocean waters

The depth dependence for which the downward diffuse attenuation coefficient, the upward-to-downward plane irradiance ratio, the vertically upward radiance-to-downward plane irradiance ratio, and the mean cosine of the radiance depend negligibly on the surface incident illumination have been examined. The depths at which these coefficients approach to within a specified percent of their asymptotic values depends significantly on the characteristics of the incident illumination and on the inherent optical properties of the water. This information is useful when solving inverse ocean optics problems with a method for which the radiance is assumed to be approximately in the asymptotic regime.     

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.     

Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with a rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind 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).     

Remote sensing of ocean color: a methodology for dealing with broad spectral bands and significant out-of-band response

A methodology for delineating the influence of finite spectral bandwidths and significant out-of-band response of sensors for remote sensing of ocean color is developed and applied to the Sea-viewing Wide-Field-of-view Sensor (SeaWiFS). The basis of the method is the application of the sensor's spectral-response functions to the individual components of the top-of-the-atmosphere (TOA) radiance rather than the TOA radiance itself. For engineering purposes, this approach allows one to assess easily (and quantitatively) the potential of a particular sensor design for meeting the system-sensor plus algorithms-performance requirements. In the case of the SeaWiFS, two significant conclusions are reached. First, it is found that the out-of-band effects on the water-leaving radiance component of the TOA radiance are of the order of a few percent compared with a sensor with narrow spectral response. This implies that verification that the SeaWiFS system-sensor plus algorithms-meets the goal of providing the water-leaving radiance in the blue in clear ocean water to within 5% will require measurements of the water-leaving radiance over the entire visible spectrum as opposed to just narrow-band (10-20-nm) measurements in the blue. Second, it is found that the atmospheric correction of the SeaWiFS can be degraded by the influence of water-vapor absorption in the shoulders of the atmospheric-correction bands in the near infrared. This absorption causes an apparent spectral variation of the aerosol component between these two bands that will be uncharacteristic of the actual aerosol present, leading to an error in correction. This effect is dependent on the water-vapor content of the atmosphere. At typical water-vapor concentrations the error is larger for aerosols with a weak spectral variation in reflectance than for those that display a strong spectral variation. If the water-vapor content is known, a simple procedure is provided to remove the degradation of the atmospheric correction. Uncertainty in the water-vapor content will limit the accuracy of the SeaWiFS correction algorithm.     

Role of oceanic air bubbles in atmospheric correction of ocean color imagery

Ocean color is the radiance that emanates from the ocean because of scattering by chlorophyll pigments and particles of organic and inorganic origin. Air bubbles in the ocean also scatter light and thus contribute to the water-leaving radiance. This additional water-leaving radiance that is due to oceanic air bubbles could violate the black pixel assumption at near-infrared wavelengths and be attributed to chlorophyll in the visible. Hence, the accuracy of the atmospheric correction required for the retrieval of ocean color from satellite measurements is impaired. A comprehensive radiative transfer code for the coupled atmosphere--ocean system is employed to assess the effect of oceanic air bubbles on atmospheric correction of ocean color imagery. This effect is found to depend on the wavelength-dependent optical properties of oceanic air bubbles as well as atmospheric aerosols.     

Remote sensing of the ocean contributions from ultraviolet to near-infrared using the shortwave infrared bands: simulations

In the remote sensing of the ocean near-surface properties, it is essential to derive accurate water-leaving radiance spectra through the process of the atmospheric correction. The atmospheric correction algorithm for Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) and Moderate Resolution Imaging Spectroradiometer (MODIS) uses two near-infrared (NIR) bands at 765 and 865 nm (748 and 869 nm for MODIS) for retrieval of aerosol properties with assumption of the black ocean at the NIR wavelengths. Modifications are implemented to account for some of the NIR ocean contributions for the productive but not very turbid waters. For turbid waters in the coastal regions, however, the ocean could have significant contributions in the NIR, leading to significant errors in the satellite-derived ocean water-leaving radiances. For the shortwave infrared (SWIR) wavelengths (approximately > 1000 nm), water has significantly larger absorption than those for the NIR bands. Thus the black ocean assumption at the SWIR bands is generally valid for turbid waters. In addition, for future sensors, it is also useful to include the UV bands to better quantify the ocean organic and inorganic materials, as well as for help in atmospheric correction. Simulations are carried out to evaluate the performance of atmospheric correction for nonabsorbing and weakly absorbing aerosols using the NIR bands and various combinations of the SWIR bands for deriving the water-leaving radiances at the UV (340 nm) and visible wavelengths. Simulations show that atmospheric correction using the SWIR bands can generally produce results comparable to atmospheric correction using the NIR bands. In particular, the water-leaving radiance at the UV band (340 nm) can also be derived accurately. The results from a sensitivity study for the required sensor noise equivalent reflectance, (NE Delta rho), [or the signal-to-noise ratio (SNR)] for the NIR and SWIR bands are provided and discussed.     

Multiparameter retrieval of water optical properties from above-water remote-sensing reflectance using the simulated annealing algorithm

Water-leaving radiance, measured just above the ocean surface, contains important information about near-surface or subsurface processes that occur on or below the deep ocean and coastal water. As such, retrieving seawater inherent optical properties (IOPs) is an important step to determining water type, subsurface light field, turbidity, pigment concentration, and sediment loading. However, the retrieval (or inversion) of seawater IOPs from just above water radiance measurements is a multiparameter nonlinear problem that is difficult to solve by conventional optimization methods. The applicability of the simulated annealing algorithm (SA) is explored as a nonlinear global optimizer to solve this multiparameter retrieval problem. The SA algorithm is combined with widely known semianalytical relations for seawater's IOPs to parameter invert these properties from simulated and measured water-leaving reflectance spectra. Furthermore, given the versatility of the SA algorithm, the scheme is extended to retrieve water depth from input reflectance data. Extensive tests and comparisons with in situ and simulated data sets compiled by the International Ocean-Color Coordinating Group are presented. Field data include reflectance spectra acquired with a handheld GER 1500 spectroradiometer and absorption measurements, performed with the AC-9 instrument on waters around Singapore's nearby islands.     

Influence of the atmosphere on space measurements of directional properties

To compare measurements performed in different geometrical conditions, one must take into account the angular anisotropy of the reflection properties of natural surfaces. As use of the exact boundary conditions in the radiative transfer codes seems prohibitive, a simple but accurate formulation of the problem has been sought. In this paper, two average angular reflectances are defined from which the reflected radiance may be deduced for any distribution of the downward radiance. Calculations made for different atmospheric models show that the solar directionality is partly preserved in the downward radiation field, so that the average reflectances can be written as a linear combination of actual reflectance and spherical albedo of the surface. Finally, the feasibility of detecting directional properties from space measurements is discussed.     

Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters

The standard SeaWiFS atmospheric correction algorithm, designed for open ocean water, has been extended for use over turbid coastal and inland waters. Failure of the standard algorithm over turbid waters can be attributed to invalid assumptions of zero water-leaving radiance for the near-infrared bands at 765 and 865 nm. In the present study these assumptions are replaced by the assumptions of spatial homogeneity of the 765:865-nm ratios for aerosol reflectance and for water-leaving reflectance. These two ratios are imposed as calibration parameters after inspection of the Rayleigh-corrected reflectance scatterplot. The performance of the new algorithm is demonstrated for imagery of Belgian coastal waters and yields physically realistic water-leaving radiance spectra. A preliminary comparison with in situ radiance spectra for the Dutch Lake Markermeer shows significant improvement over the standard atmospheric correction algorithm. An analysis is made of the sensitivity of results to the choice of calibration parameters, and perspectives for application of the method to other sensors are briefly discussed.     

Phytoplankton pigment concentrations in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates

The processing algorithms used for relating the apparent color of the ocean observed with the Coastal-Zone Color Scanner on Nimbus-7 to the concentration of phytoplankton pigments (principally the pigment responsible for photosynthesis, chlorophyll a) are developed and discussed in detail. These algorithms are applied to the shelf and slope waters of the Middle Atlantic Bight and also to Sargasso Sea waters. In all, four images are examined, and the resulting pigment concentrations are compared to continuous measurements made along ship tracks. The results suggest that over the 0.08-1.5-mg/m3 range the error in the retrieved pigment concentration is of the order of 30-40% for a variety of atmospheric turbidities. In three direct comparisons between ship-measured and satellite-retrieved values of the water-leaving radiance the atmospheric correction algorithm retrieved the water-leaving radiance with an average error of approximately 10%. This atmospheric correction algorithm does not require any surface measurements for its application.     

Infrared radiance and solar glint at the ocean-sky horizon

An analytic model is developed for the mean and clutter infrared radiance emitted from the ocean surface near the horizon and in the presence of solar glint. The model is based on the identification of a characteristic facet dimension over which the ocean surface is essentially flat. Fluctuations in the facet orientation generated by the water wave motion are modeled by a parameterized wave height power spectral density that provides the two orthogonal wave slope variances. The mean and root-meansquare facet radiances are calculated with Gaussian probability-density functions for the wave slopes. One can determine the number of facets within the field of view of a single detector by estimating the exposed ocean area and dividing by the facet area. This estimation takes into account shadowing effects of the swell wave, the swell wavelength, and the transverse detector field of view. The number of exposed facets together with the central-limit theorem permits computation of the radiance clutter as a function of look-down angle below the horizon. Vertical radiance profiles, parameterized by the azimuthal offset from the solar position, are calculated over a sensor look-down angle range of ±50 mrad about the horizon. The results of this analysis are compared with infrared radiance measurements of the ocean surface near the horizon and in the presence of solar glint. Agreement between the measured and calculated values of the mean and clutter radiances is good.     

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.