Retrieval of elements of the columnar aerosol scattering phase matrix from polarized sky radiance over the ocean: simulations

We have extended the Wang-Gordon [Appl. Opt. 32, 4598-4609 (1993)] and Gordon-Zhang [Appl. Opt.34, 5552-5555 (1995)] algorithms for retrieval of omega(0)P(?, where omega(0) is the aerosol single-scattering albedo and P(?) is the aerosol phase function for scattering through an angle ?, from measurement of the radiances exiting the top and the bottom of the atmosphere over the ocean, to include polarization. This permits derivation of the P(11)(?) and P(12)(?) elements of the Mueller scattering phase matrix P(?) from measurement of the linear polarization portion of the Stokes vectors associated with the radiance exiting the top and the bottom of the atmosphere. Simulations show that good retrievals are possible for aerosol optical thicknesses as large as 2; however, the atmosphere is required to be horizontally homogeneous. We study the influence of the elements of P(?) that cannot be determined in this manner. It is shown that including surface measurements of the linear polarization of the sky radiance improves the estimation of the radiance simultaneously exiting the top of the atmosphere (TOA) and also allows reasonably accurate estimates of the TOA polarization. This is important for in-orbit calibration of ocean-color sensors.     

Radiative transfer code SHARM-3D for radiance simulations over a non-Lambertian nonhomogeneous surface: intercomparison study

Results of an extensive validation study of the new radiative transfer code SHARM-3D are described. The code is designed for modeling of unpolarized monochromatic radiative transfer in the visible and near-IR spectra in the laterally uniform atmosphere over an arbitrarily inhomogeneous anisotropic surface. The surface boundary condition is periodic. The algorithm is based on an exact solution derived with the Green's function method. Several parameterizations were introduced into the algorithm to achieve superior performance. As a result, SHARM-3D is 2-3 orders of magnitude faster than the rigorous code SHDOM. It can model radiances over large surface scenes for a number of incidence-view geometries simultaneously. Extensive comparisons against SHDOM indicate that SHARM-3D has an average accuracy of better than 1%, which along with the high speed of calculations makes it a unique tool for remote-sensing applications in land surface and related atmospheric radiation studies.     

Influence of the environment reflectance on the ultraviolet zenith radiance for cloudless sky

A three-dimensional Monte Carlo code is used to compute the ultraviolet zenith sky radiance; the code is validated by comparison with a successive-orders-of-scattering code. The amplifications of global irradiance, diffuse irradiance, and zenith radiance that are due to multiple reflectances between a snow-covered ground surface and the atmosphere are compared. For an inhomogeneous Lambertian surface, the contribution of the site environment is analyzed; it depends slightly on the atmospheric turbidity and on the surface reflectance distribution. However, in most cases one can expect approximately 12-15% of the reflected photon contribution to come from within 1 km about the observation site, 25-30% come from areas from 1 to 5 km from the site, 43-47% from 5 to 30 km, and still 10-15% reflected at larger distances. An average contribution function is proposed and used to compute an effective reflectance, which permits retrieval of the sky radiance within 2-4% with a one-dimensional model.     

Using shaded filter instruments for measurements of sky radiance: retrieval of the apparent sky-view factor from ultraviolet radiation measurements

There is a growing need for sky radiometric measurements that encapsulate spatial as well as temporal variability. Since the advent of fast data acquisition systems in the 1980s, recent studies have utilized radiation filter instruments deployed in various sky-shading platforms. One cost effective method provides azimuthally averaged sky radiance distribution data at time scales down to fractions of a minute. Successful operation of this scheme requires knowledge of the apparent sky-view factor of the deployed sensor--an artifact of the instrument input optics, instrument filter design, and the instrument shading device employed. We provide a methodology for a determination of the sensor sky-view factor by using the employed shading device and the sun as a light source. The effect of an incorrect determination of instrument sky-view factor is also analyzed in context of the measurements.     

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.     

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.     

Remote sensing of ocean color: assessment of water-leaving radiance bidirectional effects on atmospheric diffuse transmittance

Two factors influence the diffuse transmittance (t) of water-leaving radiance (L(w)) to the top of the atmosphere: the angular distribution of upwelling radiance beneath the sea surface (L(u)) and the concentration and optical properties of aerosols in the atmosphere. We examine these factors and (1) show that the error in L(w) that is induced by assuming L(u) is uniform (i.e., in treating the subsurface reflectance by the water body as Lambertian) is significant in comparison with the other errors expected in L(w) only at low phytoplankton concentration and then only in the blue region of the spectrum; (2) show that when radiance ratios are used in biophysical algorithms the effect of the uniform- L (u) approximation is even smaller; and (3) provide an avenue for introducing accurate computation of the uniform L(u) diffuse transmittance into atmospheric correction algorithms. In an Appendix the reciprocity principle is derived for a medium in which the refractive index is a continuous function of position.     

Estimation of aerosol columnar size distribution and optical thickness from the angular distribution of radiance exiting the atmosphere: simulations

We report the results of simulations in which an algorithm developed for estimation of aerosol optical properties from the angular distribution of radiance exiting the top of the atmosphere over the oceans [Appl. Opt. 33, 4042 (1994)] is combined with a technique for carrying out radiative transfer computations by synthesis of the radiance produced by individual components of the aerosol-size distribution [Appl. Opt. 33, 7088 (1994)], to estimate the aerosol-size distribution by retrieval of the total aerosol optical thickness and the mixing ratios for a set of candidate component aerosol-size distributions. The simulations suggest that in situations in which the true size-refractive-index distribution can actually be synthesized from a combination of the candidate components, excellent retrievals of the aerosol optical thickness and the component mixing ratios are possible. An exception is the presence of strongly absorbing aerosols. The angular distribution of radiance in a single spectral band does not appear to contain sufficient information to separate weakly from strongly absorbing aerosols. However, when two spectral bands are used in the algorithm, retrievals in the case of strongly absorbing aerosols are improved. When pseudodata were simulated with an aerosol-size distribution that differed in functional form from the candidate components, excellent retrievals were still obtained as long as the refractive indices of the actual aerosol model and the candidate components were similar. This underscores the importance of component candidates having realistic indices of refraction in the various size ranges for application of the method. The examples presented all focus on the multiangle imaging spectroradiometer; however, the results should be as valid for data obtained by the use of high-altitude airborne sensors.     

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.     

Effects of stratospheric aerosols and thin cirrus clouds on the atmospheric correction of ocean color imagery: simulations

Using simulations, we determine the influence of stratospheric aerosol and thin cirrus clouds on the performance of the proposed atmospheric correction algorithm for the moderate resolution imaging spectroradiometer (MODIS) data over the oceans. Further, we investigate the possibility of using the radiance exiting the top of the atmosphere in the 1.38-microm water vapor absorption band to remove their effects prior to application of the algorithm. The computations suggest that for moderate optical thicknesses in the stratosphere, i.e., tau(s) < or approximately 0.15, the stratospheric aerosol-cirrus cloud contamination does not seriously degrade the MODIS except for the combination of large (approximately 60 degrees) solar zenith angles and large (approximately 45 degrees) viewing angles, for which multiple-scattering effects can be expected to be particularly severe. The performance of a hierarchy of stratospheric aerosol/cirrus cloud removal procedures for employing the 1.38-microm water vapor absorption band to correct for stratospheric aerosol/cirrus clouds, ranging from simply subtracting the reflectance at 1.38 microm from that in the visible bands, to assuming that their optical properties are known and carrying out multiple-scattering computations of their effect by the use of the 1.38-microm reflectance-derived concentration, are studied for stratospheric aerosol optical thicknesses at 865 nm as large as 0.15 and for cirrus cloud optical thicknesses at 865 nm as large as 1.0. Typically, those procedures requiring the most knowledge concerning the aerosol optical properties (and also the most complex) performed the best; however, for tau(s) < or approximately 0.15, their performance is usually not significantly better than that found by applying the simplest correction procedure. A semiempirical algorithm is presented that permits accurate correction for thin cirrus clouds with tau(s) as large as unity when an accurate estimate of the cirrus cloud scattering phase function is provided, and as large as 0.5 when a coarse approximation to the phase function is used. Given estimates of the stratospheric aerosol optical properties, the implementation of the algorithm by using a set of lookup tables appears to be straightforward.     

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).     

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.     

Dynamical modelling of haematopoiesis: an integrated view over the system in homeostasis and under perturbation

A very high number of different types of blood cells must be generated daily through a process called haematopoiesis in order to meet the physiological requirements of the organism. All blood cells originate from a population of relatively few haematopoietic stem cells residing in the bone marrow, which give rise to specific progenitors through different lineages. Steady-state dynamics are governed by cell division and commitment rates as well as by population sizes, while feedback components guarantee the restoration of steady-state conditions. In this study, all parameters governing these processes were estimated in a computational model to describe the haematopoietic hierarchy in adult mice. The model consisted of ordinary differential equations and included negative feedback regulation. A combination of literature data, a novel divide et impera approach for steady-state calculations and stochastic optimization allowed one to reduce possible configurations of the system. The model was able to recapitulate the fundamental steady-state features of haematopoiesis and simulate the re-establishment of steady-state conditions after haemorrhage and bone marrow transplantation. This computational approach to the haematopoietic system is novel and provides insight into the dynamics and the nature of possible solutions, with potential applications in both fundamental and clinical research.     

Reciprocity principle applicable to reflected radiance measurements and the searchlight problem

In a recent paper by Di Girolamo et al. [J. Geophys. Res. D 103, 8795 (1998)] a heuristic argument was used to derive a reciprocity principle applicable to reflected solar radiation measurements. Here a formal derivation of this reciprocity principle is presented. It is also demonstrated that a purely spatial reciprocal relationship exists between one-dimensional radiative transfer theory and the three-dimensional searchlight problem for horizontally homogeneous media.