New Treatment of Strongly Anisotropic Scattering Phase Functions: The Delta-M+ Method

The treatment of strongly anisotropic scattering phase functions is still a challenge for accurate radiance computations. The new delta-M+ method resolves this problem by introducing a reliable, fast, accurate, and easy-to-use Legendre expansion of the scattering phase function with modified moments. Delta-M+ is an upgrade of the widely used delta-M method that truncates the forward scattering peak with a Dirac delta function, where the + symbol indicates that it essentially matches moments beyond the first M terms. Compared with the original delta-M method, delta-M+ has the same computational efficiency, but for radiance computations, the accuracy and stability have been increased dramatically

Inferring inherent optical properties and water constituent profiles from apparent optical properties

The BP09 experiment conducted by the Centre for Maritime Research and Experimentation in the Ligurian Sea in March 2009 provided paired vertical profiles of nadir-viewing radiances Lu(z) and downward irradiances Ed(z) and inherent optical properties (IOPs, absorption, scattering and backscattering coefficients). An inversion algorithm was implemented to retrieve IOPs from apparent optical properties (AOPs, radiance reflectance RL, irradiance reflectance RE and diffuse attenuation coefficient Kd) derived from the radiometric measurements. Then another inversion algorithm was developed to infer vertical profiles of water constituent concentrations, including chlorophyll-a concentration, non-algal particle concentration, and colored dissolved organic matter from the retrieved IOPs based on a bio-optical model. The algorithm was tested on a synthetic dataset and found to give reliable results with an accuracy better than 1%. When the algorithm was applied to the BP09 dataset it was found that good retrievals of IOPs could be obtained for sufficiently deep waters, i.e. for Lu(z) and Ed(z) measurements conducted to depths of 50 m or more. This requirement needs to be satisfied in order to obtain a good estimation of the backscattering coefficient. For such radiometric measurements a correlation of 0.88, 0.96 and 0.93 was found between retrieved and measured absorption, scattering and backscattering coefficients, respectively. A comparison between water constituent values derived from the measured IOPs and in-situ measured values, yielded a correlation of 0.80, 0.78, and 0.73 for chlorophyll-a concentration, non-algal particle concentration, and absorption coefficient of colored dissolved organic matter at 443 nm, respectively. This comparison indicates that adjustments to the bio-optical model are needed in order to obtain a better match between inferred and measured water constituent values in the Ligurian Sea using the methodology developed in this paper

Radiation, Smoke and Clouds Observed in the Southeastern Atlantic With the Research Scanning Polarimeter During ORACLES

The ObseRvations of Aerosols above Clouds and their interactions (ORACLES) project is making a series of field deployments to the southeastern Atlantic with NASA ER-2 and P3 aircraft to acquire both detailed remote sensing observations and in situ measurements of the aerosols and clouds in that region. This area is home to one of the largest low-level cloud decks on Earth that is seasonally affected by vast plumes of smoke from biomass burning, which in effect provides a natural experiment testing the radiative and microphysical interactions between the smoke and the clouds. The downward solar radiation at the surface, or cloud top, is always reduced by the presence of smoke. However, whether the amount of sunlight reflected back out to space is increased, or decreased by the presence of smoke is sensitively dependent on the brightness of the clouds and the fraction of light that the smoke absorbs each time light hits a smoke particle. In this study we use data from the Research Scanning Polarimeter, an along track scanning instrument, that provides measurements of the Stokes parameters I, Q and U at 410, 470, 555, 670, 865, 960, 1590, 1880 and 2260 nm at 150 viewing angles over a range of +/- 60 from nadir for each contiguous sub-aircraft pixel (~ 300 m in size). A retrieval algorithm is applied to the data acquired with a table look up technique, similar to that of the operational POLDER algorithm, to provide a first guess of the complex refractive index, optical depth and size distribution of the smoke particles together with cloud droplet size and optical depth. A subsequent iterative fitting procedure, where the fact that the doubling/adding method allows the construction of the Green's function for the radiative transfer equation, is used to obtain an efficient and statistically optimal estimate of the aerosol and cloud retrieval parameters. These retrieval parameters are evaluated against in situ observations, when available, and the optical depth and intensive lidar variables that are measured by the High Spectral Resolution Lidar 2. Finally, the aerosol and cloud retrievals are used to evaluate the variations in top of the atmosphere, surface/cloud top shortwave radiative forcing and atmospheric absorption that are caused by variations in the smoke and clouds

A novel approach to solve forward/inverse problems in remote sensing applications

Inversion of electromagnetic (EM) signals reflected from or transmitted through a medium, or emitted by it due to internal sources can be used to investigate the optical and physical properties of a variety of scattering/absorbing/emitting materials. Such media encompass planetary atmospheres and surfaces (including water/snow/ice), and plant canopies. In many situations the signals emerging from such media can be described by a linear transport equation which in the case of EM radiation is the radiative transfer equation (RTE). Solutions of the RTE can be used as a forward model to solve the inverse problem to determine the medium state parameters giving rise to the emergent (reflected/transmitted/emitted) EM signals. A novel method is developed to determine layer-by-layer contributions to the emergent signals from such stratified, multilayered media based on the solution of the pertinent RTE. As a specific example of how this approach may be applied, the radiation reflected from a multilayered atmosphere is used to solve the problem relevant for EM probing by a space-based lidar system. The solutions agree with those obtained using the standard lidar approach for situations in which single scattering prevails, but this novel approach also yields reliable results for optically thick, multiple scattering aerosol and cloud layers that cannot be provided by the traditional lidar approach

Linking lidar multiple scattering profiles to snow depth and snow density: an analytical radiative transfer analysis and the implications for remote sensing of snow

Lidar multiple scattering measurements provide the probability distribution of the distance laser light travels inside snow. Based on an analytic two-stream radiative transfer solution, the present study demonstrates why/how these lidar measurements can be used to derive snow depth and snow density. In particular, for a laser wavelength with little snow absorption, an analytical radiative transfer solution is leveraged to prove that the physical snow depth is half of the average distance photons travel inside snow and that the relationship linking lidar measurements and the extinction coefficient of the snow is valid. Theoretical formulas that link lidar measurements to the extinction coefficient and the effective grain size of snow are provided. Snow density can also be derived from the multi-wavelength lidar measurements of the snow extinction coefficient and snow effective grain size. Alternatively, lidars can provide the most direct snow density measurements and the effective discrimination between snow and trees by adding vibrational Raman scattering channels

Retrievals of Cloud Droplet Size from the Research Scanning Polarimeter Data: Validation Using In Situ Measurements

We present comparisons of cloud droplet size distributions (DSDs) retrieved from the research scanning polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). The airborne portion of this field experiment was based out of St. John's airport, Newfoundland, Canada with the focus of this paper being on the deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring the polarized and total reflectance in 9 spectral channels. Its uniquely high angular resolution allows for characterization of liquid water droplet sizes using the rainbow structure observed in the polarized reflectance over the scattering angle range from 135 to 165.degrees The rainbow is dominated by single scattering of light by cloud droplets, so its structure is characteristic specifically of the droplet sizes at cloud top (within unit optical depth into the cloud, equivalent to approximately 50m). A parametric fitting algorithm applied to the polarized reflectance provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, the Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution itself. The latter is important in the case of clouds with complex microphysical structure, or multiple layers of cloud, which result in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparisons between remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was near the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons generally show good agreement (better than 1 micron for effective radius and in most cases better than 0.02 for effective variance) with deviations explainable by the position of the aircraft within the cloud, or by the presence of additional cloud layers between the cloud being sampled by the in situ instrumentation and the altitude of the remote sensing segment. In the latter case, the multi-modal DSDs retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The results of these comparisons provide a rare validation of polarimetric droplet size retrieval techniques, demonstrating their accuracy and robustness and the potential of satellite data of this kind on a global scale