Vector Radiative Transfer Theory Research Articles

A comparative study on the efficacy of dual-pol and full-pol ASAR data in radiative transfer modeling for forest above-ground biomass estimation

ABSTRACT In this study, a comprehensive evaluation of the potential of dual-polarization and full-polarization L- and S-band airborne SAR (LS-ASAR) data (ISRO’s dual-frequency airborne SAR mounted on NASA’s Gulfstream III aircraft) in forest above-ground biomass (AGB) estimation has been carried out. The study area comprises the temperate forests of the Lenoir landing site in Southwest Alabama, United States of America. A trunk scattering model based on Vector Radiative Transfer (VRT) theory is used in this study to estimate the AGB. Full-polarization ASAR data inversion retrieves three critical biophysical parameters: tree height, diameter at breast height (DBH), and tree count, whereas with dual-polarization ASAR data, the model is limited to retrieving only two parameters (tree height and DBH). These parameters are then employed in a suitable allometric equation to estimate the AGB over the study area. Validation of the retrieval results is performed through comparison with ground-truth measurements taken from the study site. The findings demonstrate that the inversion of L-band full-polarized data yields the highest correlation (R2 = 0.87, RMSE = 20.37 t/ha), revealing high accuracy in AGB estimation. The L-band dual-polarized data shows a high correlation (R2 = 0.83, RMSE = 30.66 t/ha), indicating reasonable accuracy. However, the S-band data, both full and dual-polarized, reveals weaker correlations with higher RMSE values (R2 = 0.59, RMSE = 55.07 t/ha, and R2 = 0.49, RMSE = 58.31 t/ha, respectively), suggesting a lower degree of reliability. This study emphasizes the pre-eminence of L-band fully polarized data inversion for reliable and accurate AGB estimation while also showing the utility of relatively ubiquitous dual-pol data (L-band) to achieve reasonable accuracy for the same.

A Composite Scattering Model of the Vegetated Ground With a Target

In this study, a composite scattering model of the vegetated ground with a target is developed. In the composite scattering model, a Facet-based Modified Two-scale Model (FMTSM), combining the advantages of Kirchhoff Approximate (KA) and Integral Equation Model (IEM), is established to calculate the electromagnetic (EM) scattering of the rough ground, which can enhance precision and extend application range comparing with the traditional TSM. Based on the FMTSM and Vector Radiative Transfer Theory (VRT), an improved two-layered vegetation model is developed to deal with the EM scattering of vegetated ground. Besides, two typical scattering problems, including the rough ground and vegetated ground, are performed to prove the validity of FMTSM and FMTSM-VRT methods. Simulation results agree well with the measured value. Finally, the composite scattering model of the vegetated ground with a target is proposed by combing the FMTSM-VRT method with Shooting and Bouncing Ray (SBR) algorithm. Meanwhile, the composite scattering characteristics of the vegetated ground with a missile are explored.

Efficient calculation of radiative intensity including the polarization effect in moderately thick atmospheres using a truncation approximation

The computational efficiency of solving the radiative transfer equation is an important issue for remote sensing and monitoring of aerosols and radiation. This study developed a novel calculation method for polarized radiance named Pn-IMS (Improved Multiple and Single scattering approximation by n-th order multiple scattering correction of the forward Peak Pn), consisting of P1-IMS, P2-IMS and P3-IMS. The P1- and P2-IMS methods are extended versions of the TMS (Truncated Multiple and Single scattering approximation) and IMS (Improved Multiple and Single scattering approximation) methods of Nakajima and Tanaka (1988), and are, respectively, the first and secondary order scattering corrections of the forward peak of the scattering phase function in the scalar approximation of the radiation field. We extended these methods to include the polarization effect based on the vector radiative transfer theory. We also developed the third order scattering correction named P3-IMS method and generalized the formula for any n-th order scattering. A series of numerical tests were performed to indicate that the P1-IMS method is accurate enough to reconstruct the Stokes parameters to within 0.2% with a hemispheric Gaussian stream number as low as N = 10 in the hemisphere, except for total radiance. The total radiance in the solar aureole region requires a higher order scattering correction by the P2- and P3-IMS methods. Numerical tests indicated that the P2- and P3-IMS methods have an accuracy within 5 and 1%, respectively, with N = 10 in the 340–1020 nm spectral region in a moderately thick atmosphere at an aerosol optical thickness at 500 nm of < 1. Thus, the P3-IMS method is an efficient calculation method more than the single scattering correction method required N > 20.

FluLCVRT: Reflectance and fluorescence of leaf and canopy modeling based on Monte Carlo vector radiative transfer simulation

Chlorophyll fluorescence simulation is a hot topic in vegetation remote sensing as it allows to link measurements at leaf and canopy scales to the leaf photosynthetic activity. This work tries to simulate light propagation, scattering and fluorescence emission using 3-D vector radiative transfer theory that allows dealing with polarization. The model is called Fluorescence Leaf Canopy Vector Ratiative Transfer, FluLCVRT. Realistic 3-D mock-up of leaf is used to do simulation based on Monte Carlo ray tracing. Fluorescence is created when radiation passes through chloroplasts. The emission is proportional to the absorbed amount of radiation within the latter. Emitted fluorescence exits chloroplast in a random direction, therefore ray tracing is done separately for original radiation and fluorescence. Bidirectional reflectance, transmittance, and fluorescence are estimated at leaf level within a discrete tessellation for input and output angles, that are afterward saved as databases. Then at canopy level, ray tracing is done leaf by leaf, and at each iteration, original radiation is traced in addition to an auxiliary one relative to fluorescence. Both phenomena are governed by their leaf bidirectional distributions and the precalculated databases are used. Results at leaf level point out the variation of the bidirectional distributions. Particularly, reflectance and upward fluorescence are characterized by high specular effect and hot spot peak, respectively. Horizontally polarized radiation emits fluorescence less than the vertical one because its surface highly reflects radiation in the specular direction. Fluorescence in red and near-infrared increases and decreases with respect to chlorophyll content, respectively. Fluorescence is emitted from shallow chloroplasts in upward case. Meanwhile, in the downward one, it is mainly originated from shallow and deep chloroplasts in the red and near-infrared bands, respectively. At canopy level, the same chlorophyll, polarization, and bidirectional effects are observed except that hot spot peak becomes clear in reflectance. When LAI increases, fluorescence saturates at LAI equal 2 and 3 in red and near-infrared. Soil contribution in fluorescence is not too much since it does not diffuse an important amount of radiation in the chlorophyll absorption domain. A comparison between our model and Fluspect at leaf level shows differences in scattering and fluorescence. They are mainly due to the decrease of the chlorophyll efficiency in FluLCVRT due to the clumping of the chloroplasts within cell cytoplasm. Such an effect is not modeled in Fluspect.

Development of a snow kernel to better model the anisotropic reflectance of pure snow in a kernel-driven BRDF model framework

The linear kernel-driven RossThick-LiSparseReciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model was originally developed from the simplified scenarios of continuous and discrete vegetation canopies, and has been widely used to fit multiangle observations of vegetation-soil systems of the land surface in many fields. Although this model was not developed explicitly for snow surfaces, it can capture the geometric-optical effect caused by the shadowing of rugged or undulating snow surfaces. However, in this study, this model has been further developed to better characterize the scattering properties of snow surface, which can also exhibit strongly forward-scattering behavior. This study proposes a new snow kernel to characterize the reflectance anisotropy of pure snow based on the asymptotic radiative transfer (ART) model that assumes snow can be modeled as a semi-infinite, plane-parallel, weakly absorbing light scattering layer. This new snow kernel adopts a correction term with a free parameter α to correct the analytic form of the ART model that has been reported to underestimate observed snow reflectance in the forward-scattering direction in the principal plane (PP), particularly in cases of a large viewing zenith angle (>60°). This snow kernel has now been implemented in the kernel-driven RTLSR BRDF model framework in conjunction with two additional kernels (i.e., the volumetric scattering kernel and geometric-optical scattering kernel) and is validated using observed and simulated multiangle data from three data sources. Pure snow targets were selected from the extensive archive of the Polarization and Directionality of the Earth's Reflectance (POLDER) BRDF data. Antarctic snow field measurements, which were taken from the top of a 32-m-tall tower at Dome C Station and include 6336 spectral bidirectional reflectance factors (BRFs), were also utilized. Finally, a set of simulated BRFs, generated by a hybrid scattering snow model that combines the geometric optics with vector radiative transfer theory, were used to further assess the proposed method. We first retrieve the value of the free parameter α for a comprehensive analysis using single multiangle snow data with a sufficient BRDF sampling. Then, we determine the optimally fixed value of the α parameter as prior information for potential users. The new snow kernel method is shown to be quite accurate, presenting a high correlation coefficient (R2 = ~0.9) and a negligible bias between the modeled BRFs and the various snow BRDF validation data. The finding demonstrates that this snow kernel provides an improved potential compared to that of the original kernel-driven model framework for a pure snow surface in many applications, particularly those involving the global water cycle and radiation budget, where snow cover plays an important role.

Optimized decoy state QKD for underwater free space communication

Quantum cryptography (QC) is envisioned as a solution for global key distribution through fiber optic, free space and underwater optical communication due to its unconditional security. In view of this, this paper investigates underwater free space quantum key distribution (QKD) model for enhanced transmission distance, secret key rates and security. It is reported that secure underwater free space QKD is feasible in the clearest ocean water with the sifted key rates up to 207[Formula: see text]kbps. This paper extends this work by testing performance of optimized decoy state QKD protocol with underwater free space communication model. The attenuation of photons, quantum bit error rate and the sifted key generation rate of underwater quantum communication is obtained with vector radiative transfer theory and Monte Carlo method. It is observed from the simulations that optimized decoy state QKD evidently enhances the underwater secret key transmission distance as well as secret key rates.

Reliable Approach for EM Scattering Calculation from Sea Surface Covered with Foams Based on MFBM and VRT Theory

A reliable approach based on modified facet-based model and Vector Radiative Transfer theory is presented to calculate electromagnetic scattering from a particular electrically large sea surface superimposed with foams, which can handily give both monostatic and bistatic scattering results and could be applied to synthetic aperture radar imagery simulation. The facet model is derived from Fuks’ first-order small perturbation method function, and then the Kirchhoff model is introduced to revise the results in view of the dependency on cut-off wave number at near vertical incidence angles. Additionally, the contributions of foams are taken into consideration on the basis of Vector Radiative Transfer theory. The accuracy and superiority of this proposed approach are demonstrated in comparison with traditional facet model, which illustrates that the results of this approach agree better with experimental results. Moreover, several examples are given to verify that the proposed approach is of more significance at large incidence angles and high wind speed.

Rearch on Electromagnetic Scattering from ocean covered by foams

Back scattering of ocean surface is investigated by considering the foams coverage on its surface. Firstly, by adopting modified two-scale mode and the vector radiative transfer theory, zero and first order scattering coefficients are obtained by solving VRT equations. Then, MIE theory is used to get the scattering from foams, and fraction of foams coverage is analyzed by changing parameters of wind speed and temperature difference of ocean-air. Finally, the modified two-scale model and algorithms are verified by comparing its results with measured results, and simulations of calculating back scattering from ocean surface with and without foams are carried out. The conclusion is obtained that wind speed has different influence on back scattering under different incident angles.

Research on electromagnetic scattering from ocean surface with foams by the modified facet-model

ABSTRACTThe ocean surface electromagnetic (EM) scattering properties have important applications in marine environmental monitoring and detection of target on the sea. In this article, the accurate model is built to calculate the permittivity of sea water at different sea areas with foams. The relationships between the foam coverage and air-sea temperature and wind speed are analyzed. Then based on the facet-model theory, the modified two-scale model (MTSM) and Vector Radiative Transfer (VRT) theory, the modified facet-based two-scale model (MFBTSM) with foams is presented. To make the scattering model conform better to the practice, the cut-off wavenumber at actual wind speed and frequency of incident wave is considered. Based on satellite data of ocean salinity and temperature at the Western Pacific and Southeast coast, the electromagnetic scattering properties from complex ocean surface with foams at different sea areas are analyzed. On this basis, the Brewster effect at different sea areas is further analyzed. The producing mechanism and changing rules of ocean surface Brewster effect are summarized and analyzed.

Photopolarimetric properties of leaf and vegetation covers over a wide range of measurement directions

The optical scattering property of the target is the essential signal for passive remote sensing applications. To deepen our understanding of the light reflected from vegetation, we present results of photopolarimetric laboratory measurements from single leaf and two vegetation covers (planophile and erectophile) over a wide range of viewing directions. The bidirectional polarized reflectance factor (BPRF) was used to characterize the polarization property of our samples. We observed positive and negative polarization (−BPRFQ) of all samples in the forward scattering and backward scattering directions, respectively. Based on the comparison of the BPRF among single leaf, planophile vegetation and erectophile vegetation, our measurements demonstrate that the orientation of the leaf is a key factor in describing the amount of polarization in the forward scattering direction. Our measurements also validated certain model results stating that (1) specular reflection generates a portion of polarization in the forward scattering direction and diffuses scattering of polarized light in all hemisphere directions, (2) BPRFU is anti-symmetric in the principal plane from a recent study in which the authors simulated the polarized reflectance of vegetation cover using the vector radiative transfer theory. These photopolarimetric measurement results, which can be completely explained by the theoretical results, are useful in remote sensing applications to vegetation.

Surface and Volumetric Scattering by Rough Dielectric Boundary at Terahertz Frequencies

Materials that could be considered as homogeneous and smooth at microwave frequencies may begin to present surface and volumetric scattering behaviors in the terahertz (THz) band. In this paper, theoretical endeavors are presented to explain the surface and volumetric scattering phenomena observed in the experimental data. We first apply the integral equation method (IEM) to fit the measured data of an aluminum plate. Good agreements prove the applicability and superiority of IEM to metallic materials. Nevertheless, for dielectric materials, the inner microstructures or particles, such as the rusty textures or silicon carbide particles whose sizes are comparable to the THz wavelength, need to be taken into account. We found that for dielectric materials, it can only be fit to the experimental data by using the vector radiative transfer theory combined with IEM. The results show that, for metallic materials, we only need to consider the scattering effect due to the surface roughness. While for the materials that present dielectric features, it needs to consider the influence of the inner microstructures or particles. The two modeling methods presented in this paper are suitable to solve the backscattering problems in the THz band, to predict the bistatic scattering coefficients, and can be extended to apply to real-world targets.

Equivalence of internal and external mixture schemes of single scattering properties in vector radiative transfer.

Polarized radiation fields in a turbid medium are influenced by single-scattering properties of scatterers. It is common that media contain two or more types of scatterers, which makes it essential to properly mix single-scattering properties of different types of scatterers in the vector radiative transfer theory. The vector radiative transfer solvers can be divided into two basic categories: the stochastic and deterministic methods. The stochastic method is basically the Monte Carlo method, which can handle scatterers with different scattering properties explicitly. This mixture scheme is called the external mixture scheme in this paper. The deterministic methods, however, can only deal with a single set of scattering properties in the smallest discretized spatial volume. The single-scattering properties of different types of scatterers have to be averaged before they are input to deterministic solvers. This second scheme is called the internal mixture scheme. The equivalence of these two different mixture schemes of scattering properties has not been demonstrated so far. In this paper, polarized radiation fields for several scattering media are solved using the Monte Carlo and successive order of scattering (SOS) methods and scattering media contain two types of scatterers: Rayleigh scatterers (molecules) and Mie scatterers (aerosols). The Monte Carlo and SOS methods employ external and internal mixture schemes of scatterers, respectively. It is found that the percentage differences between radiances solved by these two methods with different mixture schemes are of the order of 0.1%. The differences of Q/I, U/I, and V/I are of the order of 10-5∼10-4, where I, Q, U, and V are the Stokes parameters. Therefore, the equivalence between these two mixture schemes is confirmed to the accuracy level of the radiative transfer numerical benchmarks. This result provides important guidelines for many radiative transfer applications that involve the mixture of different scattering and absorptive particles.

Multiple Scattering Effects With Cyclical Correction in Active Remote Sensing of Vegetated Surface Using Vector Radiative Transfer Theory

The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical thickness and scattering albedo of the vegetation layer are large. When both the albedo and the optical thickness exceed 0.4, higher orders contribute significantly (e.g., vertical polarization at L-band). The approach is applied to vegetated surfaces using typical crop structure for backscattering from L-band to Ku-band. For corn fields at L-band, multiple scattering effects are more important for vertical scattered wave with vertical incidence (VV). For example, when vegetation water content (VWC) is $3 \text{kg}/{\text{m}}^2$ , the deviation between first order and multiple scattering for corn field for VV could be 3.5 dB while 0.7 dB for horizontal scattered wave with horizontal incidence (HH). The iterative approach also allows the separation of the contribution to backscattering from each scattering order and scattering mechanism. Each scattering mechanism is associated with a unique scattering path. By examining the duality of the paths, we are able to identify the cyclical terms with existence of a reflective boundary. The cyclical correction to the backscattering accounts for backscattering enhancement effects on the copolarization by a factor of two. The approach is validated against the SMAPVEX12 L-band corn dataset over the entire crop growth and large soil moisture variations. The model prediction matches the observation with 1.93 and 1.46 dB root-mean-square error (RMSE) for VV and HH, respectively, while correlations are 0.67 and 0.88, respectively. Time-series retrieval is also applied successfully for both soil moisture and VWC with 0.06 $\text{cm}^{3}/\text{cm}^{3}$ and $0.44 \text{kg}/\text{m}^{2}$ RMSE, respectively, while correlations are 0.7 and 0.92, respectively. For large VWC, this approach corrects the underestimated backscatters in the single scattering caused by large attenuation.

A New Hybrid Snow Light Scattering Model Based on Geometric Optics Theory and Vector Radiative Transfer Theory

Light scattering models of snow are very important for the remote sensing of snow. Many previous models have used unrealistic assumptions about the snow particle shape and microstructure. In this paper, a new model is proposed, wherein a bicontinuous medium is used to simulate the snow microstructure, and geometric optics theory is used in combination with the Monte Carlo method to simulate the scattering properties of snow. Then, using the radiative transfer equation, the snow reflectance, including the polarized reflectance, can be simulated. Unlike other models that use Monte Carlo ray tracing, the new model is computationally efficient and can be used for massive simulations and practical applications. The simulation results of the new model are compared with the ground measurements and simulation results of a traditional model based on the Mie theory. Through validations and comparisons, the new model is shown to demonstrate a significantly improved capability in simulating the bidirectional reflectance of snow. The importance of the grain shape and microstructure modeling in the light scattering models of snow is confirmed by the comparison of the simulation results.

Future Ocean Scatterometry: On the Use of Cross-Polar Scattering to Observe Very High Winds

This paper investigates the potential of cross polarization (VH) to extend the upper dynamic range of the wind measurements from ocean scatterometry. An analytical model for the VH polar scattering of the microwave radiation from ocean is proposed. The model combines the second-order small-slope approximation theory with the vector radiative transfer theory to obtain a statistical expression of the ocean scattering in presence of foam. Cross-polarized backscatter signals from RADARSAT-2 C-band synthetic aperture radar imagery, which were acquired during severe weather events, and collocated/time-coincident stepped-frequency microwave radiometer wind measurements by the National Oceanic and Atmospheric Administration's hurricane-hunter aircraft are used to verify the model. The validity of the model has been also proven against European Centre for Medium-Range Weather Forecasts forecasted winds. The results suggest that the present scattering model can be a valuable tool for understanding VH at very high wind speeds and for interpreting the data collected by the future dual polarimetric wind scatterometer (SCA), which will be flown on the Second Generation Meteorological Operational satellite program (MetOp-SG) as an evolution of the Advanced Scatterometer instrument on board MetOp.

Backscattering modeling of wheat using vector radiative transfer theory

A microwave backscattering model of winter wheat based on the vector radiative transfer theory has been established. The model focused on the distribution of wheat ears that are directly related to the yield. In addition, characteristics of the wheat growth have been adequately considered. Compared to the measured values, the model effectively simulated the microwave backscattering characteristics of winter wheat. Intercomparison of the winter wheat model and modified Michigan Microwave Canopy Scattering (MIMICS) model using experimental data shows that the winter wheat model had better cross-polarized simulation results than the modified MIMICS model did. This improvement was attributed to the special attention paid to the cross-polarization after the booting stage. After booting, wheat ear started to appear and grow in size. Wheat ear contributed greatly to cross-polarized backscatter. The inclusion of the ear as one of the model components was significant in modeling the observed cross-polarized backscattering.

Channel analysis for single photon underwater free space quantum key distribution.

We investigate the optical absorption and scattering properties of underwater media pertinent to our underwater free space quantum key distribution (QKD) channel model. With the vector radiative transfer theory and Monte Carlo method, we obtain the attenuation of photons, the fidelity of the scattered photons, the quantum bit error rate, and the sifted key generation rate of underwater quantum communication. It can be observed from our simulations that the most secure single photon underwater free space QKD is feasible in the clearest ocean water.

The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI): a new tool for aerosol and cloud remote sensing

Abstract. The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) is an eight-band (355, 380, 445, 470, 555, 660, 865, 935 nm) pushbroom camera, measuring polarization in the 470, 660, and 865 nm bands, mounted on a gimbal to acquire multiangular observations over a ±67° along-track range. The instrument has been flying aboard the NASA ER-2 high altitude aircraft since October 2010. AirMSPI employs a photoelastic modulator-based polarimetric imaging technique to enable accurate measurements of the degree and angle of linear polarization in addition to spectral intensity. A description of the AirMSPI instrument and ground data processing approach is presented. Example images of clear, hazy, and cloudy scenes over the Pacific Ocean and California land targets obtained during flights between 2010 and 2012 are shown, and quantitative interpretations of the data using vector radiative transfer theory and scene models are provided to highlight the instrument's capabilities for determining aerosol and cloud microphysical properties and cloud 3-D spatial distributions. Sensitivity to parameters such as aerosol particle size distribution, ocean surface wind speed and direction, cloud-top and cloud-base height, and cloud droplet size is discussed. AirMSPI represents a major step toward realization of the type of imaging polarimeter envisioned to fly on NASA's Aerosol-Cloud-Ecosystem (ACE) mission in the next decade.

Monte Carlo study on pulse response of underwater optical channel

Pulse response of the underwater wireless optical channel is significant for the analysis of channel capacity and error probability. Traditional vector radiative transfer theory (VRT) is not able to deal with the effect of receiving aperture. On the other hand, general water tank experiments cannot acquire an accurate pulse response due to the limited time resolution of the photo-electronic detector. We present a Monte Carlo simulation model to extract the time-domain pulse response undersea. In comparison with the VRT model, a more accurate pulse response for practical ocean communications could be achieved through statistical analysis of the received photons. The proposed model is more reasonable for the study of the underwater optical channel.

Modeling polarimetric radar scattering from the lunar surface: Study on the effect of physical properties of the regolith layer

[1] A theoretical model for radar scattering from the lunar regolith using the vector radiative transfer theory for random media has been developed in order to aid in the interpretation of Mini-SAR data from the Chandrayaan-1 and Lunar Reconnaissance Orbiter missions. The lunar regolith is represented as a homogeneous fine-grained layer with rough upper and lower parallel interfaces that possesses embedded inclusions with a different dielectric constant. Our model considers five scattering mechanisms in the regolith layer: diffuse scattering from both the surface and subsurface, volume scattering from buried inclusions, and the interactions of scattering between buried inclusions and the rough interfaces (both the lunar surface and subsurface). Multiple scattering between buried inclusions and coherent backscatter opposite effect are not considered in the current model. The modeled radar scattering coefficients are validated using numerical finite difference time domain simulations and are compared with incident angle–averaged Earth-based radar observations of the Moon. Both polarized and depolarized radar backscattering coefficients and the circular polarization ratio (CPR) are calculated as a function of incidence angle, regolith thickness, surface and subsurface roughness, surface slope, abundance and shape of buried rocks, and the FeO+TiO2 content of the regolith. Simulation results show that the polarized (opposite sense) radar echo strength at S and X bands is mostly dominated by scattering from the rough surface and buried rocks, while the depolarized (same sense) radar echo strength is dominated by scattering from buried rocks or ice inclusions. Finally, to explore the expected polarimetric signature of ice in the polar permanently shadowed areas, four parametric regolith models are considered and the possibility of detecting diffuse ice inclusions by the CPR is addressed. Our study suggests that detection of ice inclusions at the lunar poles using solely the CPR will be difficult given the small dielectric contrast between the regolith and ice.