Monte Carlo Radiative Transfer Model Research Articles

A low-time complexity semi-analytic Monte Carlo radiative transfer model: Application to optical characteristics of complex spatial targets

The Monte Carlo method (MCM) is one of the most accurate methods for calculating the optical characteristics of spatial targets. However, there are two limitations when using the MCM to build a dataset for a priori phenomenology. One is the multiple scattering effects. The other is photon number configurations in multiple random links (e.g., various irradiance sources, spatiotemporal spectra, complex geometries and structures). Without a reasonable photon number configuration, the dataset's granularity, image quality and computation time will not be compatible. The present work proposes a semi-analytical Monte Carlo radiative transfer model (Semi-MCM), which offers a low order of magnitude time complexity when calculating the scattering properties of the complex spatial target. First, the Semi-MCM was validated theoretically and procedurally. Subsequently, the efficiency of the Semi-MCM is evaluated. The Semi-MCM show a standard double-log-linear relationship between the time complexity and uncertainty. The correlation coefficient is greater than 0.9987. It implies that time complexity can be represented analytically by the single point estimate during calculation. On this basis, the number of photons required for each probabilistic link can be predicted and allocated adaptively to achieve coordination of the probabilistic links. Finally, the distortion from multiple scattering effects is analyzed in terms of the peak signal-to-noise ratio (PSNR). The distortion caused by self-emission is non-negligible, with PSNR in the range of 20–40 dB. For the far-field illumination processes of Lambert, the PSNR is in the range of 30–40 dB, i.e., the distortion is perceptible but acceptable. The method can provide a basis for generating samples in prior phenomenology and analyzing the influences of multiple scattering effects.

Impact of 3D cloud structures on the atmospheric trace gas products from UV–Vis sounders – Part 2: Impact on NO2 retrieval and mitigation strategies

Abstract. Operational retrievals of tropospheric trace gases from space-borne spectrometers are based on one-dimensional radiative transfer models. To minimize cloud effects, trace gas retrievals generally implement a simple cloud model based on radiometric cloud fraction estimates and photon path length corrections. The latter relies on measurements of the oxygen collision pair (O2–O2) absorption at 477 nm or on the oxygen A-band around 760 nm to determine an effective cloud height. In reality however, the impact of clouds is much more complex, involving unresolved sub-pixel clouds, scattering of clouds in neighbouring pixels, and cloud shadow effects, such that unresolved three-dimensional effects due to clouds may introduce significant biases in trace gas retrievals. Although clouds have significant effects on trace gas retrievals, the current cloud correction schemes are based on a simple cloud model, and the retrieved cloud parameters must be interpreted as effective values. Consequently, it is difficult to assess the accuracy of the cloud correction only based on analysis of the accuracy of the cloud retrievals, and this study focuses solely on the impact of the 3D cloud structures on the trace gas retrievals. In order to quantify this impact, we study NO2 as a trace gas example and apply standard retrieval methods including approximate cloud corrections to synthetic data generated by the state-of-the-art three-dimensional Monte Carlo radiative transfer model MYSTIC. A sensitivity study is performed for simulations including a box cloud, and the dependency on various parameters is investigated. The most significant bias is found for cloud shadow effects under polluted conditions. Biases depend strongly on cloud shadow fraction, NO2 profile, cloud optical thickness, solar zenith angle, and surface albedo. Several approaches to correct NO2 retrievals under cloud shadow conditions are explored. We find that air mass factors calculated using fitted surface albedo or corrected using the O2–O2 slant column density can partly mitigate cloud shadow effects. However, these approaches are limited to cloud-free pixels affected by surrounding clouds. A parameterization approach is presented based on relationships derived from the sensitivity study. This allows measurements to be identified for which the standard NO2 retrieval produces a significant bias and therefore provides a way to improve the current data flagging approach.

Can the Violent Merger of White Dwarfs Explain the Slowest Declining Type Ia Supernova SN 2011aa?

We present optical observations and Monte Carlo radiative transfer modeling of the Type Ia supernova (SN Ia) SN 2011aa. With a Δm 15(B) of 0.59 ± 0.07 mag and a peak magnitude M B of −19.30 ± 0.27 mag, SN 2011aa has the slowest decline rate among SNe Ia. The secondary maximum in the I band is absent or as equally bright as the primary maximum. The velocity of C ii is lower than the velocity of Si ii. This indicates either the presence of C at lower velocities than Si or a line-of-sight effect. Application of Arnett’s radiation diffusion model to the bolometric light curve indicates a massive ejecta M ej 1.8–2.6 M ⊙. The slow decline rate and large ejecta mass, with a normal peak magnitude, are well explained by a double degenerate, violent merger explosion model. The synthetic spectra and light curves generated with SEDONA considering a violent merger density profile match the observations.

FORTE Measurements of Global Optical Lightning Waveforms and Implications for Optical Lightning Detection

AbstractLightning processes generate a diverse collection of optical pulses from current traversing the lightning channels. These signals are then broadened spatially and temporally via scattering in the clouds. The resulting waveforms measured from space with instruments like the photodiode detector (PDD) on the Fast On‐orbit Recording of Transient Events (FORTE) satellite have a variety of shapes. In this study, we use coincident optical and Radio‐Frequency measurements to document the properties of optical PDD waveforms associated with different types of lightning, estimate delays from scattering in the clouds, and comment on how pulse shape impacts optical lightning detection. We find that the attributes of optical pulses recorded by the PDD are consistent with prior studies, but vary globally and with event amplitude. The most powerful lightning tends to be single‐peaked with faster rise times (median: ∼100 µs) and shorter effective widths (median: ∼400 µs) than normal lightning. Particularly dim events, meanwhile, include cases of broad optical waveforms with sustained optical emission throughout the PDD record, which the pixelated FORTE Lightning Location System (LLS) instrument has difficulty detecting. We propose that this is due to the optical signal being divided between individual LLS pixels that are each, individually, not bright enough to trigger. We use PDD waveforms and Monte Carlo radiative transfer modeling to demonstrate that increasing the temporal and spatial resolution of a pixelated lightning imager will make it more difficult to detect these broad/dim pulses as their energy becomes divided between additional pixels/integration frames.

Effective parameterization of absorption by gaseous species and unknown UV absorber in 125–400 nm region of Venus atmosphere

We present an effective parameterization of molecular absorption of shortwave solar radiation in Venus atmosphere. It is addressed to general circulation modeling to accelerate radiative transfer calculations in the spectral interval 125 – 400 nm (25000 – 80000 cm−1). In F-UV and M-UV regions strong absorption of CO2 and SO2 enables to parameterize gaseous absorption with only three effective cross-sections. In N-UV region absorption of SO2 and unknown UV absorber are parameterized with six effective cross-sections for each species. For treatment of Rayleigh scattering and optical properties of Venus clouds eight effective spectral points are recommended. The parameterizations were validated by the original reference line-by-line Monte-Carlo radiative transfer model. The outcome of the validation shows discrepancy in fluxes less than 3%. Thus, it takes only eight-fold solution of radiative transfer equations to correctly describe solar fluxes and heating rates in the whole ultraviolet region.

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Orion Protostars. VI. Insights from Radiative Transfer Modeling

We present Markov Chain Monte Carlo radiative transfer modeling of a joint ALMA 345 GHz and spectral energy distribution data set for a sample of 97 protostellar disks from the VLA and ALMA Nascent Disk and Multiplicity Survey of Orion Protostars. From this modeling, we derive disk and envelope properties for each protostar, allowing us to examine the bulk properties of a population of young protostars. We find that disks are small, with a median dust radius of au and a median dust mass of M ⊕. We find no statistically significant difference between most properties of Class 0, Class I, and flat-spectrum sources with the exception of envelope dust mass and inclination. The distinction between inclination is an indication that the Class 0/I/flat-spectrum system may be difficult to tie uniquely to the evolutionary state of protostars. When comparing with Class II disk dust masses in Taurus from similar radiative transfer modeling, we further find that the trend of disk dust mass decreasing from Class 0 to Class II disks is no longer present, though it remains unclear whether such a comparison is fair owing to differences in star-forming region and modeling techniques. Moreover, the disks we model are broadly gravitationally stable. Finally, we compare disk masses and radii with simulations of disk formation and find that magnetohydrodynamical effects may be important for reproducing the observed properties of disks.

Scattering and sublimation: a multiscale view of µm-sized dust in the inclined disc of HD 145718

ABSTRACT We present multi-instrument observations of the disc around the Herbig Ae star, HD 145718, employing geometric and Monte Carlo radiative transfer models to explore the disc orientation, the vertical and radial extent of the near-infrared (NIR) scattering surface, and the properties of the dust in the disc surface and sublimation rim. The disc appears inclined at 67–71°, with position angle, PA = −1.0 to 0.6°, consistent with previous estimates. The NIR scattering surface extends out to ${\sim}75\,$ au and we infer an aspect ratio, hscat(r)/r ∼ 0.24 in J band; ∼0.22 in H band. Our Gemini Planet Imager images and VLTI + CHARA NIR interferometry suggest that the disc surface layers are populated by grains ≳λ/2π in size, indicating these grains are aerodynamically supported against settling and/or the density of smaller grains is relatively low. We demonstrate that our geometric analysis provides a reasonable assessment of the height of the NIR scattering surface at the outer edge of the disc and, if the inclination can be independently constrained, has the potential to probe the flaring exponent of the scattering surface in similarly inclined (i ≳ 70°) discs. In re-evaluating HD 145718’s stellar properties, we found that the object’s dimming events – previously characterized as UX Or and dipper variability – are consistent with dust occultation by grains larger, on average, than found in the ISM. This occulting dust likely originates close to the inferred dust sublimation radius at $0.17\,$ au.

On the influence of erect shrubs on the irradiance profile in snow

Abstract. The warming-induced expansion of shrubs in the Arctic is transforming snowpacks into a mixture of snow, impurities and buried branches. Because snow is a translucent medium into which light penetrates up to tens of centimetres, buried branches may alter the snowpack radiation budget with important consequences for the snow thermal regime and microstructure. To characterize the influence of buried branches on radiative transfer in snow, irradiance profiles were measured in snowpacks with and without shrubs near Umiujaq in the Canadian Low Arctic (56.5∘ N, 76.5∘ W) in November and December 2015. Using the irradiance profiles measured in shrub-free snowpacks in combination with a Monte Carlo radiative transfer model revealed that the dominant impurity type was black carbon (BC) in variable concentrations up to 185 ng g−1. This allowed the separation of the radiative effects of impurities and buried branches. Irradiance profiles measured in snowpacks with shrubs showed that the impact of buried branches was local (i.e. a few centimetres around branches) and only observable in layers where branches were also visible in snowpit photographs. The local-effect hypothesis was further supported by observations of localized melting and depth hoar pockets that formed in the vicinity of branches. Buried branches therefore affect snowpack properties, with possible impacts on Arctic flora and fauna and on the thermal regime of permafrost. Lastly, the unexpectedly high BC concentrations in snow are likely caused by nearby open-air waste burning, suggesting that cleaner waste management plans are required for northern community and ecosystem protection.

Radiative Transfer Modeling of an SN 1987A Light Echo—AT 2019xis

Abstract We use a Monte Carlo radiative transfer model (MCRTM) to simulate the UBVRI light curves, images, and linear polarization of a light echo from supernova SN 1987A in the Large Magellanic Cloud (LMC) using various dust cloud shapes, sizes, and optical properties. We compare the theoretical simulations to the observations of AT 2019xis, a light echo detected at a large angular distance (4.′05) from SN 1987A. We estimate the size and optical thickness of the dust cloud based on the simulation results and the observations of the Optical Gravitational Lensing Experiment (OGLE-IV) Transient Detection System (OTDS) I-band light curve. The mass of the dust cloud is calculated using the estimated size, optical thickness, and extinction coefficient. If the dust cloud is assumed to correspond to a gas-to-dust ratio of 300, the total mass of the dust cloud is approximately 7.8–9.3 M ⊙. Based on these theoretical models, we show that the morphological shapes of the light echoes in the wavelength range of or shorter than the U band to be very different from those in the longer wavelength bands, and the difference carries important information on the early UV radiation of SN 1987A.

Study of a laser echo in an inhomogeneous dust environment with a continuous field Monte Carlo radiative transfer model.

A continuous field Monte Carlo radiative transfer model with an improved semianalytic approach is developed to study laser propagation in an inhomogeneous dust environment. In the proposed model, the photon step size can vary with the mass concentration of the dust environment. Additionally, the scattering properties of the dust particles are calculated with the T-matrix method and the T-matrix scattering phase function is applied to the Monte Carlo simulation with a rejection method. Using this model, the influences of the particle sizes and shapes on the backscattering properties are studied. Finally, the laser echoes simulated by our proposed model are compared with those of traditional Monte Carlo method and experimental results. Different mass concentration distributions indeed influence the simulated laser echo. The simulated results (of our proposed model) agree well with the measured data, demonstrating the effectiveness and accuracy of our approach for inhomogeneous media.

Remote Sensing of Dispersed Oil Pollution in the Ocean-The Role of Chlorophyll Concentration.

In the contrary to surface oil slicks, dispersed oil pollution is not yet detected or monitored on regular basis. The possible range of changes of the local optical properties of seawater caused by the occurrence of dispersed oil, as well as the dependencies of changes on various physical and environmental factors, can be estimated using simulation techniques. Two models were combined to examine the influence of oceanic water type on the visibility of dispersed oil: the Monte Carlo radiative transfer model and the Lorenz–Mie model for spherical oil droplets suspended in seawater. Remote sensing reflectance, Rrs, was compared for natural ocean water models representing oligotrophic, mesotrophic and eutrophic environments (characterized by chlorophyll-a concentrations of 0.1, 1 and 10 mg/m3, respectively) and polluted by three different kinds of oils: biodiesel, lubricant oil and crude oil. We found out that dispersed oil usually increases Rrs values for all types of seawater, with the highest effect for the oligotrophic ocean. In the clearest studied waters, the absolute values of Rrs increased 2–6 times after simulated dispersed oil pollution, while Rrs band ratios routinely applied in bio-optical models decreased up to 80%. The color index, CI, was nearly double reduced by dispersed biodiesel BD and lubricant oil CL, but more than doubled by crude oil FL.

An HST Survey of Protostellar Outflow Cavities: Does Feedback Clear Envelopes?

Abstract We study protostellar envelope and outflow evolution using Hubble Space Telescope NICMOS or WFC3 images of 304 protostars in the Orion molecular clouds. These near-IR images resolve structures in the envelopes delineated by the scattered light of the central protostars with 80 au resolution, and they complement the 1.2 μm to 870 μm spectral energy distributions (SEDs) obtained with the Herschel Orion Protostar Survey program. Based on their 1.60 μm morphologies, we classify the protostars into five categories: nondetections, point sources without nebulosity, bipolar cavity sources, unipolar cavity sources, and irregulars. We find point sources without associated nebulosity are the most numerous, and show through monochromatic Monte Carlo radiative transfer modeling that this morphology occurs when protostars are observed at low inclinations or have low envelope densities. We also find that the morphology is correlated with the SED-determined evolutionary class, with Class 0 protostars more likely to be nondetections, Class I protostars to show cavities, and flat-spectrum protostars to be point sources. Using an edge detection algorithm to trace the projected edges of the cavities, we fit power laws to the resulting cavity shapes, thereby measuring the cavity half-opening angles and power-law exponents. We find no evidence for the growth of outflow cavities as protostars evolve through the Class I protostar phase, in contradiction with previous studies of smaller samples. We conclude that the decline of mass infall with time cannot be explained by the progressive clearing of envelopes by growing outflow cavities. Furthermore, the low star formation efficiency inferred for molecular cores cannot be explained by envelope clearing alone.

Development of a Predictive Monte Carlo Radiative Transfer Model for Ablative Fractional Skin Lasers.

It is possible to enhance topical drug delivery by pretreatment of the skin with ablative fractional lasers (AFLs). However, the parameters to use for a given AFL to achieve the desired depth of ablation or the desired therapeutic or cosmetic outcome are hard to predict. This leaves open the real possibility of overapplication or underapplication of laser energy to the skin. In this study, we developed a numerical model consisting of a Monte Carlo radiative transfer (MCRT) code coupled to a heat transfer and tissue damage algorithm. The simulation is designed to predict the depth effects of AFL on the skin, verified with in vitro experiments in porcine skin via optical coherence tomography (OCT) imaging. Ex vivo porcine skin is irradiated with increasing energies (50-400 mJ/pixel) from a CO2 AFL. The depth of microscopic treatment zones is measured and compared with our numerical model. The data from the OCT images and MCRT model complement each other well. Nonablative thermal effects on surrounding tissue are also discussed. This model, therefore, provides an initial step toward a predictive determination of the effects of AFL on the skin. Lasers Surg. Med. © 2020 The Authors. Lasers in Surgery and Medicine published by Wiley Periodicals LLC.

Spectral solar irradiance on inclined surfaces: A fast Monte Carlo approach

Estimating spectral plane-of-array (POA) solar irradiance on inclined surfaces is an important step in the design and performance evaluation of both photovoltaic and concentrated solar plants. This work introduces a fast, line-by-line spectral, Monte Carlo (MC) radiative transfer model approach to simulate anisotropic distributions of shortwave radiation through the atmosphere as photon bundles impinge on inclined surfaces. This fast Monte Carlo approach reproduces the angular distribution of solar irradiance without the undesirable effects of spatial discretization and thus computes detailed POA irradiance values on surfaces at any orientation and also when surfaces are subjected to the anisotropic ground and atmospheric scattering. Polarization effects are also easily incorporated into this approach that can be considered as direct numerical simulation of the physics involved. Here, we compare our Monte Carlo radiative transfer model with the most widely used empirical transposition model, Perez4, under various conditions. The results show that the Perez4 model reproduces the more detailed Monte Carlo simulations with less than 10% deviation under clear skies for all relevant surface tilt and azimuth angles. When optically thin clouds are present, observed deviations are larger, especially when the receiving surface is strongly tilted. Deviations are also observed for large azimuth angle differences between the receiving surface and the solar position. When optically thick clouds are present, the two models agree within 15% deviation for nearly all surface orientation and tilt angles. The overall deviations are smaller when compared with cases for optically thin clouds. The Perez4 model performs very well (∼6.0% deviation) in comparison with the detailed MC simulations for all cases, thus validating its widespread use for practical solar applications. When detailed atmospheric profiles and cloud optical properties are available, the proposed fast Monte Carlo radiative model reproduces accurate spectral and angular POA irradiance levels for various atmospheric and cloud cover conditions, surface orientations, and different surface and ground properties.

Simplified 3D GCM modelling of the irradiated brown dwarf WD 0137−349B

ABSTRACT White dwarf–brown dwarf short-period binaries (Porb ≲ 2 h) are some of the most extreme irradiated atmospheric environments known. These systems offer an opportunity to explore theoretical and modelling efforts of irradiated atmospheres different to typical hot Jupiter systems. We aim to investigate the three-dimensional (3D) atmospheric structural and dynamical properties of the brown dwarf WD 0137−349B. We use the 3D global circulation model (GCM) Exo-Flexible Modelling System (FMS) with a dual-band grey radiative transfer scheme to model the atmosphere of WD 0137−349B. The results of the GCM model are post-processed using the 3D Monte Carlo radiative transfer model cmcrt. Our results suggest inefficient day–night energy transport and a large day–night temperature contrast for WD 0137−349B. Multiple flow patterns are present, shifting energy asymmetrically eastward or westward depending on their zonal direction and latitude. Regions of overturning are produced on the western terminator. We are able to reproduce the start of the system near-infrared (IR) emission excess at ≳1.95 μm as observed by the Gemini Near-Infrared Spectrograph (GNIRS) instrument. Our model overpredicts the IR phase curve fluxes by factors of ≈1–3, but generally fits the shape of the phase curves well. Chemical kinetic modelling using vulcan suggests a highly ionized region at high altitudes can form on the dayside of the brown dwarf. We present a first attempt at simulating the atmosphere of a short-period white dwarf–brown dwarf binary in a 3D setting. Further studies into the radiative and photochemical heating from the ultraviolet irradiation are required to more accurately capture the energy balance inside the brown dwarf atmosphere. Cloud formation may also play an important role in shaping the emission spectra of the brown dwarf.

Diffraction-limited Titan Surface Imaging from Orbit Using Near-infrared Atmospheric Windows

Abstract The selection of Dragonfly enables regional Titan surface science, but global Titan geophysics, geology, hydrology, and meteorology require an orbiter. We consider the sources of signal and noise that would contribute to near-infrared surface imaging from such an orbiter both analytically and numerically. The fraction of light arriving at an orbiting camera directly from Titan’s surface, and therefore conveying full-resolution surface information, decreases at shorter wavelengths as additive atmospheric scatter and light blurred on the way out increase with higher haze optical depths. We apply the Monte Carlo radiative transfer model SRTC++ and show that up to 75% of observed flux in Titan’s 5 μm window comes directly from the surface, up to 47% comes directly at 2 μm, and up to just 7% comes directly in the 0.94 μm window. We find that diffraction-limited surface imaging with 10 m pixels is possible with a signal-to-noise ratio for surface features of 100 in the near-infrared at 5 and 2 μm using a 50 cm aperture. A Titan orbiter camera could image in color using 5 μm, 2 μm, and potentially other wavelengths using a pushbroom strategy with time-delay integration.

A Comparative Analysis of the OI 130.4‐nm Emission Observed by NASA's TIMED Mission Using a Monte Carlo Radiative Transfer Model

AbstractRemote sensing of the OI 130.4‐nm emission is potentially a useful means for routine monitoring of the atomic oxygen abundance in the upper atmosphere, especially for altitudes above 300 km where the OI 135.6‐nm emission becomes too dim to be useful. However, to date, the interpretation of the OI 130.4‐nm emission as a proxy for the O density remains ambiguous in that the relative contribution of the external and internal sources to the production of this emission has not been fully understood. In this study, we perform a comparative analysis of the OI 130.4‐nm dayglow observed by NASA's Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) mission using a Monte Carlo radiative transfer model to investigate the consistency between models and the TIMED/Global UltraViolet Imager (GUVI) data. The solar 130.4‐nm flux is measured by TIMED/Solar EUV Experiment (SEE). The Global Airglow (GLOW) and the Atmospheric Ultraviolet Radiance Integrated Code (AURIC) models are used to calculate the initial volume emission rates due to photoelectron impact excitation, and the NRLMSISE‐00 model is used to provide the atmospheric density and temperature profiles. Our data‐model comparisons suggest that the model predicted contributions from photoelectron impact excitation need to be scaled by a factor of 0.1–0.5 to achieve good fits with the data. Moreover, the modeled solar contributions need to be scaled up/down to fit the observations at small ( 20 )/large ( 60 ) solar zenith angles, with a factor of 0.5–1.7. These scale factors are larger than the uncertainties in the GUVI and SEE instrument calibrations, which might suggest inaccurate model predictions of the dayside O density and temperature variations with solar zenith angles.

A semianalytic Monte Carlo radiative transfer model for polarized oceanic lidar: Experiment-based comparisons and multiple scattering effects analyses

The polarization characteristic of oceanic lidar returns includes a great deal of seawater information, which plays an important role in subsurface layer detection and seawater optical property retrieval. Along with the microphysical properties of particles, the multiple scattering effect between laser light and particles in seawater is also a source of polarization, which obscures the original depolarization properties of the seawater. However, modeling multiple scattering in polarized oceanic lidar with analytical methods is a complex problem. In this paper, a semianalytic Monte Carlo (MC) polarization radiative transfer model is established to assess the impact of multiple scattering on the backscattering depolarization measurement of oceanic lidar. The MC-simulated lidar returns of both the parallel and perpendicular channels and the depolarization ratios coincide well with the experimental results from three stations in the Yellow Sea of China by shipborne polarized lidar. Further analyses show that the multiple scattering effect enhances the depolarization of seawater; specifically, the depolarization ratio of the lidar return increases with increasing penetration depth, receiver's field of view (FOV), single scattering albedo and beam attenuation coefficient of seawater. This semianalytic polarized MC model is useful for understanding the mechanism of polarized multiple scattering in seawater and for further improving the precision of optical property retrieval using oceanic polarized lidar.

On the Computation of Apparent Direct Solar Radiation

Abstract Near-forward-scattered radiation coming from the vicinity of the sun’s direction impacts the interpretation of measurements of direct solar radiation by pyrheliometers and sun photometers, and it is also relevant for concentrating solar technology applications. Here, a Monte Carlo radiative transfer model is employed to study the apparent direct solar transmittance t(α), that is, the transmittance measured by an instrument that receives the radiation within a half-field-of-view (half-FOV) angle α from the center of the solar disk, for various ice cloud, water cloud, and aerosol cases. The contribution of scattered radiation to t(α) increases with increasing particle size, and it also depends strongly on ice crystal morphology. The Monte Carlo calculations are compared with a simple approach, in which t(α) is estimated through Beer’s law, using a scaled optical depth that excludes the part of the phase function corresponding to scattering angles smaller than α. Overall, this optical depth scaling approach works very well, although with some degradation of the performance for ice clouds for very small half-FOV angles (α < 0.5°–1°), and in optically thick cases. The errors can be reduced by fine-tuning the optical depth scaling factors based on the Monte Carlo results. Parameterizations are provided for computing the optical depth scaling factors for water clouds, ice clouds, aerosols, and for completeness, Rayleigh scattering to allow for a simple calculation of t(α). It is also shown that the optical depth scaling used in delta-two-stream approximations is inappropriate for simulating the direct solar radiation received by pyrheliometers.

Theoretical extension of universal forward and backward Monte Carlo radiative transfer modeling for passive and active polarization observation simulations

This paper extends the theoretical framework of universal forward and backward Monte Carlo radiative transfer modeling for passive and active polarization observation simulations. The framework is built upon newly derived forward and backward vector scattering order-dependent integral radiative transfer equations (IRTEs). The unified mathematical formalism not only establishes the design of object-oriented software architecture, but also speeds up software development via the reuse of developed scalar code. The polarization simulations are implemented with the addition of the Stokes vector and the Mueller matrix weight tracing schemes. To improve numerical performance order by order, the extension implementation of hybrid scattering order-dependent variance reduction techniques are given detailedly, with a focus on the formulation of scattering phase matrix truncation on the basis of remodeling vector IRTEs. To enrich polarization simulation features, not only scattering operators but also source vector function and detector response matrix function are formulated in unified mathematical forms for the hierarchies organization of various atmosphere, surface, source and detector classes.The framework was fully implemented in Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model. For passive simulation, it not only can handle all one- and three-dimensional (1D and 3D) test cases in the Phase A and B of the International Polarized Radiative Transfer (IPRT) intercomparison project by simulating area-averaged polarized radiance using forward and backward algorithm, but also can simulate polarized radiance in a specified direction at a specified position using backward algorithm; For active simulation, lidar backscatter range-resolved signals can be simulated using forward algorithm. The source package is freely available for research purpose from the corresponding author, with online documentation from https://intersharp.gitlab.io/mscart-docs or http://mscart.nuist.edu.cn.