Radiative Transfer Parameterizations Research Articles

Rapid inverse radiative transfer solver for multiparameter spectrophotometry without integrating sphere.

Multiparameter spectrophotometry (MPS) provides a powerful tool for accurate characterization of turbid materials in applications such as analysis of material compositions, assay of biological tissues for clinical diagnosis and food safety monitoring. This work is aimed at development and validation of a rapid inverse solver based on a particle swarm optimization (PSO) algorithm to retrieve the radiative transfer (RT) parameters of absorption coefficient, scattering coefficient and anisotropy factor of a turbid sample. Monte Carlo (MC) simulations were performed to obtain calculated signals for comparison to the measured ones of diffuse reflectance, diffuse transmittance and forward transmittance. An objective function has been derived and combined with the PSO algorithm to iterate MC simulations for MPS. We have shown that the objective function can significantly reduce the variance in calculated signals by local averaging of an inverse squared error sum function between measured and calculated signals in RT parameter space. For validation of the new objective function for PSO based inverse solver, the RT parameters of 20% Intralipid solutions have been determined from 520 to 1000nm which took about 2.7 minutes on average to complete signal measurement and inverse calculation per wavelength. The rapid solver enables MPS to be translated into easy-to-use and cost-effective instruments without integrating sphere for material characterization by separating and revealing compositional profiles at the molecular and particulate scales.

Optical closure in highly absorptive coastal waters: significance of inelastic scattering processes.

In hydrological optics, "optical closure" means consistency between the apparent optical properties (AOPs) determined from radiometric measurements and those derived from radiative transfer modelling based on concurrently measured inherent optical properties (IOPs) and boundary conditions (sea and sky states). Good optical closure not only provides confidence in the data quality but also informs on the adequacy of the radiative transfer parameterization. Achieving optical closure in highly absorptive coastal waters is challenging due to the low signal-to-noise ratio of radiometric measurements and uncertainties in the measurements of IOPs, namely the spectral absorption and backscattering coefficients. Here, we present an optical closure assessment using a comprehensive set of in situ IOPs acquired in highly absorptive coastal waters optically dominated by chromophoric dissolved organic matter (CDOM). The spectral remote sensing reflectance, Rrs(λ), was modeled using the software HydroLight (HL) with measured IOPs and observed boundary conditions. Corresponding in-water in situRrs(λ) was derived from radiometric measurements made with a Compact Optical Profiling System (C-OPS; Biospherical). The assessment revealed that the inclusion of inelastic scattering processes in the model, specifically sun-induced CDOM fluorescence (fDOM) and sun-induced chlorophyll fluorescence (SICF) from Chlorophyll-a ([chl]), significantly improved the optical closure and led to good agreement between measured and modeled Rrs (i.e., for 440 ≤ λ ≤ 710 nm with no inelastic processes: R2=0.90, slope=0.64; with inelastic processes: R2=0.96, slope=0.90). The analysis also indicated that fDOM and SICF contributed a substantial fraction of the green-red wavelength Rrs in these waters. Specifically, fDOM contributed ∼18% of the modeled Rrs in the green region and SICF accounted for ∼20% of the modeled Rrs in the red region. Overall, this study points out the importance of accounting for fDOM in remote sensing applications in CDOM-dominated waters.

An assessment of Arctic diurnal water‐vapour cycles in Canada's weather forecast model and ERA5

AbstractThe diurnal water‐vapour cycle is a critical component of the hydrological cycle, yet it is one of the hardest components to accurately reproduce in forecast and climate models. Previous studies have shown that both forecast and climate models underrepresent the diurnal water‐vapour cycle, which leads to errors in precipitation, cloud, and radiative transfer parameters. Most diurnal cycle studies were conducted in the Tropics, and very few model evaluations of this process exist for the Arctic. Additionally, the majority of studies focus on total column water‐vapour cycles; almost none use height‐resolved measurements. In this study, we evaluate the diurnal water‐vapour cycles in Environment and Climate Change Canada's Global Environmental Multiscale–High Resolution Deterministic Prediction System (GEM–HRDPS) numerical weather forecast model and the European Centre for Medium‐Range Weather Forecasts Reanalysis v5 (ERA5) using a Vaisala preproduction differential absorption lidar (DIAL) and a co‐located Global Positioning System (GPS) located in Iqaluit, Nunavut (63.75° N, 68.55° W). Both numerical products reproduce the phase of the diurnal cycle well below 1 km year‐round. However, ERA5's diurnal amplitudes are significantly smaller than the DIAL and GPS amplitudes. GEM–HRDPS amplitudes are consistently larger in the first few hundred metres but smaller above 1 km; it also underrepresents the amplitude of the total column diurnal cycle. Neither ERA5 nor GEM–HRDPS accurately reproduce the 12‐hr component of the diurnal cycle in either the height‐resolved or total column cycles. The inability to accurately reproduce the 12‐hr component in both numerical products suggests that the representation of some underlying process is incomplete, which can impact the accuracy of precipitation and radiative transfer algorithms. In conclusion, we find that the numerical products are able to reproduce the general behaviour and shape of the cycle but still require improvement at certain altitudes.

Impact of Horizontal Resolution on the Robustness of Radiation Emulators in a Numerical Weather Prediction Model

Developing a machine-learning-based radiative transfer emulator in a weather forecasting model is valuable because it can significantly improve the computational speed of forecasting severe weather events. To replace the radiative transfer parameterization in the weather forecasting model, the universal applicability of the radiation emulator is essential, indicating a transition from the research to the operational level. This study investigates the degradation of the forecast accuracy of the radiation emulator for the Korea peninsula when it is tested at different horizontal resolutions (100–0.25 km) concerning the accuracy attained at the training resolution (5 km) for universal applications. In real-case simulations (100–5 km), the forecast errors of radiative fluxes and precipitation were reduced at coarse resolutions. Ideal-case simulations (5–0.25 km) showed larger errors in heating rates and fluxes at fine resolutions, implying the difficulty in predicting heating rates and fluxes at cloud-resolving scales. However, all simulations maintained an appropriate accuracy range compared with observations in real-case simulations or the infrequent use of radiative transfer parameterization in ideal-case simulations. These findings demonstrate the feasibility of a universal radiation emulator associated with different resolutions/models and emphasize the importance of emulating high-resolution modeling in the future.

A Physics‐Incorporated Deep Learning Framework for Parameterization of Atmospheric Radiative Transfer

AbstractThe atmospheric radiative transfer calculations are among the most time‐consuming components of the numerical weather prediction (NWP) models. Deep learning (DL) models have recently been increasingly applied to accelerate radiative transfer modeling. Besides, a physical relationship exists between the output variables, including fluxes and heating rate profiles. Integration of such physical laws in DL models is crucial for the consistency and credibility of the DL‐based parameterizations. Therefore, we propose a physics‐incorporated framework for the radiative transfer DL model, in which the physical relationship between fluxes and heating rates is encoded as a layer of the network so that the energy conservation can be satisfied. It is also found that the prediction accuracy was improved with the physic‐incorporated layer. In addition, we trained and compared various types of DL model architectures, including fully connected (FC) neural networks (NNs), convolutional‐based NNs (CNNs), bidirectional recurrent‐based NNs (RNNs), transformer‐based NNs, and neural operator networks, respectively. The offline evaluation demonstrates that bidirectional RNNs, transformer‐based NNs, and neural operator networks significantly outperform the FC NNs and CNNs due to their capability of global perception. A global perspective of an entire atmospheric column is essential and suitable for radiative transfer modeling as the changes in atmospheric components of one layer/level have both local and global impacts on radiation along the entire vertical column. Furthermore, the bidirectional RNNs achieve the best performance as they can extract information from both upward and downward directions, similar to the radiative transfer processes in the atmosphere.

Updated GOES-13 Heliosat-2 Method for Global Horizontal Irradiation in the Americas

Increasing the utilization of renewable energy is at the center of most sustainability policies. Solar energy is the most abundant resource of this type on Earth, and optimizing its use requires the optimal estimation of surface solar irradiation. Heliosat-2 is one of the most popular methods of global horizontal irradiation (GHI) estimation. Originally developed for the Meteosat satellite, Heliosat-2 has been modified in previous work to deal with GOES-13 data and named here GOES_H2. This model has been validated through the computation of indicators and irradiation maps for the Guiana Shield. This article proposes an improved version of GOES_H2, which has been combined with a radiative transfer parameterization (RTP) and the McClear clear-sky model (MC). This new version, hereafter designated RTP_MC_GOES_H2, was tested on eight stations from the Baseline Surface Radiation Network, located in North and South America, and covered by GOES-13. RTP_MC_GOES_H2 improves the hourly GHI estimates independently of the type of sky. This improvement is independent of the climate, no matter the station, the RTP_MC_GOES_H2 gives better results of MBE and RMSE than the original GOES_H2 method. Indeed, the MBE and RMSE values, respectively, change from −11.93% to −2.42% and 23.24% to 18.24% for North America and from −4.35% to 1.79% and 19.97% to 17.37 for South America. Moreover, the flexibility of the method may allow to improve results in the presence of snow cover and rainy/variable weather. Furthermore, RTP_MC_GOES_H2 results outperform or equalize those of other operational models.

Robustness of neural network emulations of radiative transfer parameterizations in a state-of-the-art general circulation model

Abstract. The ability of machine-learning-based (ML-based) model components to generalize to the previously unseen inputs and its impact on the stability of the models that use these components have been receiving a lot of recent attention, especially in the context of ML-based parameterizations. At the same time, ML-based emulators of existing physically based parameterizations can be stable, accurate, and fast when used in the model they were specifically designed for. In this work we show that shallow-neural-network-based emulators of radiative transfer parameterizations developed almost a decade ago for a state-of-the-art general circulation model (GCM) are robust with respect to the substantial structural and parametric change in the host model: when used in two 7-month-long experiments with a new GCM, they remain stable and generate realistic output. We concentrate on the stability aspect of the emulators' performance and discuss features of neural network architecture and training set design potentially contributing to the robustness of ML-based model components.

Sensitivity Analysis of Canopy Structural and Radiative Transfer Parameters to Reconstructed Maize Structures Based on Terrestrial LiDAR Data

The maturity and affordability of light detection and ranging (LiDAR) sensors have made possible the quick acquisition of 3D point cloud data to monitor phenotypic traits of vegetation canopies. However, while the majority of studies focused on the retrieval of macro scale parameters of vegetation, there are few studies addressing the reconstruction of explicit 3D structures from terrestrial LiDAR data and the retrieval of fine scale parameters from such structures. A challenging problem that arises from the latter studies is the need for a large amount of data to represent the various components in the actual canopy, which can be time consuming and resource intensive for processing and for further applications. In this study, we present a pipeline to reconstruct the 3D maize structures composed of triangle primitives based on multi-view terrestrial LiDAR measurements. We then study the sensitivity of the details with which the canopy architecture was represented for the computation of leaf angle distribution (LAD), leaf area index (LAI), gap fraction, and directional reflectance factors (DRF). Based on point clouds of a maize field in three stages of growth, we reconstructed the reference structures, which have the maximum number of triangles. To get a compromise between the details of the structure and accuracy reserved for later applications, we carried out a simplified process to have multiple configurations of details based on the decimation rate and the Hausdorff distance. Results show that LAD is not highly sensitive to the details of the structure (or the number of triangles). However, LAI, gap fraction, and DRF are more sensitive, and require a relatively high number of triangles. A choice of 100−500 triangles per leaf while maintaining the overall shapes of the leaves and a low Hausdorff distance is suggested as a good compromise to represent the canopy and give an overall accuracy of 98% for the computation of the various parameters.

Robustness of inverse solutions for radiative transfer parameters from light signals measured with different detection configurations

Spectroscopic characterization of turbid samples needs to solve inverse scattering problems (ISPs). With the radiative transfer (RT) theory as the framework for modeling light-matter interaction, accurate characterization becomes feasible but practical implementation remains challenging. We have evaluated the uniqueness and robustness of ISP solutions for a multiparameter spectrophotometer system without integrating spheres using different detection configurations for signal measurement. A novel parameter of area descending rate (ADR) has been developed to sample globally the distribution of an objective function in the 3D space of RT parameters and quantify uniqueness and robustness of ISP solutions. Analysis of the objective function for different sample types show the uniqueness of solutions for different detection configurations with increased complexity for samples of very larger single-scattering albedo values. The robustness of ISP solutions as quantified by ADR was found to be insensitive to the changes in detection configurations. Such stability provides strong evidences that the multiparameter spectrophotometry using only three photodiodes combined with Monte Carlo simulations yields a valuable and practical approach for turbidity characterization.

Formulation of space-angular fractional radiative transfer equation in participating finite slab clumpy media

Space-angular fractional radiative transfer equation has been derived depending on the invariance of the functional potential and the Euler–Lagrange functional of the radiative-transfer intensity. Pomraning–Eddington technique is employed to unzip the space-fractional radiative transfer through a clumpy medium. The medium is considered as an anisotropic scattering participating finite slab with specular reflecting boundaries. The fractional differential operator is taken in terms of the Jumarie Riemann–Liouville representation. The resultant space-fractional equation has diffusion parameter depends on both the single scattering albedo and the anisotropic parameter of the medium. Laplace transformation method is used to solve the obtained space-fractional differential equation, whose solution is obtained in terms of the Mittag–Leffler function. Numerical calculations are carried out to investigate the effects of the fractional exponent and the other radiative-transfer parameters on the radiation density and net flux through the medium. In addition, the reflectivity and transmissivity from the medium boundaries are calculated and represented graphically.

L-band vegetation optical depth as an indicator of plant water potential in a temperate deciduous forest stand

Abstract. Vegetation optical depth (VOD) retrieved from microwave radiometry correlates with the total amount of water in vegetation, based on theoretical and empirical evidence. Because the total amount of water in vegetation varies with relative water content (as well as with biomass), this correlation further suggests a possible relationship between VOD and plant water potential, a quantity that drives plant hydraulic behavior. Previous studies have found evidence for that relationship on the scale of satellite pixels tens of kilometers across, but these comparisons suffer from significant scaling error. Here we used small-scale remote sensing to test the link between remotely sensed VOD and plant water potential. We placed an L-band radiometer on a tower above the canopy looking down at red oak forest stand during the 2019 growing season in central Massachusetts, United States. We measured stem xylem and leaf water potentials of trees within the stand and retrieved VOD with a single-channel algorithm based on continuous radiometer measurements and measured soil moisture. VOD exhibited a diurnal cycle similar to that of leaf and stem water potential, with a peak at approximately 05:00 eastern daylight time (UTC−4). VOD was also positively correlated with both the measured dielectric constant and water potentials of stem xylem over the growing season. The presence of moisture on the leaves did not affect the observed relationship between VOD and stem water potential. We used our observed VOD–water-potential relationship to estimate stand-level values for a radiative transfer parameter and a plant hydraulic parameter, which compared well with the published literature. Our findings support the use of VOD for plant hydraulic studies in temperate forests.

Similarity solution for magnetogasdynamic shock wave in a perfectly conducting dusty gas with axial or azimuthal magnetic field in rotating medium under the influence of radiative and conductive heat fluxes

The effect of magnetic field, the ratio of the density of solid particles to the initial density of the gas, non-idealness of the gas, mass concentration of micro size solid particles, adiabatic exponent, and the heat transfer parameters effect on one-dimensional shock wave propagation in a dusty gas with conductive and radiative heat fluxes in the presence of azimuthal or axial magnetic field in rotating medium have been investigated for cylindrical geometry. By using the similarity method a system of ordinary differential equations are derived from the system of governing equations of motion. The dusty gas is taken to be perfectly conducting mixture of non-ideal gas and small inert solid particles of micro size, in which solid particles are continuously distributed. It is understood that variable energy input is constantly supplied by the moving piston and the equilibrium flow conditions are maintained in the whole flow-field region. The results of numerical integration for the system of ordinary differential equations show that the magnetic field, mass concentration of solid particles, the ratio of the solid particles density to the gas initial density, non-idealness of the gas, adiabatic exponent and the heat transfer parameters have strong influence on the shock wave and on the flow variables. It is found that the presence of magnetic field, an increase in conductive and radiative heat transfer parameters and non-idealness of the gas have decaying effect on the shock wave; whereas the ratio of the solid particles density to the gas initial density or the adiabatic exponent have effect to increase the shock strength.

Mechanisms of tropical precipitation biases in climate models

We investigate the possible causes for inter-model spread in tropical zonal-mean precipitation pattern, which is divided into hemispherically symmetric and anti-symmetric modes via empirical orthogonal function analysis. The symmetric pattern characterizes the leading mode and is tightly related to the seasonal amplitude of maximum precipitation position. The energetic constraints link the symmetric pattern to the seasonal amplitude in cross-equatorial atmospheric energy transport $$ {\text{AET}}_{0} $$ and the annual-mean equatorial net energy input $$ {\text{NEI}}_{0} $$ . Decomposition of $$ {\text{AET}}_{0} $$ into the energetics variables indicates that the inter-model spread in symmetric precipitation pattern is correlated with the inter-model spread in clear-sky atmospheric shortwave absorption, which most likely arises due to differences in radiative transfer parameterizations rather than water vapor patterns. Among the components that consist $$ {\text{NEI}}_{0} $$ , the inter-model spread in symmetric precipitation pattern is mostly associated with the inter-model spread in net surface energy flux in the equatorial region, which is modulated by the strength of cooling by equatorial upwelling. Our results provide clues to understand the mechanism of tropical precipitation bias, thereby providing guidance for model improvements.

Multiparameter Spectrophotometry Platform for Turbid Sample Measurement by Robust Solutions of Radiative Transfer Problems

Multiparameter spectrophotometer instruments based on the radiative transfer (RT) theory differ fundamentally from conventional ones in their ability to determine absorption and scattering coefficients and anisotropy factor. Ease of use and robustness of inverse solutions are of necessity for general-purpose applications. We have developed a new instrument platform design incorporating a compact three-photodiode detection configuration without integrating spheres, four-channel signal-processing unit, and Monte Carlo (MC) simulation-based software for accurate and rapid inverse solutions. To verify the platform design, two sphere suspension samples of different size distributions were measured and RT parameters were determined by a sample model with the Henyey and Greenstein (HG) phase function between 460 and 1000 nm. System validation is achieved by comparison of the RT parameters and spectral dependence against the results by Mie theory for single-sized spheres of nominal diameter values. Five wavelengths from 560 to 960 nm were selected for quantitative evaluation of the robustness of the HG sample model and two Mie theory-based sample models assuming light scattering by independent and single spheres. We found that only the HG-based sample model yields high accuracy and strong robustness for inverse determination of RT parameters even for the cases of sphere suspensions in which the assumptions of sample uniformity and scattering by independent and single spheres are not satisfied. These results demonstrate that the new platform with MC simulation-based inverse algorithm combined with the HG sample model is capable of robust and rapid measurement of RT parameters for turbid samples with optical thickness up to 30.

Spectral determination of μa, μs and g from single and multiple scattering signals with one optically thick sample

Development of robust and easy-to-implement methods for quantitative turbidity characterization by inherent properties of absorption and scattering can have wide applications. We report a new method for multiparameter characterization of turbid samples with three photodiodes based on the radiative transfer (RT) theory. Instead of acquiring collimated transmittance by spatial filtering and scattered light signals by integrating spheres, the method determines RT parameters from forward transmittance dominated by light of single scattering and non-hemispherical diffuse reflectance and transmittance dominated by light of multiple scattering. A Monte Carlo based inverse algorithm has been developed to rapidly obtain absorption coefficient μa, scattering coefficient μs and anisotropy factor g at multiple wavelengths. The method has been validated with different sphere suspensions against the Mie theory. RT parameters for suspensions of spheres of 0.966 µm and 11 µm in nominal diameter values has been determined in a spectral region of 460–1000 nm and the uniqueness of the inverse solutions has been proved at selected wavelengths.

Modeling study of the impact of complex terrain on the surface energy and hydrology over the Tibetan Plateau

The long-term effects of complex terrain on solar energy distributions and surface hydrology over the Tibetan Plateau (TP) are investigated using the 4th version of the global Community Climate System Model (CCSM4) coupled with a 3-D radiative transfer (RT) parameterization. We examine the differences between the results from CCSM4 with the 3-D RT parameterization and the results from CCSM4 with the plane-parallel RT scheme. In January (winter), the net surface solar flux (FSNS) displays negative deviations over valleys and the north slopes of mountains, especially in the northern margin of the TP, as a result of the 3-D shadow effect. Positive deviations in FSNS in January are found over the south slopes of mountains and over mountain tops, where more solar flux is intercepted. The deviations in total cloud fraction and snow water equivalent (SWE) exhibit patterns opposite to that of FSNS. The SWE decreases due to the 3-D mountain effect in spring and the magnitude of this effect depends on the terrain elevations. The SWE is reduced by 1–17 mm over the TP in April, with the largest decrease in SWE at an elevation of 3.5–4.5 km. Negative deviations in precipitation are found throughout the year, except in May and December, and they follow the seasonal variations in the deviations in total cloud fraction. The total liquid runoff at 3.5–4.5 km elevation increases in April due to earlier (March) snowmelt caused by increased downward solar radiation. The possible deviations in surface energy and SWE over the TP, caused by plane-parallel assumption in most climate models may result in biases in the liquid runoff and the river water resources over the TP and downstream.

Spatially Continuous Characterization of Forest Canopy Structure and Subcanopy Irradiance Derived from Handheld Radiometer Surveys

Abstract Small-scale variations in radiative transfer through forest canopies are strongly linked to canopy structural heterogeneity. To date, upscaling of radiative transfer parameterizations developed at the point scale is hampered by (i) poor representation of canopy structure variability and (ii) limited spatially explicit subcanopy irradiance data to assess the performance of radiative transfer schemes at typical resolutions of land surface models. This study presents a novel approach for efficient in situ characterization of canopy structure and subcanopy irradiance over large spatial extents. The method involves a handheld radiometer assembly mounted on a motorized gimbal developed for nonstationary continuous measurements of shortwave and longwave radiation along forest transects. In combination with radiation and temperature data from a stationary reference station, spatially resolved estimates of sky-view fraction, canopy transmissivity, and longwave enhancement could be obtained. Under favorable meteorological conditions, validation against sky-view fraction data from hemispherical photographs yielded an RMSE of 0.03 (i.e., 3%). Irradiance measurements under heterogeneous canopy cover revealed strong spatial coherence between longwave radiation enhancement, shortwave radiation attenuation, and sky-view fraction on overcast days. Under clear-sky conditions, however, sun flecks caused highly variable shortwave radiation transmissivity patterns. This study demonstrates the potential of handheld radiometer surveys to deliver valuable spatially distributed datasets of collocated canopy structure and subcanopy irradiance which can be used (i) as reference data for alternative approaches to derive canopy structure parameters, (ii) to improve modeling of subcanopy radiation across a wide range of canopy distributions, and (iii) to support respective model upscaling efforts.

On Radiative Transfer and Gray Body Parameter for Partially Transparent Media

We obtained a solution to radiative heat transfer equations, which describes a multi-layer gray semi-transparent medium in terms of an opaque body. It is shown that the thermal disturbance between the layers of a medium qualitatively changes its optical properties. We introduced a gray body parameter, which allowed us to describe multilayer gray semi-transparent media with low thermal conductivity. We propose a method for calculating heat transfer by thermal radiation in a gray semi-transparent medium and present the results of radiative heat transfer calculations for screen-vacuum and powder insulation materials as examples of such media.

Correcting Himawari-8 Advanced Himawari Imager Data for the Production of Vivid True-Color Imagery

AbstractObservations of top-of-atmosphere radiances from the Advanced Himawari Imager (AHI) blue, green, and red spectral bands can be used to produce high-temporal-resolution, true-color imagery at 1-km spatial resolution over the Asia–Pacific region. To enhance interpretability and aesthetic appearance of these images, the top-of-atmosphere radiance data are processed to remove the Rayleigh-scattered atmospheric component, corrected for limb effects, blended with brightness temperature data from a thermal infrared window band at night, and the resultant imagery adjusted to optimize contrast. The contribution of Rayleigh scattering to the AHI observations is calculated by interpolating radiative transfer parameters from a preconstructed set of lookup tables, which are specifically created for the Himawari-8 AHI instrument. A surface reflectance value for each pixel is calculated after the Rayleigh contribution is removed. The spectrally dependent reflectance values produced from the lookup table differ from the exact calculation by up to 18% at the planetary limb, over 100% at the solar terminator, and by less than 0.5% at low to moderate solar and sensor zenith angles. The subsequent corrections applied for limb effects mitigate the areas with high interpolation error, which slightly reduces the spatial coverage, but provides Rayleigh-corrected surface reflectance products that have interpolation errors at or below 0.5%. Resolution sharpening increases the nominal pixel size from 1000 to 500 m while still producing sharp images. The resultant images are colorful, visually intuitive, high contrast, and of sufficient spatial and temporal resolution to provide a unique and complementary observational tool for use by weather forecasters and the general public alike.

Cylindrical shock wave generated by a moving piston in a rotational axisymmetric non-ideal gas with conductive and radiative heat-fluxes in the presence of azimuthal magnetic field

The propagation of a cylindrical shock wave in a rotational axisymmetric non-ideal gas with heat conduction and radiation heat-flux, in the presence of a spatially decreasing azimuthal magnetic field, driven out by a moving piston is investigated. The fluid velocities and the azimuthal magnetic field in the ambient medium are assume to be varying and obeying power laws. The gas is assumed to be electrically conducting and obey a simplified van der Waals equation of state. The shock wave moves with variable velocity and the total energy of the wave is non-constant. Similarity solutions are obtained for the flow-field behind the shock and the effects of variation of Alfven Mach number, the conductive and radiative heat transfer parameters, the parameter of the non-idealness are worked out in detail. An increase in the value of Alfven Mach number or in the non-idealness parameter of the gas, decreases the compressibility of the gas and hence there is a decrease in the shock strength; whereas the reverse effects on compressibility and shock strength are obtained with an increase in conductive or radiative heat transfer parameter. It is shown that due to the consideration of rotating medium the compressibility of the gas and the shock strength increase. Further, it is investigated that with an increase in the parameters of conductive and radiative heat transfer the tendency of formation of maxima in the distribution of pressure and minimum in magnetic field and non-dimensional axial component of vorticity vector decreases. It is interesting to note that the pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the axis of symmetry, which is in excellent agreement with the laboratory conditions to produce a shock wave. A comparison between the cases of rotating and non-rotating medium is also made.