Minnaert Model Research Articles

Evaluation of regression models' accuracy for estimating soil heavy metals content from topographic rectified satellite imagery (Case study: Irankouh from Iran)

Although the traditional approach is vital in environmental studies, satellite images have recently become one of the main tools for estimating soil pollution due to their advantages. Among sources of soil pollution, heavy metals (HMs) play a crucial role; in this regard, evaluating the soil contamination anomaly is indispensable due to an enormous number of HMs mines and agricultural land irrigation by industrial sewage in developing countries. Therefore, the main goals of this study are: to evaluate Landsat-8 image capability for estimating HMs content (Cr, Cd, Co, and AS) of the soil, performance evaluation of linear and nonlinear regression models, and topographic influence on the estimation accuracy of heavy metals. To do so, we applied multivariate-linear, partial least square, exponential regression, and neural network models to achieve a relation between the HMs content and soil spectral reflectance. Regarding the R2 value of models, the neural network demonstrated a more acceptable performance than other models. The results show that topographic correction improves the accuracy of HMs estimation; for example, the Minnaert model obtained the highest score (equal to 30.02), which is sufficient to support the preceding sentence. Furthermore, the neural network and Minnaert (with a score of 17.56) would produce the best results for estimating HMs content.

A Synthetic Angle Normalization Model of Vegetation Canopy Reflectance for Geostationary Satellite Remote Sensing Data

High-frequency imaging characteristics allow a geostationary satellite (GSS) to capture the diurnal variation in vegetation canopy reflectance spectra, which is of very important practical significance for monitoring vegetation via remote sensing (RS). However, the observation angle and solar angle of high-frequency GSS RS data usually differ, and the differences in bidirectional reflectance from the reflectance spectra of the vegetation canopy are significant, which makes it necessary to normalize angles for GSS RS data. The BRDF (Bidirectional Reflectance Distribution Function) prototype library is effective for the angle normalization of RS data. However, its spatiotemporal applicability and error propagation are currently unclear. To resolve this problem, we herein propose a synthetic angle normalization model (SANM) for RS vegetation canopy reflectance; this model exploits the GSS imaging characteristics, whereby each pixel has a fixed observation angle. The established model references a topographic correction method for vegetation canopies based on path-length correction, solar zenith angle normalization, and the Minnaert model. It also considers the characteristics of diurnal variations in vegetation canopy reflectance spectra by setting the time window. Experiments were carried out on the eight Geostationary Ocean Color Imager (GOCI) images obtained on 22 April 2015 to validate the performance of the proposed SANM. The results show that SANM significantly improves the phase-to-phase correlation of the GOCI band reflectance in the morning time window and retains the instability of vegetation canopy spectra in the noon time window. The SANM provides a preliminary solution for normalizing the angles for the GSS RS data and makes the quantitative comparison of spatiotemporal RS data possible.

A comprehensive evaluation method for topographic correction model of remote sensing image based on entropy weight method

AbstractThe effect of topographic correction (TOC) has a profound influence on the quantitative application of remote sensing image. With regard to the invalid evaluation of the TOC model with such a single topographic correction assessment (TCA) method, we have selected five TCA indexes from five different perspectives: the difference in mean radiance radiometry between sunlit and shaded slopes, the cosine empirical relationship, stability, heterogeneity, and outlier ratio. The entropy weight method was used to assign weight to each TCA indexes, and the comprehensive evaluation value (CEV) of TOC for each band of remote sensing image was obtained by weighted superposition. After that, the weight of each band of the remote sensing image is determined by the entropy weight method, and the CEV of the TOC of the remote sensing image is obtained by weighting and superposition, so as to realize the effect evaluation of the six TOC models of C, SCS + C, VECA, Teillet, Minnaert, and Minnaert + SCS. The results indicate that the proposed method can effectively evaluate the correction effect of the TOC model. Results indicate that the SCS + C model has the best correction effect, while the Minnaert model performs the worst. The results generated from the Minnaert + SCS, Teillet, and Minnaert models typically show inferior quality. The SCS + C, VECA, and C models are better suited for generating images with high spectral fidelity, and these three correction models are recommended for TOCs over mountainous areas.

A comparative analysis of different terrain correction methods based on Landsat-8 OLI data

The topographic effect has long been recognized as one of problems for quantitative remote sensing. The paper compares the correction results of OLI data based on C model, Cosine model, SCS model, Minnaert model and pixel-based Minnaert Correction Method. The visual inspection, statistical analysis and regression analysis of images were used to analyze the results before and after correction of image. The results show that the C model has a better correction effect. The Cosine model and SCS model were significantly overcorrected. However, C model, Minnaert model and slope-based Minnaert model weakened the influence of terrain. By comparative analysis, the C correction method was optimal model for OLI image.

A new insight on a mechanism of airborne and underwater sound of a drop impacting a liquid surface

We report on an experimental study of the impact of a water drop on a liquid surface in the regime of the so-called irregular entrainment. The hydrodynamics of the phenomenon has been correlated finely to the features of the acoustic signal, both underwater and in the air, thanks to the synchronization of images and sounds in a home-made setup. If the origin of the acoustic signal is known to be caused by the capture of a bubble during the hydrodynamic flow following the impact, for the first time, a new mechanism responsible for the formation of the air bubble is highlighted. The latter is caused by the closing, like a liquid zipper, of the cavity induced by the retraction of the Rayleigh jet, by a secondary droplet detached from this jet. The comparison of the experimental data with the Minnaert model and plane wave theories reveals: (i) the time-dependence of the instantaneous oscillation frequency, (ii) a dominant frequency about 30% higher than the Minnaert prediction, (iii) a higher damping characteristic time, and (iv) a two orders of magnitude higher water–air transmission coefficient. All these results can be explained by the proximity of the bubble to the air–water interface, and by the too small dimensions of the tank to avoid underwater echoes in the measured underwater signal.

An analysis research of terrain correction methods considering the slope ranges based on OLI image

In mountainous terrain, the topographic correction often be used in image pre-processing. Recently, some correction approaches considering slope ranges have been developed to improve topographical effects. The paper explores the C correction and Minnaert methods considering the slope ranges to evaluate if the methods considering slope ranges can effectively reduce the topographic effects. The C model constants and Minnaert constants in different slope range were obtained based on the image samples. Then, the scatterplots were used to evaluate the correction results. The model constants analysis shows that the Minnaert constant has a nonlinear relation with slope. The scatterplots analysis shows that the image reflectance using a single correction constant value has a better correction result. When the slopes are greater than 43 degrees, the Minnaert model considering slope has overcorrected the topographic effects. The study has demonstra-ted the Minnaert correction models considering slope range did not better reduce topographic effects and the method need be improved, especially in the high slope ranges.

Radiative Heat Transfer in Two-Dimensional Cylindrical Medium Coupled with BRDF Surface

For radiative heat transfer analysis and temperature measurements, the surface is usually assumed to be blackbody, diffuse, or specular, which may cause obvious errors under actual working conditions. The bidirectional reflectance distribution function (BRDF), which is considered as a relatively strict approach for characterizing a real surface, has been adopted in heat transfer analysis. In this study, two BRDF models—the Minnaert model and the Torrance and Sparrow model—are applied to investigate the effects of different boundary conditions on the radiative heat transfer. Additionally, the distribution of ratios of energy scattered by the medium or reflected by the boundary surface method is extended to solve the radiative transfer in a two-dimensional graded-index medium coupled with BRDF surfaces in a cylindrical coordinate system. The results show that greater deviation of the BRDF surface from the diffuse characteristics yields a larger difference of the radiative heat flux and intensity distributions between the BRDF and the diffuse surface. The radiative heat flux deviation reaches 12.78%, and more significant differences exist in the radiative intensity along some directions under different boundary conditions. The specular reflection plays a leading role at high reflection angles. However, the increased scattering ability can weaken the influence of the reflection of the BRDF on the radiative intensity distributions.

Electron transfer between cytochrome c and the binuclear center of cytochrome oxidase

The Minnaert model, which can account for the reaction kinetics between cytochrome oxidase and cytochrome c (Cytc), has been used to justify equal binding rate constants for reduced and oxidized Cytc. Here we extend the model beyond reversible binding of Cytc and its irreversible oxidation to include CuA, heme a and the oxidation cycle of the binuclear center. The model reproduces the experimental reduction of CuA and heme a during turnover and the low population of the ferryl and ferrous heme a3. It predicts that the off rate constants for reduced and oxidized Cytc can be unequal and that the non-Nernst response of CuA and heme a is due to disequilibrium between free Cytc and CuA rather than redox anticooperativity.

Experimental characterization of the opposition surge in fine-grained water–ice and high albedo ice analogs

We measured the bidirectional reflectance in the VIS–NIR spectral range of different surfaces prepared from small-grained spherical water–ice particles over a wide range of incidence and emission geometries, including opposition. We show that coherent backscattering is dominating the opposition effect on fresh sample material, but its contribution decreases when particles become more irregularly shaped and the bulk porosity increases. Strong temporal evolution of the photometric properties of icy samples, caused by particle sintering and resulting in a decrease of backscattering, is shown. The sintering of the ice particles is documented using cryo-SEM micrographs of fresh and evolved samples. To complement the photometric characterization of ices, multiple high albedo laboratory analogs were investigated to study the effects of shape, grain size distribution, wavelength and surface roughness. In addition to the main backscattering peak, the phase curves also display the effect of glory in the case of surfaces of granular surfaces formed by either spherical ice or glass particles. We show that the angular position of the glory can be used to determine accurately the average size of the particles. Reflectance data are fitted by the Hapke photometric model, the Minnaert model and three morphological models. The resulting parameters can be used to reproduce our data and compare them to the results of other laboratory experiments and astronomical observations.

The DRESOR method for one-dimensional transient radiative transfer in graded index medium coupled with BRDF surface

Most research on transient radiative transfer is coupled with blackbody, specular or diffuse surface, which may only provide limited or inefficient information to analyze transient radiation transfer problems under particular circumstances. This study aims to extend the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to solve the transient radiative heat transfer in a one-dimensional, non-emitting, absorbing and isotropically scattering medium with a linear graded index coupled with the BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to a real surface and can offer more accurate information. Here, a Minnaert model for the BRDF surface is applied. Numerically computed results of the time-resolved reflectance and transmittance are compared with those obtained by DOM and DFEM with blackbody surfaces, which verifies the DRESOR method. Meanwhile, the comparison between BRDF surface and diffuse surface has also been carried out. With the increase of optical thickness, the time-resolved reflectance and transmittance profiles change from a single peak, to a double-peak, and finally to a single peak with a relatively large scattering albedo, especially under the graded index. The scattering albedo has a significant influence on the peak values of the reflectance and transmittance. With the increase of parameter k of Minnaert model, the difference between BRDF surface and diffuse surface enlarges significantly. Furthermore, compared with the corresponding diffuse surface, the relative time-resolved reflectance difference of the BRDF surface can reach 16.7% and the transmittance can reach 7.4% at some dimensionless time. The intensities with the change of time in some directions show an evident difference between BRDF and diffuse surface. These discrepancies imply that the BRDF surface has an important influence on the transient radiative transfer.

Photometric models of disk-integrated observations of the OSIRIS-REx target Asteroid (101955) Bennu

We used ground-based photometric phase curve data of the OSIRIS-REx target Asteroid (101955) Bennu and low phase angle data from Asteroid (253) Mathilde as a proxy to fit Bennu data with Minnaert, Lommel-Seeliger, (RObotic Lunar Orbiter) ROLO, Hapke, and McEwen photometric models, which capture the global light scattering properties of the surface and subsequently allow us to calculate the geometric albedo, phase integral, spherical Bond albedo, and the average surface normal albedo for Bennu. We find that Bennu has low reflectance and geometric albedo values, such that multiple scattering is expected to be insignificant. Our photometric models relate the reflectance from Bennu’s surface to viewing geometry as functions of the incidence, emission, and phase angles. Radiance Factor functions (RADFs) are used to model the disk-resolved brightness of Bennu. The Minnaert, Lommel-Seeliger, ROLO, and Hapke photometric models work equally well in fitting the best ground-based photometric phase curve data of Bennu. The McEwen model works reasonably well at phase angles from 20° to 70°. Our calculated geometric albedo values of 0.047-0.014+0.012,0.047-0.014+0.005, and 0.048-0.022+0.012 for the Minnaert, the Lommel-Seeliger, and the ROLO models respectively are consistent with the geometric albedo of 0.045±0.015 computed by Emery et al. (Emery, J.P. et al. [2014]. Icarus 234, 17–35) and Hergenrother et al. (Hergenrother, C.W. et al. [2014]. <http://arxiv.org/abs/1409.4704>). Also, our spherical Bond albedo values of 0.016-0.004+0.005,0.015-0.001+0.003, and 0.015-0.005+0.007 for the Minnaert model, Lommel-Seeliger, and ROLO models respectively are consistent with the value of 0.017±0.002 presented by Emery et al. (Emery, J.P. et al. [2014]. Icarus 234, 17–35). On the other hand, the semi-physical models such as the Hapke model, where several assumptions and approximations were necessary, and the McEwen model are not supported by the global disk-integrated data, indicating that disk-resolved measurements will be necessary to constrain these models, as expected.

Research of Improved Minnaert Topographic Correction Model and Application

The topographic correction of remote sensing images is an important factor to improve the precision of quantitative remote sensing data processing. In the existing topographic correction models,the Minnaert model is the only model based on the assumption of non-Lambertian.the Minnaert coefficient K is an effective factor for the correction results. To improve the correction accuracy,we correct the image in accordance with the slope grading idea to select different areas from the image, then use different k values in different slope regions.In this paper, the topography correction is efficiently corrected by SCS model, Minnaert model and improved Minnaert model, based on HJCCD image and the corresponding DEM in Heihe . The results showed that the improved Minnaert model can eliminate the effect of topography better than other methods and can be widely used.

The effect of BRDF surface on radiative heat transfer within a one-dimensional graded index medium

The traditional diffuse or specular surface assumption, which is simple but provides limited information, is insufficient to fully characterize a real surface. The BRDF (Bidirectional Reflectance Distribution Function) surface, which is closer to the real surface, is introduced into the radiative heat transfer problem for the first time. A Minnaert model for the BRDF surface is applied and the genetic algorithm is used to obtain the parameters of the proposed model. The DRESOR (Distribution of Ratios of Energy Scattered by medium Or Reflected by surface) method and the RMC (Reverse Monte Carlo) method are extended to solve the radiative heat transfer within a 1-D absorbing, emitting and scattering graded index medium with BRDF surfaces. The temperature and radiative flux distributions under radiative equilibrium are analyzed under different kinds of graded indexes, optical thicknesses and scattering albedos. The results obtained by the DRESOR method and the RMC method coincide well with each other, which indicates the accuracy of the calculation. Compared with the corresponding diffuse surface, though the relative temperature difference of the BRDF surface is slightly within ±2%, the radiative flux increases significantly by 3.5–12%. And this influence is enhanced by the shortening of the optical thickness while varies little with the changes of graded index and scattering albedo.

Global photometric properties of Asteroid (4) Vesta observed with Dawn Framing Camera

Dawn spacecraft orbited Vesta for more than one year and collected a huge volume of multispectral, high-resolution data in the visible wavelengths with the Framing Camera. We present a detailed disk-integrated and disk-resolved photometric analysis using the Framing Camera images with the Minnaert model and the Hapke model, and report our results about the global photometric properties of Vesta. The photometric properties of Vesta show weak or no dependence on wavelengths, except for the albedo. At 554nm, the global average geometric albedo of Vesta is 0.38±0.04, and the Bond albedo range is 0.20±0.02. The bolometric Bond albedo is 0.18±0.01. The phase function of Vesta is similar to those of S-type asteroids. Vesta’s surface shows a single-peaked albedo distribution with a full-width-half-max ∼17% relative to the global average. This width is much smaller than the full range of albedos (from ∼0.55× to >2× global average) in localized bright and dark areas of a few tens of km in sizes, and is probably a consequence of significant regolith mixing on the global scale. Rheasilvia basin is ∼10% brighter than the global average. The phase reddening of Vesta measured from Dawn Framing Camera images is comparable or slightly stronger than that of Eros as measured by the Near Earth Asteroid Rendezvous mission, but weaker than previous measurements based on ground-based observations of Vesta and laboratory measurements of HED meteorites. The photometric behaviors of Vesta are best described by the Hapke model and the Akimov disk-function, when compared with the Minnaert model, Lommel–Seeliger model, and Lommel–Seeliger–Lambertian model. The traditional approach for photometric correction is validated for Vesta for >99% of its surface where reflectance is within ±30% of global average.

Photometric analysis of the nucleus of Comet 81P/Wild 2 from Stardust images

The disk-resolved flyby images of the nucleus of Comet 81P/Wild 2 collected by Stardust are used to perform a detailed study of the photometric properties of this cometary nucleus. A disk-integrated phase function from phase angle 11° to about 100° is measured and modeled. A phase slope of 0.0513 ± 0.0002 mag/deg is found, with a V-band absolute magnitude of 16.29 ± 0.02. Hapke’s photometric model yields a single-scattering albedo of 0.034, an asymmetry factor of phase function −0.53, a geometric albedo 0.059, and a V-band absolute magnitude of 16.03 ± 0.07. Disk-resolved photometric modeling from both the Hapke model and the Minnaert model results in 11% model RMS, indicating small photometric variations. The roughness parameter is modeled to be 27 ± 5° from limb-darkening profile. The modeled single-scattering albedo and asymmetry factor of the phase function are 0.038 ± 0.004 and −0.52 ± 0.04, respectively, consistent with those from disk-integrated phase function. The bulk photometric properties of the nucleus of Wild 2 are comparable with those of other cometary nuclei. The photometric variations on the surface of the nucleus of Wild 2 are at a level of or smaller than 15%, much smaller than those on the nucleus of Comet 19P/Borrelly and comparable or smaller than those on the nucleus of Comet 9P/Tempel 1. The similar photometric parameters of the nuclei of Wild 2, Tempel 1, and the non-source areas of fan jets on Borrelly may reflect the typical photometric properties of the weakly active surfaces on cometary nuclei.

Post-fire vegetation regrowth detection in the Deiva Marina region (Liguria-Italy) using Landsat TM and ETM+ data

Obtaining quantitative information about the recovery of fire-affected ecosystems is of utmost importance from the management and decision-making point of view. Nowadays the concern about natural environment protection and recovery is much greater than in the past. However, the resources and tools available for its management are still not sufficient. Thus, attention and precision is needed when decisions must be taken. Quantitative estimates on how the vegetation is recovering after a fire can be of help for evaluating the necessity of human intervention on the fire-affected ecosystem, and their importance will grow as the problem of forest fires, climate change and desertification increases. This article performs a comparison of methods to extract quantitative estimates of vegetation cover regrowth with Landsat TM and ETM+ data in an area that burned during the summer of 1998 in the Liguria region (Italy). In order to eliminate possible sources of error, a thorough pre-processing was carried out, including a careful geometric correction (reaching RMSE lower than 0.3 pixels), a topographic correction by means of a constrained Minnaert model and a combination of absolute and relative atmospheric correction methods. Pseudo Invariant Features (PIF) were identified by implementing an automated selection method based in temporal Principal Component Analysis (PCA), which has been called multi-Temporal n-Dimensional Principal Component Analysis (mT-nD-PCA). Spectral Mixture Analysis (SMA) was compared against quantitative vegetation indices which are based on well known traditional vegetation indices like Normalized Difference Vegetation Index (NDVI) and Modified Soil Adjusted Vegetation Index (MSAVI). Accuracy assessment was performed by regressing vegetation cover results obtained with each method against field data gathered during the fieldwork campaign carried out in the study area. Results obtained showed how vegetation cover fractions extracted from the NDVI based quantitative index were the most accurate, being superior to the rest of the techniques applied, including SMA.

Intercomparison of Two BRDF Models in the Estimation of the Directional Emissivity in MIR Channel From MSG1-SEVIRI Data

This work intercompared two Bi-directional Reflectance Distribution Function (BRDF) models, the modified Minnaert's model and the RossThick-LiSparse-R model, in the estimation of the directional emissivity in Middle Infra-Red (MIR) channel from the data acquired by the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) onboard the first Meteosat Second Generation (MSG1). The bi-directional reflectances in SEVIRI channel 4 (3.9 microm) were estimated from the combined MIR and Thermal Infra-Red (TIR) data and then were used to estimate the directional emissivity in this channel with aid of the BRDF models. The results show that: (1) Both models can relatively well describe the non-Lambertian reflective behavior of land surfaces in SEVIRI channel 4; (2) The RossThick-LiSparse-R model is better than the modified Minnaert's model in modeling the bi-directional reflectances, and the directional emissivities modeled by the modified Minnaert's model are always lower than the ones obtained by the RossThick-LiSparse-R model with averaged emissivity differences of approximately 0.01 and approximately 0.04 over the vegetated and bare areas, respectively. The use of the RossThick-LiSparse-R model in the estimation of the directional emissivity in MIR channel is recommended.

Visible–infrared and radar imagery fusion for geological application: a new approach using DEM and sun-illumination model

Radar-multispectral imagery fusion has been successfully used in several application fields. In this study, a new technique to merge an ERS-1 (Synthetic Aperture Radar precision image, SAR-PRI) image and a Landsat Thematic Mapper (TM ) image for the geological study of the western Aspromonte (southern Italy) was investigated. Spectral information provided by the TM image can be effectively combined with texture and pattern data from the radar imagery to produce a synergistic image. Landsat bands are normalized for shadowing effects using the semi-empirical Minnaert model and thereafter multiplied by the ERS1 image. The visible-infrared (VIR) and radar fused bands can be composed into colour images. This technique leads to the production of images in which the geologically relevant information were integrated. These images were compared with the imagery produced by the intensity-hue-saturation (IHS) transformation approach, commonly used for image fusion. The sun-illumination normalization method gives bet...

A Spectro‐Photometric Model of Mars in the near‐infrared

The present model provides estimates of the spectral radiance of Mars in the 0.4–5.7 µm domain. The model is based on several composite surface spectra that correspond to the main types of materials observed. Photometric effects are simulated with both a Minnaert model and a phase function derived from ISM spectra. Aerosols scattering is taken into account for small opacities (single scattering). Thermal emission is accounted for through an emissivity model previously used to derive reflectance from IRS data. Emission and scattering by molecules are also included. Temperature and pressure are allowed to vary with season, local time, and latitude; regional effects, including surface elevation, are averaged out in this version. Results are validated by comparisons with various data sets. One of the main discrepancies with observations is related to atmospheric absorptions deeper than observed, which is probably due to coupling between absorption and scattering.

Visible?infrared and radar imagery fusion for geological application: A new approach using DEM and sun-illumination model

Radar-multispectral imagery fusion has been successfully used in several application fields. In this study, a new technique to merge an ERS-1 (Synthetic Aperture Radar precision image, SAR-PRI) image and a Landsat Thematic Mapper (TM ) image for the geological study of the western Aspromonte (southern Italy) was investigated. Spectral information provided by the TM image can be effectively combined with texture and pattern data from the radar imagery to produce a synergistic image. Landsat bands are normalized for shadowing effects using the semi-empirical Minnaert model and thereafter multiplied by the ERS1 image. The visible-infrared (VIR) and radar fused bands can be composed into colour images. This technique leads to the production of images in which the geologically relevant information were integrated. These images were compared with the imagery produced by the intensity-hue-saturation (IHS) transformation approach, commonly used for image fusion. The sun-illumination normalization method gives better results in image fusion, enhancing subtle spectral features. Compared to the individual images, the synergistic SAR-TM images produced by this technique improve the interpretation of lithology boundaries and recognition of structural features.