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Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory

An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.

Pollack, J. B.↗

Double scattering corrections for the theory of the sun's aureole

Double scattering corrections for aureole radiances are calculated by adding the effects of two successive single scatterings. Atmospheric absorption, polarization, and variation of refractive index with altitude are ignored. Corrections due to spherical atmosphere were taken into account by the use of a generalized Chapman function. Realistic scattering phase functions based upon the Lorenz-Mie theory and model altitude-size distribution are used. The model distribution is assumed to be representable in terms of two separable particulate components. It was found that for a moderately clear day, tau (0) is approximately equal to 0.5, and for forward scattering angles, the radiance, B sub 2, due to double scattering is less than 6 percent of that due to single scattering.

Deepak, A.↗

Implementation of A New Microwave Scattering Database and A Forward Model for Active Microwave Sensors in CRTM

Radiative transfer models are extensively used for the assimilation of satellite observations into NWP models as well as retrieving geophysical products from satellite measurements. CRTM is a community model developed by NOAA JCSDA and widely used for different purposes requiring RT calculations. CRTM requires bulk scattering lookup tables in order to perform all-sky RT calculations. However, the current CRTM lookup tables for microwave frequencies were generated based on the Mie theory by assuming spherical frozen particles. The scattering lookup tables generated using the DDA technique has shown to largely improve the RT scattering calculations in the MW region. This presentation targets (i) the implementation and validation of a DDA database that was originally developed for the ARTS RT model into CRTM, and (ii) developing the CRTM active sensor module that takes advantage of the backscattering coefficients computed using the DDA method. The DDA database only provides single scattering properties of different habits, while CRTM requires bulk scattering properties. The CRTM cloud coefficients were previously generated based on the effective radius for representing the size of the particles. However, effective radius is neither measurable nor provided by the NWP models, thus need to be estimated from other geophysical variables such as water content. Therefore, in addition to calculating the CRTM bulk scattering properties from the DDA single scattering database, the CRTM was also largely modified to use cloud water content (kg.m-3), instead of effective radius, for performing the interpolation over size/mass of the particles. CRTM already requires water content as input, thus no extra variables are required for performing scattering calculations using the new ARTS DDA database. The CRTM scattering modules search for effective radius in cloud coefficient files and will use the cloud water content if the effective radius dimension is not found in the cloud coefficient files. Figure 1 shows the CRTM simulated brightness temperatures computed using different cloud coefficients versus ATMS observed values over Hurricane Irma on September 7, 2017 at 18:00 UTC. We used all the cloud water content values included in ERA5 with default CRTM/DDA habits for water, rain, snow, ice, hail, and graupel. ERA5 does not provide separate water content values for ice, hail, and graupel, thus the ice water content values were divided between ice, hail, and graupel clouds similar to what was explained in the previous section. In channels with a frequency lower than 90 GHz, emission from water and rain clouds can compensate for cloud scattering so that cloud contaminated Tbs are larger than corresponding clear sky Tbs. The DDA simulations for channels 1-7 largely perform better than the Mie simulations. The DDA simulations show a mix of small negative and positive simulated minus observed values, while the Mie results show large negative biases. The weighting functions for some of the ATMS temperature sounding channels (channels 9-15) peak mostly above the clouds, therefore the measured Tbs become less sensitive to clouds so that the results of both Mie and DDA become very similar. The Mie lookup tables generate excessive scattering for channel 16, but not enough scattering for the water vapor channels. In the specific case of Hurricane Maria, the DDA lookup tables do not generate enough scattering for channel 16, but the DDA results are much more consistent with observations for water vapor channels than for channel 16. It should be noted that the results may vary if we use other habits to represent snow, hail, and graupel in the DDA simulations. Although these results clearly show the advantage of the DDA database over the Mie dataset, different error sources such as error in the observations, displacement of clouds in the ERA5 reanalysis, and also lack of convective clouds or in general errors in the input atmospheric and cloud profiles contribute to the differences between the simulated and observed values. Aside from the improvements in the simulations, a major advantage of the new dataset is a large number of habits that can be used to tune the data assimilation systems to perform well in different weather conditions.

Isaac Moradi↗

Optical radar studies of the atmosphere.

Optical radar studies of lower atmosphere, giving Mie theory calculations of clear atmosphere volume backscattering cross sections for four laser wavelengths

Lawrence, J. D., Jr.↗

Models of the zodiacal light

Zodiacal light theoretical models, considering interplanetary particles optics, Mie theory and multicolor polarization

Greenberg, J. M.↗

Transfer of thermal microwaves in the atmosphere, volume 1

The Mie theory is used to determine the absorption and scattering properties of liquid hydrometeors at 27 microwave frequencies from 500 MHz to 60 GHz. Based on the Marshall-Palmer distribution of drop sizes, regression equations are developed for the volume absorption coefficient of rain as a function of its temperature and content of liquid water.

Paris, J. F.↗

Transfer of thermal microwaves in the atmosphere, volume 2

Figures and tabular information that are supplemental to a study on transfer of thermal microwaves in the atmosphere are presented. The numerical values for the absorption and scattering cross sections of a pure, liquid, water drop are given for drop diameters ranging up to 6 mm, and for various drop temperatures. These values were obtained through the Mie theory. For a Marshall-Palmer distribution of drop sizes, the volume absorption and scattering coefficients of rain are given for the same temperatures and microwave frequencies shown above and for contents of liquid water in the rain mass. Also, scattergrams are given of the katabatic and upwelling brightness temperatures of up to 582 model atmospheres over a calm ocean versus the equivalent depths of liquid water in cloud form, rain form, or combined cloud and rain form.

Paris, J. F.↗

A catalogue of normalized intensity functions and polarization from a cloud of particles with a size distribution of alpha to the minus 4th power

The Mie theory of light scattering by spheres was used to calculate the scattered intensity functions resulting from single scattering in a polydispersed collection of spheres. The distribution used behaves according to the inverse fourth power law; graphs and tables for the angular dependence of the intensity and polarization for this law are given. The effects of the particle size range and the integration increment are investigated.

Craven, P. D.↗

Formation of spectral lines in planetary atmospheres. III - The use of analytic scattering diagrams in computations of synthetic spectra for cloudy atmospheres.

Results of some comparisons that have been made of line profiles and equivalent widths computed from atmospheric models where the scattering has been represented by the Mie theory and a simple analytic expression, the Heyney-Greenstein function. These results show that the spectroscopic features for these models are indistinguishable and demonstrate the value of using this simple analytic function in terms of the great saving in computer time when computing synthetic spectra for any cloudy planetary atmosphere.

Hunt, G. E.↗

Preliminary data on the optical properties of solid ammonia and scattering parameters for ammonia cloud particles.

The infrared absorption spectrum of solid ammonia is obtained from 2 to 125 microns as a composite of the published measurements. From this, the absorption coefficient and the complex refractive index are calculated as a function of frequency by integration of the Kramers-Kroenig dispersion relations. These data are used in a Mie theory analysis to obtain the basic parameters for scattering of long wavelength radiation by solid ammonia particles; this is believed to be an important process in radiative transfer within the atmospheres of the giant planets.

Taylor, F. W.↗

Optical modeling of agricultural fields and rough-textured rock and mineral surfaces

Review was made of past models for describing the reflectance and/or emittance properties of agricultural/forestry and geological targets in an effort to select the best theoretical models. An extension of the six parameter Allen-Gayle-Richardson model was chosen as the agricultural plant canopy model. The model is used to predict the bidirectional reflectance of a field crop from known laboratory spectra of crop components and approximate plant geometry. The selected geological model is based on Mie theory and radiative transfer equations, and will assess the effect of textural variations of the spectral emittance of natural rock surfaces.

Suits, G. H.↗

Coherent optical instrumentation for measurements of particle parameters

The application of cross-beam Laser Doppler Velocimeter (LDV) for sizing small particles was investigated from September 1973 to August 1974. Theoretical results were obtained by analyzing the scattering characteristics of small particles in a cross-beam LDV system. Theoretical calculations based on scalar diffraction theory and Mie scattering theory were performed. Experimental results were also obtained to compare with theoretical predictions. It is concluded that the forward scattering characteristics of small particles in a cross-beam LDV system can be used for particle sizing.

Chu, W. P.↗