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Black carbon (BC) aerosol plays an important role in the atmosphere as an absorber of solar radiation and contributes significantly to global warming. The optical properties of BC are fundamental for both direct radiative effect studies and remote sensing of BC properties. However, due to the complex aggregation structures of BC particles, accurate simulations of their optical properties are limited and computationally expensive, while equivalent spherical models or approximate methods could easily introduce relative errors up to 30%. This study generates a comprehensive database to calculate aggregate optical properties efficiently and accurately. The database covers a wide range of BC properties including aggregation structure, refractive index, and particle size (both monomer size and number of monomers). An accurate numerical model, i.e. the multiple-sphere T-matrix method, is used to calculate the single-scattering properties of BC clusters in the form of fractal aggregates. By interpolation, the database can be used to give the scattering properties of aggregates with monomer number from 1 up to 3000, monomer size parameter from 0.05 to 0.5, real part of refractive index from 1.2 to 2.0, and imaginary part from 0.2 to 1.0. The relative errors caused by the interpolation are much less than 1% for the single scattering properties. The pre-calculated database and the implementation used to calculate the required aggregate optical properties are publicly available for users interested in remote sensing of BC aerosols and performing radiative effect calculations.

The optical properties of black carbon (BC) are fundamental for radiative transfer and remote sensing. BC geometry is successfully represented by an idealized model named “fractal aggregate”, and numerous methods are available and widely used to simulate the corresponding optical properties. This study systematically evaluates the performance of the Discrete Dipole Approximation (DDA) for optical simulations of BC aggregates. The Multiple Sphere T-Matrix (MSTM) results are used as references for accuracy evaluation. The differences between the DDA and MSTM can be controlled to be less than 3% by using dipole size much smaller than the monomer size, and the DDA efficiency is sensitive to aggregate structures, e.g. lacy or compact. We find that shape representation for small-sized monomers during DDA discretization leads significant errors, i.e., up to 10%, and relatively large refractive indices of BC also affects the DDA accuracy. However, the MSTM treats the BC monomers as perfect spheres without overlapping, and the imperfect structure that is implicitly introduced in the DDA simulations due to the spatial discretization may be a better representation of realistic BC particles. Moreover, the efficiency of the DDA can be improved by defining dipoles on the particle boundary to have refractive indices given by the effective medium approximation (EMA). This leads to the adequate shape representation even using larger dipole sizes, and results in the DDA accuracy comparable to that of the reference MSTM solution.

A High-performance Atmospheric Radiation Package (HARP) is developed for studying multiple-scattering planetary atmospheres. HARP is an open-source program written in C++ that utilizes high-level data structure and parallel-computing algorithms. It is generic in three aspects. First, the construction of the model atmospheric profile is generic. The program can either take in an atmospheric profile or construct an adiabatic thermal and compositional profile, taking into account the clouds and latent heat release due to condensation. Second, the calculation of opacity is generic, based on line-by-line molecular transitions and tabulated continuum data, along with a table of correlated-k opacity provided as an option to speed up the calculation of energy fluxes. Third, the selection of the solver for the radiative transfer equation is generic. The solver is not hardwired in the program. Instead, based on the purpose, a variety of radiative transfer solvers can be chosen to couple with the atmosphere model and the opacity model. We use the program to investigate the radiative heating and cooling rates of all four giant planets in the Solar System. Our Jupiter's result is consistent with previous publications. Saturn has a nearly perfect balance between the heating rate and cooling rate. Uranus has the least radiative fluxes because of the lack of CH4 and its photochemical products. Both Uranus and Neptune suffer from a severe energy deficit in their stratospheres. Possible ways to resolve this issue are discussed. Finally, we recalculate the radiative time constants of all four giant planet atmospheres and find that the traditional values from (Conrath BJ, Gierasch PJ, Leroy SS. Temperature and Circulation in the Stratosphere of the Outer Planets. Icar. 1990;83:255-81) are significantly overestimated., 28 pages, 8 figures

The Principal Component Analysis (PCA)-based fast radiative transfer method has been shown to have at least an order of magnitude increase in computational speed while maintaining an overall accuracy of 0.01% (compared to line-by-line calculations) over narrow and broad spectral bands. In this paper, we describe several improvements made to the method and provide a discussion of the method’s performance over a diverse set of atmospheric profiles and land surface types. We also test the model over uniform pressure level profiles. The method is now capable of providing atmospheric spectra with residuals under 0.1%, calculated with respect to the continuum, throughout the shortwave region between 0.3−3μm at high resolution, which is substantial improvement over errors reported in earlier work. Future directions for applications and further optimization are examined.

Accurate radiative transfer (RT) calculations are necessary for many earth-atmosphere applications, from remote sensing retrieval to climate modeling. A Principal Component Analysis (PCA)-based spectral binning method has been shown to provide an order of magnitude increase in computational speed while maintaining an overall accuracy of 0.01% (compared to line-by-line calculations) over narrow spectral bands. In this paper, we have extended the PCA method for RT calculations over the entire shortwave region of the spectrum from 0.3 to 3 microns. The region is divided into 33 spectral fields covering all major gas absorption regimes. We find that the RT performance runtimes are shorter by factors between 10-100, while root mean square errors are of order 0.01%.

Hyperspectral observations have become one of the most popular and powerful methods for atmospheric remote sensing, and are widely used for temperature, gas, aerosol, and cloud retrievals. However, accurate forward radiative transfer simulations are computationally expensive since typical line-by-line approaches involve a large number of monochromatic radiative transfer calculations. This study explores the feasibility of machine learning techniques (using neural network (NN) as an example) for fast hyperspectral radiative transfer simulations, by performing calculations at a small fraction of hyperspectral wavelengths and extending them across the entire spectral range. Results from the NN model are compared with those from a principal component analysis (PCA) model, which uses a similar principle of dimensionality reduction. We consider hyperspectral radiances from both actual satellite observations and accurate line-by-line simulations. The NN model can alleviate the computational burden by two to three orders of magnitude, and generate radiances with small relative errors (generally less than 0.5% compared to exact calculations); the performance of the NN model is better than that of the PCA model. The model can be further improved by optimizing the training procedure and parameters, the representative wavelengths, and the machine learning technique itself.

Partial column-averaged carbon dioxide (CO_2) mixing ratio in three tropospheric layers has been retrieved from Total Carbon Column Observing Network (TCCON) spectra in the 1.6 μm CO_2 absorption band. Information analysis suggests that a measurement with ∼60 absorption lines provides three or more pieces of independent information, depending on the signal-to-noise ratio and solar zenith angle. This has been confirmed by retrievals based on synthetic data. Realistic retrievals for both total and partial column-averaged CO_2 over Park Falls, Wisconsin on July 12, 15, and August 14, 2004, agree with aircraft measurements. Furthermore, the retrieved total column averages are always underestimated by less than 1%. The results above provide a basis for CO_2 profile retrievals using ground-based observations in the near-infrared region.

A major challenge in retrieving CO_2 concentrations from thermal infrared remote sensing comes from the fact that measurements in the 4.3 and 15 μm absorption bands (AIRS or TES) are sensitive to both temperature and CO_2 variations. This complicates the selection of absorption channels with maximum CO_2 concentration information content. In contrast, retrievals using near infrared (NIR) CO_2 absorption bands are relatively insensitive to temperature and are most sensitive to changes of CO_2 near the surface, where the sources and sinks are located. The Orbiting Carbon Observatory (OCO) was built to measure reflected sunlight in three NIR spectral regions (the 0.76 μm O_2 A-band and two CO_2 bands at 1.61 and 2.06 μm). In an effort to significantly increase the speed of accurate CO_2 retrieval algorithms for OCO, we performed an information content analysis to identify the 20 best channels from each CO_2 spectral region to use in OCO retrievals. Retrievals using these 40 channels provide as much as 75% of the total CO_2 information content compared to retrievals using all 1016 channels in each spectral region. The CO_2 retrievals using our selected channels have a precision better than 0.1 ppm. This technique can be applied to the retrieval of other geophysical variables (e.g., temperature or CH_4), or modified for other instruments, such as AIRS or TES.

Radiative transfer is computationally expensive. However, it is essential to many applications, in particular remote sensing retrievals. Principal component analysis of the optical depth and single scattering albedo profiles has been proposed as a possible method to help ease the computational burden. Here we show how the technique could be applied to a practical problem of CO_2 retrievals from high spectral resolution measurements of reflected sunlight in three near infrared bands. We obtain a speed improvement of more than 50 fold (compared to monochromatic computations), while reproducing the radiances to better than 0.1% accuracy.

We perform a retrieval based on optimal estimation theory to retrieve the vertical distribution of ozone from simulated spectra in the Huggins bands. The model atmosphere includes scattering by aerosol as well as Rayleigh scattering. The virtual instrument is ground-based and zenith-viewing. Using this algorithm, we show that it is possible to retrieve the ozone profile provided that the spectral resolution is at least 0.2 nm and the signal to noise ratio greater than 500. Our synthetic retrievals suggest that if we are able to measure the Stokes parameters Q, U and V with accuracy comparable to that of the intensity, the information contained in the measurements, and therefore the inversion, will improve. Furthermore, we find that the measurement of the full Stokes vector from the ground-based instrument will especially enhance the retrieval of tropospheric ozone. Utilizing concepts from information theory, our arguments are confirmed by increases in the degrees of freedom and the Shannon information content in the simulated measurements.

Sensitivity studies have been performed to evaluate the errors resulting from ignoring polarization in analyzing spectroscopic measurements of the O_2A band from space, using the Orbiting Carbon Observatory (OCO) as a test case. An 11-layer atmosphere, with both gas and aerosol loading, and bounded from below by a lambertian reflecting surface, was used for the study. The numerical computations were performed with a plane-parallel vectorized discrete ordinate radiative transfer code. Beam and viewing geometry, surface reflectance and aerosol loading were varied one at a time to evaluate and understand the individual errors. Different behavior was observed in the line cores and the continuum because of the different paths taken by the photons in the two cases. The errors were largest when the solar zenith angle was high, and the aerosol loading and surface reflectance low. To understand the effect of neglecting polarization on CO_2 column retrievals, a linear error analysis study was performed on simulated measurements from the OCO spectral regions, viz. the 1.61 and 2.06 μm CO_2 bands and the O_2A band. It was seen that neglecting polarization could introduce errors as high as 10 ppm, which is substantially larger than the required retrieval precision of ∼2 ppm. A variety of approaches, including orders of scattering, spectral binning and the use of lookup tables are being explored to reduce the errors.

Radiative transfer computation is the rate-limiting step in most high spectral resolution remote sensing retrieval applications. While several techniques have been proposed to speed up radiative transfer calculations, they all suffer from accuracy considerations. We propose a new method, based on a principal component analysis of the optical properties of the system, that addresses these concerns. Taking atmospheric transmission in the O_2A band as a test case, we reproduced the reflectance spectrum at the top of the atmosphere (TOA), obtained using the multiple scattering code DISORT, with an accuracy of 0.3%, while achieving an order of magnitude improvement in speed.

Light reflected or transmitted by a planetary atmosphere contains information about particles and molecules in the atmosphere. Therefore, accurate modeling of the radiation field may be used to retrieve information on atmospheric composition. In this paper, a multi-layer model for a vertically inhomogeneous atmosphere is implemented by using the doubling-adding method for a plane-parallel atmosphere. By studying the degree of linear polarization of the transmitted and reflected solar light in the Huggins bands, we find significant differences between tropospheric ozone and stratospheric ozone. The effects of tropospheric ozone change on the linear polarization are 10 times more than that of the same amount of stratospheric ozone change. We also show the aerosol effect on the linear polarization, but this effect is wavelength independent as compared to that caused by the tropospheric ozone change. The results provide a theoretical basis for the retrieval of tropospheric ozone from measurement of linear polarization of the scattered sunlight both from the ground and from a satellite.

Due to larger multiple scattering effects in the troposphere compared to that in the stratosphere, the optical path of tropospheric ozone is markedly enhanced (as compared with that of stratospheric ozone) in the Huggins bands from 310 to 345 nm. Model study of the direct and diffuse solar fluxes on the ground shows differences between tropospheric and stratospheric ozone. The characteristic signature of tropospheric ozone enables us to distinguish a change in troposheric ozone from that of stratospheric ozone. A simple retrieval algorithm is used to recover the tropospheric column ozone from simulated data.

A calculation of the A2 sigma --> X2 pi (0, 0) band emission rate factors and line center absorption cross sections of OH applicable to its measurement using solar resonant fluorescence in the terrestrial atmosphere is presented in this paper. The most accurate available line parameters have been used. Special consideration has been given to the solar input flux because of its highly structured Fraunhofer spectrum. The calculation for the OH atmospheric emission rate factor in the solar resonant fluorescent case is described in detail with examples and intermediate results. Results of this calculation of OH emission rate factors for individual rotational lines are on average 30% lower than the values obtained in an earlier work.

We describe a method for calculating directly the mean integrated intensity in an inhomogeneous Rayleigh scattering atmosphere using a combined variational and iterative technique. This method is particularly useful for computing dissociation rates in aeronomical problems. Simple semi-analytic expressions are derived.