Assessing analytical convolution effects in diffusion studies: Applications to experimental and natural diffusion profiles

Given that all in-situ analytical techniques have a non-zero beam size, all measured profiles, resulting from diffusion or otherwise, will be artefactually elongated to some degree. Profiles where the total length over which the concentration changes approaches the resolution of the analytical technique likely suffer from serious convolution; the measured profiles may be considerably elongated relative to the true profile. Resolving this effect is non-trivial, except for some specific combinations of profile type and beam geometry. In this study, a versatile method for numerically deconvoluting diffusion profiles acquired using techniques with Gaussian, Lorentzian, (pseudo-)Voigt, circular/elliptical or square/rectangular interaction volumes, is presented. A MATLAB code, including a user-friendly interface (PACE-the Program for Assessing Convolution Effects in diffusion studies), is also provided, and applied to several experimental and natural profiles interpreted as resulting from diffusion, showing various degrees of convolution.

1.5 years of TROPOMI CO measurements: Comparisons to MOPITT and ATom

We have analyzed TROPOspheric Monitoring Instrument (TROPOMI) carbon monoxide (CO) data acquired between November 2017 and March 2019 with respect to other satellite (MOPITT, Measurement Of Pollution In The Troposphere) and airborne (ATom, Atmospheric Tomography mission) datasets to understand better TROPOMI’s contribution to the global tropospheric CO record (2000 to present). TROPOMI and MOPITT are currently the only satellite instruments deriving CO from solar reflected radiances. Therefore, it is particularly important to understand how these two datasets compare. Our results indicate that TROPOMI CO retrievals over land show excellent agreement with respect to MOPITT: relative biases and their standard deviation (i.e., accuracy and precision) are on average −3.73 ± 11.51, −2.24 ± 12.38, and −3.22 ± 11.13 %, compared to the MOPITT TIR (thermal infrared), NIR (near infrared), and TIR+NIR (multispectral) products, respectively. TROPOMI and MOPITT data also show good agreement in terms of temporal and spatial patterns. Despite depending on solar reflected radiances for its measurements, TROPOMI can also retrieve CO over bodies of water if clouds are present, by approximating partial columns under cloud tops using scaled, model-based reference CO profiles. We quantify the bias of TROPOMI total column retrievals over bodies of water with respect to colocated in situ ATom CO profiles after smoothing the latter with the TROPOMI column averaging kernels (AK), which account for signal attenuation under clouds (relative bias and its standard deviation = 3.25 ± 11.46 %). In addition, we quantify enull (the null-space error), which accounts for differences between the shape of the TROPOMI reference profile and that of the ATom true profile (enull = 2.16 ± 2.23 %). For comparisons of TROPOMI and MOPITT retrievals over open water, we adopt a simpler approach, since smoothing with TROPOMI AK does not apply for MOPITT retrievals. To this effect, we compare TROPOMI total CO columns (above and below cloud tops) and partial CO columns (above cloud top) to their colocated MOPITT TIR counterparts. (This approximation would be most accurate for optically thick clouds.) We find very small changes in relative bias between TROPOMI and MOPITT TIR retrievals if total columns are considered instead of partial above-cloud-top columns (

Trace Gas Retrieval from AIUS：Algorithm Description and O3 Retrieval Assessment

AIUS (Atmospheric Infrared Ultraspectral Sounder) is an infrared occultation spectrometer onboard the Chinese GaoFen-5 satellite, which covers a spectral range of 2.4–13.3 μm (750–4100 cm−1) with a spectral resolution of about 0.02 cm−1. AIUS is designed to measure and study chemical processes of ozone (O3) and other trace gases in the upper troposphere and stratosphere around Antarctic. In this study, the corresponding retrieval methodology is described. The retrieval simulations based on the simulated spectra of AIUS have been carried out, with a focus on O3. The relative difference between the retrieved and the true O3 profiles is within 5% from the 15 km to 70 km and about 10% below 15 km. The corresponding averaging kernels illustrate that the overall retrieval information mainly come from the spectra, not the a priori. The retrieval experiments also demonstrate that the shape of the retrieved profiles resembles the shape of the true profile even if the shape of the a priori profile is different from that of the true profile. Further, we perform the O3 retrieval from the real ACE-FTS (Atmospheric Chemistry Experiment-Fourier Transform Spectrometer) measurements and compare the results with the official ACE-FTS Level-2 products. Overall, both profiles agree well in the stratosphere where the retrieval sensitivity is high. The relative difference between both profiles is about 15% below 70 km, which may due to the measurement errors and different forward model parameters.

Connected Price Dynamics with Revealed Preferences and Auctioneer’s Discretion in VCG Combinatorial Auction

We investigate open-bid protocols termed price-demand procedures in combinatorial auction problems. Instead of requiring buyers to reveal their entire valuation functions directly, the auctioneer gradually gathers information by offering price vectors and requiring demand responses to each buyer. The auctioneer continues to calculate the ‘provisional’ profile of valuation functions in a history-dependent manner and check whether the efficient allocations with and without any single buyer for this profile are revealed in the resultant history. Once these are revealed, the auctioneer ends the procedure and determines the VCG outcome associated with the provisional profile at the ending time. With the assumptions of revealed preference activity rule and connectedness, this paper shows that the VCG outcome associated with the provisional profile at the ending time is always the same as that associated with the true profile, even though the provisional profile is generally different from the true one. Only our procedures can achieve the correct VCG outcome. We further discuss the auctioneer’s discretion and buyers’ privacy concern.

Effective resolution concepts for lidar observations

Since its first establishment in 2000, EARLINET (European Aerosol Research Lidar NETwork) has been devoted to providing, through its database, exclusively quantitative aerosol properties, such as aerosol backscatter and aerosol extinction coefficients, the latter only for stations able to retrieve it independently (from Raman or High Spectral Resolution Lidars). As these coefficients are provided in terms of vertical profiles, EARLINET database must also include the details on the range resolution of the submitted data. In fact, the algorithms used in the lidar data analysis often alter the spectral content of the data, mainly working as low pass filters with the purpose of noise damping. Low pass filters are mathematically described by the Digital Signal Processing (DSP) theory as a convolution sum. As a consequence, this implies that each filter's output, at a given range (or time) in our case, will be the result of a linear combination of several lidar input data relative to different ranges (times) before and after the given range (time): a first hint of loss of resolution of the output signal. The application of filtering processes will also always distort the underlying true profile whose relevant features, like aerosol layers, will then be affected both in magnitude and in spatial extension. Thus, both the removal of noise and the spatial distortion of the true profile produce a reduction of the range resolution. This paper provides the determination of the effective resolution (ERes) of the vertical profiles of aerosol properties retrieved starting from lidar data. Large attention has been addressed to provide an assessment of the impact of low-pass filtering on the effective range resolution in the retrieval procedure.

Using Planar Kinematics to Construct the Full 4-D Tolerance-Map for a Line-Profile

Tolerances on line-profiles are used to control cross-sectional shapes of parts, even mildly twisted ones such as those on turbine or compressor blades. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e. an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, only one attempt has been made at modeling line-profiles [1], and the method used is a kinematic description, based largely on intuition, of the allowable displacements of the middle-sized profile within its tolerance-zone. The result presented is a 4-D double pyramid having a 3-D shape for the common base. Allowable small changes in size represent the fourth dimension in the altitude-direction of the pyramids. However, that work is limited to square, rectangular, and right-triangular profile shapes for which the 3-D transverse sections (called hypersections) of the 4-D T-Map are all geometrically similar to the base because the boundaries are doubly traced. For more generally shaped profiles, [2] the hypersections are not geometrically similar to the base. The objective of this paper is to expand the kinematic description of a profile in its tolerance-zone to include the changing constraints that take place as size is incremented or decremented within the allowable tolerance-range. It provides validation of a different method that is described in a companion paper [3].

Tolerance-Maps for Line-Profiles Constructed From Boolean Operations on Primitive T-Map Elements

For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, only one attempt has been made at modeling line-profiles [1], and the method used is an intuitive kinematic description of the allowable displacements of the middle-sized profile within its tolerance-zone. The objective of this paper is to describe an alternative method of construction, one that is much more amenable to computer automation, to obtain the T-Map of any line-profile. Tolerances on line-profiles are used to control cross-sectional shapes of parts, even mildly twisted ones such as those on turbine or compressor blades. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e. an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. The new method requires decomposing a profile into segments, creating a solid-model T-Map primitive for each, and then combining these by the Boolean intersection to generate the T-Map for a complete line profile of any shape. To economize on length, the scope of this paper is limited to line-profiles having any polygonal shape.

Modeling of Geometric Variations for Line-Profiles

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e., an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.