Aeolus L2A aerosol optical properties product: standard correct algorithm and Mie correct algorithm

Aeolus carries the Atmospheric LAser Doppler INstrument (ALADIN), the first high-spectral-resolution lidar (HSRL) in space. Although ALADIN is optimized to measure winds, its two measurement channels can also be used to derive optical properties of atmospheric particles, including a direct retrieval of the lidar ratio. This paper presents the standard correct algorithm and the Mie correct algorithm, the two main algorithms of the optical properties product called the Level-2A product, as they are implemented in version 3.12 of the processor, corresponding to the data labelled Baseline 12. The theoretical basis is the same as in Flamant et al. (2008). Here, we also show the in-orbit performance of these algorithms. We also explain the adaptation of the calibration method, which is needed to cope with unforeseen variations of the instrument radiometric performance due to the in-orbit strain of the primary mirror under varying thermal conditions. Then we discuss the limitations of the algorithms and future improvements. We demonstrate that the L2A product provides valuable information about airborne particles; in particular, we demonstrate the capacity to retrieve a useful lidar ratio from Aeolus observations. This is illustrated using Saharan dust aerosol observed in June 2020.

Aeolus L2A Aerosol Optical Properties Product: Standard Correct Algorithm and Mie Correct Algorithm

Aeolus carries ALADIN, the first High Spectral Resolution Lidar (HSRL) in space. Although ALADIN was optimized to measure winds, its two measurement channels can also be used to derive optical properties of atmospheric particles, including a direct retrieval of the lidar ratio. This paper presents the two main algorithms of the optical properties product called Level 2A product, as they are implemented in version 3.12 of the processor, corresponding to the data labelled Baseline 12. The theoretical basis is the same as in Flamant et al. (2008). Here, we also show the in orbit performance of these algorithms. We also explain the adaptation of the calibration method, which is needed to cope with unforeseen variations of the instrument radiometric performance due to the in-orbit strain of the primary mirror under varying thermal conditions. Then we discuss the limitations of the algorithms and future improvements. We demonstrate that the L2A product provides valuable information about airborne particles, in particular we demonstrate the capacity to retrieve a useful lidar ratio from Aeolus observations. This is illustrated on a case of Saharan dust emission, observed in June 2020.

Statistical validation of Aeolus L2A particle backscatter coefficient retrievals over ACTRIS/EARLINET stations in the Iberian Peninsula

Global Observing Systems (GOS) encounter some limitations due to a lack of worldwide real-time wind measurements. In this context, the European Space Agency (ESA) has developed the Aeolus satellite mission, based on the ALADIN (Atmospheric Laser Doppler Instrument) Doppler wind lidar, aimed to obtain near real-time wind retrievals at global scale. As spin-off products, the instrument retrieves aerosol optical properties such as particle backscatter and extinction coefficients. In this work, a validation of Aeolus reprocessed (baseline 10) co-polar backscatter coefficients is presented through an intercomparison with analogous ground-based measurements taken at the ACTRIS/EARLINET stations of Granada (Spain), Évora (Portugal) and Barcelona (Spain) over the period from July 2019 until October 2020. Case studies are first presented, followed by a statistical analysis. The stations are located in a hot spot between Africa and the rest of Europe, which guarantees a variety of aerosol types, from mineral dust layers to continental/anthropogenic aerosol, and allow us to test Aeolus performance under different scenarios. The so called Aeolus-like profiles are obtained from total particle backscatter coefficient and linear particle depolarization ratio profiles at 355 nm and 532 nm measured from surface, through a thorough bibliographic review of dual-polarization measurements for relevant aerosol types. Finally, the study proposes a relation for the spectral conversion of , which is implemented in the Aeolus-like profile calculation. The statistical results show the ability of the satellite to detect and characterize significant aerosol layers under cloud free conditions, along with the surface effect on the lowermost measurements, which causes the satellite to largely overestimate co-polar backscatter coefficients. Finally, Aeolus standard correct algorithm middle bin (SCAmb) shows a better agreement with ground-based measurements than the standard correct algorithm (SCA), which tends to retrieve negative and meaningless coefficients in the clear troposphere. The implementation of Aeolus quality flags entails a vast reduction in the number of measurements available for comparison, which affects the statistical significance of the results, without improving significantly the statistical agreement between satellite and ground-based measurements.

On the construction of staggered linear bases

A staggered linear basis is a specific basis for a polynomial ideal generating the ideal as a linear vector space. There are some algorithms in the literature to compute these bases and we show that they do not work properly. In this paper, due to the strong connection between Gröbner bases and staggered linear bases and by applying a signature-based structure, we present a new and correct algorithm to compute staggered linear bases. Since the output of this algorithm also remains a Gröbner basis for its input ideal, we conclude the paper by discussing the performance of this algorithm compared with the newest signature-based algorithm to compute Gröbner bases.

A Simple and Efficient Tensor Calculus

Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of these expressions. Recently, an algorithm for computing higher order derivatives of tensor expressions like Jacobians or Hessians has been introduced that is a few orders of magnitude faster than previous state-of-the-art approaches. Unfortunately, the approach is based on Ricci notation and hence cannot be incorporated into automatic differentiation frameworks like TensorFlow, PyTorch, autograd, or JAX that use the simpler Einstein notation. This leaves two options, to either change the underlying tensor representation in these frameworks or to develop a new, provably correct algorithm based on Einstein notation. Obviously, the first option is impractical. Hence, we pursue the second option. Here, we show that using Ricci notation is not necessary for an efficient tensor calculus and develop an equally efficient method for the simpler Einstein notation. It turns out that turning to Einstein notation enables further improvements that lead to even better efficiency.

Proptosis of the globe. Ten main questions and answers

Proptosis of the globe (luxatio bulbi oculi) is a traumatic displacement of the eyeball beyond the bone orbit. Globe proptosis is a fairly common emergency ophthalmic pathology among dogs and cats, which any doctor may encounter in his practice. Moreover, the outcome of the pathological condition depends both on the severity of the primary damage to the eye and on the correct algorithm for providing medical care to the patient. In this article we tried to answer the main ten questions: a clinical assessment of the severity of the condition, reposition and immibilization of the globe, methods to reduce intraorbital edema and the prevention of bacterial complications, that a veterinarion practitioner may have during his medical work with this severe pathology.

A neural network construction for pattern recognition problems with standard information on the basis of the algorithms of model with piecewise linear surfaces and parameters

In the paper for recognition problems with standard information on the basis of the operator approach and the model with parameters and piecewise linear surface has been constructed a neural network which reproduced of computations performs by the correct algorithm.