scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

scholarly journals Near infrared nadir retrieval of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (12) ◽  
pp. 2633-2657 ◽  
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Bound Constraints ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY on-board the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b-2 processing of SCIAMACHY data, a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed. BIRRA performs a nonlinear or separable least squares fit (with bound constraints optional) of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

scholarly journals Algorithm theoretical baseline for formaldehyde retrievals from S5P TROPOMI and from the QA4ECV project

2018 ◽  
Vol 11 (4) ◽  
pp. 2395-2426 ◽  
Author(s):  
Isabelle De Smedt ◽  
Nicolas Theys ◽  
Huan Yu ◽  
Thomas Danckaert ◽  
Christophe Lerot ◽  
...  
Keyword(s):  
Near Infrared ◽  
Horizontal Resolution ◽  
Retrieval Algorithm ◽  
User Requirements ◽  
Vertical Column ◽  
Ultraviolet Range ◽  
Order Of Magnitude ◽  
Shortwave Infrared ◽  
Double Channel ◽  
The Eu

Abstract. On board the Copernicus Sentinel-5 Precursor (S5P) platform, the TROPOspheric Monitoring Instrument (TROPOMI) is a double-channel, nadir-viewing grating spectrometer measuring solar back-scattered earthshine radiances in the ultraviolet, visible, near-infrared, and shortwave infrared with global daily coverage. In the ultraviolet range, its spectral resolution and radiometric performance are equivalent to those of its predecessor OMI, but its horizontal resolution at true nadir is improved by an order of magnitude. This paper introduces the formaldehyde (HCHO) tropospheric vertical column retrieval algorithm implemented in the S5P operational processor and comprehensively describes its various retrieval steps. Furthermore, algorithmic improvements developed in the framework of the EU FP7-project QA4ECV are described for future updates of the processor. Detailed error estimates are discussed in the light of Copernicus user requirements and needs for validation are highlighted. Finally, verification results based on the application of the algorithm to OMI measurements are presented, demonstrating the performances expected for TROPOMI.

scholarly journals Algorithm Theoretical Baseline for formaldehyde retrievals from S5P TROPOMI and from the QA4ECV project

2017 ◽  
Author(s):  
Isabelle De Smedt ◽  
Nicolas Theys ◽  
Huan Yu ◽  
Thomas Danckaert ◽  
Christophe Lerot ◽  
...  
Keyword(s):  
Near Infrared ◽  
Horizontal Resolution ◽  
Retrieval Algorithm ◽  
User Requirements ◽  
Vertical Column ◽  
Ultraviolet Range ◽  
Order Of Magnitude ◽  
Shortwave Infrared ◽  
Double Channel ◽  
The Eu

Abstract. On board of the Copernicus Sentinel-5 Precursor (S5P) platform, the TROPOspheric Monitoring Instrument (TROPOMI) is a double channel nadir-viewing grating spectrometer measuring solar back-scattered earthshine radiances in the ultraviolet, visible, near-infrared and shortwave infrared with global daily coverage. In the ultraviolet range, its spectral resolution and radiometric performance are equivalent to those of its predecessor OMI, but its horizontal resolution at true nadir is improved by an order of magnitude. This paper introduces the formaldehyde (HCHO) tropospheric vertical column retrieval algorithm implemented in the S5P operational processor, and comprehensively describes its various retrieval steps. Furthermore, algorithmic improvements developed in the framework of the EU FP7-project QA4ECV are described for future updates of the processor. Detailed error estimates are discussed in the light of Copernicus user requirements and needs for validation are highlighted. Finally, verification results based on the application of the algorithm to OMI measurements are presented, demonstrating the performances expected for TROPOMI.

scholarly journals Least Squares Optimization: From Theory to Practice

Robotics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 51 ◽  
Author(s):  
Giorgio Grisetti ◽  
Tiziano Guadagnino ◽  
Irvin Aloise ◽  
Mirco Colosi ◽  
Bartolomeo Della Corte ◽  
...  
Keyword(s):  
Computer Vision ◽  
Least Squares ◽  
Open Source ◽  
State Of The Art ◽  
Nonlinear Least Squares ◽  
Research Community ◽  
Specific Domain ◽  
Theory To Practice ◽  
Least Squares Optimization ◽  
Computer Vision Systems

Nowadays, Nonlinear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last few years, and this resulted in the development of several open-source solvers to approach constantly increasing classes of problems. In this work, we propose a unified methodology to design and develop efficient Least-Squares Optimization algorithms, focusing on the structures and patterns of each specific domain. Furthermore, we present a novel open-source optimization system that addresses problems transparently with a different structure and designed to be easy to extend. The system is written in modern C++ and runs efficiently on embedded systemsWe validated our approach by conducting comparative experiments on several problems using standard datasets. The results show that our system achieves state-of-the-art performances in all tested scenarios.

Molecular Parameters for the a3Πu and b3Σg− States in C2

1975 ◽  
Vol 53 (3) ◽  
pp. 299-302 ◽  
Author(s):  
L. Veseth
Keyword(s):  
Least Squares ◽  
Electronic Spectra ◽  
Nonlinear Least Squares ◽  
Experimental Information ◽  
Present Approach ◽  
Energy Separation ◽  
Molecular Parameters ◽  
Triplet Splitting ◽  
Least Squares Fit

Molecular parameters for the a3Πu and b3Σg− states in C2 (Ballik–Ramsay system) are determined by a nonlinear least squares fit directly to the observed wavelengths. No satellite lines are observed in the electronic spectra of C2, and the influence of nuclear statistics yields further restrictions with regard to observable lines. The present approach, however, yields accurate values of the various triplet splitting and Λ-doubling parameters in spite of this lack of experimental information. Finally a refined value of the triplet–singlet energy separation is obtained.

scholarly journals 2D shape deformation using nonlinear least squares optimization

2006 ◽  
Vol 22 (9-11) ◽  
pp. 653-660 ◽  
Author(s):  
Yanlin Weng ◽  
Weiwei Xu ◽  
Yanchen Wu ◽  
Kun Zhou ◽  
Baining Guo
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Shape Deformation ◽  
Least Squares Optimization

scholarly journals Retrieval Algorithm for the Column CO<sub>2</sub> Mixing Ratio from Pulsed Multi-Wavelength Lidar Measurements

2020 ◽  
Author(s):  
Xiaoli Sun ◽  
James B. Abshire ◽  
Anand Ramanathan ◽  
S. Randy Kawa ◽  
Jianping Mao
Keyword(s):  
Least Squares ◽  
Absorption Line ◽  
Linear Trend ◽  
Spectral Response ◽  
Retrieval Algorithm ◽  
Co2 Absorption ◽  
Mixing Ratio ◽  
Atmospheric Transmission ◽  
Least Squares Fit ◽  
Multi Wavelength

Abstract. The retrieval algorithm for the column mixing ratio of CO2 from the measurements of a pulsed multi-wavelength integrated path differential absorption (IPDA) lidar is described. The lidar samples the shape of the 1572.33 nm CO2 absorption line at 15 or 30 wavelengths. The algorithm uses a least-squares fit between the CO2 line shape computed from a layered atmosphere model to that sampled by the lidar. In addition to the column average CO2 dry air mole fraction (XCO2), several other parameters are also solved simultaneously from the fit. These include the Doppler shift in the received laser signal wavelengths, the product of the surface reflectivity and atmospheric transmission and a linear trend in the lidar receiver's spectral response. The algorithm can also be used to solve for the average water vapor mixing ratio, which causes a secondary absorption in the wings of the CO2 absorption line under high humidity conditions. The least-squares fit is linearized about the expected XCO2 value which allows the use of a standard linear least-squares fitting method and software tools. The standard deviation of the retrieved XCO2 is obtained from covariance matrix of the fit. An averaging kernel is defined similarly to that used for passive trace-gas sounding. Examples are presented of using the algorithm to retrieve XCO2 from the measurements from NASA Goddard's airborne CO2 Sounder lidar made at a constant altitude and during spiral-down maneuvers.

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