Existence and uniqueness proof for the minimum model error optimal estimation algorithm

In this article we give a self-contained existence and uniqueness proof for the Tits simple group T. Parrott gave the first uniqueness proof. Whereas Tits' and Parrott's results employ the theory of finite groups of Lie type, our existence and uniqueness proof follows from the general algorithms and uniqueness criteria for abstract finite simple groups described in the first author's book [11]. All we need from the previous papers is the fact that the centralizer H of the Tits group T is an extension of a 2-group J with order 29 and nilpotency class 3 by a Frobenius group F of order 20 such that the center Z(H) has order 2 and any Sylow 5-subgroup Q of H has a centralizer CJ(Q) ≤ Z(H).

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Technical note: Evaluation of profile retrievals of aerosols and trace gases for MAX-DOAS measurements under different aerosol scenarios based on radiative transfer simulations

Atmospheric Chemistry and Physics ◽

10.5194/acp-21-12867-2021 ◽

2021 ◽

Vol 21 (17) ◽

pp. 12867-12894

Author(s):

Xin Tian ◽

Yang Wang ◽

Steffen Beirle ◽

Pinhua Xie ◽

Thomas Wagner ◽

...

Keyword(s):

Radiative Transfer ◽

Trace Gases ◽

Optimal Estimation ◽

Estimation Algorithm ◽

Optical Absorption Spectroscopy ◽

Limited Information ◽

Inversion Algorithm ◽

Vertical Column ◽

Near Surface ◽

Aerosol Pollution

Abstract. Ground-based Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) is a state-of-the-art remote sensing technique for deriving vertical profiles of trace gases and aerosols. However, MAX-DOAS profile inversions under aerosol pollution scenarios are challenging because of the complex radiative transfer and limited information content of the measurements. In this study, the performances of two inversion algorithms were evaluated for various aerosol pollution scenarios based on synthetic slant column densities (SCDs) derived from radiative transfer simulations. Compared to previous studies, in our study, much larger ranges of aerosol optical depth (AOD) and NO2 vertical column densities (VCDs) are covered. One inversion algorithm is based on optimal estimation; the other uses a parameterized approach. In this analysis, three types of profile shapes for aerosols and NO2 were considered: exponential, Boltzmann, and Gaussian. First, the systematic deviations of the retrieved aerosol profiles from the input profiles were investigated. For most cases, the AODs of the retrieved profiles were found to be systematically lower than the input values, and the deviations increased with increasing AOD. In particular for the optimal estimation algorithm and for high AOD, these findings are consistent with the results in previous studies. The assumed single scattering albedo (SSA) and asymmetry parameter (AP) have a systematic influence on the aerosol retrieval. However, for most cases the influence of the assumed SSA and AP on the retrieval results are rather small (compared to other uncertainties). For the optimal estimation algorithm, the agreement with the input values can be improved by optimizing the covariance matrix of the a priori uncertainties. Second, the aerosol effects on the NO2 profile retrieval were tested. Here, especially for the optimal estimation algorithm, a systematic dependence on the NO2 VCD was found, with a strong relative overestimation of the retrieved results for low NO2 VCDs and an underestimation for high NO2 VCDs. In contrast, the dependence on the aerosol profiles was found to be rather low. Interestingly, the results for both investigated wavelengths (360 and 477 nm) were found to be rather similar, indicating that the differences in the radiative transfer between both wavelengths have no strong effect. In general, both inversion schemes can retrieve the near-surface values of aerosol extinction and trace gas concentrations well.

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Ultrasound-based optimal parameter estimation improves assessment of calf muscle-tendon interaction during walking

10.1101/778720 ◽

2019 ◽

Cited By ~ 1

Author(s):

T. Delabastita ◽

M. Afschrift ◽

B. Vanwanseele ◽

F. De Groote

Keyword(s):

Energy Cost ◽

Optimal Parameter ◽

Optimal Estimation ◽

Estimation Algorithm ◽

Calf Muscle ◽

Metabolic Energy ◽

New Approach ◽

Estimated Parameters ◽

Optimal Parameter Estimation ◽

Good Accordance

We present and evaluate a new approach to estimate calf muscle-tendon parameters and calculate calf muscle-tendon function during walking. We used motion analysis, ultrasound, and EMG data of the calf muscles collected in six young and six older adults during treadmill walking as inputs to a new optimal estimation algorithm. We used estimated parameters or scaled generic parameters in an existing approach to calculate muscle fiber lengths and activations. We calculated the fit with experimental data in terms of root mean squared differences (RMSD) and coefficients of determination (R2). We also calculated the calf muscle metabolic energy cost. RMSD between measured and calculated fiber lengths and activations decreased and R2 increased when estimating parameters compared to using scaled generic parameters. Moreover, R2 between measured and calculated gastrocnemius medialis fiber length and soleus activations increased by 19 % and 70 %, and calf muscle metabolic energy decreased by 25% when using estimated parameters compared to using scaled generic parameters at speeds not used for estimation. This new approach estimates calf muscle-tendon parameters in good accordance with values reported in literature. The approach improves calculations of calf muscle-tendon interaction during walking and highlights the importance of individualizing calf muscle-tendon parameters.

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Potential of next-generation imaging spectrometers to detect and quantify methane point sources from space

10.5194/amt-2019-202 ◽

2019 ◽

Author(s):

Daniel H. Cusworth ◽

Daniel J. Jacob ◽

Daniel J. Varon ◽

Christopher Chan Miller ◽

Xiong Liu ◽

...

Keyword(s):

Spectral Resolution ◽

Signal To Noise Ratio ◽

Optimal Estimation ◽

Estimation Algorithm ◽

Global Scale ◽

Point Sources ◽

Emission Rates ◽

Atmospheric Methane ◽

Pixel Resolution ◽

Gas Fields

Abstract. We examine the potential for global detection of methane plumes from individual point sources with the new generation of spaceborne imaging spectrometers (EnMAP, PRISMA, EMIT, SBG) scheduled for launch in 2019–2025. These instruments are designed to map the Earth's surface with a sampling distance as fine as 30 × 30 m2 but they have spectral resolution of 7–10 nm in the 2200–2400 nm band that should also allow useful detection of atmospheric methane. We simulate scenes viewed by EnMAP (10 nm spectral resolution, 180 signal-to-noise ratio) using the EnMAP End-to-End Simulation Tool with superimposed methane plumes generated by large-eddy simulations. We retrieve atmospheric methane and surface reflectivity for these scenes using the IMAP-DOAS optimal estimation algorithm. We find an EnMAP precision of 4–13 % for atmospheric methane depending on surface type, allowing effective single-pass detection of 100+ kg h−1 methane point sources depending on surface brightness, surface homogeneity, and wind speed. Successful retrievals over very heterogeneous surfaces such as an urban mosaic require finer spectral resolution. We simulated the EnMAP capability with actual plume observations over oil/gas fields in California from the airborne AVIRIS-NG sensor (3 × 3 m2 pixel resolution, 5 nm spectral resolution, SNR 200–400). We spectrally and spatially downsampled AVIRIS-NG images to match EnMAP instrument specifications and found that we could successfully detect point sources of ~ 100 kg h−1 over bright surfaces. Estimated emission rates inferred with a generic Integrated Mass Enhancement (IME) method agreed within a factor of 2 between EnMAP and AVIRIS-NG. Better agreement may be achieved with a more customized IME method. Our results suggest that imaging spectrometers in space could play a transformative role in the future for quantifying methane emissions from point sources on a global scale.

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