scholarly journals Vertical level selection for temperature and trace gas profile retrievals using IASI

2015 ◽  
Vol 8 (3) ◽  
pp. 2591-2621
Author(s):  
R. A. Vincent ◽  
A. Dudhia ◽  
L. J. Ventress
Keyword(s):  
Iterative Method ◽  
Selection Method ◽  
Trace Gas ◽  
Kernel Matrix ◽  
Iterative Approach ◽  
Selection For ◽  
Vertical Spacing ◽  
Vertical Level ◽  
New Iterative Method ◽  
Grid Based

Abstract. This work presents a new iterative method for optimally selecting a vertical retrieval grid based on the location of the information content while accounting for inter-level correlations. Sample atmospheres initially created to parametrise the RTTOV forward model are used to compare the presented iterative vertical selection method with two other common approaches, which are using levels of equal vertical spacing and selecting levels based on the cumulative trace of the averaging kernel matrix (AKM). This new method is shown to outperform compared methods for synthesized profile retrievals with IASI of temperature, H2O, O3, CH4, and CO. However, the benefits of using the more complicated iterative approach compared to the simpler method of referencing the cumulative trace of the AKM are slight and may not justify the added effort. Furthermore, comparing retrievals using a globally optimized static grid vs. an atmosphere specific one shows that a static grid is likely appropriate for retrievals of O3, CH4, and CO. However, developers of temperature and H2O retrieval schemes may at least consider using adaptive or location specific vertical retrieval grids.

scholarly journals Vertical level selection for temperature and trace gas profile retrievals using IASI

2015 ◽  
Vol 8 (6) ◽  
pp. 2359-2369 ◽  
Author(s):  
R. A. Vincent ◽  
A Dudhia ◽  
L. J. Ventress
Keyword(s):  
Trace Gas ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Infrared Observation ◽  
Atmospheric Sounding ◽  
Selection For ◽  
Vertical Spacing ◽  
Vertical Level ◽  
New Iterative Method ◽  
Grid Based

Abstract. This work presents a new iterative method for optimally selecting a vertical retrieval grid based on the location of the information while accounting for inter-level correlations. Sample atmospheres initially created to parametrise the Radiative Transfer Model for the Television Infrared Observation Satellite Operational Vertical Sounder (RTTOV) forward model are used to compare the presented iterative selection method with two other common approaches, which are using levels of equal vertical spacing and selecting levels based on the cumulative trace of the averaging kernel matrix (AKM). This new method is shown to outperform compared methods for simulated profile retrievals of temperature, H2O, O3, CH4, and CO with the Infrared Atmospheric Sounding Interferometer (IASI). However, the benefits of using the more complicated iterative approach compared to the simpler cumulative trace method are slight and may not justify the added effort for the cases studied, but may be useful in other scenarios where temperature and trace gases have strong vertical gradients with significant estimate sensitivity. Furthermore, comparing retrievals using a globally optimised static grid vs. a locally adapted one shows that a static grid performs nearly as well for retrievals of O3, CH4, and CO. However, developers of temperature and H2O retrieval schemes may at least consider using adaptive or location specific vertical retrieval grids.

scholarly journals A novel iterative approach for solving common fixed point problems in Geodesic spaces with convergence analysis

2021 ◽  
Vol 37 (2) ◽  
pp. 145-160
Author(s):  
THANATPORN BANTAOJAI ◽  
CHANCHAL GARODIA ◽  
IZHAR UDDIN ◽  
NUTTAPOL PAKKARANANG ◽  
PANU YIMMUANG
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Convergence Analysis ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Iterative Approach ◽  
Mild Conditions ◽  
New Iterative Method

In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

scholarly journals New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed S. Al-luhaibi
Keyword(s):  
Iterative Method ◽  
Analytical Solutions ◽  
Gas Dynamics ◽  
Time Derivative ◽  
Explicit Solutions ◽  
Fractional Partial Differential Equations ◽  
Approximate Analytical Solutions ◽  
Fractional Time Derivative ◽  
Burger's Equations ◽  
New Iterative Method

This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

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