Application of the Orthogonal Polynomial Fitting Method in Estimating PM2.5 Concentrations in Central and Southern Regions of China

Abstract

Sufficient and accurate air pollutant data are essential to analyze and control air contamination problems. An orthogonal polynomial fitting (OPF) method using Chebyshev basis functions is introduced to produce spatial distributions of fine particle (PM2.5) concentrations in central and southern regions of China. Idealized twin experiments (IE1 and IE2) are designed to validate the feasibility of the OPF method. IE1 is designed in accordance with the most common distribution of PM2.5 concentrations in China, whereas IE2 represents a common distribution in spring and autumn. In both idealized experiments, prescribed distributions are successfully estimated by the OPF method with smaller errors than kriging or Cressman interpolations. In practical experiments, cross-validation is employed to assess the interpolation results. Distributions of PM2.5 concentrations are well improved when OPF is applied. This suggests that errors decrease when the fitting order increases and arrives at the minimum when both orders reach 6. Results calculated by the OPF method are more accurate than kriging and Cressman interpolations if appropriate fitting orders are selected in practical experiments.

Application of Orthogonal Polynomial Fitting Method to Extract Gravity Wave Signals From AIRS Data Related to Typhoon Deep Convection

“…The OPF method is based on Chebyshev polynomials and basis functions. The raw BT can be fitted as (Junkins et al, 2013;Li et al, 2019):…”

“…The OPF method is based on Chebyshev polynomials and basis functions. The raw BT can be fitted as (Junkins et al., 2013; Li et al., 2019): $$$\tilde{T}\left({x}_{i},yi\right)=\sum\limits _{K=0}^{{K}_{0}}\,\sum\limits _{S=0}^{{S}_{0}}{A}_{K,S}{{\Phi}}_{K}\left({x}_{i}\right)\,{\xi }_{S}\left({y}_{i}\right)$$$ where x i ( i = 1, 2, …, N ) and y j ( j = 1, 2, …, M ), and K and S are the orders of polynomials in the x and y directions, respectively. K 0 and S 0 are the corresponding cutoff orders.…”

“…As is traditionally done with AIRS, The 4PF method was used to remove the background and limb‐brightening effect (Alexander & Barnet, 2007; Hindley et al., 2016; Hoffmann & Alexander, 2009; Hoffmann et al., 2014; Holt et al., 2017; Wright et al., 2017). In the present manuscript, a new OPF method, based on Chebyshev basis functions, can be also determined to remove the background and limb‐brightening effect, in the cross‐track as well as along track direction from AIRS raw radiances, and produce highly accurate temperature perturbations (Junkins et al., 2013; Li et al., 2019).…”

Assessment of Three-Dimensional Interpolation Method in Hydrologic Analysis in the East China Sea

“…In terms of multidimensional scattered data completion, there are several methods available. The inverse distance weighted (IDW) method [25], the Chebyshev polynomials fitting (CPF) method [26], and the radial basis functions (RBF) method [27] have been widely used in many fields. Especially as an effective interpolation method of the high dimensional interpolation, the accuracy of the RBF methods is determined by the matching degree between the distribution of in situ observations and the type of RBF.…”

Application of Three-Dimensional Interpolation in Estimating Diapycnal Diffusivity in the South China Sea

“…There are several methods widely used in scattered data interpolation and fitting, such as the thin-plate spline method [13], inverse distance weighted method [14], Chebyshev polynomial method [15], and trigonometric polynomial method [16]. Given the anisotropy of diapycnal diffusivity and its rapid change in the magnitude in the vertical direction, the 3D thin-plate spline (3D TPS) method, 3D inverse distance weight (3D IDW) method, 3D Chebyshev polynomial fitting (CPF) method, 3D piecewise linear (3D PL) method, and 2D thin-plate spline (2D TPS) method are used to estimate the diapycnal diffusivity in the SCS.…”