基于车载被动DOAS系统的化工园区甲醛柱浓度精确反演研究

甲醛（HCHO）是大气中含量最为丰富的羰基化合物,是非甲烷可挥发性有机化合物（NMVOCs）的最重要的中间产物之一,广泛参与大气中的光化学反应,同时也是气溶胶的重要前体物,在大气化学中承担了非常重要的作用。石油化工行业的VOCs类排放是城市大气中HCHO的重要来源,而目前化工园区中的HCHO等NMVOCs类污染物主要通过点式设备获取近地面浓度,缺乏立体监测数据。差分光学吸收光谱（DOAS）技术已成功应用于SO₂和NO₂等污染气体监测,甲醛由于其光学吸收强度相对较弱,反演波段内其他气体交叉干扰强,实际的监测应用相对较少。选取某石化企业,运用被动DOAS方法实现了甲醛柱浓度的精确反演。研究通过建立甲醛吸收截面与其他参与拟合气体吸收截面的二维相关性矩阵,选取甲醛吸收截面同其他气体吸收截面相关性最小的波段,即实现其他气体对甲醛的DOAS反演交叉干扰最小的波段的获取。同时选取外场实际采集的光谱,选择不同起始波段和截止波段做迭代DOAS反演,通过拟合残差来评估甲醛在不同波段的实际反演效果。在截面间交叉干扰小,拟合残差低的波段范围内,选择尽量宽的波段作为最佳的拟合波段,实现甲醛的精确DOAS反演。由甲醛同其他气体吸收截面的二维相关性矩阵结果,甲醛与NO₂,SO₂和O₃和O₄间在大部分波段内相关性均在0.5以下,交叉干扰小;甲醛同BrO在起始波长318～320 nm,截止波长340～346 nm以及起始波长330～334 nm,截止波长354～360 nm两个波段范围内截面间相关性小于0.5,适合作为HCHO的反演波段。通过选择不同起始波段和截止波段做甲醛的迭代DOAS反演,结合拟合截面相关性分析结果综合考虑,最终采用332.4～358.1 nm作为HCHO的反演波段,拟合残差在10-4量级。利用车载被动DOAS系统,通过建立吸收截面间二维相关性矩阵并通过实测光谱的迭代反演,获取了适用于该套系统的HCHO最佳拟合波段,拟合残差降低至10-4量级,在实现甲醛精确反演的基础上,结合系统GPS信息,获取了某化工企业甲醛柱浓度的空间分布,整个外场观测期间,HCHO的反演误差低于6%。结果表明,车载被动DOAS系统在快速获取化工园区甲醛空间分布信息上可以发挥重要作用,为城市大气中甲醛的立体监测提供了一种有效测量手段。     

单光束多组分温室气体的腔衰荡光谱同步检测

腔衰荡光谱技术(CRDS)作为一种具有高灵敏度高光谱分辨率的检测方法已被广泛用于痕量气体检测。而目前基于CRDS痕量气体检测多针对单一气体进行测量或通过多个激光器产生的多光束进行多种组分气体浓度测量。利用DFB激光器波长可调谐特性,通过强弱吸收峰结合,使用单光束实现了多种温室气体的腔衰荡光谱技术同步检测。由于大气中水汽和二氧化碳浓度较高,为实现同一衰荡系统对三种温室气体的同步测量,在平衡吸收损耗的基础上,选取1 653~1 654 nm内甲烷的强吸收峰与水汽、二氧化碳的弱吸收峰进行测量。通过光谱叠加反演矩阵,分别得到甲烷、水汽、二氧化碳的浓度。在计算测量灵敏度过程中发现,通过去除衰荡过程初期的部分数据点(过滤区间),会对噪声等效吸收系数产生影响。多数情况下,在测量灵敏度计算方面,列文伯格-马夸尔特算法(L-M)会优于离散傅里叶变换法(DFT);但当衰荡曲线的单指数性下降时,上述结论不一定成立。搭建了一个低精细度(F≈6×103)衰荡腔对上述结论进行了实验验证。相较于用于测量温室气体浓度的高精细度衰荡腔(F≈1×105),低精细度衰荡腔的衰荡速率较快,衰荡曲线的单指数性明显低于高精细度衰荡腔。实验表明,在过滤区间长度较短时,采用DFT算法计算得到的噪声等效吸收系数会小于L-M算法得到的结果。当过滤区间长度增加时,L-M算法得到的结果优于DFT算法。在受过滤区间长度影响方面,DFT算法的波动性要明显小于L-M算法。根据Allan方差分析,在512次采样平均(约8 s)下的最小噪声等效吸收系数进行计算,该CRDS装置测量灵敏度为2.4×10-10 cm-1。在25 ℃标准大气压下,对应甲烷、水汽、二氧化碳的测量灵敏度分别为0.64 ppbv,3.5 ppmv和4.0 ppmv。基于该CRDS装置,通过单光束多波长测量方法,利用光谱叠加反演矩阵,测得大气中甲烷、水汽、二氧化碳浓度分别为2.018,3 654和526 ppmv;而采用经典CRDS单波长测量得到的甲烷、水汽、二氧化碳浓度分别为2.037,3 898和630 ppmv。通过与温控调节波长,逐点扫描得到的光谱吸收曲线进行对比,采用多波长测量得到气体浓度进行复合拟合的光谱曲线残差小于单波长测量得到气体浓度进行简单拟合的光谱曲线残差。     

Fitting models to correlated data II (small samples, large correlations, and wrong models)

The estimation of experimental error, data correlation and model error by the analysis of the fit residuals in an ordered sequence of data [J. Mol. Spectrosc. 224 (2004) 73] is improved by a better insight in the calculation of the statistical relevant quantities. The biases previously observed for too small samples of data, very wrong models or highly correlated data, are partially corrected and this leads to better estimates in some extreme cases provided these unfavourable conditions are not combined. However, such results are always obtained with a decrease in accuracy.     

A Cartesian method for fitting the bathymetry and tracking the dynamic position of the shoreline in a three-dimensional, hydrodynamic model

This paper presents a Cartesian method for the simultaneous fitting of the bathymetry and shorelines in a three-dimensional, hydrodynamic model for free-surface flows. The model, named LESS3D (Lake & Estuarine Simulation System in Three Dimensions), solves flux-based finite difference equations in the Cartesian-coordinate system (x,y,z). It uses a bilinear bottom to fit the bottom topography and keeps track the dynamic position of the shoreline. The resulting computational cells are hybrid: interior cells are regular Cartesian grid cells with six rectangular faces, and boundary/bottom cells (at least one face is the water–solid interface) are unstructured cells whose faces are generally not rectangular. With the bilinear interpolation, the shape of a boundary/bottom cell can be determined at each time step. This allows the Cartesian coordinate model to accurately track the dynamic position of the shorelines. The method was tested with a laboratory experiment of a Tsunami runup case on a circular island. It was also tested for an estuary in Florida, USA. Both model applications demonstrated that the Cartesian method is quite robust. Because the present method does not require any coordinate transformation, it can be an attractive alternative to curvilinear grid model.     

On Certain Fejér and Tchebychev Type Integrals

Let m and n denote a pair of positive integers. In this paper, we call upon the Hadamard product and computer algebra techniques to evaluate the Fejér integral π ^?1 ∫₀ ^π (sin mθ / sin θ) ²ⁿ dθ. Using symmetry arguments, it is proved that the value of this integral is an odd polynomial in m of degree 2n ? 1. This permits using polynomial curve fitting methods and mathematical software packages to obtain evaluation formulas for n relatively small. Some cases of the above integral with 2n replaced by 2n + 1 are also discussed. A familiar identity shows that these yield evaluations of integrals of powers of certain Tchebychev polynomials.     

A Character Theoretic Condition for F(G) > 1

ABSTRACT

If G is a nontrivial finite group with the property that χ (1) ² divides bi| G | for all irreducible (complex) characters χ , then G has a nontrivial normal abelian subgroup.