Path-integrated concentration

Illustration of path-integrated concentrations and relationship to path average concentration for narrow plumes and widely dispersed vapor clouds. 

The first of these is the sensitivity. This expresses the minimum detectable concentration (often as a function of range) and is usually quoted in the absence of interference. It is defined mathematically by equating the product aC with the noise level of the system. It is usually stated in units of path-integrated concentration, most correctly in units of pgm , or alternatively in ppm m (where ppm is used to express the partial pressure of the target species as millionths of the total atmospheric pressure). 

A specification of range-resolved remote gas-sensing systems that is closely related to the sensitivity is the maximum range. This is simply the range at which the sensitivity passes some defined threshold, such as the path-integrated concentration being equal to a stated value. 

It was planned a field experiment series in which the sensitivity of the two s stems was measured. A 2 m polyethylene foil chamber was used as a gas cell and some free disseminations w re used in the experiments. Sensitivity of the differential absorption lidar systems are charaterized by the minimum detectable path integrated concentration of materials to be detected, their response time and their range. During the field test integration times were 1 sec for all measurements with both VTB-2 and LRS-3 systems. With post processing moving averages were calculated for 10 sec and 30 sec in 1 sec steps. 

For differential-absorption lidars the sensitivity means the lowest value of the measurable path-integrated concentration during the response time. Three groups of factors influence variation of the c 1 value ... 

Despite all the potential problems of OP/FT-IR spectrometry, remarkably good results have been found. Typical detection limits for the path-integrated concentration are less than 10 ppm-meter. Thus, for a pathlength of 100 m, the detection limits for most pollutants is less than lOOppbv. Detection limits are greater than are obtained by extractive monitoring, but the problems introduced by point sampling are eliminated. 

Basically the perturbative techniques can be grouped into two classes time-local (TL) and time-nonlocal (TNL) techniques, based on the Nakajima-Zwanzig or the Hashitsume-Shibata-Takahashi identity, respectively. Within the TL methods the QME of the relevant system depends only on the actual state of the system, whereas within the TNL methods the QME also depends on the past evolution of the system. This chapter concentrates on the TL formalism but also shows comparisons between TL and TNL QMEs. An important way how to go beyond second-order in perturbation theory is the so-called hierarchical approach by Tanimura, Kubo, Shao, Yan and others [18-26], The hierarchical method originally developed by Tanimura and Kubo [18] (see also the review in Ref. [26]) is based on the path integral technique for treating a reduced system coupled to a thermal bath of harmonic oscillators. Most interestingly, Ishizaki and Tanimura [27] recently showed that for a quadratic potential the second-order TL approximation coincides with the exact result. Numerically a hint in this direction was already visible in simulations for individual and coupled damped harmonic oscillators [28]. 

The mathematical reconstruction of a property field, F(x,y), from its projection in the 0 direction is the basis of "Computerized Tomography" (1,2). An identical technique can be used to reconstruct a field of linear absorption coefficient functions in a combusting flow field from multiangular path integrated absorption measurements. The linear absorption coefficient is the familiar N.Q. product, where is the concentration of species i and Q. is the absorption cross section of species i at the frequency v. The Bouguer-Lambert-Beer law states that... 

Figure 4..19a. Geometry of solar occultation. McCormick et aZ.(1979) Assuming that this absorbant is uniformly distributed in each atmospheric layer (and hence that its concentration varies only with height), the integrated concentration N along the optical path with tangent height i 0 (slant column density) can be derived from the observation of lu and Iv,00 through Eq. (4.61), when...

The inhalation and immersion doses that would be received by an individual standing in the path of the plume increase with the magnitude of Xt> Ihe time-integrated concentration at the point in question. According to the straight-line Gaussian plume model... 

Rice J.R. (1968) A path-independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379-386. 

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, J. Appl. Mech., 1968, 35,379 386. 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

The use of the sun or moon as the light source allows one to measure the total column abundance, i.e., the concentration integrated through a column in the atmosphere. This approach has been used for a number of years (e.g., see Noxon (1975) for NOz measurements) and provided the first measurements of the nitrate radical in the atmosphere (Noxon et al., 1978). As discussed later in this chapter, such measurements made as a function of solar zenith angle also provide information on the vertical distributions of absorbing species. Cloud-free conditions are usually used for such measurements as discussed by Erie et al. (1995), the presence of tropospheric clouds can dramatically increase the effective path length (by an order of... 

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