Vertical variation

The vertical distribution of aerosol mass concentration typically shows an exponential decrease with altitude up to a height Hp and a rather constant profile above that altitude (Gras 1991). The aerosol mass concentration as a function of height can then be expressed as 

The aerosol number concentration may increase or decrease exponentially with altitude and one suggestion of a form of the profile is (Jaenicke 1993) 

FIGURE 8.29 Representative vertical distribution of aerosol mass concentration (Jaenicke 1993). 

Because in this case N 0) SC Nb, the equation has the correct limiting behavior both for 

These vertical profiles are rough representations of long-term averages. Significant variability is observed in aerosol concentrations in anthropogenic plumes, areas influenced by local sources, or during nucleation events in the free troposphere. 

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Fluid samples will be taken using downhole sample bombs or the MDT tool in selected development wells to confirm the PVT properties assumed in the development plan, and to check for areal and vertical variations in the reservoir. In long hydrocarbon columns (say 1000 ft) it is common to observe vertical variation of fluid properties due to gravity segregation. 

Figure 4.101 displays the subtle variations in metal-carbonyl bond lengths in the group 6 M(CO) complexes. In each case one can clearly distinguish the coordinate omc bonds (solid lines) from the hypervalent toMc prebonds (dashed lines). The latter are about 0.1A longer, but exhibit a similar vertical variation within the group. 

Wang, X., Wen, X., Ye, R., LiuZ., Sun, B., Zhao, S., Shi, S., Wei, H. 2007. Vertical variation and dispersion of elements in arid desert regolith a case study from the Jinwozi gold deposit, northwestern China. Geochemistry Exploration, Environment, Analysis, 7, 163-171. 

The structure of turbulence in the transition zone from a fully turbulent fluid to a nonfluid medium (often called the Prandtl layer) has been studied intensively (see, for instance, Williams and Elder, 1989). Well-known examples are the structure of the turbulent wind field above the land surface (known as the planetary boundary layer) or the mixing regime above the sediments of lakes and oceans (benthic boundary layer). The vertical variation of D(x) is schematically shown in Fig. 19.8b. Yet, in most cases it is sufficient to treat the boundary as if D(x) had the shape shown in Fig. 19.8a. 

In each hatched two-phase region, the lever rule (Section 7.3.2) can be used as usual to determine the relative amounts of the two phases at opposite ends of the tie-line. However, the quantity of precipitated solid a and/or /3 is usually of less interest than the composition of the melt, so the principal focus is on the two liquidus lines that meet at the eutectic point. These liquidus lines are also called solubility curves or freezing-point depression curves, in that they map both the saturation-solubility limits (horizontal variations) as well as the freezing-point depression of the liquid (vertical variations). 

Table IX. Vertical Variation of Carbon and Nitrogen in Peat from Higashiyonesato ...

TabU XI. Vertical Variation of Organic Carbon, Nitrogen, and Hydrogen in a Core Sample of Sediments from Lake Kizaki-ko, Which Was Previously Dried8... 

The vertical variation of the ratios of Org. N/Org. H in the same core sample shows that with a few exceptions the ratios increase regularly with increasing core depth. This means the organic hydrogen is more easily decomposed than organic nitrogen in recent sediments. 

Kumar P, Fennell P, Langley D, Britter R (2008) Pseudo-simultaneous measurements for the vertical variation of coarse, fine and ultra fine particles in an urban street canyon. Atmos Environ 42 4304 -319... 

Li XL, Wang JS, Tu XD, Liu W, Huang L (2007) Vertical variations of particle number concentration and size distribution in a street canyon in Shanghai, China. Sci Total Environ 378 306-316... 

Why are these equations represented by 4th order polynomials and not 2nd order curves given that the vertical variation of temperature and vapor fraction are well approximated by second order functions The simple answer is that the transition from condensing water vapor to liquid water above 0 °C to condensing water ice below -20 °C, and the attendant affect on the fractionation factor (Fig. 2), results in additional structure not captured by 2nd or 3rd order curves. Each of the equations fit their respective model output with an R2 > 0.9997. The lack of symmetry of the modeled uncertainty reflects asymmetry in the probability density function and particularly the long tail toward lower values of T relative to the mean (see Fig. 2 of Rowley et al. 2001). The effect of this long tail is well displayed in both Figure 5 and 7. 

Carlson, C. A., and Ducklow, H. W. (1995). Dissolved organic carbon in the upper ocean of the central equatorial Pacific Ocean, 1992 Daily and fmescale vertical variations. Deep-Sea Research II 42(2-3), 639-656. 

The salinity of formation waters is often calculated using electrical-resistivity and spontaneous-potential (SP) logs, and the values obtained are reasonable, except in geopressured zones with high shale content (Hearst and Nelson, 1985 Rider, 1996). It is often possible to determine vertical variations in salinity over a distance of several kilometers from a single log. 

Assuming little vertical variation in the mixing ratio of total mercury in the troposphere and using the available horizontal surface-based measurements, Mason et al. (1994) estimated the total... 

Note that all these theorems can be easily understood by relying on intuition. We can assume that the frequency dependence of the field (electromagnetic skin-effect) provides information about the vertical variations of conductivity, while the spatial dependence of the data on the surface allow us to reconstruct the horizontal changes in conductivity. Thus, one can expect that these theorems can be extended to 3-D cases as well. 

T. Tomiyasu, M. Okada, R. Imura, and H. Sakamoto, Vertical Variations in the Concentration of Mercury in Soils Around Sakurajima Volcano, Southern Kyushu, Japan, Sci. Total Environ. 304(1-3), 221-230, Mar. 20 (2003). 

Coal, by virtue of its origin, is quite heterogeneous its mineral content varies considerably both vertically and laterally within coal seams. Vertical variation has resulted from changes through time in the content of mineral detritus introduced into the peat swamp, in the pH, and to some extent in the species of vegetation that inhabited the swamp at any one place or time. This variation has been measured by determining the differences in mineral content in different layers or benches of the seam at particular places. Lateral variation has been measured by analysis of the whole coal seam (channel samples) from one locality to another. 

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