Compositional Time Series

The chlorine concentration has been repeatedly measured in a well, as shown in Fig. 6.20. What hydrological conclusions may be reached Two water types, of different chlorine concentrations, intermix. What is the nature of this mixing To answer this question, the nature of the time periodicity has to be discussed. A case study of this kind has been reported by Tremblay et al. (1973) from a coastal well on Prince Edward Island (Fig. 6.21). It was pumped daily from 8 a.m. to 5 p.m., and the chlorine concentration was measured at these hours. The chlorinity increased during the day and dropped until the following morning. This simple series of 

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Zinsmeister, A. R. and Redman, T. C. (1980). A time series analysis of aerosol composition measurements, Atmos. Environ. 14,201-215. 

Fig. 6. Structural stability of major ampullate silk protein in constrained Nephila edulis. The graph shows a time series of circular dichroism spectra of major ampullate (MA) protein at 1% w/v in distilled water. The spiders prior to dissection were prevented from spinning, but fed and watered for at least 2 weeks. With time, the secondary structure of silk protein is becoming more and more disordered. The arrow indicates increasing time (days). Note that the amino acid composition of the silk protein was similar to that of a native N. edulis spider. Interestingly, silk protein extracted from the constrained spider did not respond to denaturing conditions (detergents, alcohols, pH, and salts Dicko et al, 2004a, 2005).

Lee, C., S.G. Wakeham, and J.W. Farrington. 1983. Variations in the composition of particulate organic matter in a time-series sediment trap. Marine Chemistry 13 181-194. 

Atmospheric methane has a mean 5 C-value of around —47%c (Stevens 1988). Quay et al. (1999) presented global time series records between 1988 and 1995 on the carbon and hydrogen isotope composition of atmospheric methane. They measured spatial and temporal variation in and D with a slight emichment observed for the southern hemisphere (—47.2%c) relative to the northern hemisphere (—47.4%o). The mean 5D was —86 3%c with a 10%o depletion in the northern relative to the southern hemisphere. 

Zinmeister, A.R. and Redman. T.C. (198Q). "A Time Series Analysis of Aerosol Composition Measurements," Atmospheric Environment, 14, 201. 

The problem mentioned before has led to the development of statistical receptor models (Fig. 3) which nowadays are the most widely used tools for PM source apportionment. They can be applied even to a single site and need a time series of PM mass concentrations and corresponding chemical composition data. Depending on the method, these analyses are based only on the receptor data or additionally use information on the chemical composition from the relevant emission sources (emission profiles). 

To analyze the spectral composition of the pressure variations in more detail we have made use of a wavelet approach [9]. This approach, which allows us to determine instantaneous values of the frequencies and amplitudes of the various oscillatory components, is particularly useful for biological time series that often are neither homogeneous nor stationary. 

Firstly, the relation composition-time in a batch operation is computed (Figure 14.10). The profile corresponds to series-parallel equilibrium reactions. At 60 °C the reaction rate catalyzed by NaOH is fast conversion over 98.5% can be reached in 20 min and chemical equilibrium at 99.8% in about 30 min. However, the content in mono- and diglycerides remains relatively high at 6.5 and 2.2% mol, or 2.6 and 1.6wt%, much higher than the required specifications. Lowering the... 

Figure 11.14 (A) The composite prolactin time series. (B) Sketch of the 3-dimensional attractor of prolactin generated by the data of plot A. Reprinted from [539] with permission from Blackwell.

Knapp, A. N., Sigman, D. M., and Lipschultz, F. (2005). N isotopic composition of dissolved organic nitrogen and nitrate at the Bermuda Atlantic time-series study site. Global Biogeochemical Cycles 19(1), GB1018. 

Figure l6.l6 Time series of particulate nitrogen (PN) export and isotopic composition determined from 150-m floating sediment trap collections at Station ALOHA. (Top) PN flux (pmol N m d ). Error bars represent SE of three to six individual trap measurements. (Bottom) Stable nitrogen isotopic composition (c5 N) of trap-collected material (%o vs. air N2). Error bars, where shown, represent SE of two to three individual trap measurements. Dotted lines represent the isotopic compositions of exported PN expected when supported entirely hy nitrate (6.5°/oo) or entirely by dinitrogen gas (0 %o). The solid line indicates a decreasing trend determined hy linear regression. The trend break at the end of 2002 remains to he explained. Updated and revised from Dore et al. (2002). 

Bray A. M. and Von Damm K. L. (2003b) Controls on the alkali metal composition of mid-ocean ridge hydrothermal fluids constraints from the 9— 10°N East Pacific Rise time series. Geochim. Cosmochim. Acta (in revision). 

Figure 4 Mg/Ca of different planktonic foraminifera from a Bermuda sediment trap time series, plotted versus calcification temperatures calculated from the oxygen isotopic composition of the shells (Anand et aL, 2003) (reproduced by permission of American Geophysical Union from Paleoceanography 2003, 18, 1050). The aggregate fit to all the data in the plot is Mg/Ca = 0.38 exp(0.09T), very similar to relationships derived from culturing and core-top studies.

Many analytical measures cannot be represented as a time-series in the form of a spectrum, but are comprised of discrete measurements, e.g. compositional or trace analysis. Data reduction can still play an important role in such cases. The interpretation of many multivariate problems can be simplified by considering not only the original variables but also linear combinations of them. That is, a new set of variables can be constructed each of which contains a sum of the original variables each suitably weighted. These linear combinations can be derived on an ad hoc basis or more formally using established mathematical techniques. Whatever the method used, however, the aim is to reduce the number of variables considered in subsequent analysis and obtain an improved representation of the original data. The number of variables measured is not reduced. 

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