Temporal scaling

The mechanism of Self-organized criticality, a concept first introduced by Bak, Tang and Wiesenfeld [bak87a], may possibly provide a fundamental link between such temporal scale invariant phenomena and phenomena exhibiting a spatial scale invariance - familiar examples of which are given by fractal coastlines, mountain landscapes and cloud formations [mandel82],... 

Turbulence is generally understood to refer to a state of spatiotemporal chaos that is to say, a state in which chaos exists on all spatial and temporal scales. If the reader is unsatisfied with this description, it is perhaps because one of the many important open questions is how to rigorously define such a state. Much of our current understanding actually comes from hints obtained through the study of simpler dynamical systems, such as ordinary differential equations and discrete mappings (see chapter 4), which exhibit only temporal chaosJ The assumption has been that, at least for scenarios in which the velocity field fluctuates chaotically in time but remains relatively smooth in space, the underlying mechanisms for the onset of chaos in the simpler systems and the onset of the temporal turbulence in fluids are fundamentally the same. 

Going along with these spatial scales, we can define temporal scales as well. Micrometeoro-logic processes tend to be important for times less than an hour, mesoscale processes, up to about a day, and synoptic scale, a few days or more. 

The utility of c) as a thermometer gains further support from direct measurements showing correlation of temperature and 3 of precipitation through time over seasonal cycles (Shuman et al, 1995). At longer temporal scales, temperature measurements in boreholes and gas composition measurements both provide temperature information which can be compared to 3. Results from such comparisons have so far... 

Inputs from WWTP effluents can also affect the hydrologic and nutrient concentration regimes of recipient streams at different temporal scales. Daily variations of these parameters may be exacerbated in streams below the WWTP input by the diel patterns of the effluent discharge associated with plant operation [46]. In contrast, at the annual scale, seasonal variations of physical and chemical parameters upstream of the WWTP may be dampened by the constant input of additional water and nutrients from the WWTP. At its extreme, naturally intermittent or ephemeral streams may turn into permanent streams downstream of WWTPs [28, 30]. In these effluent-dominated streams, the relative contribution of WWTP inputs may vary widely on an annual basis, as shown by the 3-100% range measured in a Mediterranean stream [47]. Finally, WWTP inputs also cause shifts in the relative availability of N and P as well as in the relative importance of reduced and oxidized forms of N in the stream [30, 47]. The magnitude of these shifts depends on the level of wastewater treatment (i.e., primary, secondary, or tertiary treatment), the type of WWTP infrastructure (e.g., activated sludge reactor. 

Equation (6a) implies that the scale (dilation) parameter, m, is required to vary from - ac to + =. In practice, though, a process variable is measured at a finite resolution (sampling time), and only a finite number of distinct scales are of interest for the solution of engineering problems. Let m = 0 signify the finest temporal scale (i.e., the sampling interval at which a variable is measured) and m = Lbe coarsest desired scale. To capture the information contained at scales m > L, we define a scaling function, (r), whose Fourier transform is related to that of the wavelet, tf/(t), by... 

Organic acid fluorescence. In a similar manner to trace constituents, such as Mg, Sr and P, concentrations of organic acids present in speleothem calcite are sufficient to observe variation at temporal scales of less than annual in some cases (e.g.. Baker et al. 1993, Shopov et al. 1994). Organic acids (humic and fulvic) are formed in the soil by humification, and transported to the cave void by percolating waters where they are entrapped in precipitating carbonates. Under certain circumstances, where precipitation patterns are strongly seasonal and the nature of vadose percolation is such that seasonal mixing is incomplete, bands with different luminescent intensities can be differentiated after excitation with UV radiation. In other cases, bands are not observable but secular... 

Temporal scaling was performed using n=3 when extrapolating to shorter time points and n=l when extrapolating to longer time points using the Cnxt=k equation. 

For AEGL-3, the 1-h LC50 of 82 ppm for squirrel monkeys (Haun et al. 1970) was reduced by a factor of 3 to estimate a lethality threshold (27.3 ppm). Temporal scaling to obtain time-specific AEGL values was described by C% t=k (where C=exposure concentration, t=exposure duration, and k=a constant). The lethality data for the species tested indicated a near linear relationship between concentration and exposure duration (n=0.97 and 0.99 for monkeys and dogs, respectively). The derived exposure value was adjusted by a total uncertainty factor of 10.2 An uncertainty factor of 3 was applied for... 

The adjusted exposure value, estimated to be the threshold for lethality (11 ppm for 15 min), was then scaled to AEGL time frames using the Cnxt=k relationship (ten Berge et al. 1986) as discussed in Section 6.3 for AEGL-2. Temporal scaling using C1 A k was then used to derive the time-specific AEGLs (Appendix A). 

Zolezzi G, Beilin A, Bruno MC, Maiolini B, Siviglia A (2009) Assessing hydrological alterations at multiple temporal scales Adige River, Italy. Water Resour 45(12) W12421. doi 10.1029/2008WR007266... 

Knapp, R. B., 1989, Spatial and temporal scales of local equilibrium in dynamic fluid-rock systems. Geochimica et Cosmochimica Acta 53, 1955-1964. 

Long-term monitoring of consumption patterns the determination of the levels of drugs of abuse on a broader temporal scale (e.g., years) would allow for the identification of changes in consumption patterns, linked to the decrease in the consumption of certain substances and the increase of new emerging dmgs. 

To help address these issues, we define a new component for use in conceptual models the units of analysis. These are the lowest levels of biological, spatial, and temporal scale used in the quantitative part of the risk assessment (e.g., individual iterations in a simulation model). They also define the biological, spatial, and temporal units of the measures that will be needed as inputs to the assessment model. 

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