Novel approaches addressing aquatic cumulative effects over broad temporal and spatial scales are required to track changes and assist with sustainable watershed management. Cumulative effects assessment (CEA) requires the assessment of changes due to multiple stressors both spatially and temporally. The province of Alberta, Canada, is currently experiencing significant economic growth as well as increasing awareness of water dependencies. There has been an increasing level of industrial, urban, and other land-use related development (pulp and paper mills, oil sands developments, agriculture, and urban development) within the Athabasca River basin. Much of the historical water quantity and quality data for this basin have not been integrated or analyzed from headwaters to mouth, which affects development of a holistic, watershed-scale CEA. The main objectives of this study were 1) to quantify spatial and temporal changes in water quantity and quality over the entire Athabasca River mainstem across historical (1966–1976) and current day (1996–2006) time periods and 2) to evaluate the significance of any changes relative to existing benchmarks (e.g., water quality guidelines). Data were collected from several federal, provincial, and nongovernment sources. A 14% to 30% decrease in discharge was observed during the low flow period in the second time period in the lower 3 river reaches with the greatest decrease occurring at the mouth of the river. Dissolved Na, sulfate, chloride, and total P concentrations in the second time period were greater than, and in some cases double, the 90th percentiles calculated from the first time period in the lower part of the river. Our results show that significant changes have occurred in both water quantity and quality between the historical and current day Athabasca River basin. It is known that, in addition to climatic changes, rivers which undergo increased agricultural, urban, and industrial development can experience significant changes in water quantity and quality due to increased water use, discharge of effluents, and surface run-off. Using the results from this study, we can begin to quantify dominant natural and man-made stressors affecting the Athabasca River basin as well as place the magnitude of any local changes into an appropriate context relative to trends in temporal and spatial variability.

Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = σ(e + e − → hadrons)/σ(e + e − → µ + µ − ), as obtained from the imaginary part of the purely-perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector-correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impose a common infrared bound on perturbative approximations to R(s), regardless of the infrared behaviour of the true QCD couplant.For center-of-mass squared-energy s, QCD corrections to R(s) ≡ σ(e + e − → hadrons)/σ(e + e − → µ + µ − ) are scaled by a perturbative QCD series (S):This series is extracted from the imaginary part of the MS vector-current correlation function [1, 2],with coefficients T n,m tabulated in Table I for 3-5 active flavors, as appropriate for the choice of the center-of-mass squared-energy s. Each order of this series depends upon the MS renormalization scale parameter µ, both through the couplantand through powers of the logarithmNevertheless, the all-orders series S must ultimately be independent of renormalization scale. R(s) is a measurable physical quantity necessarily independent of µ, the artificial scale entering QCD calculations as a by-product of the regulation of Feynman-diagrammatic infinities. Hence,The above renormalization group equation (RGE) is simply a chain-rule relation in whichwhere known [3] MS β-function coefficients β k are also tabulated in Table I. Thus, the RGE (5) is generally employed to provide scale dependence to the couplant x. "Optimal" renormalization-group (RG) improvement is the inclusion of every term in a perturbative series of the form (2) that can be extracted by RG-methods from a perturbative computation to a given order [4]. For example,

Invariance of the effective action under changes of the renormalization scale µ leads to relations between those (presumably calculated) terms independent of µ at a given order of perturbation theory and those higher order terms dependent on logarithms of µ. This relationship leads to differential equations for a sequence of functions, the solutions of which give closed form expressions for the sum of all leading logs, next to leading logs and subsequent subleading logarithmic contributions to the effective action. The renormalization group is thus shown to provide information about a model beyond the scale dependence of the model's couplings and masses. This procedure is illustrated using the φ 3 6 model and Yang-Mills theory. In the latter instance, it is also shown by using a modified summation procedure that the µ dependence of the effective action resides solely in a multiplicative factor of g 2 (µ) (the running coupling). This approach is also shown to lead to a novel expansion for the running coupling in terms of the one-loop coupling that does not require an order-by-order redefinition of the scale factor Λ QCD . Finally, logarithmic contributions of the instanton size to the effective action of an SU(2) gauge theory are summed, allowing a determination of the asymptotic dependence on the instanton size ρ as ρ goes to infinity to all orders in the SU(2) coupling constant.