Aaron S. Donahue

Discontinuous Galerkin methods for solving Boussinesq-Green-Naghdi equations in resolving non-linear and dispersive surface water waves

A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and h, p (denoted by K in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.

EOF-MSE ADAPTIVE METHOD TO ASSESS AN ACID DEPOSITION MONITORING NETWORK OVER ALBERTA, CANADA

This study provides an adaptive data analysis method that assesses Albertas acid deposition monitoring network of 9 stations and the relative importance of each station. The method is based on the assessment of the mean square error (MSE) of sampling expressed in terms of empirical orthogonal functions (EOF). The annual potential acid input (PAI) data of the 9 stations over Alberta, Canada are used in this study. The patterns of the EOFs and PCs (principal components) are analyzed to reflect the PAIs spatial-temporal distribution properties. The definition and minimization of the MSE are the basis for our assessment method. The mean PAI field in the period of 1993–2006 and the PAI fields of individual years demonstrate a strong spatial inhomogeneity of the PAI field over Alberta. The PAI level is high in the Red Deer–Calgary–Kananaskis corridor. Our optimal analysis indicates that the 9-station network is, in general, adequate in monitoring the overall PAI in Alberta. The network results in a small root-mean-square-error/standard-deviation ratio (5.6%), which demonstrates the reasonable effectiveness of the network. In the period of 14 years (1993–2006), there were only three years (1993, 1998, and 2002) during which the PAI values were higher than the monitoring load of 0.17 [keq H+ ha-1yr-1] at three locations: Red Deer, Calgary, and Kananaskis. According to a stations contribution to the reduction of sampling error, the descending order of importance for the 9 stations is as follows: Beaverlodge, Fort Chipewyan, Suffield, Red Deer, Cold Lake, Kananaskis, Calgary, Fort Vermilion, and Fort McMurray.