Estimates of plume extremes such as maximum plume width (W_max) and its location (X_wmax), maximum plume area (A_max), and maximum plume length (L_max), which are vital indicators of any site assessment work, mostly requires the use of rather complicated numerical approaches and a large number of site information. This paper focuses on simpler (semi)analytical quantification of W_max and X_wmax, and their characterization with respect to source geometry (source width S_w and source thickness S_t) for estimating A_max. A direct computation of W_max and X_wmax rather becomes a multi-dimensional nonlinear system problem for which only a few iterative methods are available. The challenge magnifies further as limited information on W_max and X_wmax are available for obtaining an initial guess of the solution. Solving over 1000 synthetic problems, this work finds the Newton–Krylov method as the most suitable nonlinear system solver. Among the most important were the limiting results such as L_max/8 ¡X_wmax¡L_max/8 and 1×S_w¡W_max¡1.4×S_w. These limiting results simplify the finding of initial guesses for W_max and X_wmax. Further characterization of W_max and X_wmax with L_max, S_t, and S_w provided an empirical relation between plume and source areas, in addition to an approximation of A_max. A field site data illustrate the potential applications of the methods developed in this work.