Sustainability is meeting the needs of the present without jeopardizing quality of life for future generations. Adaptation is adjustment of resource utilization and planning by current generations to ensure sustainability. Mitigation, for this study, narrowly refers to damage repair and restoration costs incurred after natural hazard occurrence. Climate is dynamic and ever changing. Recent observed changes in weather patterns identify that drought and intense precipitation, leading to flooding, are more likely to occur in the near future. An example dynamic probabilistic risk assessment (PRA) for flood inundation is created and applied to understand benefits to, and limitations on, PRA for sustainable water resource management. This example addresses the issue of sustainable decision making related to outdated, but historically regulatory compliant, infrastructure. The observed increase in likelihood for large floods means that many assets were designed for inapplicable conditions and are more likely to be damaged in the future. Results from this example PRA demonstrate that it provides for optimizing the degree of sustainability included in resource management and decision making. Sustainability optimization is obtained by balancing likelihood for future mitigation costs against potential cost savings garnered from present-day adaptation.

One way to determine the fluid velocity, or concentration, at a time and point in space is to trace a particle pathline backwards through space and time to the starting location at the previous solution time. The departure point is the beginning point for the pathline from the previous solution time. Because the spatial distribution, or field for the constituent which moves with the fluid, is known at the previous solution time, the value for the previous solution time can be determined using spatial interpolation from the known values at the departure point. A new way to determine departure point location, called the semi-analytical upwind path line tracing (SUT) method, is presented that uses a semi-analytical solution for particle tracking rather than a discrete numerical solution like the Euler and Runge-Kutta methods. The semi-analytical solution provides a way to move entirely across a cell in one calculation while the discrete methods must divide the calculation into small pathline segments, or sub-calculations, for accuracy. Consequently, the SUT method has equivalent accuracy to discrete numerical solution approaches and can provide significantly improved computational efficiency for relatively long time step durations.

MOD_FreeSurf2D is a generally applicable computer model to simulate water movement and depth in rivers, streams, and shallow estuaries. It uses MATLAB to implement well established semi-Lagrangian and semi-implicit numerical algorithms that solve the depth-averaged, shallow water equations. MOD_FreeSurf2D has been validated against a dam-break flume experiment and three-dimensional river velocity and depth observations at the reach scale. An advantage of MOD_FreeSurf2D is that it can explicitly find and simulate the moving land/water boundary during flooding and tidal surge from topography and bathymetry.