  In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that
combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function
(RBF) interpolation method to construct efficient reduced order models for
time-dependent problems arising in large scale environmental flow applications.
The performance of the POD-RBF NIROM is compared with a traditional nonlinear
POD (NPOD) model by evaluating the accuracy and robustness for test problems
representative of riverine flows. Different greedy algorithms are studied in
order to determine a near-optimal distribution of interpolation points for the
RBF approximation. A new power-scaled residual greedy (psr-greedy) algorithm is
proposed to address some of the primary drawbacks of the existing greedy
approaches. The relative performances of these greedy algorithms are studied
with numerical experiments using realistic two-dimensional (2D) shallow water
flow applications involving coastal and riverine dynamics.
