  Hammack & Segur (1978) conducted a series of surface water-wave experiments
in which the evolution of long waves of depression was measured and studied.
This present work compares time series from these experiments with predictions
from numerical simulations of the KdV, Serre, and five unidirectional and
bidirectional Whitham-type equations. These comparisons show that the most
accurate predictions come from models that contain accurate reproductions of
the Euler phase velocity, sufficient nonlinearity, and surface tension effects.
The main goal of this paper is to determine how accurately the bidirectional
Whitham equations can model data from real-world experiments of waves on
shallow water. Most interestingly, the unidirectional Whitham equation
including surface tension provides the most accurate predictions for these
experiments. If the initial horizontal velocities are assumed to be zero (the
velocities were not measured in the experiments), the three bidirectional
Whitham systems examined herein provide approximations that are significantly
more accurate than the KdV and Serre equations. However, they are not as
accurate as predictions obtained from the unidirectional Whitham equation.
