In existing experiments it is known that the slow evolution of nonlinear deep-water waves exhibits certain asymmetric features. For example, an initially symmetric wave packet of sufficiently large wave slope will first lean forward and then split into new groups in an asymmetrical manner, and, in a long wavetrain, unstable sideband disturbances can grow unequally to cause an apparent downshift of carrier-wave frequency. These features lie beyond the realm of applicability of the celebrated cubic Schrödinger equation (CSE), but can be, and to some extent have been, predicted by weakly nonlinear theories that are not limited to slowly modulated waves (i.e. waves with a narrow spectral band). Alternatively, one may employ the fourth-order equations of Dysthe (1979), which are limited to narrow-banded waves but can nevertheless be solved more easily by a pseudospectral numerical method. Here we report the numerical simulation of three cases with a view to comparing with certain recent experiments and to complement the numerical results obtained by others from the more general equations.

Accurate parameter estimation is important for reliable rainfall-runoff modeling. Previous studies emphasize that a sufficient length of continuous events is required for model calibration to overcome the effect of initial conditions. This paper investigates the feasibility of calibrating rainfall-runoff models over a number of limited storm flow events. For a subcatchment having a moderate influence from initial soil moisture conditions, this study shows that rainfall-runoff models could still be calibrated reliably over a set of representative events provided that the events cover a wide range of peak flow, total runoff volume, and initial soil moisture conditions. This approach could provide an alternative calibration strategy for a small watershed that has a limited data length but consists of runoff events with a wide range of magnitudes. Compared to continuous-event calibration, event-based calibration appears to perform better in simulating the overall shape of hydrograph, peak flow and time to pea...