## 1. Introduction

[2] The effects of rainstorm movement on runoff hydrographs and peak flows were pioneered by *Maksimov* [1964]. *Yen and Chow* [1968, 1969] demonstrated the importance of the rainstorm movement to the shape of the runoff hydrograph through a series of laboratory experiments using the watershed experimentation system (WES). *Black* [1972] studied watershed models to investigate the effect of watershed characteristics on hydrograph parameters. From the study, it was found that most of the contribution to the peak discharge was dependent on the lower half of the drainage. Thus, the direction of storm movement had little effect on the time of concentration. However, the direction change significantly affected the peak discharge and lag time at the outlet of the watersheds.

[3] By using a numerical kinematic wave model, *Ogden et al*. [1995] found a specific relation between the speeds of equivalent moving storms and the flow velocities during runoff processes. In particular, the equivalent moving storms had a common storm length but the moving storms with different speeds had different rainfall intensities in proportion to the storm movement speeds. Previously, equivalent moving storms were defined by *Yen and Chow* [1969] as storms moving at different speeds but having the same rainfall duration at every point on the watershed and having the same total rainfall volume. *Singh* [1998] proposed analytical solutions of kinematic wave equations to model the flow on a plane when storms moved upward or downward. *Lee and Huang* [2007] used a nonlinear numerical kinematic wave model to examine the criteria for equilibrium discharge by nonequivalent moving storms. Based on the numerical simulations for an overland plane and a V-shaped watershed, it was found that runoff can reach an equilibrium discharge even if the storm length is shorter than the watershed length and the rainfall duration is less than the time to equilibrium of the watershed for stationary uniform storms. Recently, consideration of the effect of rainstorm movement has not been constrained to flow hydrographs but extended to other interests such as the interaction between rainstorm movement and building environments [*Isidoro et al*., 2012], erosion [*Nunes et al*., 2006; *de Lima et al*., 2009; *Heng et al*., 2009, 2011], or sediment transport [*de Lima et al*., 2008, 2011].

[4] To obtain results more physical than those of kinematic wave approaches, dynamic wave models based on the Saint Venant equations, or shallow water equations (SWE), can be used. The SWE can be derived by depth averaging the Navier-Stokes equations when the horizontal length scale is much greater than the vertical length scale. In addition, the SWE assume that the flow is under hydrostatic pressure and the horizontal velocity field is constant throughout the water depth. *Liang* [2010] compared a one-dimensional (1-D) kinematic wave model and a 1-D dynamic wave model. The results showed that due to the backwater effects the peak flows estimated at the watershed outlet by the dynamic wave model were different from the results estimated by the kinematic wave model. Recently, two-dimensional (2-D) dynamic wave models have been developed and applied for rainfall-runoff predictions [*Ajayi et al*., 2008; *Yeh et al*., 2011; *Costabile et al*., 2012a, 2012b; *Caviedes-Voullième et al*., 2012]. *Yeh et al*. [2011] and *Costabile et al*. [2012a], similar to *Liang* [2010], reported that a full dynamic wave model should be used to obtain accurate results for complex flows. Only under simple flow conditions will simplified versions of full dynamic wave models yield acceptable computational results.

[5] However, it should be noted that few studies have incorporated dynamic wave models to evaluate the effect of rainstorm movement on the resulting hydrographs. Although various researches have been conducted to investigate the effects of moving storms on hydrographs, most of the interest has been focused on what happens at the watershed outlet. In fact, it is difficult to find thorough investigations based on dynamic wave modeling approaches of the effects of storm movement on runoff processes throughout the interiors of watersheds. Hence, this paper presents a detailed quantitative analysis based on a 2-D dynamic wave model of the rainfall-runoff processes caused by moving storms throughout an idealized V-shaped watershed. In turn, we precisely examine the justification of various routing models simplified on the basis of scales that have traditionally been assumed. In addition, this paper provides the mechanism by which the storm movement affects the characteristics of loop-rating curves.