HYDROLOGICAL PROCESSES Hydrol. Process. 20, 1027–1046 (2006) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5922 One- and two-dimensional modelling of overland flow in semiarid shrubland, Jornada basin, New Mexico David A. Howes, 1 * Athol D. Abrahams 2 and E. Bruce Pitman 3 1 Compliance Services International, 7501 Bridgeport Way West, Lakewood, WA 98499, USA 2 Department of Geography, University at Buffalo, The State University of New York, Buffalo, NY 14261, USA 3 Department of Mathematics, University at Buffalo, The State University of New York, 244 Mathematics Building, Buffalo, NY 14260, USA Abstract: Two distributed parameter models, a one-dimensional (1D) model and a two-dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event-based and represent each watershed by an array of 1-m 2 cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite-difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second-order predictor–corrector finite-difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large-scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright  2006 John Wiley & Sons, Ltd. KEY WORDS runoff; overland flow; infiltration; drainage basin; hydrology INTRODUCTION Distributed parameter modelling is the most widely used method of modelling runoff in semiarid environments (e.g. Zhang and Cundy, 1989; Goodrich et al., 1991; Moore and Grayson, 1991; Vertessy et al., 1993; Flanagan and Nearing, 1995; Smith et al., 1995). This approach provides a detailed representation of the watershed and an accurate description of the runoff processes using physically based relationships. A watershed is represented as a set of spatial (distributed) elements and the model simulates (1) the hydrologic processes operating within each element (i.e. the conversion of rainfall to runoff), and (2) the flow of water between the elements (i.e. surface runoff). Distributed parameter models are classified according to (1) the description of the runoff processes and (2) the dimensionality of the flow description. In the first case, models are classified as deterministic, stochastic, or mixed, depending on the degree of certainty with which the runoff processes are described in the model (Singh, 1996). In the second case, models are classified as either one-dimensional (1D) or two-dimensional (2D). For the simulation of runoff in very small watersheds, both types of model typically employ the kinematic wave approximation to the Saint Venant flow equations. This method involves numerically solving the continuity or mass balance equation using a uniform flow approximation to compute flow velocity. *Correspondence to: David A. Howes, Compliance Services International, 7501 Bridgeport Way West, Lakewood, WA 98499, USA. E-mail: dhowes@complianceservices.com Received 23 April 2003 Copyright  2006 John Wiley & Sons, Ltd. Accepted 19 January 2005