INTERACTIONS BETWEEN MODEL PREDICTIONS, PARAMETERS AND DTM SCALES FOR TOPMODEL JAMES BRASINGTON 1 and KEITH RICHARDS 2 1 Department of Geography, University of Hull, Hull, U.K. HU6 7RX, and 2 Department of Geography, University of Cambridge, Downing Place, Cambridge, U.K. CB2 3EN (e-mail: J.Brasington@geo.hull.ac.uk) (Received 3 January 1997; revised 2 July 1997) AbstractÐThe scale-dependence of the popular rainfall-runo model, TOPMODEL, is assessed for a small headwater catchment in the Nepal Middle Hills. Digital terrain analysis is used to calculate the frequency distributions of slope, tanb, upslope contributing area, a, and the combined hydrological wet- ness index ln(a/tanb) for a range of digital elevation model (DEM) grid sizes between 20 and 500 m. The resulting distributions of the topographic index are strongly sensitive to grid size, in which chan- ging estimates of the upslope contributing area are identi®ed as the ®rst-order control. Sensitivity analy- sis reveals that model predictions are consequently grid-size dependent, although this eect can be modulated by recalibrating the saturated hydraulic conductivity parameter of the model as grid size changes. An analytical link between this parameter and the shape of the probability distribution of the index is tested and found to be reliable over a wide range of scales. A signi®cant change in the model response to scale is identi®ed between grid sizes of 100 and 200 m. This change in grid size is also marked by rapid deterioration of the topographic information contained in the DEM, measured in terms of the statistical entropy. It is suggested that this break in the scaling relationship corresponds to typical hillslope lengths in the dissected terrain, and this scale thus marks a fundamental natural threshold for DEM-based applications. # 1998 Elsevier Science Ltd. All rights reserved Key Words: TOPMODEL, Digital Elevation Models, Scale-dependence, Parameter compensation, Entropy. INTRODUCTION Topography is now recognised as a ®rst-order con- trol on the hydrological response of a catchment to rainfall. This re¯ects the role that topography plays in determining the spatial distribution of catch- ment-scale ¯ow pathways resulting from the down- ward force of gravity. By accounting for local variations in hillslope gradient and curvature, a wide variety of hydrological processes can be re- lated to catchment topography, including the spatial distribution of soil moisture, the generation of run- o and basin response times (Dunne and Black, 1970; Anderson and Burt, 1978; Maidment and others, 1996) TOPMODEL (Beven and Kirkby, 1979), TOPographic MODEL, is a catchment scale rain- fall-runo model which makes an explicit link between catchment topography and the generation of stream¯ow. The model is based on a spatially distributed topographic index which is used to pre- dict local variations in water table depths. This topographic index is de®ned as ln(a/tan b) i , where a is the total upslope area which drains through point (pixel) i, and tan b is the local downslope topographic gradient. The upslope area, a, re¯ects the tendency for subsurface water to drain to i, whereas tanb can be considered to be an approxi- mation of the hydraulic gradient forcing water downslope. It follows that drainage will tend to ac- cumulate in areas with high values of the topo- graphic index. A consequence of this formulation is that areas of the catchment with approximately equal values of the topographic index may be assumed to behave in a hydrologically consistent manner. The index can, therefore, be considered as a measure of hydrological similarity. The TOPMODEL approach has been applied to a wide range of topics, including ¯ood-frequency esti- mation (Beven, 1986), scaling theory in hydrology (Wood and others, 1988), water table estimation (Merot and others, 1995; Moore and Thompson, Computers & Geosciences Vol. 24, No. 4, pp. 299±314, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0098-3004/98 $19.00 + 0.00 PII: S0098-3004(97)00081-2 299