Aim of the study:
There are two main aims of this paper: to present equations that can predict the stream-order-law ratios on the basis of length, slope of the stream, and area of the catchment; to apply the predicted stream-order-law ratios in estimating direct runoff of catchments by GIUH method.

Material and methods:
In order to use GIUH model, the stream network’s characteristics, such as bifurcation ratio (RB), stream-length ratio (RL), stream-area ratio (RA), stream-slope ratio (RS), and overland slope ratio (RSO) must be evaluated. For this purpose, accurate GIS based information of topography and hydrography is often necessary, and yet in many catchments such information is missing. In this study, equations have been presented that are related to the available geomorphological information about the catchment, such as area, slope and length of the main river. The equations presented herein have been developed based on non-linear regressions of data from nine catchments.

Results and conclusions:
To validate the proposed method, the data of three other catchments were used. Based on the presented equations, the runoff of Heng-Chi (Taiwan) and Kasilian (Iran) catchments was calculated by GIUH method. The results indicate that the peak runoff error calculated using the GIUH model based on regression equations was 10% higher than model calculations based on the data obtained from GIS. The average error of the regression equations in estimating the coefficients of RB, RL, RA, and RS in the three case study catchments are 4.7%, 23.5%, 7.1%, 41.3% and 22.9%, respectively. The relative sensitivity coefficient of RB, RL, RA, and RS ratios on peak flow was observed as 0.56, 0.01, 0.92, 0.042, and 1.33 respectively.