The spatial variability of two fundamental morphological variables is investigated for rivers having a wide range of discharge (five orders of magnitude). The variables, water-surface width and average depth, were measured at 58 to 888 equally spaced cross-sections in channel links (river reaches between major tributaries). These measurements provide data to characterize the two-dimensional structure of a channel link which is the fundamental unit of a channel network. The morphological variables have nearly log-normal probability distributions. A general relation was determined which relates the means of the log-transformed variables to the logarithm of discharge similar to previously published downstream hydraulic geometry relations. The spatial variability of the variables is described by two properties: (1) the coefficient of variation which was nearly constant (0.13-0.42) over a wide range of discharge; and (2) the integral length scale in the downstream direction which was approximately equal to one to two mean channel widths. The joint probability distribution of the morphological variables in the downstream direction was modelled as a first-order, bivariate autoregressive process. This model accounted for up to 76 per cent of the total variance. The two-dimensional morphological variables can be scaled such that the channel width-depth process is independent of discharge. The scaling properties will be valuable to modellers of both basin and channel dynamics. Published in 2002 John Wiley and Sons, Ltd.