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. [...]