For some selected field studies of longitudinal dispersion the variances of observed concentration distributions increase linearly with time, as predicted by solutions to the one‐dimensional Fickian‐type diffusion equation. However, observed values of the skewness coefficient are almost constant, so deviations from the theoretical values become greater with increasing time. The usual assumption that concentration distributions converge to the Gaussian solution of the one‐dimensional diffusion equation is not supported by the empirical observations. One explanation for the persistence of the skewness is the existence of dead zones which temporarily trap portions of the dispersant. The coefficients of skewness predicted by a dead zone model fit the observed values more closely, but this model is, like the Fickian model, characterized by a decay in the skewness, which is not exhibited by the observed distributions.

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 0Ð13-0Ð42 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.

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[1] The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km 2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a nonstationary climate due to global warming but its slope and intercept would change. Citation: