The downstream change in the average channel gradient derived from order data can be expressed in terms of either area or discharge in the form of a power function. Similarly, the average channel profile based on link slope can be related to link magnitude or discharge in the form of a power equation. Finally, from the downstream hydraulic geometry equation the change in stream gradient can be expressed in terms of discharge or area as a power function. Because these relations are identical in form and in their independent parameters, rates of change in slope obtained by all three approaches should be equivalent. The rates of change in stream gradient derived from the power functions above yield almost identical averages for entire channel networks. The order data give a rate of −0.63, whereas link slope exponents average −0.60. These values are well within the range of variation for published data obtained for the hydraulic geometry equation (averages between −0.49 and 0.95) and may represent a quasi‐equilibrium tendency for entire fluvial systems.

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The sequence of units (from the base up) in the Sixteen Mile Creek lagoon (Lake Ontario) mimics the longitudinal sequence of surficial environments: pink silt-overbank (flood plain -dry marsh); bottom sand-stream channel and beach; orange silt-marsh; gyttja-wet marsh and very shallow (deltaic) lagoon; and brown and grey clay-open-water lagoon. This entire sequence accumulated over the last 4200 years under slowly deepening, transgressive conditions caused by the isostatic rise of the lake outlet. Land clearing by European settlers dramatically increased the supply of clastic sediment and terminated the deposition of the organic-rich silty clays (gyttja) that make up most of the lagoon fill.Because the gyttja and beach sand are interpreted to have accumulated in water depths of less than 0.5 m, the elevationtime plot of 14C dates from these units can be used to reconstruct a very closely constrained lake-level curve. The data indicate that water levels have risen at an average rate of 0.25 cmla over the last 3300 years as a result of differential, isostatic rebound. Superimposed on this trend are water-level oscillations with amplitudes on the order of 1 m and periods of several hundred years. These oscillations are synchronous and in phase with water-level fluctuations in Lake Michigan, and with a variety of other climatic variations in North America and Europe. We propose, therefore, that the water-level oscillations are a result of long-term, climatically produced variations in precipitation in the Great Lakes drainage basin.La sCquence des unites (de bas en haut) dans la lagune de Sixteen Mile Creek (lac Ontario) correspond ti une sCquence longitudinale dCvelopp6e en surface : limon rose-alluvion (plaine de d6bordement -marais sec); sable de couches de fond-chenal de rivibre et plage; limon orangC-marais; gyttja-marais humide et lagune peu profonde (deltaique); argile brune et grise-lagune ouverte. I1 a fallu les derniers 4200 ans pour accumuler cette s6quence en entier, dans des conditions de transgression et de d6pression lente, dues ti la remontee isostatique de I'orifice du lac. Le dCfrichage des terres par les colons europCens a dramatiquement augment6 l'apport en sediment clastique et s'est termin6 par l'accumulation d'argiles riches en matibre organique (gyttja) remplissant la majeure partie de la lagune.Vu que les sCdiments de type gyttja et les sables de plage ont vraisemblablement sediment6 dans moins de 0,5 m d'eau, la courbe altitude-temps des dates 14C de ces unitCs peut servir pour reconstruire une courbe des variations bien dCfinies des niveaux du lac. Les donnees rCvblent que le rebondissement isostatique differentiel est responsable de 1'61Cvation des niveaux de l'eau avec un taux moyen de 0,25 cmla durant les derniers 3300 ans. En plus, il y a eu superposition d'oscillations du niveau de l'eau de l'ordre d'un mbtre avec amplitudes de plusieurs s2cles. Ces oscillations correspondent dans le temps et en phase avec les fluctuations du niveau de l'eau du lac Michigan, et avec diverses autres vari...

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The link slope distribution for given magnitude links from 18 basins in the Appalachian Plateau changes from a left skewed, to a normal, to a right skewed distribution resembling a log normal distribution as the average stream gradient decreases. Variations in the link slope distribution can be partly explained by the decrease in the tendency of streams to move downward with a change in available relief or distance and by the effects of local geologic and geomorphic conditions prevailing in a basin. Downstream interior link slopes vary with magnitude following a power function. Their scatter about the log of the power function is constant in most basins. Based on these elementary properties of link slopes and the probability of occurrence of links of any one magnitude, a general model representing the distribution and expectation of interior !ink slopes for an entire channel network is formulated. The observed interior link slope distributions for different basins vary in shape from a monotonic decrease in frequencies with increasing stream gradient to a unimodal and sometimes bimodal distribution when exterior links are included. In spite of the large changes in the shape of the histograms for different basins, the theoretical distributions provide a good reproduction of the data.

The concept of channel diameter can be extended to define the number of links along the trunk channel of tributaries in a basin. In topologically random channel networks, the occurrence of tributaries with a specified diameter can be expressed by recursive equations for basins of given magnitude. Comparison with two sets of stream data indicate a close resemblance with calculated values.