ABSTRACT Field data reveal how the discharge ( Q ), channel area ( A ), and average water velocity ( V avg ) of natural streams functionally depend on the effective stage ( h ) above channel bottom. A graphical technique allows the level that corresponds to a dry channel, denoted “ h 0 ,” to be determined, permitting the dependent variables Q , A , and V avg to all be expressed as simple functions of h , equal to h L – h 0 , where h L is the local stage that is typically reported relative to an arbitrary, site-specific datum. Once h 0 is known, plots of log Q , log A , and log V avg versus log h can be constructed using available data. These plots define strong, nearly linear trends for which the slopes (1) quantify the power relationships among these variables; (2) show that V avg varies nearly linearly with h , unlike behaviors assumed in the Chezy and Manning equations; (3) distinguish the individual contributions of A and V avg to discharge, which is their product; (4) provide quantitative means with which to compare different sites; and (5) offer new insights into the character and dynamics of natural streams.

ABSTRACT Lateral accelerations require lateral forces. We propose that force imbalances in the unique Earth-Moon-Sun system cause large-scale, cooperative tectonic motions. The solar gravitational pull on the Moon, being 2.2× terrestrial pull, causes lunar drift, orbital elongation, and an ~1000 km radial monthly excursion of the Earth-Moon barycenter inside Earth’s mantle. Earth’s spin superimposes an approximately longitudinal 24 h circuit of the barycenter. Because the oscillating barycenter lies 3500–5500 km from the geocenter, Earth’s tangential orbital acceleration and solar pull are imbalanced. Near-surface motions are enabled by a weak low-velocity zone underlying the cold, brittle lithosphere: The thermal states of both layers result from leakage of Earth’s internal radiogenic heat to space. Concomitantly, stress induced by spin cracks the lithosphere in a classic X-pattern, creating mid-ocean ridges and plate segments. The inertial response of our high-spin planet with its low-velocity zone is ~10 cm yr –1 westward drift of the entire lithosphere, which largely dictates plate motions. The thermal profile causes sinking plates to thin and disappear by depths of ~200–660 km, depending on angle and speed. Cyclical stresses are effective agents of failure, thereby adding asymmetry to plate motions. A comparison of rocky planets shows that the presence and longevity of volcanism and tectonism depend on the particular combination of moon size, moon orbital orientation, proximity to the Sun, and rates of body spin and cooling. Earth is the only rocky planet with all the factors needed for plate tectonics.

ABSTRACT Most differences in the gross surface morphologies, tectonic styles, overall geologic histories, and atmospheres of the rocky bodies in the solar system can be explained by contributions and dissipation of gravitational and radiogenic energy over geologic time. These two energy sources are large and measurable and can be extrapolated back in time. Accretion was likely cold, and directly converted gravitational potential energy into axial spin, a prominent feature of planets that is otherwise unexplained. Impact heating was mostly limited to planetary surfaces in the final stages of accretion. Frictional dissipation of spin contributed sufficient energy to ignite the primordial Sun and heated Earth and Venus by nearly as much as has the radioactive decay of K, U, and Th over geologic time. Energy inputs have been continuously offset by loss of heat to the surroundings. The magnitudes of most important energy contributions depend on the planet radius R and also on the distance r to the Sun. Quantitative, albeit approximate, relationships show that the net specific energy (kJ/kg) contributed to the rocky bodies over geologic time goes as: Earth ~ Venus >> Mars ~ Mercury ~ Moon >> asteroids. Net energy inputs increased the average internal temperatures of Earth and Venus by ~3000 K but heated asteroids by only a few hundred kelvins.

Perception of the Earth as vigorous rests on substantial overestimates of global heat flux and Rayleigh numbers. Weak, layered mantle convection is indicated by downward revision of these parameters and by new theoretical models and measurements on the variation of thermal conductivity ( k ) with temperature ( T ) and depth. Revision of the global heat flux from a model-dependent estimate of 44 to 31 terra-watts, obtained directly from measurements, is necessary because hydrothermal systems near the ocean ridges are too weak to perturb seafloor older than ca. 1 Ma. The lower estimate is consistent with recent compositional models and nearly uniform release of heat over the surface, and compatible with our aged Earth's now being quasi–steady state. Rayleigh numbers have been overestimated by assuming whole-mantle convection, which is inconsistent with evidence of chemical layering. Different dynamical styles above and below 670 km are required by k ( T ) because T depends on depth, implying layered mantle convection. Geodesic and tomographic studies indicate that lower-mantle flow is dominated by a double torus. We propose that the upper-mantle system is organized in reponse to the nonhydrostatic triaxial stress field arising from convective motions of the lower mantle. Simple conjugate shears in the lithosphere resulting from triaxial deformation of this stiff outermost layer are occupied by oceanic ridges and make a striking “X” pattern in polar projection. Their orientation creates alternating thermal and mechanical couplings between the upper- and lower-mantle systems, leading to largely east-west continental drift and to longitudinal concentration of subducting slabs and continents. Upper-mantle magma production is attributed to thermal runaway and near-solidus temperatures rather than to material exchange with lower mantle, which is strongly impeded.