Implicit single-sequence methods for integrating orbits

The solutions of \(\ddot x = F(x,t)\) , and also \(\dot x = F(x,t)\) , are developed in truncated series in timet whose coefficients are found empirically. The series ending in thet ⁶ term yields a position at a final prechosen time that is accurate through 9th order in the sequence size. This is achieved by using Gauss-Radau and Gauss-Lobatto spacings for the several substeps within each sequence. This timeseries method is the same in principle as implicit Runge-Kutta forms, including some not described previously. In some orders these methods are unconditionally stable (A-stable). In the time-series formulation the implicit system converges rapidly. For integrating a test orbit the method is found to be about twice as fast as high-order explicit Runge-Kutta-Nyström-Fehlberg methods at the same accuracies. Both the Cowell and the Encke equations are solved for the test orbit, the latter being 35% faster. It is shown that the Encke equations are particularly well-adapted to treating close encounters when used with a single-sequence integrator (such as this one) provided that the reference orbit is re-initialized at the start of each sequence. This use of Encke equations is compared with the use of regularized Cowell equations.     

Stability Dependence of the Eddy-Accumulation Coefficients for Momentum and Scalars

From a set of turbulence data collected with a three-axis sonic anemometer/thermometer and described in a companion paper, we simulate the eddy-accumulation process for sensible heat and momentum fluxes. The resulting eddy-accumulation coefficient for momentum clearly depends on surface-layer stability; at neutral stability, its value is 0.63. On supplementing the scalar eddy-accumulation coefficients that we derive from our sensible heat flux data with values of sensible and latent heat flux coefficients reported by Businger and Oncley, we also find that scalar eddy-accumulation coefficients depend on stability, though more weakly than does the momentum coefficient. The coefficients for sensible and latent heat show no significant difference; we, thus, fit them with one function of stability whose value is 0.52 for neutral stratification.     

Statistics of Surface-Layer Turbulence Over Terrain with Metre-Scale Heterogeneity

Refuge has patchy vegetation in sandy soil. During midday and at night, the surface sources and sinks for heat and moisture may thus be different. Although the Sevilleta is broad and level, its metre-scale heterogeneity could therefore violate an assumption on which Monin-Obukhov similarity theory (MOST) relies. To test the applicability of MOST in such a setting, we measured the standard deviations of vertical (_w) and longitudinal velocity (_u), temperature (_t), and humidity (_q), the temperature-humidity covariance (¯tq), and the temperature skewness (S_t). Dividing the former five quantities by the appropriate flux scales (u_*, _*, and q_*) yielded the nondimensional statistics _w/u_*, _u/u_*, _t/|t_*|, _q/|q_*|, and ¯tq/t_*q_*. _w/u_*, _t/|t_*|, and S_t have magnitudes and variations with stability similar to those reported in the literature and, thus, seem to obey MOST. Though _u/u_* is often presumed not to obey MOST, our _u/u_* data also agree with MOST scaling arguments. While _q/|q_*| has the same dependence on stability as _t/|t_*|, its magnitude is 28% larger. When we ignore ¯tq/t_*q_* values measured during sunrise and sunset transitions – when MOST is not expected to apply – this statistic has essentially the same magnitude and stability dependence as (_t/t_*)². In a flow that truly obeys MOST, (_t/t_*)², (_q/q_*)², and ¯tq/t_*q_* should all have the same functional form. That (_q/q_*)² differs from the other two suggests that the Sevilleta has an interesting surface not compatible with MOST. The sources of humidity reflect the patchiness while, despite the patchiness, the sources of heat seem uniformly distributed.     

Jovian proton Aurora

The planet Jupiter possesses a magnetic field and is surrounded by a magnetosphere. The occurrence of auroral and polar cap phenomena similar to those found on earth is very likely. In this work auroral and polar cap emissions in a model Jovian atmosphere are determined for proton precipitation. The incident protons, which are characterized by representative spectra, are degraded in energy by applying the continuous slowing down approximation. All secondary and higher generation electrons are assumed to be absorbed locally and their contributions to the total emissions are included. Volume emission rates are calculated from the total direct excitation rates with corrections for cascading applied. Results show that most molecular hydrogen and helium emissions for polar cap precipitation are below the ambient dayglow values. Charge capture by precipitating protons is an important source of Lyman α and Balmer α emissions and offers a key to the detection of large fluxes of low energy protons.     

Spatio‐temporal changes in bog pool bottom topography – temperature effect and its influence on pool development: an example from a raised bog in Estonia

Increases in pool water and peat temperature in summer accelerate peat decomposition and production of biogenic gases, which can be trapped in peat pores and cause oscillation of peatland surfaces and the rise of peat from the bottom of bog pools. Associated changes in peat water conductivity, holding capacity and transpiration also affect bog hydrology. Our multi‐year study is the first to show in detail the extent and dynamics of changes in bog pool depth and bottom topography associated with changes in temperature, peat type and other factors. The true seasonal rise of peat from the pool bottom begins once the water temperature at the pool bottom exceeds 13–14 °C, although the speed and extent of the rise depends on peat properties, making the rise more erratic than its subsequent descent. The more rapid descent occurs after the first large drop in the temperature of the pool's surface water at the end of summer, resulting from the combination of reduced methane production and increased gas solubility with less influence by peat properties. Much higher dissolved organic carbon concentrations (216 ± 26 mg l^?1) in the pore water of peat risen from the bottom to the pool surface compared with that in the same type of peat at the pool bottom (62 ± 20 mg l^?1) indicate an acceleration of peat decomposition at the warmer pool surface. We show the extent and character of changes in pool depth and bottom topography and how annual differences relate to temperature. Only a few degrees' increase in pool water temperature could induce the pool bottom to rise faster and more extensively for a longer period and enhance decomposition in the peat at the pool surface. This should be evaluated in greater detail to assess the effects of temperature increase on the carbon budget and hydrology of peatlands. Copyright © 2012 John Wiley & Sons, Ltd.     

Melting experiments on SiO2-rich lamproites to 6.4 GPa and their bearing on the sources of lamproite magmas

Summary Supra-solidus phase relations at temperatures and pressures ranging from 800 to 1700 °C and 2 to 6.4 GPa have been determined experimentally for three silica-rich lamproites: hyalo-leucite phlogopite lamproite (Oscar, West Kimberley); sanidine richterite lamproite (Cancarix, Murcia-Almeria); and phlogopite transitional madupitic lamproite (Middle Table Mountain, Wyoming). All samples have extended melting intervals (500–600 °C). Bulk composition has a significant control on the nature of the initial liquidus phases, with orthopyroxene occurring at low pressures (<4 GPa) in the relatively calcium-poor Oscar and Cancarix lamproites. At higher pressure (>6 GPa) orthopyroxene is replaced by garnet plus clinopyroxene as near-liquidus phases in the Oscar lamproite and by orthopyroxene plus clinopyroxene in the Cancarix sample. Clinopyroxene is a near-liquidus phase at all pressures in the Middle Table Mountain lamproite. Near-solidus phase assemblages at high pressure (>5 GPa) are: clinopyroxene + phlogopite + coesite + rutile + garnet (Oscar); clinopyroxene + garnet + coesite + K–Ti-silicate (Cancarix); clinopyroxene + phlogopite + apatite + K–Ti-silicate (Middle Table Mountain). In all compositions olivine is never found as a liquidus phase at any of the temperatures or pressures studied here. The phase relationships are interpreted to suggest that silica-rich lamproites cannot be derived by the partial melting of lherzolitic sources. Their genesis is considered to involve high degrees of partial melting of ancient metasomatic veins within a harzburgitic-lherzolitic lithospheric substrate mantle. The veins are considered in their mineralogy to be similar to the experimentally-observed, high pressure, near-solidus phase assemblages. The composition of silica-rich primary lamproite magmas differs between cratons as a consequence of differing mineralogical modes of the source veins and different relative contributions from the veins and wall-rocks to the partial melts. Received February 21, 2000; revised version accepted July 3, 2001     

The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z ₀) scales as au_*²/g{\alpha u_\ast^2/g}, where u _* is the friction velocity, g is the acceleration of gravity, and α is an empirical constant. Data analyses seem to support this scaling: many published plots of z ₀ measured over snow demonstrate proportionality to u_*²{u_\ast^2 }. In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u _*, was used to compute z ₀ in the first place; the plots thus suffer from fictitious correlation that causes z ₀ to unavoidably increase with u _* without any intervening physics. For these two datasets, when I plot z ₀ against u _* derived from a bulk flux algorithm—and thus minimize the fictitious correlation—z ₀ is independent of u _* in the drifting snow region, u _* ≥ 0.30 ms⁻¹. I conclude that the relation z₀ = au_*²/g{z_0 = \alpha u_\ast^2/g} when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.     

Manmade Vulnerability of the Cancun Beach System: The Case of Hurricane Wilma

Climate change and resultant coastal erosion and flooding have been the focus of many recent analyses. Often these studies overlook the effects of manmade modifications to the coastline which have reduced its resilience to storm events. In this investigation, we integrate previous reports, historical photo analysis, field work, and the application of numerical models to better understand the effects of Wilma, the most destructive hurricane to affect Cancun, Mexico. Huge waves (of significant height, >12 m), long mean wave periods (>12 s), devastating winds (>250 km/h), and powerful currents (>2 m/s) removed >7 million cubic meters of sand from the Cancun beach system, leaving 68% of the sub‐aerial beach as bedrock, and the rest considerably eroded. Numerical simulations show that the modifications to the barrier island imposed by tourist infrastructure have considerably increased the rigidity of the system, increasing the potential erosion of the beach under extreme conditions. If there were no structural barriers, a series of breaches could occur along the beach, allowing exchange of water and alleviating storm surge on other sections of the beach. If the effects caused by anthropogenic changes to Cancun are ignored, the analysis is inaccurate and misleading.