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.     

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.     

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.     

Heat capacities of Tschermak substituted Fe-biotite

Six members of the annite–siderophyllite join were synthesized in a three step process – crystallization of biotite from gels, decomposition of the fine-grained biotite under oxidizing conditions and resynthesis of Fe-Al biotite with planned compositions from these products – producing biotite crystals with thicknesses of up to 10 μm. The biotite was characterized by microprobe, electron microscopy and X-ray diffraction. Heat capacities of these biotites were measured with a DSC (differential scanning calorimeter) over the temperature range 143 to 623 K. Using a least-squares technique, the data were fitted to a c_p-polynomial, c _p =k ₀+k ₁ T ^−0.5+ k ₂ T ⁻²+k ₃ T ⁻³. In the temperature range 143 to 250 K, heat capacities of the different annite–siderophyllite members decrease linearly with increasing Al content. At higher temperatures, however, the c_p-polynomial of biotites with intermediate composition (except Ann₇₉Sid₂₁) exhibit a steeper slope than those of other biotites. This produces positive excess heat capacities in the annite–siderophyllite join at higher temperatures. The activity-composition data of the same binary derived from phase equilibrium experiments (Benisek et al. 1996) and the data of this study suggest two compositional regions along this join, with different extent of deviation from ideality. One at X _Sid < 0.3, characterized by a small deviation, one at X _Sid > 0.3 showing a higher nonideality, resulting in a discontinuity visible at this composition. Powder IR-spectra of these solid solutions were measured with a FTIR-spectrometer and used to calculate heat capacities according to the vibrational model of Kieffer (1979). The comparison of the vibrational function with the c_p-polynomials shows that the vibrational function reproduces well the DSC-data of the siderophyllite-poor and -rich members, but deviates for intermediate compositions, where the excess heats of mixing occur. With increasing Tschermak vector, the tetrahedral rotation angle α increases from 0 to 13° for annite to siderophyllite, respectively. At the composition of the discontinuity, this rotation angle α reaches a value of ∼8^∘. The processing of ∼300 chemical data of natural biotites indicates that over 90% of them have a tetrahedral rotation angle that lies between 7 and 9°. It would appear that biotites with these structural characteristics are most stable. Received: 27 August 1998 / Accepted: 10 November 1998     

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.     

Dynamical Implications of Block Averaging

We show that traditional Reynolds (block) averaging produces turbulence statistics whose time evolution is incompatible with the Navier–Stokes equation. Specifically, the zero integral scale that block averaging always produces leads to a trivial (zero-equals-zero) solution of the Navier–Stokes equation for autocovariances. We suggest alternative methods for analyzing turbulence time series that do not always generate a zero integral scale and, as a result, yield autocovariances whose time evolutions are compatible with the Navier–Stokes equation.     

Approximation formulas for the microphysical properties of saline droplets

Microphysical theory has proven essential for explaining sea spray's role in transferring heat and moisture across the air–sea interface. But large-scale models of air–sea interaction, among other applications, cannot afford full microphysical modules for computing spray droplet evolution and, thus, how rapidly these droplets exchange heat and moisture with their environment. Fortunately, because the temperature and radius of saline droplets evolve almost exponentially when properly scaled, it is possible to approximate a droplet's evolution with just four microphysical endpoints: its equilibrium temperature, T_eq; the e-folding time to reach that temperature, τ_T; its equilibrium radius, r_eq; and the e-folding time to reach that radius, τ_r.Starting with microphysical theory, this paper derives quick approximation formulas for these microphysical quantities. These approximations are capable of treating saline droplets with initial radii between 0.5 and 500 μm that evolve under the following ambient conditions: initial droplet temperatures and air temperatures between 0 and 40 °C, ambient relative humidities between 75% and 99.5%, and initial droplet salinities between 1 and 40 psu.Estimating T_eq, τ_T, and τ_r requires only one-step calculations; finding r_eq is done recursively using Newton's method. The approximations for T_eq and τ_T are quite good when compared to similar quantities derived from a full microphysical model; T_eq is accurate to within 0.02 °C, and τ_T is typically accurate to within 5%. The estimate for equilibrium radius r_eq is also usually within 5% of the radius simulated with the full microphysical model. Finally, the estimate of radius e-folding time τ_r is accurate to within about 10% for typical oceanic conditions.     

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.