Effects of Temporal Discretization on Turbulence Statistics and Spectra in Numerically Simulated Convective Boundary Layers

Six state-of-the-art large-eddy simulation codes were compared in Fedorovich et al. (Preprints, 16th American Meteorological Society Symposium on Boundary Layers and Turbulence, 2004b) for three airflow configurations in order to better understand the effect of wind shear on entrainment dynamics in the convective boundary layer CBL). One such code was the University of Oklahoma large-eddy simulation (LES) code, which at the time employed a second-order leapfrog time-advancement scheme with the Asselin filter. In subsequent years, the code has been updated to use a third-order Runge–Kutta (RK3) time-advancement scheme. This study investigates what effect the upgrade from the leapfrog scheme to RK3 scheme has on turbulence statistics in the CBL differently affected by mean wind shear, also in relation to predictions by other LES codes that participated in the considered comparison exercise. In addition, the effect of changing the Courant number within the RK3 scheme is investigated by invoking the turbulence spectral analysis. Results indicate that low-order flow statistics obtained with the RK3 scheme generally match their counterparts from simulations with the leapfrog scheme rather closely. CBL growth rates due to entrainment in the shear-free case were also similar using both timestepping schemes. It was found, however, that care should be given to the choice of the Courant number value when running LES with the RK3 scheme in the sheared CBL setting. The advantages of the largest possible (based on the stability criterion) Courant number were negated by degrading the energy distribution across the turbulence spectrum. While mean profiles and low-order turbulence statistics were largely unaffected, the entrainment rate was over-predicted compared to that reported in the original code-comparison study.     

Estimating the world's potentially available cropland using a bottom-up approach

Previous estimates of the land area available for future cropland expansion relied on global-scale climate, soil and terrain data. They did not include a range of constraints and tradeoffs associated with land conversion. As a result, estimates of the global land reserve have been high. Here we adjust these estimates for the aforementioned constraints and tradeoffs. We define potentially available cropland as the moderately to highly productive land that could be used in the coming years for rainfed farming, with low to moderate capital investments, and that is not under intact mature forests, legally protected, or already intensively managed. This productive land is underutilized rather than unused as it has ecological or social functions. We also define potentially available cropland that accounts for trade-offs between gains in agricultural production and losses in ecosystem and social services from intensified agriculture, to include only the potentially available cropland that would entail low ecological and social costs with conversion to cropland. In contrast to previous studies, we adopt a “bottom-up” approach by analyzing detailed, fine scale observations with expert knowledge for six countries or regions that are often assumed to include most of potentially available cropland. We conclude first that there is substantially less potential additional cropland than is generally assumed once constraints and trade offs are taken into account, and secondly that converting land is always associated with significant social and ecological costs. Future expansion of agricultural production will encounter a complex landscape of competing demands and tradeoffs.     

Resonance bond numbers: A graph-theoretic study of bond length variations in silicate crystals

The resonance bond number n, as defined in this paper, is designed to describe the strength of an XO bond as a function of the kinds of atoms present and which atoms are bonded. The calculation of n is made on a fragment extracted from the crystal encompassing the XO bond. If this fragment consists of only the X atom and its coordinating O atoms, then n is numerically equal to the Pauling bond strength, s. In this study a graph-theoretic algorithm is developed permitting the calculation of n using fragments including up to 50 atoms. This algorithm was used to calculate n for all of the bonds in ten silicate crystals. Since bond strength is be inversely related to bond length, we examined the relationship between these two variables and found that n can be used to explain over 70 percent of the variation of XO bond lengths from their average values in the crystals. A fit of the parameter n/r, where r is the row number in the periodic table of the metal atom X, to the observed bond lengths in these crystals yielded the equation R(XO)=1.39(n/r)^?0.22 which explains over 95.5 percent of the variation of bond lengths in the crystals. The fact that the same formula with s replacing n was found in an earlier study to be a good estimator of average bond lengths in crystals shows that n relates to individual variations in bond lengths in crystals in the same way that s relates to average bond lengths in crystals. Using minimum energy SiO, AlO and MgO bond lengths and harmonic force constant data calculated for these bonds in hydroxyacid molecules, theoretical equations similar to those used by Pauling to explain bond length variations in hydrocarbons are derived. Bond lengths calculated with these equations for the 10 crystals shows that 95 percent of the variation of the observed bond lengths in these crystals can be explained in terms of n by this purely theoretical model.