A Simple Temporal and Spatial Analysis of Flow in Complex Terrain in the Context of Wind Energy Modelling

A simple temporal and spatial analysisis done on wind speed and direction data from a number ofmeteorological towers separated by distances between roughly 1 and 100 kilometres. The analysis is done in the context of expected model error in wind energy calculations. The study first uses single point statistics to show the evolution of mean values with time. It is shown that strong seasonal signals are present and that stable means are achieved only after averaging periods of a year or more. The study then uses discrete Fourier transforms to show that significant amounts of spectral energy reside in modes with periods of a few days to less than a day. Frequency dependent cross correlation values are then derived and used to show how correlation between towers diminishes with increasing frequency. The mechanism responsible for this diminished correlation is shown through the comparison of cross-correlation phase as a function of frequency and its relationship to distance between towers. Error in wind energy estimates are shown to be strongly related to correlation and therefore distance over which the prediction is made. In summary, much of the inaccuracy in modelling flow in the context of wind energy calculations is due to a lack of scale separation between the deterministic part of the flow, which is well modelled, and that part of the flow that is stochastic at the length and time scales modelled.     

THE DEMOGRAPHIC CONSEQUENCES OF METROPOLITAN POPULATION DECONCENTRATION IN THE U.S.

Although the recent growth in the nonmetropolitan population of the U.S. is now well documented, little attention has been given to the consequences these trends will have on the future composition and growth of metropolitan and nonmetropolitan regions. This paper discusses the feedback effects of migration on the future age structure and population growth of both regions during the period 1975–2000.     

Internal Boundary Layers: I. Height Formulae for Neutral and Diabatic Flows

The notion of an internal boundary layer (IBL) appeared in studies of local advection within the atmospheric boundary layer when air flows over a change in surface conditions. These include surface roughness, thermal and moisture properties. An ability to predict the height of the IBL interface in the atmosphere under neutral stability, accompanied by certain assumptions on the form of the mean flow parameters, have been a means of obtaining information on the velocity profile after step changes in roughness for more than half a century. A compendium of IBL formulae is presented. The approach based on the diffusion analogy of Miyake receives close attention. The empirical expression of Savelyev and Taylor (2001, Boundary Layer Meteorol. 101, 293–301) suggested that turbulent diffusion is not the only factor that influences IBL growth. An argument is offered that an additional element, mean vertical velocity or streamline displacement, should be taken into account. Vertical velocity is parameterized in terms of horizontal velocity differences employing continuity constraints and scaling. Published data are analyzed from a new point of view, which produces two new neutral stratification formulae. The first implies that the roughness lengths of adjacent surfaces are equally important and a combined length scale can be constructed. In addition new formulae to predict the height of the region of diabatic flow affected by a step change in surface conditions are obtained as an extension of the neutral flow case.     

Phase relationships in Buchan facies series pelitic assemblages: calculations with application to andalusite-staurolite parageneses in the Mount Lofty Ranges,South Australia

Low-pressure, medium- to high-temperature (Buchan-type) regional metamorphism of pelitic rocks in the Mount Lofty Ranges, South Australia, is defined by the development of biotite, staurolite-andalusite, fibrolite, prismatic sillimanite and migmatite zones. K-feldspar makes its first appearance in the prismatic sillimanite zone and here we restrict our discussion to lower grade assemblages containing prograde muscovite, concentrating particularly on well-developed andalusitestaurolite parageneses. In general, the spatial distribution and mineral chemical variation of these assemblages accord with the predictions of petrogenetic grids and P-T and T-X _Fe pseudo-sections constructed from the internally consistent data set of Holland and Powell (1990) in the system KFMASH, assuming a(H₂O) 1, although analysed white mica compositions are systematically more aluminous than predicted. Importantly, the stability ranges of most critical assemblages predicted by these grids and pseudo-sections coincide closely with P-T estimates calculated using the data set of Holland and Powell (1990) from the Mount Lofty Ranges assemblages. With the exception of Mn in garnet and Zn in one staurolite-cordierite-muscovite assemblage non-KFMASH components do not significantly appear to have affected the stability ranges of the observed assemblages. An apparent local reversal in isograd zonation in which andalusite first appears down-grade of staurolite suggests a metamorphic field gradient concave towards the temperature axis and, together with evidence for essentially isobaric heating of individual rocks, is consistent with the exposures representing an oblique profile through a terrain in which heat was dissipated from intrusive bodies at discrete structural levels.Mineral abbreviations used in figures als Al₂SiO₅ phase - bi biotite - chl chlorite - ky kyanite - ph phengite - sill sillimanite - and andalusite - cd cordieritc - gt garnet - mu muscovite - q quartz - st staurolite     

High resolution regional climate model simulations for Germany: Part II—projected climate changes

The projected climate change signals of a five-member high resolution ensemble, based on two global climate models (GCMs: ECHAM5 and CCCma3) and two regional climate models (RCMs: CLM and WRF) are analysed in this paper (Part II of a two part paper). In Part I the performance of the models for the control period are presented. The RCMs use a two nest procedure over Europe and Germany with a final spatial resolution of 7 km to downscale the GCM simulations for the present (1971–2000) and future A1B scenario (2021–2050) time periods. The ensemble was extended by earlier simulations with the RCM REMO (driven by ECHAM5, two realisations) at a slightly coarser resolution. The climate change signals are evaluated and tested for significance for mean values and the seasonal cycles of temperature and precipitation, as well as for the intensity distribution of precipitation and the numbers of dry days and dry periods. All GCMs project a significant warming over Europe on seasonal and annual scales and the projected warming of the GCMs is retained in both nests of the RCMs, however, with added small variations. The mean warming over Germany of all ensemble members for the fine nest is in the range of 0.8 and 1.3 K with an average of 1.1 K. For mean annual precipitation the climate change signal varies in the range of ?2 to 9 % over Germany within the ensemble. Changes in the number of wet days are projected in the range of ±4 % on the annual scale for the future time period. For the probability distribution of precipitation intensity, a decrease of lower intensities and an increase of moderate and higher intensities is projected by most ensemble members. For the mean values, the results indicate that the projected temperature change signal is caused mainly by the GCM and its initial condition (realisation), with little impact from the RCM. For precipitation, in addition, the RCM affects the climate change signal significantly.     

Effects of Mesoscale Surface Thermal Heterogeneity on Low-Level Horizontal Wind Speeds

Using large-eddy simulation, we investigate characteristics of horizontal wind speed at 100 m above the ground, with surface heat-flux variations that are sinusoidal with amplitudes of 0, 50, and 200 W m⁻² and wavelengths of 16, 32, and 128 km, and no background flow. When the amplitude is 200 W m⁻², wind speeds induced by the surface-flux variations on scales of 16 and/or 32 km have multiple temporal oscillations from 0600 to 1800 local standard time. The positive peaks first appear before noon. In contrast, for wind speeds induced by the 128-km surface heterogeneity, a single oscillation occurs in the late afternoon, which is much larger than those generated by the 16- and 32-km surface heterogeneity. In addition, at the oscillation onset the kurtosis of the velocity increment over a distance of 1 km significantly increases, which implies intermittency in the generation of 1-km scale eddies. The spatially intermittent energy cascade generated by surface heterogeneity scaled down to 1-km eddies is analogous to the well-known intermittent energy cascade in the inertial subrange. The kurtosis of the 1-km eddies is much larger with the 128-km surface heterogeneity than with the 16- and 32-km heterogeneities. Thus we conclude that localized rapid changes of low-level horizontal wind speed may be caused by significant local surface heterogeneity on scales between a few tens and a few hundreds of kilometres.     

Critical soil conditions for oxygen stress to plant roots: Substituting the Feddes-function by a process-based model

Effects of insufficient soil aeration on the functioning of plants form an important field of research. A well-known and frequently used utility to express oxygen stress experienced by plants is the Feddes-function. This function reduces root water uptake linearly between two constant pressure heads, representing threshold values for minimum and maximum oxygen deficiency. However, the correctness of this expression has never been evaluated and constant critical values for oxygen stress are likely to be inappropriate. On theoretical grounds it is expected that oxygen stress depends on various abiotic and biotic factors. In this paper, we propose a fundamentally different approach to assess oxygen stress: we built a plant physiological and soil physical process-based model to calculate the minimum gas filled porosity of the soil (_{gas_min}) at which oxygen stress occurs.First, we calculated the minimum oxygen concentration in the gas phase of the soil needed to sustain the roots through (micro-scale) diffusion with just enough oxygen to respire. Subsequently, _{gas_min} that corresponds to this minimum oxygen concentration was calculated from diffusion from the atmosphere through the soil (macro-scale).We analyzed the validity of constant critical values to represent oxygen stress in terms of _{gas_min}, based on model simulations in which we distinguished different soil types and in which we varied temperature, organic matter content, soil depth and plant characteristics. Furthermore, in order to compare our model results with the Feddes-function, we linked root oxygen stress to root water uptake (through the sink term variable F, which is the ratio of actual and potential uptake).The simulations showed that _{gas_min} is especially sensitive to soil temperature, plant characteristics (root dry weight and maintenance respiration coefficient) and soil depth but hardly to soil organic matter content. Moreover, _{gas_min} varied considerably between soil types and was larger in sandy soils than in clayey soils. We demonstrated that F of the Feddes-function indeed decreases approximately linearly, but that actual oxygen stress already starts at drier conditions than according to the Feddes-function. How much drier is depended on the factors indicated above. Thus, the Feddes-function might cause large errors in the prediction of transpiration reduction and growth reduction through oxygen stress.We made our method easily accessible to others by implementing it in SWAP, a user-friendly soil water model that is coupled to plant growth. Since constant values for _{gas_min} in plant and hydrological modeling appeared to be inappropriate, an integrated approach, including both physiological and physical processes, should be used instead. Therefore, we advocate using our method in all situations where oxygen stress could occur.     

Cavity expansion in cross‐anisotropic rock

Schistous rock can be considered—in a first approximation—as cross‐anisotropic linear elastic material. The determination of the corresponding material constants on the basis of the laboratory investigation of rock samples often fails, as the extraction of appropriate cores proves to be unfeasible (the cores disintegrate if the schistosity is pronounced). In this paper a new method is presented to determine the material constants of a linear elastic cross‐anisotropic rock on the basis of cavity expansion field tests, e.g. with a radial jack. To this purpose, an analytic approximation for the deformation of a hydrostatically loaded cylindrical cavity in cross‐anisotropic rock is derived which serves to the inverse analysis of the material parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Flow and fracture maps for basaltic rock deformation at high temperatures

Understanding how the strength of basaltic rock varies with the extrinsic conditions of stress state, pressure and temperature, and the intrinsic rock physical properties is fundamental to understanding the dynamics of volcanic systems. In particular it is essential to understand how rock strength at high temperatures is limited by fracture. We have collated and analysed laboratory data for basaltic rocks from over 500 rock deformation experiments and plotted these on principal stress failure maps. We have fitted an empirical flow law (Norton’s law) and a theoretical fracture criterion to these data. The principal stress failure map is a graphical representation of ductile and brittle experimental data together with flow and fracture envelopes under varying strain rate, temperature and pressure. We have used these maps to re-interpret the ductile–brittle transition in basaltic rocks at high temperatures and show, conceptually, how these failure maps can be applied to volcanic systems, using lava flows as an example.