Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.

Internal wave drag in stratified flow over mountains on a beta plane

The impact of the variation of the Coriolis parameter f on the drag exerted by internal Rossby-gravity waves on elliptical mountains is evaluated using linear theory, assuming constant wind and static stability and a beta-plane approximation. Previous calculations of inertia-gravity wave drag are thus extended in an attempt to establish a connection with existing studies on planetary wave drag, developed primarily for fluids topped by a rigid lid. It is found that the internal wave drag for zonal westerly flow strongly increases relative to that given by the calculation where f is assumed to be a constant, particularly at high latitudes and for mountains aligned meridionally. Drag increases with mountain width for sufficiently wide mountains, reaching values much larger than those valid in the non-rotating limit. This occurs because the drag receives contributions from a low wavenumber range, controlled by the beta effect, which accounts for the drag amplification found here. This drag amplification is shown to be considerable for idealized analogues of real mountain ranges, such as the Himalayas and the Rocky mountains, and comparable to the barotropic Rossby wave drag addressed in previous studies.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

The effect of wind shear and curvature on the gravity wave drag produced by a ridge

The analytical model proposed by Teixeira, Miranda, and Valente is modified to calculate the gravity wave drag exerted by a stratified flow over a 2D mountain ridge. The drag is found to be more strongly affected by the vertical variation of the background velocity than for an axisymmetric mountain. In the hydrostatic approximation, the corrections to the drag due to this effect do not depend on the detailed shape of the ridge as long as this is exactly 2D. Besides the drag, all the perturbed quantities of the flow at the surface, including the pressure, may be calculated analytically.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.

On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Probabilistic forecasting: why model imperfection is a poison pill

This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

Forecasting extinction risk of ectotherms under climate warming: an evolutionary perspective

1. It has been postulated that climate warming may pose the greatest threat species in the tropics, where ectotherms have evolved more thermal specialist physiologies. Although species could rapidly respond to environmental change through adaptation, little is known about the potential for thermal adaptation, especially in tropical species. 2. In the light of the limited empirical evidence available and predictions from mutation-selection theory, we might expect tropical ectotherms to have limited genetic variance to enable adaptation. However, as a consequence of thermodynamic constraints, we might expect this disadvantage to be at least partially offset by a fitness advantage, that is, the ‘hotter-is-better’ hypothesis. 3. Using an established quantitative genetics model and metabolic scaling relationships, we integrate the consequences of the opposing forces of thermal specialization and thermodynamic constraints on adaptive potential by evaluating extinction risk under climate warming. We conclude that the potential advantage of a higher maximal development rate can in theory more than offset the potential disadvantage of lower genetic variance associated with a thermal specialist strategy. 4. Quantitative estimates of extinction risk are fundamentally very sensitive to estimates of generation time and genetic variance. However, our qualitative conclusion that the relative risk of extinction is likely to be lower for tropical species than for temperate species is robust to assumptions regarding the effects of effective population size, mutation rate and birth rate per capita. 5. With a view to improving ecological forecasts, we use this modelling framework to review the sensitivity of our predictions to the model’s underpinning theoretical assumptions and the empirical basis of macroecological patterns that suggest thermal specialization and fitness increase towards the tropics. We conclude by suggesting priority areas for further empirical research.

Wave-breaking characteristics of midlatitude blocking

In this article, Northern Hemisphere winter midlatitude blocking is analysed through its wave-breaking characteristics. Rossby wave breaking is identified as a key process in blocking occurrence, as it provides the mechanism for the meridional reversal pattern typical of blocking. Two indices are designed to detect the major properties of wave breaking, i.e. the orientation (cyclonic/anticyclonic–direction of breaking or DB index) and the relative contribution of air masses (warm/cold–relative intensity or RI index). The use of the DB index differentiates between the anticyclonic cases over Europe and Asia and the cyclonic events over the oceanic basins. One of the three regions displaying cyclonic type was found over the Atlantic Ocean, the other two being over the Pacific Ocean. The first of these is located over the western side of the Pacific and is dominated by warm air extrusions, whereas the second is placed northward of the exit region of the jet stream, where the meridional θ gradient is much weaker. Two European blocking types have been detected using the RI index, which separates out the cases dominated by warm and cold air masses. The latter cases in particular exhibited a well-structured dipole, with associated strong anomalies in both temperature and precipitation. Copyright © 2011 Royal Meteorological Society

The potential inefficiency of using marketing margins in applied commodity price analysis, forecasting and risk management

This paper examines the implications of using marketing margins in applied commodity price analysis. The marketing-margin concept has a long and distinguished history, but it has caused considerable controversy. This is particularly the case in the context of analyzing the distribution of research gains in multi-stage production systems. We derive optimal tax schemes for raising revenues to finance research and promotion in a downstream market, derive the rules for efficient allocation of the funds, and compare the rules with an without the marketing-margin assumption. Applying the methodology to quarterly time series on the Australian beef-cattle sector and, with several caveats, we conclude that, during the period 1978:2 - 1988:4, the Australian Meat and Livestock Corporation optimally allocated research resources.

Characteristics of high-resolution versions of the Met Office unified model for forecasting convection over the United Kingdom

With many operational centers moving toward order 1-km-gridlength models for routine weather forecasting, this paper presents a systematic investigation of the properties of high-resolution versions of the Met Office Unified Model for short-range forecasting of convective rainfall events. The authors describe a suite of configurations of the Met Office Unified Model running with grid lengths of 12, 4, and 1 km and analyze results from these models for a number of convective cases from the summers of 2003, 2004, and 2005. The analysis includes subjective evaluation of the rainfall fields and comparisons of rainfall amounts, initiation, cell statistics, and a scale-selective verification technique. It is shown that the 4- and 1-km-gridlength models often give more realistic-looking precipitation fields because convection is represented explicitly rather than parameterized. However, the 4-km model representation suffers from large convective cells and delayed initiation because the grid length is too long to correctly reproduce the convection explicitly. These problems are not as evident in the 1-km model, although it does suffer from too numerous small cells in some situations. Both the 4- and 1-km models suffer from poor representation at the start of the forecast in the period when the high-resolution detail is spinning up from the lower-resolution (12 km) starting data used. A scale-selective precipitation verification technique implies that for later times in the forecasts (after the spinup period) the 1-km model performs better than the 12- and 4-km models for lower rainfall thresholds. For higher thresholds the 4-km model scores almost as well as the 1-km model, and both do better than the 12-km model.

Towards global drought early warning capability: expanding international cooperation for the development of a framework for global drought monitoring and forecasting

Drought is a global problem that has far-reaching impacts and especially 47 on vulnerable populations in developing regions. This paper highlights the need for a Global Drought Early Warning System (GDEWS), the elements that constitute its underlying framework (GDEWF) and the recent progress made towards its development. Many countries lack drought monitoring systems, as well as the capacity to respond via appropriate political, institutional and technological frameworks, and these have inhibited the development of integrated drought management plans or early warning systems. The GDEWS will provide a source of drought tools and products via the GDEWF for countries and regions to develop tailored drought early warning systems for their own users. A key goal of a GDEWS is to maximize the lead time for early warning, allowing drought managers and disaster coordinators more time to put mitigation measures in place to reduce the vulnerability to drought. To address this, the GDEWF will take both a top-down approach to provide global real-time drought monitoring and seasonal forecasting, and a bottom-up approach that builds upon existing national and regional systems to provide continental to global coverage. A number of challenges must be overcome, however, before a GDEWS can become a reality, including the lack of in-situ measurement networks and modest seasonal forecast skill in many regions, and the lack of infrastructure to translate data into useable information. A set of international partners, through a series of recent workshops and evolving collaborations, has made progress towards meeting these challenges and developing a global system.